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THE LIBRARY

THE UNIVERSITY
OF CALIFORNIA

GIFT OF

Dr. William H. Ivie

THE GASOLINE AUTOMOBILE

Its Design and Construction

VOLUME II

Transmission, Running
Gear and Control

P. M. HELDT
Technical Editor of The Horseless Age

Second Edition

P. M. HELDT

Nyack, N. Y.

1917

Copyrighted by
P. M. HELDT

1917
Previous Copyright, 1913.

GUT

"T vA

PREFACE.

DURING the period that intervened between the original writ-
ing of this volume and the present revision, a number of
notable evolutions took place in the design of some of the
component parts which are dealt with here. The most important
of these was undoubtedly the introduction of the helical bevel
gear drive. The adoption, of this drive confronted automobile
engineers with new problems, chiefly in regard to bearing loads;
these are discussed in some detail in the present edition and rules
for the calculation of the bearing loads are given.

While the bevel-spur and the internal gear drive were both in
use at the time the. first edition was prepared, only a single firm
was prominently identified with each in the United States, so
they were not deemed of sufficinent importance to warrant special
treatment. Since then, however, the internal gear drive has made
notable progress in this country and the bevel-spur drive has
assumed some importance in England. At the same time addi-
tional interest has been aroused in the four wheel drive for mili-
tary and similar trucks, so it was decided to add a chapter cover-
ing these three forms of final drive.

The advent of the high speed motor, together with a great in-
crease in the use of unit power plants, resulting in the lengthening
of propeller shafts, has compelled designers to give more atten-
tion to the problem of critical speeds in shafts. Some matter on
this subject has been incorporated in the Chapter on The Bevel
Gear Drive and Rear Axle, the theory of critical speeds being
explained and rules for their calculation given.

Another branch of automobile engineering in which great com-
mercial development has taken place during the past four years
is that relating to the worm drive. The chapter devoted to this
subject has been largely rewritten and brought up to date. Minor
additions and changes have been made throughout the book, and
a number of typographical and other errors that occurred in the
first edition have been corrected. For pointing out such errors
the author wishes to thank some of his readers.

M80S109

PREFACE.

It may appear that in the chapters on the Sliding Change Gear
and on Rear Axles, the annular ball bearing receives more atten-
tion than is warranted by the scale of its present day use. Owing
— at least in part — to the interruption of imports of ball bearings
from Europe, roller bearings now predominate largely in auto-
mobile construction. The problems of mounting, however, are
very much the same as with ball bearings, and numerous examples
of mounting roller bearings are given in the plates at the end of
the book as well as in 'the text illustrations. In the most expen-
sive cars the annular ball bearing still retains a prominent place,
and it was, therefore, not deemed necessary to rewrite this part of
the work.

As nearly all of the old plates had to be discarded it was de-
cided to incorporate the plates in the book itself. Chassis views
are shown for the most part in half tone, so the line cuts show
only chassis components and these can be presented on a suffi-
ciently large scale on a 5j4x8j4 sheet.

THE AUTHOR.

LIST OF CHAPTERS

CHAPTER I.
GENERAL LAYOUT OF CARS 3

CHAPTER II.
FRICTION CLUTCHES 13

CHAPTER III.
SLIDING CHANGE SPEED GEARS 70

CHAPTER IV.
PLANETARY CHANGE SPEED GEARS 125

CHAPTER V.
FRICTION Disc DRIVE 147

CHAPTER VI.
UNIVERSAL JOINTS 160

CHAPTER VII.
DIFFERENTIAL GEARS 180

CHAPTER VIII.
UNIT POWER PLANTS, TRANSMISSION AXLES 193

CHAPTER IX.
BEVEL GEAR DRIVE AND REAR AXLE ; 203

CHAPTER X.
THE WORM GEAR DRIVE 293

CHAPTER XI.
THE CHAIN DRIVE 323

CHAPTER XII.
BEVEL-SPUR GEAR, INTERNAL GEAR AND FOUR WHEEL DRIVES. 341

CHAPTER XIII.
BRAKES 357

CHAPTER XIV.
FRONT AXLES 386

CHAPTER XV.
STEERING GEARS 411

CHAPTER XVI.
CONTROL 441

CHAPTER XVII.

FRAMES 471

CHAPTER XVIII.
SPRINGS . 497

CHAPTER XIX.

ROAD WHEELS 528

APPENDIX 543

PLATES , 571

LIST OF PLATES.

CHANGE SPEED GEAR OF THE PACKARD TWELVE 571

DRY Disc CLUTCH OF CHALMERS 6-30 572

BROWN-LIPE DRY Disc CLUTCH ON CUNNINGHAM CAR 573

MARMON CONE CLUTCH 574

SIMPLEX LUBRICATED Disc CLUTCH 575

MUNCIE CLUTCH AND CHANGE GEAR 576

CASE CLUTCH AND CHANGE GEAR 577

BORG & BECK PLATE CLUTCH AND COVERT CHANGE GEAR 578

TIMKEN TRUCK FRONT AXLE (7200 LBS. MAX. LOAD) 579

"AMERICAN" PLEASURE CAR REAR AXLE 580

TIMKEN PLEASURE CAR REAR AXLE 581

TIMKEN WORM DRIVE TRUCK REAR AXLE 582

TORBENSEN INTERNAL GEAR DRIVE TRUCK AXLE 583

Two FRENCH INTERNAL GEAR TRUCK DRIVES 584

'AMERICAN" PLEASURE CAR FRONT AXLE 585

FRANKLIN STEERING GEAR 586

BENZ STEERING GEAR 587

PEERLESS TRUCK STEERING GEAR 588

SPICER PROPELLER SHAFT ASSEMBLY 589

FRANKLIN THROTTLE CONTROL ASSEMBLY 589

PLAN VIEW OF LIPPARD- STEWART 1000 LB. TRUCK CHASSIS 590
SIDE ELEVATION OF LIPPARD-STEWART 1000 LB. TRUCK

CHASSIS 591

WINTON SPARK AND THROTTLE CONTROL (ABOVE) AND

CLUTCH AND BRAKE CONTROL (BELOW) 592

PLAN VIEW OF INTERSTATE FOUR CYLINDER CHASSIS 593

LEXINGTON-HOWARD Six CYLINDER CHASSIS 594

PLAN VIEW OF LEXINGTON-HOWARD CHASSIS 595

CADILLAC EIGHT CYLINDER CHASSIS MODEL 55 596

PLAN VIEW OF CADILLAC EIGHT CYLINDER CHASSIS 597

PACKARD FIVE TON TRUCK CHASSIS 598

PLAN VIEW OF PACKARD FIVE TON TRUCK CHASSIS 599

PLAN VIEW OF STUDEBAKER FOUR CYLINDER CHASSIS 600

PLAN VIEW OF AUBURN FOUR CYLINDER CHASSIS 601

PLAN VIEW OF HUDSON SUPER- Six CHASSIS.. 602

CHAPTER I.

GENERAL STRUCTURE OF THE CAR.

Location of Motor — In the first attempts to build road
vehicles propelled by gasoline motors the general lines of
horse vehicles were followed. The latter were then regarded
as the highest type of vehicular design, and any departure
from their lines was thought to be undesirable, as it offended
the eye. This made it necessary to place the power plant
under the body, and considerable difficulty was often experi-
enced in getting it into this cramped space. It was thought
essential to conceal the mechanical part of the vehicle as
much as possible, because what people wanted was a self-
moving carriage and not a road locomotive or a machine akin
thereto. Before long, however, some bold spirit stood up for
the idea that the pov/cr plant deserved such a location on the
vehicle that it could be designed without regard to the space
available in the body, and that when it required attention it
zould be reached quickly and without disturbing the passen-
gers. The precedent then set has since been generally fol-
lowed, and with very few exceptions the motor is now located
at the front of the car under a bonnet. It is hardly neces-
sary to add that the public's conception of what a motor ve-
hicle should look like has greatly changed since then.

Spring Suspension of Power Plant — The early automo-
biles built in this country, almost without exception, had reach
rods or perches extending between the front and rear axles,
the object of which was to free the body springs of the driv-
ing thrust. Some designers then placed the power plant on
these reaches, so as to simplify the problem of transmission
to the wheels. It was soon recognized, however, that, even
though pneumatic tires were used, the vibration was so strong
that it was practically impossible to keep the motor intact.
Moreover, the hammering effect of the heavy unsprung weight

4 GENERAL STRUCTURE OF CAR.

on the axles, wheels and tires greatly reduced the life of these
parts. The principle was thus established that as much as
possible of the weight of the car should be supported on
springs, and above all the more delicate parts, such as the
motor.

Number of Wheels — The great majority of all automobiles
have four wheels. This is the minimum number which in-
sures stability under all reasonable conditions. Howevei
cars have been and are being built with as few as three and
as many as eight wheels. The smaller number of wheels is
used to reduce the manufacturing cost of small vehicles, while
the larger numbers, above four, are used either to keep the
load per wheel inside a certain maximum (as required by the
road laws in some countries) or to insure greater comfort of
riding. However, certainly more than 99 per cent, of all auto-
mobiles (not including motorcycles) are of the four wheeled
type, and this construction may be considered standard.

Steering and Driving — With the number of wheels decided
upon, the question arises as to how many and which shall be
used for steering, and how many and which shall be used for
driving. With a four wheeled vehicle it is possible to steer
with either the front wheels, the rear wheels or all four
wheels, and to propel the vehicle by either one front wheel,
one rear wheel, both front wheels, both rear wheels or all
four wheels. In this connection it must be borne in mind
that the effectiveness of both steering and driving depends
upon the adherence — the resistance to slippage — between the
wheels and the ground, which in turn depends upon the
weight carried by the wheels. As far as steering is con-
cerned, at least two wheels have to be used for it in a four
wheeled vehicle, and if one-third or more of the total load is
carried on these wheels, then the requirement of positive
steering is met in a satisfactory degree. As regards the
choice between the front and rear wheels for steering pur-
poses, the front wheels possess one important advantage over
the rear wheels, and tha* is that, if a car stands alongside
of a curb or other barrier, and it is desired to drive away
from it, with rear steering this can only be done by back-
ing up, because in order to cause the car to turn away from
it in driving forward, the steering wheels would have to be
turned toward the curb and would run into it. Rear steer-
ing was used fcr many years on electric cabs in New York
City, but the disadvantage mentioned is greatly against it,

GENERAL STRUCTURE OF CAR. 5

and has been one of the points that led to its abandon-
ment. The only advantage of four wheel steering would be
that with a certain maximum deflection or "lock" of the
steering wheels, a car with four wheel steering could turn
in a much smaller radius than one with two wheel steering.
Four wheel steering, however, would be subject to the disad-
vantage of rear wheel steering referred to in the foregoing,
and the further disadvantage of the complication involved in
combined driving and steering wheels, which more than offset
its slight advantage, and it is therefore never used.

As regards the number of driving wheels, it would greatly
simplify the problem of transmitting the power from the
motor to its point of application if only a single wheel was
used for driving. The simplification which results from this
arrangement, as compared with that in which two wheels are
used for driving, is one of the main considerations which lead
to the selection of three wheeled construction in certain in-
stances. However, in order that a vehicle may have plenty
of traction or road adherence under all conditions, even on
steep grades with greasy road surface, at least 50 per cent,
of the total weight to be propelled must be carried on the
driving wheel or wheels. Besides, in the ordinary four
wheeled vehicle, if power was applied to one wheel — in other
words, at one side only — it would tend to cause the car to
slew or skid easily and affect the steering unfavorably. Driv-
ing through at least two wheels is therefore considered essen-
tial to successful operation. As to whether the front or the
rear wheels should be driven, one thing that is largely deter-
mining in this matter is that the front wheels are used for
steering, and it involves considerable mechanical complica-
tion to use the same wheels for both driving and steering.
Moreover, if the motor is located at the front end of the car
it can more easily be placed in driving connection with the
rear wheels than with the front wheels. It must be remem-
bered that the motor is carried upon a spring supported
frame, and therefore constantly changes its position with rela-
tion'to the axles; this relative change in position must be
allowed for by some form of flexible connection, and this can
be done more easily if the motor is at a considerable distance
horizontally from the axle to which it is connected in driv-
ing relation. There are several real advantages in front driv-
ing. Owing to the fact that the propelling force acts at a
tangent to the circumference of the driving wheels, if the

6 GENERAL STRUCTURE OF CAR.

front wheels are drivers, and they drop into a mud puddle,
for instance, they tend to climb out of it, as it were, while
with rear drive the combined effect of the forward thrust of
the rear wheels and the weight on the front wheels may force
the latter deeper into the mud. Another advantage of front
driving is that with it there is much less tendency to skid
than with rear driving. The problem of driving through the
steering wheels can, of course, be solved, but it involves the
use of two universal joints, preferably of a type which insures
uniform transmission of motion irrespective of the angle be-
tween the connected shafts, which must be so placed that the
point of intersection of the two connected shafts lies in the
centre line of the steering knuckle pin.

Four Wheel Drive — Driving on all four wheels has been
employed to some extent, particularly on army wagons, which
may under conditions have to travel off the roads. Four
wheel driving makes the whole weight of the vehicle and load
available for traction purposes, which is an advantage when
the streets are covered with ice or snow, or for some other
reason are exceedingly slippery. This system of driving
would become more important if steel tires should ever come
into common use for commercial vehicles, since the adherence
between steel and the different road surfaces is very much less
than that between rubber and these road surfaces. Where rub-
ber tires are used sufficient traction is obtained under all nor-
mal conditions by so arranging the design that from one-half
to two-thirds of the weight of the car and load is always car-
ried on the driving wheels, while under abnormal conditions
such traction devices as tire chains or steel studded tire covers
are resorted to.

Thus, while the front drive and four wheel drive are being
exploited to some extent, at least 99 per cent, of all automo-
biles built are steered by their front wheels and driven by their
rear wheels.

Differential Gear — If both driving wheels were positively
connected to the single source of motive power, they could not
rotate at unequal speeds, as is required in turning corners. If
the wheels had to drive the car forward only, the problem
could be solved by driving them through ratchet clutches, but
since they must drive the car backward as well as forward,
it is necessary to incorporate a so-called differential gear in
the drive through which the driving torque is always equally
divided between the two driving wheels, in driving both for-

GENERAL STRUCTURE OF CAR 7

ward and backward, and which allows the two wheels to turn
at different speeds as required by the course followed, or by
any slight difference in their diameters. With the four wheel
drive it is necessary to use three differential gears, one be-
tween the front and rear axles and one between the two
wheels on each axle.

Friction Clutch— Owing to the fact that the gasoline motor,
unlike steam and electric motors, does not start from a stand-
still with full torque, but must be started either by means of a
hand crank or some starting device which generally produces
only sufficient torque to just turn the motor over against the
compression, it is necessary to disconnect the motor from the
driving parts of the vehicle for starting it, and after the motor
has attained speed, to connect it to the vehicle again. For this
purpose a device must be used which will allow of a certain
amount of slippage, until the motor speed has been reduced
and the vehicle speed increased to such a point that the two
correspond. This is accomplished by means of a friction
clutch, which is always placed close to the engine and gen-
erally built together with the flywheel — except in those cars
provided with frictional means of power transmission, such as
belts, friction pulleys and friction discs, which latter devices
serve the dual purpose of changing the gear ratio between the
engine crankshaft and the road wheels and of disconnecting
the former from the latter.

Change Speed Gear — With any but the very lightest of
gasoline motor vehicles it is necessary to provide means for
connecting the motor to the driving wheels in several different
ratios. The gasoline motor differs from other light motors
in that when running at its speed of maximum economy or
its speed of maximum output, it produces nearly the maximum
torque of which it is capable. The motor, of course, must be
so geared that under normal conditions of operation — that is,
when the car is traveling over a level road at a good speed — it
runs at about its speed of maximum economy, and it is then
impossible for the motor to provide the propelling effort re-
quire'd in climbing steep hills or in passing through deep sand,
through the same gear reduction. It is, of course, understood
that when two shafts or other rotating machine parts are con-
nected together in driving relation, the torques of the two bear
to each other the inverse ratio of their respective speeds. Thus,
by providing a hill climbing gear giving a speed reduction,
say, four times as great as the normal speed reduction, the

8 GENERAL STRUCTURE OF CAR

driving effort at the road wheel rims can be quadrupled for hill
climbing. But since the hill climbing or low gear gives a com-
paratively low vehicle speed, it is customary in all but the
lightest vehicles to provide either one or two intermediate
gears, for use on moderate hills, on soft or uneven roads, etc.
The change gear mechanism, therefore, provides either three
or four forward gear ratios as a general thing, and also one re-
verse gear ratio. In this country gear boxes with three forward
speeds are considerably more common, while in Europe the four
speed gear is the most popular, the difference being no doubt due
to the fact that we employ relatively more powerful motors.

Single and Double Reduction — There is now a tendency
to use a stroke of about 5 inches in motors of all sizes. Pleas-
ure car motors make about 1800 revolutions at normal speed or
at their speed of maximum output. For pleasure cars it is
customary to use wheels of 30 to 36 inches diameter. If we
assume that the wheels are 36 inches in diameter and that the
car is to be geared to make 45 miles per hour at normal engine
speed, then the wheels must turn at

45 X 5,280 X 12

i=~ — 2 --- -- = 420 r. f. m.

60 X 36X3.14

and the gear reduction ratio from the engine to the road wheels
must be 1800 to 420, or about 4.25 to 1. This ratio can easily
be obtained by means of a single reduction gear of the helical
bevel type.

Now let us take the case of a heavy truck which has wheels
of, say, 40 inches diameter and is to be geared to make 15
miles per hour at 1,200 revolutions per minute of the motor.
The driving wheels must then turn at

o4o 3,14

Hence the gear reduction ratio must be 1,200 to 140, or 8.5 to
i. This cannot be obtained in a practical way by a single bevel
or spur gear set or a chain and sprocket gear, for the reason
that the outside diameter of the driven gear or sprocket on
the rear wheels or axle is limited, since the car must clear the
road by a certain amount. This reduction can be obtained by
means of a worm and worm wheel, but if either a bevel gear or
chain drive is used, a double reduction is necessary. It is cus-
tomary in such cases to employ a first reduction by bevel gears
to a jackshaft and a second reduction by chain to the rear
wheels, although occasionally the two reductions are obtained

GENERAL STRUCTURE OF CAR. 9

by means of one spur gear set and one bevel gear set, both con-
tained in a housing on the rear axle. All pleasure cars
employ a single reduction for normal speed operation, obtained
by either a set of bevel gears, a chain and sprocket wheels or
a worm and worm wheel. Commercial vehicles of the lighter
type with pneumatic tires are geared the same, while the heavier
commercial vehicles have either a single worm gear reduction or
a double reduction by bevel gears and chains, by bevel gears
and spur gears, or by bevel gears and internal gears.

Dead and Live Axles — The driving wheels may either,, be
mounted upon bearings on the rear axle and driven through
chains or spur gears, in which case the axle is called a dead axle,
or they may be fixed upon the ends of driving shafts extending
through the rear axle housing, or be placed in driving connec-
tion with such shafts through driving dogs or positive clutches,
in which case the axle is a live axle. Dead axles are used on a
good many heavy commercial cars and live axles on nearly all
pleasure cars. When a dead axle is used the rear wheels are
driven from a countershaft — except in the very few cases where
two motors are used — and the differential gear is mounted on
the countershaft. With live axles it is customary to mount the
differential gear at or near the middle of the axle, though some-
times it is mounted on the propeller shaft through which the
power is transmitted to the driving axle. Live axles may be
driven through a chain and sprockets or through bevel, worm
or spur gears. Only a single driving connection is required in
the case of a live axle, while in the case of a dead axle there
must be provided an individual drive to each of the driving
wheels. Though the chain drive is applicable to live axles, and
was at one time extensively used on low priced pleasure cars, it is
now, as a rule, used only in connection with dead axles, in
the form of the so-called side chains. Nearly all live axles
of pleasure cars are driven through a set of bevel gears.

Frames— One of the rules which have been established in
automobile design is that the vehicle body should be as inde
pendent as possible of the mechanical part, so that it can be
removed without disturbing any of the mechanical parts,
motor, transmission and control members are, therefore, carried
upon a substantially rectangular frame made of pressed steel,
rolled steel or laminated wood, which is supported upon the
axles through the so-called body springs. The motor sets upon
this frame in front; in the conventional type of pleasure car
chassis the motor space is walled in by the radiator in front

10 GENERAL STRUCTURE OF CAR.

and the dashboard at the rear, and the motor is covered by a
sheet metal bonnet. This same arrangement is also used to
some extent in heavy commercial vehicles, but for this class
of vehicles there are two alternate arrangements, viz., having
the driver's seat on top of the motor or at the side of the motor.
In fact, there may be said to be still one more alternative, since
the motor may be under the seat proper or under the footboard
of the driver's seat. These latter arrangements make that por-
tion of the length of the frame which would otherwise be oc-
cupied by the driver's seat available for loading space.

In the conventional type of vehicle the space on the frame back
of the dashboard is occupied by the body. It is one of the
rules of design that no part of the mechanism back of the dash-
board, except the control members, should project above the
top plane of the frame. Formerly half elliptic springs were
used almost exclusively and were often placed directly under-
neath the frame side members, whose top edge was then made
straight from end to end. Now, however, three-quarter elliptic
and even full elliptic springs are widely used at the rear on
pleasure cars, and in order to preserve a comparatively low
centre of gravity, the frame has a drop directly in front of the
point of attachment of the rear springs, or the springs, even if
semi-elliptic, are placed outside the frame and there is a so-
called "kick-up" in the frame directly over the rear axle, so it
will not strike the latter when the springs are fully compressed.
The frame side members are generally swept in at the front end
in order to allow of a greater limiting deflection of the steer-
ing wheels.

The so-called reach or perch has been entirely done away
with. The rear axle transmits its driving thrust to the frame
either through radius rods or the rear springs and the frame
transmits driving thrust to the front axle through the springs.

Tread and Wheel Base — The distance between the centre
lines of ground contact of the wheels on opposite sides is
known as the track or tread. This distance is generally 56 inches
in pleasure cars and the lighter commercial vehicles, and 62
inches or more in heavy trucks. The National Automobile
Chamber of Commerce has adopted a standard of 56 inches for
the tread of pleasure cars, but there is no standard for truck
treads. Practically all light horse vehicles used in the northern
part of the country have a track of 56^ inches, which is
measured from and to the outside of the tires at the point of
contact with the road, so an automobile with the standard 56 inch
tread ^will run in ruts made by the wheels of horse vehicles.
In the South a tread of 60 inches is much used on horse vehicles,

GENERAL STRUCTURE OF CAR. 11

and since many of the roads there are deeply rutted a large
part of the year, several automobile manufacturers have been
furnishing their cars with a 60 inch tread to customers in that
part of the country, but the practice has been discontinued.

The distance between the centre of road contact of the front
and rear wheels, respectively, is known as the wheelbase.
This, of course, is the same as the centre distance between the
axes of the front and rear wheel spindles. The wheelbase
differs widely in different types and sizes of machines. A long
wheelbase makes for a more comfortable riding car and also
tends to prevent skidding. On the other hand, a long car can-
not be handled so well in crowded streets, since it cannot turn
in such a short radius. Besides, a long wheelbase car is
necessarily comparatively heavy, since the frame must be
made of larger cross section in order to support the same
weight, as well as be made longer. In passenger vehicle
practice there is a fair -degree of uniformity with respect to
wheelbases, the latter ranging between the following limits for
different types of cars.

Four cylinder runabouts and roadsters, 30 horse power and
under, 90-105 inches.

Four cylinder runabouts and roadsters over 30 and not over
40 horse power, 105-115 inches.

Four cylinder taxicabs, 4-5 passengers, 96-100 inches.

Four cylinder touring cars, 30 horse power and under, 100-
115 inches.

Four cylinder touring cars over 30 and not over 40 horse
power, 110-120 inches.

Four cylinder touring cars over 40 horse power, 120-130
inches.

Six cylinder cars, about 10 inches longer than four cylinder
ones of the same class.

CHAPTER II.

FRICTION CLUTCHES.

The friction clutch, as already pointed out, serves the purpose
of connecting the motor, after it has been started running, with
the driving gear of the car, in such a way that the car may be
gradually accelerated and the motor at the same time pulled down
in speed, until the speeds of the two correspond, thus pre-
venting shock and jar.

In motor cars employing a single friction clutch which serves
to connect the engine to the driving wheels through all of the
different gear reductions, the clutch is normally held in engage-
ment by a spring or springs, and when it is desired to discon-
nect the engine in order to stop the car, or to change the gear,
the clutch is first disengaged by compressing its spring by means
ot a pedal, then the gear is disengaged or changed, and finally
the clutch is let in again. In other cars, where a clutch serves
for a single gear reduction only, it is normally disengaged, and
is engaged by pressure exerted on a hand or foot lever, the
mechanism transmitting the pressure to the frictional surface of
the clutch being self locking in the engaged position.

There are quite a number of different types of clutches, all
more or less extensively used, viz.:

Conical clutches.

Multiple disc clutches.

Dry plate clutches.

Band clutches.

Coil clutches.

Expanding segment clutches.

Multiple disc and dry plate clutches are identical as tar as
their general principle is concerned, but they differ 'n respect to
detail of design. Dry plate clutches are in very extensive use
on American cars, as are conical clutches. The latter are par-
ticularly suited to cars of relatively low power. Lubricated
disc clutches also are quite popular, especially in Europe.
The other three types mentioned have been used more or less

FRICTION CLUTCHES.

in the past, but arc now seldom met with, the practice of
assembling cars from parts built by specialists having tended
toward the standardization of types. The different types of
clutches will be taken up in succession.

Cone Clutch — Conical clutches may again be divided into
three sub-classes, viz., the direct cone, the inverted cone and the
double cone clutch. The direct cone is the oldest and most
popular of these types. As shown in Fig. i, with this type the
flywheel is bored out to form the female cone, into which the
male cone is forced by the pressure of a coiled spring concentric

FIG. i. — DIAGRAM OF DIRECT FIG. 2. — DIAGRAM OF INVERTED
CONE CLUTCH. CONE CLUTCH.

with its hub. In the inverted cone clutch (Fig. 2) the female cone
is formed by a cast iron or steel ring bolted to the rim of the
flywheel, into which the male cone enters from the flywheel or
engine end. The inverted type of cone clutch was originally
adopted in order to make it possible to place the change gear box
nearer the engine, under the floor boards of the driver's seat,
since the clutch spring is placed between the flywheel and the
clutch cone, instead of to the rear of the latter. The double cone
clutch is a combination of a direct and an inverted cone clutch,
and is particularly suited where great powers have to be trans-
mitted.

14 FRICTION CLUTCHES.

Clutch Calculations— In calculating any part of the trans-
mission we will assume that the mean effective pressure in the
engine cylinder multiplied by the mechanical efficiency (T? p ) is 80
pounds per square inch at low engine speeds and 65 pounds per
square inch at the speed of maximum output. These figures are
fairly representative though a little low for some engines. Now
let & = bore of cylinder in inches.

/= length of stroke in inches.
n — number of cylinders.
p = mean effective pressure.
P = mean total pressure on one piston.
T- torque in pounds-feet.

Then the energy developed during one revolution of the
crankshaft is

n TT I

E = ~ £2/^~I foot-pounds.

If there is a torque T on the engine shaft, or a turning effort
of T pounds at a radius of I foot, the energy transmitted during
one revolution is

E=2ir Tfoot pounds.
Hence

and

nib2 p
T - Ig2 pounds-feet ..................................... (i)

A diagram of a cone clutch is shown in Fig. 3. The spring
pressure P forces the male cone against the female cone, pro-
ducing a normal pressure N at their contact surface. According
to the principle of the parallelogram of forces

P _
^ — sin a,

hence

P — Nsin a. ................................................ (2)

where a is the angle of the clutch cone. The adherence or
frictional force F between the clutch cones is equal to the
normal pressure multiplied by the coefficient of friction /

F=Nf

Angle of Cone — Cone clutches faced with leather or asbestos
fabric are given an angle of cone of from 10 to 13 degrees,
but the most common angles are 12 and i2l/2 degrees. . With
metal to metal clutches an angle of 10 degrees can be used
without risk of trouble, but such a small angle in a leather

FRICTION CLUTCHES 15

faced clutch is liable to cause it to stick. From equation (2)
it will be seen that the spring pressure P required to produce
a certain normal pressure decreases as the angle of the cone
decreases, hence there is an advantage in using as small an
angle as practical. However, a cone with a relatively large
angle is less given to "fierceness" in action, i. e., sudden
gripping.

Coefficients of Friction — The coefficient of friction between
leather and cast iron varies greatly according to the condition
of the cast iron surface and the state of lubrication. James
Angelino in experiments made with a piece of old clutch leather
found the coefficient of friction to vary from f = o.i$ to f =

FIG. 3.— COMPOSITION OF CONE CLUTCH FORCES.
Kent gives the coefficient of leather on greasy metals as 0.23
In the calculations it, therefore, is the best plan to figure on a
coefficient of friction of 0.2, since the leather is generally
boiled in tallow or soaked in castor oil prior to being applied
to the clutch, and hence is always somewhat greasy. Cast
iron on cast iron cone clutches, lubricated, have been used to
some extent, and in their case the friction coefficient is com-
paratively low, not exceeding 0.07, depending upon the nature
of the lubricant. Asbestos fabric is also used to some extent
as a facing for clutch cones. It possesses the advantage that
it is not affected by high temperatures. The coefficient of friction
is also somewhat greater than that of leather.

16 FRICTION CLUTCHES.

Diameter of Cone — It is desirable to make the diameter
of the cone small, for the following reason: The sliding gears
or jaw clutches of the change gear practically never run at
equal peripheral speeds just previous to being meshed, but
from the moment they become meshed they must run at the
same speed. This means that at the moment of engagement
one of the connected parts must suddenly change its speed, and
this results in a clash or hammer blow at the point of engage-
ment. Now, one of these parts is mechanically or positively
connected to the driving wheels of the car, and therefore can-
not quickly change its speed. The other consists of the clutch
cone and of a train of gears, and the resistance to a change in
the speed of .these parts is proportional to the sum of their
polar inertias, of which the inertia of the clutch cone is by far
the greatest. The inertia of a revolving body is proportional
to its weight, and to the square of its radius of gyration, which
latter, in the case of a clutch cone, varies substantially as the
mean outside diameter. Hence, the force of the clash increases
and decreases substantially as the square of the mean outside
diameter or radius of the cone. On the other hand, the radius
must be made large enough to keep down the unit normal
pressure (which determines the wear of the clutch facing) and
the spring pressure required to transmit the torque of the
motor, since a clutch with a very stiff spring is "harsh" and
difficult to operate. As a general rule, the flywheel would be
designed first and the clutch made of a corresponding diameter.

Unit Normal Pressure — In conical clutches lined with
leather, asbestos fabric or similar material the unit normal
pressure generally ranges around 12 pounds per square inch.
However, in some of the largest cone clutches it is nearly 20
pounds per square inch, and yet satisfactory service is ob-
tained. Cone clutches are used mainly for the smaller engines
and multiple disc clutches for larger powers, and if the former
are used on engines of 60 horse power and over it is necessary
to employ large unit pressures, because the available diameter
is not much greater than is used in clutches for smaller powers,
and unduly wide clutch faces are also out of the question.
While the clutches work satisfactorily under the higher pres-
sures, it is natural to expect them to wear out quicker, and
wherever the space available permits it is best to keep the unit
pressure down to 12 pounds. In metal-to-metal cone clutches
the unit normal pressure must be several times that used with
leather faced clutches in order to transmit the same power.

FRICTION CLUTCHES

The foregoing figures are based upon the normal pressure re-
quired to hold the clutch from slipping when fully engaged. The
actual normal pressures are some-
what greater because the clutch spring
must be made stronger than required
to produce this normal pressure
under conditions of rest. Suppose
that the normal pressure* N is just
insufficient to produce the necessary
driving torque and the clutch slips.
The normal pressure can only be in-
creased by forcing the cone further
into the flywheel, and this necessitates
overcoming the resistance to .motion
of the leather over the cast iron sur-
face in a direction normal to that of
slippage.

Referring to Fig. 4, let N repre-
sent the effective normal pressure
between the clutch friction surfaces,
and P the spring pressure necessary
to produce this normal pressure.
Let F represent the frictional force
in the direction of a generatrix of
the cone; Pi, its component parallel
to the clutch axis, and 0 the so-called
friction angle (tan 0 = /), then

P = N sin a,

F = N tan <i>
and

Pi —F cos a== N tan <j> cos <*.

The total spring pressure necessary to cause the clutch to engage
firmly without slipping is

P2 = P + Pi = N (sin a + cos a tan 0) (3)

In applying this equation it is permissible to use for tan <i> a con-
siderably smaller value than the normal coefficient of friction
between leather and cast iron. This is due to the fact that when
one body moves frictionally over another in a given direction, it
requires but an insignificant effort to start it moving at right
angles to its original direction of motion. That is, the coeffi-
cient of friction encountered in any given direction is virtually
reduced by motion in a direction at right angles thereto. An
illustration of this principle is furnished by the fact that when a

FIG. 4. — COMPOSITION OF

CLUTCH FORCES DURING

ENGAGEMENT.

18 FRICTION CLUTCHES.

mechanic wants to force a tight fitting collar over a shaft he
will twist it angularly back and forth on the shaft, whereby the
effort required to move it in an axial direction is greatly reduced.
We may assume that the coefficient of friction in this case is
one-fourth of its normal value, or 0.05. Hence, the general
equation for the spring force required to engage a leather-faced
cone clutch becomes
P = N (sin a + 0.05 cos a) ............ *. ..................... (4)

The frictional force at the mean circumference of the cone is

TX 12

— pounds.
^m

The area of the cone face is

2 ir rm w,

and since there is to be a normal pressure of 12 pounds per
square inch, the total normal pressure is

12 X 2 7T rm TV = 24 7T rm "W.

This multiplied by the friction coefficient 0.2 gives the total
frictional force —

O.2 X 24 7T rm IV = 4.8 7T rm tV.

Equating this to the expression for the frictional force found
above, we have

TX 12

— - - = 4.8 TT rm iv,

and

•"-srr^n ............................................. (5)

from which equation the necessary width of face may be found.

It is also possible to derive an equation for the necessary
spring pressure in terms of the fundamental clutch data. The
normal pressure

N = 12 X 2 if rm TV = 24 TT rm w.

Substituting the value of w, found above,

and substituting this value of N in equation (4) we have

xr *r»

p _ - (sz-n a _f. 0 .05 cos a) ............................... (6)

' m

In order to facilitate the determination of the necessary face
width and spring pressure, according to equations (5) and (6),
Chart I has been drawn. From this chart can be found the
low speed torque of four and six cylinder motors of any cyl-
inder dimensions within the usual range of automobile practice,
as well as the necessary width of clutch face and of the clutch

FRICTION CLUTCHES.

Spring Pressure For Six Cylinder JYIofor

Lbs. 300 450 JOO 750 900 W50

f"~ Spring Pressure for Four Cylinder Motor

Lbs. 200 JOO 400 500 600 700

Face 5 Width For 4" Six Cylinders

CHART i.— GIVING Low SPEED TORQUE OF FOUR AND Six CYLINDER

MOTORS AND WIDTH OF FACE AND SPRING PRESSURE

REQUIRED FOR A LEATHER-FACED CONE CLUTCH

TO TRANSMIT THIS TORQUE.

20 FRICTION CLUTCHES.

spring pressure required with different mean radii of clutch and
angles of cone. The method of using the chart is indicated in
diagram.

Constructional Details — Since the inertia of the clutch must
be as small as possible, the clutch cone is generally cast of
aluminum, though of late pressed steel clutches have come into
quite extensive use, mainly abroad. In the case of aluminum
cones the rim is generally made of a mean thickness of
one-quarter inch, tapering from the edges toward the joint
with the web, which latter should preferably be at the middle
of the rim. In order to obtain the necessary strength in the web
with the least amount of material the latter, instead of being made
radial, is inclined considerably toward its axis, so the material will
work partly under compression. The dimensions of the web or
spokes are largely a matter of foundry limitations. For the smaller
powers a plain web is used, tapering from about three-sixteenths
inch near the rim to one-quarter inch where it joins to the steel
centre, which is lightened by large holes being formed in it.
Some designers, however, prefer to leave the rim solid, as it
keeps out dust. When spokes are used they are often of cross-
shaped section or ribbed, so as to provide additional lateral
strength in the cone and also to support the rim more rigidly.

Clutch leather is generally treated before being applied to
the clutch by being either boiled in tallow or soaked in castor
oil, the excess oil or grease being removed by passing the leather
through rolls. The leather must be cut to form a sector of an
annular ring of an inside radius o-a and an outside radius o-b
(Fig. 3). The* length of the inner edge of the annular sector
must evidently be 2 TT r, Now, the radius

o-a = — : — '
stna.

and the circumference of a circle of radius o-a therefore is

2 TT r

sin a

Hence the angle 0 to which the leather should be cut can bt
found from the proportion

2 irr

— — : 360 degrees = 2 v r : <f>

<f> = sin a X 360 degrees.

Therefore, in laying out the pattern of the leather (Fig. 5),
strike two concentric circles of radii

and o.fr -- — : — 4- -uj

stria '

FRICTION CLUTCHES.

where w is the width of the face of the clutch. Then from the
annular ring thus formed cut out a sector subtending an angle
sin a X 360 degrees at the centre.

Some designers form a small radial flange on the edge of the
rim at its bigger end which will retain the facing, and thus take
some of the stress off the retaining means and off the facing
itself. When leather facing is used it is retained by means of
copper rivets whose heads are countersunk beneath the surface
of the leather and whose ends on the inside of the clutch rim
are hammered over. Usually two rows of one-eighth inch rivets
are used, spaced about an inch apart. After the leather is riveted

FIG. 5.— PATTERN FOR CLUTCH LEATHER.

to the cone it is accurately turned off in a lathe. An improved
method of holding the leather in place consists in the use of
six or eight T bolts, and the provision of depressions in the rim
of the cone parallel with generatrices of the latter, for the re-
ception of the heads of the T bolts. This method of securing
the facing, which is particularly applicable to asbestos fabric,
(which does not lend itself well to riveting) is illustrated in Fig. 6.
Provisions for Smooth Engagement — Cone clutches have a
tendency to grip with a jerk, especially in case the car is oper-

FRICTION CLUTCHES.

FIG. 6. — CLUTCH LEATHER FASTENED BY T-BOLTS.

ated by a novice driver or the clutch operating linkage is such
that the driver must exert a very strong pressure on the clutch
pedal. In order to overcome this tendency, which is detrimental
to the whole car, various devices are resorted to, all based on
the principle that a portion of one of the engaging surfaces is
raised by spring force above its normal height, and thus that
portion alone first contacts with the opposing surface. The plan
most commonly followed consists (Fig. 7) in turning a shallow
circumferential groove on the outside of the aluminum cone near
its large end, in which are placed a number of equally spaced
flat steel springs which are fastened to the cone by one rivet
each, or to a screw secured in the rim of the cone. These steel
springs are of such form that they slightly lift the leather when
the clutch is disengaged, so that certain portions of the leather
come in contact with the flywheel rim first. These "auxiliary"
springs are fully extended when the clutch surfaces first engage
each other, and the pressure of contact therefore starts from
nothing.

A similar device, comprising coiled instead of flat springs, is
illustrated in Fig. 8. It consists of a small shell cast integral with
or. riveted to the clutch rim from the inside, which contains a
coiled spring and a plunger pressed outward thereby. The head

FIG. 7. — FLAT SPRING UNDEP CLUTCH FACING.

FRICTION CLUTCHES.

of the plunger, which presses against the clutch facing from
underneath, may be either fillister shaped or in the form of a
crossbar extending underneath the leather the entire width of
the clutch face.

Where either a male or female cone of steel is used it is pos-
sible to cut slits in it length-
wise and circumferentially, as
shown in Fig. 9, or at an
angle to the edge, and then
bend the flaps so formed
slightly outward or inward, as
the case may be. This prac-
tice is or has been followed
by Renault, Cadillac, Pullman
and others.

FIG. 8. — SPRING PLUNGER UNDER
CLUTCH FACING.

Cork inserts are used with"
leather-faced cone cluches by
a number of manufacturers, mainly with the object of making
the engagement more gradual. The properties of these corks
will be discussed in connection with plate clutches, in which
they are more extensively used. Corks used in leather-faced
cone clutches vary in diameter from
five-eighths to one inch and cover from
5 to 30 per cent, of- the surface of
the cone. When the area presented
by the corks does not exceed 10 per
cent, of the total frictional area,
they do not materially affect the co-
efficient of friction, but some advan-
tage is gained in this respect when
from 20 to 30 per cent, of the surface
is made up by the corks. The fric-
tion is then somewhat greater than
that between leather and cast iron,
and consequently the spring pressure can be reduced.

Multiple Springs— A few makers use three clutch springs
placed at equal angular distances and about midway between the
clutch shaft and the rim. One advantage of this arrangement
is that the clutch is more easily adjusted, owing to the greater
accessibility of the adjusting means. A typical design of this
kind is shown in Fig. 10. A three armed spider is placed on
the tailshaft just behind the web of the flywheel, whose arms
carry studs or spring bolts extending backward parallel with

FIG. 9. — SLOTTED CLUTCH
FEMALE CONE.

FRICTION CLUTCHES.

the tail shaft, through
holes in the web of the
clutch cone. The por-
tions of the three spring
bolts extending through
the clutch cone are sur-
rounded by coiled springs,
whose rearward ends
bear against washers
supported by adjusting
nuts. The spring thrust
is taken up on a ball
thrust bearing carried on
the tail shaft. Construc-
tions similar to the one
here shown are used by
several English manu-
facturers.

Clutch Centre — The
clutch may be regarded
as composed of three
main parts, viz., the
cone with its web or
spokes, the supporting
bearing, and a spring housing or hollow shaft by which the
power is transmitted to the change gear. Generally these
three parts are made separate, though sometimes the cone is
formed integral with the bearing. The clutch bearing is oper-
ating only when the clutch is disengaged, and evidently carries
very little load. It therefore may be of relatively small diameter
and free fitting. The bearing is practically always a plain one,
and generally the non-fluid oil in the clutch spring housing is
depended upon for its lubrication, it being drilled with several
large oil holes and cut with deep oil grooves, but some makers in
addition provide a pressure grease cup on the outside of the
clutch which can be screwed down at intervals, the grease being
forced through a drill hole directly to the bearing surface.

The clutch spring generally surrounds the bearing, its forward
end resting against a flange thereon and its rear end against a
ball thrust bearing on the end of the tailshaft or on a cap screw
screwed into the end of that shaft. This thrust bearing works
only when the clutch is disengaged, whereas when it is engaged
both ends of the spring press against parts rotating in unison
and incapable of moving further apart. In other words, the

FIG. io.— MULTIPLE SPRING CLUTCH.

FRICTION CLUTCHES. 25

spring pressure is then self-contained. This is contrary to con-
ditions in the earlier cone clutches, in which the clutch spring
took purchase on a shoulder on the transmission shaft, thus
creating end thrust in both the transmission shaft and the crank-
shaft

It is quite desirable to keep down the length of the tailshaft,
so the change gear box may be located underneath the floor
boards of the driver's seat, and enough space should be allowed
between the rear end of the tailshaft and the forward end of the
transmission driving shaft, so the clutch can be removed from the
car without removing either the engine or the gear box. If the
web of the clutch cone is inclined backward, for the purpose of
increasing its strength, the flange for connecting it to the clutch
centre usually comes at a considerable distance from the fly-
wheel flange, and it is therefore advantageous to make the bear-
ing of a form similar to a cake mold, as shown in Fig. n, so its
forward end will come within a short distance of the flywheel,
making allowance only for the wear of the clutch leather.

In designing the clutch centre, attention must be paid to the
exigencies of assembling. The clutch spring housing covers the
spring and extends beyond the end of the tail shaft, hence the
spring must be put in place and adjusted before the housing is
put in place. Some makers bolt the web of the cone and the
flange of the bearing together by, say, three bolts, and pass three
intermediate bolts through the web of the cone and the flanges of
both the bearing and the clutch housing. This admits of assem-
bling the cone with the bearing, then placing them on the engine
tail shaft, putting the clutch spring and its retaining nut in place,
and finally bolting the clutch spring housing to the cone and
bearing. Others place the web of the cone between the
flange of the bearing and the flange of the clutch spring housing,
and pass all of the retaining bolts through all three connected
parts. This makes it necessary to assemble these parts after the
clutch spring is in place, which, of course, can be done only with
a spoked cone. Still other makers connect the clutch housing
with the clutch bearing by means of radial bolts or set screws.

Spring Thrust Bearing— When the clutch is disengaged and
at rest its spring bears with one end against a rotating part
(tailshaft spring rest) and with its other against a stationary
part, and to prevent undue wear and friction under these condi-
tions the spring usually exerts its pressure through a ball thrust
bearing at the rear end. In fact, if no ball thrust bearing were
provided, the friction between the spring and its support would

FRICTION CLUTCHES.

FRICTION CLUTCHES. 27

likely be great enough to cause the clutch cone to keep on spin-
ning. The ball thrust bearing may be passed over the end of
the tailshaft and held in place by means of a castellated nut, or
this bearing may be supported by means of a cap screw screwed
into the end of the tail shaft. With either arrangement the
spring pressure may be adjusted; with the latter it can be ad-
justed through a considerable range, and, besides, the tail shaft
will be shorter, so the change gear can be brought closer to the
engine. In any case it is necessary to provide a lock for the
adjustment, and with a cap screw carrying the ball thrust
bearing this lock usually assumes the form depicted in. Fig. n.
The cap screw is drilled through its centre and slightly tapered
out and split at its outwardly threaded end, to receive a small
screw, with a correspondingly tapered head. By means of this
inner screw and its nut the split end of the cap screw can be
expanded and the screw thus securely locked in place.

Clutch Springs— The springs which hold the clutch in engage-
ment are generally helical or coiled springs made of either round
or square steel wire. Formulae for the safe load and the deflec-
tion of round steel wire coiled springs were given in Vol. I in
the chapter on Valves and Valve Gear. The corresponding
formulas for square steel wire springs are

= 0.471^-
n P D3

D = mean diameter of coil.

W = maximum safe load in pounds.

r = compression of spring.

d = side of cross section of wire.

n = number of coils in spring.

5" = maximum safe fibre stress of material.

£ = torsional modulus of elasticity.

P = load in pounds.

Occasionally, in order to save space in a longitudinal direction,
so-called volute springs, made of flat metal, as shown in Fig. 12,
are used.

Pressed Steel Cones — Pressed steel cones are very attractive
to the designer, owing to their light weight and their low cost
when made in large numbers. Some trouble is said to have been
encountered with these cones owing to insufficient rigidity and
consequent shattering, and it has been recommended to press* the
cone with radial ribs to overcome this difficulty. One English

28 FRICTION CLUTCHES.

manufacturer makes the web of his pressed steel cone in the
form of a zone of a sphere, evidently with the same object.
Either J4 inch or 3/16 inch stock is used. A recent develop-
ment in the line of clutches is a pressed steel clutch with a
leather facing secured to the driving cone. This should reduce
the moment of inertia of the driven cone in such a degree as. to
eliminate all obj ection to the cone clutch on this score.

The several designs of clutches here shown are particularly
simple. A great deal of ingenuity has been applied by designers
in working out the details of clutch centres, and much variety is
to be found in the designs extant. With cone clutches of the
inverted type it is not easy to provide adjusting means for the
clutch spring, and none is generally provided.

Shifting Collar — To disengage a cone clutch the driven cone
must be withdrawn from the driving cone against the pressure of
the clutch spring. This necessitates a sliding connection between
the clutch pedal shaft, which usually extends across the vehicle
frame directly above the clutch housing, and this housing. The
latter is usually provided with a circumferential groove, in which
is located a sliding collar. If both flanges of the groove are
integral with the housing, the shifting collar, of course, has to
be made in halves in order to get it into tht groove, the halves
being bolted together. However, generally only one flange of
the groove is integral, so the shifting collar can be slipped over
the housing from one end.

When the clutch is withdrawn the entire pressure of the clutch
spring is taken up on one face of the shifting collar, and to
obviate the necessity of constant attention to the lubrication of
this collar a ball thrust bearing is generally placed in the groove
to one side of the shifting collar, so as to take the thrust of the
spring. This, of course, necessitates the use of one removable
flange, in order to get the ball thrust bearing into place.

A typical shifting collar design is shown in Fig. 14. The
collar itself is made of brass and provided with two radial pins,
with which engage the free ends of the forked clutch shifting
lever. These lever ends are formed with oblong holes for the
pins to pass through, to make allowance for the fact that they
move in an arc of a circle, while the shifting collar is constrained
to move in a straight line. A grease cup is usually screwed into
either one or both of the shifting collar trunnions.

In some cases the shifting collar is made in the form of a cir-
cular disc, and the forked shifting lever is made cam-shaped and
bears against one face of the disc. Pressure has to be transmitted

FRICTION CLUTCHES

FIG. 12.— VOLUTE CLUTCH SPRING.

FIG. 13.— PRESSED STEEL CONE CLUTCH.

30 FRICTION CLUTCHES,

from the clutch pedal to the clutch housing in one direction only,
and if the clutch shifter fork is held against the shifting collar
by means of a spring no groove for the collar is necessary.

Clutch Brakes — By lightening the cone, and especially by
reducing its diameter, it has been endeavored to reduce the shocks
due to clashing of the gears, but there have also been efforts in
other directions to insure the possibility of smooth meshing. The
clashing, of course, is due to unequal pitch velocities of the two

FIG. 14. — CLUTCH SHIFTING COLLAR.

gears meshed. If the speed of one of the gears can be increased
or reduced previous to meshing until it corresponds to that of
the other, then the gears can be meshed without shock or jar.

Suppose that a car is ascending a hill and it becomes necessary
to change to a lower gear. It is evident that if the second gear,
say, is disengaged, and an attempt is made to immediately engage
the first gear, the driven wheel of the latter will run too fast or
the driving pinion too slow to permit of easy meshing:. The

FRICTION CLUTCHES.

driver has no control over the driven gears, except through the
use of the car brake, and it would be inadvisable to apply that
while ascending a hill. However, as the car is on an up-grade, its
speed and that of the driven gear decrease rapidly when the motor
is disconnected, and the gears can be readily meshed after a short
interval of time. In changing down on the level the driver
speeds up the pinion of the first gear by allowing the clutch to
partially engage momentarily. If the driver is skilled in han-
dling the clutch and gears, he will be able to shift the gears
when the two to be engaged are running at about' the same
pitch line velocity.

FIG. 15. — CLUTCH BRAKE.

Thus in changing down the gears automatically approach the
condition of equal pitch line velocity, or the condition of easy
mesh. Not so in changing up. The driven gear of the pair to be
meshed is now running too slowly and the driving gear too fast.
The latter can only be reduced to the proper speed by applying a
brake to the clutch. Many of the larger cars are now equipped
with such clutch brakes, which act automatically when the driver
completely pulls out the clutch. One design of such a brake is
shown in Fig. 15. The clutch housing is formed with a flange B,
against which bears a fibre block A, carried on an arm on the
clutch pedal shaft, when the clutch pedal is fully depressed.
Another type of clutch brake is illustrated in Fig. 16. This is a

FRICTION CLUTCHES.

clutch of the plate type, and the power is transmitted from the
clutch shaft through a pinion and an internal gear, which latter is
formed integral with a shaft coupling made in halves. This
coupling is provided with an annular friction ring B, which when
the clutch is fully withdrawn presses against a corresponding disc
A, secured to the clutch shifting ring, which latter, of course, does
not rotate.

There is quite a variety of designs of clutch brakes, the under-
lying principle of all of them being that a part rotating with the
clutch is brought into contact with a non-rotary part when the
clutch pedal is fully depressed, and the friction engendered
between the two parts causes the speed of the clutch to be
reduced.

FIG. 16. — Disc CLUTCH BRAKE.

Multiple Disc Clutches— Disc and plate clutches are based
on the same principle, but constitute in a sense opposite extremes
in design. A disc clutch consists of two sets of annular .discs,
one set of driving discs and one set of driven discs. These are
placed together in alternate order, each driving disc being located
between two driven discs. As generally used on automobiles, the
driving discs are provided with key slots on their outer circum-
ference into which fit keys on the inside of a drum shaped hous-
ing secured to the flywheel, and the driven discs are provided
with lugs or key slots on their inner circumference, which place
them in driving connection with a drum secured upon the driven
shaft. Generally there is one more driving disc than there are

FRICTION CLUTCHES.

driven discs, so that the two end discs are of the same kind. The
drum carrying the driven discs has a radial flange at one end
which forms a stop for the discs in respect to axial motion, and
against the disc at the other end presses a compressing spider or
presser, against which the clutch spring exerts its pressure.

Types of Disc Clutches — Multiple disc clutches operating in
oil are of three different types of design, the differences depend-
ing upon the manner in which the pressure of the clutch spring is
transmitted to the flange or back stop of the discs on the clutch
drum. Some of these clutches employ three clutch springs, the

FIG. 17.— MULTIPLE SPRING TYPE OF Disc CLUTCH.

same as some cone clutches, and a design of this type is shown
in the sketch Fig. 17. An outer drum A is secured to the flywheel
and is provided with a number of equally spaced keys on its
inner circumference. With these keys engage the driving discs,
which are shown sectioned. Between adjacent driving discs are
located the driven discs, shown in black. The latter are carried
on the inner drum B, which is provided with keyways for the
lugs formed on the inner circumference of the driven discs.
From the web of the clutch drum B extend three lateral spring
bolts which carry the clutch springs C pressing against the disc
compressing spider D. Drum B is keyed to clutch shaft E, which
is connected with the driving shaft of the change gear, and the

FRICTION CLUTCHES.

disc compressing spider D is provided with a hub surround-
ing shaft E and a groove for the clutch releasing collar, or merely
a flange.

A multiple disc clutch with a single clutch spring surrounding
the clutch shaft is illustrated in Fig. 18. The arrangement of
the outer drum, driving and driven discs and inner drum is the
same as in Fig. 17. In this case one end of the clutch spring
bears against an inward flange on the hub of the disc compres-
sing spider D, and the other against a collar on the clutch shaft
E. The latter has the inner drum B securely keyed to it and
held against endwise motion by a nut. Hence, the pressure of

FIG. 18. — SPRING PRESSURE TRANSMITTED THROUGH SHAFT.

the clutch spring is transmitted to the forward end plate or stop
P of the discs through the clutch shaft E and the clutch drum B.

In Fig. 19 is shown a design of multiple disc clutch in which
the spring pressure is transmitted to the stop P of the discs
through the clutch housing A. The most forward disc bears
against a stop ring P secured to the flywheel and against the rear-
most disc presses the compression plate D in the usual way. This
disc or spider D is acted upon by the coil spring C which rests
against the flange of the casing A. Figs. 17, 18 and 19 are
sketches only, not showing all of the necessary details of these
clutches.

The spring forces the separate ftiscs together and causes the

FRICTION CLUTCHES.

driven discs to rotate in unison with the driving discs, provided
the resistance to the motion of the driven discs is not greater than
the adherence between the driving and driven discs. It will read-
ily be seen that the pressure betwen any two discs is equal to
the pressure of the spring, and the adherence or resistance to
slipping at any contact surface is equal to the product of the
spring pressure by the coefficient of friction. But if there is slip-
page on one contact surface there must be slippage on all of them,
and since the pressure on any contact surface is the same as on
any other, the total resistance to slippage is equal to the prod-
uct of the resistance to slippage at one surface by the num-
ber of contact surfaces, which latter is equal to one less than

FIG. 19. — SPRING PRESSURE TRANSMITTED THROUGH CASE.

the number of discs. In a multiple disc clutch the frictional sur-
face can be made much greater than in a cone clutch, and the
frictional force per unit surface can be made smaller.

Calculation of Disc Clutches — In Fig. 20 is shown one
disc of a multiple disc or plate clutch. In this figure dr is the
width of an extremely narrow annular ring of radius r. Sup-
pose that the unit pressure on the surface of this disc is p pounds
per square inch. The area of the annular ring of width dr is

A = 2 if r dr
and the normal pressure on it is

FRICTION CLUTCHES.

N = 2 T r dr p.
This causes a frictional force

2 TT r dr p f,
where / is the coefficient of friction, and a torque

r TT r2 dr p f

12 6

Now, in order to find the torque which the friction over the entire
surface of the disc will produce we have to integrate the above
expression between the limits r0 (outside radius) and n (inside
radius)

Sdrpf

FIG. 20.

•*

= — p f (n3 — n*) pounds-feet,
18

(9)

n 6

Equation (9) is useful in the case of clutches whose discs have
a very small inside radius. In the original type of this clutch the
discs were often mounted directly upon the driven shaft, and the
inside radius of the clutch disc was less than one-quarter the
outside radius. However, in modern automobile clutches the
inside radius is generally more than three-fourths the outside
radius, and the so-called discs are really in the form of narrow
annular rings. There are two main reasons for making the ele-

FRICTION CLUTCHES. 37

ments of the clutch ring-shaped rather than disc-shaped. The
first is that the wear of the disc increases with the distance from
the centre of rotation, owing to the fact that the speed of slippage
increases with the distance from the axis. Hence, if there is a
great proportional difference between the outside and inside radii,
the rates of wear near the inner and outer edges will be greatly
different. The result will be that as the outer portion of the disc
becomes thinner than the inner portion, the pressure over its sur-
face will become unevenly distributed, the unit pressure being
greater near the inner edge than near the outer edge, and conse-
quently the clutch will transmit less power than originally with
the same spring pressure.

The other reason is that the resistance to lateral motion of
the discs depends directly upon the pressure between the driven
discs and their keys or keyway walls, which is less the greater
the inner radius of the discs. When the clutch is disengaged the
discs are not positively pulled apart, but are supposed to be either
jarred apart by the vibration or to be forced apart by auxiliary
springs, and especially in the former case is it desirable that the
resistance to their lateral motion be as little as possible, as there
is then less danger of dragging.

In the case of clutch discs or rings whose inner radius is more
than two-thirds of the outer radius it is permissible to consider
the engaging pressure (and hence the frictional force) concen-
trated at a distance from the axis of rotation equal to the arith-
metical mean between the outer and inner radii (rm ) . The fric-
tional force at any contact surface then is P f, the aggregate fric-
tion force (n — i) P f, and the moment of the frictional force or
torque.

In any given problem of design the torque to be transmitted
is a fixed quantity, but the limiting torque of the clutch is the
product of four variables, viz., the mean radius of the discs, the
number of contact surfaces, the spring pressure and the friction
coefficient. Since these factors are independently variable, it is
not surprising that practice in disc clutch design is not in the
least uniform. The tendency is rather toward small mean radii
and a very considerable number of discs, since the inertia
increases as the square of the radius and directly as the number
of discs, whereas the capacity of the clutch increases directly with
both the radius and the number of discs. The coefficient of fric-

38 FRICTION CLUTCHES.

tion, of course, can be changed only by changing the material of
the discs or the lubricant.

Material of Discs — In the type of disc clutch which has
been used the longest in automobile practice, both sets of discs
are metallic and run in oil. The discs are generally made from
saw steel, about 3s inch thick, stamped rings of any desired
diameter, with driving lugs or key slots, as desired, being fur-
nished by several saw steel manufacturers. Some manufacturers
believe that steel on bronze gives better wear and make one set
of the discs of the latter material. Saw steel is a. very -suitable
material, being hardened and more uniform in thickness than
ordinary sheet steel. Sheet copper is also used together with
sheet steel. Whatever material is used, the greatest care must
be exercised to get the thickness as nearly uniform as possible
and to give the surfaces a smooth finish.

Laws of Friction — The coefficient of friction between metals
with lubrication varies widely according to conditions. Some of
the laws of friction which have a bearing on the value of the
coefficient of friction in disc clutches may be stated as follows:
The coefficient of friction between two metallic surfaces separated
by a film of lubricant is much greater when the surfaces are at
rest relative to each other than when there is sliding motion
between them. The friction does not depend so much upon the
material of the discs as upon the lubricant. When the discs are
stationary the coefficient of friction increases with the specific
pressure. On the contrary, when there is sliding motion between
the surfaces the coefficient of friction decreases as the specific
pressure increases (up to a certain limit which, however, is far
beyond the pressure used in disc clutches). The coefficient of
friction also varies with the speed; it seems to be a minimum at
loo to 150 feet per minute, increasing as the speed is increased or
diminished, and approaching the static friction coefficient at very
low speeds.

From the above it will be seen that it is difficult to assign a
definite value to the coefficient of friction f for use in the calcu-
lation of friction clutches. However, the author believes it to be
on the safe side to use a coefficient ^ = 0.04 for steel on steel,
phosphor bronze or copper with lubrication.

Disc Clutch Data— Denoting the mean radius of the discs
by rm and the number of f rictional surfaces by na , the equation
for the limiting torque of a disc clutch may be written

FRICTION CLUTCHES. 39

Now, even if the material of the discs is settled, so that / is a
fixed quantity, there remain three independent variables, and
the desired torque, therefore, can be obtained in many different
ways. In this connection it is to be remembered that if we
increase the mean radius rm we increase the inertia of the
clutch, even if we correspondingly decrease the number of discs
so as to retain the same limiting torque. On the other hand, if
we increase either the number of discs or the spring pressure we
increase the work which must be done by the operator in disen-
gaging the clutch, because the spring must be compressed an
amount proportional to the number of discs, in order that there
may be sufficient clearance between adjacent discs, and the work
done in compressing the spring is measured by the product of the
clutch spring pressure by the distance of the compres-
sion of the spring during the process of declutching. The
foot has only a small range of comfortable motion, and the
pressure which can be exerted by it is also limited. It is evident
that the product Pna is a measure of the work to be done in dis-
engaging a clutch, and it has been found that this product should
not exceed 12,000 if clutch operation is not to be irksome. The
friction force per unit of contact surface varies from 0.6 pound
per square inch to 2 pounds, the average value being i pound.
In clutches of this type (metal-to-metal-in-oil) the average ratio
of the inside to the outside radius is five-sixths.

If we made Pn, = 12,000 for all clutches, then the small clutch
would be as hard to operate as a large one, which is not exactly
desirable. Besides, the mean radius rm would increase in direct
proportion to the torque to be transmitted; it should increase
with the torque, but not in direct proportion. It may well increase
as the square root of the torque, and the following equation gives
a good value:

3-4

We may therefore recapitulate the rules for multiple disc
clutch design as follows :
n

- =s in average practice.
fo

Friction force = I pound per square inch.
Coefficient of friction / = o.O4.
The area of one friction surface is

TT (r02 — n2) square inches.
and the frictional force between adjacent discs, expressed in

40 FRICTION CLUTCHES.

pounds, is the same. The total frictional force at the mean
radius of the discs is

TX i2?

hence the number of friction surfaces required is
12 T
rm 12 T

ir(r02 — n2) — TT rm (r02 —
and the number of discs required

The spring force required is

P= -v up ^ -i (I2)

Both of the above equations can be materially simplified if the
ratio of the inner to the outer radius is fixed.

For n= P =

n _ 21.2 T

^ ~™

n — A
,o-f

•£=»

If we assume an inner radius equal to five-sixths the outer
radius and substitute in the equations the value of the torque
of a -four cylinder, 4x5 inch motor we find that the mean radius
of the discs should be 3.4 inches, the outer radius 3.71 inches —
say 3.75 inches — and the inner radius 3.12 inches — say 3^ inches.
The number of discs figures out to 35 and the spring pressure to
337 pounds. An uneven number of discs is generally employed.

When the spring exerts its pressure through the clutch shaft
or through spring bolts secured into the web or spokes of the
inner drum, it is well to have one more driven disc, whereas when
the spring exerts its pressure through the clutch housing it is best
to have one more driving disc. In either of these cases if the

FRICTION CLUTCHES.

j^ 4" 4±" 5" ~3p

Outside Radius o/ Discs
Jf umber of Discs

41
/ooo'

900

800-%

600 ^

500 ^

400

300

' \

/ ^

70,

V «-

X
\

r0 =

*s^

\ /

' \

\
j

X \

s X

Ss.

^ \

"x^x*

^\,

\
\

7"orque in J^ou nets- feet

CHART II.— GIVING NUMBER OF Discs AND SPRING PRESSURE RE-
QUIRED IN MULTIPLE-DlSC-IN-OlL CLUTCHES.

FRICTION CLUTCHES.

clutch is slipping there will be no relative rotary motion between
the two parts against which the clutch spring bears, hence no ball
thrust bearing will be required to take up the thrust of the spring.

Number of discs and spring pressures required in metal-to-
metal multiple disc clutches can be readily found from Chart II,
after the torque of the motor has been obtained from Chart I.
Chart II is based on a unit frictional force of i pound per square
inch and a coefficient of friction of 0.04. If a very light clutch
is desired the number of discs found from the chart can be re-
duced, and the spring pressure found increased in proportion.

Methods of Releasing Discs— In order to insure positive
separation of the discs when the spring pressure is removed, and
thus prevent dragging of the clutch, it is necessary to provide

FIG. 21. — METHODS OF SEPARATING Discs.

alternate discs with tongues sprung to one side, as shown in Fig.
21 at A, or some similar means. Two such tongues on each
driving disc, one opposite the other, are sufficient. An alternate
method of insuring positive separation is illustrated in the same
figure at B, and consists in providing the driving discs with
radial lugs on the outside circumference into which are riveted
buttons whose heads are slightly thicker than the driven discs, so
that the lugs are slightly sprung when the discs are forced to-
gether by the clutch spring. The driving discs may be provided
with four lugs, at quarters, and rivets inserted into two of these
lugs, located oppositely. The discs may then be assembled in
such a manner that the riveted lugs of adjacent driving discs are
at quarters. Where separating springs of this kind are used,
the clutch spring must be made sufficiently strong to overcome

FRICTION CLUTCHES.

the force of these springs and still give enough frictional force
between the discs.

Constructional Details—Multiple disc clutches, the same as
other types, are generally combined with the flywheel, but occa-
sionally they are enclosed in a special compartment of the change
gear case, which can be done without difficulty, since these
clutches can be made of a relatively small diameter. When thus
enclosed in the gear box or when used in a unit power plant,
there is no need to specially enclose the clutch. But in other
cases an oil-tight housing must be provided. This housing is
sometimes made of one-eighth inch pressed steel in a single
piece, with a radial flange at its open end for bolting to the
flywheel web and a hub portion either formed integral or riveted

FIG. 22. — METHODS OF DRIVING Discs.

to it which takes the adjusting bushing for the spring if the
spring pressure is transmitted through the housing, and forms
an oil-tight joint with the hub of the disc compressing spider.
This housing may also be made of two castings — a cylindrical
shell and an end plate. Some designers even provide a stuffing
box in the hub of the clutch housing to insure oil tightness.

If the clutch has no special housing it may be driven from the
flywheel by radially extending driving pins secured into the web
of the latter (A, Fig. 22). If a housing is used the driving is
done either through keys riveted to the cylindrical shell (B, Fig.
22), or through bolts which hold both the shell and the end plate
to the flywheel (C, Fig. 22). The key slots on the outside of the

FRICTION CLUTCHES.

driving discs are cut either in the full ring, or the rings are
formed with driving lugs which have key slots or driving pin
holes cut in them. The latter form of construction leads to a
saving in weight, but necessitates a somewhat more expensive
die for stamping out the discs. In any case, there must be a
liberal clearance between the inner surface of the driving keys
and the outer edge of the driven discs and between the inner
edge of the driving discs and the surface of the inner drum so
there will be no dragging owing to contact at these surfaces after
slight wear.

Practice as to the number of driving pins or keys and driving
lugs on the driven discs varies greatly. Some designers pro-
vide as many as ten or twelve
large size keys, which seems
to be more than necessary.
The number and size of
keys do nol affect the
freedom of lateral motion
of the discs, but, of course
affect the wear of keys and
key slots, but clutches with
only three one-half inch
driving pins with an aggre-
gate maximum pressure of
three hundred pounds on
them are known to give
good results.

It is generally considered
that one-hundredth of an
inch is the minimum clear-
ance between discs which
will insure freedom from
dragging, and in the de-
sign of the housing and
the inner drum allowance
must be made for end

motion of at least — inch. In practice the allowance made

TOO

varies from i/ioo to 1/64 inch per friction surface. However,
one well known manufacturer of multiple disc clutches allow?
only from 1/125 to 1/175 inch.

The inner drum or the shaft to which it is secured is usually
supported upon or in a radial ball bearing. The reason for the

FIG. 23. — INNER DRUM.

FRICTION CLUTCHES.

use of a ball bearing at this point is that the bearing, if plain,
would be hard to lubricate effectively except through the engine
tailshaft, and, besides, the friction of this bearing tends to pro-
duce dragging, and the tendency to drag is already the weak
point of the multiple disc clutch. Usually the radial bearing is
carried upon a short tailshaft, and its outer race is forced into a
counterbore in the drum, but in some constructions the bearing
is carried upon the end of the clutch shaft and its outer race
rests in the bore of the flywheel web. The drum (Fig. 23) is
preferably made of a steel or malleable iron casting and milled
with from four to twelve key slots in which engage the key lugs
formed on the driven discs. The end plate which forms the stop
for the discs is made separate from the drum and is secured to
its rim by machine screws, or else passed over the drum against
a small flange turned thereon.

The rim of the drum should be made sufficiently longer than
the combined thickness of the discs to allow the latter to separate
completely without passing beyond the rear edge of the rim.

FIG. 24. — SKELETON FORM INNER DRUM AND PRESSER.

FRICTION CLUTCHES.

Owing to the fact that the rirn of the compressing spider must
move Over the rim of the inner drum for a considerable distance,
while at the same time the web ot this spider must be quite
close to the web of the inner drum, so the clutch spring will not
extend too far to the rear of the clutch proper, this compression
spider usually has a rather awkward form and is quite heavy.
This difficulty can be overcome by making the inner drum in
skeleton form, as shown in Fig. 24, cutting away its rim between
those portions where the keyways are, and making the compres-
sion spider spoked, the spokes entering between the lateral projec-
tions of the inner drum rim. Besides reducing the weight of the
driven part of the clutch, this construction allows of a more
compact housing.

Hele-S-haw Clutch — A special type of multiple disc clutch
which is extensively used both in this country and abroad is the
Hele-Shaw, which consists of alternate discs of steel and phos-
phor bronze with V-groove corrugations whose walls form an
angle of 35 degrees. Only the walls of the V-grooves come in
frictional contact, and the remaining parts of the discs merely
serve to help radiate the heat engendered during slippage. Oil
holes are drilled through the inner walls of the grooves near
the peak, so the oil can enter and escape freely. It is obvious
that in this clutch there is a sort of wedge action, the same as

FIG. 25.— HELE-SHAW CLUTCH.

FRICTION CLUTCHES.

FIG. 26.— CLUTCH SPRINGS INSIDE SHAFT.

in a cone clutch, and much less spring pressure is required to
produce a certain amount of frictional force than with a flat disc
clutch of the same number of discs and the same mean diameter.
On the other hand, the discs have to be moved laterally consid-
erably farther to obtain the proper clearance between them, and
the number of discs that can be used is therefore more limited.
The Hele-Shaw clutch shown in Fig. 25 is provided with a clutch
brake, as are most large size disc and plate clutches.

Springs Inside of Shaft — Generally the clutch spring sur-
rounds the clutch shaft, as shown in Figs. 17, 18 and 19, but some
designers prefer to place it inside the clutch shaft or the engine
tailshaft. Two such designs are shown in Fig. 26. In the first
of these (Panhard) the spring acts through a plug and a key
which extends through a long diametral slot in the shaft, against
the clutch compressing spider. In the second (Hudson "33")
the clutch spring is located inside the rear bearing of the crank-
shaft and presses through a steel washer, a collar on the clutch
shaft, a ball thrust bearing and a screw collar against the hub of
the inside clutch drum. It should be explained that in this
clutch the usual order of things is reversed, the inner drum
being moved in an axial direction in order to disengage the
clutch, thus serving as "presser."

48 FRICTION CLUTCHES.

Lubrication of Discs — The surfaces of the discs should be
covered with lubricant when there is slippage, but it is also de-
sirable that all or at least most of the lubricant be squeezed out
from between them when the full pressure of the spring is ap-
plied, since the clutch will hold the better the less lubricant there
is on the discs. In order to insure these conditions, some manu-
facturers provide the discs with radial slots extending over half
their width, as shown in
Fig. 27, through which
the oil may escape when
the discs are pressed to-
gether.

Whereas the weak point

of the ordinary cone FIG. 27. — CLUTCH Discs

clutch is its great inertia, WITH OIL SLOTS.

that of the multiple disc-

in-oil clutch is its tendency to drag if the oil in the clutch
housing is not suitable for the purpose, or if too much is intro-
duced. Most makers recommend a mixture of machine oil or
gas engine oil with kerosene. It is obvious that the thinner the
lubricant the better the clutch will hold, while the more viscous
the lubricant the more gradually it will pick up its load.

Dry Plate Clutches— In order to overcome the dragging evil
the dry plate clutch was introduced. In this one set of plates

FIG. 28. — CORK INSERT CLUTCH.

FRICTION CLUTCHES. 49

is either faced with asbestos fabric on both sides or else pro-
vided with cork inserts. Both of these materials when in contact
with steel have a much greater friction coefficient than steel or
bronze on steel. Cork on steel is claimed to have a friction co-
efficient of about 0.34 when not lubricated. The cork, of course,
is quite compressible. It is customary to make the plugs of such
size that when free they project about & inch above the sur-
face of the metal plate. Hence when the discs are forced together
the contact is1 at first between metal and cork only, and owing
to the compressibility of the cork the engagement is very smooth.
However, when the full pressure of the spring is applied to the
friction surfaces the corks are compressed flush with the plate
surface, and one of the surfaces is then part metal and part cork.
This, of course, will reduce the effective friction coefficient some-
what, depending upon the relative area of the corks and of the
metal and upon the compression of the cork at the moment metal
to metal contact is established. As a rule, the cork covers from
25 to 50 per cent, of the total area of the discs, though there are
extreme cases in which either more or less than the above range
is covered.

The majority of disc clutches with cork inserts are of the three
plate type, the middle plate containing the corks, though occa-
sionally cork inserts are also used in multiple disc clutches. More-
over, it is not necessary to run the cork insert clutches dry.
Lubrication will reduce wear of the corks, but, of course, it will
also reduce the friction coefficient. A typical cork insert clutch
is illustrated in Fig. 28.

Asbestos fabric is also used for facing clutch discs. This is a
fabric composed very largely of asbestos fibre and containing
some brass wire and cotton, which latter give the necessary
tenacity, while the asbestos is used on account of its good fric-
tional qualities and its resistance to heat. The asbestos fabric is
secured to the metal discs by means of rivets passing through the
metal and asbestos on opposite sides of it. The frictional force
in asbestos-faced disc clutches varies from less than one pound
to about four pounds per square inch. With lower friction per
unit surface the life of the clutch will, of course, be greater.
The friction coefficient of asbestos fabric on steel seems to be
approximately 0.3, and for ordinary purposes a normal pres-
sure of 10 pounds per square inch will give satisfactory results.
This gives a frictional force of three pounds per square inch, and

50 FRICTION CLUTCHES.

the formulas for number of discs and spring pressure required
become

and

/>== I0 TT (r02 — n2) ......................................... (14)

From the data at hand it seems that these same equations are
applicable to cork insert clutches in which the spring acts
on the discs directly and in which the corks cover1 from 25 to 50
per cent, of the total surface.

It may here be pointed out that a clutch for a vehicle in which
the gear has to be changed frequently and the clutch therefore
slipped a great deal should logically be designed with a somewhat
lower unit friction force than a clutch for a high powered touring
car, for instance, the speed of which can be largely controlled by
the throttle. A lower unit frictional force will result in less
wear and less heating.

The asbestos is generally secured to the driving discs, so
the driven member may have the least possible inertia, but in
one design the asbestos rings are free between the two sets of
metal discs. The latter are made about % inch thick to get
sufficient bearing surface on the keys ; if lighter stock is to be
used the edges may be flanged to get additional driving area.
Fig. 29 shows the Packard dry disc clutch which comprises
six driving and five driven discs.

Three Plate Clutches — Another method of obviating the
dragging tendency of disc clutches is to use only three discs or
plates, without lubricant. These discs are made of cast iron
and bronze, or of cast iron and steel. Since there are only
two friction surfaces, for moderately high powers it is necessary
to use rather large discs and to multiply the pressure of the clutch
spring by levers or toggle mechanisms. Fig. 30 shows a typical
design of this kind in which the spring pressure is multiplied by a
toggle mechanism. One of the three discs is a driving disc, and
the other two are driven discs. The driving disc is driven from
the flywheel through keys riveted to the inside of the flywheel
rim. One of the driven discs, the one nearest the flywheel, is
secured to the clutch shaft and is provided with four sets of
laterally extending lugs on which bell cranks are fulcrumed. One
arm of these bell cranks connects through a link with a sliding
sleeve on the clutch shaft on which the clutch spring acts. The
other arm of the bell crank is provided with a set screw, the
point of which presses against the rearmost driven disc. This
latter disc is provided with driving lugs which enter between the

FRICTION CLUTCHES

FRICTION CLUTCHES.

lugs on the other disc serving as a fulcrum for the bell crank.
The set screws permit of making adjustment for wear of the
discs. Separation of the discs is effected by means of small coiled
springs inserted into drill holes in one of the driven discs and
pressing against the other driven disc.

The multiplying factor of the toggle mechanism attains the
infinite as the toggles assume a radial position. In practice, of

FIG. 30.— THREE PLATE TOGGLE TYPE CLUTCH.

course, the set screws must be so adjusted that this cannot hap-
pen, as the toggle links would pass by the radial position and the
clutch would disengage again. If the links make a small angle 0
with a radial line then the multiplying factor is equal to co-
tangent 0. This may be readily seen by reference to Fig. 31, in

FRICTION CLUTCHES.

which A B represents a link of the toggle. Let P be the pres-
sure of the spring and N the radial pressure exerted on the bell
crank arm. Now let point B be moved the slightest distance
under the force of the spring P, so that the angle B A C (0)
decreases to 0 — d 0. Now we have

C B = A B sin 0
A C = A C cos 0
When 0 decreases to 0 — d <t>,
A B sin 0 decreases by A B
cos 0 d 0 and A B cos 0 in-
creases by A B sin 0 d <f>. But
the product of the force into
the distance through which it
works represents the work
done, and this must be the
same at both points A and B.
Hence,

PX A £ cos <j> d <j> =

N X ABsin<t>d$

and

*L
p

cos 0

FIG. 31.

sin 0 "

A plate clutch in which the
spring pressure is multiplied
by double armed levers is illustrated in Fig. 32. In this clutch there
are two driving discs, one being constituted by the web of the
flywheel, and one driven disc. The free driving disc is driven
from the flywheel through a stud bolt passing through the fly-
wheel web and an annular flange bolted to the flywheel rim. The
stud bolt is provided with a collar against which the short arm
of the double armed lever takes purchase. This lever is fulcrumed
on lugs cast integral with the free driving plate, and its long
arm extends radially inward and is pressed against by the sliding
sleeve which contains the clutch spring and is formed with the
groove or flange for the shipping collar.

Band Clutches— Band clutches are of two kinds, viz., con-
tracting and expanding. A contracting band clutch consists of
a drum and a metal band surrounding it, which may be lined
with friction material. One end of the band is fixed to a spider
or housing carried upon one of the connected shafts, and the
other end can be displaced angularly with relation to the first
so as to contract the band into frictional contact with the drum.
Contracting band clutches are of three different types. The

FRICTION CLUTCHES.

first of these, shown in Fig. 33, comprises two bands of which
each extends substantially half way around the circumference
of the clutch drum. The bands are generally made from thin
strip steel, and lined with leather. One end of each band is
hinged to one arm of a two armed spider secured to the driven
shaft or clutch shaft, and the other end to the short arm of
a double armed lever fulcrumed on the arm of the spider, the

FIG. 32. — PLATE CLUTCH, LEVER TYPE.

inwardly extending arm of the lever being adapted to be moved
outward from the clutch axis by a sliding cone or wedge under
the pressure of the clutch spring. When the levers are thus
moved around their fulcra the bands are drawn tight on the
clutch drum, and driving connection is established.

FRICTION CLUTCHES.

Fig. 34 shows the Mercedes coil clutch, which may also be
regarded as a form of band clutch. The band in this case con-
sists of a coil of steel, one end of which is anchored to the hous-
ing of the clutch and the other end of which is attached to one
arm of a double armed lever whose fulcrum support is in the
end wall of the housing. The long arm of this lever is acted
upon by a sliding cone against which the clutch spring presses.
When the sliding cone is forced under the lever arm the steel
coil is contracted upon the clutch drum and grips the latter. The

FIG. 34. — 'MERCEDES COIL CLUTCH.

housing is formed integral with the flywheel and the drum is se-
cured to the clutch shaft. This clutch is entirely enclosed and
runs in oil.

Theory of Band Clutch — In Fig. 35 is shown a sketch
of a band clutch in which d9 represents a small arc of con-
tact of the band on the drum and 6 the angle or arc of contact
between this section dO and the point of contact between band
and drum nearest to the free end of the band. At the free end
a pull Pi is exerted on the band. Owing to the friction between

FRICTION CLUTCHES.

the band and drum the pull on the band varies from point to point
of its length. Let the pull at one side of the differential section
d 0 be represented by P and that on the other side by P + d P,
as indicated in the sketch. Also let the normal pressure between
the band and drum on the section d 0 be represented by N and the
f rictional force resulting therefrom by / N. When the. system is
in equilibrium the forces in any direction are equal to zero.
Hence, taking the forces in the horizontal plane,
dd d8

(P + dP)cos- -fN — Pcos— = O

2 2

But the cosine of an infinitely small angle is equal to unity,
hence
dP = fN (15)

FIG. 35. — DIAGRAM OF BAND CLUTCH.
Now, taking the forces in the vertical plane,

dO d6

N — (P + d P) sin -- P sin — = O

and since the sine of an infinitely small angle is equal to the
arc, we may write $0 je

N — (P + d P) -- P — = O
2 2

The term d P — , a differential expression of the second

order, may be neglected, and we may write
N = P d 0

58 FRICTION CLUTCHES.

= 7* ; (16)

Dividing equation (15) by equation (16) we get
dP

= f d e

dX
Now the integral of a differential expression of the form

x
is log x (the natural logarithm, whose base is 2.71828. Hence

log P = / 0 + C
or

log P = / 0 4- log c (17)

Remembering that in all logarithmic systems the logarithm of the
base is 1, we may write

log e* 0 = fO X 1 =fO
Inserting this value of / 6 in equation (17) we have

log P = log ef 0 + log c
and taking antilogs —
P = c e< e (18)

To find the value of the constant c we make 0 equal to zero,
in which case P equals the initial pull Pi applied to the free
end of the band.

Pi = c e°.
But any term with the exponent zero is equal to unity, hence

C = Ft

and inserting this value in equation (18) we have

P = Pi ef 0 (19)

This latter equation gives the pull on the band at any angle 6
from the point of contact between band and drum nearest the
point of application of the initial pull. The total frictional force
F between the band and drum is equal to the difference be-
tween the initial pull and the pull at the point of contact between
band and drum farthest from the point of application of the
initial pull —

F = P, ef e — P, = P, (ef 0 — 1)
and

P1 = — — (20)

efe—i

In using this equation the arc 0 must be expressed in radians.
Values of the expression ef & — 1 for various values of / 9 may be
found from Fig. 36.

FRICTION CLUTCHES.

«/?/-

£.0 20

l.Q 16
1.6 16
14 H
1.2 12.
1.0 1O
0.6 6
O.G 6
0.4 4
0.2 2

c
tfl

./*

"•"'

***

r LZ 1.4 1C 1.6 Z 22 2* Z.6 2.<3 3
J 0£ O7 0.8 09 1.0 U

Value of /e

FIG. 36. — CURVE GIVING RATIO BETWEEN FRICTIONAL FORCE AND

PULL ON BAND.

Sample Calculation— Now let it be required to design a band
clutch for a four cylinder 4x5 inch motor, which, as we have
seen, develops a torque of 133 pounds-feet. Suppose we choose
a drum 12 inches in diameter, then the frictional force required
at the surface of the drum is

133 X I2 = 266 founds.
6

Let the band be made of steel and lined with leather, so we
can figure on a coefficient of friction f = o.2. In the case of a
clutch comprising a band extending all around the drum the arc
of contact will be about 5.5 radians, and in the case of a clutch
with two bands, each extending half way around the drum, the
arc of contact of each will be about 2.5 radians. These figures
are approximate and the correct arcs of contact would have to
be determined from the drawings.

Let us take the case ot a single band brake. Inserting values
in equation (20) we have

60 FRICTION CLUTCHES.

This is the pull which must be exerted on the free end of the
band. The pull of the fixed end on its anchorage is equal to the
pull on the free end plus the friction,

133 + 266 = 399 pounds,

and the band and its anchorage must be designed sufficiently
strong to withstand this stress.

If the band is of uniform width the normal pressure at its
contact surface varies from end to end, being least near the free
end and most near the fixed end. From equation (16) it will be
seen that N varies directly as the pull P on the band. We know
that the f rictional force F = 266 pounds, and since the coefficient
of friction is 0.2, the aggregate normal pressure is

OAA

Q 2 = 1,330 pounds.

Also, if we allow an average unit pressure of 18 pounds per
square inch, then the frictional area required is

1,330
— jg— = 74 square inches,

and since the drum has a diameter of 12 inches, and consequently
a circumference of 37.68 inches, it would have a width of

3; 53 = 2 inches (appr.)

The normal pressure, as already stated, will not be uniform but
greater near the fixed end than near the free end in the propor-
tion of 399 : 133 or 3 to 1. Hence the lining will wear faster
near the fixed end.

Effect of Centrifugal Force — At high "speeds, like those em-
ployed in automobile clutches, the centrifugal force on the band
h:,s quite an effect on the friction between the band and the drum,
and this is the cause of the chief difference between a contracting
band clutch and an expanding band clutch. The above analysis
with respect to the frictional force between band and drum
at low speeds applies equally to both types of band clutches, but
the centrifugal force tends to expand the band, and hence to
decrease the frictional force of a contracting clutch, and to in-
crease the frictional force of an expanding clutch.

Let w be the weight of a section of the band 1 inch in length.
Then the weight of an element d & of the band is w r d Q and the
centrifugal force on this element (see equation 31, Vol. 1) is

1.226 (iv rdB)1r — = 0.102 w if r* d e,

FRICTION CLUTCHES. 61

where w is the speed in revolutions per second and r the radius
in inches. This force, which we will denote by Fc d 0 (Fc being the
centrifugal force on a section of the band equal to one radian),
in a contracting clutch acts in the same direction as force N.
Hence we may write the equation of the forces in the vertical
plane —

Transposing and contracting,

(P — Fc)
and

But since Fc is constant,

d (P — Fc) =dP = f N (equation 15).
Hence

Integrating both sides of the equation,

log (P — Fc) =f 0 + C = f 0+ log a
and taking antilogs —

P— Fc-=ae*d

In order to determine the constant for this case, let 0 = o, then
P = Pi, and

hence

and

j?= P pl = (Pl — Fc) e* 6 -{- Fc — PI

Multiplying out,

Transposing

and dividing by the coefficient of Pi,

Comparing equation (21) with equation (20) we see that the
effect of the centrifugal force on the band of a contracting clutch
is to increase the required pull on the free end of the band by an
amount equal to the centrifugal force on a section of the band
one radian in length. This might have been expected, since the
total centrifugal force on the band is 2irFc, and if the band

62 FRICTION CLUTCHES.

moves radially outward under this force a distance x, then the
free end of the band will be moved a distance 2 •* x. Hence the
motion of the free end is 2 TT times greater than the radial mo-
tion, and the force in the direction of motion of the free end
2 v times smaller than the radial (centrifugal) force.

Equation (21) is applicable to contracting band clutches at all
speeds. A similar analysis may be applied to expanding band
clutches, and the resulting equation for the initial pull required
is the same as (21), except that the sign of the term Fc is
reversed, the centrifugal force in this case adding to the normal
pressure, instead of subtracting from it. Therefore, for expand-
ing clutches —

P> = — Fc (22)

e'0-1

Returning to the examples of a band clutch for a motor devel-
oping a torque -of 133 pounds-feet, let the band weigh 0.1 pound
per inch of length ; then

Fc = 0.102 X 0.1 X 202 X 62 = 147 pounds
the initial pull becomes

p* = 3?IT+ 147 = 28° Pounds,
and the pull at the anchorage of the band is

280 + 266 = 546 pounds.

Expanding Band Clutches — Expanding band clutches of the
type shown in Fig. 37 require comparatively little pressure to
hold them in engagement at high speed, since the centrifugal
force on the band presses it against the inside of the clutch
drum. The advantage of this fact is doubtful, however, since
the greatest torque is produced by the motor — and, conse-
quently, the greatest frictional force required of the clutch —
at low motor speed. If in this type of clutch the spring
were to act against a sliding cone, which through a connecting
linkage acted on the free end of the band, the latter at high
speed would not be released from the drum when the sliding
cone was withdrawn, owing to the fact that the centrifugal
force on the band would then produce the necessary fric-
tional force betwen band and cone to hold the load. Conse-
quently, the operating mechanism must be so arranged that
when the sliding sleeve is moved by pressing on the clutch
pedal the band is positively released from the drum. The
band rs made of band steel, faced with leather, and supported
by a skeleton drum which can be cast of aluminum, or the band
may be made of a ribbed iron casting yieldingly supported

FRICTION CLUTCHES.

by a bracket. The engaging pressure is furnished by a
tension spring, whose one end is anchored to the web of
the band supporting drum. In some designs a second spring
must be provided to keep the sliding cone in contact with the
operating lever, which spring may either surround the clutch
shaft and press directly against the cone, or may be anchored
to some part of the car frame and draw the clutch pedal in
the direction corresponding to clutch engagement.

In another type of band clutch both ends of the band are
free and the middle is anchored to a bracket on the driving
shaft. In this case one-half of the band is drawn tighter on

FIG. 37.— EXPANDING BAND CLUTCH.

the drum by the friction between band and drum, and the
other half is unwound, as it were. Hence the effects of the
friction on the pull or tension in the halves of the band
exactly neutralize each other and can be neglected in cal-
culating the frictional force. Let P be the pull exerted on
each free end of the band, and suppose that under this pres-
sure the ends move together a distance x. Then, if the band
is supposed to be of circular shape, both before and after

FRICTION CLUTCHES.

FRICTION CLUTCHES. 65

the contraction, the radius will be reduced by — • Since the

27T

ratio of circumferential to radial motion is 2 ^ the ratio of
circumferential to radial pressure is — and the total normal

2 IT

pressure is 2-rrP, which when multiplied by the coefficient of
friction gives the total frictional force.

Expanding Block Clutches — This type of clutch, which is
widely used in stationary work, is rarely found in automobile
practice. It consists of a drum and two or more blocks or
segments which by means of toggles or right and left hand
screws can be expanded against the rim of the drum. The
blocks are in driving connection with a spider secured to
the clutch shaft. The calculation of such a clutch is very
simple. From the arrangement of the mechanism the multipli-
cation of the spring pressure at the friction surface can be
readily calculated and the frictional force is then equal to
the product of the normal pressure by the friction coefficient.
These blocks or segments are often faced with fibre or leather.
though they may also have metallic surfaces. The Metallurgique
clutch, a typical expanding segment clutch with right and left
hand screw operating mechanism, is shown in Fig. 38. In the
Mais truck clutch, the clutch surface, instead of being a cyl-
indrical envelope, is corrugated, so as to increase the normal
pressure on the frictional surface on the principle of a wedge.

Clutch Shaft Dimensions — The torsional strength of shafts
is calculated by means of the formula
M = 0.196 d3 S,

where M is the torsional moment in pounds-inches, d the
diameter of the shaft .in inches, and 5" the safe torsional stress
in pounds per square inch. 6" can be figured at 5,000 pounds per
square inch for carbon steel and 7,000 pounds for nickel and
chrome-nickel steel. The torsional moment of a four cylinder
4x5 inch engine would be

12 x 133 = 1,596 pounds-inches.
Hence

0.196 d*x 5,000= 1,596
and

d=\/ - ? - = 1.18 — say i T3s inch,

r 0.196 X 5000
for carbon steel.

Of course, if the shaft is weakened in any way, as by being
squared for a coupling, the diameter should be made propor-
tionally heavier. The stress allowed in the shaft seems to be

FRICTION CLUTCHES.

very low, bat a high factor of safety is necessary, since, owing
to changes in the coefficient of friction of the clutch facing and
adjustment of the spring pressure, the torque transmitting ca-
pacity of the clutch may be greatly increased and much greater
torques than that of which the engine is capable continuously
may be produced by "jamming in" the clutch while the engine
is racing, thus withdrawing some of the energy stored up in
the flywheel. All other parts of the clutch transmitting the
torque of the motor should be calculated on the same basis,
allowing a factor of safety of about 10.

In these calculations, as well as in the calculations of other
transmission members, unless exceptions are specifically men-

FIG. 39. — BLOCK AND TRUNNION TYPE UNIVERSAL AND SLIP JOINT.

tioned, a torque based upon a brake mean effective pressure of
80 pounds per square inch is to be used. That is to say, the
constants of all formulae to be given will be based on this engine
torque, which may be found from Chart I.

Connection Between Clutch and Change Gear — In a cone
clutch the torque of the motor is transmitted by the cone and
the hollow shaft to which it is secured, and since the cone must
move in an axial direction when it is engaged and disengaged,
there must of necessity be a slip joint in the transmission line
between the clutch and the change gear. The same applies to
some other types of clutches, as, for instance, multiple disc
clutches in which the inner drum serves also as the presser.
Moreover, unless the change gear housing and engine crank case
are rigidly secured together, it is very desirable that a double
universal joint be interposed between clutch and change gear, so
there may be no binding of the bearings of either member when
the vehicle frame "weaves" or distorts in consequence of road
shocks, and also so as to obviate the necessity of absolute align-
ment in assembling. A favorite construction of universal and

FRICTION CLUTCHES.

slip joint in connection with cone clutches is the block and trun-
nion type illustrated in Fig. 39. The shaft is forged with a
transverse hub which is drilled to receive a trunnion. Over this
trunnion are slipped two square blocks of steel, adapted to slide
lengthwise in slots formed on the inside of the hollow shaft.
These slots may be cut in a planer or shaper in a short length
of hollow shaft which is flange-bolted to the adjacent trans-
mission part, or the slots may be milled entirely through the wall
of the hollow shaft, for a certain distance from the end, and a
piece of steel tubing forced over the end of the shaft as far as
the slots extend.

In calculating the necessary size of the blocks and trunnions
a unit pressure of 1,200 pounds per square inch can be figured

FIG. 40.— INTERNAL AND SPUR GEAR TYPE OF UNIVERSAL AND
SLIP JOINT.

on between the blocks and the walls of the slots in which they
slide, and a unit pressure of 1,800 to 2,000 pounds per square inch
between the trunnions and the blocks. In order to obtain the
maximum bearing surface with a given outside diameter of hol-
low shaft, the blocks are often beveled off on the outside and
beveled out on the inside. These blocks are hardened and the
hollow shafts case hardened, to reduce wear. To obviate rattling
of the intermediate shaft against the ends of the hollow shaft, a
spring is sometimes placed between one of the hollow shafts and
the intermediate shaft, which takes up the end play. Another
method of accomplishing the same result consists in using a
standard form of universal joint at one end of the short inter-
mediate shaft and a block and trunnion type of joint at the
other. The block and trunnion type of joint must be packed in

68 FRICTION CLUTCHES.

grease, and to this end must be provided with a leather "boot, as
shown in Fig. 39.

Another type of universal and sliding joint employed between
clutch and change gear consists of spur and internal gears. A
design of this kind is used on the Oldsmobile, and is illustrated
in Fig. 40. The intermediate shaft is forged with flanges at
both ends which are cut with spur teeth on their circumference.
These teeth mesh with the teeth of internal gears bolted re-
spectively to the clutch shaft and a coupling fixed to the change
gear driving shaft. Since the two sets of gears do not run
together it is not necessary that their teeth should be of any
particular form, and substantially square teeth probably are the
most advantageous. Leather discs bolted to the sides of the two
gears respectively here take the place of the usual leather boots,
and at the same time limit the endwise play of the intermediate
shaft and thus prevent rattling.

Leather disc universals are also much used between the clutch
and transmission. These are discussed in the chapter on Uni-
versal joints.

End Thrust Due to Pedal Pressure. — Most modern auto-
mobile clutches are so designed that when they are engaged
the spring pressure is self-contained. However, when the clutch
is disengaged the end thrust due to the pressure on the clutch
pedal has to be taken up in some way. The clutch itself is not
supported by any structural part, and this thrust may be trans-
mitted either to the engine crankshaft or to the driving shaft
of the change speed gear, whichever seems the most convenient
and practical in any particular design. Another thing to be con-
sidered is the possibility of dismounting the clutch without re-
moving the engine or gear box — especially those clutches vith
renewable wearing surfaces.

CHAPTER III.

SLIDING CHANGE SPEED GEARS.

Historical — Many different devices have been tried for
changing the gear ratio between the motor and the driving
wheels of an automobile, and the change gear was long thought
to present the most difficult problem in automobile design.
Daimler and Benz, the pioneers of the gasoline automobile, both
used belts and stepped pulleys in their earliest designs. The
Daimler motor was taken up in France by the firm of Panhard
& Levassor, and after a few experiments with belts M. Levassor,
the engineer of the concern, introduced the sliding pinion change
speed gear in combination with the leather faced cone clutch.
The idea of meshing toothed gears by shifting them axially
was at first ridiculed as crude and unmechanical, but in the
end the system, after having undergone a number of important
refinements and modifications, proved more satisfactory on the
whole than all others, and it is now in almost universal use.

Levassor's change gear is illustrated in Fig. 41. It con-
sists of two parallel shafts mounted in bearings in an alumi-
num gear box. The first of these shafts, known as the pri-
mary shaft, is in driving connection with the clutch. This
shaft is squared and carries a set of three toothed gears or
pinions, whose common hub has a square hole broached through
it to make a sliding fit with the square shaft. On the
secondary shaft are carried three other toothed gears, each
of such a diameter as to properly mesh with one of the gears
on the primary shaft. The gears on both shafts are so
spaced that by shifting the primary set corresponding gears
on the two shafts can be brought in to mesh successively with-
out interference from the other gears. Shifting of the sliding
set is accomplished by means of a hand lever located con-
venient to v the operator, and a suitable connecting linkage.
The secondary shaft at its rear end carries a bevel pinion
meshing with a bevel gear on a cross shaft or jackshaft, from

SLIDING CHANGE SPEED GEARS.

which the power is transmitted to the rear wheels by means
of side chains.

One disadvantage of Levassor's gear set was that the
power was transmitted through a pair of toothed gears — with
consequent power loss, noise and wear — even at high car
speeds, when there was absolutely no occasion for it, since
the speed was not changed by the gearing. This objection
was overcome in a change gear brought out some years
later by Louis Renault, which differed from Levassor's in
that the gears of the two shafts were rolled into mesh instead

FIG. 41. — SKETCH OF LEVASSOR'S SLIDING CHANGE SPEED GEAR

of being slid into mesh. The primary shaft of this gear set
was in two parts, the forward or driving part, and the rear-
ward or driven part, the latter being journaled at its forward
end inside the former. The secondary shaft served as a
countershaft through which the motion was transmitted for
low and intermediate speed and for reversing. For high
speed the two parts of the primary shaft were locked together
by means of jaw clutches formed integral with gears on the
two parts of the primary shaft, which could be slid into en-
gagement. This gave the so-called direct drive, the power
being carried directly through the gear set without being
transmitted through the toothed gears. The direct drive fea-
ture was soon also incorporated in the Levassor type of slid-

SLIDING CHANGE SPEED GEARS.

ing gear, as shown in Fig. 42. This gear, which is known as
the three speed and reverse progressive sliding gear with
direct drive on high, was used very extensively for many
years, and is still being used to some extent, especially on
commercial vehicles.

As the speed capabilities of automobiles increased it be-
came customary to fit change gears giving iour forward gear
changes and one reverse, so as to enable the operator to run
the engine near its most advantageous speed under all road
conditions. Now, a four speed gear constructed on either the
original Levassor principle or the direct drive principle comes
out exceedingly long, as may be seen from Fig. 43, which
represents the non-direct type. Not only does this lead to a
bulky and heavy gear box, but the shafts, being relatively

FIG. 42. — SLIDING GEAR WITH DIRECT DRIVE.

long, are likely to be insufficiently rigid and to spring and
bend under the thrust on the gear teeth, the gear thus oper-
ating noisily and inefficiently. The great length with this
construction is mainly due to the fact that the gears on each
of the shafts must be spaced relatively far apart so as to
avoid interference. This difficulty was first overcome by
Wilhelm Maybach, engineer of the Daimler Motor Company,
of Cannstadt, Germany, who with a non-direct drive type of
sliding gear used two sliding sets. This principle was later also
applied to the direct drive type, and proved so popular that
at present it is used on pleasure cars almost exclusively, and
also largely on commercial vehicles, and not only for four
speed gears but for three speed as well.

SLIDING CHANGE SPEED GEARS.

Three speed and reverse gears usually have two sliding sets
and four speed and reverse gears three. The several sliding
sets are operated by means of a single lever, convenient to the
driver, which lever, in addition to its motion for shifting the
gears, has a motion at right angles to the plane of the former
motion, for picking up and dropping the different sliding sets.
This type of change gear is known as the selective type of
sliding gear. It has the advantage over the other, the pro-
gressive type, that the driver may change directly from any
one gear to any other without passing through intermediate
ears, which is not possible with the progressive type of gear.

FIG. 43.— PROGRESSIVE TYPE FOUR SPEED AND REVERSE SLIDING GEAR.

A sketch of a four speed selective sliding gear is shown in
Fig. 44. By comparing this figure with Fig. 43 the saving in
length by the use of the selective principle becomes apparent.
Gear Material— It is absolutely necessary to use high grade
materials for the gears of sliding gear sets. Owing to the
fact that driving and driven gears are often running at greatly
different pitch line velocities when they are meshed, the
teeth "clash" together with considerable force, and their ends
would soon be battered up if they were made of soft metal.
Hardening the gears involves considerable difficulty, because
if they are hardened after they are finished they are very
likely to warp on being quenched, and hence to run noisily,
whereas if they are hardened before being finished they can
be finished only by grinding.

SLIDING CHANGE SPEED GEARS. 73

The gears may be made of either ordinary low carbon steel (so-
called case hardening steel), low carbon nickel or low carbon
chrome vanadium steel, all of which steels are case hardened;
or they may be made of high carbon chrome nickel or high
carbon chrome vanadium steel, gears of these materials having
been used both in the natural state and hardened by quenching.
The last two materials have exceedingly high elastic limits when
properly heat treated, but they are so difficult to forge and
machine that gears made of them are very expensive. These
materials are fairly hard in the natural state, and gears of
them therefore can be used in that state; but such gears wear
faster than case hardened gears, and since they are more ex-
pensive they are now no longer used, except possibly in ex-
ceptional cases. Gears of chrome nickel and chrome vana-
dium steel with a carbon content of 0.45 per cent., hardened

FIG. 44. — SELECTIVE TYPE FOUR SPEED AND REVERSE SLIDING GEAR

through and through, are used on the higher grades of cars.
When gears are carbonized for case hardening the carbon is
allowed to penetrate to a depth of 3*2 inch. Following are the
standard specifications and heat treatments of steels suitable
for sliding gears that have been adopted by the Society of
Automobile Engineers:

Specification No. 1020—0.20 per cent, carbon steel. The fol-
lowing composition is desired :

Carbon 0.15% to 0.25% (0.20% desired)

Manganese 0.30% to 0.60% (0.45% desired)

Phosphorus not over 0.045%

Sulphur not over 0.05%

This steel forges and machines well and is particularly

74 SLIDING CHANGE SPEED GEARS.

suited for case hardening. It has an elastic limit of 35,000
pounds per square inch in the annealed state and as high as
70.000 pounds when cold rolled or cold drawn. For sliding
gears this steel should be treated as follows: After forging,
machining and cutting the teeth, carbonize at a temperature of
between 1,600° and 1,750° Fahr., cool slowly in the carboniz-
ing mixture, reheat to 1,550-1,625 ° Fahr., quench, reheat to
1, 400° -1, 450°, quench and draw in hot oil at a temperature of
from 300° to 450° Fahr.

Specification No. 2320—3^ per cent, nickel steel. The fol-
lowing composition is desired:

Carbon 0.15% to 0.25% (0.20% desired)

Manganese 0.50% to 0.80% (0.65% desired)

Phosphorus not over 0.04%

Sulphur not over 0.045%

Nickel 3.25% to 3.75% (3.50% desired)

The elastic limit of this material in an annealed condition
is 45,000 pounds per square inch, with good reduction and
elongation. When suitably heat treated the elastic limit may
be brought up to 60,000 pounds, and even 70.000 pounds per
square inch, with better reduction of area than in the annealed
state. This material is carbonized and heat treated as fol-
lows: After the gears are cut. carbonize at between 1,600°
and 1,750° Fahr., cool slowly in the carbonizing material, reheat to
1,500°-1,550° Fahr., quench ; reheat to 1,300°-1,400° Fahr., quench ;
reheat to 250-500° Fahr. and cool slowly. The last quenching
operation must be conducted at the lowest temperature at
which the material will harden, which will sometimes be as
low as 1,300° Fahr.

Specification No. 3140. — 0.40 per cent, carbon, chrome nickel
steel. The following composition is desired:

Carbon 0.35% to 0.45% (0.40% desired)

Manganese 0.50% to 0.80% (0.65% desired)

Phosphorus not over 0.04%

Sulphur not over 0.045%

Nickel 1.00% to 1.50% (1.25% desired)

Chromium 0.45% to 0.75% (0.60% desired)

This steel contains a sufficient amount of carbon to harden
without being carbonized. Heat treatment produces an elas-
tic limit as high as 200,000 pounds per square inch, with good
reduction of area and elongation. The steel is difficult to
forge and must be kept at a thoroughly plastic heat while
being forged, and not hammered or worked after dropping
to ordinary forging temperature, as cracking is liable to fol-

SLIDING CHANGE SPEED GEARS. 75

low. Since the temperature range within which forging is per-
missible is small, the steel must be frequently reheated. The
heat treatment is as follows: Heat to 1,500°-1,600° Fahr.,
quench; reheat to 1,450°-1,500° Fahr., quench; reheat to 600°-
1,200° Fahr. and cool slowly. This steel cannot be machined un-
less thoroughly annealed. The desired Brinell hardness for
gears is between 430 and 470, the corresponding Shore hardness
between 75 and 85.

Specification No. 6120. — 0.20 carbon, chrome-vanadium steel.
The following composition is desired:

Carbon 0.15% to 0.25% (0.20% desired)

Manganese 0.50% to 0.80% (0.65% desired)

Phosphorus not over 0.04%

Sulphur not over 0.04%

Chromium 0.70% to 1.10% (0.90% desired)

Vanadium not less than 0.12% (0.18% desired)

The treatment of the above steel is as follows : Carbonize at
a temperature between 1,600° and 1,750° Fahr. ; cool slowly in
the carbonizing mixture; reheat to 1,65.0°-1,750° Fahr., quench;
reheat to 1,475°-1,550° Fahr., quench; reheat to 250°-550°, and
cool slowly. The heating for the second quench should be con-
ducted at the lowest temperature that will harden the carbonized

Specification No. 6145. — 0.45 per cent, carbon chrome-vanadium
steel. The following composition is desired:

Carbon 0.40% to 0.50% (0.45% desired)

Manganese 0.50% to 0.80% (0.65% desired)

Phosphorus not over 0.04%

Sulphur not over 0.04%

Chromium 0.70% to 1.10% (0.90% desired)

Vanadium not less than 0.12% (0.18% desired)

This steel hardens without being carbonized and attains an
elastic limit of as high as 200,000 Ibs. per square inch. The
proper treatment for gears is as follows : Heat to 1,525°-1,600°
Fahr.; hold at this temperature one-half hour to insure thor-
ough heating; cool slowly; reheat to 1,650°-1,700° Fahr.,
quench; reheat to 350°-550° Fahr., and cool slowly.

For the gear shafts 0.45 per cent, carbon steel, 3^ .per
cent, nickel (0.30 per cent, carbon) or 0.30 per cent, carbon
chrome nickel steel is used.

Gear Reduction Ratios — With very few exceptions sliding
pinion change gears pfbvide either three or four forward
speeds, besides one reverse speed. Four speed gear sets are

76 SLIDING CHANGE SPEED GEARS.

fitted, as a rule, to the more expensive pleasure cars and to the
larger sizes of commercial vehicles manufactured. It is cus-
tomary to proportion the different gear reductions so they will
substantially form a geometrical series. For instance, in a
three speed gear the reduction ratio of the intermediate gears
is generally about 1.8, and that of the low gears 3.2, which
latter figure is substantially the square of 1.8. If the motor is
relatively powerful in respect to the weight of the car and the
speed to which it is geared on direct drive, then these reduction
ratios of the gear set can be made somewhat smaller; in the
opposite case they should preferably be somewhat greater.

In four speed gears the reduction ratio of the low gears
(first speed set) varies from 3.25 to 4.25, being generally near
4. With a geometrical progression, calling the first speed

ratio r, the second speed ratio would be (ty \ and the third

speed ratio ^ r t There is a tendency, however, to make the
reductions of the two intermediate gears a little smaller, the
idea being that the speed shall not be too low while driving
on the intermediate gears, but the first speed gear must be
sufficiently low to provide ample driving torque for all emer-
gencies. The general run of ratios falls within the following
limits :

First speed 3.75—4.25

Second speed 2 --2.2

Third speed 1.4—1.6

Fourth speed Direct drive.

The reverse gear ratio is generally made somewhat greater
than that of the low gear — as great as the design permits.

Arrangement of Gears — Referring to Figs. 42 and 44, it will
be seen that in these gears (which represent the modern
types) the driving part of the primary shaft carries a pinion
which meshes with a gear on the secondary shaft. These
two gears remain constantly in mesh, while the rest of the
gears are shifted into mesh when it is desired to use them.
It will be noticed that the gear on the secondary shaft has
about twice the pitch diameter as the driving pinion on the
primary shaft, hence the secondary shaft runs at all times at
about one-half the speed of the engine. There is an alternate
construction in which the constantly meshed set of gears is
located at the rear end of the gear box, but this is subject

SLIDING CHANGE SPEED GEARS. 77

to the disadvantage that when the direct drive is in operation,
which it is a very large proportion of the time the car is in
use, the secondary shaft runs at substantially twice engine
speed, and the pitch line velocity of the constantly meshed
gears is practically twice as great. This arrangement is now
nearly obsolete, and with it has passed the practice of en-
tirely disconnecting the primary and secondary shafts from
each other when engaging the direct drive.

Form of Gear Teeth— There are two forms of gear teeth
in use, the i4l/2 degree involute and the stub tooth. The latter,
which was specially created to meet automobile requirements, is
used in the great majority of cases. The involute tooth, shown in
Fig. 45 at A, is the standard form of tooth for machine cut gear-
ing for ordinary purposes. Its general proportions are given in
the Appendix to Volume I. The tooth contact surfaces make an
angle of 14^ degrees with a radial plane through the axis of the
gear. The stub tooth, illustrated in Fig. 45 at B, is not as high as
an involute tooth of the same circular pitch, and has a greater
contact angle (20 degrees). Rules for the general proportions of
stub teeth were also given in the Appendix to Volume I.

Stub tooth gears
are much stronger
than involute tooth
gears of the same
circular pitch, and
that is the reason
they have sup-
planted the latter.
It is sometimes
FIG. 45.— INVOLUTE 14^ DEGREES TOOTH urged against the
AND STUB TOOTH. stub tooth gear

that the radial

thrust between centres of shafts, which is proportional to the
tangent of the pressure angle, is somewhat greater with the stub
tooth, but since the radial thrust is only a fraction of the whole
gear load on the shafts, this objection is not a very serious
one. Another special form of tooth, intended to have some of
the same advantages as the stub tooth, is known as the "long
addendum." While the total working height is tbe same as
that of the standard involute tooth, seven-tenths of this height
is above the pitch circle and only three-tenths below it in the
pinion ; three-tenths above and seven-tenths below it in the gear.
Calculation of Gears — In determining the necessary di-
mensions of change speed gears it is advisable to calculate the
engine torque on the basis of 65 pounds per square inch brake
m. e. p., because the permissible stress in the gear teeth decreases

78 SLIDING CHANGE SPEED GEARS.

rapidly as the pitch line velocity increases, hence the torque at
normal engine speed should be figured with. The dimensions of
gears necessary to transmit a certain torque at a certain angular
velocity are calculated by means of a formula given by Wilfred
Lewis in a paper read before the Engineers' Club of Philadelphia
in 1893. This formula reads

w = S p f y,

where w is the tangential force in pounds; 5", the stress in the
material of the teeth, in pounds per square inch ; p, the circular
pitch ; f, the face of the gear in inches, and y a constant depend-
ing upon the form and number of teeth in the gear. The follow-
ing table gives the values of y for 14^2 degree involute teeth for
that range of tooth numbers which is likely to be used in auto-
mobile work :

TABLE I— VALUES OF y FOR 14# DEGREE INVOLUTE TEETH.

12 teeth 0.067 21 teeth 0.092

13 " 0.070 23 " 0.094

14 " 0.072 25

15 " 0.075 27

16 " 0.077 30

17 " 0.080 34

18 " 0.083 38

19 " 0.087 43

20 " 0.090 50

0.097
0.100
0.102
0.104
0.107
0.110
0.112

The above formula may be rearranged so as to directly give
the width of face required —
w

f = (23)

Spy

With stub tooth gears, owing to the fact that the height of the
tooth is not proportional to the circular pitch, the Lewis formula
is not directly applicable, since the value of the constant y
changes with the pitch of the gear as well as with the number
of teeth. For this form of gearing the following simplified
formula may be used:

w
f = , (24)

S 2

where z is a constant depending upon the pitch and the number
of teeth in the gear. The values of z for the three pitches and
the numbers of teeth that are likely to be used in automobile
change geans are given in the table on the following page.

Pitch Line Velocity and Allowable Stress — In three speed
gears the pitch line velocity of the two gears that remain
constantly in mesh (where these are located at the motor end)
varies between 90 and 100 per cent, of the piston speed ; in other
words, the pitch diameter of the constantly meshed pinion varies

SLIDING CHANGE SPEED GEARS. 79

TABLE II— CONSTANTS FOR STUB TOOTH GEARS.

No. of Teeth

5-7 Pitch.

6-8 Pitch.

7-9 Pitch.

0.078

0.061

0.051

0.081

0.064

0.053

0.083

0.066

0.054

0.084

0.067

0.055

0.086

0.068

0.056

0.088

0.069

0.058

0.090

0.071

0.059

0.091

0.072

0.060

0.093

0.074

0.061

0.095

0.07S

0.062

0.098

0.077

0.064

0.100

0.079

0.066

0.104

0.082

0.068

0.108

0.085

0.071

0.111

0.088

0.073

0.116

0.091

0.075

between 57 and 64 per cent, of the length of piston stroke, the
higher figure being more suitable for high powered motors. In
four speed gears the pitch diameter of the constantly meshed
pinion is made from 57 to 77 per cent, of the length of stroke.
The average ratio between length of stroke and pitch diameter
of the constantly meshed pinion is 0.6 in three speed gears, and
0.7 in four speed gears.

As to the allowable stress in the material of the teeth, this
varies greatly with the pitch line velocity, and, of course, also
depends directly upon the physical properties of the material
used. Besides, it is logical that the stress in the constantly
meshed pair of gears should be somewhat less than the stress
in the gears pertaining only to one particular speed, since the
constantly meshed pair works under load as much as the several
other pairs collectively. The author has gone over the data of
a great many sliding gear sets, and finds that the following
stresses in gear teeth give good results in the intermittently
meshed pairs of gears :

TABLE III— ALLOWABLE UNIT STRESS IN ALLOY STEEL GEAR
TEETH, CASE HARDENED.

Pitch Line Velocity. Allowable Stress.

(Ft. P. M.) (Lbs. P. Sq. In.)

750 30,000

900 27,000

1050 24,000

1200 21,000

1350 18,000

1500 . 15,000

80 SLIDING CHANGE SPEED GEARS.

TABLE IV— ALLOWABLE UNIT STRESS IN CHROME NICKEL

AND CHROME VANADIUM STEEL GEAR TEETH,

HARDENED ALL THROUGH.

Pitch Line Velocity. Allowable Stress.

(Ft. P. M.) (Lbs. P. Sq. In.)

750 60,000

900 53,000

1050 47,000

1200 42,000

1350 38,000

1500 34,000

1650 30,000

1800 27,000

In the above two tables the pitch line velocity is based on a
piston speed of 1,500 feet per minute.

For the constantly meshed pair of gears the stress in the teeth
should be taken 15 per cent, less than for the intermittently
meshed gears.

In calculating the face of the gear it is to be remembered
that the engaging edges of the teeth have to be chamfered in
order to insure positive meshing, and this chamfering necessarily
somewhat reduces the effective width of the gear face. In pro-
gressive sliding gears some of the gears are chamfered on both
sides, while in selective sliding gears the gears are chamfered
on one side only. The loss in the effective width of the face
amounts to about & inch for each chamfer. Another thing that
deserves consideration is that, after the gear shifting linkage has
become somewhat worn, there is a possibility that when the gears
are meshed by the operator they will not be accurately opposite
each other, with the result that some of the face width will be
ineffective, and it is well to also allow iV inch for inaccurate
meshing 01 the sliding gears. This makes a total allowance, for
chamfer and inaccurate meshing, of l/% inch for sliding gears
chamfered on one side only and $s inch for sliding gears cham-
fered on both sides. If it is desired to make the gears of carbon
steel, case hardened, the stresses in the teeth must be taken
somewhat lower than the allowable stresses in alloy steel case
hardened, for the same pitch line velocity.

Application of Formula. — We will now calculate the dimen-
sions of a change speed gear for a four cylinder 4x5 inch
motor, the gear to be of the three speed selective type. The
driving pinion would have a pitch diameter of

0.6 x 5 = 3 inches.
We will use gears with 6-8 pitch teeth, hence the pinion will

SLIDING CHANGE SPEED GEARS. .81

have 18 teeth. We found that in three speed gears the low speed
reduction is usually about 3.2, and it is customary to make the
reduction ratio of the constantly meshed set of gears the same
as that of the low gear set. Hence the reduction ratio of either
set should be about

3.2 = 1.8 (approximately),
and the number of teeth for the driven member of the con-
stantly meshed set should be

1.8 X 18 = 32 (approximately).

The low gear set should have the same number of teeth as the
constantly meshed set, and the intermediate gear set should both
have an equal number of teeth, since the constantly meshed set
gives the full reduction (1.8) desired for the intermediate speed.
Since the sum of the numbers of teeth must be the same for each
set, each gear of the intermediate speed set must have
18 + 32
- = 25 teeth.

The torque of the motor, on the basis of 65 pounds per square
inch brake m. e. p. is (Equation 1) :
4X5X4X4X65
- — - = 108 pounds-feet

The pinion of the constantly meshed set has a pitch radius of 1^4
inches, hence the tangential force on the pitch circle is
108 X 12

= 864 pounds.

At 1,500 feet piston speed the pitch line velocity is
1.5 TT
- X 1500 = 1413 ft. p. m.

We will assume that the gears are to be made from low carbon
alloy steel and to be case hardened, and from Table III we see
that at this pitch line velocity the permissible stress is

16,800 pounds — 15 per cent. = 14,300 pounds.
From Table II we find the value of the constant z for an 18
tooth 6-8 pitch gear to be 0.068. Hence, according to equation
(24), the necessary face width is

864

- = 0.888— say tt inch.
14,300 X 0.068

The tangential force on the pitch line of the intermediate gears
is greater than that on the pitch line of the constantly meshed set
in the proportion of the number of teeth of those members of
the constantly meshed and the intermediate sets which are se-
cured to the secondary shaft. In the present case the force is

82 SLIDING CHANGE SPEED GEARS.

32
864 X — = 1,106 pounds.

The pitch line velocity of this set at 1,500 feet piston speed per
minute is 25

1,413 X — = 1,104 ft. p. m.

•j£

At this speed the allowable stress in the teeth (see Table III)
is 23,000 pounds per square inch. The value of constant z for
25 teeth of 6-8 pitch is 0.075. Hence the effective width of the
face should be

= 0.641 inch,

23,000 X 0.075
and the total width of face

0.641 + 0.125 = 0.766 inch — say it inch.

For the low gear set the pitch line pressure figures out to 1,536
pounds, and the pitch line velocity to 530 ft. p. m. From Table
III we hnd the allowable stress in the teeth to be 29,000 pounds
per square. inch, and the value of constant z for 18 teeth is 0.068.
Hence the total width of face of the low gear should be

- - £§- - - + o. 125 = 0.905— soy \\ inch.
29,000X0.068

It will be seen that the widths of face of the three gears come
out almost the same, and, as a matter of fact, in many three speed
sliding gears all of the gears are made of the same face width.
Some designers simplify their calculations by merely calculating
the required width of face for the constantly meshed set and
making all other gears of the same width of face.

In practically every case the sliding member of the low gear
set serves also to give the reverse, hence the face width of the
reverse pinions is fixed by the face width of the low speed gears

Pressure on Bearings — The earlier change gears of the slid-
ing type were fitted with plain bearings, but anti-friction
bearings present such important advantages that they are
now almost invariably used in this part of a motor car,
radial ball bearings being used in the majority of gear boxes,
and roller and cup and cone ball bearings in some instances.
The bearing; have considerable influence on the design of the
case, and ;n order that the proper sizes may be selected the
gear loads on them have to be accurately calculated.

In Fig. 46 is shown a diagram of a pair of gear teeth in
mesh. We will assume the teeth to be of stub form and their
contacting surfaces to make an angle of 20 degrees with the
plane through the axes of the two shafts. The pressure be-

SLIDING CHANGE SPEED GEARS.

tween the two teeth, which is represented by the line A D
is normal to the contact surface. On the other hand, the tan-
gential load on the gear, which is represented by the line A C,
is normal to the plane of the axes and, therefore, makes an angle
of 20 degrees with the tooth pressure A D. In fact, the tooth
pressure A D may be resolved into two components: one, A C,
normal to the plane of the gear axes and tangential to the pitch
circles, which causes the driven gear to turn, and the other, A B,
in the plane of the gear axes, which tends to force the gear shafts
apart.

FIG. 46.— COMPOSITION OF GEAR TOOTH REACTION.
Let T be the torque transmitted by the driving gear and r
its pitch radius, then the tangential force is

and the tooth pressure is

A D =

TX 12

r X cos 20

There is, however, another factor to be taken into account,
namely, trie friction of the teeth as they move over each other.

84 SLIDING CHANGE SPEED GEARS.

When the teeth first come together their outer ends touch each
other, and they partly slide and partly roll over each other until
they are in full mesh. This frictional force is in the plane of
the contact surface and is represented in the diagram by A E.
The resultant of this frictional force and the normal pressure
on the tooth surfaces is represented by A F. The friction angle
D A F may be taken at 5 degrees, which will make the angle
between the tangential force and the resultant of the tangential
force, the radial bearing pressure and the frictional force on the
teeth, 25 degrees. Neglecting the fact that D F is not quite in
line with C D, we may write
T X 12

A F =

(25)

r X cos 25°

Equation (25) gives the resultant reaction at the tooth surface
of any pair of meshing gears, if T is made equal to the torque

FIG. 47.

of the driving member and r equal to its pitch radius. It is
now to be shown what bearing pressure results from this tooth
reaction.

In Fig. 47, A represents the shaft of the driving pinion which
has a torque T impressed upon it at some point in front of the
bearing. This shaft is provided with a lever arm B, representing
a portion of the driving pinion, which lever presses against the
end of another lever C, similarly mounted upon the secondary
shaft. The contact surfaces of the two lever arms make an
angle of 25 degrees with the plane of the axes of rotation, so
that the pressure between them makes an angle of 25 degrees
with a tangent to the circles described by the centres of the con-
tact surfaces. Now, the reaction of lever C on lever B produces
a moment P X r around the axis of primary gear shaft A. The
principle that action and reaction are equal and opposite applies

SLIDING CHANGE SPEED GEARS.

[

LtJ.

ii-

[

to moments the same as it does to forces, and the reaction of
the bearing on shaft A tends to turn lever B around the centre
line of contact D, with the same torque, but in the opposite
direction, as the contact pressure P tends to turn the arm
around the axis of p

shaft^. Hence Pi
represents the re-
action of the bear-
ing on shaft A and
P2 the pressure of
shaft A on the
bearing.

Each of the gears
i s supported o n
two bearings,
these bearings
being on opposite
sides of the gear FIG. 48.— DISTRIBUTION OF TOOTH PRESSURE
respective- BETWEEN BEARINGS.

ly, and the bearing

pressure is distributed between them in a certain proportion
which we shall investigate presently. The constantly meshed
pinion in many gears is an exception to this rule, since it over-
hangs its bearing support. From the above we see that the
pressure on the bearings supporting any gear is equal to the
resultant tooth reaction, and in direction parallel to it. Another
thing to 'be observed is that the pressures on the shafts of two
meshing gears due to the pressure between the teeth are equal
but in opposite directions. This is easily seen, since the pressure
of the driving gear teeth against the driven gear teeth is equal
to the reaction of the driven gear teeth, but in the opposite di-
rection.

Next it becomes necessary to determine the division of the
bearing pressure due to the tooth reaction, between the two
bearings supporting any gear. The shaft forms a beam sup-
ported at both ends, with a concentrated load at the centre
of the gear. Referring to Fig. 48, let Ri and R* be the reac-
tions at the supports, or loads on the bearings; P the total
bearing load due to one pair of gears; x, the distance of the
centre of the gear from the centre of the left hand bearing
and y the distance from the centre of the right hand bearing.

Then, taking moments around the centre plane of the gear

g<5
and

SLIDING CHANGE SPEED GEARS.

(P—

Except when the direct drive is being used, two pairs of
gears are in mesh and transmitting power simultaneously, viz.,

FIG. 49. — CONSTANTLY MESHED AND INTERMEDIATE SPEED GEARS
(SEEN FROM ENGINE END.)

the constantly meshed pair and one of the other pairs. However,
the bearing pressures due to these two pairs of gears are not in
the same direction, and therefore cannot be added together
directly, but must be added by means of the parallelogram of
forces. This may be seen from Fig. 49, which is a front view
of the constantly meshed and intermediate speed pairs of gears.
In this figure, Pi represents the reaction of the contsantly
meshed gear C on the constantly meshed pinion A, and P2 the
pressure of the intermediate pinion D on the intermediate speed
gear B. The loads on the bearings of the primary shaft R are
equal and parallel to Pi and P2, while the loads on the bearings

SLIDING CHANGE SPEED GEARS.

of the secondary shaft are equal and parallel to Pi and P2, but
oppositely directed. All of these forces make an angle of 25
degrees with the vertical.

Therefore, in order to determine the total load on the different
bearings of the gear set corresponding to any particular speed or
gear, we first calculate the bearing load due to one pair of
gears, then find the proportion of this on each bearing; next

FIG. 50. — LAYOUT OF GEARSET UNDER CALCULATION.

we determine the bearing load due to the other pair of gears,
then find the proportion of this on each bearing and finally add
the two loads on each bearing together by means of the parallelo-
gram of forces, which can be done either graphically or trigo-
nometrically.

We will now carry this calculation through for the gear set
whose gear dimensions were calculated in the foregoing. This

88 SLIDING CHANGE SPEED GEARS.

gear with its bearings is laid out in Fig. 50. The tangential
forces on the pitch circles we found to be :

864 pounds on the constantly meshed gears;
1,106 pounds on the intermediate gears;
1,536 pounds on the low speed gears,

and if we assume that the reverse pinion has 14 teeth, it is
1,975 pounds on the reverse gears.
Since the bearing loads are equal to
Tangential Force

cos 25 degrees

and the cosine of 25 degrees is 0.906, we have for the bearing
loads due to these tangential forces :

953 pounds due to the constantly meshed gears ;
1,222 pounds due to the intermediate gears;
1,693 pounds due to the low speed gears;
2,180 pounds due to the reverse gears.

Now, assume the intermediate pair of gears to be in operation.
The load on bearing I due to the tooth pressure of the con-
stantly meshed gears is

7.469

953 X = 832 pounds.

8.563
That on bearing II due to this pressure is

953 — 832 = 121 pounds.

The load on bearing I due to the tooth pressure of the inter-
mediate gears is

4.219

1,222 X = 602 pounds.

8.563
That on bearing II due to this pressure is

1,222 — 602 = 620 pounds.

Adding the two loads on each bearing graphically, as shown
in Fig. 51, we find the loads on bearings I and II to be 642 and
550 pounds, respectively. The directions of these loads are as
indicated by the arrows, the gear being looked at from the front.
The load on bearing V due to the tooth pressure of the inter-
mediate gears is

4.219

1,222 X = 708 pounds.

7.25

The load on bearing VI due to the tooth pressure on the inter-
mediate gears is

1,222 — 708 = 514 pounds.

The load on bearing IV due to the tooth pressure on the inter-
mediate gears is

SLIDING CHANGE SPEED GEARS.

2.969

708 X = 1,271 pounds.

1.656

The load on bearing III due to the tooth pressure on the inter-
mediate gears is

1,271 — 708 = 563 pounds.

The load on bearing III is opposite in direction to the load on
bearing IV.

Secondary Shaft Bearings

Primary Shaft Bearing*

FIG. 51. — BEARING LOADS FOR INTERMEDIATE GEAR OPERATION
The load on bearing IV due to the tooth pressure on th3 con-
stantly meshed gears is

953 X fffiff* *,&o pounds.

The load on bearing III due. to the tooth pressure on the con-
stantly meshed gears is

1,580 — 953 = 627 pounds.

90 SLIDING CHANGE SPEED GEARS.

The loads on bearings III and IV while the intermediate
gear is in operation are added together graphically in the right

Secondary Shaft Bearings » Primary Shaft Searing
FIG. 52. — BEARING LOADS FOR Low GEAR OPERATION.

hand diagram in Fig 51, and the magnitude and direction of
the load on bearing VI are also shown.

When the low gears are in mesh the bearing loads due to
the tooth pressure on the constantly meshed pair of gears will
be the same as when the intermediate gears are in mesh, which

SLIDING CHANGE SPEED GEARS.

loads we have already found. The load on bearing I due to the
tooth pressure on the low speed gears is
3.219

1,693 X = 637 pounds.

8.563

The load on bearing II due to the tooth pressure on the low
speed gears is

1,693 — 637 = 1,056 pounds.

Adding the two forces on each bearing graphically, as in Fig.
52, we find the loads on the secondary shaft bearings for low

FIG. 53. — MAGNITUDE AND DIRECTION OF TOOTH PRESSURE ON

REVERSE GEARS.

gear operation to be 645 pounds on bearing I and 981 pounds
on bearing II.

The load on bearing V due to the tooth pressure on the low
speed gears is

3.219

1,693 X = 753 pounds.

7.25

The load on bearing VI due to the tooth pressure on the low
speed gears is

1,693 — 753 = 940 pounds.

The load on bearing IV due to the tooth pressure on the low
speed gears is

2.969

753 X = 1,350 pounds.

1.656

92 SLIDING CHANGE SPEED GEARS.

The load on bearing III due to the tooth pressure on the low
speed gears is

1,350 — 753 = 597 pounds.

The loads on the bearings of the primary shaft corresponding
to low gear operation are added graphically in the right hand
diagram in Fig. 52, and we find that the load on IV is 1,263
pounds and on III, 513 pounds.

The direction of the tooth pressures on the reverse gear and

Secondary <5haft 3ectring>s.

FIG. 54.— BEARING LOADS FOR REVERSE GEAR OPERATION.
pinion may be found graphically from Fig. 53. It is seen that
the pressure of the idler gear on the reverse gear makes an
angle of 10^ degrees with the vertical, and the reaction of the
idler gear teeth on the teeth of the reverse pinion makes an
angle of 46l/2 degrees with the horizontal.

The load on bearing I due to the tooth pressure between the
reverse pinion and idler is

1094

2,180 X - - = 278 pounds.
8.563

SLIDING CHANGE SPEED GEARS. 93

The load on bearing II due to the tooth pressure between the
reverse pinion and idler is

2,180 — 278 = 1,902 pounds.

The load on bearing VI due to the tooth pressure between the
reverse gear and idler is*

6.156

2,180 X = 1,851 pounds.

7.25

The load on bearing V due to the tooth pressure between the
reverse gear and idler is

2,180 — 1,851 = 329 pounds.

The load on bearing IV due to the tooth pressure between the
reverse gear and the idler is

2.969

329 X = 590 pounds.

1.656

The load on bearing III due to the tooth pressure between the
reverse gear and the idler is

590 — 329 = 261 pounds.

Adding the two loads on each bearing graphically (see Fig.
54) we find the loads on bearings I and II to be 570 pounds
and 1,789 pounds, respectively, and the loads on bearings III
and IV, 627 pounds and 2,094, respectively.

The following table shows at a glance the load on each
bearing for each speed:

Bearing. I. II. III. IV. V. VI.

Reverse 570 1789 627 2094 329 1851

Low gear 645 981 513 1263 753 940

Intermediate gear 642 550 519 1263 708 514

High gear

Bearing Load Due to Bevel Gears — Cars fitted with side
chain drive have a bevel gear set enclosed in the rear portion of
the change gear box, the bevel pinion being keyed to the rear
end of the primary shaft. Of course, the tooth reaction of the
bevel gears throws considerable load on bearing VI, and this
must be taken into account. In very powerful cars the bevel pin-
ion is sometimes located between ball bearings on opposite sides
of it, but the more common arrangement is to have only a single
large radial ball bearing directly back of the bevel pinion. We
will assume that in the change gear under calculation the above
arrangement is used and that the ratio of the bevel gear set is
3 to 1. We will further assume that the pinion has eighteen teeth
of 6 pitch and the gear fifty-four. This makes the maximum
pitch diameter of the pinion 3 inches and the pitch angle such

SLIDING CHANGE SPEED GEARS.

that its tangent is 0.333, viz., 18° 26'. If the bevel pinion has a
face of \y% inches, then the mean pitch diameter is
3 — (1^ X sin 18° 26') =
3 — (!3/£ X 0.316) = 2.567 inches,

and the mean pitch radius, 1.283 inches. • Since the motor develops
a torque of 108 pounds-feet, the tangential force on the gear teeth,

FIG. 55.— TOOTH REACTION IN BEVEL GEARS.

figured as though it was concentrated at the middle of the face
length, is

103 X 12

— 1,010 pounds.

1.283

The tooth reaction makes an angle of 20 degrees with the
tangential force, hence its value is

1,010

= 1,074 pounds.

0.94

Now, in a bevel gear the tooth reaction is not in a plane per-
pendicular to the axis of the gear, and for this reason the bearing

SLIDING CHANGE SPEED GEARS. 95

pressure is not equal to the tooth reaction, as in the case of a
spur gear. We have to resolve the tooth reaction into two com-
ponents, one in a plane perpendicular to the gear axis, which is
equal and parallel to the load of the shaft supporting bearings,
and the other in a direction parallel to the gear axis, which is
equal to the end thrust. This requires three successive steps.

In Fig. 55, A B represents the normal pressure on the tooth
contact surfaces. We first resolve this into a component A C in a
vertical plane perpendicular to the gear axis, and a component
C B in a horizontal plane through the axis of the gear and at
right angles to the element of the gear tooth surface on which
the tooth pressure comes. A D represents this latter component
both in direction and magnitude.

AD = CB = AC tan 20° = T tan 20°.

The latter may be resolved again into a component A E perpen-
dicular to the gear axis and a component D E parallel to the gear
axis.

A E = A D cos B = T tan 20° cos 6

D E = A D sin Q — T tan 20° sin 6 ......................... (26

D E represents the end thrust of the bevel pinion which is
usually taken up on the radial ball bearing, though some designers
provide a special thrust bearing, or use a combined radial and
thrust bearing at this point. This equation is general in its
nature, applying to all 14^/2 degree involute gears; while for
stub tooth bevel gears tan 25° should be substituted for tan 20°.

The radial bearing load is equal to the resultant of A C and
A E which is

an 20° co 3 0)2 ..................................... (27

In our example 7 =1,010 pounds. The tangent of 20° is equal
to 0.364, the cosine of 0 (18° 25') is 0.949 and the sine of 0, 0,316.
Substituting these values in equations (26) and (27) we find the
end thrust to be

1,010X0.364x0.316=116.2 pounds,
and the radial bearing load

vijOio2 + (1,010 X 0.364 X o-949)2= 1,051 pounds.

The arrow heads in Fig. 55 indicate the direction of the reac-
tion of the bevel gear teeth on the bevel pinion teeth and of its
components, and the resultant radial bearing pressure is in the
direction of A F, which in this case makes an angle of 22>y2 de-
grees with the vertical.

Like the constantly meshed pinion, the bevel pinion overhangs
its bearing. From the centre of the rear ball bearing to the centre

96 SLIDING CHANGE SPEED GEARS.

cf the bevel pinion would be about i% inches, and since the dis-
tance between centres of the two bearings of the bevel pinion
shaft is 7^4 inches, we have for the load on bearing VI due to the
tooth reaction on the bevel pinion :

1,051 X ^T= 1,232 pounds,

and the load on bearing V due to the tooth reaction on the
bevel pinion,

1232 — 1051 = 181 pounds.

When the direct drive is employed these are the only loads on
bearings V and VI, but when either of the lower gears or the
reverse is in mesh the loads on bearings V and VI due to the
bevel pinion tooth pressure are multiplied by the reduction fac-
tor of the particular gear, and there is in addition the load
due to the reduction gears on bearings V and VI which must
be combined with the loads due to the bevel gears by means of
the parallelogram of forces. For bearing VI this is done in
Fig. 56, the values of the loads on VI shown in Figs. 51, 52
and 54 being used, and the value of the load due to the bevel
gears represented in Fig. 55, multiplied by the reduction factor
of the particular gear combination. It will be seen that the
bearing loads due to the bevel and spur gears respectively
partly neutralize each other, and that with a gear of this kind
the load on the rear bearing of the primary shaft is greatest
when the low gear is in operation. The tooth pressure of the
bevel gears has little influence on the load on bearing V and its
effect may be neglected.

Sizes of Bearings — Manufacturers of ball bearings issue tables
of load capacities with the aid of which the proper size of bearing
for each point can be determined. These load capacities are the
loads the bearing will stand under continuous running at normal
speed. Now, it will be seen from the table of bearing loads above
given that the loads on all the bearings except 7 and V are a
maximum when the reverse gear is in operation, and these maxi-
mum loads in most instances are far greater than the loads corre-
sponding to the other gear combinations. It will be remembered
that the bearing loads were calculated on the basis of full engine
power, and it practically never happens that the engine works at
full load while the reverse gear is being used. The reverse gear
is made extremely low for the sake of safety in backing, and not
because an unusually large torque is needed. Hence the calcu-
lated bearing loads for the reverse gear never obtain in practice,
and they may be neglected when selecting the proper size of bear-

SLIDING CHANGE SPEED GEARS.

FIG. 56. — LOADS ON PRIMARY SHAFT

REAR BEARING (VI) WHEN

CARRYING A BEVEL PINION.

ings, though it is well to
make sure that the calcu-
lated load on bearing II
does not exceed the rated
load by more than 100 per
cent.

Various constructional
and operative considera-
tions often influence the
choice of bearing sizes.
Thus, although there is a
very considerable differ-
ence between the maxi-
mum loads on 7 and //,
these bearings are often
chosen of the same size ;
for one reason, because it
simplifies the boring of the
bearing holes in the gear
case, since the holes at op-
posite ends can be bored
in one operation. Another
reason is to be found in
the advantage there is in
reducing the number of
different parts in a car,
due to the fact that a
smaller stock of repair
parts will suffice. When
it is thus decided to use
the same size of bearing
at both ends of the sec-
ondary shaft the size of
bearing selected should
have a rated load capacity
intermediate between the
maximum, loads on the
two bearings for forward
running. Thus in our ex-
ample the loads are 550,
642, 645 and 981 pounds,
and the No. 306 bearing
would probably be selected
which has a rated capacity
of 860 pounds. To give a
general rule, the bearings
should be selected to have

98 SLIDING CHANGE SPEED GEARS.

a rated load capacity of from 75 to 125 per cent, of the calcu-
lated maximum gear loads due to other than the reverse gear,
depending upon the general quality of construction.

Intermediate Bearings — In the construction Fig. 50 the
most heavily loaded bearing is IV, which is due to the fact that
the constantly meshed pinion overhangs this bearing. Although
the primary driving shaft is supported in two bearings, the
load due to the tooth pressure is not divided between these bear-
ings, as might possibly be supposed. The gear overhangs the
bearings and the load on bearing IV from the constantly meshed
gears alone is equal to the tooth pressure on the constantly
meshed pinion plus the load on bearing ///. The load on bear-
ing IV resulting from that on bearing V is also nearly twice the
latter. The conditions are somewhat more favorable when a
plain bearing is used at V, extending a considerable distance
into the primary driving shaft, so that the middle of its length
lies substantially in the plane of bearing IV, in which case the
load on V is transferred directly to IV. In the case of unit
power plants and designs of clutches requiring no slip joint in the
clutch shaft, it is advantageous to use only a single bearing on
the primary driving shaft, as the load on the bearing will then
be less than that on IV in Fig. 50.

In large gear boxes the constantly meshed pinion is some-
times supported in two bearings, as shown in Fig. 57, one on
either side, the inside bearing being carried on a pedestal or in
a partition wall in the case. The loads are then divided be-
tween the two bearings in the inverse proportion of the centre
distances. Bearing / may also be placed inside the constantly
meshed gear, causing the latter to overhang, an arrangement
that naturally suggests itself when the constantly meshed pinion
is carried in two bearings. It increases the load on bearing I
and reduces that on bearing //, so their maximum loads will
be about equal, which may be considered an advantage if both
are to be made of the same size. However, this construction
is rare.

Truck Change Gears. — In change gears designed for motor
trucks the unit stresses are kept lower, for the reason that trucks
are operated a great deal of the time in congested thorough-
fares where it is necessary to do much driving on the lower
gears. Besides, a little extra weight does not count for so much
in a truck as in a high speed pleasure car. For this same reason
chrome nickel or other high tensile steels are seldom, if ever,
used for the gears and pinions of truck transmissions. With

SLIDING CHANGE SPEED GEARS. 99

carbon steel and low carbon alloy steel, case hardened, the fol-
lowing unit stresses may be allowed in the gears \/ -

Pitch Line Allowable
Velocity. Stress.

(Ft. p. m.) (Lbs. p. sq. in.)

500 20,000

600 18,000

700 16,000

800 14,000

900 12,000

1000 10,000

The bearings of commercial change gears should also be of

FIG. 57. — CONSTANTLY MESHED PINION WITH BEARINGS ON
BOTH SIDES.

somewhat more liberal size than those in pleasure car gears, for
the same reason.

Shaft Dimensions — One of the chief requirements in a
change gear box is quiet operation, and this necessitates rigid
shafts. The sizes of the shafts are, therefore, more dependent
upon the maximum permissible flexure than upon the torque to
be transmitted. The tooth pressure on the gears located midway
between bearings creates an appreciable flexure of the shafts,
and the pairs of gears located near the bearings also create some
flexure, but this may be neglected. The shafts should be made
of such a diameter that the maximum flexure due to any pair of
gears is not more than 0.003 to 0.005 inch. In Chapter XI of
Volume I is given a formula for the flexure of shafts supported

100 SLIDING CHANGE SPEED GEARS.

at their ends and carrying a concentrated load between hear-
ings, viz., .

where P is the load on the shaft in pounds ; /, the length of the
shaft between the centres of bearings, in inches ; d, the diameter
of the shaft in inches, and x the ratio of the distance of the load
from the farthest support to the distance between supports.

Applying this equation to the secondary shaft of the gear box
calculated in the foregoing, in which the flexure is evidently a
maximum when the low gear is in operation, we have
P = 1,693 pounds I = 8.563 inches

2 x* + 2 x* — 4 x* = 0.11

If we decide to allow a maximum flexure of 0.005 inch, then
1,693 X 8.563

X a11

8,800,000 X
and

. 1,693 X 8.563 X 0.11 , „ , */.* • ,

d =^ 8,800,000X0.005 = L28 ~ say 1 5/16 wch'

In some designs of change gears the secondary shaft is made
of somewhat greater diameter in the middle than at the ends,
•with the object of securing the most rigid shaft with the least
material.

The primary shaft, since it has substantially the same span
between the supports and is subjected to the same loads similarly
located, should be made of practically the same diameter as the
secondary shaft ; or, rather, it should have a cross section equiva-
lent to that of the secondary shaft with respect to bending
stresses.

Reverse Gear Arrangement — Various arrangements of gears
for obtaining the reverse motion are in use. The most common
is that already illustrated in Fig. 50, in which the secondary
shaft carries a reverse pinion sufficiently smaller than the low
speed pinion to allow the low speed gear to clear it when shifted
opposite it. This reverse pinion meshes with a reverse idler on
a special shaft mounted parallel with the primary and secondary
shafts, usually in the lower part of the gear box.

A somewhat different arrangement is shown in Fig. 58, in
•which A is a pinion of double width serving for both the low
gear and the reverse; B is the low speed and reverse gear and

SLIDING CHANGE SPEED GEARS.

101

FIG. 58. — REVERSE GEAR WITH Two IDLERS.

Ri R2 are reversing idler gears on a special short shaft. Sliding
gear B is shown in the position corresponding to the reverse
motion. By sliding it to the left until it meshes with A the low
forward speed is obtained. One advantage possessed by the ar-
rangement Fig. 58 over that of Fig. 50 is that with the former
there is less strain on bearing II (at the rear end of the second-
ary shaft) than with the latter when the reverse gear is oper-
ating.

The two types of reverse gear so far shown are used in three
speed selective and in progressive type gears. In four speed
gears the reversing idlers may be arranged slidably (see Fig. 59),

FIG. 59.— REVERSE GEAR WITH SLIDING IDLERS.

102 SLIDING CHANGE SPEED GEARS.

and by means of a separate sliding bar slid into mesh with both
the low speed pinion and gear while the latter are out of mesh.
To obtain the low speed forward, gear B is shifted to the right
into mesh with pinion A. On the other hand, when it is desired
to back up, gear B is placed in the neutral position (which it
occupies in the illustration) and reversing pinions Ri and Rz are
slid to the left into mesh with A and B respectively, as shown.

Direct Drive Clutch — There are two types of direct drive
clutches in common use, viz., the jaw type, illustrated in Fig. 60,
and the spur and internal gear type, shown in Fig. 61. The
former type consists of jaws formed on the adjacent faces
of the constantly meshed pinion and the intermediate speed gear
respectively. Usually each part has four such jaws, equal in
size, and subtending at the axis of the shaft an angle slightly
smaller than that subtended by the space between them. The
outer edges of the jaws are chamfered to facilitate engagement.
The radial width of these jaws is usually made about one-
quarter the shaft diameter and the length the same.

Where the spur and internal gear type of clutch is employed
the constantly meshed pinion often serves as the spur member,
and the intermediate speed gear is cut with internal gear teeth,
in addition to its regular spur teeth, to serve as the other mem-
ber. It is somewhat difficult to cut these internal gear teeth.
The job can be done by counterboring the rim of the spur gear
and then planing the teeth, but it is a much preferable plan to
use a form of mongrel teeth made by drilling holes into a solid
gear blank from the side and then chambering the blank out so
as to cut away half of the stock between the holes (see Fig. 61).

Front Bearing of Sliding Gear Shaft— Notwithstanding the
difficulty of keeping such a bearing effectively lubricated, a plain
bearing is often used at the forward end of the squared or fluted
shaft, on which the gears slide. This construction renders non-
fluid oil unsuitable as a gear box lubricant. With a fluted shaft
the journal would be made about three-quarters the diameter of
the shaft proper so as to give a substantial shoulder, and about
three diameters long. As in the case of the engine tailshaft, large
oil holes and grooves are necessary, and the scheme of lubri-
cation should be carefully worked out.

Instead of a plain bearing, a cylindrical roller bearing consist-
ing of long, thin rollers is sometimes used, extending into the
counterbore of the shaft, the same as the plain bearing. How-
ever, a more common construction is to use either a single or a
double row non-adjustable ball bearing, as illustrated in Fig. 61.

SLIDING CHANGE SPEED GEARS.

103

FIG. 60. — DIRECT DRIVE JAW CLUTCH.

Some designers use a specially large constant mesh pinion in
order to be able to accommodate a ball bearing of sufficient
capacity, obtaining the required reduction ratios by using very
small intermediate, low speed and reverse pinions on the second-
ary shaft. The light series of ball bearings is naturally best
adapted for this purpose, since it has the least radial depth for a
given load capacity. However, double row bearings seem to be
preferred for this point, since it is difficult to find room for a
bearing of ample capacity.

Sliding Gear Shaft — As already pointed out, in the earlier
sliding change gears the sliding pinions were slid on squared
shafts. These are still used to a slight extent, but have for the

FIG. 61. — DIRECT DRIVE SPUR AND INTERNAL GEAR CLUTCH.

104

SLIDING CHANGE SPEED GEARS.

most part been replaced with splined or integral key shafts. The
two types of shafts are shown in cross section in Fig. 62. So-
called squared shafts are not absolutely square, but have rounded
corners. They are made from round shafts by milling four flats
on them to such a depth that the distance between opposite flats
is 0.8 the diameter across the corners, or the diameter of the
original shaft. Denoting the side of the square formed by the
flats by h, the torsional strength of such a shaft is about 0.21 h3S
pounds-inches, h being given in inches. The flats are often fin-
ished by grinding, and if the shaft is to carry long sleeves sup-
porting the sliding gears, they are sometimes cut with wavy oil
grooves so that oil may flow to parts of the shaft that are never
exposed by the sliding members. Some makers bore the hole
in the gear to a slightly greater diameter than the side of the

•OJ8<f-

FIG. 62. — SECTIONS OF SQUARED AND SPLINED SHAFTS.

squared shaft, so that when the hole is broached out, from two-
thirds to three-fourths of its side will be a plane surface and
the rest cylindrical. (See Fig. 63.) This facilitates the broach-
ing, tends to obviate gripping of the sliding members an^ does
not appreciably reduce the effective bearing surface, because the
pressure is localized near one edge of the flat.

As compared with the squared shaft, the splined shaft pos-
sesses the advantage that it takes the torsional load perpendicu-
larly on the sides of the splines, whereas in a squared shaft most
of this load comes close to one edge of the flats, with the result
that in the latter the unit pressure may become very high and
the lubricant may in consequence be squeezed out, which is not
likely to occur with a splined shaft.

SLIDING CHANGE SPEED GEARS.

105

In American practice, splined gear shafts are made with four
splines for small and moderate sized gear boxes, while in large
gear boxes six splines are used. European practice tends to a
more general use of six splines. Uneven numbers of splines
have also been used, but they are subject to the disadvantage
that they make it very difficult to caliper the diameters of the
shaft accurately. The ratio of the bottom diameter of a splined
shaft to the top diameter or diameter over the splines is gen-
erally about 0.8, and the width of the splines is made about one-
quarter the bottom diameter, or 0.2 times the outside diameter.
(For S. A. E. standard splined fittings see Appendix.)

Practice varies as to the manner of locating the gears. Some

FIG. 63. — BROACHED SLIDING
GEAR WITH PART OF
FLAT RELIEVED.

FIG. 64. — FLANGE
BOLTED GEARS ON
SECONDARY
SHAFT.

manufacturers grind the outside of the shaft— that is, the top
surfaces of the keys, and let the gear ride on these surfaces,
using the broached hole in the gear. Others grind out the hole
in the gear (after the latter has been hardened) true with the
pitch circle or the bottom circle, and let the gear ride on the
bottom surface of the splined shaft. Both methods involve cer-
tain difficulties, and it is hard to say which is the better of the
two, everything considered.

Proportions of Gears — The rims of gears below the tooth
annulus are made of a thickness varying from 0.5 to 0.6 the
circular pitch, and the webs about the same. Since teeth of 6 and
6-8 pitch are used almost exclusively in sliding gears, whose cir-

106

SLIDING CHANGE SPEED GEARS.

cular pitch is' 0.52 inch, both rim and webs are generally made
Y&, inch thick. When the web is located to come flush with one
side of the rim, the latter may taper from */i to 5/16 inch in
width, but it is undoubtedly preferable to have the web central.
In this connection it is worth remembering that substantial rims
and webs and liberal fillets tend to quiet operation, and the
general tendency seems to be toward a slight increase in the
thickness of the sections. The smaller pinions, of course, are
made solid, and only the larger gears are webbed. As regards
the secondary shaft gears, in American practice they are gener-
ally secured to the shaft by means of Woodruff keys, while
European designers, as a rule, flange-bolt the gears to the shaft

FIG. 65.— SECONDARY SHAFT ASSEMBLED WITH GEARS AND
BEARINGS.

or to a sleeve keyed to the shaft. Frequently the gears for
the two intermediate speeds are bolted to the same flange, as
shown in Fig. 64. One of the reasons for flange-bolting the
gears is that they are then of very simple form and are not
so likely to distort in hardening. To insure concentricity the
web of the gear is bored out to fit accurately over an enlarge-
ment of the shaft. The gears may also be riveted to the flanges.
The gears on the secondary shaft must be accurately and
securely fixed in position longitudinally, and this is generally
accomplished by turning the shaft with a collar near its middle
against which a gear is forced from either end, and using tubu-
lar spacers between these inner and the outer gears on the shaft,
as shown in Fig. 65.

SLIDING CHANGE SPEED GEARS.

107

Instead of keying the gears on the shaft and supporting the
latter in antifriction bearings in the housing, the entire set of
secondary gears may be made in a single forging, which re-
volves on a stud secured in the housing, as illustrated in Fig.
66. Bronze bearing bushings are forced into the hub of the
gear set from both ends. This construction is made possible
by modern methods of gear planing. It is obvious that a sec-
ondary gear set so arranged may be made quite rigid, and as
the journal diameter is small, the frictional loss should be
low. If the gear case has a separate end plate the shaft may

FIG. 66. — SECONDARY GEAR ASSEMBLY ON STATIONARY SHAFT.

even be dispensed with, the gear set then being forged with
journals at both ends which have a bearing in the housing.

Manufacture of Gears — Blanks for the pinions and gears
of sliding gear sets are made either from bar stock or from
drop forgings, the larger blanks being generally -forged on
account of the saving in machine work. Before any work is
done upon the blanks they should be annealed to remove the
forging strains, and thus obviate undue distortion during the
subsequent heat treatment.

It is not intended to go extensively into the question of gear
cutting in this volume, because it is an involved subject and has

108

SLIDING CHANGE SPEED GEARS.

been ably treated in special works. Suffice it to say that gear
teeth are either milled by means of formed cutters, or planed
with ordinary cutters, which by means of templates or other
devices are moved so as to produce the proper shape of tooth.
In all gear cutting there are two operations, the rough cutting
or stocking and the finish cutting. Only very little stock should
be left for the latter operation, so that there may be very little

FIG. 67.— FORCING GEARS ONTO SECONDARY SHAFT.

strain on the cutting tool, and thus the highest degree of ac-
curacy attained.

After the teeth are finish-cut, the ends from- which the gears
are to be meshed have to be chamfered. This may be done by
means of a milling machine attachment, as illustrated in Fig.
68. The attachment is clamped to the table of the milling ma-
chine, and the chamfering tool is held in the spindle of the latter.

SLIDING CHANGE SPEED GEARS.

109

The attachment comprises a work spindle on which the gear to
be chamfered is mounted, which is alternately fed toward and
away from the revolving cutter by means of a cam driven
through gearing from the main shaft of the attachment. On a
secondary shaft is mounted a worm of the same pitch as that
of the gear to be chamfered and in which it is meshed. This
secondary shaft is driven through gears from the main shaft.
The main shaft is driven by belt from an overhead countershaft,
which is entirely independent of the milling machine counter-
shaft. As the main shaft revolves the worm, meshing with the

FIG. 68. — "LONG ARM" TOOTH CHAMFERING ATTACHMENT.

gear to be chamfered, turns it, and at the proper intervals the
cam mechanism feeds it toward and away from the V-shaped
revolving cutter. The gear to be chamfered is thus automati-
cally indexed.

The contour of the chamfering may be changed by using spe-
cial cams, or special cutters, or both. The profile at the end
of the tooth may be changed by swiveling the attachment on the

110 SLIDING CHANGE SPEED GEARS.

table. The end of the tooth may thus be left at right angles
with the axis of the gear or at any desired angle.

The next operation in the manufacture of the gears is to harden
or case-harden them. In case-hardened gears, if it is desired
that any portion of the surfaces should remain soft, this can
easily be accomplished by leaving about 1/32 inch extra stock on
these surfaces and removing it after the gear is carbonized and
before it is quenched. This practice also tends to prevent undue
distortion of the gear during the quenching. Another process
designed to accomplish the same purpose, and which is undoubt-
edly less expensive, consists in copper-plating the gears just
before the finishing cut is taken and the ends are chamfered.
The result is that when the gears are carbonized after these
machining operations only those portions of the gear from which
the copper shell is removed will take up carbon from the pack
and will become hardened on being quenched. Gears thus treated
are so little distorted by the quenching that they can readily be
corrected to the desired degree of accuracy.

Every effort must be made in the manufacture of gears to
get every part as nearly true as possible. It would not seem
to matter much whether or not the sides of the gear blanks are
turned absolutely true. This, however, is quite essential, for the
reason that gears are generally cut in "gangs," a considerable
number of them being forced over the mandrel and the milling
cutter, etc., then being fed through the whole set in one opera-
tion. Now, if the sides of the blanks are not absolutely parallel
there is a tendency to distort the mandrel when the nut is turned
up, and thus to produce irregularity in the teeth.

For the grinding of the hole after the teeth are cut, as re-
ferred to in the foregoing in connection with splined shafts, a
special fixture is required for holding the gears. This consists
of a face plate with Several studs driven into it parallel with its
axis and at such a distance therefrom that they fit accurately
between the teeth of the gear at the pitch circle. These locate
the gear concentrically with the grinder spindle, and it may then
be held in position by means of a couple of clamping plates and
bolts. The fixture serves also as a rough gauge for indicating
the accuracy of the gear cutting operation. If the teeth have
been cut too deep, the gear will be loose in the fixture, whereas
if they have not been cut deep enough it will not enter between
the studs.

Tester for Gears — A more delicate gauge or gear tester
is made as follows (Fig. 69) : A vertical shaft A is fixed to a

SLIDING CHANGE SPEED GEARS.

Ill

base and provided with a bushing over which fits the gear to be
tested. An eccentric stud B is mounted on the base in such a po-
sition that when the line between its centres is perpendicular to
the line between the axis of its top portion and that of the fixed
stud, the distance between the latter two axes is the exact dis-
tance between the axes of the gear shafts. An indicating hand
or pointer C secured to the eccentric stud then points to zero.
The pointer moves over a double scale, and therefore shows
exactly how much the gear is either too small or too large.

Unless the teeth are finished by grinding after hardening — a
process that is seldom applied at present — some allowance must

FIG. 69. — GEAR TESTER.

be made for swelling or distortion during the hardening process,
by either cutting each of the gears 0.005 to 0.010 inch small on
the pitch diameters, or else placing the two shafts that much
farther apart than the calculated distance.

Sliders— The individual sliding members in a gear set are
operated by means of sliding bars, ^ to ^ mcn m diameter, and
arranged parallel with the gear shafts, which carry forks that fit
into grooves formed in the projecting hubs of the gears. Two
such sliding bars are provided in all three speed gears, and three
in some four speed gears. Generally the sliding bars are placed

112

SLIDING CHANGE SPEED GEARS.

side by side, but sometimes they are arranged concentrically.
The sliders are located inside the gear box near one of the side
walls thereof, and have their bearings in the end walls. In order
to insure accurate meshing of the gears, as well as to lock them
out of mesh, a locking arrangement similar to that illustrated
in Fig. 70 must be provided. It consists of a spring pressed
plunger or ball which enters V slots in the sliding bar, corre-
sponding to the neutral position of the sliding set and the two
or more positions of engagement, respectively. These locking
dogs will hold the slider in the neutral position when it is dis-
connected from the operating lever and enable the driver to find
the correct meshing position when it is connected thereto. While
this method of locking the sliders is not positive, it is sufficiently
dependable for all practical purposes. In most designs of selec-

FIG. 70. — LOCKING DOG FOR GEAR SLIDER.

tive gear the operation of picking up one slider with the shifting
lever entails the automatic and positive locking of the other
sliders.

Mounting of Bearings — If the gear case is made of aluminum
and anti-friction bearings are used, the latter are generally
mounted in bronze bushings, instead of directly in the casing.
This practice was introduced because the aluminum was con-
sidered too soft, and it was thought necessary to distribute the
pressure over a greater surface than that of the bearings alone.
With the improvements which have been made in aluminum al-
loys in recent years this is no longer absolutely necessary, but
the practice is still adhered to by some designers. The bushings
are provided with outward radial flanges so as to be held secure-
ly against endwise motion.

SLIDING CHANGE SPEED GEARS.

113

The inner races of radial ball bearings should always be
forced onto the shaft under moderate pressure, and should be
securely clamped between a substantial shoulder on the shaft
and a nut which is locked by some approved means. Of the
outer races on a single shaft not more than one should be firmly
secured in a lengthwise direction, as otherwise there is danger
of subjecting the bearings to undue end thrust.

Taking up the bearings on the secondary shaft first, the inner
races are secured to the shaft as above described. Of the outer
races one may be clamped between an inward flange on the
bushing and the bearing end cap, as shown in Fig. 71A, and the
other one made a sliding or "suction" fit in the casing or bush-

FIG. 71.— MOUNTING FOR SECONDARY SHAFT BEARINGS.

ing and left free to move endwise. An alternate arrangement
consists in leaving both outer races free endwise and taking up
the end thrust on hardened thrust buttons fitted into the shaft
ends and the bearing caps, respectively. Set screws with rounded
points may be screwed through the centres of the caps to take the
place of the buttons therein as shown at B in Fig. 71.

The rule that the inner races must be firmly clamped between
a shoulder and a nut or spacer applies to all bearings. Like-
wise, if there are two or more bearings on one shaft, the outer
races of all but one of them should be free endwise, and if a
thrust bearing is used in addition to radial bearings, the outer
races of all the latter should be free. In some cases the for-

114

SLIDING CHANGE SPEED GEARS.

ward bearing on the primary shaft is subjected to the end thrust
of the clutch spring, and should then be provided with a ball
thrust bearing. This is generally placed between the two radial
bearings. However, the necessity of firmly clamping both of the
inner races on the shaft and allowing the outer races some end-
wise motion should not be lost sight of in this case. Fig. 72
shows two ways in which these requirements can be met. At A
is shown the Alco design, which employs a single thrust bearing.
The design shown at B is taken from a paper read by F. G.
Barrett before the Institute of Automobile Engineers, London,
on February 14, 1912. With the latter design the thrust bear-
ings can be properly adjusted and the adjustments locked before
these bearings are placed on the shaft.

Geared-up Fourth Speed — The greatest transmission effi-
ciency and the most silent operation are obtained with the direct

A B

FIG. 72.— MOUNTINGS FOR PRIMARY SHAFT BEARINGS.

drive, and the designer, therefore, should strive to so propor-
tion his gear reduction that the car can be driven on direct
drive under all normal conditions. This means that there should
be a relatively large reduction between the gear box and rear
wheels. However, in many types of cars very high maximum
speeds are desired, which conflicts with the requirement of a
high reduction ratio in the final drive. These conflicting require-
ments led to the construction of four speed gears in which the
direct drive is the third speed, and the fourth is a geared-up
speed, 25 to 30 per cent, higher than the direct drive. Fig. 73
shows the lay-out of the Winton change gear, with indirect fourth
speed. The geared-up speed is obtained by placing on the second-
ary shaft near its rear end a gear with a larger pitch diameter

SLIDING CHANGE SPEED GEARS.

115

than the constantly meshed gear, adapted to be meshed with a
sliding pinion on the driven primary shaft of a smaller pitch
diameter than the constantly meshed pinion. In a gear of this
type it is advantageous to keep the reduction ratio of the con-
stantly meshed pair of gears low, as otherwise the pitch line
velocity of the high speed gears will be very high and their
operation is likely to be attended by considerable noise.

Gear Cases — The gear cases of nearly all pleasure cars are
cast of aluminum alloy of the same composition as that used

FIG. 73. — LAYOUT OF WINTON CHANGE GEAR WITH GEARED- UP
FOURTH SPEED.

for the engine crankcase. However, manganese bronze is also
used for that part of the case which supports the shafts and on
which the greater part of the strain comes. The gear boxes of
many motor trucks, especially those of European design, are
made of cast steel, and cast iron cases are also in use.
There are two common arrangements of the shafts in a gear

116

SLIDING CHANGE SPEED GEARS.

box. Either the secondary shaft is located directly underneath
the primary shaft or the two shafts are located in a horizontal
plane. There is, of course, a third possible arrangement, where
the plane of the shafts is neither horizontal nor vertical, but this
is seldom met with. Taking up first the case of shafts in a verti-
cal plane, the gear box may be cast in a single piece except for a
large hand-hole cover plate (Fig. 74) ; it may be made of a
shell, two end plates and a hand-hole cover, or it may be divided
horizontally through the centre of the primary shaft bearings.
Where the shafts are in a horizontal plane the box may be cast
in a single piece with a large cover plate (Fig. 75), or it may be

FIG. 74.— ONE-PIECE GEAR CASE WITH GEAR SHAFTS IN VERTICAL

PLANE.

in halves joined through the centres of the bearings (Fig. 76).
One-piece gear boxes with shafts in a vertical plane seem to be
preferred in connection with unit power plants, probably on
account of the symmetry of outline obtainable with them. An
approach to symmetry can also be obtained with a gear box
whose shafts are in a horizontal plane, by placing the shifter
bars on a level with the gear shafts and allowing about the same
space in the case for these bars, the selecting lever and the lock-
ing dogs as for the secondary shaft and gears.

The cases must accommodate not only the gears and shafts
but also the slider bars, and in most cases also the selecting
lever, though in some instances this is located outside the case.

SLIDING CHANGE SPEED GEARS.

JOL

117

FIG. 75.— ONE-PIECE GEAR CASE WITH GEAR SHAFTS IN HORI-
ZONTAL PLANE.

Usually there is a special lever house formed integral with or
secured to the cover plate or top half of the case, in which the
shifter lever moves, the shaft of the gear shifting hand lever
passing through the side walls of this housing.

The tendency among American designers is to use "functional"
gear cases; that is cases with an irregular projection on a plane
parallel to that of the gear shafts, whose walls at nearly every
point lie close to some part to be enclosed. European designers,
on the other hand, seem to be inclined toward box-like gear
cases whose longitudinal walls are parallel and whose section is

FIG. 76.— GEAR CASE DIVIDED THROUGH AXES OF SHAFTS.

118 SLIDING CHANGE SPEED GEARS.

such as to cover with a margin the end projection of the entire
gear. The functional case is less bulky and probably somewhat
stronger than the box-like case, but the latter requires a simpler
pattern and is easier to keep clean.

Wall and Joint Dimensions — Gear cases cast of aluminum
are made with walls from 3/16 to % inch thick. At the joint a
flange is run around the outside on each part which makes the
width from y2 to §^ inch, the flange being made *4 to y% inch
high and joined to the wall of the case with a liberal fillet. The
halves are held together by 5/16 inch bolts and nuts (^ inch in
extra large gears) spaced 3 to 4 inches apart. Substantial lugs
must be provided for these bolts, not less than y2 inch high.

Supporting Methods — Gear cases are supported on a sub-
frame, on cross-members of the main frame or on the main
frame itself, the latter arrangement being rare. Where a sub-
frame is employed for carrying the engine and gear box, the
axis of both usually lie from 1 to \y2 inches below the top or
supporting surface of the frame members, whereas if the parts
are supported on the main frame their axis lies from 4 to 7
inches below the top surface of the latter. The simplest method
of supporting the gear case is that by means of a sub-frame, and
this is generally used where the shafts are in a vertical plane.
Four short arms are then cast integral with the case, whose sup-
porting surface is from 1 to \l/2 inches above the axis of the
primary shaft, and the gear box is rested on top of the sub-
frame. Gear cases are also often provided with what is known
as a three-point support; that is, the case is cast with two arms
at one end, resting either on a sub-frame or on a cross-member
of the main frame, and at the other end is supported in a trun-
nion carried on a cross-member of the frame and surrounding
the primary bearing hub. This gives a true three-point support.
An approximation to a three-point support is obtained by using,
instead of the trunnion, two bolts passing through lugs on the
gear box on opposite sides of the primary bearing, and through
a cross-member of the frame.

When cross-members of the main frame are used for support-
ing the gear box, the latter is frequently hung or suspended from
them, s*o that it drops right out of the car when the supporting
bolts are removed. Gear cases divided through the centres of
the shafts may have the arms cast on either half. The arms are
often extended out from the sides of the box and are swung to
die front and rear respectively, so that the frame cross-members

SLIDING CHANGE SPEED GEARS. 119

will clear the box proper, endwise, thus making it possible to
place these supporting members lower.

Machining of gear cases involves little difficulty. If the case
is made in halves the first operation consists in milling the faces
of the joint, of the seat for the cover plate and of the supporting
arms. Next the holes of the joint are drilled in a multiple
spindle drill, and finally the bearing holes are bored out and
faced off. If the whole case is cast in a single piece, the machin-
ing of the joint is eliminated and considerable work is saved.
Divided gear cases are used only on the more expensive cars.

Lubrication of Gear Boxes — Gear boxes, as a rule, are par-
tially filled with non-fluid oil, but those having a parallel bearing
on the sliding shaft generally require a fluid lubricant. For easy
introduction of lubricant a hole is provided in the cover plate,
closed by means of a screw plug, and for washing out stale lubri-
cant with kerosene or gasoline a drain plug is provided at the
lowest point in the bottom of the case. Proper precautions must
be taken to prevent the oil or grease from working out through
the joints of the case and around the bearings. The ends of the
secondary shaft bearings are closed by caps, and stuffing boxes
or felt washers should be placed on the primary shaft where
it extends through the bearings. Paper gaskets are placed be-
tween the several parts of the case.

It has been found that when the gears in a gear box are
running under load, the temperature within the box is raised
considerably and the resulting air pressure tends to force the
lubricant out around the protruding shafts and through joints
in the box. To obviate this, gear boxes are now often provided
with breathers similar to those on engine crankcases.

Running-in of Change Gear — After ' a change gear is as-
sembled it is run from a line shaft for some time in order to
limber up its parts. While this running-in is taking place
the case must be well supplied with lubricant. It was formerly
customary to "lap" the gears in by running -them with the case
partly filled with a mixture of emery powder and oil, using
dummy bearings for the purpose, but this is no longer considered
necessary.

The reverse idler is carried on a plain bearing. A short
shaft is usually secured into a hub cast on the wall of the casing
and an integral support rising from the base of the latter, and
the idler is bushed with bronze and runs free on this shaft.
Large oil holes are drilled radially through this gear and large
oil grooves are cut in the shaft.

120 SLIDING CHANGE SPEED GEARS.

Efficiency of Operation — Comprehensive tests of the ef-
ficiency of a sliding pinion change gear were made some years
ago by the H. H. Franklin Mfg. Company, of Syracuse, N. Y.,
and were reported in THE HORSELESS AGE of February 12, 1908,
by G. Everett Quick. The gear tested was of the three speed
and reverse progressive sliding type. Its shafts were mounted
on radial ball bearings but the forward bearing of the sliding
shaft was hardened steel in bronze. All gears were cut with six
pitch teeth of % inch face and were made of ZVz per cent, nickel
steel, heat treated. The method of making the test was as
follows :

A direct current electric motor was provided with a counter-
shaft and a pulley thereon capable of serving as the pulley of a
brake dynamometer. The electric motor was then carefully
calibrated; that is, tests were made to accurately determine the
horse power output for any input in amperes, the voltage re-
maining constant. After a calibration curve had been plotted,
the electric motor was connected to the driven end of the change
gear and the brake dynamometer was transferred from the elec-
tric motor to the driving end of the change gear. When a run
was then made and the electric motor consumed a certain num-
ber of amperes, the power applied to the change gear could be
read off directly from the calibration curve of the electric motor
and the power delivered by the change gear could simultaneously
be determined by taking readings of the dynamometer. The
quotient of the power delivered by the change gear to the power
applied to it then gave the efficiency. The results obtained are
plotted in the curves Fig. 77. It will be seen that on the direct
drive the efficiency under the most favorable conditions of speed
and output is about 98 per cent. On the intermediate gear the
efficiency rises slightly above 95 per cent. On the low gear it
attains 94 per cent, and on the reverse about 87 per cent.

The change gear used in making the tests had been run about
1,000 miles in a demonstrating car, and the case was about half
full of heavy lubricating oil during the test A study of the
curves will show how a difference in the pitch line velocity of
the gear and different ratios affect the efficiency. Most previous
investigations of gearing efficiency were made at lower pitch
line velocities. The speeds indicated in the curves are those
at the driven end of the gear.

Positive Clutch Change Gears — A design of change gear
somewhat related to the sliding gear type is that in which all of

SLIDING CHANGE SPEED GEARS.

121

100
95

90
G5

100
95

fi.PJYT.

Direct

oJ)

tf.PJYT.

X.PJYT.
500 fi.P.M.

Speed

* 3 4 6 d /o J2
Worse Power In put

FIG. 77.— EFFICIENCY CURVES OF FRANKLIN GEAR Box

/6 J8

122

SLIDING CHANGE SPEED GEARS.

the gears remain constantly in mesh and the gears on the primary
shaft are normally free to turn thereon but may be fixed to the
shaft by means of positive clutches. These clutches, if of the
jaw type, are proportioned the same as those used for the direct
drive in sliding change gears. Difficulties due to meshing of the
teeth are avoided by the construction, but a gear of this type is
considerably longer than a sliding gear of the same capacity and
number of gear changes. Instead of jaw clutches, internal and
external gear clutches may be used. The gears on the primary
shaft must be held against endwise motion while the movable
clutch members must be free to slide on the primary shaft on
keys or squares. Two change gears of this type are illustrated
in Figs. 78 and 79.

FIG. 78. — COTTA POSITIVE CLUTCH CHANGE GEAR.

Silent Chain Change Gears — The recent quest for silent
operation has led to the adoption of silent chains instead of spur
gears in change gear boxes by a few European manufacturers.
A notable example of the use of these chains is found in the
gear boxes of London motor omnibuses. Fig. 80 illustrates this
change gear, which employs Coventry silent chains. As in the
case of constantly meshed gear sets, positive clutches of either
the jaw or internal-external gear type have to be used, and this
combined with the fact that for the transmission of a certain
amount of power the chain must be considerably wider than the
face of a spur gear, makes the gear set rather long. This ne-
cessitated the use of a pair of intermediate bearings in the design
here shown. Naturally, the shaft centre distance also has to be

SLIDING CHANGE SPEED GEARS.

123

greater than in a sliding gear, and this results in a rather bulky
gear box. However, the London experience with these gear
boxes has shown that not only do they operate noiselessly, but
the chains, notwithstanding their short length, have a very sat-
isfactory length of life, even under the very severe conditions of
omnibus service necessitating frequent stops and acceleration of
a 5 ton load. One advantage claimed for the chain gear box
over the spur type is that, whereas careless or unskilled operation
with the latter may result in stripping of the gears, necessitating
expensive repairs, with the former the worst that may happen is
treakage of the chain, and a new link may easily be inserted. In

FIG. 79. — Dux POSITIVE CLUTCH CHANGE GEAR.

view of the possibility of such breakages the gear box must be
designed with enough room at the bottom to contain the chain
without it touching the chain wheels, and there must also be a
liberal clearance all around the chain wheels.

Some of the points to be observed in the design of silent chain
change gears are as follows : The distance between shaft centres
must be sufficient to allow of joining up three or four different
drives without excessive slack in any of them. In the London
omnibus gear boxes chains of two different pitches (§^j and 24
inch) are used in order to solve the problem of substantially
equal centre distances without slack in the chains for the dif-

124

SLIDING CHANGE SPEED GEARS.

ferent drives. Pinions of less than 23 teeth should preferably
have an odd number of teeth, in order to insure the maximum
service from the faces of the teeth, and the number of links in
each chain should be even. The reverse motion in a silent
chain change speed gear is obtained in a very simple manner by
means of a pair of spur gears which are slid into and out of
mesh.

In conclusion it may be stated that silent chain gear boxes
owe their introduction to an order of the London police depart-
ment to compel the London General Omnibus Company to re-
duce the noise of its omnibuses (mainly due to worn gear
boxes) or to take them off the streets. As yet these change
gears are very little used on stock cars, but in view of the great
importance at present attached to silent operation of pleasure

FIG. 80. — SILENT CHAIN CHANGE GEAR.

cars, their more extensive introduction is within the realm of
possibility. In all silent chain gear boxes so far built all of the
chains run continuously, but it would not be particularly dif-
ficult to render all but one of the chains stationary when the
direct drive is in action.

In a sliding change gear helical gears may be used for the
constantly meshed pair of gears to reduce noise. These put ad-
ditional end thrust upon the bearings and it is well to keep the
angle of spiral moderate, say at 20 degrees, unless thrust bear-
ings are fitted.

CHAPTER IV.

THE PLANETARY CHANGE GEAR.

Planetary or epicyclic gear sets were quite extensively used in
automobile transmissions at one time, but have lost much of their
popularity. They are still being used, however, on low priced
cars of both the pleasure and commercial types. This gear set is
much cheaper to manufacture than a sliding gear set, and its
operation calls for less skill on the part of the driver. Being
used almost exclusively on low priced cars, such refinements in
construction as hardened alloy steel gears and radial ball bear-
ings are not employed in planetary gears. Generally these gears
are designed to give only two forward speeds and one reverse.
It is possible to obtain three forward speeds and one reverse,
and the Cadillac Motor Car Co. produced a car with a three
speed and reverse planetary gear set for several seasons, but the
addition of a third speed introduces considerable complication
and entails great frictional loss, and two forward speeds is gen-
erally considered the practical limit with this type of gear.

Principle of the Internal Gear Type — There are two gen-
eral types of planetary gears, viz., those comprising internal gears
in their make-up and those consisting solely of spur gears, the
latter being sometimes referred to as the "all-spur" type. The
principle of the former is illustrated in Fig. 81. A is a driving
pinion mounted either upon an extension of the engine crank-
shaft or upon a shaft connected to same, which we will call the
driving shaft. This gear is in mesh with two, three or four equal
sized planetary pinions B, evenly distributed over the circumfer-
ence of pinion A. Pinions B are supported upon short shafts
secured into the pinion carrier C, which may be a disc, drum or
spider having a bearing upon the driving shaft. Planetary pin-
ions B B also mesh with the internal gear D, which latter is
also supported by having a bearing on the driving shaft. Two
such planetary sets as illustrated in Fig. 81 are required for a
two speed forward and reverse gear set.

125

126

THE PLANETARY CHANGE GEAR.

The low speed forward is obtained in the following manner :
Internal gear D can be held from rotating by applying a band
brake to its circumference. If pinion A is then rotated by the
motor in a clockwise direction, as indicated by the arrow, pinions
B will thereby be rotated around their respective axes in a
counter-clockwise direction, and since internal gear D is held sta-
tionary by its brake, they will roll on it and carry pinion carrier
C around in a clockwise direction ; that is, in the same direction
as the driving shaft, but at a lower speed. Pinion carrier C is
in permanent driving connection with the driven shaft.

For the high speed forward the driven shaft of the gear is

FIG. 81. — INTERNAL GEAR PLANETARY COMBINATION.

directly connected to the driving shaft by means of a friction
clutch forming part of the planetary gear set. Hence, by holding
internal gear D stationary, motion will be imparted to the driven
shaft in the same direction as when it is direct connected to the
engine shaft by the high speed clutch, but it is revolved at a
lower speed.

Calculation of Speed Ratios— Let a be the number of teeth
in pinion A, and b the number of teeth in each of pinions B.
Then the number of teeth in internal gear D is evidently a + 2b.
We found that the planetary pinions, together with the pinion

THE PLANETARY CHANGE GEAR. 127

carrier, would rotate right-handedly around the centre of the
driving shaft. Now, suppose these pinions to make one complete
revolution around the driving shaft. By rolling on the internal
gear D they will be revolved around their own axes the number
of times their number of teeth is contained in the number of
teeth of internal gear D, viz. :

"-+; ............................................ (18)

b b

However, this number of revolutions about their own axes
represents only a part of the motion of planetary pinions B; they
have also at the same time made a complete revolution about the
axis of the driving shaft, and both these motions must have been
imparted to them by driving pinion A. By calculating the motion
of the driving pinion required to produce each of these motions
in the planetary pinions, and then adding the two motions, we
find the number of revolutions of the driving pinion necessary
to produce one revolution of the pinion carrier C, and this, of
course, is equal to the ratio of reduction.

The angular motion of the driving pinion to produce the first
motion of the planetary pinions — that around their own axes —
may be found by multiplying the number of revolutions of the

planetaries / — + 2) by the ratio of the number of teeth in

the planetaries to that in the driving pinion, viz., — , which gives

a \b / a

To produce the planetary motion of one complete revolution
about the driving shaft axis it is obvious that the driving pinion
must make one revolution in the same direction as that necessary
to produce the first motion of the planetary pinions. Hence the
total motion of the driving pinion will be

(29)

which is the expression for the low gear reduction with this type
of planetary gear.

Studying this expression, we see that under no conditions can
the ratio of reduction be as small as 2. When the planetary pin-
ions have the same number of teeth as the driving pinion, the
ratio is 4, and when they have half the number of teeth (as in
Fig. 81), the ratio is 3.

For the reverse motion an arrangement of gearing similar to

128 THE PLANETARY CHANGE GEAR.

that shown in Fig. 81 is used. However, in this case the pinion
carrier C is held from rotating, being provided with a brake drum
to which a brake band can be applied. If, then, the driving pinion
A is rotated in a clockwise direction, the planetary pinions B
will turn in a counter-clockwise direction around their axes, and
the internal gear D will be rotated by them in a counter-clock-
wise direction around the driving shaft axis. In this case internal
gear D is in permanent driving connection with the driven shaft
of the gear, which latter is therefore rotated in the opposite direc-
tion to the driving shaft. The ratio of reduction is merely the

FIG. 82.— INTERNAL GEAR PLANETARY COMBINATION WITH
DOUBLE PLANETARY SETS.

ratio between the number of teeth in internal gear D and driving
pinion A; that is, using the same designations as in the fore-
going, the reverse speed reduction ratio for this type of plane-
tary gear is

a + 2b 2b

= _ + 1 (30)

a a

In a somewhat modified design, illustrated in Fig. 82, the plan-
etary pinions are made in sets of two of unequal pitch diameter
placed side by side and rigidly connected to each other or formed
integral, the smaller pinion B being in mesh with driving pinion

THE PLANETARY CHANGE GEAR. 129

A, and the larger one, B', with the internal gear D. Calling the
number of teeth in the smaller planetary pinion b and the num-
ber of teeth in the larger one b', the reduction ratio for this case
when internal gear D is held stationary may be calculated as
follows :

The number of teeth in the internal gear is now a + b+b', and
the number of revolutions of the planetanes around their axes
corresponding to one revolution around the driving shaft axis
will be

a + b + b'

In order to produce this motion the driving pinion must make
b (a + b + b'\ __ b I \

a ( ---- y -- ) ~ a^ ( a + b + b ) revolutions.
To this must again be added one revolution to produce the plane-
tary motion of the planetary pinions, which gives for the low
speed reduction ratio for this type of gear

From this equation it will be seen that the reduction ratio in-
creases with b and increases as a and b' decrease.

For the reverse motion the pinion carrier is held stationary
by means of a brake band. In this case, denoting the angular
velocity of internal gear D by unity, the angular velocity of the
two planetary pinions will be

a-\-b + b'

b'
and the angular velocity of the driving pinion is found by mul-

tiplying this by the factor — which gives

+ +., ....................... (32)

abf \ I b' abf a

When several planetary pinions are used in an internal type
of planetary gear, the numbers of teeth in the driving pinion and
in the planetary pinions must bear certain relations ^to each other,
else the gears cannot be assembled. Let us take the case of a
planetary combination with three pinions. The number of teeth a
may be divisible by 3, a — I may be divisible by 3, and a + 1 may
be divisible by 3. Hence there are three different cases which
must be investigated separately. We will assume that a — i is
divisible by 3. Then we may write

a — 3 x + i
c — a -h zb

130

THE PLANETARY CHANGE GEAR.

—b H pitch

Referring to Fig. 83, if a driving pinion tooth centre coincides
with the line connecting the axes of the driving pinion and the
top planetary, then a driving pinion tooth centre is at a dis-
tance of Yz circular pitch from the line connecting the driving
pinion axis with the axis of the right hand planetary pinioa

FIG. 83.

When the planetaries have an even number of- teeth, two of their
tooth centres are opposite. Hence, since a tooth centre on the
driving gear is Yz pitch ahead of the line joining the driving
pinion axis and the right hand planetary axis, a tooth centre of
the internal gear will be Yz pitch beyond this line produced.
Similarly, when the planetaries have an odd number of teeth, a

THE PLANETARY CHANGE GEAR. 131

space will be directly opposite a tooth, hence a space centre of
the internal gear will be on the line connecting the axis of the
driving pinion to the axis of the top planetary produced, and
another space centre of the internal gear ^ pitch beyond the line
connecting the axis of the driving pinion to the axis of the right

c 1

hand planetary produced. Therefore, in either case — + — is an

3 3

integer which we may denote by n. Substituting the value of —

3
we have

2b 1 1
* + — + — + — = «.

333
Multiplying both sides by 2

4b 4
2x + — + — = 2»

3 3
But since x and b are integers we may write

b 4
_ + _ = ni

3 3
Multiplying each side by 3, we have

b + 4 = 3 th.
Subtracting 3 from each side

b + 1 = 3 (m — 1)

In other words, the number of teeth in the planetaries must be
such that when 1 is added to it, it is divisible by 3.

The following compilation covers every possible case with 2, 3
and 4 planetary pinions :

TWO PLANETARIES.

Both the driving pinion and the planetaries may have either an
even or an odd number of teeth.

THREE PLANETARIES.

If a is divisible by 3, b must also be divisible by 3.

If a — 1 is divisible by 3, b + 1 must be divisible by 3.

If a + 1 is divisible by 3, then b — 1 must be divisible by 3.

FOUR PLANETARIES.

If a is even, b must be even.

If a is odd, b must be odd.

The object in using more than one set of planetary pinions
obviously is to divide the work between these pinions and to re-
duce the strain on the teeth of the other gears.

Principle of the All-Spur Type— One form of the "all-
spur" type of planetary gear is illustrated in diagram in Fig. 84.

132

THE PLANETARY CHANGE GEAR

It consists of three adjacent, independent gears A B D on
the driving shaft and three corresponding pinions A1 B1 D1
forming a single rigid planetary unit. Gear A is the driving
and gear D the driven member. For the reverse motion, gear
B, which is mounted free on the driving shaft, is held from
rotation. Assume that the pinion carrier rotates left handedly,
causing pinion B1 to roll on B. For one left hand revolution

FIG. 84.— DIAGRAMS OF "ALL SPUR" PLANETARY SET.

of the pinion carrier, A* B1 D1 make — left hand revolutions

D1
around their own axis. This results in A making

6 01

— X — right hand revolutions

b1 a

around its axis, which, combined with the one left hand revo-
lution due to the motion of the pinion carrier, gives a total
motion of A of

THE PLANETARY CHANGE GEAR. 133

a1 b

1 right hand revolution

which expression gives a positive value if a^ft1. Similarly,
the motion of the planetary pinions around their own axis
causes D to make

— X — right hand revolutions

ft1 d

which combined with the one left hand revolution due to the
motion of the pinion carrier gives

1 — left hand revolutions

for D. If this expression gives a positive value, D will revolve
in the reverse direction, and this is the case if d1<b1.
The reduction ratio then is

a1 ft a1 ft — a ft1
1

a ft1 a ft1

b d1 ft1 d ~~~ b d1

ft1 a" ft1 a"

ft1 d (a1 6 — a b1) d (a1 b — a ft1)

As the sum of any pair of mating teeth must be the same,
calling this sum x we have

a1 = x — a

d1 = x — d

Substituting in the above equation for the reduction ratio
we have

d[b (a? — a) — a (a?— ft)]

r =

a[d (x — ft) — ft (a? — a")]
d (6 x — aft — ax •

a (dx — db —
d (ft — a)

a (d — b)

Hence the reverse reduction ratio is dependent only on the
relative number of teeth of the gears and independent of the
planetary pinions. It will be seen at once that this reduction
ratio is positive if ft>a and

134

THE PLANETARY CHANGE GEAR.

Another possible combination in which only spur gears are
used is shown in Fig. 85. A is the driving gear, which meshes
with planetary pinion B. An intermediate pinion B1 meshes
with both B and the driven gear D. If pinion carrier C is held
from rotation, driven gear D will revolve in the reverse direc-
tion to that in which driving gear A rotates. The variety of
gear arrangements possible is very large but by means of the
rules explained in the foregoing the direction of rotation and
gear ratio of any combination can readily be determined.

FIG. 85. — ALL-SPUR PLANETARY WITH DOUBLE PLANETARY
PINIONS.

Assembly of Internal Gear Type — A sectional view of an
internal gear type of planetary gear is shown in Fig. 86. A is
the driving shaft, which has secured to it the low speed driving
pinion B and the reverse driving pinion C. Pinion B meshes
with two planetary pinions D, which latter in turn mesh with the
internal gear E. The rim of the latter gear also serves as a
brake drum to which a brake band F may be applied, so as to
hold the gear stationary. The planetary pinions D will then re-
volve around the axis of the driving shaft at a low speed, as
already explained, and will carry with them the pinion carrier G,
which latter is keyed to the hollow driven shaft H.

For the reverse, the brake band / is applied to brake drum J,
which serves also as a pinion carrier for the reverse planetary

THE PLANETARY CHANGE GEAR.

135

pinions K. The latter mesh both with the reverse driving pinion
C and the reverse internal gear L. Internal gear L and pinion
carrier G are rigidly connected together, not only by pinion pins
M, as shown in the drawing, but also by bolts between the pin-
ions. Hence, when drum / is held in position by brake band I,
reverse pinion C will revolve internal gear L through the inter-
mediary of pinions K in the reverse (left-handed) direction, and
gear L will communicate this reverse motion through the inter-
mediary of pinion carrier G to driven shaft H.
For the direct drive the multiple disc clutch O is engaged by

FIG. 86. — ASSEMBLY OF INTERNAL GEAR TYPE OF PLANETARY
GEAR SET.

pushing sliding cone Q to the left under the clutch dogs S. One
set of discs of the clutch is driven by means of studs extending
from the web of internal gear E, and the other set drives through
keys of the clutch hub P, which is keyed to the driven shaft H.
When the clutch is engaged internal gear E and pinion carrier G
are locked together, hence planetary pinions D cannot rotate
around their pins M, and driving pinion B drives directly through
pinions D, pinion carrier G and shaft H. The high speed clutch

^ 136 THE PLANETARY CHANGE GEAR.

can be closely adjusted by turning screw-threaded collar R on
clutch hub P. When the clutch is engaged the entire gear re-
volves together as a unit, none of its pinions working.

It is interesting to determine the speeds of the different parts
while the low gear is in operation. We will assume that A re-
volves right-handedly at 1,000 r.p.m., that B has 24 teeth ; D, 16 ;
C, 18, and K, 18. The low gear carrier and driven shaft will
then revolve (equation 29) at
1,000

Fx"l6 ' r'P'm'

+ 2

24
Planetary pinions D will revolve on their pins at

724 \

I — + 2 1300 = 1,050 r.p.m. (equation 28)

\16 /

One set of clutch discs will be stationary and the other set will
revolve at the speed of the driven shaft, viz., 300 r.p.m. In-
ternal gear L will revolve right-handedly at 300 r.p.m. and
pinion C at 1,000 r.p.m. Hence pinion C revolves at 700 r.p.m.
relative to internal gear L, and drum / will be revolved right-
handedly at

. 700

2X18 ^'^

1-2

Planetary pinions K will rotate on their pins at
3 X (300 — • 175) = 375 r.p.m.
All of these speeds are quite low.

All- Spur Planetary Assembly — Fig. 87 shows a longitudinal
sectional view of an all-spur type of planetary gear. A is the
driving shaft which carries the driving pinion B, meshing with
planetary pinions C. The latter form part of sets of three pin-
ions, which are either made integral or keyed together. D is the
low speed planetary pinion meshing with low speed gear E, which
latter is secured to driven shaft F. By applying brake band G to
the combined pinion carrier and brake drum H, the planetary pin-
ions are held stationary in space and act like a back gear.
Pinion B, rotating right-handedly, turns pinions C and D on their
pin left-handedly, and pinion D turns pinion E and driven shaft
F right-handedly; that is, in the same direction as driving pinion
B. For the reverse, brake band / is applied to brake drum /,
-which has the reversing pinion K keyed to it. Gear K being thus
held stationary, when pinion B is rotated by the engine, planetary

THE PLANETARY CHANGE GEAR.

137

pinion L is forced to roll on K in planetary fashion in a left-
handed direction, carrying the pinion pin M and pinion carrier
H with it.

The direct drive is obtained by engaging the high speed clutch
N, which locks the reversing gear K to driving shaft A, and
since two unequal gears (B and K) are now secured to shaft A,
the planetary pinions are locked against axial motion and the
whole gear revolves as a unit.

FIG. 87.— ASSEMBLY OF "ALL-SPUR" TYPE OF PLANETARY
GEAR SET.

In an "all-spur" combination, instead of applying the power
through one of the central pinions and transmitting it through the
pinion carrier, it may be applied through the latter and trans-
mitted through one of the central pinions. The Ford change
gear, illustrated in Fig. 88, is of this type. In this case the fly-
wheel rim A serves as the pinion carrier and driving member,

138

THE PLANETARY CHANGE GEAR.

having lateral studs secured into it which carry triple planetary
pinions. Gear B is the driven member, being keyed to the hub of
clutch drum C, which in turn is secured to driven shaft D. By
applying a brake band to drum E, gear F is held stationary, pin-
ion G rolls on it, and the smaller pinion H causes gear B to turn
slowly in the same direction as pinion carrier A. By applying a
brake band to drum / gear / is held stationary, pinion K rolls on
it, and the larger pinion H turns gear B slowly in the reverse
direction. For the high gear or the direct drive the friction clutch

, — FORD PLANETARY GEAR SET.

locks the clutch drum C to the engine tailshaft, and the gear
rotates as a unit.

Gear Stresses and Bearing Pressures — The Pressure on
the pitch line of the driving pinion can be calculated from the
engine dimensions by the method already explained. If there are
several planetary pinions in mesh with the driving pinion, then
the total pressure on the pitch circle of the driving pinion must
be divided by the number of these planetary pinions in order to
get the pressure on one tooth. The necessary width of face of the
teeth can then be calculated by the formula for the strength of

THE PLANETARY CHANGE GEAR. 139

gear teeth given in the previous chapter, allowing a stress in
the teeth (of machinery steel gears) at full engine load of about

8,000 pounds per square inch for 1,400 feet per minute

10,000 pounds per square inch for 1,200 feet per minute

12,000 pounds per square inch for 1,000 feet per minute

14,000 pounds per square inch for 800 feet per minute

pitch line velocity corresponding to 1,000 feet per minute piston
speed. For nickel steel gears the stress in the teeth can be made
20 per cent, greater. In this connection it should be pointed out
that it is customary to use ten pitch gears in planetary gear sets
for very small powers, say up to 15 horse power, and eight pitch
gears for gear sets of from 15 to 30 horse power. In the few
instances where planetary gears have been used for larger powers
six pitch teeth have been used.

Now, let it be required to calculate the dimensions of a
planetary gear for a double cylinder engine of 4^ inch bore by
4 inch stroke. The calculations are somewhat different for the
internal type of planetary gear and the all-spur type, and we will
carry the calculation through, first for the one and then for the
other. As far as the strength of gears and the bearing surface
required for the planetaries are concerned, the stresses and
pressures during low gear operation, of course, are much more
important than the stresses and pressures corresponding to the
reverse motion, for the reason that the reverse is never used con-
tinuously for any length of time. Suppose that a gear reduction
of 3 is desired for the low speed forward.

The normal-speed torque of our motor is
2 X 4 X 4^2 X 65

= 55 pounds-feet.

192

We will first carry the calculation through for the internal type
of planetary gear. In order that we may get the desired reduc-
tion ratio the driving pinion and planetary pinions must be made
with such numbers of teeth, a and b, respectively, that

2JL

hence

The smallest practical number of teeth in a pinion is 12, and it
is well to use a few more. We will make b = 14 and a = 28.
Also, we will use 8 pitch standard 14J4 degree involute teeth.
Hence the pitch diameter of the driving pinion is Z1A inches and

140 THE PLANETARY CHANGE GEAR.

the pitch radius 1^4 inches. Since the torque that must be trans-
mitted by this pinion is 55 pounds-feet, the pitch line pressure is

55 X 12

- = 377 pounds.

134

We will assume that two oppositely located planetary pinions
are used, so this pressure is exerted by two teeth of the driving
pinion, and the pressure of each tooth is

377 ==I88. 5 pounds.

At 1,000 feet piston speed per minute the 4 inch stroke motor
turns at

1,000 X 12

2X4 =I'5°° r.t-™->
and the pitch line velocity of the driving pinion is

1,500X3-5X3-14
~~

Hence we may figure on a stress of 8,000 pounds per square inch
in the teeth. Then, according to Lewis' equation,

188.5 = 8,000X0.4X^X0.072,
and

/= - J^5 -- = 0.81 - say, 1L inch.
8,000 X 0.4 Xo.oy2 16

The tangential force P on one of the planetary pinions we
found to be 188.5 pounds. As indicated in Fig. 89, this force is
exerted by the driving pinion on the planetary pinion, and there
is an equal reaction of the internal gear on the opposite side of
the planetary pinion. Hence the pressure on the bearing of the
planetary pinion is

188.5 4- 188.5 = 377 pounds.

In a gear of the internal planetary type it is difficult to provide
large enough bearing surfaces, and the unit pressure on the pinion
pins is usually in the neighborhood of 600 pounds per square
inch. This unit pressure in our case calls for a bearing surface of

377 -,

g^ = Y& square inch.

If we make our pin $/& inch in diameter it must have a length
of I inch, or slightly more than the face of the gear.

It is customary to make the pinions of the reverse combination
of the same width of face as the pinions of the low gear combina-
tion.

A reduction of 3 to I is practically the lowest obtainable with

THE PLANETARY CHANGE GEAR

141

this type of gear, because for lower reductions the planetary
pinions become very small and their rotative speeds excessively
high. On the other hand, with only two speeds forward the low
speed ratio is generally wanted comparatively small, between
2 anci 3, so that the step from high to low speed may not be
too great.

Calculation of "All Spur" Type— With the usual "all spur"
type we obtain our low forward speed by means of a back
gear. The low gear ratio should be approximately 3:1. If
two sets of planetary pinions are to be used then each of the
central gears must have an even number of teeth. Gear com-
binations which give the required reduction ratios can be

FIG. 89. — TANGENTIAL AND

BEARING PRESSURES IN

INTERNAL GEAR TYPE

OF PLANETARY.

FIG. 90.— TOOTH PRESSURES IN

ALL-SPUR TYPE OF

PLANETARY.

found only by trial. In selecting combinations it must be re-
membered that d must be greater than & and & greater than a
and that the sums of the teeth of all mating pairs must be
alike. A suitable combination is as follows:

a = 16 & = 28 d = 32

a1 = 28

&1 = 16

d1 = 12

Since the low gear ratio is equal to a1 &/ a b1 we get for it

28 X 28

= 3.06

16 X 16

142 THE PLANETARY CHANGE GEAR.

The expression for the reverse ratio is
d (b — a)

a(d — b)
hence its value is

32 (28 — 16)

= 6

16 (32 — 28)

This reverse ratio is somewhat greater than usually em-
ployed, but a great reduction seems to be desirable as it in-
sures safety in backing. With the usual sliding gear transmis-
sion the reverse gear ratio is always made as great as possible.
The pitch radius of the 16 tooth 8 pitch driving pinion is 1 inch,
hence the pitch line pressure is
55 X 12
= 660 pounds.

Of this one-half, or 330 pounds, comes on one tooth. The pitch
line velocity is

1,500 X 2 X 3.14

= 785 ft. p.m.,

hence we may allow a tooth stress of 14,000 pounds per square
inch. Inserting in the Lewis formula we have

330 = 14,000 X 0.4 X / X 0.077
and

330

/ = = 0.755, say ft inch.

14,000 X 0.4 X 0.077

In this case the low speed motion is not transmitted through the
gear carrier, and the whole force of the drive does not come on
the pinion pin. In Fig. 89 are shown the pressure of the driving
pinion tooth on the planetary pinion tooth and the reaction of the
stationary gear tooth on the tooth of the second planetary pinion.
The tangential pressure on the driving gear we found to be
660 pounds. The tooth reaction between the driving pinion and
the first planetary is

330

= 350 pounds.

cos 20°

The tooth reaction between the second planetary pinion and the
stationary pinion is

— X 350 = 612 pounds.

These two pressures make an angle of 140 degrees with each
other, and their resultant is found graphically to be 410 pounds.

THE PLANETARY CHANGE GEAR. 143

In gears of this type the unit pressure can be made about 200
pounds per square inch, hence we require
410

= 2.05 square inches

200

bearing surface. Allowing a distance of % inch between pinions,
the total length of the pin bearing will be 2% inches, and the
diameter of the pin should be

2.05 13

= 0.82. say, — inch.

2.5 16

Constructional Details — Owing to the fact that in an all-
spur planetary only a short key could be used far securing the
driving pinion to its shaft, it is advisable to forge this pinion
integral with the shaft so as to avoid possible trouble from a
loose key. In the older designs of planetary gears the planetary
pinions revolved on pins supported at one end only. This con-
struction leaves much to be desired, for the reason that it permits
considerable flexure of the pinion pins and leads to rapid wear
of the pinion bushings, and consequent noisy operation. A spe-
cially weak point often found in connection with this construc-
tion was the method of fastening the pin to the pinion carrier.
The pin was somewhat reduced in diameter at one end, and the
reduced portion was threaded to screw into the pinion carrier.
This makes the section of the pin weakest at the very point where
the maximum stress occurs. It is much preferable to turn the
pin with a small flange to provide a shoulder for the joint, and
have the diameter at the joint the same as inside the pinion.
However, pinion pins supported at both ends are to be recom-
mended in every case, because of the more rigid support they
give to the pinions. In determining the diameter of the pins it is
advisable to calculate the stresses occurring in them under full
load, and the deflection produced thereby.

Brakes — In the design of the brake for holding rotary parts
stationary for the low speed and the reverse, efforts should be
made to keep down the radial load on the bearing of the brake
drum due to the brake pull, so as to reduce the wear of that
bearing. It is quite possible to entirely eliminate this radial load
by dividing the brake bands into halves, with the two points of
anchorage located diametrically opposite on the brake circle, and
dividing the brake pull equally between the two bands. How-
ever, owing to the slightly greater complication in the operating
mechanism this is never done in practice. One manufacturer
uses disc brakes instead of band brakes, thereby entirely eliminat-
ing radial brake load.

144

THE PLANETARY CHANGE GEAR.

Since in a shaft driven car the axis of the gear lies in the
direction of the length of the car and the brake operating shaft
transverse thereto, the brake bands are usually operated by
means of face cams, as illustrated in Fig. 91. The brake band
is made of steel and lined with leather or fibre. Lugs are riveted
to its ends, which are drilled to pass over the operating shaft.

FIG. 91. — BRAKE CONSTRUCTION FOR PLANETARY GEAR.

These lugs are provided with cam faces, and corresponding face
cams are secured to the shaft, so that when the latter is rotated
in a particular direction the ends of the band are forced together
and the band is contracted upon the drum. A coiled spring be-
tween the lugs of the band releases the latter when the driver
removes his foot from the pedal by means of which the particu-

THE PLANETARY CHANGE GEAR.

145

lar speed is engaged. Any wear of the friction lining can be
compensated by adjustment of the face cams on their shaft.

One common fault in planetary gears is that the brake bands
are not fully released but drag when not in use. To prevent this
the ends of the band should be allowed considerable motion, and
an adjustable set screw should be provided at a point opposite
the ends of the band to act as a stop and limit the release motion
at that point.

In some planetary gears the brakes are exposed, but it is cer-
tainly preferable to enclose the entire gear inclusive of the brakes.

FIG. 92. — GEAR AND BEARING PRESSURES IN AN ALL-SPUR PLAN-
ETARY SET.

Efficiency of Operation — Although, so far as the author has
been able to learn, no accurate efficiency tests of planetary change
speed gears have ever been made, this type of gear has a poor
reputation in respect to efficiency. Of course the speeds which
involve no planetary motion, such as the low speed in a simple
"all-spur" planetary gear (Fig. 87), should be as efficient as the
corresponding gear in a sliding gear set, provided mechanical de-
sign and workmanship are the same. But the efficiency of such

146 THE PLANETARY CHANGE GEAR.

a combination as that of the reverse in an all-spur combination
is quite low, as may easily be shown. The losses are due partly
to tooth friction and partly to bearing friction. Such a combina-
tion is represented diagrammatically in Fig. 92, and in order to
somewhat exaggerate the conditions resulting in inefficient opera-
tion, the two planetary pinions are shown to be of nearly equal
pitch diameter. The gear tooth pressures are drawn in making
an angle of 20 degrees with the plane of the gear axes, 15 de-
grees of which represent the tooth flank angle and 5 degrees the
friction angle. We found in the previous chapter that the load
on the bearing of a spur gear is equal in magnitude and direction
to the load on the gear teeth, and since the two planetary pinions
have a common bearing, we can transfer the tooth pressures to
the bearing axis. This has been done in Fig. 92, A B representing
the bearing load due to the pressure of the driving pinion and
A C the bearing load due to the reaction of the stationary gear.
A D is the resultant of these two and represents the actual load
on the pinion pin. It is hardly necessary to emphasize the fact
that a pressure in the direction A D applied to the pinion pin
does not act very advantageously in turning the pin around
centre O. This pressure can be resolved into two components, a
radial one A F and a tangential one A E. The latter component
represents useful turning force impressed upon the pinion carrier
at the radius of the pinion pin axis with the driving shaft axis
as a centre. The useful work is proportional to this force or
pressure, which, it will be seen, is quite small, while the gear
losses are proportional to the much greater forces A B and A C
and the bearing loss in the pinion pin bearings is proportional to
A D, also much greater than A E. In ordinary spur gearing the
power transmitted is directly proportional to the tooth pressure,
as are all of the losses. In the above planetary combination the
tangential (useful) component of the pinion pin load becomes
zero as the two planetary pinions become equal.

The chief advantage of the planetary gear set is that on the
direct drive it consumes absolutely no power, having no bearings
then in operation, and its weight, which revolves, adds to the
flywheel effect, tending to steady the engine motion. This ad-
vantage can be made the most of on cars provided with relatively
powerful engines, making it possible to drive on the high gear
under all ordinary road conditions, so that the low gear is needed
only in starting and on extremely steep hills.

CHAPTER V.

THE FRICTION DISC DRIVE.

Types of Friction Drives—Undoubtedly the simplest of all
variable transmission mechanisms for gasoline automobiles is the
so called friction drive. There are several types of frictional
transmission mechanisms, and they may be roughly classified as
follows : Disc and wheel, multiple discs and wheels, bevel wheels,
plain wheels and grooved wheels. The first class mentioned is
the only one extensively used. This change speed mechanism
(A, Fig. 93) consists of a disc A carried on an extension of the
engine shaft, and of a mill board or fibre-faced friction wheel B,
which can be slid along a cross shaft and brought into frictional
engagement with the disc A at a greater or smaller distance from
its centre. The ratio between the speeds of revolution of wheel
and disc is substantially equal to the reciprocal of the ratio be-
tween the diameter of the wheel and the diameter of the mean
contact circle on the disc. By moving the wheel from the centre
of the disc outward the speed of the wheel can be changed from
nothing to the maximum by infinitesimal increments, and by
sliding the wheel over to the opposite side of the disc its direc-
tion of motion may be reversed. Before the wheel is slid in the
direction of its axis it must be disengaged from the disc, which
is accomplished either by moving the bearings of the cross shaft in
planes perpendicular to their axis or by moving the bearing directly
behind the disc in the direction of its axis. After the wheel has
been slid to the desired position, wheel and disc are again brought
into frictional engagement by the reverse operation. This so
called friction disc drive, therefore, serves not only as a speed
changing and reversing gear, but also performs the function of a
friction clutch. It possesses a number of advantages, viz., ex-
treme simplicity, low cost of construction and maintenance, abso-
lutely silent operation, and the fact that it furnishes an unlimited
number of speed gradations. Among the weak points of this
transmission are the unavoidable loss of power due to slipping at

147

148 THE FRICTION DISC DRIVE.

the contact surfaces and the fact that the frictional conditions
are impaired by oil, mud, etc., on the frictional surfaces. Owing
to the necessary bulk of this mechanism it is impossible to prop-
erly enclose it.

Before taking up the technical discussion of this drive it will
be well to briefly describe some of the numerous varieties of
friction transmissions used in automobile work. Most of the
drives described in the following have been used only in single
cases, ana none can be regarded as in common use in the industry.

B in Fig. 93 illustrates a drive consisting of two oppositely
located friction discs and two friction wheels between them.
Each wheel is in frictional contact with one disc only, and each
has a separate drive to one of the rear road wheels. It will be
noted that one of the cross shafts is set slightly farther to the
rear than the other, so that each wheel may contact with one
disc and clear the other. As compared with the single disc drive
the construction has the advantage — purchased at the cost of
some complication — that the over-all dimensions for a certain
transmission capacity are less and that the need of a differential
gear is dispensed with. At least no differential is used with this
construction, although it would seem that the certainty of steering
might be somewhat affected by its absence.

At C is shown the Seitz design of friction drive, which com-
prises a single disc and two pairs of friction wheels, oiie pair on
either side of the disc. Each friction wheel has its individual
shaft, and by means of a suitable linkage the bearings of the
shafts to one side of the centre of the disc can be moved together
so the wheels on them will pinch the disc, thus establishing fric-
tional driving connection with it. One pair of wheels serves for
the forward drive and the other for the reverse, the latter pair
being fixed on their respective shafts, thus giving only a single
reverse reduction. Power is transmitted to a transverse jack-
shaft by means of roller chains which run over sprockets on each
of the two friction wheel shafts corresponding to one direction
of motion. The chief advantage of this construction is that there
is no end thrust on the disc and its shaft, hence no provision
need be made to take it up on thrust bearings, and there is no
chance of the frame being distorted by the "off centre" pressure
on the disc.

The arrangement illustrated at D combines a direct drive for
yuse under all ordinary road conditions. For slow speed and re-
Verse operation the power is transmitted from the driving disc A
(which may be the engine flywheel) to the two fraction wheels

THE FRICTION DISC DRIVE.

149

BB, and thence to the friction whqel C, which is slidably mounted
on the driven shaft. Wheel C is shown in the position corre-
sponding to the reverse motion. Pushing it toward the driving
disc past the centres of wheels BB gives the forward motion, the
speed gradually increasing until wheel C is close to the driving
disc A. Then the side wheels BB are moved apart out of contact
with wheel C, and the forward conical projection of the latter is
forced into a conical recess formed in the flywheel rim, these

FIG. 93. — TYPES OF CONTINUOUSLY VARIABLE FRICTION DRIVES.

parts acting as a cone clutch and connecting the driven to the
driving shaft for the direct drive. This obviates the frictional
loss inherent in the operation of the disc and wheel and also
makes the drive positive.

In all of the friction drives so far described the transmission
ratio is continuously variable. However, there are other fric-
tional drives which do not possess this feature of an "infinite

150

THE FRICTION DISC DRIVE

number of gear changes," giving generally only two forward
speeds.

These change gears are used on account of their simple con-
struction and quiet operation. Among these is the friction cone
type, shown at A in Fig. 94.^ This drive comprises two driven
members C with double conical friction surfaces and three driv-
ing cones A, B and R, all mounted slidably on a feathered driv-
ing shaft. A gives the high speed forward, B the low speed for-
ward, and R the reverse, engagement being effected by moving
the driving cones axially into contact with the driven cones.

Counterparts of sliding and planetary change speed gears con-
taining friction wheels instead of gear pinions have also been

\ R

FIG. 94. — TYPES OF STEPPED FRICTION DRIVES.

used, but have been discarded. B, Fig. 94, illustrates the grooved
friction wheel drive used by Charles E. Duryea on light vehicles.
Less normal pressure between wheels is required when the
frictional surfaces are formed with V grooves than when they
are smooth, but to balance this there is somewhat greater loss
at these surfaces.

Materials— The disc of a friction disc drive always has a
metallic surface. Aluminum is claimed to possess superior fric-
tional qualities and is used by one concern manufacturing fric-
tion driven automobiles, which has a patent on its use for this
purpose. However, cast iron is also successfully used. The
•wheels are always faced with some kind of fibrous material
which is more or less compressible and has a relatively high
coefficient of friction in contact with metal. Mill board is

THE FRICTION DISC DRIVE.

151

commonly employed, and is sometimes indurated with a tarry
substance to improve its frictional qualities. The friction co-
efficient between cast iron and mill board under ordinary con-
ditions varies between 0.25 and 0.30. The facing material is
cut into rings which are assembled between steel flanges.

Theoretical Efficiency — It is obvious that the motion of the
wheel rim on the face of the disc cannot be a pure rolling motion,
since both sides of the wheel have the same circumference,
whereas the outer circumference of the contact ring on the disc
is considerably longer than the inner circumference. This con-
dition entails sliding motion and consequent frictional loss. An
analytical investigation of this loss has been made by Professor

FIG. 95.

Benjamin Bailey (THE HORSELESS AGE, July 6, 1910), whose
method we may here follow.

Referring to Fig. 95, let n be the inner and rz the outer
radius of the contact ring on the disc. Imagine that the disc
is stationary and that the wheel rolls around it. A little con-
sideration will show that the total slippage during one revolu-
tion will be the same as if the wheel were rotated once around
the centre point of contact on the disc. This occurs when the
wheel is at the entre of the disc. Let P be the frictional force
on the circumference of the wheel, and let it be supposed that
the normal pressure between disc and wheel is just sufficient

152

THE FRICTION DISC DRIVE.

to prevent slippage of the wheel,
in width of the contact ring then is

The frictional force per inch

p
pounds. In Fig.

96 the circle of diameter t represents the whole area over which
the slipping takes place. Imagine that the wheel is stationary
at the centre of the disc and that the latter is turning under
it When the disc then makes one complete revolution, every
portion of the circle of diameter t is passed over twice by an
element of the wheel circumference. Now, consider an infinitesi-

-t-rrr2
FIG. 96.

mal ring of width dr. If W represents the frictional work done
on the entire circle during one revolution, then the work done
on the ring dr is

irr dr.

— r\

Integrating this between the limits r = o and r= (ra — n)/2 we
get

This, therefore, represents the power lost in friction during

THE FRICTION DISC DRIVE. 153

each revolution of the disc. The useful work transmitted dur-
ing one revolution is ri -j- r2

2 TT p = TT p (ri + r.)

2
hence the efficiency is •* p (ri + r2)

e = ,

7TP

TP(rx + r,) + (r2 — n),

which may be reduced to 2 (r± + r8)

3 r, + n

Let f be the width of contact of the wheel and r the radius from
the centre of the disc to the middle point of contact, then the
formula for the efficiency may be written

e = (33)

1 + —

With a width of contact equal to 1^ inches and a mean
radius of contact of 9 inches (typical of high speed operation
on a moderate sized car), the efficiency figures out to about 96
per cent. With a mean radius of contact of 3 inches (low gear)
the efficiency figures out to 88.8 per cent.

In actual practice the normal pressure between disc and wheel
is always greater than that required to just keep the wheel from
slipping, and may be far greater. This, of course, will propor-
tionately increase the loss due to slippage. If the ratio of the
actual normal pressure to that required to just prevent slippage
be k, then the efficiency is

e = (34)

1+ •

This efficiency, moreover, is only an ideal efficiency, not taking
account of bearing losses and any slippage there may be beyond
that required by the difference in the lengths of the inner and
outer circumference of the contact ring on the disc.

Dimensions of Disc and Wheel. — From equation (33) it will
be seen that the efficiency increases with the mean radius of con-
tact and as the width of contact decreases. Hence it is desirable
to use as large a disc as constructional limitations permit and
make the wheel as narrow as the rigidity and wearing qualities
of the facing will allow of. For pleasure cars a disc diameter of
20 inches is about the limit, because the motor must be located

154 THE FRICTION DISC DRIVE.

low for the sake of stability, and yet a ground clearance of
about 10 inches must be maintained. In commercial cars, in
which the power plant can be placed somewhat higher, the disc
may be as large as 24 inches in diameter. The wheel is gener-
ally made of about the same diameter as the disc, so that when
it is in the position farthest from the centre of the disc the
power is transmitted without change of speed.

Suppose that a friction drive is to be designed for a four cylin-
der 4x5 inch touring car. The disc would be made, say, 20 inches
in diameter and the friction wheel rim 134 inches wide. This
would make the mean radius of the contact ring, with the wheel
in the extreme high speed position, 9l/& inches. The above men-
tioned motor develops a normal-speed torque of 108 pounds-feet.
Hence the force to be transmitted at a radius of 9J4 inches is
12 X 108
— = 142 pounds,

. ?**
and figuring on a friction coefficient of 0.3, the necessary normal

pressure is 142

= 473 pounds.

0.3

On the other hand, the friction device must also be capable of
transmitting the full power of the motor when the wheel is at
only, say, 3 inches mean distance from the centre of the disc, for
low speed operation. The frictional force then is
12 X 108
= 432 pounds,

and the required normal pressure
432

= 1440 pounds.

0.3

Hence the mechanism for applying the wheel to the surface of
the disc must enable the driver to exert at least this pressure.

It is obvious that the torque which may be transmitted by a
friction wheel and disc is directly proportional to the diameter
of the disc, and it also increases with the width of face of the
wheel, provided the latter is not too large. In determining the
dimensions it is well to make the disc as large in diameter as
is permissible from the viewpoints of height of centre of gravity
and ground clearance required, and then give the wheel a width
of face

/ = — .. (35)

4D
where T is the maximum torque of the motor (Table 1) and D

THE FRICTION DISC DRIVE

155

the outside diameter of the disc. In no case should / be greater

than — .
10

Wheel Sliding Mechanism. — The friction wheel is arranged
on a cross shaft either of the fluted type or provided with one or
more long keys. The hub of the wheel is formed with a groove
for a sliding collar for connection to the operating lever. Owing
to the great range of motion of the wheel, long armed levers
must be employed in the operating mechanism. Fig. 97 illus-
trates a typical arrangement of this mechanism. The position

FIG. 97. — WHEEL SLIDING MECHANISM.

of the friction wheel is controlled by a hand lever moving over
a notched quadrant.

Friction driven cars practically always have a final drive by
chain, either one or two chains being used. With the single
chain the sprocket pinion is fixed to the shaft of the friction
wheel just beyond the range of motion of the wheel on the re-
versing side, and the shaft is carried in bearings secured to the
frame side members. With the double chain drive the differen-
tial gear must be incorporated in the cross shaft. The friction

156

THE FRICTION DISC DRIVE.

wheel then slides on a hollow shaft which is secured to the
housing of the differential gear, the cross shaft proper being
divided and each part fastened to one side gear of the differential.
There should be an extension of the hollow shaft beyond the
differential so that this shaft may be supported in bearings hung

FIG. 98. — MOUNTING FOR WHEEL AND Disc SHAFTS.
(JAKOB'S DESIGN.)

from the side frame members, which relieves the differential or
inner shafts of much strain.

Means for Engaging Wheel and Disc — Considerable im-
portance attaches to the method of mounting the bearings for
the disc shaft and of taking up the various stresses due to the
normal pressure between the disc and wheel. As has already
been shown, these stresses are of considerable magnitude, and
they may produce serious distortions of the frame unless suit-
able means are provided for taking them up. Fig. 98 illustrates
a design due to Victor Jakob. The cross shaft is supported in

THE FRICTION DISC DRIVE.

157

two brackets riveted to the frame, being provided with ball bear-
ings mounted in spherical housings. If required for renewing the
facing of the wheel, the cross shaft can easily be removed toward
the rear after the caps have been taken off.

In order to avoid twisting of the frame side members, due to
the reactions between disc and wheel, the bearings are placed
close to the frame and the axis of the shaft intersects the neu-
tral axis of the frame member. This arrangement necessitates
a somewhat higher location of the motor than customary with
gear drives, but this is required, anyhow, in order to obtain the
necessary road clearance under the disc and wheel.

From each of the cross shaft bearing brackets a tension rod

f=n - =

FIG. 99. — CAM MECHANISM FOR APPLYING Disc TO WHEEL.

is run straight forward to a cross member which is riveted to
the frame. The centre part of this cross member is widened out
and has a hole in the web so as to accommodate a barrel which
serves as a support for the disc shaft, the barrel being fastened
to the cross member by an integral flange. The front end of
the barrel is supported on another cross member by means
which permit of raising or lowering this end, whereby the disc
shaft and the cross shaft can be leveled up properly. Their con-
tinued perpendicularity is assured by two tie rods which run
diagonally from the front end of the barrel to the point at which
the parallel tie rods are connected to the cross member.

The disc shaft is carried in the barrel on two ball bearings,
the one near the disc being of a combined radial and thrust type,
so as to be able to take the end thrust due to the pressure of
engagement. Only little end thrust has to be taken up on the

158

THE FRICTION DISC DRIVE.

forward bearing, viz., that due to the disengaging spring, one end
of which rests against the outer race of this bearing, while the
other end rests against a shoulder in the barrel. The bearings
are rigidly secured to the shaft and their outer races slide in the
housing when the disc and wheel are engaged and disengaged.

The disc shaft is coupled to the motor by a floating shaft hav-
ing a universal joint at either end, one of which joints also has

FIG. 100. — DIAGRAM OF REACTIONS DUE TO PRESSURE OF
APPLICATION.

a sliding motion. Engagement of the friction members is ef-
fected by two cams, one on either side of the barrel (Fig. 99).
These cams form an integral piece with a lever, which is con-
nected to a pedal operated in the usual manner by the driver.
The cams, which are shaped according to a certain curve, press
against rollers mounted on studs which project through slots in
the barrel. The studs are screwed into a sleeve adapted to slide

THE FRICTION DISC DRIVE. 159

inside the barrel and resting against the baM bearing arrange-
ment which carries the rear end of the disc shaft. The slots
through which the roller studs project are sufficiently wide to
permit a slight degree of rotation of the sleeve, by which the
contact of both cams with their rollers is insured.

A special feature of Mr. Jakob's design is that the reactions
caused by the engagement of the friction mechanism are taken
up entirely within a truss and tie rod system, with the exception
of the pull on the cam lever exerted by the driver. This force,
however, is not very large, and is well taken care of by the diag-
onals and two cross-members. That the remaining forces are
completely taken up within the system is shown by the diagram
Fig. 100. In drawing this diagram it was assumed that in engag-
ing the disc and wheel at the point of maximum speed the driver
applied to the pedal the pressure necessary to hold the two in
engagement in the position of low speed under full engine power,
viz., 1,440 pounds. Compression and tension are indicated by
arrow heads turned toward each other for the former, and away
from each other for the latter.

One of the possible troubles with a friction disc drive that
should be provided against is that of wearing flats on the wheel
by allowing the disc to slip for extended periods on using the
gear as a brake. Manufacturers formerly sometimes recom-
mended the use of the friction transmission for braking purposes,
but this practice is to be condemned. Of course, only an inex-
perienced driver will cause the disc to slip for a long time on a
stationary wheel,

CHAPTER VI.

UNIVERSAL AND SLIP JOINTS.

Universal joints serve the purpose of connecting shafts or con-
trol rods whose axes lie in the same plane but make an angle
with each other. They are particularly required when the angle
between the shafts varies in service. In an automobile the most
important application of universal joints is in the transmission
line between the spring-supported parts and those carried by the
driving axle. Every shaft driven car must have at least one
universal joint in the propeller shaft, and many have two.

The simplest form of universal joint consists of a squared
block secured to one of the shafts to be connected, fitting in a
square hole in a sleeve secured to the other shaft. The four
faces of the block are curved in the direction of the axis of the
shaft to which the block is fastened. This type of universal joint
is illustrated in Fig. 101. It will 'readily be seen that owing to
the curvature of the faces of the block, one of the shafts can be
moved angularly with relation to the other in two planes at
right angles to each other. This joint also constitutes a slip joint.

The prototype of the modern universal joint is the Hooke or
Cardan joint, illustrated in Fig. 102. It consists of two forks,
each of which is secured to one of the shafts to be connected, and
of a cross-shaped part which is connected to each of the forks
by means of a pin. In the form here illustrated and as used in
stationary work, the axes of the two pins do not intersect, but
are at some distance from each other to allow of the pins passing
each other. However, there is an advantage in having the pins
both in the same plane. This end can be attained by using pins
of different diameters and passing one through the other, or by
using one long and two short pins. Cardan joints thus modified
are used in automobile work. In the design illustrated one pin
locks the other in position and is itself locked by a cap screw

160

UNIVERSAL AND SLIP JOINTS

161

FIG. 101. — SQUARE BLOCK TYPE OF UNIVERSAL AND SLIP JOINT.

through one arm of the cross and passing beneath the surface of
the pin.

A design in which the cross is replaced by a ring is illustrated
in Fig. 103. This also comprises two forks, but instead of the
outer ends of the forks having radial bearing holes drilled through
them, they are provided with bearing pins extending radially
outward. The ring has bearings for these pins formed in it. It
is made in halves, being split through the centre lines of the four
bearings so as to permit of assembling the joint. The halves
are secured together by means of cap screws and nuts.

A slight variation from the design just described consists in
a ring formed with four radial bearing pins and forks with sepa-
rate bearing caps, as illustrated in Fig. 104. This type offers
particular advantages when the universal joint is to be secured
to a brake drum, clutch drum or similar member, as only one

FIG. 102.— CROSS TYPE OF UNIVERSAL JOINT.

162

UNIVERSAL AND SLIP JOINTS.

FIG. 103. — SPLIT RING TYPE OF UNIVERSAL JOINT.

fork is required in that case, the part of the other fork being
taken by a pair of lugs cast integral with the web of the brake
drum, etc. This is shown in the illustration. Again, one member
may be made in the form of a disc keyed to the driving shaft,
which forms part of the universal joint housing.

Probably the most extensively used type of universal joint is
the slotted shell and trunnion block type, illustrated in Fig. 105.
This consists of a cup-shaped steel forging secured to one of the
shafts, with two diametrically opposite longitudinal slots milled

FIG. 104.— INTERNAL RING TYPE OF JOINT.

UNIVERSAL AND SLIP JOINTS.

163

FIG. 105. — BLOCK AND TRUNNION TYPE UNIVERSAL JOINT.

in its shell. The other shaft is provided with a ball shaped end
fitting the interior of the shell and provided with pins or studs
extending into the slots. Hardened steel trunnion blocks are in-
terposed between the pins and the walls of the slots to distribute
the bearing pressure. This type of joint, it will be noted, serves
also as a slip joint, and it can be easily enclosed.

Periodical Speed Fluctuations. — A feature of all of the
universal joints described above is that they do not transmit mo-
tion uniformly when the shafts are at an angle with each other;
that is to say, if the driving shaft runs at uniform speed, the speed
of the driven shaft will vary periodically, being soon less and
soon greater than the speed of the driving shaft. The common
feature of all of these joints is that they have two rocking axes
at right angles to each other.

To gain an idea of the magnitude of the variation in angular
velocity, we will assume a universal joint connecting two shafts

FIG. 106.

164 UNIVERSAL AND SLIP JOINTS.

in a vertical plane, the driving shaft being placed horizontally,
as in Fig. 106. The axes of the two pins intersect each other,
their ends being designated by AA and BE, respectively. When
the joint is in motion the line A A describes a circle in a vertical
plane, and the line BB a circle in a plane making with the vertical
an angle <t>, equal to the angle between the two shafts. These two
circles are great circles of the same sphere, the common diameter
being a line through the point C perpendicular to the paper.
Points A and B always remain at the same distance from each
other, viz., one quadrant of a great circle. The deviation in the
direction of travel is the greatest when either point A or point
B coincides with the points of intersection of the great circles.
When the points A coincide with these points of intersection, the
angular speed of the driven shaft is smaller than the angular
speed of the driving shaft, and when points B coincide with these
points of intersection the angular speed of the driven shaft is
greater than the angular speed of the driving shaft. There are
four points in each revolution in which driving and driven shafts
rotate at equal angular speeds, these being located substantially
midway between the points of maximum and minimum speeds
of the driven shaft.

Let the two large arcs in Fig. 107 represent the great circles in
which the points A and B travel. Let point A travel from the
point of intersection to point A' and point B travel at the same
time to B', which is determined by the fact that A' B' must be a
quadrant. Now, lay off from the point B' on the line of travel
of point B a quadrant, or 90 degrees, which will give point C.
Through A' and C draw an arc of a great circle. Angles B' A'
C and B' C A' are both right angles (because their opposite sides
are quadrants), hence angle A C A' is a right angle. We, there-
fore, have a right-angled spherical triangle A A' C, the angle A'
A C of which is equal to the angle between the two connected
shafts, the side AA' of which represents the angular motion of
the driving shaft, and the side A C the angular motion of the
driven shaft during a short period after the point A has passed
through the point of intersection; in other words, when the pin
of the driving shaft is at right angles to the plane through the
two connected shafts.

According to a theorem of spherical trigonometry

cos A'AC = tan A C cot A A' (36)

Since the tangent is the reciprocal of the cotangent we may
write this

tan AC cosA,AC,
t^nA A'

UNIVERSAL AND SLIP JOINTS.

165

and since for very small angles the tangents are proportional to
their angles, we have
A C

A A'

= cos A' A C.

(37)

Therefore, when the pin of the driving shaft is perpendicular to
the plane through the connected shafts the angular velocity of
the driven shaft is smaller than the angular velocity of the driv-
ing shaft in the proportion of the cosine of the angle between the
two shafts to unity. It may be shown in a similar way that when
the pin on the driving shaft is in the plane of the two connected

FIG. 107.

shafts the driven shaft runs faster than the driving shaft in the
inverse proportion.

It is also of interest to find an expression for the momentary
ratio of angular velocities at any point in the revolution of the
driving shaft. To simplify the expressions, we will denote the
angle A' A C by <£, the side A A' by a and the side A C by b.
Then we have as betore (liquation 36)
tan b = cos (f> tan a (38)

166 UNIVERSAL AND SLIP JOINTS.

Differentiating, we have

sec2 b db = cos <t> sec2 a da
and

db sec2 a
= cos 0 1 , (39)

da sec2 b

which gives the ratio of angular velocities at any moment in
terms of 0, a and b. It is preferable, however, to express the
value in terms of 0 and a only, as b is not directly known, and
the latter can be easily eliminated. Squaring equation (38) we
have

tan2 b = cos2 <t> tan2 a.
Adding 1 to each side of the equation —

1 + tan2 b = 1 + cos2 <t> tan2 a (40)

But since

1 + tan2 b = sec2 b}

we may substitute the right hand term of equation (40) for sec* b
in equation (39)
db sec2 a

— = cos<t> . , (41 )

da 1 + cos2 <j> tan2 a

which gives the ratio of angular velocities after any angular
move a of the driving shaft from the zero position in which the
pin of the driving fork is perpendicular to the plane through the
two shafts. When a = o equation (41) reduces to
db

= COS 0.

which is the same as already found for the position of minimum
speed of the driven shaft.

The curve, Fig. 108, shows the variation in speed of the driven
shaft during a motion of one-half a revolution or 180 degrees
the driving shaft making 1,000 r. p. m. and the angle between the
shafts (0) being 30 degrees. We start with the position where
the pin of the driving fork is perpendicular to the plane of the
two shafts. In this position the driven shaft rotates at the rate
of 866 r. p. m., its lowest speed. The speed of the driven shaft
increases until after a little more than 45 degrees motion of the
driving shaft it equals the speed of the latter. It keeps on
increasing, and after 90 degrees motion, when the pin of the
driving fork is in the plane of the connected shafts, it attains its
maximum speed of 1,155 r. p. m.. Then it decreases again, ac-
cording to the same curve, until after 180 degrees, or one-half
revolution, it again attains its minimum speed of 866 r. p. m. Dur-
ing one revolution the speed of the driven shaft, therefore, passes

UNIVERSAL AND SLIP JOINTS.

167

through two maxima and two minima. Its average speed, of
course, is the same as that of the driving shaft, and the speed
fluctuation amounts to

(1155-566) X 100
1,000

= 28.9 per cent.

The following table gives the speed fluctuations in the driven
shaft corresponding to different angles between shafts, the speed
of the driving shaft being assumed to be constant :

Angle &

(Degrees.)

8
10
12
14

Fluctuation
(Per Cent.)

0.15

0.5

1.1

4.4

Angle <£
(Degrees.)
16
18
20
22
24
26
28

Fluctuation
(Per Cent.)
7.9

10.

12.4

15.

18.

21.3

25.

7200
fjOO
1000
900
fOO

. —

-Driven
'Drtvint

c ^W?

— •-'

""K

•— _

JKofion of Driving Shaft
FIG. 108. — VARIATION OF DRIVEN SHAFT SPEED.

(Angle Between Shafts, 30 Degrees.)

This fluctuation in the speed of transmission is a matter of
great moment. In a gasoline automobile we have at one end of
the transmission line the motor, whose speed is maintained sub-
stantially constant by a heavy flywheel, and at the other end the
car, which, when running at high speed, also has its speed main-
tained by inertia. But if the transmission is effected through a
single universal joint working at an appreciable angle, the speed
of either the car or the engine, or of both, must of necessity
change greatly in a quarter revolution of the driving shaft. The
flywheel inertia strongly resists such a change in the speed of the
engine, and the car inertia a change in the speed of the car, and

168 UNIVERSAL AND SLIP JOINTS

the result is that every part of the transmission line is subjected
to enormous stresses. Not the least to suffer under these stresses
are the tires, which tend to slip on the ground as the car tends to
suddenly accelerate. To minimize these stresses the drive must be
so arranged that the two shafts are always nearly in line with
each other. They can be entirely eliminated by using two uni-
versal joints in series. We found that the speed of transmission
is reduced in a certain ratio when the pin of the driving fork is
perpendicular to the plane through the shafts and increased in the
inverse proportion when the pin of the driving shaft is in the
plane of the shafts. These two positions are 90 degrees apart.
Hence, by arranging two universal joints in series (Fig. 109) in
such relation that the driving fork or corresponding member of

FIG. 109. — ANGUT.AR RELATION OF DOUBLE UNIVERSAL JOINTS
TO INSURE UNIFORM TRANSMISSION OF MOTION.

the second is set at an angle of 90 degrees with respect to the driv-
ing fork of the first, and so that the driving and driven shafts are
parallel, both making the same angle with the intermediate shaft,
then motion will be uniformly transmitted from the driving to the
driven shaft. In other words, the pins at the ends of the
intermediate shaft must be in the same plane, or parallel. The
intermediate shaft, of course, will still revolve non-uniformly
if there is an angle between it and either of the shafts con-
nected by it, but since it has very little inertia this is of no
importance.

The Square Block Type — The square block type of joint
can hardly be recommended for such important work as in the
transmission from the gear box to the rear axle. It has given very
good satisfaction in individual cases, but failed absolutely in other
cars of the same make. It must be remembered that in this type
of joint there is a line contact only, and the bearing pressures are

UNIVERSAL AND SLIP JOINTS. 169

necessarily very high. Therefore, if lubrication is neglected or if
the bearing surfaces are not uniformly hardened, cutting sets in,
and once there is a little play the joint is soon hammered out.
This type of joint was employed in the 1909 model of a popular
American make of medium priced car, but was discarded the
next season. For a four cylinder 3%x4^ inch engine the block
measured 2x2 inches and was ^ inch wide.

The contact surfaces of the block are made cylindrical. If the
block were made a good fit in the sleeve it would, of course, be
possible to rock it in one or the other of two planes, but not in
both simultaneously. However, the block in service has to rock
relatively to the sleeve in every direction, and to make this possi-
ble it must have a certain amount of play in the sleeve when
their axes are parallel. This play, of course, must be made as
small as possible, because it is a source of noise and wear, and
it will naturally increase in use. The problem of the amount of
play required in square, pentagonal and hexagonal block joints
to allow operation at certain limiting angles has been investigated
by O. Winkler (Der Motorwagen, Nos. 3 and 4, 1912), who

D
finds that the ratio — of the diameter of the block and that of

the recess should be as follows for various limiting angular mo-
tions.

Limiting

Angle of

Operation. Ratios of Block to Recess Diameters

(Degrees.) Square. Pentagon. Hexagon.

.00031 1.00022 l.OOOi;

.00122 1.00088 1.00062

.00276 1.00198 1.00139

.00490 1.00353 1.00247

.00766 1.00551 1.00386

.01102 1.00793 1.00555

.01501 1.01080 1.00756

16 1.01960 1.01411 1.00988

18 1.02481 1.01785 1.01250

20 1.03062 1.02204 1.01543

Calculation of Forked Types. — In designing the forks for
universal joints comprising such members, conflicting require-
ments are met with. That is, if the fork arms are spread far apart
the pressures on the bearings will be reduced and the frictional
loss consequently will be less, but, on the other hand, the joint has
to be enclosed and forks of wide spread necessitate a bulky and
heavy casing. Usually the joint is made as compact as possible,
and the bearings are made large enough to withstand the pres-
sure. The distance between the middle points of opposite bearings
is usually about three times the shaft diameter. This distance,
of course, is a matter of choice, but a good approximation to

170 UNIVERSAL AND SLIP JOINTS.

average modern practice in the universal joints of propeller shafts
is obtained by making it

d= 0.8 ^/T (42)

where T is the normal speed torque of the motor. Of course,
the greatest torque is transmitted by the propeller shaft uni-
versals when the low gear is in operation, and in the calculation
of the parts for mechanical strength it is well to start with the
maximum torque available on the low gear. On the other hand,
in determining the bearing surfaces the pressures on direct drive
should be figured with, as in most cars the direct drive is used
a very large proportion of the time; and, besides, the rubbing
speed at the bearing surfaces of the universal is far greater when
the direct drive is in operation than when the power is trans-
mitted through the low gear. The bearings of universal joints of
the types shown in Figs. 102-105 are so proportioned that the unit
bearing pressure at full engine load on direct drive is 500 pounds
per square inch. The length and diameter of the bearings usually
bear to each other the ratio of 4 to 3.

We will now illustrate the calculation of a universal joint by a
practical example. The joint, we will suppose, is to transmit the
powtr of a four cylinder 4x5 inch motor (normal speed torque =
108 lbs.-ft.), and the low gear ratio is 3.2.

The distance between the middle points of the bearings would be

o . 8 I/ ^s = 3 • 8 1 — say 3! inches.

This gives a mean bearing radius of 1% inches and makes the
bearing pressure for the direct drive

Io8*12 ^691 pounds.

This pressure being taken up on two bearings, the pressure on
each is 345-5 pounds, and at 500 pounds per square inch the pro-
jected area of each must be

345 -5 — o>6g! SqUare inch.

500

If the length of the bearing is to be 4/3 the diameter, then the
projected area is 4/3 d2 and

JL, d2 = 0.691 square inch.
3

c£2 = Ji-X 0.691 =0.518 square inch
4

and

d = N/o.i8 =0.72 — say, f inch.

UNIVERSAL AND SLIP JOINTS.

171

The length is

— X 0.72 = 0.96 — say, 1 inch.

It is to be remembered that if the bearings are spaced farther
apart their dimensions can be made smaller.

The low speed or maximum torque of our motor is 133
pounds- feet, and the torque to be figured on in calculating parts
for strength is

3.2 X 133 = 425.6 pounds-feet.

If the universal joint is to be secured to the shaft with a key its
hub is generally made with a diameter of 1.6 the shaft diameter,
and its length is made about the same as its outside diameter.

FIG. 110. — DETERMINATION OF STRESS IN FORK ARM.

Assuming the propeller shaft to be of \y^ inches diameter, the
hub diameter and length should be

1.6 X 1.25 = 2 inches.

We now have the sizes of the hub and the bearings and their
relative positions. We lay these down on the drawing board and
sketch in the arms, as shown in Fig. 110. When the car is run-
ning under full power on the low gear there is a normal force of
425 X 12 = ^Qpounds

2X if

acting at point a. Now, we take any section of the arm like A A
and draw a perpendicular cb to the middle point of this section.
Next we construct a right-angled triangle with cb as the base and
a as the apex. Evidently the force of 1,360 Ibs., acting normally to
the paper at a produces in the section AA of the arm a torsional

172 UNIVERSAL AND SLIP JOINTS.

stress proportional to the arm ab (which by measurement is found
to be % inch), and a bending stress proportional to arm cb
(which is found to be 1^4 inches). Hence the torsional moment is

Aft = H X 1360 = 850 pounds-inches.
and the bending moment,

Mb = \Y4 X 1360 = 1700 pounds-inches.

As drawn in Fig. 110, the section of the arm at A A is equiva-
lent to a rectangle measuring l/2 inch x 1^4 inches. The proper
method of procedure is to assume a section like this, and then
calculate the stress in the arm under the combined bending and
torsional moments, and if it figures out either too high or too
low to change the section accordingly.

We first find the stress due to the bending moment, and that
due to the torsional moment separately, and then combine the
two. The bending stress is found by means of the equation

Ob j

where M is the bending moment, c the distance of the outermost
fibre from the neutral axis, and / the moment of inertia of the
section around the neutral axis for bending stresses. M in our
case is 1700 pounds-inches; c, fy& inch, and /

= 0.0814

Hence the bending stress is
1,700 X 0.625
- . - = 13,050 pounds per square inch.

0.0814

The formula for the shearing stress due to the torsion is ex-
actly the same as that for the bending stress, but / in this case
represents the polar moment of inertia of the section, and M and
c, of course, have different values.

M = 850 pounds-inches.

= 0.673

y2 x iy45 iy4 x y2*

+ - = 0.0944.

12 12

Hence* the stress due to torsion is

850 «X 0.673
- = 6,060 pounds per square inch.

0.0944
Calling the bending stress S\> and the torsional stress St, the

total stress in the material is

y2 sb + \ss + y4ss

(Merriman, Mechanics of Materials, • Fourth Edition, p. 152).

UNIVERSAL AND SLIP JOINTS. 173

Hence -in this case the combined stress is

-f- <4/6,o6o2 -I- I3>°5°2 = 15,430 pounds per square inch.

13-050

which is reasonable, though somewhat higher than the stress in
the shaft. If it is thought desirable, a similar calculation can be
carried through for another section of the arm, but usually a
single calculation would .be considered sufficient, the arm being
tapered slightly from end to end. The forks are generally drop
forged and occasionally ca^st, and the section must be given the
necessary draft of about 8 degrees. The thickness of the walls
of the bearing hubs and the cross can be made

— 4- -I inch, where d is the diameter of the pin.
4 16

This makes the bearing diameter larger than the cross diameter
by twice the thickness of the bushing. For the sake of appear-
ance it is well to have the two diameters approach each other
gradually at the junction, and this can be accomplished by either
making the bearing hub barrel shaped, as shown, or else provid-
ing the cross with circumferential flanges at the ends of its arms.
These flanges strengthen it considerably and permit of reducing
the thickness of the metal between them.

Calculation of Block and Trunnion Type — In this type of
universal joint the bore of the shell is made sufficiently large
to allow the shaft the necessary freedom of angular motion,
and, therefore, can be best determined on the drawing board.
The pins are so proportioned that the unit pressure on them
when the engine is driving direct at normal speed under full
power, figures out to about 1,000 pounds per square inch. The
unit pressure between the blocks and the walls of the slot
can be made between 600 and 700 pounds per square inch. The
trunnions are generally made of about the same length as their
diameter. As a precaution, the stress at the bottom section of
the pin corresponding to maximum engine torque and low gear
operation, should be calculated. All of the bearing parts of a
joint of this type should be hardened or case hardened and
ground. It is the hardened steel bearing surfaces that make
possible the greater unit bearing pressures as compared with
other types of universal joints. The length of the slots will
depend somewhat on the spring action and on the length and
inclination of the shafts to be connected. It is generally about
equal to the outside diameter of the shell.

This type of joint is very largely used at the rear end of a
propeller shaft provided with two universal joints, serving both

174 UNIVERSAL AND SLIP JOINTS.

as a universal and slip joint. Occasionally two of these joints
are used in a single shaft, in which case it is necessary to hold
the ball of one joint between stops or to centre the shaft be-
tween springs, as illustrated in Fig. 105. Neglect of this pre-
caution will not only result in noisy operation, but will make
it difficult to keep the lubricant in the joint housing. The slid-
ing blocks should preferably be cut with slanting oil grooves
across their bearing surfaces to insure effective lubrication.

Lubrication and Dust Protection— On the earlier shaft
d-riven cars the universal joints were not enclosed and k was
found very difficult to lubricate them effectively. Centrifugal
force would cause the joint to throw the oil off and grit would
work into the bearings and cause their rapid destruction. This

FIG. in. — LEATHER BOOT FOR UNIVERSAL JOINT.

was remedied to an extent by making the bearing bushings
thimble shaped, that is, "blind" at their outer end, but the most
effective remedy undoubtedly consists in enclosing the whole
joint oil and dust proof. There are various methods of accom-
plishing this.

The universal joint which is easiest to enclose is the block
and trunnion type. As shown in Fig. in, it is provided with a
tight fitting tubular steel housing over the part which we have
called the shell, fitted against a shoulder turned thereon and
secured in position by means of a couple of machine screws.
This housing can have a groove formed on it at its open end
to which a leather boot can be fastened whose other end is
tied around the shaft. It is a good plan to rivet a fitting,

UNIVERSAL AND SLIP JOINTS.

175

closed by a quarter inch pipe plug, to the leather boot, for
convenience in replenishing the lubricant. The leather boot is
fastened in place by means of clamps, similar to hose clamps.
If one end is clamped tight to the shaft, sufficient slack must
be allowed in the boot to permit the shaft to swing freely in
all directions through its maximum operating angle. Some
makers clamp the small end of the boots to a sliding sleeve
on the shaft, enabling the boot to readily accommodate itself
to varying angularities between the two shafts.

Another form of universal joint housing is illustrated in Fig.
112. One member of the joint is made in the form of a plate to

FIG. ii2.— SHEET METAL HOUSING.

which is bolted a spun sheet metal housing which is partly
cylindrical and partly spherical. Against the spherical portion
of this housing bears another sheet metal part in the form
of a spherical zone, the latter being secured to the hub of the
universal joint fork. This type of housing is applicable only
to joints whose two axes intersect, and the centre of the spher-
ical portions must be at the point of intersection of these two
axes. The cover plate is formed with a groove near its edge
which is filled with packing material.

Fig. 113 shows still another form of housing. It is sub-
stantially ball shaped and consists of three parts. Two of
these are bolted together and form, between them, bearings for
two of the trunnions of a cross, one of these two parts being
keyed to one of the connected shafts. The arms of the cross

176

UNIVERSAL AND SLIP JOINTS.

are of unequal length, the two longer arms having bearings in the
housing, and the two shorter ones in the ends of the arms of a
fork secured to the other shaft. The latter shaft extends through
a circular opening in the ball shaped housing, sufficiently larger
than the shaft to permit of its swinging to the maximum angle
of operation in any direction. This opening is closed by a zone
shaped cover which is pressed against a machined surface on the
inside of the housing by a coiled spring.

Where a single universal joint is used in the propeller shaft
and the latter is surrounded by a torque tube, the forward end
of this torque tube is often supported by a ball and socket

FIG. 113. — ENCLOSED UNIVERSAL JOINT.

joint, secured to a cross frame member, the ball being made
hollow and serving as a housing for the universal.

Anti-Friction Bearing Universals. — Anti-friction bearings
have been used in universal joints to a small extent. Fig. 114
shows the Lancia joint which is fitted with radial ball bearings.
It is of the fork and internal ring type. The use of ball bear-
ings has led to a special method of assembling. It will be
seen that the fork ends are slotted, the slots being just large
enough to permit of the trunnions being passed through them-
The ball bearings are then slipped over the trunnions and into
their seats in the fork ends and the outer races are secured in
place by means of cap plates. The H. H. Franklin Mfg. Co.
uses rollers in the blocks of a block and trunnion type of uni-
versal joint. These entirely fill the space between block and

UNIVERSAL AND SLIP JOINTS.

177

trunnion, and are held in place by end washers, no cages being
used.

It is hardly to be expected that much saving in power will
result from the use of anti-friction bearings at this point, be-
cause of the small angularity of the shafts and the consequent
limited motion at the joint bearings in modern cars. Probably
the chief advantage of such bearings in this place is that they
are not so easily damaged as plain bearings if the lubrication
should be neglected.

Slip Joints. — Unless a combined universal and slip joint like
the square block type or the block and trunnion type is used

t FIG. 114.— LANCIA BALL BEARING UNIVERSAL JOINT.

in the propeller shaft, a special slip joint must be provided
to allow for variations in the distance between the change gear
box and the rear axle housing, due to play of the springs. This
may be either a squared or a fluted shaft with a corresponding
hub or sleeve. It -may be stated at once that the block and
trunnion type of joint is far preferable, since the sliding motion
occurs farther away from the axis of rotation, hence the pres-
sure on the sliding surface, and consequently the resistance to
sliding, is much smaller. Fig. 114 illustrates a four fluted sliding
joint. Six fluted shafts are also used. The Society of Automo-
bile Engineers has standardized fluted shafts and given rules for
their load capacity (see Appendix).

Leather Disc Universal Joints. — Leather universal joints
have been used chiefly between the clutch and change

178

UNIVERSAL AND SLIP JOINTS.

speed gear. These universals are silent in operation and they
are not subject to bearing friction, consequently they are highly
efficient as regards the transmission of power. A leather uni-
versal joint consists of two similar spiders, usually three-armed,
fastened to the ends of the shafts to be connected and of a
number of leather discs or rings bolted between the spiders.
The arms of the two spiders are staggered, so that any arm
of one of the spiders is located midway between two arms of
the other spider. Three, four or five discs may be used and
individual discs are often spaced by steel washers. It will at
once be seen that the ability of such a universal to transmit
motion between shafts at an angle is limited as to the angle.

FIG. 115. — TYPICAL DESIGN OF LEATHER Disc UNIVERSAL JOINT.

A typical leather universal is illustrated in Fig. 115. This
shows four leather discs between the two spiders, each pair of
discs separated by steel washers at the points where the bolts
pass through. These steel washers distribute the driving strain
over a larger area and also increase the flexibility or freedom
of action of the joint.

It is impossible to calculate the actual stress in the leather
when the joint works at an angle. It increases, of course, rap-
idly with the angle. For insertion between the clutch and
chpnge gear, where very little universal action is called for, a
stress in the leather of 200 Ibs. per square inch may be allowed.
Thus, let T be the maximum torque of the engine; n, the num-
ber of discs; do, the outside diameter; di, the inside diameter,

UNIVERSAL AND SLIP JOINTS. . 179

and t, the thickness of the leather. Then with three-armed
spiders the load is divided between 3 n sections of the leather
with a combined cross-sectional area of 3 nt square inch. The
tangential force is

2 T X 12
p =

do + di,

which may be solved for do after first assuming a certain rela-
tion between do and di.

FIG. 116. — LEATHER DOUBLE UNIVERSAL JOINT (OVERLAND).

Experience with leather universal joints has not been uni-
formly successful and the greatest care is required in their
design. The bosses of the spider arms where they bear against
the leather, and the washers must be carefully rounded, and
only the best grade of chrome leather must be used. Some
manufacturers are said to treat the leather with linseed oil to
make it more flexible and proof against, the effects of moisture.
If there is too much end strain on the universals the leather
discs will "cup" and pull apart. One scheme to prevent this
consists in inserting two or three thin sheet steel rings between
adjacent leather rings and riveting the whole together.

Rubberized fabric discs are sometimes used in place of the
leather. TLe discs are built up of layers of fabric with the
warp of succeeding layers at slightly different angles. In fact
the whole circle is divided into a number of parts equal to the
number of layers in the discs and the angle thus arrived at is
the angle between the warp of adjacent discs.

CHAPTER VII.

THE DIFFERENTIAL GEAR.

The purpose of the differential gear, as explained in Chapter 1,
is to permit of equally dividing the driving effort of a single
source of motive power between two driving wheels and to allow
cars driven through wheels on opposite sides to be freely steered.
There are two general types of differential gears, viz., the bevel
type and the spur type.

A bevel type differential gear consists of two bevel gears ar-
ranged coaxially and facing each other, and a varying number
of bevel pinions between them meshing with both of the gears.
Generally either three or four pinions are used, which are placed
at/ equal angular distances. The pinions are capable of rotating
on radial studs which are clamped at their outer ends between
the two halves of a housing or skeleton frame. This frame is
provided with hubs carried in ball or roller bearings in the rear
axle or jackshaft housing and with a flange to which the driven
bevel gear, sprocket, etc., can be secured.

Action of the Differential— Power is thus applied to the
frame or housing of the differential. The housing transmits it to
the bevel pinions, the latter to the bevel gears and these to the
rear axle shafts or jackshafts. Under any given conditions of
operation a certain torque is impressed upon the differential
housing. This torque is divided equally between the three or
four bevel pinions. Each bevel pinion constitutes a balance lever
between the two bevel gears and evenly divides its torque be-
tween them. Thus the total torque impressed upon the differ-
ential housing is at all times equally divided between the two
bevel gears, also called the master gears.

The relative motion of the two side gears depends upon the
position of the steering gear and upon the traction conditions.
Suppose first that both driving wheels run on dry road surface
sc there is plenty of road adherence. Then the rate of revolu-

180

THE DIFFERENTIAL GEAR. 181

tion of each wheel and that of the corresponding master gear of
the differential will depend upon the length of the path followed
by that wheel. If the steering road wheels are in the straight-
ahead position and both driving wheels have exactly the same
diameter, then both will rotate at the same speed, as will the
differential master gears. On the other hand, if the steering road
wheels are deflected from the straight-ahead position the vehicle
is constrained to travel in a curve, and the wheels on the outside
of the curve will be forced to turn faster than those on the
inside. Under these conditions the pinions of the differential will
turn on their studs, allowing one master gear to run faster than
the other. The speed of the frame or housing of the differential
is always equal to the algebraic mean of the speeds of the two
master gears.

In case one of the wheels stands on slippery ground and has
insufficient road adherence, it will slip. The differential gear
under these conditions also divides the propelling effort equally
between the two driving wheels, and the wheel which stands on
dry surface can exert no more propelling effort than the one on
slippery surface. The car will thus be stalled, and the wheel on
slippery ground will be spun around at twice the rate at which
it would otherwise turn with the engine running at the same
speed, whereas the other wheel will remain stationary. This
quality may be regarded as a defect of the differential gear, espe-
cially in the case of very heavy vehicles, and such vehicles are
often provided with a differential lock, consisting of some means
for so connecting the two master gears of the differential to-
gether that they must rotate in unison.

Calculation of Bevel Type Differential. — Differential gears
are made very compact, being almost a solid box of gears. In
calculating their dimensions it is advisable to base the calculation
upon the maximum torque on the rear axle under low gear, for
the reason that the pinions and gears operate only occasionally
and then only for short periods at a time. They are, however,
constantly subjected to the stress due to the torque being trans-
mitted through their teeth.

The torque-transmitting capacity of a bevel type differential
gear varies as the square of the largest pitch diameter of the
master gears, because the lever arm through which the tooth
pressure acts is proportional to this pitch diameter and the face
width of the tooth, and hence the permissible tooth pressure, also
varies with the largest pitch diameter. It also varies as the cir-
cular pitch of the teeth and as the number of bevel pinions em-

182

THE DIFFERENTIAL GEAR.

ployed. Of course, the strength of the material also has an in-
fluence on the capacity of the differential, but inasmuch as
low carbon steels are used in almost every instance, the tensile
strengths of which do not vary much, we may neglect it. A con-
siderable amount of practical data from modern cars shows that
the largest pitch diameter of the master gears may be determined
by means of the equation

pdm =

70 pn

where T is the maximum low gear torque on the rear axle, p
the circular pitch of the teeth and n the number of pinions.

FIG. 117. — LONGITUDINAL SECTION THROUGH BEVEL TYPE
DIFFERENTIAL GEAR.

The numbers of teeth generally range between 28 and 36 for
the master gears and 16 and 20 for the pinions, the gears having
about 1.8 times the number of teeth as the pinions. The maxi-
mum pitch diameter of the master gear having been determined,
the pitch is chosen to give a number of teeth within the range
mentioned. Gears of 8 pitch are generally used for small and
moderate powers and 6 pitch for high powers. The face of the
gears is made from ^ to ^ the distance from the intersection of

THE DIFFERENTIAL GEAR.

183

the two maximum pitch diameters to the centre of the differential.
The unit pressure on the pinion pins is calculated on the basis of
4,500 pounds per square inch under maximum engine torque and
low gear, and the pin diameter is generally made equal to three-
fourths the bearing length.

After the dimensions of the differential have been roughly de-
termined by means of the above rules, a layout can be made
and the design checked up by calculating the stress in the teeth
of the bevel pinion, which should be in the neighborhood of
45,000 pounds per square inch. We will carry these calculations

FIG. 118.— BEVEL DIFFERENTIAL PARTLY IN SECTION.

through for a rear axle differential for a car with four cylinder
4x5 inch motor, a low gear reduction of 3.2 and a bevel gear ratio
of 3.5. The maximum rear axle torque therefore is

3.2 X 3.5 X 133 = 1,490 pounds-feet.

Let the differential be made with four pinions of 8 pitch; then,
according to equation (43) the maximum pitch diameter of the
master gears should be approximately

1,490

= 3.65 inch,

70 X 0.4 X 4

and the number of teeth figures out to 29. However the number

184 THE DIFFERENTIAL GEAR.

of teeth must be divisible by 4, there being four pinions. Hence
we will choose 28 teeth. The pinions then should have

— = 16 teeth

1.8

and their maximum pitch diameter will be 2 inches. The distance
of the intersection of the two largest pitch diameters from the
centre of the differential is

3.52 + 22

= 1.88 inches,

4
hence the face of the gears can be made

0.35 X 1.88 = 0.66 — say, 11/16 inch.
Since we are making the face of the pinion equal to
0.68 X 100

= 36

1.88

per cent, of the distance from the point of intersection of the
largest pitch diameters to the vertex of the cone, and since the
strength of the tooth section varies uniformly from the outer to
the inner end of the tooth in proportion to the distance from the
centre of the differential, the load on the tooth may be considered
to be concentrated on the pitch line at

P /100 + 64 \

\IIOQP — I - X 36 1= 84 per cent.*

of the distance between the outer end of the tooth and the apex
of the cone, from the apex. Hence the arm through which
this pressure acts is

3.5 X 84

= 1.47 inches,

2 X 100

and the tangential pressure on the mean pitch circle is
1,490 X 12

= 12,150 pounds.

1.47

In Fig. 119 is shown a portion of the top view of an 18 tooth
bevel pinion meshing with a 32 tooth bevel gear. Gear and pin-
ion are shown meshed in three relative positions, and it will be
seen that in each position there are two or more teeth of the
pinion in contact with teeth of the gear. Hence we can figure
that the load is taken up on two teeth at each meshing point, and
since there are eight meshing points in a four pinion differential,
the total load is taken up on 16 teeth, which makes the load per
tooth 12>15Q

= 760 pounds.

16
* For an explanation of the method employed see page 225.

THE DIFFERENTIAL GEAR.

185

The strength of bevel gear teeth can be calculated by a method
similar to that of Lewis for spur teeth. The largest section of a
bevel gear tooth has the same strength as a tooth of a spur gear
of the same pitch and number of teeth, and the strength of the
bevel tooth decreases uniformly as the apex of the cone is ap-
proached. Since the tooth in the present case extends 36 per
cent, of the distance from the base to the apex of the cone, the
average strength of the tooth will be about 26 per cent, less th<an

FIG. 119.— EIGHTEEN TOOTH BEVEL PINION AND THIRTY-TWO TOOTH

BEVEL GEAR IN DIFFERENT POSITIONS OF MESH, SHOWING THAT

THE PRESSURE Is ALWAYS DIVIDED BETWEEN AT LEAST

Two TEETH.

that of a corresponding spur tooth. Substituting in the Lewis
formula the values applying to our case, we have

760 = 5 X 0.4 X 11/16 X 0.083 X 0.74,
and

760

•S* r = 45,000 pounds per square inch.

0.4 X 11/16 X 0.083 X 74
This tooth stress is in harmony with the stresses allowed in

186 THE DIFFERENTIAL GEAR.

change gear pinions as given in the chapter on sliding change
gears, remembering that the differential pinions and gears run
together little. In reality the stress is lower because the Lewis
formula is based on the assumption that the whole tangential
force comes on the end of the tooth, and it is obvious that when
two or more teeth of one gear are in contact with teeth of the
other at the same time, at least one tooth takes its pressure at a
point considerably nearer its root, whereby the moment of the
pressure is reduced.

The pressure on each pinion pin is
12,150

= 3,040 pounds

and with a unit bearing pressure of 4,700 pounds per square inch
the required bearing surface figures out to
3,040

= 0.675 square inch.

4,700

Since the bearing length is to be to the diameter as 4 to 3, the
area will be 4

— d2 = 0.675 square inch.
3
Hence

d2 = Y4 X 0.675 = 0.506 square inch,
and

d ="\/0.506 = 0.71 inch— say, 11/16 inch,
whereas the length should be
4 11

_ X — = 0.916— say, 15/16 inch.
3 16

The pinion pins are generally made integral with a central
ring having a bearing on the hubs of the master gears, thus
forming a spider. Their outer ends may be clamped between the
halves of the frame or housing, or they may be flattened off
and the holes for them made rectangular, with their long sides
parallel with the axis of the differential so the spider may slide
in these holes and automatically adjust itself to the position
where the pinions mesh equally with both master gears. The hubs
of the master gears are generally broached out square to fit to
the squared ends of the rear axle shafts. These hubs are pro-
vided with a radial face which bears against a corresponding face
on the outside of the housing to take up the bevel gear end
thrust. Some designers provide bronze bearing bushings and
thrust washers, but the majority do not. The flange for the
driven bevel gear is formed integral with one-half of the

THE DIFFERENTIAL GEAR. 187

differential housing, and is often so far offset to one side as
to bring the centre of the differential in line with the driving
pinion centre.

The Spur Differential— Referring to Figs. 120 and 121 a
spur differential consists of two spur master gears mounted on
the inner ends of the differential shafts, of a varying number
of pairs of spur pinions and of a housing or frame surrounding
the whole. The spur pinions are of substantially double the width
of the spur gears; the latter are placed some distance apart
and the extra width of the pinions extends into this inter-
mediate space where the two pinions of each pair mesh together,

FIG. 120. — LONGITUDINAL ELEVATION OF SPUR DIFFERENTIAL, HALF
SECTIONED.

The action of this type of differential is exactly the same as
that of a bevel differential.

The pinions of spur gear differentials are made with a very
small number of teeth, generally about ten, because any small
increase in their size entails a large increase in the bulk of the
differential housing. Stub teeth are preferably used, and some
makers use a special form of mongrel teeth of still greater
strength than stub teeth.

158

THE DIFFERENTIAL GEAR.

Spur differentials can be calculated on the basis of a tooth
stress of about 35,000 pounds per square inch under low gear
and full engine power, if the gears are made of carbon steel,
heat treated. The stress may seem high, but it must be re-
membered that the calculation is based on the full engine power,
whereas from 15 to 25 per cent, of the engine power will be
lost in the change gear, universal joints and rear axle bevel
gears. Moreover, in very powerful cars the adherence of the
driving wheels to the ground limits the load which can be
placed on the differential to a figure smaller than is obtained by

FIG. i2i.— END ELEVATION OF SPUR DIFFERENTIAL, HALF SEC-
TIONED.

multiplying the engine torque by the reducing factor between
engine and rear axle.

The master gears may be made of a pitch diameter of from
3 to 4 inches, at the option of the designer or according to
the size of the driven bevel gear, and either three or four sets
of pinions may be used. We will illustrate their calculation by
the example of a differential gear for a four cylinder 4x5 inch
motor and the reduction ratios mentioned above. We found
the maximum rear axle torque to be 1,490 pounds-feet. We

THE DIFFERENTIAL GEAR. 189

will assume that the master gears have a 3^ inch pitch diam-
eter and 8-10 pitch stub teeth. The pitch line pressure then
will be

1,490 X 12

Assuming that there are eight pinions, this pressure is trans-
mitted by eight teeth, and the pressure on each is

«»«? = 1,277 pounds.
8

Assuming the pinion to have 10 teeth, for which the constant is
0.041, the necessary width of face is

= o . 89 — say, y* inch .

0.041 X 35»ooo

The cases for spur gear differentials are made in two parts
which are held together by bolts. The halves should preferably be
provided with a telescoping joint, to insure the continued align-
ment of all parts. One part is usually made in the form of a
circular plate, and the other in the form of a cylinder open at
one end. Sometimes the driven bevel gear or sprocket is
bolted to a flange on the cylindrical part, and the two parts
of the housing are held together by means of through bolts.
In another design the cylindrical part has a flange at its open
end, and bolts are passed through this flange, the end plate of
the differential housing and the web of the bevel gear, as
shown in Fig. 120.

The lighter spur differentials sometimes have no regufar hous-
ing, the end bearing plates being held together by bolts and
separated by spacers surrounding the bolts.

Lately a number of designs of differential gears have been
brought out which prevent a car from losing traction when one
wheel stands on slippery ground. Most of them involve some
form of one-way transmission device, that is, a mechanism
through which power can be transmitted in one direction but
not in the other. With the ordinary differential, if one wheel
is held from rotating and the frame or housing of the differ-
ential is rotated, the other wheel will be rotated at twice the
speed of the differential frame. Also, if the housing is held
from rotation and one wheel is rotated, the other wheel will
rotate in the opposite direction at the same speed. With one
of the special differentials, if one wheel is locked or held from
rotating, by turning on the other wheel the housing may be
rotated, but it is impossible to turn the free road wheel by turn-
ing on the housing.

190

THE DIFFERENTIAL GEAR.

It is self-evident that such a differential does not equally
divide the torque between the two driving wheels, for if it did,
then, when one wheel was spinning, the other wheel would
have no more torque impressed upon it than the spinning one,
which would be insufficient to propel the car. The relative
torques impressed upon the two wheels respectively depend
upon the resistance encountered by them. Ordinarily in
straight-ahead motion, both wheels encounter substantially
equal resistances, and the driving torque on both is therefore
the same. But in turning a corner the outer wheel is com-

FIG. 122.— M & S HELICAL DIFFERENTIAL GEAR.

pelled to run ahead of the differential housing or frame, and
all the torque is taken by the inner wheel, the conditions then
being the same as when one wheel has no traction.

One of the best known of these special differentials is the
M & S, illustrated in Fig. 122. Each of the axle shafts carries
a helical gear and the differential spider carries three helical
pinions with radial axes and six such pinions of which each
one meshes both with one of the radial pinions and with one of
the gears on the axle shafts. It is well known that in helical
gears, if the angle of spiral of the driving gear is very small,
power cannot be transmitted through the pair in the reverse

THE DIFFERENTIAL GEAR.

191

direction, because the frictional resistance is too great, and this
is the principle made use of in this differential.

Gearless Differential — From the above it will be gathered
that the special feature of these differentials is that it is im-
possible to transmit motion from the differential spider to one
of the side members. Differentials embodying this feature can
also be made without the use of toothed gears, and one such
design is illustrated in Pig. 123. The right and left ratchets,
which are keyed to their respective axle shafts, are independent
and free to rotate inside of the housing. The two round mem-
bers with knobs at their ends and centre are the pawls which
form the interlocking media between the driving sectors and
ratchets. The right hand view shows the right hand end of
the top pawl in a tooth of the right hand ratchet, being driven
by the contact face of the driving sector and driving the

FIG. 123.— GEARLESS DIFFERENTIAL.

ratchet forward. In the same manner the left ratchet is driven
forward by the lower pawl, which is engaged at its left end.
Thus both wheels are driven forward positively and neither
can spin, as with the common differential.

To drive backwards, the differential housing starts to move
to the left and pushes the end of the pawl out of the ratchet
tooth, which throws the opposite end of the pawl down into
the tooth of the opposite ratchet. The contact face of the re-
verse driving sector engages and drives the wheel backward.
The lower pawl acts in the same manner. In turning a corner,
imagine that the car is being driven forward and is to be
turned to the left. The right wheel starts to revolve faster
than the left and causes the right hand ratchet to move
faster than the differential housing, which latter can only go

192

THE DIFFERENTIAL GEAR.

as fast as the inner or slower moving wheel. The ratchet
pushes the end of the pawl out of its tooth thus allowing the
ratchet to have a free movement forward. As soon as the cor-
ner has been made and both wheels are revolving at equal
speed, the spring at the centre of the pawl pushes the end of
the pawl back into engagement and the drive is again taken
up by both wheels.

When the wheels propel the drive shaft, as in case of coast-
ing or braking through it, both ratchets start to turn faster

FIG. 124. — DIFFERENTIAL LOCK.

than the housing, and push the engaged ends of the pawl out
of engagement and the opposite ends into the driving position
in the opposite ratchet teeth, thus causing the ratchets to
propel the drive shaft.

Differential Lock. — A few of the heavier designs of trucks
are provided with differential locks which enable the driver to
put the differential gear out of operation at will. The problem
of working out a neat and all round satisfactory differential lock
presents considerable difficulty, which is probably the reason that
this device is not more extensively used. Fig. 124 illustrates a
differential lock of typical design. A jaw clutch is provided,
sliding on a squared section of one of the differential shafts, by
which the differential housing may be locked to this shaft.

CHAPTER VIII.

UNIT POWER PLANTS AND TRANSMISSION AXLES.

When a line of shafting is supported in several bearings, it
Is necessary to either mount all of the bearings in absolute
alignment and keep them so, or to make the shaft in sections
and connect the sections by universal joints. In an automobile
power plant we have such a line of shafting extending through
the motor and change gear box, which may be supported by
from four to ten bearings. It is an easy matter to keep all of
the bearings in the crankcase or those in the gear case in
alignment. However, it is virtually impossible to insure
continued alignment of the gear box bearings with those of
the crankcase if the two cases are mounted separately on a
light pressed steel frame, as is customary. Owing to the severe
shocks and wrenches which it receives in driving at speed over
rough roads, the frame "weaves" and distorts and cannot at
all be depended upon to maintain the bearings in alignment.

Two courses are open to the designer for overcoming this
difficulty. He may either connect the crankshaft to the primary
shaft of the gear box through a double universal and sliding
joint, or he may tie the gear box to the crankcase in such a
manner that the whole forms a single rigid structure. The
former arrangement permits of slight displacements of one of
the cases with respect to the other in every direction. The second
arrangement gives what is known as the unit power plant, which
is used more especially on low and moderately powered cars.

What is perhaps the most common type of unit power plant
is illustrated in Fig. 125. Engine, clutch and gear box are located
in their usual relative positions, the gear box being brought as
close to the engine as possible. The crankcase is provided at
the rear with a flat cylindrical extension designed to house the
flywheel. This extension has a flange at its open end to which
the gear box is bolted, the latter being formed with a forward

193

194 UNIT POWER PLANTS AND TRANSMISSION AXLES.

UNIT POWER PLANTS AND TRANSMISSION AXLES. 195

extension designed to house the friction clutch. The exact loca-
tion of the vertical joint varies somewhat in the different de-
signs, but a common feature of this type of unit power plant
is that the entire unit may be separated into two parts longi-
tudinally and forms three chambers, for the engine crankshaft,
for the flywheel and clutch, and for the change gear, respectively.
Of course the crankcase may be divided horizontally through
the centre of the crankshaft, but the tendency is to use barrel
type crankcases in connection with this type of unit power plant.
In practically all unit power plants the two shafts of the change
speed gear lie in a vertical plane, this arrangement tending to
greater symmetry of the whole design.

Access to the crankshaft bearings is afforded by 'either a re-
movable bottom plate of the crankcase or large hand-hole cover
plates on one side, while the interior of the clutch and gear
compartments may be reached through large hand-holes.

Among the advantages of such a unit power plant may be men-
tioned the fact that it simplifies the construction in that it ob-
viates the need of a double universal joint between the engine
and change gear and makes it possible to support the whole unit
upon the frame at three or four points instead of an equal num-
ber of supports for either part. Moreover, the complete en-
closure of all moving parts tends to the reduction of noise, to
increased cleanliness and to better lubrication and protection of
wearing parts from dust and grit. The change gear is brought
somewhat closer to the engine and is therefore likely to come
in a more accessible position underneath the front seat floor
boards. However, the main object of unit construction and its
chief advantage is that if the bearings are once properly lined
up, they will remain in alignment, and hence there is no danger
of binding and consequent injury to the bearings.

Three Point Support. — Although the three point support is
applicable to engines and gear boxes mounted separately, it
is specially advantageous in the case of unit power plants. The
principle involved in the three point support is perhaps best ex-
plained by reference to a three legged stool which will stand
securely on an uneven floor, whereas a four legged one will
not. In a motor car, if the frame supporting the power plant
should be distorted, it would not subject the case and arms to
any stress if the power plant were supported at three points,
whereas if it was supported at four points the rigidity of the
case and its arms would resist distortion of the frame, and
hence these parts would be severely stressed by distorting in-

196

UNIT POWER PLANTS AND TRANSMISSION AXLES.

UNIT POWER PLANTS AND TRANSMISSION AXLES. 197

fluences. Crankcases and gear boxes supported at four points
are sometimes broken by excessive road strains on the frame.

In Fig. 125 the power plant has one point of support at the front,
a cross member of the frame passing underneath the crankcase,
and having the latter fastened down to it by two bolts located close
together at the middle of the crankcase bottom. The other two
points of support are at the side of the flywheel housing, which is
cast with laterally extending arms which rest on top of the sub-
frame or connect through hangers with the main frame. An
alternate method consists in casting the crankcase with two
lateral supporting arms near its front end and have the third
point of support at the rear of the gear box, the rear bear-
ing hub of the latter being developed in the form of a sup-
porting bracket resting on a cross member of the frame. There
are two distinct arrangements of this rear support. The
simplest consists in passing two long bolts through the rear
bearing hub and the supporting frame cross member. This
does not give a true three point support, as there are in reality
two points at the rear, but since they are comparatively
close together, they act substantially as a single sup-
port. In order to obtain a single support at the rear, the rear
bearing hub has a part spherical surface turned upon it which
rests in a spherical socket bolted to the frame cross-member.
The socket must, of necessity, be made in halves, and for con-
venience in machining the rear bearing hub is made separate
and bolfed to the casing. A similar supporting method may be
applied to the front bearing of the engine.

Of course, where a supporting arm has a large flat bearing
surface and is bolted down to the supporting member it is
not quite correct to speak of a "point" of support. In such a
case there are in reality three or four supporting surfaces in-
stead of three or four points of support, and it is easily seen
that if the surfaces of a "three point support" are fairly large
there must still be considerable strain in the material near the
supporting surfaces if the frame is distorted. In order to
eliminate these strains as far as possible the Midland Motor
Car Company makes the two forward supports of the power
plant on the main frame in the form of trunnions and sliding
blocks, the trunnions being formed on the ends of a trussed cross
member and the blocks sliding in the channel of the frame.
The latter is "swept in" in front, which allows the cross member
to be inserted into the frame channel from the rear.

198 UNIT POWER PLANTS AND TRANSMISSION AXLES.

UNIT POWER PLANTS AND TRANSMISSION AXLES. 199

Flywheel in Front — One of the chief difficulties encountered
in combining the engine and the change gear in a single unit
is due to the fact that the flywheel is located between them
and to enclose it requires a great deal of metal, adding both
to the weight and the cost of the car. In four cylinder motors
there is a tendency to use a flywheel of rather inadequate capacity
when it is to be enclosed, which somewhat detracts from the
steady running qualities of the car. To overcome this difficulty
two expedients may be resorted to. The first consists in placing
the flywheel at the front of the engine, as shown in Fig. 126.
This eliminates the flywheel housing, and permits of bringing
the gear box considerably closer, but there are also a number
of objections to this practice. Its purpose being to equalize the
torque of the engine before it is transmitted to the change gear,
the logical place for the flywheel seems to be between these two
parts. The crankshaft and its bearings are undoubtedly sub-
jected to more severe usage with the flywheel located in front.
With the very considerable weight of the flywheel almost directly
over the front axle the strains on the front tires are increased.
However, with the flywheel in this position its diameter is less
closely limited, and some manufacturers use the front mounted
flywheel as a radiator fan. With this construction the timing
gears of the engine are usually placed at the rear end, where
they are more accessible.

An alternate construction consists in joining the crankcase
and gear box by a yoke running around the flywheel, as illus-
trated in Fig. 127. Either both cases and the yoke may be cast
in a single piece; half of the yokes may be cast with either case
(as in Fig. 127), or the yoke pieces may be separate and secured
to the two cases by cap screws or bolts. This method enables
a saving in weight to be effected as compared with that illus-
trated in Fig. 125, and is free from the objections urged against
the front mounted flywheel. It has been adopted on several
American cars in recent years. The yoke around the flywheel
is conveniently situated for supporting the bearing for the clutch
and brake pedal shaft.

Unit power plant construction has become extremely popular
in this country.

Transmission Axles — Instead of combining the gear box with
the engine, some makers secure it rigidly to the rear axle
housing, thus forming what is known as a transmission axle.
The leading exponent in America of this system of construction
has been the Packard Co. The advantages of this arrange-

200 UNIT POWER PLANTS AND TRANSMISSION AXLES.

ment are that it does away with a separate gear box, thus elim-
inating one unit, that it permits of using a comparatively long
propeller shaft whose angularity will not vary much under the
play of the body springs and the absolute value of which will
always be small, and that the propeller shaft and universal joint

FIG. 128. — SECTIONAL VIEW OF PACKARD CHANGE GEAR AND REAH

AXLE DRIVE (OLD MODEL).

run always at engine speed, and are never subjected to any
greater torque than the maximum of which the engine is capable,
hence they can be made somewhat lighter. Besides this, the
system does away with two or more universal joints in the
transmission line, requiring the use of only one such joint on

UNIT POWER PLANTS AND TRANSMISSION AXLES. 201

at most two. The chief disadvantage of the transmission axle
is that it materially increases the unsprung weight supported by
the rear wheels and tires, and thus tends to increase the wear
of the tires. Some difficulty is also met with in arranging the
control connections between the change gear lever on the spring
supported frame and the sliding bars in the unsprung gear box
in such a manner that the play of the springs will neither affect
the position of mesh of the sliding gears nor cause the control
lever to move on its sector or quadrant and produce an un-
pleasant rattle.

The majority of the transmissions built together with the rear
axle are of the three speed and reverse selective sliding type.
It is important that the length of the gear box be kept as small
as possible so that the moment of its weight around the axis
of the rear axle may not be too great. Those types of reversing
gears which economize space in the longitudinal direction are
therefore particularly suitable for rear axle gear boxes. In

FIG. 129. — GEAR Box ON FORWARD END OF TORQUE TUBE.

these gear boxes the two shafts usually lie in a horizontal plane
(Fijj. 128), since it is not practicable to place the secondary
below the primary shaft, as that would reduce the road clearance
too much, and the secondary shaft cannot well be on top, since it
is desirable to have the secondary gears run in oil and the height
of the oil in the case is limited by the level of the protruding
shafts. The constantly meshed gears and direct drive clutch are
generally placed at the rear, as some space in the longitudinal
direction can be saved in this way.

An arrangement of the gear box which affords some of the
advantages of the transmission axle and does away with some
of its disadvantages is illustrated in Fig. 129. The gear box
and rear axle here also form a unit, the two being connected
by the propeller shaft tube, or torque tube, and the gear box
hung from a cross member of the frame by a ball and socket
joint at its forward end. As in the case of transmission axles,

202 UNIT POWER PLANTS AND TRANSMISSION AXLES.

the angle between the two members of the universal joint varies
but little and is always small. Most of the weight of the gear
box is spring-supported and although it changes its position
relative to the frame as the body springs compress and extend,
this change in position is relatively much smaller and the difficulty
of properly connecting up the control lever is correspondingly
reduced.

Straight Line Drive — The last two mentioned arrangements
of the gear box lend themselves particularly to that form of
construction known as the straight line drive — that is, such an
arrangement of the different parts that when the car carries a
normal load the engine crankshaft, gear box primary shaft and
propeller shaft are in a straight line. Under these conditions
motion is transmitted uniformly through a single universal joint,
and owing to the relatively large distance between the rear axle
and the universal joint the play of the body springs has little
influence on the drive. In order to insure this straight line
relation of crankshaft and propeller shaft it is generally neces-
sary to carry the engine in a slightly tilted position, with the rear
end somewhat lower than the front, as if the engine crankshaft
were placed at the same level as the rear axle shafts the engine
flywheel would not clear the ground sufficiently. In all con-
structions in which there is only a single universal joint in the
propeller shaft, a substantially straight line drive should be
aimed at, for, as shown in the chapter on Universal Joints,
when the two shafts make an appreciable angle with each other
there are serious fluctuations in the ratio of transmission, and
consequently the transmission parts, and particularly the tires,
are subjected to extra severe strains.

CHAPTER IX.

BEVEL GEAR DRIVE AND REAR AXLE.

At present the great majority of pleasure cars are driven
through a shaft and bevel gears. The advantages of this drive
are that it can readily be completely enclosed, oil and dustproof,
and that it is reasonably efficient and noiseless. Any desired gear
reduction up to 5 to 1 can easily be obtained. A disadvantage
of the bevel gear drive, as compared with the chain drive, is
that with the former it is difficult to provide more than one gear
ratio.

The two chief elements of a shaft drive are the propeller
shaft and the bevel gearset. The drive also comprises either one or
two universal joints. It was shown in a previous chapter that
two such joints are necessary if an absolutely uniform transmis-
sion of motion from the gear box or engine to the rear axle is
required, and on the higher grades of cars two universals are
generally employed. However, by making the propeller shaft
comparatively long, and placing the gear box and rear axle in
such relation to each other that when the vehicle carries a normal
load, the primary shaft of the change gear and the propeller
shaft are nearly in line, many designers get along with a single
universal, which they insert between the transmission tail shaft
and the propeller shaft.

Types of Rear Axles. — Rear axles are divided into live
and dead axles. A live axle is an axle through which the pro-
pelling power is transmitted to the driving road wheels, and a
dead axle is one which merely Carries the weight of the frame
and body. Cars driven by shaft and bevel gears, shaft and worm
gears, or by a single chain, have live axles, whereas cars driven
by double (side) chains have dead axles.

A live axle has two principa1 functions to perform, viz., to
support the weight carried upon the rear springs, and to transmit
the power to the road wheels. These two functions can be per-
formed by a simple revolving axle, but in that case the direc-

203

204

BEVEL GEAR DRIVE AND REAR AXLE.

BEVEL GEAR DRIVE AND REAR AXLE. 205

tion of the stress due to the weight carried changes constantly,
and since the resistance of the material is greatly lessened if
the stress alternates in direction, it is much preferable to support
the weight on non-rotating parts. Some of the earlier shaft and
single chain driven cars had rear axles consisting merely of a ,
revolving shaft running in bearings secured to the body springs.
The axle had one road wheel rigidly secured to it, the other
wheel being secured to a sleeve free upon the shaft; one master
gear of the differential was secured to the shaft, and the other
to the sleeve. However, for the reason above stated, practically
all modern live axles comprise one part — the housing — for sup-
porting the load, and another — the axle shafts — for transmitting
the power.

In the normal operation of a car there are three distinct
sources of stress in a rear axle, viz., the weight of the frame
and body resting on the axle, the bearing load due to the bevel
gear tooth pressure, and the torsion on the axle shafts. An
axle in which all of these stresses come on the axle shafts is
known as a plain live axle. An axle in which the axle shafts are
subjected only to torsional stress and the stress due to the weight
of the frame and body, is known as a semi-floating axle, and an
axle in which the shafts are relieved of all except torsional
stress, is known as a full floating axle.

Each rear axle has two sets of bearings, viz., those supporting
the differential and those through which the axle is supported'
in the road wheels. The former, which we may call the differ-
ential bearings, are subjected to a load due to the tooth pressure
of the bevel driving gears, while the latter are subjected to a
load due to that part of the weight of the frame and body which
rests on the rear springs. It is directly apparent that in the plain
live axle, illustrated in Fig. 130, the load due to the bevel gear
tooth pressure is taken up by the axle shafts, as is the load due
to the weight of the rear part of the car. The stress in the
shafts due to these loads reverses twice every revolution of the
axle, and since it adds to the torsional stress of driving, it can
readily be seen that the axle shafts in this type of axle must be
made very rugged in order to stand up to the work. As a
matter of fact, axle breakages were rather frequent when axles
of this type were common.

In the semi-floating axle illustrated in Fig. 131 the axle shafts
are relieved of the bevel gear tooth pressure. This is accom-
plished by carrying the differential gear directly in bearings in
the axle housing, instead of supporting it upon the axle shafts.

206 BEVEL GEAR DRIVE AND REAR AXLE.

BEVEL GEAR DRIVE AND REAR AXLE. 207

The latter are made somewhat smaller in diameter than the bore
of the hubs of the differential housing, and pass through these
hubs without contacting with them, establishing driving connec-
tion with the differential master gears by square, hexagonal or
fluted driving joints.

The next step in axle development was to relieve the outer
end of the axle shafts of bending stress, in the same way as
the inner ends. This is accomplished (see Fig. 132) by extending
the axle tubes entirely through the wheel hubs, and mounting
the wheel bearings on the outside of these tubes, so that the
weight load is transmitted directly from the axle housing to the
wheel hub. The axle shafts extend through the housing, and
their outer ends connect with the wheel hubs through driving
dogs or positive clutches. With an axle of this design it is possi-
ble to entirely withdraw the driving shafts from the axle without
removing the axle from the car.

An intermediate type between the full floating and semi-floating
axles has recently been used to some extent, differing from the
full floating in that its shafts are rigidly connected to the wheel
hubs — which latter are mounted on bearings on the outside of
the axle housing — by driving flanges bolted to the wheel hubs,
and either forged integral with the axle shafts or securely keyed
thereto. In an axle of this type the shafts, although relieved of
weight carrying loads, are subjected to endwise stresses due to
skidding, and it has been suggested to call these three-quarter
floating axles. In a three-quarter floating axle there is only one
bearing in each wheel hub, which results in economy of manu-
facture. There is also less strain on the bearings from lateral
shocks on the wheels than in a full floating axle.

Full floating axles in which the shafts are entirely relieved of
all but torsional stresses are generally regarded as the most
highly developed type, and are widely used on high grade cars.
They are more expensive to manufacture than semi-floating and
plain live axles.

Shaft Materials. — Propeller shafts and rear axle driving
shafts may be made from 30 point carbon steel, 45 point carbon
steel, 30 point carbon 3l/2 per cent, nickel steel, vanadium steel or
chrome nickel steel. In each case the material must be heat
treated, as a suitable heat treatment almost doubles the elastic
limit in some instances. The heat treatment generally consists

208

BEVEL GEAR DRIVE AND REAR AXLE.

I
k

BEVEL GEAR DRIVE AND REAR AXLE. 209

in quenching the steel in oil at a suitable temperature, and then
reheating it to a certain lower temperature from which it is
cooled slowly. Thus the standards committee of the Society of
Automobile Engineers recommend the following treatment for
35 point carbon steel : After forging or machining heat to
1500°-1550° Fahr., cool slowly, reheat to 1450°-1500° Fahr.,
quench, reheat to 600° -1200° Fahr., and cool slowly. The higher
the reheating temperature the tougher the steel will be, but the
lower the reheating temperature the greater will be its tensile
strength. The steel has a tensile strength of 50,000 pounds per
square inch in the annealed condition, and about twice that when
heat treated and drawn at a low temperature. For the 45 point
carbon steel the same heat treatment is recommended. In both
cases the parts may be machined after they have cooled from the
first heating. The 45 point carbon steel attains a tensile strength
of 125,000 pounds when drawn at a low temperature and 95,000
pounds when drawn at a high temperature. The elastic limit
of this steel when heat treated varies between 90,000 pounds
and 60,000 pounds. The heat treatment for the 3^ per cent,
nickel steel is comparatively simple, consisting in heating to
1500°-1600° Fahr., quenching, heating to 600°-1200° Fahr., and
cooling slowly. This treatment increases the elastic limit of the
steel from 55,000 to as much as 160,000 pounds per square inch.
The elastic limit of chrome nickel steel after heat treatment may
be as high as 175,000 pounds per square inch.

The heat treatments giving the extreme elastic limits can-
not, however, be used for transmission shafts, which must be
made of relatively tough material and also must be worked
after being heat treated, which means that the material must
not be too hard to machine satisfactorily. An elastic limit of
100,000 Ibs. per square inch for nickel steel and 120,000 Ibs.
per square inch for chrome nickel steel is about all that is
generally obtained in shafting material. That the elastic limit
even of steel of the same denomination may greatly vary with
the composition and the heat treatment is shown by figures
given in a paper read before the American Society of Me-
chanical Engineers by John Younger, of the Fierce-Arrow
Motor Car Company. This concern, in its 5-ton trucks, orig-
inally used rear axle shafts made of chrome nickel steel con-
taining 0.20% carbon, 1.5% chromium, 0.30% manganese, 4%
nickel, 0.20% silicon and less than 0.04% phosphorus and
sulphur, which showed an elastic limit of 90,000 Ibs. per square
inch and an ultimate strength of 105,000 Ibs. per square inch.
These shafts gave trouble by breaking at the ends of the fluted

210 BEVEL GEAR DRIVE AND REAR AXLE.

portion, and another steel was then substituted containing
0.30% carbon, 0.50% manganese, 1.5% chromium and 3.5%
nickel, which after heat treatment showed an elastic limit of
175,000 Ibs. per square inch and an ultimate strength of
185,000 Ibs. per square inch. This proved entirely satisfactory.

Higher grades of steel are usually employed in the rear
axle drive shafts than in the propeller shaft, for the reason
that an increase in the diameter of the axle shafts, necessitat-
ing a corresponding increase in the diameter of the axle tubes,
bearings, etc., entails a comparatively large increase in weight,
and that dead weight. Besides, with the usual reduction ratios
the torque on each rear axle shaft is twice as great as the
torque on the propeller shaft, or more. Of fourteen propeller
shafts investigated by Russell Huff, eleven were made of
medium carbon steel, containing for the most part 0.35% car-
bon; two were made of chrome nickel steel and one of chrome
vanadium steel. Of the rear axle shafts of the same cars only
one was of carbon steel, while eight were of chrome nickel
steel, four of nickel steel and one of chrome vanadium steel.
Mr. Huff calculated the factor of safety in each case and found
the average value to be 5.8 for the propeller shafts and 2.7
for the rear axle shafts, both based on the elastic limits of the
materials. Half of the cars had transmission axles. For the
other half the average propeller shaft factor of safety was only
3.75.

Calculation of Shaft Diameters— Propeller shafts and driv-
ing shafts of full floating type rear axles are subjected to tor-
sional stresses only, and may therefore be calculated by the same
methods. The diameters of these shafts depend to quite an ex-
tent upon the method of fastening employed at their ends.
One formerly common method consists of milling down the
ends of the shaft to an approximate square whose width of face
is about 0.8 times the diameter of the shaft, and broaching out
the hub of the universal joint fork, etc., correspondingly. Un-
fortunately this greatly reduces the strength of the shaft at the
joints, and the excess strength of the shaft proper is absolutely
useless. The square portion of the shaft should gradually merge
into the round section, in order that there may be no concentra-
tion of stress at a sudden change in the section. The strength
of the square portion of the shaft is only about 0.7 times that
of the full shaft. In order to save the excess weight in the
propeller shaft, due to the greater torsional strength of the full
round, as compared with the square section, some manufacturers
use propeller shafts of square section, thereby saving about 20

BEVEL GEAR DRIVE AND REAR AXLE.

211

per cent, in weight. Hexagonal joints cause less loss of strength
than square joints, and are used to some extent.

A second method of fastening the universal joint forks, gears,
etc., to the shafts consists in keying them to a tapered seat. This
also slightly reduces the strength of the shaft, but just how much
can only be conjectured. The most approved method of securing
these parts to driving shafts consists in fluting the shafts and
broaching out the hubs, using either four or six flutes. The loss
in strength due to the flutes is considerably less than that due to
squaring the shaft. If it is desired to use the lightest possible
propeller shaft, or rear axle driving shafts, the ends are upset
so that after they are squared or fluted they are at least the
same strength as the circular section of the shaft proper. This
practice prevails to a large extent in the manufacture of the
highest grade of cars.

Tests of Fluted Shafts — Comprehensive torsion tests of
plain and fluted shafts have been made by C. E. Larard, whose re-
sults are contained in a paper presented to the Incorporated In-
stitution of Automobile Engineers in London in January, 1911.
Mr. Larard's tests covered two
materials, viz., mild steel and
nickel steel. These tests were
made more particularly with a
view to determine the strength of
fluted shafts for change gear
boxes, hence the use of mild steel
of only about 0.15 per cent car-
bon. This steel is suitable for
case hardening, a treatment re-
quired by sliding gear shafts, but
is not adapted for propeller shafts
owing to its low elastic limit.
The results are here given to
show the effect of fluting on the
torsional strength of shafts.

FIG. 133. — SECTIONS OF FLUTED

Mr. Larard's tests on carbon steel SHAFTS TESTED...

were made on four pairs of specimens, one specimen of each pair
having six keyways, while the other one was a plain cylinder of a
diameter equal to the bottom diameter of the fluted shaft. The
largest fluted shaft was of 2^ inches, and the smallest of IJ4
inches outside diameter, the corresponding plain shafts were of
2 and 1 inch diameter respectively. The angular extent of the

212

BEVEL GEAR DRIVE AND REAR AXLE.

keyways is shown in Fig. 133. In the following table are given
the most important results of the tests on these specimens.

TABLE VII.— TORSION TESTS OF MILD STEEL SHAFTS.

Diameter of Particulars of
Specimen. Keyway.

Out- Bottom of Depth at

side, Keyway, Width,
Ins. Ins

'eptl
Edge,
Ins.

Limit of
Elasticity

Pounds -
Inches.

Torque at
Fracture

Pounds-
Inches.

155,000
90,800
57,700
41,600
38,000
28,100
16,550
11,700

Form

Specimen. Ins. Ins. " Ins.

Fluted 24 2 i A 16,100

Plain 2 14,800

Fluted 1W Hf A A 7,400

Plain Hi 6,400

Fluted If It H * 4,430

Plain Hi 4,850

Fluted li 1 i * 2,750

Plain 1 2,680

Comparing the figures of the several pairs in the above table,
it will be seen that in each case the elastic limit of the plain speci-
mens is slightly less than that of the fluted specimens, thus show-
ing that some strength is added by the keys. The maximum
torques which the shafts will withstand also are slightly greater
in the case of the fluted shafts than in that of the corresponding
plain shafts. It was found from these tests that a fluted shaft of
diameter d is equal to a plain shaft of diameter 0.86d, as far as
the elastic limit is concerned.

Similar tests were made with two sets of fluted shafts of nickel
steel, of the dimensions shown in Fig. 133. One of each pair was
tested in the condition (except for the machining) in which it was
delivered from the forge, while the other was oil hardened before
machining and testing. The results of these tests are given in the
following table :

TABLE VIII.— TORSION TESTS OF NICKEL STEEL SHAFTS.

Treatment

of
Material

Normal ....... 2$

Oil Hardened. .

Normal Hi

Oil Hardened..

Normal If

Oil Hardened..

Normal li

Oil Hardened

The most remarkable result of Mr. Larard's test is perhaps the
low elastic limit of mild steel as compared with the breaking
strength. It will be seen from Table VIII that oil hardening sub-
stantially doubled the elastic limit.

Diameter of Particulars of Limit of
Specimen. Keyway. Elasticity
Out- Bottom of Depth at in

Torque at
Fracture
in

side,
Ins.

Keyway,
Ins.

Width, Edge,
Ins. Ins.

Pounds-
Inches.

Pounds -
Inches.

41,800

226,200

78,100

265,200

23,000

107,200

Iff

Hi-

39,600

116,000

11,800

68,000

26,800

77,000

5,900

30,360

12,200

33,400

BEVEL GEAR DRIVE AND REAR AXLE.

213

In calculating the diameter of the shafts a stress of 20,000
pounds per square inch may be allowed in the case of heat
treated carbon steel, 30,000 pounds per square inch in the case
of heat treated nickel steel, and stresses proportional to their re-
spective elastic limits in the cases of other steels. The conven-
tional formula for the torsional strength of cylindrical shafts is

T X 12 = 0.196 d?S,

and since a squared shaft is only 0.7 times as strong, and the
maximum safe stress for carbon steel is 20,000 pounds per square
inch, we find the maximum safe load to be

T X 12 = 0.7 X 0.196 X 20,000 X d*
Hence, for a carbon steel shaft with square ends

d =

6.12

Similarly, for a carbon steel shaft with fluted or hexagonal ends
^~T~ ,M

d = ;

6.53

for a nickel steel shaft with
square ends

d =

6.94

for a nickel steel shaft with
fluted or hexagonal ends

for a carbon steel shaft with
upset ends

FIG. 134. — DIAGRAM OF BENDING
MOMENT IN SEMI-FLOATING AXLE.

for a nickel steel shaft with upset ends

d =-

7.8

Shafts of Semi-Floating Axles. — In a semi-floating axle
the shafts are subjected not only to torsional loads, but also to a
bending moment. The length of the lever arm (Fig. 134) is
equal to the distance between the centre plane of the road wheel
and the centre line of the outboard axle bearing, and the load
is equal to the weight supported by one of the rear wheels. The

214 BEVEL GEAR DRIVE AND REAR AXLE.

load on the rear axle is not known when a car is designed, but
can be determined approximately by means of the following
formulas :

Two passenger runabout

wheel base2

W = + 200 pounds.

Five passenger open touring car
wheel base2

W = + 600 pounds.

Seven passenger open touring car
wheel base2

W = + 800 pounds.

The maximum bending moment on the shaft occurs at the
centre of the bearing and is equal to wl, where w is the load
carried by one of the wheels, and / the distance between the
centre plane of the wheel and the centre of the bearing. Let T
equal the maximum torque on one of the axle shafts in pounds-
feet; that is, one-half the product of the maximum engine torque
by the low gear reduction ratio and the bevel gear reduction
ratio. If the diameter of the shaft is d, the distance c of the

outermost fibre from the neutral axis is — and the moment of

inertia / of the cross section is , hence inserting in the well

64
known formula for bending stress

we have

The polar moment of inertia of the circular section is - ,
and inserting in the formula for torsional stress 32

St=~T'

we get 192 T

ird5

These two stresses can be combined by means of the equation
given on page 172, as follows :

16 wl / 192 TV 1 /32W/V

BEVEL GEAR DRIVE AND REAR AXLE. 215

Hence

(61.14 7T + -- (10.18 wlY
d= ! (45)

This diameter is required at the bearing. The bending moment
decreases uniformly from the centre of the bearing to the centre
of the road wheel and the centre of the master gear hub, re-
spectively, and if the lightest possible construction is desired
the shaft diameter may be decreased from the value calculated
by equation (45) at the bearing to the diameter required for
the torsional stresses only at the centre of the road wheel and
the master gear, respectively.

Helical Bevel Gears. — There are two types of bevel gears
employed in rear axle drives, viz., the ordinary bevel gear whose
tooth elements are straight lines, and the helical bevel gear whose
tooth elements curve around the gear cone.

The helical-bevel gear type of final drive was introduced
in 1913 by the Packard Motor Car Company, and this drive has
since been widely adopted for pleasure cars. Helical bevel
gears with gear axes at right angles bear the same relation to
straight bevel gears as helical spur gears with parallel axes to
straight spur gears. Their chief advantage is their noiseless
operation at all speeds, but they have a number of other impor-
tant advantages which together were responsible for their al-
most instant popularity. These advantages are more or less
inter-related. For instance, with helical bevel gearing a smaller
minimum number of teeth can be used than with straight bevel
gearing. What limits the minimum number of pinion teeth in
straight bevel gearing is the fact that as the number of teeth is
decreased the non-uniformity of motion, and consequently the
noise, increases. But helical bevel gearing is inherently far
more silent, hence this limitation is practically eliminated and
pinions with a smaller number of teeth may be used.

Cause of Non-Uniform Gear Motion. — Before proceeding
with the helical bevel gear, it will be well to consider the cause
of non-uniform motion and noise in straight bevel and spur
gears, because it is the absence of this cause in the helical gear
to which it owes its valuable properties. In a correctly cut
pair of involute spur gears there is — assuming proper spacing of
shafts and absolute rigidity of same — uniform transmission of
motion as long as the arc of contact or arc of action is not less
than the circular pitch. As the number of teeth decreases the

216 BEVEL GEAR DRIVE AND REAR AXLE.

arc of contact approaches the circular pitch and with the 15
degree involute system 12 is the smallest number of teeth with
which the arc of contact exceeds the circular pitch and with
which uniform transmission of motion is theoretically obtain-
able.

The above applies to perfectly cut teeth while they are new.
Spur gear teeth have a combined rolling and sliding motion
and they are naturally subject to wear, the wear on any part
of the tooth flank being substantially proportional to the rela-
tive sliding motion at that part of the flank and to the load
supported by it. Now, unfortunately, the relative sliding mo-
tion, and, consequently the wear, varies greatly at different
points of the tooth flank.

Referring to Fig. 135, in which two teeth of a pair of meshed
gears are shown to be in contact at the pitch points — the points
of intersection of the flanks with the pitch circles — the mo-
mentary direction of motion of the contacting points of both
wheels is the same, tangential to the pitch circles at their point
of contact. Hence, there is at this moment no sliding of one

FIG. 135. — SHOWING DIRECTION AND MAGNITUDE OF MOTION OF

TOOTH CONTACT SURFACES AT DIFFERENT POINTS OF MESH.
tooth over the other, the motion being purely rolling. Now
consider the other pair of teeth shown in contact in the same
figure. The motion of each point is in the direction of a tangent
to a circle through this point concentric with the corresponding
pitch circle. These lines diverge considerably, and it is obvi-
ous that when two surfaces in contact move in different direc-
tions they must slide over each other. In our example the
sliding motion is represented by the dotted line connecting
the ends of the arrows representing the motion of each point.
Sliding in spur gears has been investigated by O. Lasche, and
Fig. 136 represents his wear characteristic showing the distribu-
tion of wear over the tooth flank. There is no sliding at the
pitch line, and wear increases from the pitch line both toward
the top and the root of the tooth. This effect can often be
plainly seen on an old straight spur or bevel gear on which
there is a line on the tooth flank at pitch height which does not
show any wear while all the rest of the flank is polished.

BEVEL GEAR DRIVE AND REAR AXLE. 217

When a tooth flank is thus unevenly worn, the condition of
uniform motion — that a normal to the contact surfaces must
always pass through the pitch point — is no longer fulfilled. The
result is that the gears transmit motion non-uniformly, the
driven gear is alternately accelerated and allowed to decelerate,
and, in consequence, the gear is noisy. True helical bevel gears
are gears cut from blanks of frustrated conical form, the teeth
of which curve around the gear axis in such a way that the
elements of the tooth in the pitch cone surface always make the
same angle with a pitch surface element. This angle is known
as the angle of spiral. In practice the elements of the teeth
form circular arcs of given radius and the gear approximates
the true helical bevel form.

Arc of Approach Arc of Recess

FIG. 136.— WEAR CHARACTERISTIC OF GEAR TOOTH.

Helical bevel gears may be either right hand or left hand,
according to the direction in which the teeth wind around the
gear. Only gears of unlike denomination will mesh together,
that is, a right hand pinion with a left hand gear, or a left
hand pinion with a right hand gear. The question of whether
to use right hand or left hand pinions is of much importance,
as the denomination of the pinion determines the direction and
magnitude of the end thrust, which is much greater with helical
bevel than with ordinary bevel gears.

Angle of Spiral. — In laying out a pair of helical bevel gears
one of the factors to decide on is the angle of spiral. This

218 BEVEL GEAR DRIVE AND REAR AXLE.

should be such that the angular advance corresponding to the
face length of the gear is somewhat greater than the circular
pitch. If this relation holds, then there is at all times pitch
line contact at some part of the teeth and this obviates any
tendency of the gear teeth to wear away more quickly on some
part of their flanks than on others; for, as soon as any part
of the flank wore ever so little more than the pitch line, the
pressure at that part would be reduced and the wear thereby
automatically cut down. This is the principle which insures
that tooth contact in a helical bevel gear does not deteriorate
with age and that such a gear remains quiet throughout its
life.

Minimum Number of Teeth. — High speed motors, espe-
cially those of moderately powered cars, require a high gear re-
duction and the helical bevel gear has made it possible to obtain
this higher reduction in a single step without running the risk
of non-uniform and noisy tooth action.

Helical bevel drives with pinions of ten teeth are entirely
practical and these permit of obtaining any gear ratio that
may be needed for pleasure cars. In the case of such small
numbers of teeth the pinion must be made integral with its
shaft. As regards strength it is believed that a helical bevel
pinion of a given pitch diameter and cut with teeth of a certain
diametral pitch will safely transmit the same power at a certain
speed as a straight bevel pinion with the same pitch diameter
and diametral pitch; this notwithstanding the fact that the
normal load on the teeth is considerably greater than with the
straight bevel gear. If the power transmitted is the same the
tangential force will be the same in the two cases. On the
other hand the end thrust is much greater with the helical
than the straight pinion and the normal tooth load usually
figures out about 15 per cent higher in the case of the former.
Probably the chief reason for the greater strength of the helical
pinion is that since there is always pitch line contact there
can be no non-uniform motion to cause heavy extra strains.
There is, however, another reason for the greater strength of
a helical bevel pinion, and that is that it has more teeth in
contact at one time. If the spiral advance corresponding to
the width of face is greater than the circular pitch, then the
arc of action includes always at least one more tooth, than in a
similar straight bevel set. The two outer teeth will be in con-
tact over only a part of their length, but as far as breakage is
concerned practically their whole strength counts.

BEVEL GEAR DRIVE AND REAR AXLE. 219

In practice the angle of spiral is usually 30 degrees or close
to it, as with the pitches and proportions of face width to
centre distance this gives a spiral advance somewhat greater than
the circular pitch.

Since the circular pitch

P*
and the spiral advance

s = f sin 0

where PA is the diametral pitch; /, the face width and 0, the
angle of spiral, we have in the case of a 50 tooth 5 diametral
pitch gear with 30 degree angle of spiral and 1^-inch face,

3.146
PA = - = 0.628 inch

s = 1.5 X 0.5 = 0.75 inch

which gives an overlap of about 20 per cent. For unusually
small pitches or relatively large face widths smaller angles of
spiral will give the necessary overlap of teeth, and with the
reverse conditions a greater angle of spiral must be used, but
makers of gear cutting machinery advise against an angle larger
than 35 degrees.

Calculation of Blanks. — The calculation of the blanks for
the pinions and gears partakes of the methods used for calculat-
ing the blanks for straight bevel gears and helical spur gears
respectively. Thus, for instance, the pitch diameter is calculated
by the same equation as used in the case of helical spur gears,
viz., N

pn X cos a

where N is the number of teeth ; />n, the normal diametral pitch
and a the angle which the tooth flank element makes with the
pitch cone element (angle of spiral). With regard to the adden-
dum there is no complete agreement. In spur gears the ad-
dendum is made equal to 0.3183 pc = I/pa, and the dedendum,
0.3683 />c = 1.157//M, the latter being the sum of a working
depth of 0.3183 pc below the pitch circle and a clearance of
0.05 pc = 0.157//>d. Therefore, the total working depth of
0.6866 pc = 2//>d extends equally above and below the pitch
circle. Now it is known that in a pinion with a small number
of teeth there is a tendency to undercutting and consequent
weakening of the pinion teeth. To obviate this it is customary
in helical bevel pinions to have most of the working depth

220 BEVEL GEAR DRIVE AND REAR AXLE

above the pitch circle. One maker of helical bevel gear cutting
machines recommends that on the pinion 0.7 of the working
depth be above the pitch circle and 0.3 below the pitch circle.
In the gear the proportion must be reversed, that is, 0.3 of the
working depth must be above the pitch circle and 0.7 below the
pitch circle.

Let it be required to lay off the blanks for a helical bevel
gear and pinion of 48 and 12 teeth respectively, 5 pitch, 30 de-
gree angle of spiral with 0.7 of the working depth above and 0.3
below the pitch circle in the pinion. We have in the first place
for the maximum pitch diameters
12

= 2.771 inches

5 X 0.866
and

48
= 11.085 inches.

5 X 0.866

The total working depth of the 5 pitch teeth is
2

— = 0.4 inch
5

hence, in the pinion the working depth above the pitch circle
or the addendum is

0.7 X 0.4 = 0.28 inch
and the working depth below the pitch circle

0.3 X 0.4 = 0.12 inch.
The clearance is 0157

— = 0.0314 inch.

The pitch angle of the pinion is such that

2.771

tangent pitch angle = = 0.25

11.085

pitch angle = 14 degrees.

The face angle of the pinion is greater than the pitch angle by
an angle such that its tangent is
0.28

= 0.0487

V1.3852 + 5.S432
and the angle is 2° 47'.
Hence, the face angle is 16° 47'.
The face diameter of the pinion is

2.771 + (2 X 0.28 X cos 14°) = 3.314.

The pitch angle of the gear is the complement of the pitch angle
of the pinion or

BEVEL GEAR DRIVE AND REAR AXLE

221

90° _ 14° = 76°

and the angle which the addendum adds to the pitch angle is
such that its tangent is

0.12

= 0.0208

V1.3852 + 5.543s

FIG. 137.— LAY-OUT OF A PAIR OF HELICAL BEVEL GEARS.

and the angle is 1° 12',
hence, the face angle is

76° + 1° 12' = 77° 12'

222 BEVEL GEAR DRIVE AND REAR AXLE.

Strength of Bevel Gears. — As was stated previously, a pair
of helical bevel gears of given pitch diameters and pitch will
transmit the same power as a pair of straight bevel gears of
the same pitch diameters and pitch, and the following consid-
eration applies to both kinds of gears. A modification of the
Lewis formula has been worked out for bevel wheels, according
to which the strength of a bevel pinion is equal to that of a spur
pinion of the same face, pitch and number of teeth, multiplied
by the ratio of the smallest to the largest pitch diameter. It
is at once apparent that this formula is not a rational one, for
if the pinion face extended nearly to the apex the formula
would make the strength almost nil, which is far from being
correct. It is therefore stipulated that the formula shall be
applied only if the small pitch diameter is not less than two-
thirds the big pitch diameter. But if this formula is applied
to existing automobile bevel gears it is found to give such
high values for the stress that it is at once seen to be incorrect.
The trouble is mainly with the Lewis formula, which is based on
wrong assumptions. Instead of the whole tangential force com-
ing at the end of one tooth, the force is always divided between
two or more teeth, and when the contact is at the end of one
tooth it is not at the end of the other tooth or teeth. G. H.
Marks, who made a series of tests on cut gears at Leland Stan-
ford, Jr., University, which were reported in a paper read before
the American Society of Mechanical Engineers in 1912, showed
that the Lewis formula is partly based on erroneous premises
and that the arc of action must be taken into account to get a
tolerably accurate result if gears of all kinds are considered.

The bevel gear tooth, whether straight or helical, decreases
in pitch uniformly from the outer end, where the pitch has
the nominal value, to the apex of the gear cone. Let the face
width be equal to 1 — <* per cent of the distance from the
outer end of the tooth to the apex, which distance we may desig-
nate by L. Now let us take any small section dx of the tooth
at a distance x from the apex. The tangential pressure which
this section will support we know to be proportional to the
circular pitch and to the width of face dx. But the circular
pitch at this part of the face width, if p is the nominal circular
pitch, is

Also, a tangential force Fx on the pitch circle at a distance x

BEVEL GEAR DRIVE AND REAR AXLE. 223

from the apex is equivalent to a tangential force on the maxi-
mum pitch circle

X L

Hence we may write for the tangential force which the
section dx of the tooth will support (using the Lewis formula)
x Spy

L L

and this is equivalent to a tangential force on the pitch circle
of the large end of

Spy x Spy

d F _ x2dx X — = x2 dx

L L L-

If we integrate this expression between the limits x = L and
x = a L we get

f L

I Spy Spy /L3 a8L8 \

F = x2dx = ( )

I L2 L2 \3 3 /

JaL

SLpy / \

= -^-(1-aS) (46)

in which F is the tangential force on the pitch circle at the
large end; S, the permissible stress in pounds per square
inch ; p, the circular pitch at the large end ; L, the pitch line
length from the large end of the pinion; y, the Lewis con-
stant for the particular number of teeth, and a, the proportion
of the pitch line length from the inner end of the pinion to
the apex, to the pitch line length from the outer end of the
pinion to the apex of the cone. To be absolutely correct the
equation should also contain a factor depending upon the num-
ber of teeth in contact at one time and a factor dependent upon
the pitch line velocity. But both of these items vary only
within relatively narrow limits in pleasure cars, and as there is
some uncertainty as to their exact influence on the strength of
the gears it is permissible to neglect them. Practical data in
the author's possession shows that if a heat treated alloy steel,
such as 3l/> per cent nickel or its equivalent, is used, the value
of the stress in the above equation may be 25,000. This
stress has been arrived at by analyzing the gears of several
rather high powered cars and is based on the direct torque of
the engine, not the geared-up torque. It appears that in mod-
erately powered cars in which the full engine power is used a

224 BEVEL GEAR DRIVE AND REAR AXLE.

greater part of the time and where space restrictions are not
so severe, the gears are made somewhat more liberal and a
stress of 20,000 may be used. Also, if the material is not
equivalent to 3l/2 per cent nickel steel, the stress should be chosen
lower in proportion to the elastic limits. Using a somewhat
lower stress, which leads to gears of larger dimensions, has the
advantage, at least in the case of straight bevel gears, that, ow-
ing to the larger contact surfaces the tendency to noisy operation
is reduced.

Direction of Thrust Loads. — When a car is being driven for-
ward, the propeller shaft and bevel pinion turn right-handedly,
while when the car is being backed the bevel pinion turns left-
handedly. Therefore, a right-hand pinion tends to draw into
the gear when the car is being driven forward, as a result of
the curvature of the teeth. The other causes of end thrust,
viz., the taper of the pinion cone and the pressure angle, tend
to force the pinion out of the gear. Of these two forces the
former is always the greater, and the net end thrust on the
shaft of a right-hand pinion is in the direction toward the gear
center and equal to the difference between the end thrust due
to the curvature of the teeth on the one hand and that due to
the pinion cone angle and the pressure angle on the other.

In backing, the end thrust due to the curvature of the teeth
of a right-hand helical pinion is away from the gear center and
in the same direction as the end thrust due to the cone angle
and pressure angle. The resultant is, therefore, in the direc-
tion away from the gear center and equal to the sum of the
end thrusts due to tooth curvature, cone angle and pressure
angle, respectively. Evidently, therefore, with a right-hand
pinion the end thrust is a maximum when the car is being
backed.

With a left-hand pinion all end thrusts add together for for-
ward drive and are in the direction away from the center of
the 'gear, while for the reverse drive the end thrust, though
still in the same direction, is equal in amount to the difference
between that due to tooth curvature on the one hand and to
the cone angle and pressure angle on the other. The maximum
end thrusts are the same whether a right or left-hand pinion
is used. As the car is being driven forward most of the time,
the right-hand pinion seems to have the advantage, but some
designers prefer the left-hand pinion because heavy thrust loads
in the direction away from the gear center can be accommodated
more readily than those in the opposite direction.

BEVEL GEAR DRIVE AND REAR AXLE.

225

Center of Load Distribution. — In attempting to calculate the
thrust loads we must first determine the center of load distri-
bution on a pinion tooth. We will assume that the load is dis-
tributed along the tooth in proportion to the strength of the
tooth section, which is an ideal condition. In actual practice
the adjustment of the gears will, of course, have much to do
with the load distribution. Let n be the ratio of the tooth face
to the pitch line length from the large end of the tooth to the
pitch cone apex, and let m be the proportion of the pitch line
length represented by the distance from the apex to the center
of the tooth load. From the well-known formula for strength
of gears it is known that the strength of a tooth section is
directly proportional to the circular pitch at that section, and
the pitch, of course, decreases uniformly from the large end
of the tooth to the apex, where it is zero. The strength of a
section of the bevel gear is also proportional to the width of
that section. In Fig. 138 the vertical lines ab, cd and ef repre-

FIG. 138. — LOCATING CENTER OF DISTRIBUTION OF TOOTH LOAD.

sent the circular pitch at the respective points and the line cd
is supposed to divide the entire gear into two parts of equal
strength. As the strength . of a gear is proportional to the
product of its circular pitch into its width of face, the two
areas A and B should be equal. If this is the case, then

[Lsin*+.L (l-n)sin
| n L cos 5

'L sin 5 + m L sin 5

— mL) cos8X2

+ L(1 — n)

nL= (L + mL) (L — nL)

2L — nL

n L

— m2 L2

226 BEVEL GEAR DRIVE AND REAR AXLE.

n* L2

= L2 — m2 L2

n = 1 — w2

Multiplying the pitch diameter by this value m we get the
effective pitch diameter, and with the aid of this we get the
tangential effort on the corresponding pitch circle by means of
the equation

TX24

FIG. 139.— SHOWING RELATION BETWEEN TANGENTIAL FORCE
AND NORMAL TOOTH PRESSURE.

The normal load on the tooth contact surface is, of course,
considerably greater than the tangential force, owing to the
inclination of the tooth elements against the pitch cone elements
(angle of spiral) on the one hand, and to the inclination of the
tooth flank (pressure angle) on the other. If we designate the
angle of spiral by a and the pressure angle of the tooth by P,
the normal pressure on the tooth is

F
P =

co s cc co s P

as may be readily seen from Fig. 139 in which AB represents
the tangential force on the pinion, AC the force in a plane

BEVEL GEAR DRIVE AND REAR AXLE.

\ I

FIG. 140. — SHOWING RELATION BETWEEN TANGENTIAL FORCE AND
PRESSURE ALONG PITCH CONE ELEMENT.

tangent to the pitch cone and perpendicular to the tooth ele-
ment, and CD the force normal to the contact surfaces. While
in determining the bearing loads of straight spur and bevel
gears a friction angle of 5 degrees is generally figured with,
this does not seem necessary in the case of helical gears, as
there is always pitch line contact at some point, and, conse-
quently, pure rolling motion at this point, with very little slid-
ing motion on the whole. The problem now is to resolve the
pressure P into a component parallel to the pinion axis (thrust
load) and another component perpendicular to the pinion axis
(radial load).

We first find the components of the tooth pressure along an
element of the pitch cone and perpendicular to that element,

FIG. 141.— PRESSURE ALONG PITCH CONE ELEMENT RESOLVED
INTO AXIAL AND RADIAL COMPONENTS.

228

BEVEL GEAR DRIVE AND REAR AXLE.

respectively. In Fig. 140 is shown a plan view of a right-hand
pinion supposed to rotate right-handedly. The horizontal arrow
represents the tangential force F on the inclined tooth and the
vertical arrow the resulting pressure along the pitch cone ele-
ment. It will be seen that

'Ce

= tan cc, hence Ce = F tan a

This pressure along the pitch cone element can again be re-
solved into two components, as shown in Fig. 141, one parallel to
the pinion axis and the other perpendicular thereto. It is here
necessary to take account of the direction of the forces and we
will call axial forces in the direction from the small to the

FIG. 142. — COMPONENTS OF NORMAL TOOTH PRESSURE PERPEN-
DICULAR TO PITCH CONE ELEMENT.

large end of the pinion, or away from the apex of the cone,
positive, and those in the opposite direction, negative. Radial
forces from the point of contact toward the axis will be called
positive and those oppositely directed, negative.

Resolving the force along the pitch cone element we get for
the axial component

Ca = — F tan cc cos 8
and for the radial component

CT = F tan cc sin 5.

We next take up the component of the normal tooth pressure
perpendicular to the pitch cone element through the point of
contact. From Fig. 142 it can be seen that this component Cp
is equal to

F sin j3 tan ft
p sin ft = = F •

cos cc cos /3

cosv

BEVEL GEAR DRIVE AND REAR AXLE

229

This component perpendicular to the pitch cone element also
may be further resolved into axial and radial components, as
illustrated in Fig. 143, the axial component being

tan /3 sin 8
C«a = F

and the radial component

COS Ct.

tan 8 cos 8

FIG. 143. — COM-
PONENT PERPEN-
DICULAR TO PITCH
CONE ELEMENT
RESOLVED INTO
AXIAL AND RA-
DIAL C o M P o -

NENTS.

cos a.

We now add like components of the forces
along the pitch cone element and perpen-
dicular to that element respectively and ob-
tain for the end thrust on a right-hand heli-
cal pinion turning right-handedly (forward
drive)

tan 8 sin 8 \

La = F ( — tan oc cos 8 + I

cos a /
and for the radial load on such a pinion

tan 8 co s 5 \

Lr = F (tan cc sin S -f- I

cos a I

These same equations apply to the case of a
left-hand pinion turning left-handedly (re-
verse motion). If a left-hand pinion turns
right-handedly (forward motion), the com-
ponent along the pitch cone element is in
the direction away from the apex of the
cone and the sign of its axial component
becomes positive. The same applies to a
right-hand pinion turning left-handedly.
However, the radial component of the force
acting along the pitch cone element is in this
case directed from the axis through the
point of contact and is, therefore, negative.
We, therefore, have for the axial and radial
forces on a left-hand helical pinion turning
right-handedly (forward drive) or a right-
hand helical pinion turning left-handedly
(reverse drive.). tan $ sin 8
La = F (tan cc cos 8 +

and

F ( — tan cc sin 8 +

cos cc
tan 8 cos 8

COSCf.

230

BEVEL GEAR DRIVE AND REAR AXLE

Axial and Radial Loads on Gear — Since action and reaction
are equal and opposite, the axial load or end thrust or* the gear
is equal and opposite in direction to the radial load on the pinion,
and the radial load on the gear is equal and opposite in direction
to the axial load on the pinion. There is, therefore, no need of
separately calculating the gear-bearing loads. We may summar-
ize our equations as follows:

FIG. 144. — GLEASON AUTOMATIC HELICAL BEVEL GEAR GENERATING
MACHINE.

Right-Hand Pinion Turning Right-Handedly.

Left-Hand Pinion Turning Left-Handedly.

End Thrust on Pinion — Radial Load on Gear.

tan /3 sin 5 \

Li = F ( — tan cc cos 5 + 1

cos a. /

Radial Load on Pinion, End Thrust on Gear.

tan j3 cos 5 \
L2 = F (tan cc sin 5 + 1

COSCf. /

BEVEL GEAR DRIVE AND REAR AXLE.

Right-Hand Pinion Turning Left-Handcdly.
Left-Hand Pinion Turning Right-Handedly.
End Thrust on Pinion, Radial Load on Gear.

tan P sin 8 \

L3 = F (tan a cos 5 -f I

cos a. /

Radial Load on Pinion, End Thrust on Gear.

tan P cos 5 \

£4 = F (_ tan cc sin 8 + — — - 1

cos a. /

231

FIG. 145.— CUTTER FOR FINISHING HELICAL BEVEL GEARS.

in which

F is the tangential force at the mean effective pitch radius
of the pinion ; a, the angle of spiral ; p, the pressure angle of the
teeth ; 5, the pinion pitch angle.

Manufacture of Helical Bevel Gears — By the Gleason method
the teeth of a helical bevel gear or pinion are cut by means of
a revolving cutter 12 inches in diameter with twenty inserted
blades. Half of the blades (alternate ones) serve for finish-
ing the inside flank of the teeth and the other half for finish-
ing the outside flank. The machine works on the generating

232 BEVEL GEAR DRIVE AND REAR AXLE

principle, the tooth flank being generated by relative motion
of the cutter holder and the work. One side of the tooth is
finished at a time, and when all the teeth have been finished on
one side the setting of the cutter and gear is changed before
work is begun finishing the other side of the teeth. The cutter
carriage is mounted on a vertical column which is supported
on a cradle with circular ways. A reversing mechanism is
employed to roll the cradle and rock the work. By means of
compound change gears the proper relative motion of the cradle
and work may be secured.

FIG. 146. — TYPICAL HELICAL BEVEL GEAR SET.

One advantage of the helical bevel gear over straight bevel
gears is that with the former not nearly the same degree of
adjustment is required in order to insure good tooth contact
and noiseless operation.

Straight Bevel Gears — Straight bevel gears can be made with
six pitch teeth for pleasure cars of the very smallest size, say
those with engines up to 100 Ibs.-ft. torque; five pitch for cars
with engines of 100-200 Ibs.-ft. torque, and four pitch for cars
with engines of more than 200 Ibs.-ft. torque. The pinions are

BEVEL GEAR DRIVE AND REAR AXLE 233

made with from eleven to eighteen teeth. In the largest cars the
pitch diameter of the bevel gear is limited to about 12 inches,
and in medium sized cars to 11 inches by reason of the required
ground clearance. The capacity of straight bevel gears may be
found by means of the same equation (46) as for helical bevel
gears, and the thrust and radial bearing loads can be calculated
by the methods explained in Chapter III.

In extremely powerful cars the gear dimensions have to be
made somewhat smaller, and in low powered cars they can be
made slightly more liberal as the lower unit pressures result in
greater silence of operation and the wear, of course, is also
reduced. In America straight bevel gears are now used only on
the cheaper pleasure car and on light delivery wagons.

Axle Housings — There are two general types of rear axle
housings, viz., built-up housings consisting of a central driving
gear housing of cast metal and of tubes forced into or bolted to
them, and integral pressed steel or drop forged housings. The
latter are a comparatively recent development, and since they
possess important advantages in the way of strength and mini-
mum weight, they are rapidly coming into extensive use. We
will first consider the older type, the built-up axle.

The central cast portion or driving gear housing, which is
generally cast of either steel or malleable iron, and occasionally
of aluminum, may be made in different ways, as shown in
Fig. 147. It must be of such a form as to accommodate the
differential and driving bevel gears, and it must be either split
in halves or provided with an opening big enough to admit the
driven bevel gear. Some designers give this housing such a
form that its walls at every point lie close to some contained
part, which necessarily leads to a more or less irregular outside
shape, whereas others employ regular housings of bulbous, spher-
ical or cylindrical shape. In order to secure the necessary
strength with a minimum weight of material it is often neces-
sary to rib the housing. The ribs may be placed either on the
outside or on the inside, but internal ribbing has gained con-
siderably in favor of late, as a smooth outside form is much
easier to keep clean.

Formerly housings split substantially in halves, as shown at
A and B, Fig. 147, were much used, and both are still met with.
It is now, however, more common practice to make the greater
part of the case in a single piece, with a segmental cover either
on top, as at C, or at an angle, as at D, so the opening is most
accessible from the rear of the car. As stated, these large open-

234

BEVEL GEAR DRIVE AND REAR AXLE

ings primarily serve the purpose of introducing the bevel gear
and differential. In some designs of rear axle the differential
is carried by a special plate bolted to the front of the driving
gear housing, which latter has large openings both in front and
rear.

Axle Tubes—Besides the driving gear housing the supporting
structure of the built-up rear axle comprises a pair of so-called
axle tubes. These are generally made from drawn material, but
occasionally they are cast. In a semi-floating axle the tubes
may be of uniform section from end to end, but in a full

C D

FIG. 147. — TYPES OF DRIVING GEAR HOUSINGS.

floating axle they are generally swaged down to a smaller
diameter where they pass through the hubs, so that it is not
necessary to use inordinately large bearings in the hubs. The
inner portion of the tubes should preferably be of considerable
diameter, as less weight of material is then required in order to
produce a certain resistance to bending and torsional strains.

The tubes may be fitted to the driving gear housing in different
ways. Ordinarily they are forced under pressure into integral
hubs of the driving gear housing and are then riveted, as shown
in Fig. 148 at A. This makes a very good job. They may also

BEVEL GEAR DRIVE AND REAR AXLE.

235

be screwed into the hubs of the housing and riveted. Instead
of being riveted the tubes may be secured by brazing, but this
is open to the objection that in brazing there is some danger of
accidentally overheating the metal and thus depriving it of a
great deal of its strength. The hubs of the housing should
preferably be beaded at their outer end. Some designers pro-
vide flanged sleeves which are brazed onto the tubes and are
bolted to the driving gear housing. This makes it possible to

FIG. 148. — METHODS OF SECURING AXLE TUBES TO DRIVING
GEAR HOUSING.

renew one of the tubes at any time without the necessity of
bringing it to a well-equipped machine shop. This construction
is illustrated in Fig. 148 at B. A very excellent though little
used method consists in splitting the hub of the driving gear
housing and clamping the tube by means of four bolts, the bolts
passing slightly beneath the surface of the tube so as to lock
it against endwise motion (C, Fig. 148). What is probably the

236

BEVEL GEAR DRIVE AND REAR AXLE.

best method of making a built-up axle consists in the use of
tapered and flanged swaged axle tubes which are bolted to the
driving gear housing, as shown at D, Fig. 148.

In order to insure a rigid axle housing it is necessary to have
a relatively long bearing for the axle tube in the hub of the
driving gear housing. This bearing is generally made from
two to two and a half times the outside diameter of the tube.
With the best class of workmanship a somewhat smaller length
of bearing is permissible. It is also advantageous, from the
standpoint of rigidity, to make the driving gear housing of con-
siderable width in the transverse direction of the vehicle, so the
tubes need not be so long. In some constructions the entire
portion of the axle housing between wheel hubs is made in two

FIG. 149.— FLANGED OUTER END OF AXLE TUBE RIVETED TO
COMBINED BRAKE SUPPORT AND BEARING HOUSING.

castings, and short tubes are inserted into these for the wheels
to run upon. Constructions may be found ranging all the way
from this extreme to that in which the tubes extend close up to
the differential bearings.

In a plain live or semi-floating axle a bearing housing has to
be provided at the outer end of the axle tube. While it is pos-
sible to expand the tube itself for this purpose, this construction
is rarely seen. The bearing housing is usually made in a separate
piece which is forced into or over the end of the axle tube and
secured by riveting or brazing. In one construction, illustrated
in Fig. 149, the axle tube is flanged at the outer end and riveted
to a casting which forms the brake carrier and bearing housing.

BEVEL GEAR DRIVE AND REAR AXLE.

237

Stresses on Axle Tubes — In discussing the stresses on the
housing of a driving axle we have to consider three distinct
cases, viz. :

(1) When the car is being started;

(2) When the car is being driven;

(3) When the car is being braked.

The first two cases are similar in that the kinds of stresses
produced are the same, only, since the clutch will transmit a

FIG. ISO.— LOADS ON HOUSING CORRESPONDING TO FORWARD
DRIVING.

greater torque than the motor is capable of developing, if the
former should be allowed to grip suddenly, the flywheel inertia
would cause a greater torque to be impressed on the rear axle
than would ever occur in regular driving. Just how much
greater it would be it is impossible to determine. When the car

238 iSEVEL GEAR DRIVE AND REAR AXLE.

is being started or driven forward the loads and reactions on
the axle structure are as shown in Fig. 150. There is a down-
ward pressure w on each of the two spring saddles. Then there
is the weight uh of the axle itself, which may be considered con-
centrated at the centre. Then there are also the loads b b on
the differential bearings, the load b' on the pinion bearing and
the reaction c at the point of support of the torque arm on the
frame. Finally there is the reaction P of the road surface on the
driving wheel causing the forward motion of the car.

It can easily be shown that the bearing loads b b are equal to
b', hence the pressures on the inner bearings create no stress in
the axle tubes. Also, the moments of forces b' and c around the
rear axle axis are equal and opposite, and therefore have no
effect on the axle tubes. There remain only the vertical bending
moments due to the weights w w on the spring seats, the vertical
bending moment due to the weight wi of the axle, and the hori-
zontal bending moment due to the propelling thrust P.

When the brakes are applied we have the same moments in
the vertical plane due to the weight resting on the spring seats
and the weight of the axle. The horizontal moment is in the
opposite direction and is proportional to the maximum braking
force instead of to the maximum propelling force, which former
is at least equal to the latter. In addition we have in this case
a torsion moment on the tubes, since the brake supports are se-
cured to the outer ends of the axle tubes, and when the brakes are
applied the friction between brake band and drum tends to carry
the brake supports around with the drums. This tendency is
counteracted by the torque tube or rod which is generally fixed
to the axle housing near its middle.

It will thus be seen that when braking, the axle tubes are sub-
jected to the same bending stresses as when driving, and, besides,
they are subjected to torsion. Hence the combined stress is
greatest when the brakes are applied, and only this case needs
to be considered. Owing to the fact that the weight of the axle
is not known in advance, and since it is small in comparison
with the weight on the springs, it is advisable to neglect this
factor.

In respect to the vertical load, the axle housing forms a beam
freely supported at both ends and loaded at the centre and two
intermediate points, the equivalent point of support being at the
centre of the road wheel in the case of a full floating axle and at
the centre of the outboard bearing in the cases of semi-floating
and plain live axles. The bending moment increases from noth-

BEVEL GEAR DRIVE AND REAR AXLE. 239

ing at the point of support to the maximum at the centre of the
spring seats and is constant between spring seats. (See Fig. 151.)

In respect to the horizontal bending moment, each half of the
axle may be considered as a cantilever, the middle of the axle
being the fixed end of the lever and the load being applied to
the outer, free end. The variation of all of the moments is shown
in the three-plane diagram, Fig. 151.

Now, let us take any section of the tube inside the spring seat
at a distance x from the centre plane of the road wheel. The

FIG. 151. — BENDING MOMENTS ON AXLE TUBE.

A, Bending Moment Due to Weight on Springs; B, Bending Moment
Due to Axle Weight; C, Bending Moment Due to Retarding Force of Rear
wheels.

moment at this section due to the weight on the spring seat
is wl, and the moment due to the retarding force of the brakes
is P x. The maximum retarding force P is reached when the
wheels are locked on dry macadam surface, under which condi-
tion the coefficient of friction with rubber tired wheels is about
0.6. Hence, P = o.6 w and P x = o.6 w x. These two bending
moments are in planes at right angles to each other and their

240 BEVEL GEAR DRIVE AND REAR AXLE.

resultant (Fig. 152) is equal to the square root of the sum of
their squares. That is,

Denoting the radius of the road wheel by r, the torsional mo-
ment on the axle tube is

Aft = Pr = 0.6 w r.
The unit bending stress is

_ M*c

*J b "*~ j

and the unit torsional stress, ,

Mtc

St = - .
/ .
The combined stress is

21 \\ j

Remembering that for a circle / = 21, we may write this in
the form

Now let D denote the outside diameter of the axle tube and
d the inside diameter. Then

and 2~

Inserting these values and those of ,Mt and Mb found above, in
equation (46) we get

_ ^

•S'c=0 ._, -w /2 + 0.36 x* + w "VO^r2 + P + 0.36

£T(U — d

SDw

+ 0.36 S + f + 0.36 xz + 0.36 r2

&—P

Denoting the part in parentheses by 3; we may write

D* Sc — 5 D w y = d * S°

BEVEL GEAR DRIVE AND REAR AXLE.

241

d ^==~-
and replacing the value of y —

'(48)

The great majority of rear axles are provided with trusses.
No matter how strongly a rear axle housing is constructed, un-
less it is provided with an under running truss it will sag slightly
in the middle. This causes the rear wheels to spread at the
bottom, which makes for an unsightly appearance and poor work-
ing conditions of the bearings. By means of the under running
truss the axle tubes can be practically entirely relieved of vertical
bending stresses. In that case 'only two stresses are to be con-
sidered, viz., the torsional stress and the horizontal bending stress.

FIG. 152. — COMPOSITION OF BENDING MOMENTS AND COUPLE
ON AXLE TUBE.

The value of the latter is 0.6 w x. Substituting the values for
this case in equation (46) we have

By the same processes as used in the preceding case we then
find that

'=y Z?*-

3 D zv (x -f

(50)

242 BEVEL GEAR DRIVE AND REAR AXLE.

The stress 5"c may be chosen at 15,000 Ibs. per square inch for
carbon steel tubing, and 20,000 Ibs. per square inch for
nickel steel tubing. In determining the diameters of the tube, the
outside diameter is usually chosen about twice the diameter of
the axle shaft, and the required inside diameter may then be
calculated by equation (48) or (50). Steel tubing has been
standardized by the Society of Automobile Engineers and the
standard sizes should be selected. (See Appendix.)

To illustrate the use of the equations we will calculate the
necessary diameters of axle tubes for a car carrying 2,000 pounds
on the rear axle, having wheels 32 inches in diameter and in
which the distance x from the centre plane of the rear wheel to
the point where the axle tube enters the hub of the driving gear
housing is 18 inches. The weight on the rear axle corresponds
to that in the average five passenger touring car, loaded, and we
may assume that it is medium-powered and has rear axle driving
shafts i% inches in diameter. Hence the outside diameter of
the axle tubes might be made 2l/2 inches. We then have

D = 2l/2 inches,

r = 16 inches,

* = 18 inches,

w=i,ooo Ibs.

Assuming that the tubes are to be of carbon steel, we put
S0 = 15,000. Inserting values in equation (50) we have

- / = z. 06 inches
15,000

This is the minimum section for any point between the brake
support and the driving gear housing. Beyond the brake sup-
port the axle tube is subjected to bending stresses only. Since
the truss rod is generally anchored to the brake support, the
vertical bending moment comes on this part of the tube whether
the axle is provided with a truss rod or not. The inside diameter
of the tube at this point would generally be made about l/% inch
larger than the diameter of the axle shaft and the outside diameter
calculated to give a unit stress of 15,000 or 20,000 pounds per
square inch under the combined bending moments. The outside
diameter of the tube would then be made such as to correspond
with the bore of the next largest size of bearing. However, if
the axle tube is continued through the wheel hub with the same
thickness of wall as it has between the spring seat and the driving
gear housing, the outer portion of the tube will be amply strong.

BEVEL GEAR DRIVE AND REAR AXLE.

243

Pressed Steel Housing — Pressed steel presents the same
advantages for rear axles as it does for other parts subjected to
varying loads and to shock. It gives the maximum strength for

FIG. 153.— FIAT PRESSED STEEL AXLE.

a given weight, and when a sufficient number of parts are needed
to make the pro rata cost of the dies small, pressed steel parts
are usually lower in cost than equivalent parts made by other
processes.

BEVEL GEAR DRIVE AND REAR AXLE.

BEVEL GEAR DRIVE AND REAR AXLE 24b

One of the earliest automobile concerns to bring out a pressed
steel rear axle was the Fiat Automobile Company, of Turin, Italy,
whose axle is illustrated in Fig. 153. In this design the entire
rear axle and propeller shaft housing are made in two identical
pressed steel parts which are bolted together. The housing is
heavily ribbed and is used without a truss rod. A large drop
forged fork surrounds the forward end of the propeller shaft
housing and is hinged to a cross member of the frame. The
differential and driving shaft bearings are carried by a frame
riveted into the enlarged portion at the middle of the pressed
steel housing.

Another type of pressed steel axle is represented by the Timken
shown in Fig. 154. In this case the housing has two large open-
ings, in the front and rear respectively. It is pressed from sheet
steel, in halves which are welded together by the oxy-acetylene
process. In the axle illustrated the joint is in the horizontal
plane, while in another it is in the vertical plane and the welded
joint forms a strengthening rib.

A third type of pressed steel axle which is used on several
makes of American low priced cars made in very large numbers
is illustrated in Fig. 155. The axle housing is made in halves
which are joined in a vertical plane at the centre of the driving
gear. Each half is again made of two parts, viz., the central
casing which is made by the swaging process, and a plain tube
which is joined to the latter by the oxy-acetylene welding process.

For cars of small size and in which the springs are sup-
ported on the axle close to the road wheels, so that the bending
moment is small, pressed steel axle housings can be made of
y8 inch stock. For touring cars of moderate size the axle
housings are made of 3/16 inch stock, the diameter of the
housing' increasing with the weight of the car from 2% inch
for a 2,000 Ibs. car to 3 inch for 4,000 Ibs. car. The material
used in these housings is a low carbon steel having an elastic
limit of about 34,000 Ibs. per square inch. In a full floating
axle the maximum stress comes at the point where the spring
seats are attached, and in order to avoid the necessity of using
comparatively heavy material for the whole housing, alloy
steel reinforcing tubes are forced into the housing at this
point and are supported near the centre of the axle.

Gear Carrier — With the type shown in Fig. 154 it is com-
mon to carry all of the bearings for the differential gear and
driving pinion on a structure known as the gear carrier or dif-
ferential carrier, which is bolted to the pressed steel housing. In
some designs this carrier forms the closure for the front opening"

246 BEVEL GEAR DRIVE AND REAR AXLE.

BEVEL GEAR DRIVE AND REAR AXLE.

247

in the pressed steel housing and has the torque tube or rod secured
to it, while in other cases it is inserted through the rear opening
and bolted to the rear flange of the housing, but does not serve
as a cover for this opening. The use of a differential carrier has>
the advantage that all of the bearings for the driving gear are
carried in a single integral part and cannot be thrown out of
alignment by the stresses on the axle housing. Moreover, the
bearings can be adjusted before the axle is assembled.

Drop Forged Axles — Drop forged axles present substantially
the same advantages as pressed steel axles. They do not require
any welding to be done upon them, and, besides, they permit of
variations in the thickness of the walls at different points and of
integral flanges for the spring seats, etc. The advantage over the

FIG. 157.— DIAGRAM OF ARCHED AXLE AND DISHED WHEELS.

pressed steel axle that no welding is required is offset, however,
by the fact that the tubular portions must be bored out. One
design of drop forged housing is shown in Fig. 156. The central
portion of this particular housing is in the form of a ring, and a
gear carrier and a large rear cover plate are used. Ten bolts
pass through the flange of the gear carrier and that of the cover
plate, but only four of these pass through holes in the drop
forged housing. The housing is heavily ribbed between the
annular and tubular portions and no truss rod is used.

Arched Rear Axles— Dished wood wheels present considerable
advantage over plain wheels in the way of strength, and on horse
vehicles these wheels are used exclusively. But in order to run
properly, dished wheels must be mounted on a cambered axle

BEVEL GEAR DRIVE AND REAR AXLE.

whose "set" is equal to the angle of dish of the wheel, so that the
lowermost spoke, which carries the load on the wheel, stands in
a vertical position. (See Fig. 157.) It is customary to give a
slight "set" to the front wheel spindles, and when the side chain
drive was common the rear axle spindles also were often given a
set of a few degrees, the flexibility of the chain making this
possible. With the ordinary design of shaft driven rear axle,
however, it is impossible to incline the rear axle spindles, and if
it is desired to employ dished road wheels it is necessary to re-

FIG. 158.— CENTRAL PORTION OF PEERLESS ARCHED AXLE.

sort to special constructions. One plan consists in dividing each
rear axle shaft into two parts and connecting these parts by
some form of universal joint This construction is exemplified
in the Peerless rear axle shown in Fig. 158. The axle tubes are
set into the driving gear housing at an angle equal to the desired
angle of set, and an internal and spur gear type of universal joint
is used.

In another design the differential gear is mounted upon an
extension of the propeller shaft, as shown in Fig. 159. Each
master gear is provided with a long sleeve which carries a bevr*

BEVEL GEAR DRIVE AND REAR AXLE.

pinion at its outer end. The two pinions mesh, respectively, with
bevel gears secured to the rear axle driving shaft In order that
there may be no interference between the two sets of bevel gears,
the two pinions are made of different pitch diameters, and the
two gears the same, but of course the ratio between the number
of teeth in the pinion and gear is the same for both sets. This
construction has the advantage that the differential gear is driven
at a relatively high rate of speed and therefore can be made
smaller. The differential is operated in a somewhat unusual man-
ner in that power is applied to the pinion spider through the

FIG. 159.— ARCHED AXLE WITH DIFFERENTIAL ON PROPELLER
SHAFT.

central shaft instead of through the differential housing or frame,
as ordinarily. This type of rear axle is used by the Daimler
Motor Company in Germany and by the La Buire Automobile
Company in France. It is, of course, obvious that with this con-
struction the axle tubes may be inclined at any angle desired.

Types of Bearings — Anti-friction bearings are used almost
exclusively on live rear axles, and all of the different types are
well represented in this part of the car. In addition to the radial
load resulting from the weight of the frame and body carried
on the axle, and from the reaction of the bevel gears, there arp

250 BEVEL GEAR DRIVE AND REAR AXLE.

thrust loads due to driving on one side of a strongly crowned
road or to skidding and to the reaction of the bevel gears. AH
these thrust loads must be provided for in some way. Owing to
the fact that the thrust load in skidding may assume very
considerable values and that radial ball bearings should not be
subjected to thrust loads of more than 10 per cent of their
radial load capacity, a great many rear axles are fitted with some
form of combined radial and thrust bearing. When bearings are
used which do not take any thrust load whatever, as, for in-
stance, cylindrical roller bearings, it is absolutely necessary to
provide special thrust bearings. It is not customary to provide
thrust bearings inside the rear wheel hubs when radial ball bear-
ings are fitted. These bearings are generally of considerable size,
and are depended upon to carry the thrust load as well. In some
designs of axles the thrust load is transmitted from the wheels
through the axle shafts to the thrust bearings at the side of the
differential gear. In the latter case it is necessary that the
axle shaft be securely fastened to the master gear of the differen-
tial as well as to the road wheel hub.

Bearing Pressures — Taking up first the bearings for the
bevel pinion shaft, there are two general arrangements. The
most common of these consists in mounting the shaft in two
bearings, both back of the pinion, one as close to it as possible
and the other a considerable distance away. The other method
consists in placing one bearing on either side of the pinion. The
total bearing load is much smaller when the pinion is mounted
between bearings, and this arrangement, no doubt, would be
used much more extensively if it were not so difficult to find
sufficient room for the inner bearing. As it is, some bearing
makers rather oppose the latter arrangement on the ground that
too small bearings are generally used on the inner side of the
pinion, and much trouble is experienced in consequence. Owing
to the fact that the spur type differential gear has no projecting
hubs on its circumference, this type is preferable where a bearing
is to be placed on the inner side of the pinion. If the bevel type
of differential is used it is customary to place it on the back side
of the bevel gear, if an inner bearing is to be fitted on the pinion
shaft.

A modification of the first design described is that in which
the forward end of the propeller shaft tube rides on the propeller
shaft through the intermediary of a ball bearing. In this case
there is only a single bearing at the bevel pinion, and the load
on the bearing is less than it would be if there were another

BEVEL GEAR DRIVE AND REAR AXLE.

251

bearing close to it. However, while the bearing load is reduced
the stress in the propeller shaft is increased.

Besides the radial load the pinion shaft is subjected to thrust
loads. There is, first, the end thrust, due to the tooth reaction
of the bevel gears. With straight bevel gears this is always in
the forward direction and is comparatively slight. Besides
this, there is a thrust load due to the friction at the
sliding joint in the propeller shaft. This changes in direc-
tion with the direction of slippage at the joint and varies in value
according to the mean radius from the axis of rotation of the

FIG; 160.— P INION SHAFT
MOUNTING WITHOUT THRUST
BEARING.

FIG. 161.— PINION SHAFT
MOUNTING WITH SINGLE
THRUST BEARING.

surfaces on which the slippage takes place, and according to the
state of their lubrication. This load is greatest when a squared
or fluted shaft type of slip joint is employed, and smallest with
the block and trunnion type of joint. When the sliding takes
place in one direction the thrust load due to this cause adds to that
due to the tooth reaction, whereas if it takes place in the opposite
direction, the two end thrusts are opposed and the resultant may
possibly be directed backward.

The bevel pinion end thrust in the case of straight bevel gears
varies considerably with changes in the gear reduction ratio.
With large gear reduction ratios and block and trunnion type
slip joints it is quite possible to take up the end thrust on the
radial ball bearings, which, as already pointed out, have a thrust

252 BEVEL GEAR DRIVE AND REAR AXLE.

load capacity of 10 per cent, of their radial load capacity. A
design in which end thrust in both directions is taken up on
radial bearings is shown in Fig. 160. In this construction it is
essential that the measurements x and y be exactly alike, as
otherwise the bearings will be cramped when the inner races are
drawn tight on the shaft. Both outer races are close up against
a shoulder at one end, but are free at the other end.

In the design shown in Fig. 161, end thrust in the forward di-
rection is provided for by a special ball thrust bearing. This
construction is suitable where the bevel gear gives a small re-

FIG. 162. — PINION SHAFT MOUNTING WITH DOUBLE THRUST
BEARINGS.

duction and the slip joint is of the block and trunnion type, so
that there is little chance of the end thrust ever changing in
direction. These designs can be used with straight gears only.

The most highly developed design provides double thrust bear-
ings on the pinion shaft, as shown in Fig. 162. In this design a
central thrust plate is clamped between collars, which in turn
are clamped between a shoulder in the bearing housing and the
end plate. This thrust plate forms part of the double thrust
bearing, which is assembled on a sleeve mounted on the pinion
shaft. This sleeve also serves as a spacer for the radial ball
bearings, the inner races of both of which are securely clamped to
the shaft, while the outer races are free to move endwise. With
this construction the pinion is held positively endwise, thus insur-
ing continued accuracy of mesh, and the radial bearings are re-

BEVEL GEAR DRIVE AND REAR AXLE

253

lieved of all thrust loads, and consequently operate at their high-
est efficiency.

It will be seen that the construction Fig. 162, which takes
account of all possible bearing loads, is somewhat complicated
and for this reason many designers prefer combined radial and
thrust bearings for the pinion shaft, such as conical roller bear-
ings, cup and cone ball bearings, etc. Fig. 163 illustrates a pinion
shaft mounted in two conical roller bearings. The outer rings
of the roller bearings lie close up to internal flanges on the

FIG. 163.— PINION SHAFT MOUNTED IN CONICAL ROLLER BEARINGS.

bearing housing at their inner ends, and both of the bearings
can be adjusted by means of a single nut and check nut at the
outer end, which are very accessible. This design also provides
means for adjusting the mesh of the gears, consisting of an inner
and an outer housing, the inner housing being screwed into the
outer one and locked in position when the gears have once been
properly adjusted. This type of bearing is very popular in con-
nection with helical bevel gear drives.

The Hyatt type of flexible roller bearing is also used to some
extent on pinion shafts. A typical mounting of these bearings is
shown in Fig. 164. The outer sleeve of the bearing is pressed
into the bearing housing and held from rotating by means of a

254

BEVEL GEAR DRIVE AND REAR AXLE.

set screw. The inner sleeve is forced over the pinion shaft, and
its forward end presses against a thrust plate, forming one
member of a ball thrust bearing, the other plate of which bears
against an adjusting nut screwed into the bearing housing. This
design is intended for cars with only a single universal joint in
the propeller shaft, and the forward end of the shaft is to be car-
ried in another roller bearing, designated a "steadying bearing."
Calculation of Pinion Shaft Bearings— In determining the
proper sizes of bearings for the pinion shaft we first calculate
the torque on the shaft corresponding to full engine power and
direct drive, then calculate the tooth pressure on the pinion, based
upon the mean pitch diameter of the latter, resolve this tooth

FIG. 164.— PINION SHAFT MOUNTED IN HYATT ROLLER BEARINGS.

pressure into a radial and a thrust load, and finally divide the
radial load between the two bearings supporting the pinion shaft.
The method of calculation may be illustrated by means of a
practical example of a straight bevel gear drive.

We will take the case of an engine developing a maximum
normal speed torque of ±08 pounds-feet (four cylinder, 4x5 inch).
Suppose that the bevel pinion has 16 teeth of five pitch and the
gear 54 teeth, thus givkig a reduction of 3.5 to I. According to
equation (44) the proper width of face for the pinion would be

KA^ *33 — — = i . 205 — say i J inches.
54X3-2X0.63

The largest pitch diameter of the gear is 10.8 inches, and that of
the pinion 3.2 inches. Hence the distance from the point of inter-

BEVEL GEAR DRIVE AND REAR AXLE. 255

section of the two largest pitch diameters to the point of intersec-
tion of the axes of the pinion and gear, respectively, is

>5 . 42 + i • 68 = 5 . 63 inches.
The middle of the length of the tooth is at a distance

5.63 — 0.625 = 5 inches

from the point of intersection of the shaft axes, hence the mean
pitch diameter of the pinion is

3 . 2 X — - — = 2.84 inches

5-63

and the mean pitch radius is 1.42 inches. The tangential pressure
on the bevel pinion then is

108 *I2 = gI2 pounds.

1.42

The radial component of this pressure can be found by means
of equation (27) after the angle of the bevel pinion pitch line
with the axis of the pinion has been found. The tangent of this
angle is

14=0.30

10.8

and the angle is found to be equal to 16° 42'. Inserting values in
equation (27),

Pr = -s/9122 -f (912 X o. 364 X 0.958)2 = 970 pounds.
If both bearings are back of the pinion, as in Fig. 148, the dis-
tance a will be about i*/& inches and the distance b 5M$ inches.
Hence the load on the bearing close to the pinion is

970 X — =1,243 -pounds,

4
and the load on the bearing farthest from the pinion,

1,243 — 970 = 273 pounds.

These are the maximum loads on the bearings when the car
is being driven through the direct drive. When it is driven on
any of the other gears the maximum loads on the bearings will
be equal to the product of the above loads by the reduction ratio
of the particular gear. For instance, if the low gear reduction
ratio of the change gear be 3.2, then the maximum load on the
bearing directly back of the pinion would be
3.2x1,243 = 3,977 pounds
and that on the other bearing

In selecting the size of bearing it must be borne in mind that
the rated capacity of the bearing is very conservative, and that,
on the other hand, it is a very rare occurrence that the motor

256 BEVEL GEAR DRIVE AND REAR AXLE.

operates under full power on the low gear. In view of this fact
the bearing can be so chosen that the maximum load under low
gear is about 100 per cent, above the rated capacity of the bear-
ing, or that the rated capacity is about 50 per cent, higher than
the maximum load on the bearing on the direct drive. For the
most highly loaded bearings the heavy series of ball bearings is
usually selected. In the present case the No. 407 would probably
be chosen, which has a rated capacity of 1,900 pounds. The for-
ward bearing is comparatively lightly loaded, but it must have
a bore somewhat larger than the required propeller shaft di-
ameter. For this place a bearing of the medium series would be
the most advantageous, and the No. 307, which has a rated load
capacity of 1,100 pounds, would probably be chosen.

Now, consider the case where the bearings are placed on oppo-
site sides of the pinion, as in Fig. 161. The distance a here
measures about IT^ inches, and the distance b i& inches. Hence
the load on the inner bearing would be

r 3 ^T 5 X 97o = &i Pounds

XT* T JT8

and that on the outer bearing

970 — 461 = 509 pounds.

It will be seen that in this case the bearing loads are much
smaller than in the preceding case. The space available for the
inside bearing is rather limited, yet a somewhat higher factor of
safety is attainable in this case than in the previous one. A No.
404 bearing, having a rated capacity of 1,050 pounds, could be
used on the inner end of the pinion, and a No. 307, having a
rated capacity of 1,100 pounds, on the other end. The rated
capacities, therefore, are about 100 per cent, higher than the maxi-
mum bearing loads on the direct drive. If the outside diameter
of the bearing is limited and the load to be carried is large, bear-
ings of the so-called heavy series should always be selected. In
Fig. 161, in order to throw as much of the bearing load as pos-
sible on the bearing back of the pinion, the pinion is provided
with a projecting hub, and the bearing on -the inside is located at
some distance from the pinion proper. This, of course, can only
be done where the differential gear is entirely back of the bevel
gear. The housing for the inside bearing in this design is made
cup-shaped, so as to permit of the largest possible size of bear-
ing without sacrificing strength in the supporting housing.

Differential Bearings — It is not necessary to consider the
plain live axle mathematically, as that type is practically obsolete
In nearly all modern axles the inner axle bearings are mounted

BEVEL GEAR DRIVE AND REAR AXLE. 257

on the hubs of the differential housing, and with the full floating
type of axle at least the loads on these differential bearings are
due solely to the bevel tooth reaction. The normal pressure on
the teeth of the gear is the same as the normal pressure on the
teeth of the pinion, and the tangential pressures on gear and
pinion are also the same. Hence — continuing our example — the
tangential force on the gear is 912 pounds. The pitch line angle
of the gear is such that its tangent is

10.8

= 3.38

3.2

and the angle is found to be equal to 70° 30'. Inserting values in
equation (27) for this case we have

P* = -\J9122 + (912 X 0.364 X 0.284)2 = 917 pounds.
The thrust load is found by inserting values in equation (26) as
follows : 912 x 0 364 x 0 959 = 31g pounds

The radial load is divided between the two differential bearings
in the inverse proportion of their distances from the centre plane
of the bevel gear. Owing to the fact that these bearings must
have a relatively large bore in comparison with the load they
have to carry, bearings of the medium series are usually chosen
if radial ball bearings are to be used. The most heavily loaded
of these bearings usually has a rated load capacity 50 to 100
per cent, greater than the maximum load coming on it when the
car is driven on the direct drive. In many cases the bevel gear
is much closer to one bearing than to the other, and the load on
one bearing therefore is much greater than that on the other.
However, notwithstanding this fact, bearings of the same size
are frequently chosen, for the sake of symmetry and minimum
number of different parts. In any case, the bore of one bearing
could hardly be made smaller, and all that could be done would
be to choose a bearing of the light series.

End Adjustment — With the highest class of workmanship
it is unnecessary to provide means for longitudinal adjustment
of the bearings. However, since measurements have to be taken
from the pitch lines of the gears, which involves considerable
difficulty, some provision is usually made to allow of adjusting
the mesh of the gears. The simplest means consists in placing
a washer back of the thrust bearing and another washer on the
opposite side of the differential housing, between the end of its
hub and a shoulder on the inside of the driving gear housing, and
changing the thickness of these washers until the gears mesh
properly. Quite a number of designers, however, provide screw

258

BEVEL GEAR DRIVE AND REAR AXLE.

adjustment of the bearings. Such a means of adjustment is illus-
trated in Fig. 165. The radial bearing is mounted in a bushing
which is carried in the bearing support forming part of the driv-
ing gear housing. One end of this bushing is made somewhat
larger in diameter than the other end,
and is threaded on the outside, the
threaded portion screwing into corre-
sponding internal threads on the bear-
ing support. The outer end of the
bearing bushing has an internal flange
against which the outer plate of the
thrust bearing rests, and by screwing
the bearing bushing farther into or
out of the support the thrust bearing
can be moved back and forth in the
direction of its axis. A lock nut is
provided for locking the bearing bush-
ing when the adjustment has been
made. It may be pointed out that
when a pair of bevel gears has once
been properly adjusted there should

FIG. 165.-ScR^TAD- ^crwbear0ofatShrteef°h cannot b^com
JUSTMENT OF BEVEL GEAR. JJ^S^to by^SmeT'

The problem of endwise adjustment is very readily solved with
conical roller or cup and cone bearings. As shown in Fig. 166,
all that is necessary is to lodge the outer race or ring of the
bearing in a suitable recess in the driving gear housing and
mount the inner race or ring on the end of the differential gear
housing hub, making the inner portion of this hub of somewhat
larger diameter and threading it, and passing a nut over this
threaded portion. This is done at both ends of the differential
gear, and by means of the two nuts the differential can be moved
in either direction at will. The nuts may be split and provided
with a clamp screw, or they may be provided with any other
suitable locking device.

Wheel Bearings — The wheel bearings support the loads car-
ried by the wheels and also take the load due to the propelling
and braking efforts. We found that the limiting value of the
braking effort is 0.6 times the weight resting on the wheel, and
the limiting value of the driving effort the same. Since driving
and braking efforts act at right angles to the weight, the resultant

BEVEL GEAR DRIVE AND REAR AXLE.

259

of the two simultaneous loads is equal to the square root of
the sum of the squares, viz.:

However, this is an entirely different load from that on the
differential bearings, for instance. The actual load, owing to the
unevenness of the road surface, changes from instant to instant,
and at times greatly exceeds the so-called "dead" load. The
maximum load to which the bearings are ever subjected depends
upon the weight carried, the size of the wheels, the width of
the tires and the state of their inflation, the flexibility of the
springs, the nature of the road surface, the speed of the car, etc.
The only factor that can be taken account of in selecting the
bearings is the load carried by each wheel. The bearings should
have a rated load capacity from 50 to 100 per cent, higher than
the maximum load they will have to carry, provided the rated
capacity represents ability to carry uniform loads.

In the case of semi-floating and three-quarter floating axles, the
entire load on each wheel is carried on a single bearing, whereas

FIG. 166. — ENDWISE ADJUSTMENT OF DIFFERENTIAL MOUNTED IN
ROLLER BEARINGS.

260

BEVEL GEAR DRIVE AND REAR AXLE.

in the case of full floating axles it is carried on two bearings.
When two bearings are used the ideal arrangement in some re-
spects would be to place them symmetrically on opposite sides of
the centre plane of the wheel, in which case both would carry
an equal load, and both could be made of the same size. How-
ever, since the brake and brake support must be very close to the
spokes of the wheel, the inner bearing generally has to be placed
rather close to the centre plane of the wheel. In fact, in many
designs the arrangement is such that the inner bearing supports
nearly the whole load, and the outer bearing serves only as a
"steadying" bearing.

FIG. 167. — DRIVING WHEEL HUB MOUNTED ON Two RADIAL BALL
BEARINGS.

The driving effort is always parallel to the planes of the rear
wheels, and any thrust load on the rear wheel bearings, is the
result of sideward inclination of the road surface, centrifugal
force or impact due to skidding. For this reason it is not essen-
tial to provide thrust bearings in the hubs, even when radial ball
bearings are used.

Mounting of Wheel Bearings — When two radial ball bear-
ings are used in the wheel hubs of a full floating axle, the inner
races of both are securely clamped to the axle tube, a projection
of the brake support hub or a collar forced over the axle tube
against the shoulder thereof serving as a stop; a tubular spacer
is inserted between the two inner races, and a nut is screwed

BEVEL GEAR DRIVE AND REAR AXLE. 261

FIG. 16Q. — DRIVING WHEEL HUB ON SINGLE BALL BEARING,
(THREE-QUARTER FLOATING.)

FIG. 169. — DRIVING WHEEL HUB ON HYATT ROLLER BEARING.
(THREE-QUARTER FLOATING.)

262

BEVEL GEAR DRIVE AND REAR AXLE.

BEVEL GEAR DRIVE AND REAR AXLE. 263

over the end of the tube, as shown in Fig. 167. The outer race
of only the inner, larger bearing is clamped tight in the hub, so
this bearing will take the end thrust in both directions.

In the so-called three-quarter floating type of axle only a
single bearing is used inside the wheel hub, as shown in Fig. 168.
This bearing must be located in the centre plane of the wheel, and
both of its races must be secured against endwise motion, so it
will take both radial and thrust loads. The driving dog in this
design of axle is either welded to the axle shaft or else rigidly
secured to it, and is also firmly secured to the wheel hub. The
single hub bearing may be either a radial ball bearing, a combined
radial and thrust ball bearing (Two-in-One), as shown in Fig.
168, or a cylindrical roller bearing, as shown in Fig. 169. The
latter bearing, of course, does not take any end thrust, and in
this design provisions are made for transmitting the end thrust
through the axle shafts to the thrust bearings at the sides of the
differential housing.

A similar arrangement was suggested by F. G. Barrett in his
paper on Ball Bearings, read before the Institution of Automo-
bile Engineers. Mr. Barrett's suggested design is shown in Fig.
170. A double ball thrust bearing is mounted to .one side of the
differential gear. The outer races of the two radial bearings in
the wheel hub are clamped tight, but the inner races are made a
free fit on the axle tube so these bearings will not take any end
thrust. The end thrust is transmitted through the wheel hub,
the axle shaft, the master gear of the differential, the differential
spider, the other master gear and the differential housing to the
double ball thrust bearing, which latter is firmly supported by
the axle housing. The practice of using two ball thrust bearings
at the differential is quite prevalent in Europe, but usually one
thrust bearing is placed on either side of the differential, whereas
Mr. Barrett places both on 'the same side.

Lubrication — The rear axle housing is generally filled with
non-fluid oil, and in order to prevent this from working through
the bearings into the axle tubes, packings are generally provided
at the inner ends of the tubes, as illustrated in Figs. 158 and 159.
It is a good idea to provide a plugged hole for replenishing the
grease, in the cover plate or near the top of the casing, so as
to make it unnecessary to remove the entire cover plate for this
purpose, and a drain plug should be provided at the lowest point
of the casing, so all lubricant and dirt may be conveniently
washed out with gasoline or kerosene. In Europe the cases are
often provided with large filling spouts.

264

BEVEL GEAR DRIVE AND REAR AXLE.

Truss Rod— Probably more than 90 per cent, of all live axle
designs have an under-running truss to relieve the axle housing
of the vertical bending moment. The middle of the truss is gen-
erally retained between projections at the bottom of the gear
case, and the ends are secured to fittings fastened to the axle
housing between the spring supports and the end, these anchor-
ages being generally integral with the brake support. The truss
may be tightened by means of nuts on both ends outside the
brake support, or by means of a turnbuckle, as shown in Fig. 171,
in which latter case the ends of the rod are hinged to the axle
tube. The threaded ends of the rods should preferably be upset
so the thread will not reduce the strength of the rod.

The downward bending moment due to the weight on the
springs at any point between the spring seats is w I, where w
is the weight on one spring seat and / the distance between the

FIG. 171.— REAR AXLE TRUSS.

centre plane of the wheel and the centre of the spring seat. The
truss produces an upward bending moment which is a maximum
at the middle of the axle and decreases uniformly toward the
truss anchorages. Its bending moment diagram therefore is a
triangle, whereas the diagram of the bending moment due to the
load on the springs is a trapezoid. Consequently, the two bend-
ing moments cannot entirely neutralize each other, except at
certain points.

Let T be the tension in the truss rod. Then the vertical com-
ponent of this force, which presses upward on the driving gear
housing is T sin 0, and the bending moment at the middle of the
axle housing due to this upward pressure is T I' sin 0, where /'
is the horizontal distance from the centre of the axle to the truss
anchorage. Since the angle 0 is in every case small, it is
permissible to substitute for sin 0

which makes the upward bending moment T h. The permis-
sible tension T in the rod, of course, is proportional to the

BEVEL GEAR DRIVE AND REAR AXLE. 265

cross sectional area of the rod or to the square of its diame-
ter d. hence the moment is proportional to d* h. The upward
bending moment due to the truss should be proportional to
the downward bending moment wl due to the weight on the
springs. Hence we may write

d2 h ^ «//.
and

d~y tfLi
The data at hand shows that in average modern practice

d=J~^ri (so

V 7,000 h

The actual tension in the truss rods, of course, depends upon
how tightly they are drawn up, and the load that must be
carried by the truss in any particular design depends upon
the rigidity of the axle housing itself. A large part of the
load on the truss results from the shocks on the unsprung
weight at the middle of the axle, and if this weight is unusu-
ally great, as in the case of a transmission axle, for instance,
the truss may be made somewhat heavier than given by the
formula.

Rear Axle Torsion and Thrust— The reaction between the
teeth of the bevel gear and pinion causes a pressure on the
bearing of the bevel pinion shaft, and this pressure tends to
cause the axle housing to rotate around the axle. As in all
similar cases, action and reaction are equal and opposite,
and the axle housing tends to turn "backward" with the same
torque as is impressed upon the axle shafts in the "forward"
direction. Therefore, it is obvious that the torsional effect
on the axle housing may, under certain conditions, as in driv-
ing on the low gear under full engine power, assume very
high values, and means must be provided to prevent the hous-
ing from yielding to this torque. In a considerable number of
cars the body springs are depended upon to keep the axle
housing in position against the torsional reaction. In cars
fitted with a single universal joint in the propeller shaft the
latter is often surrounded by a so-called torque tube, whose
forward end may have a bearing on the propeller shaft or
be suspended from a cross member of the frame, and whose
rear end is rigidly fitted into the rear axle housing. In cars
with two universal joints a torque arm rigidly secured to the
rear axle housing extends forward to a frame cross member
to which it is linked in some manner.

266 BEVEL GEAR DRIVE AND REAR AXLE.

Besides the torsional effect, there is also a forward thrust
on the axle housing. All of the propelling effort is produced
by the reaction of the driving wheels on the ground, whereas
a good deal of the resistance to motion is made up of the
road resistance encountered by the front wheels and the air
resistance on the body. The force necessary to overcome
these latter resistances must be transmitted from the rear
axle housing to the body. On the other hand, when a car
is to be stopped quickly, by the application of the brakes,
most of the kinetic energy that has to be dissipated is stored
up in the parts supported by the vehicle frame, whereas the
braking resistance takes effect at the ground contact of the
rear wheels. Hence there is a strong retarding pull exerted
by the rear axle housing on the vehicle frame, which in the
absence of special members is transmitted by the body
springs. However, some designers provide special thrust rods
between the axle housing and the frame, these generally ex-
tending underneath the side frame members, being hinged to
both connected parts so as to allow of free spring action.

frT addition to the torsion and thrust on the rear axle
housing, due to the transmission of power, the axle is sub-
jected to other stresses, which are the result of impacts be-
tween the driving wheels and road obstructions. , For in-
stance, if one of the driving wheels strikes an obstruction
rising some distance above the road surface, the shock tends
to throw the axle out of alignment with the frame. This
is provided against in some designs by diagonal brace rods
running from the forward end of the torque tube to the
outer ends of the axle housing. On the other hand, the axle
must be allowed freedom of motion in a vertical plane so it
may follow the irregularities of the road surface without
straining any portion of the running gear.

Torque Tubes — The maximum bending moment on the torque
tube or torque rod may be calculated on the basis of the
torque necessary to slip the rear wheels on a road surface on
which rubber tires have a friction coefficient of 0.6. For
instance, if the rear axle carries a maximum load of 2,000
pounds and the wheels have a radius of 16 inches, then the
maximum torque is

1 6 x 2,000 x 0.6 = 19,200 pounds-inches.

Suppose that the distance from the axis of the rear axle to
the point of support of the torque tube is 40 inches, then
the maximum reaction of the support is

BEVEL GEAR DRIVE AND REAR AXLE. 267

19,200 =

The bending moment at any point along the tube may then
be found by multiplying this reaction by the distance of the
particular point considered from the point of support. The
most important point in this connection is generally where
the tube enters the cast fitting. We will assume this distance
to be 24 inches. Then the bending moment at this point is

24 x 480 = 1 1,520 pounds-inches.

Owing to the fact that the torque figured on is not the normal
working torque but the very maximum that can be trans-
mitted, only a small factor of safety need be figured on. With
the ordinary carbon steel tubing a stress of 25,000 pounds
per square inch can be allowed.

The maximum forward or backward thrust of the rear axle
is equal to the adhesion of the wheels to the ground, viz.:

0.6 x 2,000 = 1,200 pounds.

This, too, is more than is ever attained in normal operation;
for, assuming the car with load to weigh 3,200 pounds, the
propelling effort up a 20 per cent, grade at low speed on fair
roads is only about 720 pounds, and not even all of this has
to be transmitted to the frame. About the only condition
under which a thrust of 1,200 pounds would be attained is
when the wheels are locked by the brakes.

Owing to the fact that the bending moment varies from
nothing at the point of support to the maximum at the joint
of the tube to the driving gear housing, it is customary to
reinforce the rear end of the tube by slipping another tube
over it or into it. The forward end of the reinforcement
should be tapered down to a sharp edge so as to avoid an
abrupt change in section tending to localize the stresses, and
in the case of an outside reinforcement also for the sake of
appearance.

Let us assume that in our example we use a propeller shaft
tube of 2 inches outside diameter and one-eighth inch thickness
of wall. At 25,000 pounds per square inch this will sustain
a bending moment of

32X2

This is the maximum bending moment at a distance

8>I17 = 17 inches (aptr.)

480

from the support and the remaining length of the tube, there-
fore, should be reinforced.

268

BEVEL GEAR DRIVE AND REAR AXLE.

The practice of taking both the driving thrust and torque re-
action on the chassis springs, or using what is known as the
Hotchkiss drive, is now quite prevalent in both pleasure car
and truck work.

Torque Tube Supports— The axle tube may either take up
Doth the torque and the forward thrust on the rear axle
housing, or it may take up only the former, and the method
of supporting its forward end varies accordingly. Fig. 172
illustrates a construction in which only the torque is taken
up by the tube, the forward end of the latter riding on the
propeller shaft through the intermediary of an anti-friction
bearing. The forward end of the propeller shaft is supported
by the universal joint which is secured to the rear end of the
change gear primary shaft. A disadvantage of this construc-
tion is that the torque reaction has to be taken through the

FIG. 172. — TORQUE TUBE RIDING ON. PROPELLER SHAFT.

universal joint bearings. The pressure due to the torque
reaction also comes on the rear bearing of the change gear
box, but this is not an unmitigated evil, since the torque re-
action is directed perpendicularly upward, whereas the gear
load on this bearing when either of the lower gears is in
operation is directed almost perpendicularly downward, hence
the torque reaction partly neutralizes the gear load. Of
course, with the direct drive in operation, there is no gear
load on the rear bearing, the only load on it being that due
to the torque reaction, and since this is always far below
the rated capacity of the bearing there is no serious disad-
vantage in this.

A second method of supporting the forward end of the
torque tube is by means of a fork hinged to a cross member
of the frame or to the change gear box, as shown in Fig. 173.
In order that the rear axle may be able to move freely in the

BEVEL GEAR DRIVE AND REAR AXLE.

269

vertical plane, as required by road unevennesses, the fork
must swivel on the front end of the torque tube. The joints
of the fork and the abutting surfaces of its hub should be
liberal in size and provided with means for lubrication. The
fork is usually drop forged, and its arms are made of T-section.
The axis of the hinged joint should coincide with the axis of the
universal joint so that the propeller shaft will always be concentric
with the torque tube.

A third method of supporting the forward end of the torque
tube is by means of a spherical joint which generally also forms

FIG. 173. — FORKED SUPPORT OF TORQUE TUBE.

a protecting housing for the universal joint in the propeller shaft
As shown in Fig. 174, an acorn-shaped housing is bolted to the
rear of the change gear case and also to a cross-member of the
frame which is of special shape, with a hole at the centre for the
propeller shaft and torque tube to pass through. The rear end of
this housing is turned off spherically to form a seat for a spherical
flange formed on the forward end of a sleeve secured to the
forward end of the torque tube. A ring with a spherical bearing
surface is bolted to the frame cross-member in such a manner that
the spherical portion secured to the torque tube works freely be-

270

BEVEL GEAR DRIVE AND REAR AXLE.

tween the two parts with spherical surfaces secured to the frame.
A leather boot or a packing ring has to be provided to protect the
outer working surface from dust and grit. The universal joint
is located centrally within the spherical joint and the forward
end of the propeller shaft is generally supported in a ball bearing,
though some axles have recently been designed which do away
with this forward bearing, relying on the universal joint for
"steadying" the forward end of the shaft. This type of connec-

FIG. 174.— SPHERICAL SUPPORT OF TORQUE TUBE.

tion between the frame and the rear axle takes up frame thrust
in both directions (driving and braking) as well as torsion, and
makes for a very substantial construction.

Effect of Spring Play on Drive— In Fig. 175 is shown a
shaft and bevel gear drive with a single universal joint and
a torque tube surrounding the propeller shaft. The forward
end of the propeller shaft is shown in its highest position,
22 inches above the ground. In Fig. 176 the same drive is
shown with the forward end of the propeller shaft in its low-

BEVEL GEAR DRIVE AND REAR AXLE.

271

*st position, 16 inches above the ground. A relative change
in position of axle and frame occurs very suddenly when the
rear wheels strike a waterbar, for instance. As the springs
compress the forward end of the propeller shaft drops sub-
stantially in an arc of a circle, and this angular motion of
the propeller shaft around the rear axle axis entails a corre-
sponding rotary motion of either the bevel gear or the bevel
pinion. That is, the bevel gear, and consequently the pair of
road wheels, will move around their common axis through
an angle equal to that described by the propeller shaft or
the bevel pinion, or the engine crankshaft will turn around
its axis through an angle equal to the product of the angle

FIG. 175.

described by the propeller shaft by the ratio of the num-
ber of bevel gear teeth to the number of bevel pinion
teeth. In the illustration the horizontal distance between the
axle centre and the forward end of the propeller shaft is
28 inches. With the springs compressed the propeller shaft
occupies a horizontal position, while with the springs ex-
tended it makes an angle with the horizontal whose sine is

22 — 16
-^-=0.214,

viz., about 12^ degrees. With a bevel gear ratio of 3:1, this
corresponds to an angular motion of Z7l/2 degrees of the
bevel pinion. Therefore, in the design shown in Figs. 175

272

BEVEL GEAR DRIVE AND REAR AXLE.

and 176, if the frame suddenly drops 6 inches relatively to
the axle, either the road wheels will have to accelerate so as
to move through an extra angular distance of 12*/2 degrees
during the short space of time that the compression of the
springs takes place, or else the engine has to slow up so its
crankshaft will turn through 37^ degrees less than normally
during this period. Both changes in motion are opposed by
the inertias of the respective moving parts, and in reality
the car will be slightly accelerated and the engine retarded
by the compression of the springs. Preferably the play of
the springs should have absolutely no effect on the motion

FIG. 176.

of the car and the engine, for then the springs would act most
freely and the transmission parts would not be subject to shocks
due to this cause.

In Figs. 175 and 176 the propeller shaft is unusually short,
which exaggerates the influence of spring play on the uniformity
of transmission. The designer's aim always should be to make
the propeller shaft as long as possible, especially if only a single
universal is used. If the shaft is twice as long as shown in the
cuts — which is not uncommon — the speed fluctuations will be
almost halved.

When two universal joints are used a torque rod is usually
employed instead of a torque tube concentric with the pro-
peller shaft. By supporting the front end of the torque rod

BEVEL GEAR DRIVE AND REAR AXLE.

273

between springs from the frame cross member, the shock on
the transmission members due to a sudden drop of the frame
is lessened. The reason why this is so is immediately ap-
parent, because, on account of the spring suspension of the
torque rod, the forward end of the latter need not drop as
much as the frame.

The condition insuring that there shall be no effect on the
uniformity of the drive is that the angle of the pinion axis
with the ground plane remain constant. This end can be
attained very nearly by connecting the axle housing to the
frame by means of a pair of parallel links, as shown in Fig.
177. If the two links are of absolutely the same length and

FIG. 177.

the front and rear points of linkage are the same distance
apart, then the angle made by the axis of the bevel pinion
with the plane of the frame will remain absolutely constant.
However, this does not quite meet the above mentioned re-
quirement that the pinion axis has to remain at the same
angle with the ground plane, since if only the rear springs
compress the angle of the frame plane with the ground plane
changes. For instance, suppose that when the springs are
extended both the frame and the pinion axis are absolutely
horizontal. Then when the rear springs are compressed the
frame will slant toward the rear and so will the pinion axis.
Since the pinion axis always intersects the rear axle axis it
means that the pinion has moved slightly upward, thus

274 BEVEL GEAR DRIVE AND REAR AXLE.

causing a slight retardation in the speed of the car or an
acceleration in the speed .of the motor. This effect is really so
slight as to be negligible, but it can be entirely eliminated by
making the upper rod longer or placing the rear pivots
farther apart than the front pivots. This linkage is used by
Deasy and Lanchester in England, among others.

Some experiments by means of models on the effect of
spring play on bevel gear drives were made several years
ago by S. Gerster, of Courbevoie, France, and were reported
in THE HORSELESS AGE of December 15, 1909. The experi-
mental apparatus consisted of the rear portion of a vehicle
frame, a set of rear springs, an axle, a pair of wheels and
the bevel gear drive. The rear wheels were fixed to a wooden
base, and double cords were attached to the frame at three
points, these cords passing through holes in a wooden base
and over pulleys on the under side of the base, and were
connected to a single pull rod underneath, by pulling on which
the frame could be lowered relatively to the base a distance
of 6 inches. On a cross-member of the frame was mounted
a dial, and to the forward end of the propeller shaft directly
in front of this dial was secured a pointer, which latter moved
over a scale on the dial graduated in degrees. Mr. Gerster
constructed models of this description with all of the differ-
ent types of axle linkage in common use. The length of the
propeller shaft was the same in every case. When the frame
was depressed 6 inches by pulling on, the cords the pointer
would move the following angular distances over the dial
with different linkages: Degrees

Torque tube hinged to cross member of frame 54

Triangular torque tube spring supported from frame and radius rods

at the sides 31

Only connection through three-quarter elliptic springs 5

Parallel links; top one somewhat shorter than lower ones — less than.. i

Torque Rods — In American practice three general designs of
torque rods are met with, viz., rods of round section, either
solid or hollow, which are fitted into a socket formed in-
tegral with the driving gear housing, as shown at A, Fig. 178;
pressed steel rods of channel section, as shown at B, or tri-
angular rods, as shown at C. There are also some examples
of malleable iron torque rods of I section, pressed steel torque
rods of I section made by riveting two channels together
back to back, and wooden torque bars.

A tubular torque rod, of course, is preferable to a solid
round one, since for equal strength it is lighter. The reason

BEVEL GEAR DRIVE AND REAR AXLE.

275

that solid rods are, nevertheless, used to quite an extent is
undoubtedly that it is much easier to taper the solid rod so
the strength of the section at every point is proportional to
the stress at that point. Tubular rods can be tapered only
with difficulty, and the common plan is to use tubes of
uniform diameter and insert one or two reinforcing tubes
from the rear end. The forward ends of these reinforcing
tubes should either be tapered out or else cut off at an
angle so as to avoid a sudden change in the strength of the
section.

FIG. 178.— TYPES OF TORQUE RODS.

Pressed steel and triangular torque rods are frequently
connected to the driving axle housing by means of a vertical
hinge joint, as shown at B, Fig. 178. This obviates undue
strains on the casing and torque rods in the case of severe
lateral shocks on the rear system, as in striking a curb in
skidding. It will be seen that in the construction shown at
B a drop forged or cast fork is riveted to the pressed steel
member for making the joint to the driving gear housing.
In other constructions the housing is formed with a flat to

276

BEVEL GEAR DRIVE AND REAR AXLE.

which the pressed steel member is bolted directly. In the
case of pressed steel members some of the material of the
web of the channel is generally removed, as shown in Fig. 178,
thus eliminating weight without materially reducing the
strength, since the material near the neutral axis is under
little strain.

The advantage of the triangular torque rod is that its mem-
bers work under tension and compression instead of under
bending stresses. The individual members are generally tubu-

FIG. 179. FIG. 180.

SPRING CUSHION SUPPORT FOR FORWARD END OF TORQUE ROD.

lar. Often they are secured to the driving gear housing by
two of the bolts holding the halves of the housing together,
though occasionally they are secured thereto by special bolts,
as shown in Fig. 178.

Two common methods of supporting the forward end of
the torque rod from the frame are illustrated in Figs. 179
and 180, respectively. From a bracket riveted to a frame
cross-member depends a freely swiveled cylindrical spring
housing containing two coiled springs between which the for-
ward end of the torque rod is cushioned. The end of the
rod is made either in the form of an eye, as in Fig. 179, or

BEVEL GEAR DRIVE AND REAR AXLE.

277

in the form of a ball, as in Fig. 180, in which latter case it
is held between two spring plates with part spherical de-
pressions

The simplest construction consists in a simple link con-
nection between the frame bracket and the torque rod, as
shown in Fig. 181. This, of course, does not afford the
cushioning effect that the spring support does. In order
to obtain some of this cushioning effect without the use of
springs, some foreign manufacturers of motor trucks use
wooden torque bars.

FIG. 181. — LINK SUPPORT OF TORQUE ROD.

The stresses in torque rods and the sections required are
calculated the same as in the case of torque tubes.

Diagonal Brace Rods — The tendency of the rear axle to be
thrown out of alignment with the frame when one of the
driving wheels strikes a road obstruction has already been
referred to. Some designs of axle housing, as, for instance,
the Fiat pressed steel housing, are amply strong to withstand
these stresses, but others require radius rods to be fitted
between the axle housing and the side frames, or diagonal
brace rods between the spring seats or brake supports on
the axle housing and the forward end of the torque tube. A
typical rear axle construction with diagonal brace rods is

278

BEVEL GEAR DRIVE AND REAR AXLE.

shown in Fig. 182. The braces are made either tubular or
solid, and either hinged at both ends or at the rear end only,
and screwed into the fitting at the forward end.

The spring seats and brake supports also are integral parts
of the rear axle, but they will be discussed under the headings
of springs and brakes, respectively.

ID.

FIG. 182.— DIAGONAL BRACE RODS.

Bevel Gear Efficiency—Some tests of the efficiency of trans-
mission in bevel gear driven rear axles were made several
years ago by the H. H. Franklin Mfg. Co., Syracuse, N. Y.,
and were reported by G. Everett Quick in THE HORSELESS
AGE of February 12, 1908. The tests were conducted in sub-
stantially the same manner as those of change gears, already
referred to, except that two absorption dynamometers were
used, one connected to either rear axle shaft, and the differ-
ential was locked. Fig. 183 gives the results of tests of a
full floating axle. The bevel gears had five pitch 14^2 degree

BEVEL GEAR DRIVE AND REAR AXLE.

279

involute teeth and gave a gear ratio of 15:52. They were
cut from 3l/2 per cent, nickel steel blanks, case hardened, the
hardened surfaces of the teeth being polished by running the
gears together in a mixture of emery and oil. The length
of face was \l/2 inches. The axle had been run for about
3,000 miles previous to the test. It will be seen from the
diagram that the maximum efficiency is about 97 per cent.,
and the efficiency is above 95 per cent, for a considerable
range in horse power transmitted and speed of revolution..
During the test the axle gears were run in a bath of graphite
and oil. The losses shown by the diagram include both gear
and bearing losses, but the latter are very small, as all bear-
ings were radial ball or ball thrust bearings. A semi-floating

68/0 fig '4 16 /8
Morse Power Delivered to Pinion

FIG. 183. — EFFICIENCY OF BEVEL GEAR DRIVEN, FULL FLOATING
REAR AXLE.

axle was also tested and showed substantially the same max-
imum efficiency, but a slightly higher efficiency at small loads.
Critical Speed of Shafts. — Not long after the shaft drive
became popular trouble began to develop from inordinate vibra-
tion and resulting permanent bending or breaking of the pro-
peller shafts at certain critical speeds, especially on cars with
unit power plants or transmission axles, which necessitate the
use of exceptionally long propeller shafts. The occurrence
of such trouble was first brought to public attention by the
provision in certain cars of intermediate bearings on the pro-
peller shaft. The trouble may have seemed mysterious at
first, but the phenomenon was not entirely newx as similar
trouble had been experienced with steam turbines some years
previously, and a mathematical explanation of the phenomenon

280

BEVEL GEAR DRIVE AND REAR AXLE.

of critical speeds of revolving shafts had already been given.
The explanation is, briefly, as follows :

In spite of careful workmanship the center of mass of the
revolving shaft will never lie exactly in the axis of revolution.
Owing to the eccentricity of the center of mass an unbalanced
centrifugal force is produced which causes the shaft to vibrate.
The phenomenon is the more pronounced if the shaft carries a
heavy disc at the middle of its length, whose center of mass
lies outside the axis of rotation. (See Fig. 184.) Let the center
of mass be at a distance d from the axis of revolution of the
shaft. Under the influence of centrifugal force the shaft at the
middle of its length will deflect the distance y from its neutral
position. When thus deflected there will also be an unbalanced

FIG. 184. — SHAFT CARRYING A CENTRAL UNBALANCED Disc.

centrifugal force acting on the mass of the shaft, which will add
to the centrifugal force acting on the mass of the disc, but for
the present purpose it is permissible to neglect the former. De-
noting the mass of the disc by m, the centrifugal force is ex-
pressed by

F = m (y + d) «»,
o> being the angular speed in radians per second.

This force is balanced by the elastic force of the shaft which
is proportional to the deflection and may, therefore, be repre-
sented by

Fe = a y.
Hence

m (y + e) ^ = a y
from which it follows that

BEVEL GEAR DRIVE AND REAR AXLE. 281

and

me o>2

a — m 0?

When a = m ^ the deflection becomes infinite ; that is, unless
the vibration of the shaft is limited by bearings or guards, the
shaft will break. This, therefore, is the condition defining the
critical speed. There is one other exception in addition to
that noted above which would preclude breaking of the shaft,
and that is that the speed of revolution of the shaft varies so
rapidly that it remains near the critical speed an insufficient
length of time to permit of a dangerous vibration being attained.
Since the equation defining the critical speed is

a = m w2
the value of the critical speed is evidently

In order that the centrifugal force may be expressed in pounds
(the angular speed w being given in radians per second) the
linear dimensions must be given in terms of the foot, and a
then is the force necessary to deflect the shaft one foot at the
middle of its length.

Analysis of Critical Speeds. — Now consider a section dx of
a freely supported shaft carrying only its own weight. When
the shaft rotates the shaft section dx is under the influence of
two external forces, the force of gravity and centrifugal force.
With the shaft proportions found in practice the former has
no appreciable bending effect and may be neglected. The cen-
trifugal force puts a load on the shaft which revolves with it
and subjects it to shear and bending stresses. These latter can
be determined by means of the theory of beams, the shaft being
equivalent to a simple beam supported at both ends. When
the shaft is in equilibrium the external (centrifugal) and
internal (elastic) forces must neutralize each other in every
plane.

Let the shear at the two sides of the infinitesimal section
dx of the shaft be denoted by S and S' respectively. The cen-
trifugal force on the section dx is proportional to the length
dx and may be represented by p dx, where p is the centrifugal
force per unit length. Then, since there must be equilibrium in
the vertical plane (see Fig. 185)

S' — S + p dx = O

282
But

hence

BEVEL GEAR DRIVE AND REAR AXLE.
S' — S = d S

Also, taking moments around the center of gravity of the
section dx

dx dx

Mr — M — S' -- S - = O
2 2

FIG. 185. — DIAGRAM CF CENTRIFUGAL AND ELASTIC FORCES.

and since
we have

— M = dM

S' + S
dM = • dx = S dx

This relation can now be combined with the equation of the
elastic curve of a beam, viz.,

dzy - M

dx2 El

the minus sign being used here to correspond with the designa-
tions in the cut.

BEVEL GEAR DRIVE AND REAR AXLE. 283

Since

' ^

dS dzM d*y

= _ p = = _ £ I - —

dx d.r dx'
Hence

<Ty

p = E I - = m <»* (y + d)
dx*

The general integration of this equation gives

y = a e cx a' e — cx ~h b cos ex + b' sin ex — d
in which

and e is the base of the natural system of logarithms. This
equation covers all possible conditions of rotating shafts, and
the values of the constants a a' b b' depend upon the conditions
of any particular case — whether the shaft is freely supported
or rigidly held in bearings, supported at both ends or at one
end only, etc.

If now we take a freely supported shaft like a propeller shaft
with universal joints at both ends, and if we measure the ab-
scissas from the middle of length of the shaft, then 3; must be
an even function of x, in order that the same value for y may
be obtained for equal positive and negative values of x. The
third term of the above equation for y contains a cosine and the
value of the cosine is the same for a positive and negative angle
of equal magnitude. The sines of positive and negative angles
are alike but opposite in sign. A change in the sign of x would
not give the same value of opposite signs for each of the first
two terms. Consequently variations in the first two terms due to
a change in the sign of x could not be compensated for by a
corresponding variation in the fourth term. The conclusion to
be drawn is that when x changes sign there is no variation in
the sum of the first two terms, and no variation in the value of
the fourth term. From this it follows that

a = a' and b' = o
This gives us

y = a (c cx + c — cx) + b cos cx — d
Nowv when x = I or — /

284 BEVEL GEAR DRIVE AND REAR AXLE.

d2y —M

dS El

because M = o.

Under these conditions

Hence

- = a (e c » + e ) — b cos cl = o

dxz

a (e c l + c~ ) = b cos cl

Substituting in the above equation for y and remembering
that when x = /, y = o,

2a (e «* + e~~ '') = d

a =

2 (e " + c~~ )
Also

2b cos cl = d

b =

2 cos cl

When cos cl is zero the value of b, and consequently the value
of y, the deflection becomes infinite, and the shaft runs at the
critical speed. This is the case when cl = n/2, 3 V2, 5 V2,
etc. There are, therefore, a number of critical speeds. Now,
inserting the value of c in the equation for b and equating the
latter to the smallest angle corresponding to a critical speed we
get

IE 16

16m/4
in which

w is the angular speed in radians per second
/, the moment of inertia of the shaft section
E, the modulus of elasticity
m, the mass of the shaft per inch length

BEVEL GEAR DRIVE AND REAR AXLE. 285

/, half the length of the shaft in inches.

The mass of the shaft section is equal to its weight divided
by the constant of gravity, but in this case, as the units used
must be the same throughout and as the shaft diameter and
shaft length are expressed in inches, we must express the accel-
eration of gravity in inches per second per second, instead of
feet per second per second. Therefore

g = 32.16 X 12 = 386.

From the equation for w the critical speed of any shaft can
be calculated, but this equation is in a rather inconvenient form ;
it would be much preferable if the critical speed n in revolu-
tions per minute could be calculated directly from the dimensions
of the shaft, and this can be done if the equation is suitably
transformed.

We have

60
co2 = -

3,600

64
E = 30,000,000

W
m = —

386

W = X 0.28 = 0.07

4
Hence

A A7 TT slz — j2

U.U/ « a • « a

386 5,500

** = —
16

L being the whole length of the shaft between supports.

286 BEVEL GEAR DRIVE AND REAR AXLE.

Inserting these values in the equation for w2 we get

* d* 5,500 16

= _ x — X 30,000,000 X - X —

3,600 16 64 7r<f

which when simplified gives

w2 = 2,320,000,000,000 -

L4
Therefore

vd d

n = 1,520,000 - = 4,800,000 —

L2 L2

This equation applies to solid round shafts. Equations for
shafts with other sections can easily be derived by means of
the equation for w2. It will be seen that this value varies di-
rectly as the moment of inertia of the section and inversely as
the mass per unit length, all the other factors in the equation
being independent of the section. Therefore

But m, the mass per unit length, is directly proportional to
the area of the section, which we may denote by A. Conse-
quently

or as the least radius of gyration of the shaft section. For a
solid circle of diameter d

17 \~^7* 4~~ IT d

V^ 3"V 64 »</" M6~ 4

For a hollow circle of outside diameter d and inside diameter
d*

4 /d' + A1

d2 - df) *V 16~~

64
For a solid square shaft whose side measures d,

BEVEL GEAR DRIVE AND REAR AXLE. 287

Hence a tubular shaft of outside diameter d and inside diameter
di has a higher critical speed than a solid round shaft, the ratio
between the two critical speeds being

2 +

and a solid square shaft whose sides measure d has a higher crit-
ical speed than a solid round shaft of diameter d, the ratio of
critical speeds being

d d

-- -*-.— = 1.155
3.46 4

Hence, we have the following formulae -for the critical speeds
of other than solid round shafts :
For a round tubular shaft,

V d~ + di2
nc = 4,800,000 - L!!L

L2
For a solid square shaft whose sides measure d

nc = 5,520,000 —
L2

Agreement with Practical Observations.— It has been found
in practice that the actual critical speed is always somewhat
lower than the calculated value. For instance, Stodola in
'The Steam Turbine" gives several examples of tests for criti-
cal speeds of shafts. In five of these tests the critical speed
was found to be 6 per cent., 8 per cent., 9 per cent., 13 per cent.
and 14 per cent: below the calculated value. This discrepancy
is undoubtedly due to the fact that the points of support are not
rigid. An automobile propeller shaft when running at high
speed will whirl in the same way as a heavy rope which is
being swung around by two persons. If they cease their whirl-
ing effort their hands will nevertheless be carried around in a
circle, and so with the propeller shaft supports. The latter
consist of the universal joints which are fitted to shafts over-
hanging their bearings, and under the influence of the cen-
trifugal force on the propeller shaft these short shafts will bend
in the same plane as the propeller shaft, thus virtually increas-
ing the distance between supports. The effect depends,
of course, upon the relative stiffness and amount of overhang
of the connected shafts, but it has been found that if the cal-

288 BEVEL GEAR DRIVE AND REAR AXLE.

culated critical speed is not approached closer than within 15
per cent, a sufficient degree of safety is allowed in ordinary con-
structions.

The critical speed above discussed is the lowest critical speed.
There is an endless number of higher critical speeds, but these
are of no interest from a practical standpoint, as the shaft, to
be safe, must be made of such dimensions that its lowest criti-
cal speed is never attained in practice.

The following' table gives the critical speeds of solid round
steel shafts of different diameters and lengths :

CRITICAL SPEEDS (R.P.M.) OF FREELY SUPPORTED
SOLID STEEL SHAFTS.

d L

= 35"

40"

45"

50"

55"

60"

65"

70"

3,915

3,000

2,370

1.920

1,585

1,335

1,135

980

1%"

4,400

3,375

2,660

2,160

1,785

1,500

1,275

1,105

4,900

3,750

2,960

2,400

1,985

1,670

1,420

1,225

1%"

5,400

4,125

3,260

2,640

2,180

1,835

1,560

1,350

iy2"

5,880

4,500

3,550

2,880

2,380

2,000

1,705

1,470

i%"

6,380

4,875

3,850

3,120

2,580

2,170

1,845

1,595

\y4"

6,860

5,250

4,150

3,360

2,775

2,340

1,990

1,715

Shafts Fixed at Ends. — The case of a shaft fixed at both ends
is not so common in automobile practice, but may occur, as, for
instance, when the propeller shaft is surrounded by a torque
tube mounted on roller bearings at both ends. A shaft so sup-
ported when under the influence of centrifugal force will form
a compound curve, and as the distance between inflection points
is then so much less, a greater centrifugal force is required to
cause the deflection, consequently the critical speed is higher. An
analysis of the problem shows that the critical speed of a solid
round steel shaft of length L, fixed at both ends, is :

nc = 11,240,000 — ,
L-
and the critical speed of a hollow steel shaft fixed at both ends,

I d* + d?

no = 11, 240,000 \_

Manufacture of Rear Axles. — The designs of rear axles differ
widely, and as a result there is great divergence in the methods of
manufacture, since the manufacturing processes naturally must
be adapted to the design. For this reason it is not possible to give
more than a very general description of rear axle manufacture in
this work.

BEVEL GEAR DRIVE AND REAR AXLE.

289

Among the most important parts of the axle are the bevel
gear and its pinion. These must be very accurately cut in
order that they may run with very little noise, even at high
car speeds. Besides, the cutting of bevel gears involves much
greater difficulty than the cutting of spur gears. The stock-
ing or rough cutting can be done by means of a formed

T-I. 186. — STOCKING BEVEL GEARS.

290

BEVEL GEAR DRIVE AND REAR AXLE.

cutter in a milling machine or gear cutter of similar type, as
shown in Fig. 186, but the finishing should preferably be done
in a bevel gear planer, as this insures greater accuracy. The
bevel gears must also be case hardened or oil hardened, and
to correct the defects due to warping when the gears are
quenched, the latter are often run together in a special fixture
with a mixture of emery and oil. Fig. 187 illustrates the process
of grinding the gears in the plant of the Timken-Detroit Axle Co.
by means of a machine developed in the company's own shop.

FIG. 187. — GRINDING-IN OF BEVEL GEARS.

BEVEL GEAR DRIVE AND REAR AXLE.

291

The bevel pinion and gear are mounted on spindles at right
angles to each other. The spindle on which the pinion is mounted
is driven by belt from a countershaft and the other spindle
through a pair of accurately cut bevel gears of the same ratio as
the pair to be ground. The driving bevel gears are so adjusted
as to run without back lash, and are enclosed to protect them
from the emery powder with which the other gears are ground in.

FIG. 188.— TURNING UP BEVEL PINION BLANK.

In bevel gear drives employing two universal joints in the pro-
peller shaft, the bevel pinion and its shaft are frequently made
integral, and Fig. 188 illustrates a time saving method of machin-
ing up such blanks in a Fay lathe made by the Jones & Lamson
Machine Co., of Springfield, Vt. Three cutting tools are used,
of which one is carried on the back rest, and all of the machining
operations are performed at one setting.

As a rule, there are a great many machine operations to be
performed on the driving gear housing, such as boring the
holes for the axle tubes, the seats for bearings, etc. Fig.
189 illustrates the method of boring the gear carrier of a Timken-
Detroit rear axle. In this part, the same as in the halves of a cast

292

BEVEL GEAR DRIVE AND REAR AXLE.

driving gear housing, there are a number of concentric holes to be
bored, and a turret lathe is therefore a very advantageous tool.
In order to get the bores for the axle tube and for the propeller
shaft housing absolutely at right angles with each other, some

FIG. 189. — BORING GEAR CARRIER IN VERTICAL TURRET LATHE.

manufacturers use special three spindle boring machines, one of
the spindles being at right angles to the other two. The greatest
accuracy is required in boring the seats for the bearings.

CHAPTER X.

THE WORM DRIVE.

Transmission of power by worm and worm wheel in an auto-
mobile originated in England, where it is used for both pleasure
and commercial vehicles. More than a score of British manufac-
turers of pleasure cars fit either all or some of their models with
worm drives, or give an option on this drive. The worm drive
has also secured a foothold in Germany and France and is very
largely used for commercial vehicle drives in this country.

Up to about twenty years ago the worm and wheel were con-
sidered merely a means for transmitting motion, as distinguished
from a means for transmitting power. As it to be expected, when
the teeth are not very accurately cut and when they run together
dry or without lubrication, the efficiency of the gear is very low
and its wear is rapid. Worm gearing was first developed for
commercial power transmission purposes in connection with elec-
tric motors. These were the first high speed motors to come into
practical use and high reduction ratios were required in many
lines of application. For automobile work the worm gear was
first taken up by F. W. Lanchester and the Dennis Brothers of
England.

Advantages of Worm Drive. — The worm drive is at its
greatest advantage when a high ratio of reduction is desired.
With a bevel gear or chain drive it is difficult to secure a gear
ratio of more than 5 to 1, if road wheels of the usual size are
to be used, and in types of vehicles requiring a higher reduction
ratio, including nearly all types of commercial vehicles except
those shod with pneumatic tires, it is a question of using either
the worm drive or a double reduction drive by bevel gears and
chains. The worm drive then has the advantage as regards sim-
plicity of construction. Among other advantages of this drive
may be mentioned its absolutely silent operation and the possi-

293

294 THE WORM DRIVE.

bility of providing a very wide range of gear ratios without
change in th2 distance between the axes of worm and wheel
or in adjacent parts. The worm drive gives a symmetrical rear
axle which is comparatively easy to assemble.

Theory of Worm Gearing — The worm gear as applied to
automobile driving is similar to a helical gear, the worm being
always of the multiple thread type, and some of the rules of heli-
cal gearing therefore also apply to worm gear. In a worm and
worm wheel the gear reduction is equal to the quotient of the
number of teeth in the worm wheel by the number of threads
in the worm. The lead of the worm is the distance in the di-
rection of the worm axis corresponding to one complete revo-
lution of the worm thread. The angle of lead is the angle made
by the worm thread at the pitch line with a plane perpen-
dicular to the worm axis (also the angle made by a worm wheel
tooth with the worm wheel axis). In connection with helical
gears it is the custom to speak of the angle of spiral, which is
the angle made by an element of the gear tooth with the gear
axis, and in case the two axes are at right angles to each other
(as in a worm and wheel) the angles of spiral for the two
gears together make a right angle. In a worm gear the angle
of lead corresponds to the angle of spiral for the worm wheel,
while the complement of the angle of lead corresponds to the
angle of spiral for the worm.

Following are definitions of some terms used in connection
with worm gearing:

Circular pitch _ Pitch diameter x 3. 1416
(of wheel) ~~No. of teeth

Axial pitch __ Lead
(of worm) No. of threads
Circular pitch of wheel = Axial pitch of worm.
Normal circular pitch = Circular pitch x cos of angle of lead.

In calculating worms and worm wheels the following equation-
may be used :

WORM

Pitch diameter = No. of threads x normal circular pitch

3. 1416 x sin of angle of lead.

Lead = Pitch diameter x 3.1416 x tan of angle of lead.

2 X axial pitch

Outside diameter = pitch diameter +

Normal circular pitch = — - . ;.

Normal diametral pitch.

THE WORM DRIVE. 295

WHEEL

No. of teeth X normal circular pitch
3.1416 X cos of angle of lead.

Pitch diameter X 3.1416
e tan of angle of lead.

2 X axial pitch
Throat diameter = pitch diameter + — — 3 —

The centre distance or distance between the axes of worm and
wheel is equal to one-half the sum of the two pitch diameters.
Worm and wheel must be cut both either with right hand threads
or with left hand threads. In an automobile drive with the en-
gine rotating right-handedly as usual, worm and wheel must be
cut with right hand threads when the worm is placed on top of
the wheel, and with left hand threads when the worm is at the
bottom.

If we cut a very thin section from the middle of the worm
wheel we have a spur gear. If we cut a corresponding section
from the worm, we have a rack, and since the flanks of a rack
tooth to properly mesh with an involute gear must be a straight
line, the faces of the worm teeth are straight. In the old type
of worm used for transmitting motion, usually at a very high
ratio of reduction, the sides of the teeth were made parallel, and
most of the formulae for worm gear efficiency, thrust, etc., found
in text books are based on square faced worm teeth and are
inaccurate when applied to inclined teeth. Parallel faced teeth
cannot be used on multi-thread worms for automobile drives, as
the worm wheel teeth would have to be undercut too much.

Pressure Angle. — In speaking of the inclination of the tooth
flank, a distinction must be made between the normal pressure
angle and the axial pressure angle. The axial pressure angle is
the angle made by the line of intersection of a plane through the
worm axis with the tooth flank, with the worm axis, and is repre-
sented by j8 in Fig. 190. This angle is evidently one-half of the
angle described by the tooth flanks in the section plane if they are
continued till they intersect. The normal pressure angle a is the
angle included by two lines in a plane cutting the tooth normally
or at right angles to its elements, these lines both passing through
the pitch point in the tooth flank, one being perpendicular to the
flank at that point and the other tangent to the pitch circle. The
relation between the axial pressure angle and the normal pressure
angle is illustrated in Fig. 191. In this figure the line cd is sup-
posed to be perpendicular to ac and not in the plane of the paper.

296

THE WORM DRIVE.
be

tan /3 = —
ac
cd

tan a = —
ac

cd = cb cos <t>

Substituting this value of cd in the preceding equation we have
cb cos 0

tan a = = tan ]8 cos <t>

That is, the tangent of the normal pressure angle is equal to the
tangent of the axial pressure angle multiplied by the cosine of
the lead angle.

FlG. 190. — L ONGITUD1NAL SECTION
THROUGH WORM WITH 30° AXIAL PRES-
SURE ANGLE.

FIG. 191.— RELATION
BETWEEN AXIAL
PRESSURE ANGLE AND
NORMAL PRESSURE
ANGLE.

Most makers of worm gears for automobile transmission use
an axial pressure angle of 30 degrees. With a lead angle of 35
degrees this corresponds to a normal pressure angle of 25 de-
grees 19 minutes. Normal pressure angles of 22J^ and 14^ de-
grees have been used, but with these smaller pressure angles there
is undercutting of the wheel teeth if the number of teeth is small.
With the Hindley type of worm there is the further difficulty that
the worm could not be assembled with the wheel if the pressure
angle were too small.

Axial Pitch. — In ordinary toothed gearing, as the tangential

THE WORM DRIVE. 297

pressure which can safely be imposed upon the gears is pro-
portional to the circular pitch of the teeth, the coarseness of the
teeth increases with the power to be transmitted. The same
relation between the strength of the teeth and their circular
pitch exists in worm gears, but as the load capacity depends
more upon the capacity of the gears for getting rid of the fric-
tional heat than upon the mechanical strength of their teeth,
and as the heat dispersing capacity of a gear varies little with
the pitch of the teeth, the latter is to quite an extent a matter
of choice. For pleasure cars and the lightest commercial vehi-
cles the axial pitch is generally about % inch. Axial pitches as

FIG. 192.— COMPOSITION OF NORMAL TOOTH PRESSURE.

large as 1^ inches have been used in some instances in heavy
commercial work, but pitches of about 1^4 inches are more com-
mon. The larger the pitch the smaller the bottom diameter of
the worm, and even if the worm is made integral with the shaft
there is a limit to the depth of tooth, and consequently to the
pitch, because if the proportion of the depth of tooth to the bot-
tom diameter of the worm is too great the worm will possess
insufficient torsional rigidity.

The length of the worm, if of the straight type, is usually made
2qual to 40 per cent, of the wheel pitch diameter and the included
angle of worm contact may vary between 60 and 110 degrees, but
usually is closer to the upper limit. The lead angles usually em-
ployed vary between 30 and 40 degrees. This, as will be seen from
Fig. 194, is within the high afficiency range, and it also insures
reversibility of the drive, that is, the car will coast freely down
hill and can be pushed or towed.

298 THE WORM DRIVE.

Theoretical Efficiency. — When power is being transmitted
from the worm to the wheel, there are two forces at work,
namely, the surface pressure normal to the plane of contact and
the frictional force in the plane of contact. If the material of the
worm and wheel were absolutely unyielding there would be only
a line contact, but since it is elastic the contacting parts com-
press so as to give a surface contact.

Referring to Fig. 192, the normal pressure P on the tooth sur-
face can be resolved into two components, one P cos a, perpen-
dicular to the tooth helix, and the other, P sin a, parallel thereto.

The former component is transferred to Fig. 193 and is there
again resolved into two components, one, P cos ct sin Q, in a
plane perpendicular to the worm axis and the other parallel to
the worm axis. For the present we are concerned only with the
former, which is one of the two items making up the tangential
force at the pitch line of the worm. The other item is due to the
frictional force P f (f being the coefficient of friction). This
force can also be resolved into two components, viz., P f cos 6
tangential to the worm pitch circle, and P f sin 6 tangential to
the wheel pitch circle. Hence the total tangential force on the
worm pitch line is

P cos a sin 9 + P f cos B

and the total tangential force on the pitch line of the wheel is
P cos a cos 6 — P f sin 6.

Multiplying these tangential forces by corresponding motions
on the pitch circles of the worm and the wheel respectively, gives
the input and output corresponding to that motion, respectively,
and the ratio of the latter to the former is the efficiency. Sup-
pose that there is a motion x in the direction of the line of contact.
Then the component of this motion tangential to the worm pitch
line is x cos 6 and the component in the direction of the wheel
pitch line, x sin O. Hence the ratio of velocities is

wheel pitch line velocity x sin 0

__ , = = tan 6

worm pitch line velocity x cos ©

and if the worm moves a unit distance the wheel moves a dis-
tance equal to tan 6. Therefore, the work done upon the worm
while a point in its pitch line moves a unit distance is

P cos o sin 0 + P f cos 6
and the work done upon the wheel is

(P cos a cos 0 — P f sin 6) tan 0.
The efficiency then is

THE WORM DRIVE.
(P cos a cos e -^ p f sin O) tan 0

299

P cos « sinO + P/cosO

Dividing both numerator and denominator by P cos © tan Q, we
have

cos a — / tan 6

« - - (52)

cos a + / cot Q

FIG. 193. — DIAGRAM SHOWING TANGENTIAL FORCES ON WORM AND
WHEEL, RESPECTIVELY, AS WELL AS THRUST LOADS ON SHAFTS.

which is the general formula for worm wheel efficiency. Fig. 194
shows how the efficiency varies with the lead angle for two dif-
ferent coefficients of friction, viz., 0.02 and 0.04.

300

THE WORM DRIVE.

Thrust and Radial Bearing Loads. — The thrust load on the
worm is equal to the tangential force on the wheel pitch circle
and the thrust load on the wheel is equal to the tangential force
on the worm pitch circle. The effect of tooth friction can be
neglected, as in well cut gears with proper lubrication the friction
coefficient is only about 0.02, and the error introduced by neglect-
ing it is very slight. Denoting the full load torque of the engine
by T, the worm pitch diameter by d, the wheel pitch diameter by
D and the reduction ratio by r, we have for the tangential force
on the worm pitch circle, and hence for the thrust load on the
wheel, at full engine load and direct drive.

IUU

f-o.os

^^~>~~

ficieru

9 £0 JO 40 SO 60 7O QO 3C

Angle of Lead of Worm, in Degrees

FIG. 194. — EFFICIENCY CURVES.

24 T

Lt =

(53)

and for the tangential force on the wheel pitch circle ; and, con-
sequently, the thrust load on the worm,

24 Tr

lt= .... . • (54)

The radial loads on both the worm and the wheel shafts are
made up of two components which act at right angles to each
other. The first is due to the pressure angle of. the teeth; it
passes through the center of tooth contact and is perpendicular
to both the worm axis and the wheel axis. This is the force
tending to separate the shafts and is, of course, the same for
both the worm and the wheel. If we denote the normal tooth

THE WORM DRIVE.

301

pressure by P, then this component Ci is equal to P sin a. But

It Lt

p — —

Hence

cos a cos <f> cos a sin <t>

i = P sin a =

It tan a

Lt tan a

cos <t> sin 0

The other component of the radial load, C2, is different for the
worm and the wheel, respectively. For the wheel it is equal to
the thrust load on the worm, It, and for the worm it is equal to
the thrust load on the wheel, Lt. That the two components of
the radial load on each shaft are at right angles to each other
may easily be shown. Take, for instance, the components of the
radial load on the wheel shaft. The first component, Ci is per-
pendicular to the worm shaft, while the second component, the
thrust load on the worm shaft, naturally is parallel to that shaft
and hence must be perpendicular to the first component. There-

FIG. 195.— WORM WITH FIVE THREADS, 33 DEGREES LEAD
ANGLE, 30 DEGREES PRESSURE ANGLE.

fore, the total radial load on the wheel shaft is equal to the square
root of the sum of the squares of the components

Zw r

tan a

But = tan |8,

cos <t>

so that

Lr = /t\i + tan"2 |3 ..... . (55)

and if /3, the axial pressure angle, has a constant value of 30 de-
grees then

Lr = 1.155ft

That is, the radial load on the wheel bearings is 15.5 per cent,
greater than the thrust load on the worm bearings.

302 THE WORM DRIVE.

Similarly, the total radial load on the worm shaft is

tan a tan a *

sin < sin

which, after the value of tan a is substituted, becomes

/ tan ft \ *

+ . . . .- , (56)

\tan <t> /

Center Distance. — The distance between the axis of the worm
and the axis of the wheel bears a close relation to the maximum
torque to be transmitted and therefore to the total weight of the
vehicle. In commercial vehicle practice the smallest distance
between axes, or the center-to-center distance, found in % ton
and 1 ton trucks, is about 6^4 inches. For 5 ton trucks a center-
to-oenter distance of about 9}/2 inches is used, and for worm gears
for motor trucks of other capacities the center distance may be
found approximately by the following equation

L = 0.7 t + 6 inches . . . . (57)

where t is the truck capacity in tons.
As the worm pitch diameter

n p

IT tan <t>
and the wheel pitch diameter

AT*

D =

and as the center distance

L =

we have

(58)

Capacity of Worm Gears. — The question of the amount of
power which a given worm will transmit is a very involved
one. It depends more upon the capacity of the gear for dis-
posing of the heat than upon the mechanical strength of its
teeth. As the temperature of the worm and wheel and of the

THE WORM DRIVE. 303

oil bath rises, the oil becomes thinner, and if it should become
too thin it would be squeezed out from between the teeth and
cutting would ensue. The heat produced is almost directly
proportional to the horse power transmitted. On the other hand,
the amount of heat which the gear can dispose of without an
excessive rise in temperature is proportional to the combined
surface area of the worm and wheel. Of this the surface area

FIG. 196.— THIRTY-EIGHT TOOTH WORM WHEEL, WITH 33 DEGREES
ANGLE OF LEAD AND 30 DEGREES PRESSURE ANGLE.

of the wheel is by far the greater part. The total surface area
of the gear is substantially proportional to the aggregate area
of the sides or flanks of its teeth, which varies directly as the
wheel pitch diameter, the worm pitch diameter and the sub-
tended angle of the wheel teeth. There is no doubt that the

304 THE WORM DRIVE.

capacity of a worm and gear combination increases with the
subtended angle of the wheel teeth, for by successively reducing
the subtended angle of any successful worm gear a point would
soon be reached where the gear would fail under its load. How-
ever, as an increase in the subtended angle increases only the
wheel area and that not in direct proportion, whereas the worm
area fs not increased at all, it is not to be expected that the
capacity will increase directly as the subtended angle. It will
not be wide off the mark if we assume that it increases as the
square root of the subtended angle.

There is another aspect to the problem. With a given worm
gear we could transmit a certain horse power either at high
rubbing speed and low tooth pressure or at low rubbing speed
and high tooth pressure. Within reasonable limits of speed
and tooth pressure there would not be much variation in heat
production. However, with the lower tooth pressure the tem-
perature could be carried higher without danger of the oil film
being broken down. This alone would result in an increase in
capacity, and a further increase would result from the fact that
at this higher temperature the gear would disperse more heat.
Therefore, in giving a constant for capacity it will be well to
limit its application to a small range of rubbing speeds. The
writer finds that worm gearing for motor trucks where the
rubbing speed is between 1,000 and 1,200 feet per minute is
given by

H.P. = 0.1 d D \]^~

where d is the worm pitch diameter, D the wheel pitch dia-
meter and <£ the angle (in degrees) subtended by the wheel
teeth.

Another rule for the capacity of worm gears, due to F. W.
Lanchester, is one long ton per square inch of projected worm
tooth area. Mr. Lanchester says that his worm gear will trans-
mit a load corresponding to such a pressure for an indefinite
period. Now, a worm gear for automobile transmission must
evidently have a transmitting capacity enabling it to support
pressures considerably greater than that corresponding to full
engine power on the direct drive for sometimes the full engine
power will be developed on the low gear or the reverse. This
latter condition, however, generally does not last for any length
of time, hence it is not necessary that the gear should be cap-
able of supporting the full engine power transmitted through
the low gear indefinitely. In truck transmissions the usual al-

THE WORM DRIVE.

305

lowance is 1,200-1,400 Ibs. per square inch of projected tooth
area in contact, based on full engine power on the direct drive.
If d be the pitch diameter of the worm, the outside diameter is
d + 2p*/K and the bottom working diameter d — 2/>a/7r; and if
the angle of worm contact be 0, then the projected area of worm
contact is

FIG. 197,— SHADOW VIEW OF WORM WHEEL AXLE.

/ 2 />a\2 / 2

d + I—id 1 X — X = square

V *• / \ T / 4 360 180

inches.

Efficiency Tests of Worm Gears. — Several series of effi-
ciency tests have been carried out on worm gears for autorno-

306

THE WORM DRIVE.

bile drives. One of the earliest extensive tests reported was
made by the H. H. Franklin Mfg. Co., and showed efficiencies
of 88-89 per cent, at worm speeds of 1,200 and 1,500 r.p.m. over
an output range from 8 to 20 h.p. This is a rather low effi-
ciency, but it must be remembered that these tests were made
at a rather early period and the fact that the Franklin Com-
pany discontinued the worm drive would seem to warrant the
assumption that, the gears were not particularly good examples
of the art of worm gear cutting.

FIG. 198. — LANCHESTER WORM GEAR TESTING MACHINE.

In 1912 several series of tests of Lanchester worm gears
were made by the National Physical Laboratory of England
for the Daimler Motor Company on a special testing machine
designed by Mr. Lanchester. This machine is based on a prin-
ciple similar to that of the electric cradle dynamometer. It
has been repeatedly pointed out that the rear axle housing
tends to turn in the direction opposite to that of the axle shafts,
with a torque exactly equal to that of the axle shafts. There-
fore, by mounting the rear axle housing in ball bearing sup-
ports and holding it from rotation by means of a weight on an

THE WORM DRIVE. 307

arm secured to the housing, we have a measure of the rear axle
torque. If the axle is worm driven, the housing also has a
tendency to turn in a plane perpendicular to the worm axis in
the direction opposite to that of the worm shaft, with a torque
equal to that of the worm shaft. Lanchester, therefore, gives
his worm gear housing such a support that it may rock in two
vertical planes at right angles to each other. He then measures
the torque on the propeller shaft and on the axle shaft, respec-
tively, by balancing the housing in both planes. This he does
by means of a single weight suspended from a knife edge paral-
lel with and at a given distance from the axle shaft axis.

If we denote the torque on the worm shaft by t, that on the
axle shafts by T and the worm gear reduction ratio by r, then
if there were no loss in the gear we would have

As a matter of fact T is always less than t r, and the efficiency
is measured by the ratio Tit r.

The testing machine comprises a cradle consisting of two
wheels coupled by bridges. The cradle is supported by four
ball-bearing rollers and power is transmitted to the worm and
from the rear hub universal jointed shafts, the joints being of
the ball bearing type. A balance arm is fixed to one side of the
case parallel to the worm shaft. At the end of this arm there is
a transverse knife edge arm on which a weight is suspended by
means of a rod. The weight can be slid along the transverse
arm by means of a finger wheel, and its distance from the axis
of suspension can be read off on a dial.

The gear box is supported from the cradle on ball bearings
in such a way that the axis of the worm intersects the axis of
the cradle wheels. When the worm gear housing is in equi-
librium the contact point of the knife edge is located in the
plane of the two axes of rotation. In operation the finger wheel
is adjusted until the gear box is in equilibrium. Then, as the
same weight is used to measure the torque around each axis of
support, the torques are proportional to the distances of the point
of knife edge contact from the two axes of support, respectively.
We found that

T T 1

t r t r'
and since

T OA

_ = -- (see Fig. 199)

t AB

308

THE WORM DRIVE.

OA 1

e = X —

AB r

In order to be able to make efficiency tests of large worm
gears with a small expenditure of energy, Lanchester connects
his driven shaft (or axle shaft), through a step-up bevel gear
set and a belt to the worm shaft, the step-up ratio being slightly
greater than the reduction of the worm and worm wheel, so that
the belt always slips slightly. As a result only the power lost
in the worm gear, bevel gear and in belt slip needs to be sup-
plied from an outside source. The belt tension is adjusted until
the weight hung from the knife edge is lifted and when mid-
way between stops the arm is locked in position. Readings are
then taken, and afterwards the arm is released to see whether
the torque has changed. Slight changes in torque do not affect
the efficiency, consequently it is not necessary to constantly
adjust the weight.

FIG. 199. — DIAGRAM OF TORQUE BALANCE.

The chief results of the National Physical Laboratory tests
on Lanchester worm gears are summarized in the following
tables, only the readings and calculated results for the highest
and the lowest speed in each series being given :

Worm
Speed
R.P.M.
1542

383
1532

408
1532

403
1532

373
1497

418

:33 WORM GEAR

Torque
on Driven

Calculated

Efficiency

Shaft

H.P.

P.C.

Lbs.-Ft.

31.9

95.4

449

7.9

93.9

449

45.6

95.7

645

12.1

94.0

645

59.4

95.8

841

15.6

93.8

841

73.3

95.7

1035

17.8

93.7

1037

17.5

93.5

254

4.9

93.6

254

Pressure

Thread
Lbs.
1205
1205
1733
1733
2258
2258
2786
2786
682
682

THE WORM DRIVE. 309

8:35 WORM GEAR

1532 29.8 95.7 447 1200

418 8.1 94.6 447 1200

1512 42.3 96.2 643 1727

413 11.6 95.1 643 1727

1532 69.0 95.6 1035 2780

398 17.9 93.1 1035 2780

9:34 WORM GEAR

1532 34.5 96.0 447 1200

393 8.9 95.2 447 1200

1527 49.5 96.6 613 1727

403 13.1 95.0 613 1727

1527 79.6 96.6 1035 2780

403 21.0 95.0 1035 2780

Application of Formulae — We may now illustrate the appli-
cation of the formulae developed in the foregoing by the example
of a worm gear drive for a three ton truck. Let the truck be
equipped with a four cylinder ^l/2 x 5 inch motor (torque = 165
lbs.-ft).
According to equation (57) the center distance must be about

6+ (3 X 0.7) = 8.1 inches.

The usual gear reduction for this size of truck is about 9 to 1,
hence we may choose 4 and 36 teeth, at least for a trial. We then
have (equation 58)

+ 36 )=8.1 inches
6.2832 \tan <j>
4p

- + 36 p = 50.894
tan <j>
If we choose a lead angle of 30 degrees then

+ 36 p = 50.894

0.577

42.94 p = 50.894
p = 1.185 inches.
The worm pitch diameter will be
4 X 1.185

— = 2.614 inches.

3.1416 X 0.577
The lead of the worm will be

2.614 X 3.1416 X 0.577 = 4.738 inches.
The pitch diameter of the wheel will be
36 X 1.185

= 13.579 inches

3.1416
and the lead of the wheel

13.579 X 3.1416

- = 73.932 inches.
0.577

310 THE WORM DRIVE.

The outside diameter of the worm will be
2 X 1.185

2.614 + • = 3.368

3.1416
The outside diameter of the wheel will be

2 X 1.185
13.579 + = 14.333

3.1416

The thrust load on the worm shaft will be
24 X 165 X 9

= 2625 Ibs.

13.579

The thrust load on the wheel
24 X 165

= 1514 Ibs.

2.614

The radial load on the wheel shaft

1.155 X 2625 = 3030 Ibs.
and the radial load on the worm shaft

1 i- 2140- Ibs.

/ 0.577

\ 0.577

The one thing which remains to be determined is the included
angle of the wheel rim. Suppose that the 4.^2 x 5 inch four
cylinder motor runs at 1200 r.p.m. and develops a brake mean
effective pressure of 70 pounds per square inch. Then its horse-
power is 33.8. Therefore (equation page 304).

33.8 = 0.1 X 2.614 X 13.579

= 9.5

0 = 90 degrees.

Materials. — The worm is made of low carbon steel and is case
hardened. The wheel is made of hard phosphor bronze. These
materials are used because, owing to their hardness, they will
withstand great surface pressure, and also because they may be
finished to a high polish. The phosphor bronze wheel blank
should be cast with plenty of finishing stock, so that all porous
metal may be removed in the machining. The worm and wheel
are generally cut by means of hobs. In cutting the teeth the
greatest accuracy must be aimed at and the surfaces must be
smoothly finished, so that there is no need for much polishing
after hardening.

Hardening and Polishing of Worms. — The following rules
regarding the carbonizing, quenching and polishing of worms

THE WORM DRIVE. 311

were given by T. Rapson in an article in The Automobile Engi-
neer (London) for May, 1912:

"If the worm shafts are packed carefully in a carbonizing
medium, such as bone-dust, charcoal, etc., the box is properly
'clayed up,' placed in a carbonizing furnace and kept at the
proper temperature, is then removed and the worms are left
to cool in the box, there will be little trouble from oxidation.
They should be removed from the boxes, thoroughly brushed

FIG. 200. — HOBBING A WORM WHEEL.

(In the shops of Henry Wallwork & Co., Ltd., Manchester, England.)

and cleaned (not with a stiff wire brush), then immersed in a
bath of diluted hydrochloric and nitric acid for about five
minutes, removed and washed in a soda bath, dried in sawdust,
and are then ready for hardening. During the carbonizing opera-
tion all screw threads (if any), and the centres on which the
worm shafts will run when being ground for the ball races, should
be covered with a solution of copper sulphate, about four or five
ounces to a pint of water. This will keep the places so covered

312 THE WORM DRIVE.

from being carbonized and allow the centres to be scraped, if
necessary, after the hardening process, to ensure the worm run-
ning true before grinding for the bearings or races.

"To prevent scaling the worms during the hardening opera-
tion, a salt heating bath should be used, i. e., the worms should
be heated in melted salt, which will allow them to be brought
to a temperature suitable for hardening without allowing them
to come in contact with oxidizing influences; also the salt forms
a coating when the worms are being transferred from the bath
to the quenching vat. The reader may readily try this method
by obtaining a large, gannister lined plumbago crucible, putting
in a quantity of barium chloride, and heating to from 700 to 750
degrees C. (roughly, about the temperature at which aluminum
melts), placing a worm in the melted salt and allowing it to
get to the surrounding temperature, which will take from seven
to ten minutes. It must then be removed and plunged into a
bath of cold water. After the worm is cold it can be dipped
in a hydrochloric acid bath, which will free the barium chloride,
allowing it to be washed away readily, and a soda bath, with a
good drying in sawdust will leave a surface just as though it
had not been heated.

The worm is now ready for polishing and, if the beforemen-
tioned precautions have been taken in machining, carbonizing
and hardening, this will be a comparatively easy matter. A most
satisfactory polish may be attained by mounting an endless belt,
one side of which has a section equal to the space between the
worm teeth, set at the angle of the lead of the worm, the worm
being mounted on dividing heads and a reciprocating table which
permits its lateral and rotary movement, while the position of
the belt is constant. The belt must be kept tight by a weight or
spring and its section be corrected for interference, as in the case
of the cutter for the thread milling machine, but in this case for
an infinite diameter or straight line. It should run at a surface
speed of from 6,000 to 7,000 feet per minute, and be coated with
very fine abrasive. For the finishing operation the belt should
be replaced by a soft cotton rope and fed with crocus and oil."

Hindley Worm Gear. — All worm wheels are "throated" — that
is, the face of the gears, instead of being turned off straight, is
turned to an arc of a circle of a radius slightly greater than the
outside radius of the worm. The object, of course, is to increase
the tooth contact area. It is also possible to "throat" the worm,
and this form of worm is known as the Hindley. Such a worm
insures increased bearing surface, and therefore is less liable to

THE WORM DRIVE.

313

start cutting. However, its machining involves some difficulty
and it requires additional care in mounting. The ordinary straight
worm must be mounted accurately in two planes; that is, the
worm axis must be at a definite distance from the wheel axis, and
it must also be in the median plane of the worm wheel. The
Hindley or "hour glass" worm, on the other hand, must be ac-
curately located in three planes; that is, the worm axis must
be a definite distance from the wheel axis; it must be in the
median plane of the worm wheel, and the median plane of the
worm must include the wheel axis. In cutting a Hindley worm
the cutting tool must be mounted so as to turn around a centre
at a distance from the cutting edge equal to the radius of the
worm wheel, and it must be fed in the direction perpendicular
to the plane of rotation of the worm.

FIG. 201.— HINDLEY TYPE WORM.

(Purposely shown longer than made in practice, to bring out "hour glass"
effect more clearly.)

The majority of worm drives in England seem to employ
straight worms, but the Lanchester worm, which is used on
several foreign makes of cars and is being introduced in this
country, is of the Hindley type. When proper manufacturing
equipment is available the manufacturing difficulties vanish, and
there remains only the greater difficulty involved in properly
mounting the Hindley worm to balance the advantage of a lower
unit tooth pressure. The Hindley worm is made shorter than the
straight worm, usually between one-fifth and one-quarter the
wheel diameter.

314

THE WORM DRIVE.

Location of Worm Relative to Wheel. — As already pointed
out, there are two possible arrangements of the worm and wheel
combination, viz., with the worm at the bottom and at the top
of the wheel respectively. As far as the operation of the worm
gear is concerned, the former is the preferable arrangement, be-
cause with it the worm is always submerged in oil, as is that
portion of the wheel whose teeth are at the moment meshing with
those of the worm. The heat developed by the friction at the
tooth contact has to be transmitted to the casing largely through
the oil bath, and when the worm is at the bottom the path

FIG. 202.— MOUNTING OF WORM WITH ONE PLAIN AND ONE BALL
THRUST BEARING.

FIG. 203.— MOUNTING OF WORM WITH DOUBLE BALL THRUST

BEARINGS.

for the heat to travel is shorter and more direct. However, in
American practice considerations of ground clearance required
practically exclude the bottom mounted worm, except on town
cars. Practical experience, moreover, has shown that it is per-
fectly possible to properly lubricate the top-mounted worm and

THE WORM DRIVE.

315

to keep it cool, as at moderate and high speeds the revolving wheel
throws oil over the whole interior of the driving gear housing.

Mounting of Worm. — A very heavy thrust comes on the
worm shaft when the full engine load is being transmitted, and
special thrust bearings must be provided. With a top-mounted
worm the thrust is toward the rear when the car is being driven
forward and toward the front when it is being driven backward.
Since the thrust load is greater than the radial load, and must
be carried by a single bearing, whereas the radial load is divided
between two bearings, it is customary to use separate thrust

FIG. 204. — MOUNTING OF WORM DRIVEN DIFFERENTIAL.

bearings. The reverse is used only rarely, and then generally
only under low power and for a short time; hence, a pair of
plain thrust washers are sometimes used for it, as shown in
Fig. 202, with a ball thrust bearing to take up the thrust due
to forward driving. However, the more common plan is to use
a double ball thrust bearing, as illustrated in Fig. 203. The

316 THE WORM DRIVE.

differential also has to be provided with thrust bearings for taking
thrust in both directions, and in this case either a single ball
thrust bearing may be mounted on either side of the differential
or a double thrust bearing on one side. The usual plan is to
place one thrust bearing on either side of the differential, which
is illustrated in Fig. 204. As regards the sizes of bearings,
the same rule can be followed as given for the differential
bearings of bevel driven rear axles, viz., to use bearings of 50 to
100 per cent, greater rated load capacity than the maximum load
they will have to carry with the direct drive in operation. Of
all the bearings of a worm drive shaft the worm shaft thrust
bearing has to carry the largest load, and it, therefore, should
be made of liberal size.

Driving Gear Housings. — The driving gear housing of a worm
driven axle may be divided in three planes, viz., vertically in a
fore and aft plane, vertically in a transverse plane and horizontal-
ly. It may also be made in a single casting. In the Fierce-Arrow
motor truck the housing is cast in a single piece, with a large
gear carrier fitted to the top, as illustrated in Fig. 205. In the
case of a bottom mounted worm, the casing may be cast in a
single piece with a large cover on top or at an angle of 45 de-
grees, through the opening of which the differential may be in-
serted. The worm is always located in a tunnel which is bored
out for the reception of the bearings, and generally the bear-
ings at one end, at least, are larger in diameter than the worm,
so that the whole worm shaft assembly can be inserted into the
tunnel from that end. In some designs, however, the casing is
split through the worm axis.

Undoubtedly the greatest rigidity with a given amount of
material is obtained by dividing the housing vertically per-
pendicularly to the axis of the differential, but, unfortunately,
this design is not very satisfactory from the standpoint of con-
venience in assembling. The gear carrier principle, when applied
to the worm driven axle possesses all of the advantages that
it does in connection with the bevel driven axle, accurate meshing
of teeth being fully as important with the worm gear as with
the bevel gear. In the United States practically all worm driven
axles are designed on the gear carrier principle, which has proven
absolutely satisfactory.

The torque reaction is exactly the same in a worm driven axle
as in a bevel gear driven axle, and must be taken up by the same
means. Also, the action of the body springs has exactly the
same effect on the worm drive as on the bevel gear drive, and

THE WORM DRIVE.

317

the relative merits of the different axle linkages are the same
for the worm drive as for the bevel gear drive. It, therefore, is
unnecessary to go into the design of these parts in connection
with the worm drive. The design of the axle housing with
respect to strength also is the same as for a bevel gear driven
axle, except that the worm drive is often used for commercial
vehicles of relatively low speed in which the limiting stress on

FIG. 205.— DRIVING GEAR HOUSING WITH GEAR CARRIER (FIERCE-
ARROW TRUCK).

the axle housing is less. A live axle to carry a weight of several
tons and to withstand the reactions due to the forces necessary
to propel such a load must of necessity be of great strength.
Until 1915 the majority of truck axles were dead axles, and there
was some bias against live axles for heavy vehicles among de-
signers. There seems to be no reason, however, why a live axle
cannot be made strong enough to carry any load that can pos-

318 THE WORM DRIVE.

sibly be put onto a truck. However, every effort must be made
to so arrange the design that the moments and couples are re-
duced to a minimum and to so distribute the metal that it works
to the best advantage.

Calculation of Axle Tube Dimensions. — We saw, in con-
nection with bevel driven live axles, that the axle housing is
subjected to three different stresses, as follows: (1) The ver-
tical bending stress due to the weight carried; (2) the hori-
zontal bending stress due to the driving thrust of the wheels
or the retarding force of the wheels in braking, and (3) the
torsional stress on the axle tubes due to the application of the
rear wheel brakes. Of these the first can be greatly reduced by
means of an underrunning truss, and the second can be reduced
and the third practically eliminated by using separate torque
arms for the driving and braking torque, respectively. Two
torque arms should be used for the braking torque, each close to
one of the brakes, and either integral with the brake supporting
bracket or pivotally secured to it. The forward ends £>f these
torque arms should be secured to the frame in such a manner
that they will transmit the forward driving thrust to the frame.
The lever arm of the bending moment due to the driving thrust
or braking pull is then much shorter, being equal to the distance
between the centre plane of the driving wheel and the radius
rod, instead of to the distance between the wheel and the point
where the axle tube enters the driving gear housing. Besides,
since the torque bar is directly connected to the brake support,
the reaction on the brake support is transmitted directly to it
and does not create any torsion in the axle tube. There are then
only bending stresses on the axle tube, due to the horizontal and
vertical moments, respectively.

Suppose that in a 3 ton truck the load on each rear wheel
when the truck is fully loaded is 4,000 pounds. Also that the
distance from the centre plane of the rear wheel to the centre
of the body spring is 13 inches and the distance from the centre
plane of the wheel to the centre of the radius rod 7 inches. With
a coefficient of slippage of 0.6 the maximum driving force which
can be exerted at the wheel rims is 2,400 pounds. Hence the
maximum bending moment on the axle housing is

^(4,000 X 13)2 + (2,400 X 7)2 = 54,600 pounds-inches.

THE WORM DRIVE. 319

Since the moment due to the weight supported alone is
52,000 pounds-inches it is seen that the additional moment
due to the wheel thrust is negligible when, as in this case, the
radius rods are located close to the rear wheels. In regular
operation a considerable portion of the stress on the axle hous-
ing is taken up on the axle truss rod. We will assume that the
axle tube is to be funnel-shaped with flanged ends that are bolted
to the driving gear housing and that an outer tube is to be forced
over its smaller end, with flanges between which the spring saddle
and brake support are to be held. We will assume that the
outside diameter of the tube just inside the wheel bearing is
3*/2 inches. Then, allowing a stress of 20,000 pounds per square
inch in the material of the tube we have

20,0007
54,600 = -

c
I

— = 2.73
c
The section modulus is

3.1416 (3.54 — *4)

64 150 —

3.5 35.67

150 — x*

= 2.73

35.67

x* = 52.62
x = 2.69

If nickel sheet tubing is used a slightly higher stress can be
allowed and the inside diameter made equal to 2Y*t inches, giving
a Y% inch wall.

A typical heavy worm gear axle, that used on the Daimler
motor buses operated in London, is illustrated in Figs. 206 and
207. These buses, when laden, weigh 13,440 pounds, of which
8,960 pounds are carried on the rear axle. They are fitted with
four cylinder Daimler-Knight engines of 4.6 inches bore by 4.4
inches stroke. The worm, which is of the Lanchester hour-glass
type, has four leads and the wheel 29 teeth, giving a reduction of
7l/4 :1. The distance between the axes of worm and wheel is
7% inches.

It will be noticed that the axle is of the full floating type, the
cast steel wheels running on the outside of the axle tube on cylin-

320

THE WORM DRIVE.

321

drical roller bearings. Connection between the axle driving shafts
and the wheel hub is made by bolted on caps. The tread of the
rear wheels is 69 inches and the distance between spring centres
50 inches. The rear axle shafts, which are made of high tensile
nickel steel, have an effective diameter of 1?4 inches. Both ends
of the driving axles, where they fit into the driving couplings,
are upset.

The worm and wheel are carried by a removable gear carrier
with its own radial and thrust bearings. The whole differential
can be removed through the top opening after the axle shafts
have first been withdrawn and to this end it is not necessary to
first remove the bearing caps which are held by long through
bolts. The differential, it will be seen, is of the two pinion type

FIG. 207. — SECTION THROUGH WORM GEAR OF DAIMLER Bus AXLE.

which has also found some favor in this country on account of
its economical manufacture. Brake support and spring seat are
in a single casting. A notable feature is the large capacity of the
central housing. There is no stuffing box inside the axle tubes so
the lubricant can work right out to the hub bearings, but a pack-
ing is provided at the inner end of the wheel hub to prevent oil
working onto the brake surfaces.

In American practice the housings for heavy worm-driven axles
are generally made of .steel castings, either in a single piece ex-
tending from hub to hub, or in three pieces with bolted joints

322 THE WORM DRIVE.

between the central casing and the spring seats. All three types
of axles, full floating, three-quarter floating and semi-floating,
are manufactured. For the latter the advantage is claimed that
lateral shocks on the wheels do not impose nearly such heavy
loads on the outboard bearings as in full floating axles. The
Hotchkiss drive is very popular with the makers of these axles.
This requires a substantial fastening of the springs to the axle,
and to facilitate this, those portions of the axle housing to which
the springs are secured are cast of square cross section, instead
of being made round. In the case of three-quarter and full float-
ing axles, steel tubular members are inserted into the cast hous-
ing, extending close up to the differential housing and being sup-
ported by internal flanges or bushings. These tubular members
extend beyond the cast housing and carry the bearings on which
the wheels are mounted. Such cast steel axles are, of course, of
very considerable weight. A certain design of full floating axle
for a 3l/2 ton truck weighs, with hubs and brake drum, 1200
pounds.

CHAPTER XI.

THE CHAIN DRIVE.

Transmission by means of chains and sprockets is now very
little used on pleasure cars, but is still found on commercial
vehicles. The chain possesses the advantage of a slightly greater
flexibility than the shaft drive, hence it tends to protect the
motor and tires against shocks due to too rapid engagement of
the clutch, road shocks, etc. When kept clean, oiled and prop-
erly adjusted, the chain is a very efficient means of power trans-
mission. The trouble with it on automobiles is that it is usually
exposed, and grit soon finds its way into its numerous bearing
joints, causing rapid wear. In order to keep the chain at its
best operating efficiency for any length of time, it is necessary
to enclose it in an oil tight case and run it in oil. The design
of a light chain case which shall hold oil, not rattle and permit
of ready inspection of the chains and adjustment of their tension
is a rather difficult problem, and the different designs of cases
evolved do not seem to be entirely satisfactory. In the centre
or single chain drive, sometimes used with light pleasure cars,
and particularly with friction driven cars, the difficulty of keep-
ing an exposed chain in good working condition is especially
great, since it is located directly in the path of splashing mud
and water from the wheels.

Construction of Chains. — The only type of chain used for
automobile propulsion is the roller chain, which is one form of
the general class known as machine-made chains. The chain
(Fig. 208) consists of two sets of links, inner and outer, re-
spectively, each set of one kind being joined to two sets of the
other kind by means of a bushing and a rivet for each joint.
The bushing serves to hold the pair of inner links the proper
distance apart, and the rivet has both of the outer links riveted
to it. In passing over a sprocket the rivet turns inside the
bushing through an angle which is equal to 360 degrees divided
by the number of teeth in the sprocket, first in one direction

323

324

THE CHAIN DRIVE.

and then, as it leaves the sprocket, in the other. It is this mo-
tion of the joints which is responsible for the wear on chains,
and as the motion is less the greater the number of teeth in the
sprocket the advantage of using large sprockets is obvious.

The bushing is surrounded by a roller which contacts with the
sprocket teeth. Hence the contact between the chain and the
sprocket is a rolling contact and the sliding takes place between
the bushing and roller and between the bushing and pin. The
rivets are generally made of nickel steel and the bushings and
rollers are hardened.

Capacity of Roller Chains. — The permissible working ten-
sion of a roller chain increases substantially as the square of
the pitch, because both the pin diameter and the bushing width

^ 1 ^

f —

•\

^v
xv??

\\\\\\\\X
^<SXX^\

i
1

v^.

^ p^^

FIG. 208— ROLLER CHAIN.

increase with the pitch, and the product of these two factors
is the joint area to which the working load must be proportional.
Hence, from the standpoint of strength it is advantageous to
use a large pitch. On the other hand, since the diameter of the
sprocket is limited by considerations of ground clearance re-
quired, the number of teeth in the sprocket is inversely propor-
tional to the pitch, and since the angular motion at the joints
is inversely proportional to the number of sprocket teeth it is
directly proportional to the pitch. Hence, by increasing the
pitch we reduce the unit bearing pressure, but increase the mo-
tion at the bearings. A chain of smaller pitch operates more
quietly and has a longer length of life provided the tension on
it is not too high. Roller chains for automobiles are commer-

THE CHAIN DRIVE. 325

daily made in pitches varying from ^ inch to 2 inches, in V^
inch gradations, and each pitch is made in several different
widths of rolls.

The Diamond Chain and Manufacturing Company recommend
the following sizes of chains for commercial vehicles of different
capacities :

Pitch, Width, Roller Diameter,

Tons. Inches. Inches. Inches.

% 1 % 9-16

% -. 1 % %

1 114 % %

1% 1% % %

2 1% % %

2V2 and 3 !%• 1 %

4 1% 1 1

5 and over 2 1^4 1%

These are the largest sizes used in practice, and it is not un-
common to find chains several sizes smaller than those recom-
mended on trucks of a given capacity.

In laying out a chain drive for a commercial vehicle the aim
should be to make the chain speed as high as possible, because
in any case the average chain speed will be moderate and the
higher the chain speed the less the tension in the chain for a
given horse power transmitted. The large sprocket wheel must
clear the ground by about 7 inches, hence the sprocket pitch diam-
eter must be from 15 to 16 inches less than the wheel diameter.
The pitch diameter of the front sprocket then depends upon the
gear reduction desired. In commercial vehicles fitted with solid
tires the total reduction ratio between motor and rear wheel is
generally between 6 and 9. It is. customary to make the two re-
ductions, at the bevel gear set on the countershaft and at the
chains, about equal ; hence the speed reduction by the chains and
sprockets will vary between 2l/2 and 3. This gives a front
sprocket with the necessary number of teeth to insure proper
operation. Sprockets with less than ten teeth quickly destroy
the chains. Sprockets with 12 to 13 teeth give tolerably satis-
factory service, while sprockets with 15 teeth or more are most
satisfactory.

Chain and Sprocket Calculations. — The pitch diameter of
a sprocket for roller chains may be found by means of the fol-
lowing equation :
P

A> = (59)

180°

sin

N
where DP is the pitch diameter ; P, the pitch of the chain, and N

326

THE CHAIN DRIVE

the number of teeth in the sprocket. Denoting the diameter of the
roller by d, the outside diameter of the sprocket blank is

DP + d,
and the bottom diameter

DP — d.

The distance between centres of sprockets for a certain number
of links in the chain may be found by means of the equation

L = P

N n j8 I

- __(AT_M)_

22 180 J

2 cos

where Z is the number of links in the chain; N, the number of
teeth in the large sprocket; n, the number of teeth in the small
sprocket, and j8, the angle made by the chain with the line of
centres (see Appendix to Vol. I). This equation gives the dis-
tance required for the chain to run tight on the sprockets. A
slight amount of slack is necessary and means for adjusting the
distance between centres are generally provided. The distance

FIG. 209— OFFSET LINKS.

between centres of sprockets must not be less than one and one-
half times the pitch diameter of the large sprocket. Too long
chains are also objectionable because of the whipping effect if
the chain is at all loose. In commercial vehicle practice the dis-
tane between sprocket centres is generally made equal to about
twice the pitch diameter of the large sprocket. In fixing this
distance it is preferable to figure on an even number of links,
because although the use of so-called offset links (Fig. 209)
permits of an odd number, this practice is objectionable.

Design of Sprocket Wheels — Sprocket wheels are made from
steel plate, drop forgings or, in some instances, cast steel. The
larger sprockets are practically always in the form of flat rings
which are generally bolted to the brake drums. Front sprockets,
on account of their smaller size, wear faster than rear
sprockets and should be deeply case hardened. Front sprockets
also are sometimes bolted to separate hubs, the advantages
of this construction being that when a sprocket is worn out

THE CHAIN DRIVE

327

only the steel disc need be renewed, and that a lot of sprockets
can be forced over a mandrel and cut at one time. Referring
to Fig. 210 the width B of the sprocket is made equal to twenty-
nine thirty-seconds the width A of the chain, and the sprocket
teeth are chamfered on their outer ends from the pitch line on, so
as to reduce their width C on the circumference to one-half the
width of the chain, the centre of the chamfering radius being lo-
cated on the pitch line. The clearance D for the side links below
the pitch line must be nine-sixteenths of the pitch or more.
Sprocket wheels are cut by means of formed cutters, different
cutters being used for wheels of the same tooth pitch but with
different numbers of teeth. Care must be exercised to get the
bottom diameters exactly right and that there is the proper
amount of clearance between the teeth a»d the rollers as the
chain runs onto and leaves the
sprocket. In order to insure
concentricity of the sprocket
and its hub or centre, when the
two parts are made separate,
the sprocket blank should be
made an accurate fit over a
turned portion of the hub or
centre, against the flange to
which it is bolted. From four
to eight bolts are used in se-
curing the front sprocket to
its centre and a relatively
larger number for the rear
sprocket.

FIG. 210. — SPROCKET DIMENSIONS.

Chain Pull. — If the maximum engine torque is denoted by
T, the combined speed reduction ratio of the low gear in the
transmission and the bevel gear set by r, the pitch diameter
of the sprocket pinion by d and the combined efficiency of the
low gear and the bevel gear set by e, then the maximum chain
tension is

12 T r
: 100 d

.(60)

Suppose we have a three ton truck fitted with a four cylinder
4^x5 inch motor which develops a low speed torque of 165
pounds feet. Suppose the low speed reduction in the change gear
is 3.2 and the reduction of the bevel gear set 3. Then, considering
the efficiency of the change gear and bevel gear set together to be

328

THE CHAIN DRIVE.

90 per cent., the maximum torque on the jackshaft is

165x3.2x3x0.90=1,395 pounds-feet.

The proper size of the chain to use is a il/2 inch pitch I inch
width of roll. With a 36 inch rear wheel the limiting pitch
diameter of the sprocket wheel is about 21 inches, hence we
could use 45 teeth, which gives a pitch diameter of 21.49 inches,
and if the total reduction from engine to rear wheels is to be,
say, 9, then the chain and sprocket reduction must be 3 to i and
the sprocket pinion must have 15 teeth. This will make the pitch
diameter of the sprocket pinion

/_o-x 0=7.215 inches

FIG. 211. — OVERHANGING SPROCKET PINION.
Hence the maximum tension in each chain would be

1395 X 12
7-215

= 2,321 pounds.

Such a chain has an ultimate strength of from 18,000 to 21,000
pounds, and therefore has a factor of safety of about 8 when
working under full engine load on low gear.

Overhanging Sprockets— Owing to the high tension in the
chain under low gear it is advantageous to place the jackshaft
outboard bearing in the centre plane of the chain, which requires
that the sprocket be made bell-shaped or be bolted to a bell-
shaped centre. If an ordinary symmetrical type of sprocket
were keyed to the jackshaft outside the bearing, the tension in
the chain would impose a heavy bending moment on the shaft,

THE CHAIN DRIVE.

329

which is avoided by so arranging the sprocket and bearing that
their centre planes coincide. This is illustrated in Fig. 211.

Chain Adjusting Rods — The chain adjusting rods, also
known as radius rods, serve a triple purpose. They take up the
reaction due to the chain pull, allow of adjusting the slack in
the chain, and transmit the driving thrust or braking pull from
the rear axle to the frame. These rods must be jointed at both
ends so as to permit of free play of the springs, and the joint
centres should preferably lie in the axes of the sprockets, so
that any play of the springs will not affect the sprocket centre
distances.

Fig. 212 shows a simple form of radius rod, as often fitted
to light commercial vehicles. At the forward end a T-shaped
fitting surrounds a cylindrical portion of the jackshaft bearing
bracket or the jackshaft tube. The radius rod proper consists

FIG. 212.— SIMLPE FORM OF RADIUS ROD.

of a tube which is threaded on the inside at both ends, having
a forked connector secured into it at the rear end which con-
nects with a lug formed integral with the brake support or spring
saddle on the rear axle. The forward end of the radius rod is
connected to the T fitting already referred to by means of a
turnbuckle whose opposite ends are threaded right and left re-
spectively. It is obvious that by turning this turnbuckle the
distance between the two hubs at the end of the radius rod can
be varied, and when the adjustment has been made the turn-
buckle can be locked by means of the check nuts provided.

While the above construction serves the purpose of a radius
rod in a way, it does not make proper allowance for angular
motion of the rear axle with relation to the plane of the vehicle
frame, as caused by road irregularities. In fact, with radius
rods of this type the rear axle can move freely only in such a way
that it always remains parallel to the frame. Any other motion

330 THE CHAIN DRIVE.

entails heavy strains in the rods and their connections. Besides,
if the loaded truck were running on a laterally inclined road sur-
face, or if the rear axle should receive a lateral shock, as in
striking a curb as the result of a skid, the greater part of the
strain would be taken up by the radius rods, and these would
be likely to be injured. These lateral strains should preferably
be taken by the body springs, and to this end the joints of the
radius rods to the frame and rear axle, respectively, must be of
the universal type.

FIG. 213. — RADIUS ROD DOUBLE PIVOTAL FORWARD JOINT.

Fig. 213 shows the front end of a radius rod which has a
double pivotal joint with the frame. The fitting to which the
radius rod is connected swivels on the jackshaft bearing bracket
or housing, and the rod has a pivotal connection with this fit-
ting. The forward end of the rod proper is provided with a hub
which is internally threaded to receive a bushing which is
threaded left handedly on the outside and right handedly on the
inside. The bushing receives the shank of a T-shaped con-
nector fitting. By turning the bushing by means of a wrench
the effective length of the radius rod can be increased or de-
creased, and after the adjustment has been made the parts can
be locked in position by means of a clamp screw and check nut.

Fig. 214 illustrates a spherical joint for the forward end of a
radius rod. The turnbuckle is provided with a head whose
upper and under faces are turned spherically. The upper face
of the head bears against the spherical head of a steel button
inserted into a drill hole in the wall of the fitting on the jack-
shaft bearing bracket, and against the under face of the head

THE CHAIN DRIVE. 331

presses an externally threaded ring screwed into a threaded
recess in a boss formed on the fitting, which ring is also provided
with a spherical surface. After adjustment has been made, the
nut can be locked in position by means of a clamp screw, and
the same locking means is employed for the 'threaded shank of
the turnbuckle.

The joint of the radius rod to the rear axle may also be of
either the double pivotal or spherical type. The former is illus-
trated in Fig. 215. A lug is formed on the hub of the brake
support which is swiveled on the rear axle, and the rear end of
the radius rod is connected to this lug by means of a pin which is
held in position either by means of a bolt head and nut or a
locking pin, as shown in the illustration. A spherical joint for
the rear end of a radius rod is shown in Fig. 216. One-half of

FIG. 214. — RADIUS ROB SPHERICAL FORWARD JOINT.

the socket is formed in the spring saddle, and the other half in
a fitting which is bolted to the spring saddle. The ball is pro-
vided with a threaded shank, which is screwed into the tubular
rod and secured by a lock nut.

In Fig. 217 is shown a spring cushioned radius rod as used on
the Bussing motor trucks made in Brunswick, Germany. The
rear end of the radius rod is connected to the brake support and
the forward end is made telescoping and surrounded by a volute
spring. It is obvious that in case of a sudden increase in the chain
pull, as in letting the clutch in too quickly, the volute spring
will compress and the radius rod shorten, thus cushioning the
drive.

When a spherical type of joint is used at the rear end of
the radius rod, it is not convenient to use the latter as a torque
member to take up the brake reaction. In that case the brake
reaction has to be taken up by the body springs by connection of

332

THE CHAIN DRIVE.

the brake support with the spring seat, or the brake support may
be linked to the vehicle frame.

Calculation of Radius Rods — The radius rods act as com-
pression members or columns, and their dimensions should be
calculated accordingly. The maximum chain tension can be cal-
culated by the method already explained (Equation 60). Besides
this, the rods must transmit the propelling thrust from the rear
axle to the frame. This propelling thrust can be figured on the
basis of 15 per cent, of the weight of the vehicle on the two
rods, for extreme cases. But since the rod makes an angle with
the frame, the thrust in the direction of the rod is greater than
the propelling thrust, in the ratio of unity to the cosine of this
angle.

FIG. 215. — RADIUS ROD DOUBLE PIVOTAL REAR JOINT.

Thus, in the case of our 3 ton truck we found that the maxi-
mum chain tension was 2,321 pounds. The maximum propelling
thrust on each side is 975 pounds, the weight of truck and load
being 13,000 Ibs. Assuming that in the full load position of the
spring the radius rods make an angle of 20 degrees with the
frame, the thrust along them will be

9-^- = i, 040 pounds,
0.94

and the total pressure on each of the radius rods,
2321 + 1040 = 3361 pounds.

THE CHAIN DRIVE.

333

FIG. 216. — RADIUS ROD SPHERICAL REAR JOINT.

The necessary section can be determined by means of the
equation

S —

_4_1!\

25,000 r2)

(Rankine's equation for steel columns free at both ends). In
this equation 6* is the unit compression stress; P, the total pres-
sure on the column; A, the cross sectional area; r, the least
radius of gyration of the section, and / the length of the rod or
column. In order to use this formula it is necessary to assume
a section and determine the value of the stress S, and if this
figures out either too high or too low, to make a new assumption.
Let us assume that the centre to centre distance of the radius
rod in the 3 ton truck is 40 inches; that the rod is to be tubular,

FIG. 217. — CUSHIONED RADIUS ROD.

334 THE CHAIN DRIVE.

of iJ4 inches outside and Y& inch inside diameter. Then

A - 0.6 square inch,

7 = 0.097,

^ = 0.151,
and the unit stress

S = 3i36i / , _4_JN6??\ = I5, IOoXpounds i>er sq. in.
0.6 \ '25,0000.1517

Assuming the outside diameter to be il/2 inches and the inside
i inch, the unit stress figures out to about 7,000 pounds per
square inch. With these figures and a table of standard tube
sizes a suitable tube can easily be selected, since the stress can
be allowed to reach a value of 12,000 to 15,000 pounds per square
inch. Of course, if the tube is threaded on the inside the dimen-
sion at the bottom of the thread must be taken for the effective
inside diameter of the tube.

Many radius rods serve also as brake torsion members, and
these snould also be calculated as to the torsional strains pro-
duced in them, which can be done by the same method as used
for calculating the torque rod of bevel and worm driven axles.
Such radius rods are generally made of I section, often with
parts of the web left out, and for commercial vehicles they are
mostly made of cast steel.

In designing radius rods, the designer should look to it that
the adjusting members are readily accessible. Means must be
provided for taking up all play between adjusting members, as
else the joints will be quickly worn out by the shocks of the
drive. Grease cups msut be provided for all bearings, even those
having but a very slight motion.

Effect of Spring Play on Chain Drive — In Fig. 218 is
shown a chain drive in diagram in two different positions, the
springs being assumed to be distended and compressed, re-
spectively. The sprocket pinion is supposed to have fifteen
teeth, and the sprocket wheel forty-five. The distance between
centres is assumed to be 28 inches, and the total vertical motion
of the springs 6 inches. By using these figures a direct com-
parison with the bevel gear drive is possible, although in one re-
spect this comparison is not on the proper basis, since the pro-
peller shaft of a shaft driven car is nearly always made consid-
erably longer than the radius rod of an equivalent chain driven
car. We will assume, as in the case of the bevel gear drive, that
when the springs are compressed the line of centres is horizontal.
Then when the springs distend, the line of centres moves through
an angle a determined by the relation

THE CHAIN DRIVE.

335

28
Referring to Fig. 218, a portion of the chain whose length is

A £ =

360

inches

winds up on the sprocket wheel and a portion whose length is

IT da,

CD — — — inches
360

unwinds fro*i the sprocket pinion. The length of chain between
the extreme points of contact on the two sprockets (E B, C A}
remains the same. Since the length of chain which unwinds
from the pinion is not equal to that which winds up on the

FIG. 218. — DIAGRAM ILLUSTRATING EFFECT OF SPRING ACTION ON
CHAIN DRIVE.

wheel, if we assume that the wheel remains stationary the
sprocket must turn to unwind a length of chain

ir(D —

AB—CD=

360

inches.

It must turn in the forward direction when the springs dis-
tend and in the backward direction when they compress.
A motion of

360

on the circumference of the sprocket pinion corresponds to an
angular motion

Q--=D~d 'a degrees.
d

It will be seen from this that when D = d — that is, when the
two sprockets are of the same size — the spring action has abso-

336 THE CHAIN DRIVE.

lutely no effect on the drive, and the effect is the less the smaller
the difference in the sizes of the two sprockets. In the case of our
example, since D is substantially equal to 18 inches and d to 6
inches, and a = 12° 21', the angular motion of the sprocket pinion
corresponding to a spring play of 6 inches is

12° 21' = 24° 42'

This is considerably less than the angular motion found for
the case of the bevel gear drive with single universal joint, viz.,
37° 30'.

The above analysis brings out another reason for making the
reduction ratio in the chain drive as small as possible.

Chain Cases. — Chain cases are made of sheet steel, cast steel
or^cast aluminum. A design of chain case intended for a high
grade pleasure car is illustrated in Fig. 219. The housing is made
in two main parts. The upper part is clamped and bolted to
the radius rod and the lower part is hinged to the upper part,
the hinge being at the rear end. The parts overlap at the divid-
ing line so as to insure a substantially oil-tight joint. In the
outer side of the case circular openings are left which are large
enough for the sprockets to pass through. The opening for
the front sprocket is closed by a bowl-shaped piece of sheet
metal with double rim which is held in place by being clamped
between the two parts of the case, whereas the opening for the
rear sprocket is closed by a ring bolted to one of the parts and
making a tight joint with the brake drum by means of a felt
ring in a suitably formed groove. There is an inspection hole
in the upper part which is closed by a hinge cover. It is located
near the front sprocket where access to it is not interfered
with by the driving wheel.

The radius rod has a long bearing on the axle, and, of course,
is rigid in the transverse direction. The upper part of the case is
securely fastened to the rod at various points of its length.
Near its forward end the radius rod forms a loop spanning the
jackshaft bearing bracket. The bearing bracket is surrounded
by a yoke made in halves riveted together, with guiding shanks
extending in the direction of the rod. One of these shanks is
surrounded by a sleeve having a threaded seat in the end of the
rod. In order to get the yoke and the threaded sleeve into
place the two bearings for these parts in the radius rod have to
be made with separate caps.

A form of cast steel chain case is illustrated in Fig. 220. It

THE CHAIN DRIVE.

337

338 THE CHAIN DRIVE.

is made in quarters, as shown, and bolted together. The case
also serves as a radius rod and brake support and is strength-
ened for these purposes by ribs and bosses suitably located. The
chain tension is adjusted by means of an eccentric plate sur-
rounding the bearing housing and secured to the casing by means
of cap screws. The joint between the eccentric plate and the
bearing housing is of the ball and socket type, so as to avoid
straining the case.
A similar adjustment has been proposed in which a single

FIG. 220. — CAST STEEL CHAIN CASE.

eccentric is used with worm wheel teeth cut on its circumference,
with which mesh the teeth of a worm journaled in the walls of
the case. Both the eccentric and the worm and worm wheel
being self-locking, no special locking device is required.

Another possible method of chain adjustment in connection
with a case consists in placing a square bearing block around
the end of the jackshaft tube, sliding in a rectangular groove
in the case and adjusted either by opposite set screws through
lugs on the case or by screw wedges back of the bearing block.

Owing to the difficulties encountered in devising chain adjust-
ing means in connection with chain cases, it is desirable to make
the range of adjustment as small as permissible. It must be
possible to adjust the centre distance enough to vary the chain
length one complete pitch. This necessitates a change in the
centre distance of substantially one-half a pitch.

Dead Rear Axles. — Dead rear axles are made of square

THE CHAIN DRIVE.

339

rectangular or circular cross section, the rectangular section
predominating in recent designs. By far the greatest strain on
the axle results from the vertical bending moment due to the
load on the springs, and therefore it is not to be wondered at that
a section is employed which provides greater vertical than hori-
zontal strength. The ratio of the height of the section to its
width varies from about il/2 to 1^/4. In calculating the neces-
sary section of the axle a stress of 15,000 pounds per
square inch can be allowed for hammered medium carbon steel.
Some manufacturers allow 20,000 pounds, but the lower figure
is better. Thus, let L be the load supported by one driving
wheel when the car is fully loaded; /, the distance of the
spring centre from the wheel centre ; b, the width of the axle
section, d its height, and r the ratio of d to b. Then the bending
moment on the axle is L / and the resisting moment is

Hence

and

Z/=-

(61)

Having found the height of the section the width is found by
merely dividing by the assumed ratio r.

Some manufacturers forge the spring seats integral with the

FIG. 221. — DEAD REAR AXLE

axle, while others make them separate. Beyond the spring seat
the axle is made of round section to form a seat for the radius
rod. In some cases, owing to lack of space between the sprocket
wheel and spring, the radius rod is placed on the inside of the
spring. However, the more common and the preferable arrange-
ment is to place the rod close to the chain, so that the bending
moments of the chain pull may be kept as low as possible. That
section of the axle which serves as seat for the radius rod or
brake support is always limited by a flange at the inner end, and

340

THE CHAIN DRIVE.

sometimes also at the outer end, in which latter case the radius
rod, etc., must be made with a separate cap. Beyond this por-
tion comes the axle spindle which usually has seats for two anti-
friction bearings of different size, and at the end a threaded
portion over which screws a nut which holds the inner races of
both bearings in place, a spacer being placed between the two
inner races. A typical rear axle is illustrated in Fig. 221.

The Jackshaft — In the earlier cars with side chain drive the
bevel gear set and differential on the jackshaft were usually en-
closed in the rear part of the change gear box, and Oldham
couplings were inserted in the two halves of the jackshaft. How-
ever, it has now become the common practice to make the jack-
shaft of the same general form as a bevel gear driven rear axle,

FIG. 222. — JACKSHAFT END AND SUPPORT.

using either a pressed steel or built-up housing which extends
across the frame and is supported from the frame side members.
The change gear case can either be bolted to the rear axle hous-
ing, it can be placed somewhere between the engine and the jack-
shaft, or it can be combined with the engine into a unit power
plant. The first arrangement is the most common. The same as the
rear axle, the jackshaft may be made either full floating or semi-
floating; that is, the outboard bearings may be placed either in-
side a bearing housing secured to the end of the jackshaft tube,
or they may be placed on the outside of the tube. Fig. 222
shows a typical design of a jackshaft end, including the bearing
bracket, bearing housing:, radius rod end and sprocket pinion.

CHAPTER XII.

BEVEL-SPUR GEAR, INTERNAL GEAR AND FOUR-
WHEEL DRIVES.

There are three forms of double reduction drives, each compris-
ing one pair of bevel gears to effect the right-angled transmis-
sion between the longitudinal propeller shaft or drive shaft and
a transverse shaft. The other reduction may be obtained either
by means of chains and sprockets, a pair of spur gears or a pair
of spur pinions and internal gears. Chain drive was at one time
very common for motor trucks and other commercial vehicles,
but has lost much ground. The bevel and spur gear drive has
been used by Renault in France and by several manufacturers
in England, especially on so-called subsidy models, the subsidy
regulations barring the worm drive. In this country it is used
by the Autocar Company. The internal gear drive also had its
first extensive application abroad, but has now found quite a
following in this country.

FIG. 223. — DIAGRAM OF BEVEL- SPUR DRIVE.

In a bevel and spur gear drive the whole of the gearing is
enclosed in a single case at the middle of the rear axle. As
shown in the diagram of a bevel spur drive, Fig. 223, the power
is first transmitted through the bevels, because the end thrust

341

342

BEVEL-SPUR GEAR DRIVES.

on the bevel gear is then much less and can be more readily
provided for. Large bevel gears also are more expensive to
produce than equivalent spur gears, and this is probably another
reason why the power is transmitted through the bevel gear set
first. The greater part of the reduction is obtained by means
of the spur wheels, because the spur gear is concentric with the
axle and can be of considerable diameter without interfering
with anything. While it would be possible to have the shaft
carrying the bevel gear and the spur pinion in the same hori-
zontal plane as the rear axle axis, it is generally placed con-
siderably higher. In most designs the axes of the spur pinion
and gear lie in an inclined plane, the pinion axis being generally
forward, sometimes to the rear of the gear axis, but where space
permits the pinion may be directly above the gear. The gear
carrier principle, so successfully employed on worm and bevel
gear-driven rear axles, has also been applied to the spur gear-
driven axle. In one or two English designs the differential gear

FIG. 224. — KARRIER BEVEL- SPUR DRIVE.

is mounted on the intermediate shaft and the power is trans-
mitted to the rear axle shafts by two pairs of spur wheels. This
has the advantage that a smaller differential gear will do, but the
disadvantage that two pairs of spur wheels are necessary goes
a long way toward nullifying it.

Arrangement of Gear Relative to Axle — In England, where
the bevel-spur drive has seen its widest application, it is used
chiefly in connection with drop-forged axle housings of the so-
called banjo type. Owing to the irregular shape of the pear

BEVEL-SPUR GEAR DRIVES.

343

housing it is something of a problem to properly combine the
axle and gear housings, and various solutions of this problem
have been evolved. Thus the Karrier Company places the central
ring of the axle housing horizontally, as shown in Fig. 224. A
top gear carrier and a bottom housing are secured to the axle
forging by screws. This makes a neat and handy construction,
but has the disadvantage that the material in the ring is not very
favorably disposed to support vertical bending stresses. To make
up for this, an unusual amount of material must be put into the
ring, as may be seen from the drawing. In the Pagefield axle,
shown in Fig. 225, the ring of the axle housing is placed vertically,
and this axle has the somewhat unusual feature that the bevel
gear and spur pinion are located to the rear of the axle, the bear-

FIG. 225. — PAGEFIELD BEVEL-SPUR DRIVE

ings for the shaft on which these two gears are mounted being
supported in the rear cover, while the bearings of the bevel
pinion shaft are in the front cover. The "ring" of the axle
housing in this case is not symmetrical about the axis of the
axle, extending higher above the axis than below it. In order
to combine the advantages of the two constructions above de-
scribed, the Wolseley Motor Car Company places the ring of
the axle housing at an angle, the upper part being tipped back-
ward (Fig. 226). This permits of the use of a symmetrical
axle forging and of a gear carrier supporting all of the gears
of the drive, so that the latter can be assembled and tested before
it is assembled with the axle housing. It will be observed from

344

BEVEL-SPUR GEAR DRIVES.

the drawing that the inclination of the ring toward the vertical
is not great, and not much strength is sacrificed.

Calculation of Spur Gear Drive — The spur gear on the rear
axle is made of as large a diameter as consideration of ground
clearance required will permit. The pitch diameter will vary
roughly from about 10 inches in a 1-ton truck to 15 inches in
a 5-ton vehicle. For trucks of 3 tons' load capacity and over,
4 diametral pitch teeth may be used for the spur gears and 5
diametral pitch for the bevel gears, while for lighter vehicles
the spur gears may be of 5 diametral pitch and the bevels of 6.
As regards materials, the same steels as used for bevel gears

FIG. 226. — WOLSELEY BEVEL-SPUR DRIVE AXLE.

will give satisfaction, that is, low carbon nickel or chrome nickel
steel, case hardened, or a medium carbon chrome nickel steel,
oil hardened. The spur wheel, if desired, can be made of medium
carbon steel, heat treated, as it is naturally stronger and sub-
jected to much less wear than the pinion. In calculating the
necessary width of face of the spur pinion and gear the Lewis
formula can be used, allowing a stress of 16,000 pounds per
square inch in the teeth when the engine drives direct and de-
velops its full torque. This may seem to give an excessive stress
in the teeth when the engine drives through the low gear at full
load, but it must always be remembered that the Lewis formula
gives a considerably higher stress than actually occurs.

For the bevel gear teeth the stress may be taken somewhat
lower, say, 14,000 pounds per square inch, because of the higher
pitch line velocity at which these gears run. It may be well to
illustrate the application of these rules by a practical example.

BEVEL-SPUR GEAR DRIVES. 345

We will assume that a three-ton truck is to be fitted with a

four-cylinder 4j4xSj4-inch motor, with a gear reduction of 8:1.

Figuring on a maximum brake m.e.p. of 85 Ibs. p. sq. in. the
engine torque is

4 x sy4 x 4^4 x 454 x 85

= 168 lbs.-ft.

192

Let us assume that the layout shows that the pitch diameter of
the spur wheel can be about 13 inches. Then, since it is cus-
tomary to use 4 diametral pitch in such cases, the gear can be
made with 52 teeth. For the pinion we may choose 14 teeth.
This number is about the smallest it is advisable to use, as with
a lesser number the teeth are too weak in the root. As the total
reduction is to be 1 :8 and the spur gears give a reduction of
14:52 = 1:3.71, the reduction ratio of the bevel gears must be
8/3.71 = 2.15. Hence the torque on the spur pinion shaft will be

2.15 X 168 = 361 lbs.-ft.
This pinion has a pitch diameter of

— = 3.5 inches
4

and a pitch radius of 1.75 inches, so the tangential force on the
pitch radius is

361 X 12

= 2480 Ibs.

1.75

Now, applying the Lewis formula, we have

2480 = 16000 X 0.785 X f X 0.072,
hence

2480

f = = 2.73, say, 2^4 inches.

16000 X 0.785 X 0.072

The bevel wheels will have a diametral pitch of 5. We will
choose for the pinion 22 teeth, in which case the gear must have
47 teeth, and see how the width of face figures out. If it comes
out considerably less than 30 per cent, of the pitch line length,
then we can choose a smaller number of teeth, which will result
in a greater proportionate face width, and vice versa.

The Lewis formula adapted to bevel gears is

S p y L

w = (1 — a3)

where w is the tangential load at the maximum pitch radius of
the pinion.

346

BEVEL-SPUR GEAR DRIVES.

S, the stress in the teeth,
p, the circular pitch.

y, the Lewis constant for the number of teeth.
L, the pitch line length, and

a, the ratio of the distance from the cone apex to the inner
and outer ends of the teeth, respectively.
The pitch diameter of the pinion is

— = 4.4 inches

FIG. 227.— AUTOCAR BEVEL-SPUR DRIVE, TRANSVERSE SECTION.

and that of the gear

— = 9.4 inches.
5

BEVEL-SPUR GEAR DRIVES. 347

The pitch radii arc equal to half these values, viz., 2.2 and 4.7
inches, and the pitch line length

L = \2.22 + 4.72 = 5.09 inches.

For the tangential force on the pinion pitch line radius we get
168 X 12

= 917 Ibs.

2.2

FIG. 228. — AUTOCAR BEVEL- SPUR DRIVE, LONGITUDINAL SECTION.

Therefore, inserting values in the modified Lewis formula, we
have

14000 X 0.63 X 0.093 X 5.09
917 = _____ (1 — a3)

348 BEVEL-SPUR GEAR DRIVES.

3 X 917

1 _ aa = . - = 0.659

14,000 X 0.63 X 0.093 X 5.09

a3 = 0.341

a = 0.7

That is, the distance from the apex of the cone to the inner
end of the pinion teeth must be 0.7 the distance from the apex
to the outer end of the teeth. Therefore, the face width must
be 0.3 times the pitch line length or

0.3 X 5.09 = 1.527 — say, l*/2 inches.

Figs. 227-8 illustrate the Autocar bevel-spur drive which
is used on moderate-sized commercial vehicles. The inter-
mediate shaft with which the bevel gear and spur pinion are
formed integral, is located directly above the axle and is car-
ried in two roller bearings which can be adjusted endwise
to obtain a proper mesh of the bevel gears. Driving keys are
used for the spur wheel, which is bolted to the flange of the
differential. The short shaft of the bevel pinion is carried in
two roller bearings. The axle construction is of what is known
as the double banjo type, the main axle housing being in halves
which are bolted together at the middle in a vertical plane.
Over the two large openings in this casing are bolted a gear
carrier and a rear cover plate. All of the gearing is carried
by the gear carrier, and, therefore, all adjustments can be made
before the axle is assembled.

Internal Gear Drive — While the bevel and spur gear drive
as now designed involves the use of a live axle, the internal
gear drive is used in conjunction with a dead axle. On the
ends of this dead axle the driving wheels are mounted, and
each wheel is fitted with an internal gear with which meshes
a spur pinion on the end of a differential countershaft. This
latter is designed along the lines of a live rear axle, with a
gear housing at the middle containing the differential and
bevel driving gears, from which extend the differential shafts,
sometimes surrounded by tubes. The shafts connect to the
differential gear at their inner end and carry a spur pinion
each at their outer end. The countershaft may be located
either directly in front or to the rear of the dead axle or
carrying member and is supported at the middle by connection
to that member. If the driving member is located in front
of the carrying member the bevel gear on the differential must
be located to the left of the pinion; in the opposite case it
must be located to the right (assuming the engine to turn right-
handedly, as usual).

BEVEL-SPUR GEAR DRIVES. 349

As in the bevel and spur wheel drive, the greatest reduction
is obtained by means of the second set of wheels. Ground
clearance is not such an important consideration near the wheels
as at the middle of the chassis, and the internal gear crown
can be made of considerable diameter. The pitch diameters
vary roughly from 12 inches in the lighter trucks to 14 in
the heavier ones. As regards pitches and gear materials, what
was said in connection with the bevel and spur drive applies
here also. The bevel gear set at the middle of the axle can be
designed on the same basis as for a bevel-spur drive; that is,
about 14,000 Ibs. p. sq. in. can be allowed with case-hardened
nickel or chrome nickel steel. As the internal gears are gen-
erally made of carbon steel, unhardened, a much lower stress is
allowed in these gears, about 8,000 Ibs. p. sq. in. — the calcula-
tions being based on the maximum engine torque directly trans-
mitted. One other reason for the comparatively low stress
allowed in the internal gear, besides that above mentioned, is
probably that the internal gear cannot be enclosed as effectively
as gears located in a housing at the center of the axle and cannot
be run in oil. Grit is apt to get into the gear and accelerate the
wear, to reduce which the tooth unit pressure is kept low.

Theoretically the internal gear is somewhat more efficient than
a spur gear, because there is less sliding action at the teeth of the
internal gear, but the actual difference is small.

The internal gear-driven rear axle presents quite a few prob-
lems of design aside from the proportioning of the gears. First
among these is that of the carrying member, which may be made
of solid round, tubular, rectangular or I-section. The axle ends
must, of course, be turned off to form seats for the bearings,
and as a motor truck axle requires a large lathe to handle it, the
spindles have sometimes been made separate, and, after being
machined, shrunk into the tubular central portion. Foreign
makers use parallel bearings in the wheels, while American
makers use ball or roller bearings. Great care must be taken
to so mount the internal gear ring that it will permanently run
true with the axle, in order to keep the gear quiet and efficient.
It seems preferabk to secure the gear ring directly to a flange
cast integral with the wheel hub, but usually an intermediate piece
is employed for convenience in manufacture. The support for
the gear ring usually also forms the brake drum. This construc-
tion permits of the use of either a contracting brake, directly over
the gear ring, an expanding brake (by extending the supporting
flange beyond the gear ring), or both.

350

BEVEL-SPUR GEAR DRIVES.

BEVEL-SPUR GEAR DRIVES. 351

As the spur pinion overhangs its bearings and as the pinion
usually has a very small pitch diameter, there is a heavy load
on this bearing, for which adequate provision must be made in
the selection of the bearing and its mounting. The load can
be calculated by the usual method for determining bearing loads
due to gear tooth reaction and the problem need not be entered
into further. Usually the pinion shaft has its bearing in a disc
secured to the carrying member of the axle, which disc serves
also as brake support and as a closure for the gear housing or
brake drum. As the latter rotates while the disc remains sta-
tionary, an oil-tight joint between the two cannot be obtained.
Dust may be excluded by cutting a groove in the rim of the disc
and filling it with fibrous material or by providing the disc with a
flange which overlaps the drum flange.

As the bevel gear and pinion do not differ much in size, there
is considerable end thrust on both of them, which must be pro-
vided for. This, too, can be calculated by the usual methods.

In an internal gear axle all of the load due to the weight on
the springs is taken by the carrying member which, therefore,
must be calculated like a dead axle. As the differential shafts do
not transmit the full rear wheel torque, but only a fraction of
that torque determined by the reduction ratio of the internal
gear set, they can be comparatively small and the tubes sur-
rounding them can be made very light. These tubes serve only as
housings, obviating the need for packings at the end of the bear-
ings on the differential shafts, and in some cases they are dis-
pensed with.

Four Wheel Drives — The four wheel drive, as pointed out
in a previous chapter, is especially advantageous for military
trucks and tractors which frequently must operate away from
beaten roads. It is also well adapted to use on trucks em-
ployed in certain lines of commercial work, as, for instance,
in contracting work, where the truck may have to be driven
into and out of sand pits or on rain-softened ground. The ad-
vantage of the four-wheel drive for tractors or for trucks in-
tended to haul one or more trailers, is obvious, for when the
machine must move more than, its own weight, more than the
usual percentage of its weight must be rendered available for
traction purposes. Moreover, with the four-wheel drive the
load may be evenly divided between front and rear wheels,
whereby the load on any one wheel is kept down and an exces-
sive overhang of the frame over either axle is avoided.

The problem of a four-wheel drive consists chiefly in com-

352 BEVEL-SPUR GEAR DRIVES.

bining the functions of steering and driving in a single axJ^.
As the steering wheels swing around a substantially vertic. 1
axis for steering, a universal connection between the whee s
and the propelling mechanism on the frame is necessary, un-
less the motor and drive are both supported on the axle, or on
that part of it which swings in steering. The problem is
about the same as that involved in the design of front wheel
drives, as used for converting horse fire trucks and on certain
other types of special vehicles.

One of the simplest solutions of the problem consists in
the use of an electric transmission, with an electric motor
mounted directly on each steering knuckle, or on each axle
if the whole axle swings in steering. Of mechanical solutions
there are three that are well known. The first involves the
use of a fifth wheel adapted to turn around a king-pin, so that
in steering the entire axle swings around its centre, instead
of steering knuckles swinging aroung knuckle pins. The
power plant may then be mounted so as to turn with the axle,
or the power may be transmitted to the axle by means of gear-
ing of which one member is located concentric with the king-
pin.

The second method makes use of a train of bevel gears, of
which a pair of intermediate gears is mounted concentric with
the steering knuckle pin. This arrangement has some im-
portant advantages, but it is rather complicated. In one
French design of a four-wheel driven truck employing this
construction no less than thirty-two bevel wheels are used in
the drive between the gear box and the four wheels. One of
the good points of this type of steering and driving axle is
that the pivot steering principle is employed, which is pre-
ferable to the fifth wheel principle in many respects; another
is that as the bevel gears secured to the road wheels swing
around the knuckle pivots, no irregularity in the transmis-
sion of motion is introduced. That is, whether the road
wheels are in the straight-ahead position or not, the trans-
mission of motion from the tail shaft of the gear box to the
road wheels is always effected at a constant ratio, there being
no periodic fluctuation as with ordinary universal joints.

In the third construction universal joints are employed to
transmit the motion from a shaft concentric with or parallel
to the axle to a pair of short shafts carried by the steering
knuckles on opposite ends of the axle. These three shafts,
viz., the long central shaft and the two short shafts connected

BEVEL-SPUR GEAR DRIVES.

353

to it, mar be either concentric with the axle, in which case the
short shafts connect to the wheel hubs through driving dogs,
or they may form a countershaft, in which case the short
shafts carry spur pinions which mesh with spur or internal
gear crowns on the road wheels. In either case the universal
joint centre must lie in the axis of the steering knuckle pin.

FIG. 230.— PANHARD BEVEL GEAR DRIVEN STEERING WHLEL.

With the latter construction the torque on the universal joint
is much less than with the alternate construction, and the axle
can be built lighter.

Bevel Gear Steering Wheel Drive— Fig. 230 is a vertical
section through the wheel and drive of a Panhard four-wheeJ

354

BEVEL-SPUR GEAR DRIVES.

driven truck. Only one universal joint is employed on this
truck, located at the rear end of the gear box, on a short cross
shaft which is driven by bevel gears from the gear box tail-
shaft. At each end of this cross shaft is a bevel gear through
which it drives fore-and-aft shafts extending to the front and
rear axles, there being four of these shafts in all. As the shaft
housings pivot around the axes of the cross shafts, no uni-
versal joints are required to compensate for the spring mo-
tion. Each of the fore-and-aft shafts at its outer end carries a
bevel pinion meshing with another bevel pinion on a short
cross shaft extending through a housing underneath the chas-
sis spring, which at its other end carries another bevel pinion
meshing with a bevel gear at the top e«d of a vertical shaft
concentric with the steering pivot. The bevel pinion at the

FIG. 231. — F. W. D. COMBINED STEERING AND DRIVING AXLE.

lower end of this shaft meshes with a bevel gear secured im-
side the enlarged hub of the road wheel. In a more recent
design of the Panhard Company, some of the intermediate
bevel gear sets are replaced by helical gears, whereby the total
number of gears is reduced.

Live Steering Axle— A combined driving and steering axle,
in which a universal joint is placed inside the forked axle end,
is manufactured by the Front Wheel Drice Auto Co., Clinton-
ville, Wis., and a part sectional view of this axle is shown
herewith. On the truck of this concern the change speed gear
is located at the middle of the frame, and from the tail shaft
of the gearset the power is transmitted by a silent chain to a
fore-and-aft shaft with differential gear and universal joints.
From this fore-and-aft shaft the power is transmitted to the
two driving axles by bevel pinion and gear, a sufficiently large

BEVEL-SPUR GEAR DRIVES.

355

gear reduction being obtainable because the speed is already
reduced somewhat by the silent chain connection between the
gearbox and the longitudinal shaft. Each axle contains one
differential gear, so that there are three in all on the truck.

Details of the construction of the steering and power trans-
mission joint are shown in the illustration. The steering

FIG. 232. — JEFFERY COMBINED DRIVING AND STEERING AXLE.

knuckle pivot is developed into a spherical joint which con-
tains trunnions, fully enclosing the universal joint. This
joint is of compact design, and as it has to transmit only one-
fourth of the power of the engine it is amply large for its
purpose.

356 BEVEL-SPUR GEAR DRIVES.

Internal Gear Steering Wheel Drive — A four-wheel drive by
internal gears has been used on Jeffery trucks, and a section
through the combined steering and driving wheel is shown in
Fig. 232. The sliding gear transmission is placed at the mid-
dle of the frame and has no direct drive. The propeller shafts
are gear driven from the secondary transmission shaft, this
construction bringing the forward one far enough to one side
to clear the engine, which is also mounted slightly to one
side of the frame centre. Three differentials are used and
both axles are pivoted for steering. The cross shafts are lo
cated above the springs and have universal joints direct!}
above the steering pivots. The driving pinion is supportec
on the steering knuckle between roller bearings on opposite
sides and meshes with an internal gear ring set into the en
larged wheel hub. A drum for an external brake is also fitted
to the wheel hub, and against its inside surface bears a felt
packing designed to exclude dust from the gears.

CHAPTER XIII.

BRAKES.

The automobile, being essentially a high speed vehicle, re-
quires powerful and dependable brakes for its safe operation.
Aside from the fact that the engine is occasionally used as a
brake (as described in Volume 1, Chapter XVII) and that in
cars with friction drive or planetary change speed gears the re-
verse gear may be used to retard the speed or bring the vehicle
to a stop, drum brakes are invariably used on automobiles.
These consist of a steel or cast iron drum secured to some rotat-
ing part, either the road wheels or a part in permanent driving
connection therewith, and an expanding or contracting member
supported by the vehicle frame or axle which can be brought into
frictional contact with the rotating member. When this expand-
ing or contracting friction member is pressed against the surface
of the drum, the friction created tends to stop the drum and its
connected parts from revolving. The energy dissipated in heat
at the friction surface of the drum is withdrawn from the kinetic
energy stored in the moving vehicle, and the speed of the vehicle
decreases as its store of kinetic energy is depleted. The con-
tracting and expanding brakes are shown in diagram in Fig. 233,
the black circles representing the brake drums.

Number of Brakes — In several States of the Union and in
most foreign countries two independently acting braking systems
are required by law, and sometimes it is stipulated that at least
one of these braking systems must act directly on the road
wheels. What is here referred to as a braking system consists
of a single drum and frictional member, if it is located ahead of
the differential gear, as on one of the change gear shafts ; and
of two drums and frictional members when located beyond the
differential gear, as on the wheel hubs.

In horse vehicles the brakes are generally applied to the wheel
tires. Automobiles are almost invariably fitted with rubber tires,
and while the application of brakes to these tires would un-

357

358

BRAKES.

doubtedly prove very effective, rubber is too expensive to make
this practice commercially possible. Therefore, it is customary
to secure a metal drum to the road wheels on which the friction
members act.

Location of Brakes. — The brake drums may be fitted to
either the rear wheels or the front wheels. Rear wheel braking
has the advantage that, as a rule, the rear wheels support much
more of the weight of the car and the load than the front wheels,
and since the limiting brake power depends upon the ground
adhesion of the road wheeels, which in turn depends upon the
weight carried by the wheels, it is seen that rear wheel brakes
have a greater limiting power than front wheel brakes. Be-

FIG. 233. — DIAGRAMS OF CONTRACTING AND EXPANDING BRAKES.

sides, much less difficulty is encountered in making connections
from the operating devices on the frame to brakes on the rear
wheels whose planes always retain the same position relative to
the frame, than to brakes on the pivotally mounted front wheels.
Front wheel brakes have the advantage that an application of the
brakes does not tend to cause the car to skid, as does the applica-
tion of rear wheel brakes — at least not in the same degree. Front
wheel brakes have been used to some extent in England and on
the Continent, but are practically unknown in this country.

In a bevel gear driven car either both brakes may act on drums
secured to the rear wheels or one brake may act on drums so
located, and the other on a drum located back of the change gear
box. There is, however, one exception, namely, when the trans-
mission is located on the axle, in which case both brakes must

BRAKES. 359

act directly on the wheels. In Europe it is the almost exclusive
practice to place one brake close to the gear box and the other
on the wheels.

In one respect the proper location for the brakes is as close to
the road wheels as possible, because the reaction due to the fric-
tional force on the brake surface takes effect at the road contact
of the wheel, and the closer the points of application of the
braking force and the point of its final reaction are together,
the fewer parts are subjected to strain. With brakes on the
hubs of the rear wheels only these wheels are subjected to the
strain, whereas if the brake is located back of the change speed
gear the braking force has to be transmitted through the pro-
peller shaft, universal joints, bevel driving gear set, rear axle
shafts, rear wheel driving dogs and rear wheels. One reason
that leads some designers to use a so-called transmission brake is
that they want to enclose all of their brakes, which compels them
to use the expanding type 'of hub brakes, the only type lending
itself to complete enclosure; and since conditions of space avail-
able make it difficult to fit two internal expanding brakes to each
wheel, they place one brake back of the change speed gear. As
regards the objection to the transmission brake above mentioned,
they argue that the various parts which have to transmit the
braking force must be designed strong enough to transmit the
maximum propelling force, which is about equal to the maximum
braking force, hence these parts should not be injured by the
latter force. An advantage of the transmission brake is that,
since the braking force is multiplied by the rear axle driving gear,
a great retarding effect can be produced with a comparatively
small operating effort.,

The transmission brake, however, is very little used on pleasure
cars in this country at present and is constantly losing ground.
There are three arrangements of double rear wheel brakes, all
in practical use, viz., two internal brakes acting on the same drum,
one internal and one external brake on the same drum, and two
internal brakes on concentric drums.

On commercial vehicles with side chain drive it is the practice
to place one set of brakes on the rear wheels and the other on the
ends of the jackshaft. If the worm drive is used, one brake may
be placed on the transmission shaft and the other set on the rear
wheels.

360 BRAKES.

Service and Emergency Brakes.— One set of brakes is gen-
erally designated as the service brake and is intended for all
ordinary occasions. It is operated by means of a pedal or foot
lever, because the driver can keep one foot on the brake pedal
all the time and therefore can operate such a brake with a mini-
mum of effort. The other brake is known as the emergency
brake and is intended for use only in case the service brake fails
or when an exceedingly strong braking action is required. This
emergency brake is generally operated by a hand lever located at
the side of the driver's seat. If the car is fitted with a "trans-
mission" brake, the latter is usually the service brake.

Calculation of Braking Power.— The emergency brakes at
least are generally made sufficiently powerful to slip the wheels
of the car on dry road surface. Assuming that six-tenths of the
total weight of the car and load rests on the rear wheels, and that
the ground adhesion is 0.6, the maximum brake force is
0.6*0.6 W = 0.36 W.

Suppose that the car is traveling at a speed V miles per hour
= 1.466 V feet per second. Then the kinetic energy stored up in
it is

jn±&VY_jvin_ (appr }

2^ 30

Now let the brakes be applied so as to lock the wheels and the
car be stopped after running a distance x. Then

0.36 ^* = J^2

30
and

io.8

This equation gives the minimum theoretical distance in which
a car can be stopped, provided six-tenths of the total load rests
on the rear wheels. If a greater proportion of the load is carried
by the rear wheels the minimum stopping distance will be
smaller. It will be seen that the distance is proportional to the
square of the initial speed.

In some official trials held by the Automobile Club of America
on Riverside Drive, New York City, in May, 1902, the average

distance in which the cars came to a stop was feet. In a

6.7

recent unofficial test on a macadam pavement on Kings Highway,
Long Island, New York, a car was brought to a stop from vari-
ous speeds in distances which may be represented by the ex-

BRAKES. 361

pression . It should be pointed out that it is very difficult

17.4

to obtain uniform results in such tests; first, because the results
vary with the gradient, with the direction and strength of air
currents and with the road conditions, and second, because it is
practically impossible to insure that the driver shall shut off his
power and apply his brakes exactly at a given point along the
road.

Friction of Motion

FIG. 234.

Conditions Insuring the Quickest Stop — It was found in ex-
periments made by the Westinghouse Air Brake Company
that railway car brakes exert the greatest retarding effect
when applied with such force that the wheels do not quite
lock but continue to revolve. This same condition undoubted-
ly exists in connection with automobile brakes. It may be ex-
plained on the grounds that the friction of rest is greater than
the friction of motion, and that when the wheels become locked
the rolling friction of the wheel on the ground and the bear-
ing friction of the axle and propeller shaft cease.

The braking effect certainly is the greatest if the energy
dissipated in friction in traveling a unit distance is a maxi-
mum. Let R be the starting resistance of the wheel to slip-
page on the road (friction of rest) and r the resistance of the

362 BRAKES.

wheel to slippage once it has begun (friction of motion).
Also let D be the wheel diameter and d the diameter of the
wheel brake drum. Then the maximum frictional force which
can be applied to the brake drum without causing the wheel
to slip is n

— (R — a),

where a is a very small quantity. While the car travels a
unit distance the brake drum circumference moves a distance
d

— in its rotation and the energy absorbed at the brake sur-
D

face is d D

— x — (R — a) = R — a.

D d

In addition to this we have the energy absorbed by the rolling
friction at the road contact and the bearing friction. We will
denote the sum of these two frictional forces, both referred
to the wheel rim, by B, and the energy absorbed by these two
resistances while the car moves through unit distance may
also be represented by B. Therefore, the total energy ab-
sorbed while the car travels a unit distance when the brakes
are on but the wheels are not locked is R + B — a.

On the other hand when the wheels are locked, after slip-
ping has begun, which, of course, occurs instantly, the only
resistance encountered is the sliding friction r of the wheel on
the road. The energy absorbed in unit distance due to this
friction is also r. Hence we must prove that

R + B — a > r.

It has already been stated that the friction of rest R is greater
than the friction of motion r. This holds good under all or-
dinary conditions of friction, as in bearings, etc., and no doubt,
holds true in connection with sliding friction between rubber
tires and road surfaces. Of the two remaining items B has a
definite value which on good roads is from 4 to 5 per cent of
the sliding friction. The item a, on the other hand, may be
made practically nil, as it represents the margin which, if
added to the brake friction referred to the wheel circum-
ference would cause the wheel to lock. Hence, under the most
advantageous conditions this item is insignificant and the re-
tarding action is then greater than that due to locked wheels
by the sum of the following three items: The rolling friction
of the wheels on the ground, the bearing friction in the axle,
propeller shaft and transmission, and the difference between

BRAKES. 363

the friction of rest and the friction of motion between wheel
and road.

Not only will the brakes stop the car quicker when they are not
quite locked but the wear and tear on the tires is greatly reduced.
It would, therefore, be a great adxantage if a brake could be
designed by which the wheels could not possibly be locked by the
driver but which could nevertheless be applied to such a degree
as to come very near to locking the wheels.

Determination of Dimensions — The two considerations
which determine the size of brake drums are that the brakes must
be powerful enough to practically slip the wheels, and the radiat-
ing surface of the brakes must be large enough to prevent undue
heating on long down grades. Besides, the larger the brake sur-
faces, the longer the friction linings will last.

The drums of hub brakes on pleasure cars are generally made
of a diameter equal to 35-45 per cent, of the wheel diameter,
while in heavy motor trucks the brake drum diameter is made
as high as 55 per cent, of the wheel diameter. On pleasure cars
the hub brakes should have a friction surface equal to 1 square
inch per 15 pounds of car weight; the transmission brakes, 1
square inch per 30 pounds of car weight. On commercial ve-
hicles, the hub brakes should have 1 square inch per 30 pounds
of car weight loaded; jack shaft brakes, running at a speed
intermediate between engine and rear wheel speed, 1 square inch
per 85 pounds of car weight, loaded, and transmission brakes
of commercial vehicles running at engine speed, 1 square inch
per 175 pounds of car weight, loaded. Considerable latitude is
permissible as regards the relation of face width to diameter in
transmission brakes, and no general rules can be given. If the
brake is located at the middle of the frame where there is ample
room in the direction of its axis, it is usually made comparatively
wide and of small diameter, whereas if the brakes are at the side
of the frame, where space in the axial direction is limited, the
drum diameter has to be made somewhat larger.

Brake Drums — The drums of hub brakes are now almost
invariably made of pressed steel and in many cases the brake
drum serves also as the loose flange of the artillery wheels.
The thickness of the metal is made % inch for cars weighing
with load up to 1,800 pounds ; fs inch up to 4,000 pounds ; y^
inch up to 7,000 pounds; & inch up to 12,000 pounds, and Y%
inch above 12,000 pounds. If the brake drum serves as a hub
flange it is generally pressed with an inner cylindrical flange
fitting over a machined portion of the hub. In this case the drum

364

BRAKES.

is held in position by the hub bolts. If the drum is not part of
the wheel it may be clamped to the spokes by means of clips.
A typical design of pressed steel brake drum is shown in Fig.
235.

Contracting Brakes — The contracting members of contract-
ing brakes are either made in the form of bands of thin rolled
steel encircling nearly the whole drum, or they may be made in
the form of two sectors, either of rolled steel or of cast material
— steel or malleable iron. The contracting members are generally
lined with an asbestos and wire fabric, of which there are several
on the market — Raybestos, Thermoid, Non-Burn, etc. — this lining

FIG. 235. — PRESSED STEEL BRAKE DRUM.

being secured to the metal band or segment by means of copper
rivets. The friction coefficient of asbestos on steel is about 0.3.
The contracting members must be supported in a substantial
manner, as the reaction of the braking force must be taken up
by the support. In early designs of band brakes it was cus-
tomary to fasten one end of the band to the support and exert
a pull on the other end. This gives a very powerful braking
effect for one direction of motion — the forward direction — be-
cause the friction between band and drum tends to apply the
band tighter to the drum. But when the car runs backward,
down hill for instance, the friction tends to unwind the band

BRAKES. 365

and the braking effect is then very small. Such brakes are
known as single acting and are no longer used.

In order to obtain a double acting effect, contracting brakes are
now always anchored directly opposite the contracting mechan-
ism. Brake segments are formed with eyes for the anchorage
joint, and steel bands have a fitting riveted to them which serves
the same purpose. The support is usually a bracket secured to
the rear axle tube, and in a few cases the radius rod.

FIG. 236. — CONTRACTING BAND BRAKE.

So far as contracting type hub brakes are concerned, a single
style of contracting mechanism is used for the great majority
of designs. It consists of a floating bell crank as shown in
Fig. 236.

One end of the brake band is connected by means of a riveted
bracket to the end of the short arm and the other end connects
through a short link to the fulcrum of the bell crank. The
operating rod is connected to the long arm of the bell crank.
The link is hinged to the free end of the brake band and passes
through the fulcrum pin, the bell crank being forked at the lower
end. A butterfly nut is screwed over the end of the link and
provides convenient means of adjustment for wear. The adjust-
ment is locked by the spring surrounding the link, which forces

366

BRAKES.

the arms of the bell crank over the flattened end of the wing
nut, thus preventing it from turning. The coiled spring at the
same time helps to release the band when the pressure is taken
off the brake lever.

There is one other form of contracting mechanism for hub
brakes, consisting of a short double armed lever with pins ex-
tending laterally from the ends of its arms to which the ends
of the brake band are hinged, and an operating shaft, rigidly
supported, extending from it laterally in the opposite direction
(Fig. 237).

FIG. 237.— DOUBLE-
ARMED LEVER CON-
TRACTING MECH-
ANISM.

FIG. 238.— ADJUSTABLE
BRAKE BAND SUPPORT.

Releasing Means—In addition to providing a substantial
support for the brake band and an effective contracting mechan-
ism, it is necessary to provide means which will prevent dragging
of any part of the brake band when released. In order to pre-
vent dragging near the point of anchorage, a portion of the band
extending over a considerable angle on both sides of the anchor-
age may be left unlined, or else the hole in the anchoring fitting
may be made oblong in the radial direction so that the brake
band can move outward when released. Such outward movement
is insured by placing a spring at the point of anchorage soliciting
the band radially outward, or by placing stops at 120 deg/ees
(more or less) on either side of the point of anchorage which
limit the outward movement of the band at these points and
thus tend to distribute the clearance evenly around the circum-
ference of the drum.

BRAKES. 367

The contracting mechanism may be placed on top of the drum
or on the forward side of it. The latter is the favorite location,
partly because it brings the brake connecting rods into a more
convenient level and partly because with the split in the band at
the side of the drum, mud dropping from the wheel cannot so
easily work between the band and drum.

Owing to the fact that the brake band is firmly supported at
one side only, at the anchorage, when released it tends to drop
on to the drum on top and thus drag. In order to prevent this
a brake band carrier is usually placed fon top of the brakes. In
Fig. 208 this takes the form of a little angle piece riveted to
the brake support disc and extending across the top of the brake
band underneath a little flat spring extending circumferentially
of the band and being riveted to it. When the brake is released
the spring lifts the band off the drum, but when it is applied,
the spring flexes slightly and allows the band to come in contact
with the drum. Sometimes three of these brake band carriers
are used, spaced equally around the circumference, and in some
designs the brackets themselves are springs.

The band supporters are not adjustable and must therefore be
very accurately made and fitted. Besides, if some means of ad-
justment were provided, less clearance would suffice. An ad-
justable supporter is shown in Fig. 238. A threaded pin riveted
into the brake band extends vertically upward at the top of the
brake through a hole in an angle piece secured to the brake sup-
port disc. A coiled spring is placed on top of this angle piece
and presses against a castellated nut on the end of the threaded
pin.

Contracting Transmission Brakes. — In European cars the
service brake is generally located at the rear end of the change
gear primary shaft and both expanding and contracting types are
used at this point, the latter being perhaps the most numerous.
Most of the contracting brakes have cast sectors, and these are
contracted by means of either one or two pairs of face cams
or by a square threaded screw and nut mechanism. Continental
manufacturers generally cast four or five circumferential ribs
on the brake segments (Fig. 239) to help carry off the heat in
making long descents. The brake drum of a transmission brake
is generally a casting keyed to the rear end of the gear box
primary shaft and often has two lugs cast on its web which
form part of the universal joint. The brake segments are
anchored to the gear box and the stops and supports of the

368

BRAKES.

FIG. 239. — BRAKE SEGMENT WITH COOLING FLANGES.

contracting mechanism also are secured thereto. Fig. 240 illus-
trates a design of contracting transmission brake with face earn
contracting mechanism. These brakes generally have metallic
friction surfaces. A transmission brake of the lever operated
band type is illustrated in Fig. 241.

Fir,. 240.— CONTRACTING TYPE OF TRANSMISSION BRAKE.

BRAKES.

369

Stresses in Brake Members — We have assumed the
maximum braking force to be equal to 36 per cent, of the totaJ
weignt of the car and load. The braking force being produced
on two wheels, tnat on each wheel is 0.18 W. Now let the wheel
diameter be D and the brake drum diameter d, then the tan-
gential force on the circumference of the brake drum is

F=o.*£w

The reaction due to this force is taken up in the brake sup-

FIG. 241. — CONTRACTING BAND TRANSMISSION BRAKE.

port. In Fig. 242, F represents the reaction of the support on
the brake band. Each half of the band covers an angle of aboui

165 degrees = ^~ *. In calculating the forces on the brake band

use is made of the method developed in connection with band
clutches, the band brake and band clutch depending upon the
same principle. We found (equation 19) that the relation be-
tween the initial tension Pi on the band and the pull P on the
anchorage -is such that

370

BRAKES.

where e is the base of the natural system of logarithms; / the
friction coefficient and 6 the arc of contact between band and
drum in circular measure. With a friction coefficient of 0.25

and an arc of contact for each half of the band of — *",

•/* ft

the value of / 6 is 0.72, and the value of e' is found to be;
2.08. (See Fig. 36.)

FIG. 242. — DIAGRAM OF FORCES ON A BAND BRAKE.

In Fig. 242 let us denote the tension on the band at point D
by x. Then the tension at the section CC just ahead of the point

of anchorage is . The tension at the section BB, just be-

2.08

yond the point of anchorage, is -2— -f F and the tension at tin

2.08

Doint D is

--
2.08

2.08

BRAKES. 371

Hence the tensions at the two ends of the band are x and

£^5 - respectively. A relation between these two forces can

2.08

be found from the diagram of forces acting on the contracting
bell crank.

It will be seen that the reaction on the fulcrum of the bell
crank must be equal in magnitude and direction to the tension at
the end D of the band, and the dotted line KH represents this
force. This reaction is the resultant of the forces acting on the
arms of the bell crank. We will assume that the brake rod con-
necting to the vertical arm lies in a horizontal plane, hence the
pull on this rod is horizontal. The force on the short arm of
the bell crank is tangential to the extreme point of contact of
this half of the band. This enables us to complete the diagram
of forces KHI. Ffom this we see that with this particular de-
sign of band and operating bell crank the tensions at the two
ends of the band, KH and KI, are equal. Hence

2.08
3.326 x =2.08 F
x = 0.624 F
Inserting the value of F found previously we have

* = 0.624x0.18 — W
d

The diagram also enables us to determine the proper length
for the effective lever arm KG.

In order that the operating mechanism may be in equilibrium,
the moments around any point must vanish. Taking moments
around the fulcrum K —

and

Let us assume the case of a car weighing with load 3,000
nounds, and let the ratio of wheel diameter to brake drum dia-
meter be 2.y2. Then the reaction F on the brake support is

0.18x2^x3,000 = 1,350 pounds,

372 BRAKES.

and the tension on each end of the band is

0.624 X 1,350 = 843 pounds.

The angle between the forces KH and KI being 30 degrees, the
value of HI is

2 KI sin 15° = 2 X 843 X 0.259 = 436 pounds.
Therefore, the effective lever arm KG should be to the effective
lever arm KA as 843 is to 436 ; in other words, the former should
be about twice as long as the latter.
We now have the following results :
Reaction F on brake anchorage, 1,350 pounds.
Tension on each end of the band, 843 pounds.
Tension in brake rod, 436 pounds.

These are extreme values and are hardly likely to be attained
in practice, owing to the fact that the limiting pressure which
the driver can exert on the brake pedal is about 100 pounds, and
in order to produce a tension of 436 pounds in each of the two
brake rods, the thrust on the pedal would have to be multiplied
more than eight times by the leverage, which is rather a higher
leverage than is obtainable in practice.

The value of the force F on the brake anchorage permits of
calculating the necessary size of the laterally extending stud or
pin and of the bracket which carries this stud. Thus, let the
entire overhang of the anchorage pin be 2 inches, so that the
centre point of the band overhangs 1 inch. Then the bending
moment of the force F is 1,350 pounds-inches, and
TT D3' S

= 1,350

Since the force assumed is practically the limit that can ever
come on the brake support we can make the stress comparatively
high, say 20,000 pounds per square inch. We then have
20,000 D3 = 13,750.
D3 = 0.6875.

7
D = 0.88 inch — say, — inch.

Other parts of the brake mechanism, such as the brake anchor-
age bracket and the contracting lever, can be calculated for
strength in a similar manner.

Expanding Mechanism — There are four commonly used
means for expanding the sectors of internal brakes, viz., cam,
toggle, wedge and double-armed lever mechanisms. The cam is
probably the most extensively used. Three designs of expander
cams are illustrated in Fig. 243. The symmetrical cam shown at

BRAKES.

373

FIG. 243. — EXPANDER CAMS.

A has flat sides and semi-circular ends, and its small diameter is
usually one-half its big diameter. The second design, B, has
practically the same effect as the first, but is preferable from the
standpoint of weight economy, having some useless metal cut out.
The third design, C, embodies roller cam followers carried on the
ends of the brake segments, the idea being to minimize wear of
the working parts.

The segments of cam-operated expanding brakes are provided
with flat wearing surfaces against which the cams bear, and
these wearing surfaces and the cams are case hardened. The
extreme motion provided for in the case of a i4-i6-inch drum
is usually l/2 inch for the end of each segment.

FIG. 244.— TOGGLE EXPANDER BRAKE.

374

BRAKES.

Fig. 244 illustrates a Lrake with a toggle expanding mechanism.
The ends of the segments are connected by a pair of toggle links
from the joint of which runs another link to a bell crank whose
shaft has a bearing in the brake supporting bracket. Sometimes
one or both of the toggle links are made adjustable. The toggle
mechanism, like the cams, has the advantage that it moves the
ends of the brake segments comparatively fast at first, but more
slowly as the segments come in contact with the drum. Its
mechanical advantage increases as the segments are being ex-
panded, consequently with a certain effort on the part of the
operator, the segments can be applied to the brake drum with
greater force than if the mechanical advantage remained con-

FIG. 245.— WEDGE
EXPANDER MECH-
ANISM.

FIG. 246.— DOUBLE-
ARMED LEVER EX-
PANDER.

stant. The toggle mechanism is really the only one that can be
properly adjusted for wear of the brake lining, by adjusting the
length of the toggle links. The only way in which the other
mechanisms can be adjusted is to make the expanding range
considerably larger than is necessary when the brake lining is
new, and then, as the lining wears, adjusting the operating link-
age outside the brake drum.

A wedge expander is shown in Fig. 245. The ends of the seg-
ments are beveled and a wedge pivoted to a cantilever is forced
between them. The double-armed lever mechanism j>,s applied
to an expanding brake is shown in Fig. 246, and is identical in
principle with the double-armed lever contracting mechanism
already described.

BRAKES. 375

Details of Expanding Brakes. — The anchorage of expanding
brakes is always substantially opposite the expanding mechanism.
When both internal and 'external Hub brakes are fitted, the same
brake support usually serves for both, but if there are only ex-
panding hub brakes, the brake supports ' lay be located inside
the brake drums to reduce the overhang, or the segments may
even be supported symmetrically. The brake segments are made
either of malleable iron castings, drop forgings or band steel.
When they are drop forged or cast they are usually made of T-
section, while if they are made of band steel the expanding ends
are bent triangularly to form cam faces, or suitable lugs are
riveted to them.

As regards means for releasing the segments, they may either
have a rigid hinge support, in which case the friction facing
must not come closer than about 30 degrees to the point of
support, or they may be supported yieldingly in the axial direc-
tion, in which case the friction material may extend to the very
ends of the segments. The first arrangement makes the simplest
construction, as all that is necessary to prevent dragging of the
segments when released is to provide a tension spring extending
between the two segments, preferably as close to the ends as
possible without interfering with the expanding mechanism.
With the second arrangement the supporting stud extends
through oblong holes in the end of the brake sectors and either
two or three springs have to be provided to insure clearance
between the segments and drum all around when the brake is
released. Sometimes only a single expanding member is used
(Fig. 244), forming almost a complete ring and having an
anchoring slot at the middle of its length into which extends the
flattened end of the brake supporting arm or a laterally extend-
ing stud.

Expanding brakes can be calculated by the same methods as
used for contracting band brakes, at least those in which the
expanding force is applied to the ends of the segments in a
direction substantially tangential to their circumference at the
cut. The brake rods extending forward from the brakes are
generally made either y% inch or & inch in diameter in pleasure
cars and */2 inch in trucks.

Facing Materials. — In American practice the segments of
expanding brakes are generally faced with asbestos friction
fabric. In Europe, on the other hand, the expanding members
usually have metallic friction surfaces, either cast iron or bronze,
as shown in the accompanying cut of the Panhard brakes, Fig.

376

BRAKES.

247. Cast iron on steel without lubrication has a friction coeffi-
cient of about 0.15 which is quite satisfactory. The objection-
able feature of metallic brake surfaces is that they lose very
much of their effectiveness when they are covered with oil or
grease, and since the brake drums are nearly always located close
to some bearing, it is rather difficult to keep oil out of them. It
will be seen from Fig. 247 that in the Panhard brake the lining
strips are cut with slanting grooves designed to scrape the oil

FIG. 247. — PANHARD BRAKES.

off the brake drums. In order to prevent oil from the rear axle
housing working out to the brake drums, it is necessary to pro-
vide packings at both sides of the driving gear housing, and
there also should be some kind of oil guard at the inner end of
the wheel hubs. Asbestos fabric possesses the two valuable fea-
tures that its friction is little affected by oil on it, and that it is
not spoiled by heat. Grease cups must be provided for all bear-
ings of the brake mechanism and the bearings for overhanging
parts must be made relatively long.

BRAKES.

377

The brake support is generally in the form of a malleable
casting which is riveted to the axle tube. Sometimes this sup-
port is a full disc and forms the cover for the brake drum, while
in other designs it is in the form of a bracket or spider with
ribbed arms, which has a sheet metal disc fastened to it to close
the brake drums. It is customary to have the brake drum ex-
tend over the edge of the closing disc and leave a clearance of
about 3*2 inch between the two parts.

FIG. 248.— TIM KEN BRAKES.

The Timken internal and external brakes, illustrated in Fig.
248, are good examples of American brake design.

Brake Adjustment — The facing material of the brakes wears
in the course of time and this makes adjustment necessary. With
some designs of expander mechanism, such as the toggle links,
adjustment can be made in the length of the ring formed by the
brake segments and their connections. In the case of other ex-
pander mechanisms, like the cam, the adjustment must be made
outside the brake drum. When the brake lining is worn the
cam has to be turned further in order to apply the segments
firmly to the drum, and if it is found that it cannot be turned

378

BRAKES.

sufficiently far with the original adjustment of the brake linkage,
then the lever on the cam shaft has to be moved around the
shaft. A design of adjustable brake lever is shown in Fig. 249.
The device comprises in reality two levers, one free on the shaft
and the other keyed to it. The short, fixed lever is provided
with a slotted sector to which the free lever can be secured by
means of a clamp screw. The clamping surfaces are grooved
to prevent slipping.

Brake Equalizers — Unless the brakes on opposite sides of a
car produce equal retarding effects the car has a tendency to
skid. In order to produce these equal retarding effects the first
thing necessary is to apply equal operating forces to the two

FIG. 249. — BRAKE LEVER ADJUSTMENT.

brakes of each set. This necessitates an equalizing device in the
brake operating linkage, which usually takes the form of a bal-
ance lever. A few makers, following a design which originated
in France, use a long balance lever extending entirely across
the frame, through slots in the side members or formed by
guides secured to the under side of the side members. The bal-
ance levers are made of sheet steel bent double, with the width
decreasing from the middle toward the ends, and sometimes holes
are punched through the sheet metal to lighten the levers. (F'g.
250). These balance levers are placed comparatively far to the
rear, about even with the most forward part of the road wheels,
so as to make the connections to the brakes outside the frame
short

379

FIG. 250. — LONG BAR EQUALIZER.

The more common form of brake equalizer is illustrated in
Fig. 251. The principle is the same as that embodied in the
equalizer just described, but the balance lever is much shorter
and the brake operating effort is transmitted to the sides of the
frame by members working under torsion instead of under bend-
ing stresses. Where it is not possible to support the brake equal-
izing shafts by intermediate bearings, the equalizing lever should

FIG. 251. — CONVENTIONAL EQUALIZER.

380

BRAKES.

preferably be placed close to one side of the frame, so as to
minimize the bending moments.

We have so far supposed that connection from the hub brakes
forward is made by rods located outside the frame. These rods
tend to give the chassis a "trappy" appearance, especially if they
are long enough to show in front of the wheels, and many de-
signers prefer to place all rods inside the frame. This necessi-
tates an extra pair of bearings for the brake expander shafts as
shown in Fig. 252. Sometimes these bearings are carried by
arms just inside the springs, while in some designs of rear axles
these extra bearings are close to the driving gear housing. When
located in the last described manner the equalizing lever may be

FlG. 252.— BRAKE SHAFTS CARRIED IN DOUBLE BEARINGS.

connected directly to the short levers at the inner ends of the ex-
pander snatts.

Arrangement of Brake Rods— The forward connections of
the hub brake rods should be so located that the compression and
extension of the rear springs will not affect the application of
the brakes. This point is of particular importance in connection
with motor trucks, on account of the comparatively large motion
of the springs when the truck is loaded or unloaded, but in the
past it often has been overlooked. If a motor truck has to be
stopped for loading or unloading on a grade, unless the brake
connections are properly designed, the brakes are liable to loosen

BRAKES.

381

382

BRAKES.

BRAKES. 383

as the load is put on, and the truck will begin to move down
hill; or, in the opposite case, the connecting linkage may be put
under such tension by the load as to make it difficult to disengage
the brake lever after the truck is loaded.

As the springs compress and distend, the rear axle and every
part supported by it move in circular paths around the axis of
the forward radius rod connection. Therefore, in order to ob-
viate any influence of spring action on the application of the
brakes, the centre D of the forward brake rod connection should
lie in the axis of the forward radius rod connection. This, how-
ever, is generally impossible in prajctice. The best practical solu-
tion of the problem is to place the forward connection D of the
brake rod on the line connecting the axis O of the forward
radius rod connection with the point P representing the mean
position of the centre of the rear brake rod connection with rela-
tion to the frame, as shown in Fig. 225. The forward brake rod
connection D may be either forward or to the rear of the for-
ward radius rod connection 0, but should be as close to it as
conditions will permit. Fig. 253, which is taken from an article
by Edward L. Martin in THE HORSELESS AGE of September 4,
1912, shows in the sub-figure that there is still a slight effect of
the spring action on the brake, but with relatively long brake
rods it is negligible. When D is located above the line O P
(as shown at D') the brakes tighten when the load is removed;
when D is below OP, the brakes loosen when the load is re-
moved.

Front Wheel Brakes— Front wheel brakes came into vogue
in England in 1909 and are still being fitted to perhaps a dozen
British and Continental cars, but there does not appear to be an>
likelihood that they will become universal. When such brakes
are used in conjunction with rear wheel brakes, the whole weight
of the car and load is available for braking purposes, and it
should be possible to stop a car in substantially half the distance
as with brakes on one set of wheels only. The chief advantage
of front wheel over rear wheel brakes is that the former do not
tend to cause the car to skid. Another advantage claimed for
them is that their use tends to equalize the wear on front and
rear tires.

In this connection an explanation of why the application of
brakes acting through the rear wheels tends to cause the car
to skid may be of interest. A wheel can rotate and progress
along the road by rotation only in its own plane, and this plane
for the rear wheels is determined by the motion of the front

384

BRAKES.

wheels, which latter is controlled by the driver. Hence, while
the wheels rotate they have a directing tendency, but as soon
as they are locked and begin to slide they lose all directing
tendency — unless they happen to be in deep ruts — because on
a hard, slippery surface the wheels will slide just as easily
sideways as in the direction of their plane. Skidding, of
course, occurs only when the road surface is slippery. When
the brake is applied while the car is traveling on such roads
it takes very little effort to lock the wheels. The car is then
kept in motion by the force of inertia, which acts at its centre
of gravity. This is opposed by the resistances encountered
by the four wheels and it is, of course, quite possible that the
resultant of these four resistance forces does not pass through
the centre of gravity of the car. We then have a couple which
tends to swing the car around, and as the rear wheels will
slide as easily sideways as forwards, the smallest couple of this
kind will start skidding.

FIG. 255.— SPRAG.

However, the fitting of brakes to fpont wheels involves many
mechanical difficulties and none of the designs that have come to
the writers attention are free from weak points. In the first
place, the steering pivot axis produced must pass through the
ground contact of the tires, as otherwise any difference in the
retarding action of the two brakes will affect the steering. To
prevent such interference with the steering either the steering
pivots may be placed inside the hub of the wheel or else the steer-
ing pivot or both it and the wheel may be inclined so as to in-
sure intersection of the pivot axis and wheel centre plane at the
ground contact.

BRAKES. 385

Special difficulties are involved in transmitting the operating
motion to the brake segments, because of the pivotal motion of the
brakes. One member of the operating linkage usually passes
through a hollow steering pivot pin. The manner in which the
problem has been solved by the designer of the Crossley car is
illustrated in Fig. 254. A toggle expanding mechanism is used,
a pin passing through the hollow-inclined steering pivot pin con-
necting with the toggle links through a ball and socket joint.
The top end of this operating pin is provided with a flange and
surrounded by a return spring, and is pressed against by the ball
ended arm of a bell crank fulcrumed on the steering fork.
The other arm of this bell crank connects by a short link
to a point on the vehicle frame.

It seems that the torque on the front axle produced by the ap-
plication of front wheel braked is always taken up by the front
springs, no special torque members being provided. Front wheel
braking therefore imposes additional strains upon the axle,
springs and steering connections, and in most cars these parts
would have to be strengthened if front wheel brakes were to be
fitted.

Sprags. — It has been customary among European designers to
fit touring cars with sprags to prevent them from running back-
ward down hill. Owing to the fact that the brakes now fitted are
entirely reliable as regards checking both forward and rearward
motion, the sprag has largely disappeared from pleasure cars, but
it seems to become a standard fitment of motor trucks. This
may possibly be due to the fact that in many motor trucks the
rear wheel brake connections are so arranged that the brakes will
loosen either on loading the truck or on unloading it. At any
rate, with a heavy vehicle which occasionally has to be stopped
and loaded or unloaded on very steep grades, it is certainly a
good plan to have a variety of stopping devices.

The ordinary sprag consists merely of a straight steel rod
hinged to the axle or a fitting thereon, at its forward end, and
pointed or wedge-shaped at its rear end, which is designed to dig
into the road surface. The sprag is generally formed with a
flange near its lower end, to prevent it from sinking too far into
the ground. Sprags are .made of such a length that when the
free end rests on the ground their horizontal projection is equal
to 1.75 — two times its vertical projection. Generally two sprags
are used, one near each body spring.

CHAPTER XIV.

FRONT AXLES.

Front axles for pleasure cars are almost invariably drop forged
from medium carbon steel, heat treated. The material, when
thus treated, has a tensile strength of 90,000 to 100,000 pounds
per square inch and may be worked at 10,000 pounds per square
inch. If high tensile alloy steel is used, the stress may be as
high as 15,000 pounds per square inch The axles are always
of the pivoted type, the wheel spindles being made separate from
the middle part of the axle and connected with it by a substan-
tially vertical pivot joint, thus forming so-called Ackerman
steering axles. A few use tubular axles with drop forged
steering heads or axle ends secured to them. Pressed steel
front axles consisting of either a single channel or two chan-
nels fitted into each other and having the steering head riveted
to them are used to some extent. Front axles for commer-
cial vehicles are generally forged of medium carbon steel, of
either solid rectangular section or of I-section approaching
a full rectangular section. Cast steel front axles are also used
for commercial vehicles. If the axle is forged from medium
carbon steel under a steam hammer a stress of 15,000 pounds
per square inch can be allowed, but in a cast steel axle the stress
should not exceed 10,000 pounds per square inch. Russell Huff
(S. A. E. Bulletin, July, 1916) found the average factor of safety
in front axles, based on the elastic limit, to be 5.8.

Stresses on Front Axles— When the car is at rest the front
axle is subjected to bending moments in a vertical plane, due to
the weight resting on the springs and to its own weight. When
the car is in motion there is also a horizontal bending moment,
due to the resistance to motion encountered by the front wheel.
This horizontal moment is comparatively slight when the car is
running on a smooth, level highway, but assumes considerable
values when the front wheel strikes an obstruction. The exact
limiting value of this horizontal moment is impossible of de-
termination, but accumulated experience has shown a certain

386

FRONT AXLES. 387

proportion between the vertical resisting moment and the hori-
zontal resisting moment of the axle section to be desirable.

Owing to the small weight of the axle itself as compared with
the weight resting on the springs, the former may be neglected.
Of course, when a new car is being designed, the weight that
will come on the front axle is not known in advance, but for
pleasure cars it may be predetermined with sufficient accuracy
for the present purpose by means of the following equation:
wheel base2

W = + 200 pounds.

In the case of trucks, unless a similarly proportioned vehicle
on hand permits of making a direct determination of the dis-
tribution of the weight between the two axles, it may be esti-
mated that three-eighths of the combined weight of the truck and
load is carried on the front axle, and five-eighths on the rear axle.
The approximate weights of commercial vehicles are as follows :
Load capacity (pounds) 1,500 2,000 3,000 4,000 6,000 10,000
Chassis weight (pounds) 2,400 3,000 3,500 4,500 6,000 8,000
Body weight (pounds). 750 900 1,050 1,200 1,500 1,800

In the great majority of cars this weight is supported on the
axle through the intermediary of two body springs, and one-
half of it rests on each spring saddle. The front axle itself is
supported at the centre of the front wheel, and therefore forms
a simple beam with two symmetrically located loads.

Front springs are invariably placed directly underneath the
frame side members and this determines the position of the
spring seats. The width of the forward end of the frame, in
turn, is determined by the maximum steering motion of the front
wheels desired. The spring seats are generally forged integral
with the axle, though occasionally they are bolted on, in which
case the axle is formed with lugs for the bolt holes. Between
spring seats practically all axles have a downward curve or
drop, the object being to insure proper clearance for the radiator
or whatever other part comes directly above it.

In the conventional design of chassis the only connection be-
tween the front axle and the frame is through the front springs,
but a few cars having unusual types of springs, such as single
cross springs or coiled springs, have distance rods between the
front axle and frame to transmit the driving thrust to the axle.
Hence, neglecting the weight of the front axle itself, in the con-
ventional design all the forces acting at the ground contact of
the wheels are transmitted to the frame through the springs, the
horizontal forces as well as the vertical forces. The vertical

388

FRONT AXLES.

bending moment increases from nothing in the centre plane of
the wheel to the maximum at the centre of the spring seat and
remains at the maximum between spring seats. The horizontal
bending moment, which may attain considerable values when one
wheel strikes an obstruction, increases from nothing in the centre
plane of the wheel to a maximum at the centre of the spring seat.
In the case of an axle connected to the frame by semi-elliptic
springs it practically ceases at the spring seat, being taken up by
the spring. On the other hand, in the case of an axle connected
to the frame by distance rods, the horizontal bending moment due
to forces on one wheel reaches its maximum at the centre of
the spring seat and decreases to nothing at the centre of the
other spring seat. In order to give I-section axles the necessary
strength to withstand considerable horizontal shocks on the
wheels, it is customary to gradually increase the width of the top
flange from the steering head toward the spring seat. In an axle
which connects to the frame only by semi-elliptic springs this
widening stops at the spring seat, and that part of the axle between
spring seats is made of uniform section throughout. On the other
hand, in an axle connected to the frame by distance rods the
flanges of the axle should increase in width as they approach the
distance rod connection from both sides.

I°Section Axles — The propor-
tions of the I-section vary con-
siderably in different makes of
axles, but the section shown in
Fig. 256 is a good average. De-
noting the thickness of the web by
a, the width of the section is 6 a
and the height slightly over 8 a.
The ends of the flanges are semi-
circular, of radius a/2, and the
fillet between web and flange has
a radius o. The sides of the
flanges are inclined 7 degrees to
give the necessary draught. The
dotted figure represents an equiva-
lent geometric section, and in

this the height is exactly 8 times the thickness of the web. The
thickness of the flange of the geometric equivalent section is
f-a. The moment of inertia of such a section is

FIG. 256. — I-SECTION OF
FRONT AXLE.

^ I88 a4

FRONT AXLES.

389

The distance c of the outermost fibre from the neutral section
being 4 a, the section modulus is

The moment of inertia of this same section around a vertical
axis is

2X|aX(6«)3 + 5f«Xa3_ia ,T „<

and since the distance c in this case is 3 a, the horizontal section
modulus is

of Action in Inches.
*&

6OO TOO GOO JOO /OOP S1CO

Mzscimum Load in Pounds on Each £jpringr Saddle.

CHART III FOR DETERMINING FRONT AXLE DIMENSIONS.

J200

390

FRONT AXLES.

The section modulus is a measure of the strength of the section,
and the section shown in Fig. 256 therefore is three times as
strong vertically as horizontally.

Chart III permits of quickly determining the necessary section
of axle for any load on the spring pads and any distance be-
tween the centres of the spring pad and wheel centre. In addi-
tion to the section above discussed, another, somewhat fuller
section, which was found to be the mean of a large number of
American front axle sections in 1907, is also drawn in, and the
diagram also permits of determining the necessary dimensions of
this section for various loads and lever arms. It should be

FIG. 257.— ELLIOTT TYPE STEERING HEAD WITH INTEGRAL PIVOT

PINS.

pointed out that the diagram is based on a unit stress of 10,000
pounds per square inch.

Steering Heads. — There are three types of steering heads now
in use, known, respectively, as the Elliott, the reverse Elliott and
the Lemoine. In American practice the Elliott type is most ex-
tensively used and the Lemoine least. In the Elliott type the
ends of the axle forging are forked and the steering knuckle is
T-shaped; in the reversed Elliott type the steering knuckle is
forked and the ends of the axle forms a T. In the Lemoine type
the ends of the axle as well as the steering knuckles form Ls.

FRONT AXLES.

391

Elliott Type— The spread of the fork in Elliott type steering
heads varies with the moment of the ground reaction on the
wheels at the centre of the steering pivot. The minimum dis-
tance between the branches of the fork is about 4 inches. For a
moment of 3,000 Ibs.-ins. it can be made 4^2 inches, and one inch
more for each additional 3,000 Ibs.-ins.

There are several different designs of Elliott type steering
heads and knuckles. In the first place, the knuckle may either
be provided with integral bearing pins which extend through
bearing holes in the fork arms of the axle, or its vertical member

FIG. 258.— ELLIOTT TYPE STEERING HEAD WITH PIVOT PIN BEAR-
INGS IN KNUCKLE.

may be drilled for a steering pivot pin. In case the latter con-
struction is adopted the pin may have a bearing either in the
fork ends or in the vertical member of tne knuckle. A design
of steering knuckle with integral bearing pins is illustrated in
Fig. 257. The lower arm of the fork has a hole Grilled through
it larger in diameter than the vertical member of the knuckle.
The bearing pin at the lower end of the knuckle is considerably
smaller in diameter than this hole, and the remaining space is
taken up by a bearing bushing screwed into the hole and locked
in place. In this particular design of front axle the vertical load
is transmitted from the axle to the knuckle through a single steel

392

FRONT AXLES.

ball of large diameter, which rests in the end of the drill hole in
the upper arm of the steering fork and on a spherical depressior-
on top of the vertical member of the knuckle. The steering arm
in this case is bolted right through the vertical member of the
knuckle. It can easily be seen that the entire vertical load is
taken by the upper arm of the fork, and the latter must be pro-
portioned accordingly.

A design of steering knuckle in which a pivot pin passes
through the vertical member of the knuckle is shown in Fig. 258.
The pin has its bearings in the knuckle and is a tight fit in the fork

FIG. 259. — ELLIOTT TYPE STEERING HEAD WITH BEARINGS IN
STEERING FORK.

arms. The pivot bolt is bolted into the lower arm of the fork,
being shouldered and provided with a castellated nut at the bot-
tom, and is drilled for a small grease cup. Bearing bushings are
inserted into the vertical member of the knttckle from each end,
and at the top there is a ball thrust bearing for carrying the
weight. The steering arm is bolted into a lug on the lower end
of the vertical member.

A third design in which the bearings for the pivot pin are in
the fork arms is shown in Fig. 259.

Other Types.— Fig. 260 illustrates the reversed Elliott type of
steering head and knuckle, which type was introduced by the
German Daimler Co., and is used most extensively on foreign

FRONT AXLES.

393

cars. The bearings are always in the knuckle fork, and are pro-
vided with hardened steel bushings. A ball thrust bearing may
be fitted as shown, but the majority of steering heads of this
type have plain thrust bearings, notwithstanding the fact that they
are used particularly on high grade cars. With a reverse Elliott
steering head the distance from the centre of the wheel to the
centre line of the pivot is necessarily somewhat larger than with
other types, and a ball thrust bearing tends to further increase
this distance, which is probably the reason it is generally dis-
pensed with. This difficulty is neatly overcome in several Eng-
lish cars. The pivot pin is enlarged at the lower bearing, so
as to form a shoulder which bears against the under surface of

FIG. 260. — REVERSED ELLIOTT TYPE STEERING HEAD.

the steering head, and the ball thrust bearing surrounds the. pin
on top of the steering knuckle, being held in place by means of a
castellated nut on the pin. The whole is surmounted by a sheet
metal cap. In this construction, therefore, the end thrust is
transmitted through the pivot pin.

In order to make the distance between wheel centre and pivot
axis as small as possible, the vertical part of the fork is generally
made of such a cross section as to partly envelop the steering
head. The height of the steering head with the reverse Elliott
type of axle is generally little greater than the height of the axle
section. This is considerably less than the spread of the fork in
a corresponding Elliott type axle. But the pivot pin diameter and
the length of the bearings are made correspondingly larger in
the former.

394

FRONT AXLES.

The Lemoine type of steering head was formerly much used
in France, but is now rarely met with. Fig. 261 illustrates the
Winton steering head, which is of this type. In this particular de-
sign the thrust load and part of the radial load on the bearing
are taken up on a tapered roller bearing, the remaining radial
load being taken up on a conical bearing. In all steering knuckles
a liberal fillet should be provided where the wheel spindle joins
the vertical member. As ball and roller bearings have only a
slight chamfer a washer is sometimes placed between the shoulder
on the spindle and the bearing.

Calculations of Pivot Bearings — In the illustrations, Figs. 257

FIG. 261.— LEMOINE TYPE OF STEERING HEAD (WINTON).

to 261, various methods for taking up the thrust load are shown.
This thrust load is relatively large, equal to the weight carried
by one wheel when the car is at rest or running over a smooth
road surface, and is increased by shocks on uneven pavement.
The simplest plan consists in providing two hardened steel
thrust washers between the vertical member of the steering
knuckle and the steering head. One washer must be secured by
a pin to the knuckle and the other to the steering head, so that
the motion will take place between the two hardened surfaces
and not between one hardened and one soft surface. The bear-
ing surface of the thrust washers should be made about one
square inch per 400 pounds load. In case a ball thrust bearing

FRONT AXLES.

395

is used its rated load capacity should preferably be 50 per cent.
greater than the maximum load on each front wheel, though con-
siderations of space limitation often compel the use of smaller
bearings.

The load on the radial bearings of the steering pivot may be
calculated as follows (Fig. 262) : Let P represent the maximum
reaction of the wheel on the knuckle spindle ; a the distance from
the centre plane of the wheel to the axis of the pivot; / the dis-
tance between centres of radial bearings, and P' the load on each
radial bearing.
Then

and

r i

* n

There is, however, still another load on the radial bearings of the
pivot; namely, that due
to the resistance to mo-
tion encountered by the
front wheel. The resist-
ance may attain quite
high values when the
front wheel strikes a
large obstruction while
the car is going at con-
siderable speed, but the
resulting bearing pres- FlG- 262.— DIAGRAM FOR CALCULATING
sure lasts only for a STEERING PIVOT LOADS.

moment and, therefore, need not be considered in determining
the necessary bearing surface. The resistance to motion on
smooth, hard, level roads throws a load on the pivot which
is absolutely negligible in comparison with that due to the
weight on the wheel. The radial bearings can be so proportioned
that the unit bearing pressure is about 500 pounds per square
inch. Usually the length of the bearings is about 1.5 times the
diameter d. If this relation holds, then

. P' _ P a
500 500 * /
Hence

750

(62)

If this diameter is chosen for the pin, the latter will be strong
enough to resist the shearing stress to which it is subjected.

396

FRONT AXLES.

The pivot axis is sometimes inclined in the vertical plane
through the centre of the front axle, in order to bring the point
of its intersection with the ground closer to the centre of wheel
contact on the ground. This distance forms the lever arm at the
end of which the resistance to motion of the front wheels acts
when the driver attempts to swing them around for steering.
The shorter this lever arm the easier the car will be to steer,
and some manufacturers incline the spindle so much that its axis
produced meets the ground at the centre of wheel contact, in
which case the length of the lever arm is nil (Fig. 263). How-

FIG. 263.— INCLINED STEERING FIG. 264.— FORE AND AFT IN-
PIVOT. CLINED STEERING PIVOT PRO-

DUCING TRAILER EFFECT.

ever, this construction has the disadvantage that in any but the
straight-ahead position the front wheels are considerably inclined,
in which position they are not as strong with respect to vertical
loads as when standing vertically.

Some manufacturers also incline the axles and steering pivots
in a vertical fore-and-aft plane (Fig. 264). There are two rea-

FRONT AXLES.

397

sons for this practice. The first is that the combined load due to
the weight on the axle and the road resistance encountered by
the wheel is in a slightly inclined direction, and in the case of
an I-section axle, of course, there is an advantage in making the
plane of maximum strength of the axle coincide with the direction of
the load. The other reason — and probably the more important one —
is that this construction produces a trailer effect and tends to
obviate serious consequences in the event of breakage or dis-
connection of the steering linkage. This effect is similar to that
obtained with the front wheel of a bicycle, whereby a cyclist is
enabled to ride with his hands off the handle bar. The point
of wheel contact with the ground is located to the rear of the
point at which the steering spindle axis produced meets the
ground, hence the steering wheels trail and are automatically kept
in the straight ahead position by the road resistance. The same
effect can also be obtained by placing the axis of the knuckle

\\-i--

i
— r

// 1

FIG. 265.— STEERING KNUCKLE WITH SPINDLE SET BACK FROM
PIVOT Axis.

spindle slightly to the rear of the pivot axis, as shown in Fig.
265. This latter arrangement has been used to quite an extent
in France in connection with built-up knuckles, the wheel spindle
being bolted to the vertical member of the knuckle.

Front Wheel Bearings — All of the different types of anti-
friction bearings are used in front wheels. There is considerable
end thrust on the front wheel bearings, and in case radial ball
or parallel type roller bearings are used, separate thrust bearings
for thrusts in both directions should preferably be fitted, at least
on heavy vehicles. It is not always fully realized that there are
heavy thrusts on front wheel bearings. Rear axles are often
without any thrust bearings except the one designed to take up
the thrust of the bevel gear, and from this it is sometimes
erroneously inferred that there is no need for thrust bearings in
the front wheels either. The difference is that whereas the pro-
pelling effort is always parallel to the planes of the rear wheels,

398 FRONT AXLES.

in turning a corner it may make an angle of 30 to 40 degrees
with the planes of the front wheels. The radial load on the
bearing due to the force of propulsion is proportional to the
cosine of the angle between the direction of the propelling force
and the plane of the wheel, and the thrust load is proportional
to the sine of this angle. Therefore, if the wheel stands at an
angle of 45 degrees, the thrust load due to the propelling force
is equal to the radial load due to that force. A factor tending
to aggravate the case with respect to thrust load is that when
rounding a curve at considerable speed the centrifugal force
throws nearly all of the weight of the car on the outer wheels,
and the propelling force on the outer forward wheel is increased
in the proportion of the weight on it. The thrust load being pro-
portional to the propelling force, it is also increased by this effect.
There is, moreover, a thrust load on the front wheel bearings
due to the centrifugal force. In fact, this whole force acts as a
thrust load, since it acts in the direction of the turning radius
and the axes of all the wheel spindles theoretically constitute
radii of the turning circle. On a smooth, hard, level surface the
end thrust on the wheel bearings is limited by the adherence of
the wheels to the ground, which is about 0.6 of the weight upon
them on most kinds of pavement. So far as the end thrust due
to centrifugal force is concerned, it is the same for the front
and rear wheel bearings, for unit weight upon them, but the front
wheel bearings in addition are subjected to end thrust due to the
propelling force, from which the rear wheel bearings are free.
Thrust Loads — The usual formula for centrifugal force is

F= 1.226 wn2r

where w is the weight in pounds, « the number of revolutions per
second and r the radius in feet. If the speed v is expressed in
miles per hour the car makes

5'2 °v feet per second.
3,600

and the circumference of the circle being 2 ^ r feet, the car will
turn at the rate of

revolutions per second.

5,280 v 0.2334^
3,600

Substituting this value for n in the expression for centrifugal
force we get

o.o668tvv2. t*~\

FRONT AXLES. 399

We will assume a car weighing with passengers 3,000 pounds,
whose centre of gravity is 24 inches high, rounding a corner at
a radius of 60 feet. The centrifugal force necessary to overturn
this car, with a tread of 56 inches, would be

3,000 X -^— • = 3,500 founds
To find the speed at which the car would turn over we put

o. 0668 X 3,ooo X*8 =
60

-=/

_ 7 ^ ; -

3,000X0.0686

Of course the car would turn over only if the ground ad-
herence was sufficient to prevent skidding. We will now suppose
that the car turns the corner at about half this speed, say 15
m. p. h. Also, that the weight resting on the front wheels is
1,200 pounds. Then the centrifugal force on this weight will be

0.0668 Xi.«ooX 15X15 = 300 tounds .

The centrifugal force of 300 pounds acting at the centre of
gravity will have the effect of removing

300X24 = I28 founds.

from the inner wheel and adding it to that on the outer wheel,
thus making the weight distribution 472 pounds on the inner
wheel, and 728 pounds on the outer. The resistance to motion
of the outer wheel will thus be increased in the ratio of 728 to
600. Furthermore, the propelling effort applied to the front
wheels acts at an angle whose sine is approximately 1-6, assum-
ing that the car has a wheel base of 10 feet, and the thrust load
on the bearings is one-sixth of the propelling force.

It is impossible to make a close calculation of the thrust on
the front wheel bearings under any given conditions, because of
the effect of the road surface and the uncertain distribution of
the thrust between the inner and outer wheel bearings, but the
point to be remembered is that whenever the car describes a
curve there is end thrust on the front wheel bearings, even with
the power shut off, because of the centrifugal force ; if the motor
is propelling the car there is additional end thrust, owing to the
oblique application of the propelling force to the front wheels.

Mounting of Bearings — Because of the simple construction,
combined radial and thrust bearings are much used for front
wheels, such as Timken roller, New Departure, cup and cone,

400

FRONT AXLES.

etc. The mounting of such bearings presents no particular diffi-
culty. If they are of the adjustable type the bearings are ar-
ranged with their outer races pressing endwise against internal
flanges on the hub between a shoulder and a nut on the knuckle
spindle, as shown in Fig. 266. The adjusting nut, of course, must
be properly locked. Lubricant is retained within the hub by the
hub cap at the outer end and a dust washer on the inner end.
The bearings are usually so placed that from two-thirds to three-
quarters of the load comes on the inside one, though there is
considerable variation in this respect. Of course, the aim always
is to bring the centre plane of the wheel as close to the pivot

axis as possible. A
clearance of about one-
quarter inch should be
allowed between the
vertical member of the
knuckle or the steering
head and the nearest
part of the wheel hub.

The outer bearing
serves mainly as a
steadying bearing and
must be placed at a con-
siderable distance from
the inner one to prop-
erly serve its purpose.
Adjustable roller bear-
ings on pleasure car
axles are placed at 3 to
Zl/2 inch centre distance,
while ball bearings are
placed at 4 to 5 inch

FIG. 266. — MOUNTING OF FRONT
WHEEL ADJUSTABLE BEARINGS.

centre distance. For oiling, a spring closed oil cup is usually
placed on the hub. A much used method of introducing lubricant
into the front hubs consists in removing the hub caps, filling
them with grease and replacing them.

There are many light cars in use employing only two radial
ball bearings in the front wheels. Where radial bearings only
are used, both races of one kind should be firmly secured againsl
endwise motion, as well as one race of the other kind, the re-
maining race being left free endwise. Some designers clamp
the two inner races tight on the spindle and place the inner faces
of the outer races against internal flanges of the hub. With this

FRONT AXLES.

401

construction, if the distance between the outer faces of the two
flanges and the length of the spacer between the inner races are
different, a permanent side thrust is put on the bearings, which
causes them to work hard.

A neat mounting of radial and thrust bearings for front wheel
hubs, due to F. G. Barrett, of England, is illustrated in Fig. 267.
In this design the two outer races of the radial bearings are
clamped in the hub, as is the middle race of the thrust bearing.
Both inner races of the radial bearings are free. The two thrust
bearings are assembled on a sleeve which fits closely over the

FIG. 267.— MOUNTING OF FRONT WHEEL RADIAL AND THRUST BALL
BEARINGS

tapered portion of the knuckle spindle and is held in place by
the nut on the end of the spindle.

A good solution of the front wheel bearing problem seems to
consist in the use of a radial bearing at the outer end and a so-
called two row bearing, designed to take both radial and thrust
loads, at the inner end. Both inner races are then secured end-
wise, while the outer race of the radial bearing is left free end-
wise.

Steering Spindle "Set" — The spindle of a steering knuckle
is arranged to make a slight angle with the horizontal, chiefly to

402

FRONT AXLES.

allow for flexure of the axle and play in the knuckle joints when
the axle is under load. In American practice it is common to
have the knuckle spindle make an angle of about two degrees v/ith
the horizontal, if plane wheels are to be used. If dished wheels
are to be used the angle may be as much as 6 degrees.

Spindle Diameter — As regards the diameter of the knuckle
spindle, this is generally determined by the bore of the bearings ;
that is to say, if the bearings are large enough to withstand the
load upon them, a spindle fitting their bore will easily withstand
the bending moments on it. When radial ball bearings are used
the medium series is usually selected. Russell Huff, whose paper
on factors of safety was referred to in the foregoing, found the

FIG. 268.— STEERING MOTION STOPS.

average factor of Safety in the steering spindles at the bearing
shoulder to be 26.1.

Steering Stops — A little refinement that has been applied in
a number of axles in recent years is a stop limiting the swing of
the steering knuckles, so as to prevent contact between the re-
volving wheel and the frame or the steering drag link, which is
objectionable. Such a stop (L) is most easily provided in the
case of a reversed Elliott type steering gear, as shown in Fig. 268
at A. At B in the same figure is shown the arrangement used in
the axles of the Timken-Detroit Axle Co., which have Elliott
type steering heads. In this case a lug L on the knuckle arm con-
tacting with an adjustable stop on the axle forging limits the
steering motion.

FRONT AXLES.

403

Knuckle Arms — The steering knuckles are provided with
arms for interconnection of the two knuckles on opposite sides
of the car by the tie rod and also for connection to the steering
gear through the drag link. Of course only one of the knuckles
needs to be connected to the steering gear, and usually the arm
of this knuckle is made double, though occasionally, especially
with reversed Elliott type steering heads, one knuckle is provided
with two separate arms. The necessary length of the arms and
other details will be considered in the chapter on the steering
gear. It is usually necessary to bend these arms out of the

FIG. 269.— DOUBLE STEERING ARMS FOR ELLIOTT TYPE FRONT AXLE.

horizontal plane, at least with Elliott type steering heads, because
the tie bar has to pass underneath the body springs and the drag
link must pass either over or under the axle. Moreover, the arm
for connection to the drag link must be given a considerable curve
in the horizontal plane, because with the front wheel in the central
or straight ahead position this arm usually extends practically
in the direction of the axle, hence in an Elliott type axle it must
curve around the vertical part of the steering head and it must
clear this part for any position of the front wheels. Knuckle
arms are secured to steering knuckles with a tapered seat, being

404

FRONT AXLES.

bolted and keyed. The taper is made about 1:10, and the nut is
secured by means of a cotter pin. The key is necessary because
of the crank effect due to the bend in the arm. As regards the
proper size of the arm, let W represent the maximum weight on
one front wheel; a the distance between the pivot axis and
the centre plane of the wheel, and b the distance between the pivot

FIG. 270. — STEERING ARMS FOR REVERSE ELLIOTT TYPE FRONT AXLE.

axis and the axis of the tapered portion of the knuckle arm ; then
the diameter d of the larger end of the taper should be

/
r i,

Wa for pleasure cars

and

*/ Wa

=v ^

trucks'

5006

The arm proper is generally made of oval section, of such size
as to have the same maximum section modulus as the tapered

FRONT AXLES. 405

portion near the latter, and tapering down slightly toward the free
end. Fig. 269 shows two typical designs of knuckle arms, the one
on the left being for axles in which the tie rod is located to the
rear, in which case the knuckle arm must point away from the
wheel, while the one on the right is for axles in which the tie rod
is in front, in which case the arm must approach the wheel.
Fig. 270 shows a knuckle arm designed for a reversed Elliott
type of knuckle. One of the advantages of this type of steering
head is that it interferes less with the arrangement of the
knuckle arm.

It is a good plan to provide the knuckle arm on the driver's
side with a drilled boss for the speedometer gear bracket, so as
to make a rigid mounting of this bracket possible. The location
of the holes is not a matter of great importance, for the reason
that universally adjustable mountings for the driven gear have
to be provided in any case. A drilled boss permits of rigidly
fastening the bearing bracket in place so there is no danger of
its being jarred loose and the mesh of the gears becoming dis-
turbed.

Tie Rod — The rod which connects the steering knuckles on
opposite sides of the car is practically always made tubular. It
may be placed either in front of the axle or to the rear of it.
The former arrangement has the advantage that the rod ordinarily
works under tension, while with the latter it works under com-
pression. That is to say, the road resistance encountered by the
front wheels, acting through the bell cranks formed by the steer-
ing knuckles and arms, puts a tension on the tie rod with the first
mentioned construction and a compression with the second. Of
course, the force impressed upon the rod by the driver in steering
the car produces a tension for one direction of motion and a
compression for the other with both constructions. The advantage
claimed for the second arrangement is that the relatively frail tie
rod is much better protected from injury back of the axle than in
front of it. The great majority of all cars now have the tie rod
back of the front axle.

Considering the tie rod located back of the axle, the maximum
compressive load may be represented by the expression

p_cWa
~~b~

where c is a constant; W, the maximum weight on one front
wheel ; a, the distance between the centre plane of the wheel and
the pivot axis, and b, the length of the knuckle arm. The rod

406 FRONT AXLES.

acts like a column with free ends, the permissible 'load for
which is

SA
P = Tz

(Rankin's equation), where S is the safe working stress of the
material; A, the sectional area of the rod; qt a constant; /, the
length of the rod, and r the least radius of gyration of the sec-
tion. For a solid rod,

Z)2

r" =

for a tube,

16
Hence

cWa S A

With the proportions obtaining in steering tie rods we may
write

c W a SA
b /2

<?r-T

without committing a great error. Remembering that for a hol-
low circular section

A=-- ^L(D*—d2*

4
and

we get, by substitution,

cWa

b 64 ?/

which may be transformed to read

All of the factors in the first pair of parentheses may be re-
garded as constant, and we may denote this term by (7, which
gives us

FRONT AXLES. 407

The value of C should be 1,000,000 for pleasure car axles with
the tie rod in the rear; 1,500,000 for pleasure car axles with the
tie rod in front and for truck axles with the tie rod in the rear,
and 2,000,000 for truck axles with the tie rod in front. It might
be argued that the above reasoning does not apply to the case
of a tie rod in front of the axle, because in the latter it is nor-
mally under tension instead of under compression. However,
it is the extreme conditions that determine the necessary s.^ength
of a part, and it is most likely that a tie rod in front of the axle
is subjected to the greatest unit stress when the driver suddenly
wrenches his steering wheel around in such a direction as to
put the tie rod under compression, in case the "off" wheel is
restrained from turning in that direction by a rut, etc. In
using equation (64), calculate the value of the right hand term;
assume a value for D, and calculate the necessary value of d.
If the result is unsatisfactory assume another value for D. The
wall thickness must not be chosen too small, because the tube
has to be threaded for the connector. Equation (64) is intended
for straight tie rods only; if the rod is cranked at the middle
to clear the engine or under-pan it must be made stiffen

The length of the tie rod is so adjusted that when the car
stands on the factory floor with the front wheels in the central
position, the distance apart of the wheel rims in front of the
axle at the height of the spindle is from % to y* inch less than
the corresponding distance back of the axle. This slight "toeing
in" is intended to allow for the slight play in the joints and
flexure of the members when the car is being driven on the road,
so that in actual road driving the wheels will be substantially
parallel.

Tie Rod Connectors— The ends of the knuckle arms swing
in the same plane, and the tie rod, therefore, is connected to
the arms by forked connectors. The connector (Fig. 271) is
usually screwed over the end of the tie rod, its hub being split
for some distance along its length and provided with clamp lugs,
and it is securely clamped down on the rod. The bearing of the
connector pin may either be in the knuckle arm or in the con-
nector. In high grade cars this bearing is bushed with bronze or
hardened steel, and lubricating means are provided, either a small
oil cup or, preferably, a small compression grease cup. The pro-
jected bearing area should be about

W a
A = — — square inches.

408

FRONT AXLES.

Making the length of the bearing from two to three times the
diameter gives a pin amply strong to withstand the shearing
stress. Owing to the fact that the safety of the passengers de-
pends upon the integrity of the steering linkage, the connector
pin nut must be securely locked. In fact, everything pertaining
to the steering mechanism must be absolutely reliable.

Tubular and Pressed Steel Axles— Tubular front axles are
generally made from nickel steel tubing, which has a tensile
strength of 120,000 pounds per square inch and may be worked at
12,000-15,000 pounds per square inch. Such axles have the same
strength in the horizontal as in the vertical plane, and therefore
are not easily bent by striking obstructions. In the case of cars
with comparatively wide frames the spring seats may be forged
integral with the axle ends, which are pinned and brazed or

FIG. 271.— TIE ROD CONNECTOR.

merely clamped to the axle tube. Some designers prefer clamp-
ing to brazing, because in the latter process the metal is likely
to be overheated and thus weakened. In smaller cars with a
comparatively narrow frame this scheme is not praticable and
the spring seats must be separately clamped or pinned and
brazed to the tube. In pressed steel axles both the forged axle
ends and the spring seats are riveted to the pressed steel part.
For the axle end rivets are placed both vertically and horizontally.
These pressed steel axles are made from carbon steel stock, as a
rule, and with that material the stress should be limited to
10,000 pounds per square inch.

Manufacture of Front Axles — The chief machining opera-
tions on a front axle are the facing of the ends of the steering
heads and the drilling and reaming of the holes for the pivot
pins. The four faces of an Elliott type steering head are usually

FRONT AXLES.

409

410 FRONT AXLES.

faced in one operation in a milling machine by means of four
milling cutters mounted on the same spindle the proper distances
apart. If the production is carried on at a sufficiently large
scale, a special double milling machine finishing both ends of the
axle at the same time would possess considerable advantage.
Fig. 272 shows the method employed at the plant of the Timken-
Detroit Axle Co., Detroit, for boring and reaming the holes for
the pivot pin. A special double ended machine tool is used for
this purpose, which permits of finishing both ends of the axle
at the same time. Each spindle of the tool is driven separately
by belt from countershafts.

CHAPTER XV.

THE STEERING GEAR.

Historical— Instead of the fifth wheel steering arrangement
used on horse vehicles, the divided axle is universally employed
on automobiles. This was invented by Lankensperger, of Munich,
in 1817. The English patent on it was taken out in the name of
Rudolph Ackerman, and in English speaking countries the gear, in
consequence, has come to be known as the Ackerman steering gear.
A refinement of this steering mechanism for automobile purposes
was introduced in 1878 by Charles Jeantaud, a French carriage
builder, who devised what is known as the Jeantaud diagram.
Jeantaud, it seems, recognized the principle that if the vehicle is to
turn a corner without sideward slip of any of the wheels, the link-
age of the steering wheels must be so arranged that the axles of all
the wheels produced always intersect a common vertical line, the
vertical line forming the momentary axis of rotation. Jeantaud
found that in order to approximately fulfil this condition, the
steering arms, instead of being parallel, must be inclined toward
each other when they extend to the rear of the axle, and away
from each other when they extend forward of the axle; and his
diagram, which is intended to give the correct inclination of the
arms, indicates that the centre lines of the arms produced should
meet at the middle of the rear axle. More recent investigations
of the steering problem have shown that with the ordinary
trapeze form of steering linkage it is impossible to absolutely
satisfy the condition of correct steering, and that for a minimum
error for the whole steering range the point of intersection of
the two steering arms produced lies some distance in front of
the rear axle.

Theory of Steering Mechanism — In the following investiga-
tion we will denote the length of the wheel base by W '; the dis-
tance between steering pivots by L; the inclination of the inner
wheel axis by a; the inclination of the outer wheel axis by 0; the
inclination of the knuckle arms by 0 ; the length of the arms by I.

411

412

THE STEERING GEAR.

Referring to Fig. 273, it will be seen that
a c

— cot a

and

— cot ft

Hence

bc — ac/ L

= cot /3 — cot

FIG. 273.

This equation enables us to plot the required values of /3 corre-

L
spending to different values of ct for any ratio . It expresses

the condition which should be satisfied by the gear, but furnishes
no guide as to how this may be accomplished.

Graphical Solution of Steering Problem — There is no di-
rect analytical method for determining the most advantageous
angle of the knuckle arms, and some graphical method is usually
employed. By laying the steering diagram off on the drawing
board to, say, half size, a sufficient degree of accuracy is attained.
Unfortunately, for small deflections of the front wheels, the dis-
tance of the point of intersection of the wheel axes is so far from
the axis of the car that it falls far outside the limits of an ordi-

THE STEERING GEAR.

413

nary drawing board, and accu-
racy of the linkage with small
deflections is of special import-
ance, for the reason that the
wheels are turned through a
small angle very much oftener
than through a big angle, and the
car generally runs at a much
higher speed when describing
curves of large than of small
radius. This difficulty may be
overcome as follows (Fig. 274) :
From points a and b, denoting
the steering pivots, draw lines
perpendicular to the axles which
will intersect the rear axle at
e and /. Next, draw a line from
the middle point g of the front
axle to point e. Then lines drawn
from the pivot points a and b to
any point on line g e will make
with the front axle correspond-
ing steering angles. This may be
proven as follows:

FIG. 274.

and

cot a. = =

cot /3 = — - =
ih

ag — ig

ag + ig

But

and substituting,

2ig

. r . cot p — cot a =

ih
ig ag

cot P — cot a =

a e
2ag

ac ^ W

Now assume steering arms of a definite length and making
a certain angle with the longitudinal vehicle axis. Next deter-
mine graphically the deflection of the outer wheel for various
assumed deflections of the inner wheel, say, 8, 16, 24, 32, 40 and
48 degrees, for these steering arms. This has been done in
Fig. 275 for two particular cases. The -following dimensions were
assumed in making this drawing: L = 50 inches; I =.7 inches

414

THE STEERING GEAR.

THE STERING GEAR. 415

and angle O = 15 and 20 degrees, respectively. The values of
angle |8 were determined graphically for values of angle a of 8,
16, 24, 32, 40 and 48 degrees, respectively. After these values of
angle /3 had been found, corresponding angles a and ft were laid
off on opposite ends of the line L. Through the points of inter-
section of the lines describing corresponding angles were drawn
curves, one for the 15 degree knuckle arms and the other for the
20 degree knuckle arms. These may be called steering error
curves, because their deviation from the diagonal line ge (Fig.
274) indicates the error in the steering angles. In Fig. 275 the

L
diagonal g e corresponding to the value = 0.45 is drawn in. It

will be seen that for small deflections the angle of the outer
wheel is too large with both 15 and 20 degree knuckle arms.
The 20 degree knuckle arm gives the correct deflection of the
outer wheel at about 26 degrees of the inner wheel, and the 15
degree knuckle arm gives the correct deflection of the outer
wheel at 46 degrees deflection of the inner wheel. Beyond these
points the angle of the outer wheel is too small. It may readily
be seen from this that the most advantageous angle of the
knuckle arms depends upon the turning range of the inner wheel.
Thus, if the motion of the inner wheel were limited to 32
degrees, the 20 degree knuckle arm would be the best, whereas
if the range of motion of the inner wheel were as large as 45
degrees, the angle of the knuckle arm should be about 18 de-

grees— for a value of — = 0.45.

. w
In order to use this method for the practical determination of

the proper knuckle arm angle, steering error curves for differ-
ent knuckle arm angles and lengths should be laid out very
carefully for permanent use, and in any particular case the

diagonal g e corresponding to the particular value of ~^-~ should

be placed on the chart in pencil, when the most advantageous
knuckle arm angle will at once be apparent.

An Analytical Method — An ingenious analytical method of
determining the deflection of the outer wheel corresponding to a
given deflection of the inner wheel has been published by Her-
bert C. Snow (THE HORSELESS AGE of April 13, 1910). A short
resume of this method follows :

Four different cases have to be considered, viz., with the
knuckle arms in front and in the rear, respectively, and with the
knuckle arm angle 6 greater and less than the deflection ft of

416

THE STEERING GEAR.

the outer wheel, respectively. In Fig. 276 the knuckle arms ex-
tend to the rear of the axle and angle 9 is greater than /3. In
this diagram the knuckle arms are purposely shown abnormally
long, for the sake of greater clearness. Referring to the Fig.,
M = L — 2lsinO

ga — l cos (a +
hi = jb = lsin
jf = lcos(B —

Substituting values of g e and h i,

I sin (a + 0)+Af — N + lsin
Substituting the value of M,

I sin (a + e) + L
Transposing and dividing by /,

— /3)=L

(65)

FIG. 276.

By a similar process of reasoning it is found that with P greater
than 9 and the arms extending to the rear
. ,Q 0. . / i m • 0 -A7" /66\

with P smaller than 6 and the arms in front of the axle —

sin (0 — p) = 2 sin 9 — sin (6 -f a) —

(67)

and with /3 greater than 0 and the arms in front of the axle
sin (ft — 0)= sin (6 + a) — 2 sin e -f

.(68)

These various equations cannot as yet be solved because N is
not known. The value of N in terms of known factors may be
found as follows: O=-jf — jh.

When p is smaller than e,

jf=lcos(e-?}

THE STEERING GEAR. 417

hence

O = / cos (0 — j8) — / cos (a + 6) =

/ [cos (0_/3) —cos (a + 6)] (69)

Similarly, when £ is greater than 0,

// = / cos (]S — 0) and

O = / [cos (|8 — 0) — 07.S- (a + 0)] (70)

In every case

M - N = \/M2- O2
and

AT = M — -\fj? — o2 (71)

The equations thus derived permit of accurately determin-
ing the angle of the outer wheel corresponding to any angle
of the inner wheel, the proportions of the linkage being given.
The following example shows its method of application: Sup-
pose the distance L between pivots to be 50 inches ; the length
/ of the knuckle arms, 6.5 inches; 0, 20 degrees, and «, 30 de-
grees, the knuckle arms extending to the rear of the axle. Then
according to equation (66) ^

sin (/3 — 20°) = sin (20 + 30) ° — 2 sin 20°

N
Disregarding the term — for the moment we get for a first

/
trial value

sin (£ — 20°) =0.082.

/3 = 24° 42'.

Inserting this value of j8 in equation (70) we get
O = 6.5 (0.9966 — 0.6428) = 2.2997,
M = 50 — (2 X 6.5 X 0.342) = 45.56
and inserting these values in equation (71) we get

N = 0.053.
Now using this value N in equation (66) we get

/3 = 25° 10'.

The calculations could be continued further, but Mr. Snow
has shown that the second trial value is correct within one min-
ute in the most extreme case, which is as high a degree of ac-
curacy as is required in practical work.

Using this method, Mr. Snow calculated the error in the

steering angle for each of the turning angles 25° and 30° of

the inner wheel, with the knuckle arms set at from 15° to 30°,

extending both to the front and the rear, using four ratios

— in each case, viz., 0.10, 0.12, 0.14 and 0.16. The results
L

418

THE STEERING GEAR.

of these calculations are plotted in Charts IV and V. These
charts give the best value for the angle of the knuckle arms
for limiting turning angles of 33° and 40° of the outer wheel,

when the values of — - and — are known.

rr JLt

General Arrangement of Gears — Automobiles are steered
by means of hand wheels, whi'ch in the case of pleasure car^
are located at the top of a rearwardly inclined steering col-
umn, and in the case of trucks, at the top of a vertical or
nearly vertical column. The spider of the hand wheel is se-

-asf-

26°

t'£2&

<%//

V~.3O .34 .36 .42 .4G .SO .S4 .£6 -G2

CHART IV. — PROPER KNUCKLE ARM ANGLES FOR A LIMITING DE-
FLECTION /3 OF THIRTY-THREE DEGREES.

cured to a shaft which generally passes down inside an outer
stationary tube. At the bottom of the shaft is located the so-
called steering mechanism which reduces the motion of the
hand wheel. This, in the great majority of cases, consists of
either a worm and worm wheel sector or a worm and complete
worm wheel. A worm and nut mechanism is also used to quite
an extent, particularly abroad, while spur pinion and rack, and
bevel pinion and bevel gear sector mechanisms are used in a few
cases.

THE STEERING GEAR.

419

In pleasure cars the steering motion is geared down in such a
ratio that it requires from one to one and a quarter complete
turns of the steering hand wheel to turn the front wheels
from hard over one way to hard over the other way and in
trucks, so it requires from one and one-half to two complete
turns. The linkage connecting the steering mechanism with one
of the knuckles is generally so proportioned that the steering arm
which is secured to the steering device turns through an
angle of about 60 degrees while the road wheels are 'turned

£6

1&"

CHART V. — PROPER KNUCKLE ARM ANGLES FOR A LIMITING DE-
FLECTION /3 OF FORTY DEGREES.

through their entire range. This implies a reduction ratio
of the steering mechanism of from 6 :1 to 12 :1, according to the
weight and speed of the vehicle.

Reversible and Non=Reversible Gears — For powerful,
high speed cars it is generally considered best to have the
steering gear back-locking or irreversible; that is to say, so
designed that any shocks received by the road wheels will
not be transmitted to the steering hand wheel. This un-
doubtedly makes for comfortable driving under all circum-
stances, and for safety in driving at high speed. On the other

420 THE STEERING GEAR.

hand, for moderately powered cars a slightly reversible steer-
ing gear has an advantage, because it greatly reduces the
shocks on the steering mechanism, as well as on the front
axle. It is obvious that with an absolutely irreversible mech-
anism any shocks received by the front wheels are entirely
taken up by the steering mechanism, whereas with a slightly
reversible mechanism the shocks are partly transmitted to the
steering wheel, and the strain on the steering members is
relieved by the cushioning effect due to yielding of the
driver's arm. There is no fixed angle of lead of the worm
below which the worm gear is non-reversible, as the point
where it becomes reversible depends upon the materials, the
finish and the state of lubrication of the mechanism. Assum-
ing a coefficient of friction of o.i the worm gear efficiency
formula given in a previous chapter shows that a worm gear
becomes back-locking when the angle of lead drops below
6 degrees, but this formula takes no account of the bearing
friction. Generally, when it is desired to make the steering
mechanism irreversible the angle of lead is made from 8 to
10 degrees, whereas for a slightly reversible gear a lead angle
of 12 to 16 degrees is chosen.

Calculation of Worm and Wheel — Steering mechanisms of
the worm and sector or worm and wheel types are calcu-
lated by means of the formulae for worm gearing given in an
earlier chapter. Since the steering arm usually swings only
through an angle of 60 degrees, only about 90 degrees of the
worm wheel comes in contact with the worm teeth, while
the front wheels are moved through their entire turning
range. Formerly it was customary to use a sector embracing
only about 90 degrees of the complete wheel, and this practice
still prevails abroad, but in recent years it has become the
custom in this country to employ a complete wheel, the shaft
of the wheel being squared where the steering arm is se-
cured to it, so that after one section of the wheel shows ap-
preciable wear, the wheel can be turned through an angle of
90 degrees and another quarter section brought into action.
The wearing portion- of the worm wheel can thus be renewed
three times in succession.

Both the worm and the wheel of a steering mechanism are
made of steel. The conditions differ from those under which
a worm gear transmission operates in that mechanical
strength of the teeth is the chief consideration rather than

THE STEERING GEAR. 421

minimum friction, for which reason steel is used for the wheel
instead of bronze. The worm is usually case hardened.

As regards its ability to sustain tangential loads, the worm
wheel of a steering mechanism does not differ much from a
spur gear, and the necessary size of the wheel may be deter-
mined by a method similar to that used for the calculation of
spur gears. In the chapter on the change speed gear we found
that the maximum safe tangential load of a spur gear is given
by the equation

w = Spfy,

where S is the maximum permissible unit stress; p the circu-
lar pitch; / the face width and y a constant. The constant y
may be neglected in this case because the number of teeth used
in the wheels of worm steering mechanisms does not vary much.
Roughly speaking, the face width / is proportional to the pitch
diameter of the worm, which in turn is proportional to the dis-
tance between the axes of worm and wheel. Also, the tangential
force on the worm wheel acts through an arm equal to the radius
of the wheel, which is also proportional to the distance D between
the axes of worm and wheel. Hence, the moment which the
worm wheel will sustain,

Mr ~ DZ P.

On the other hand, the maximum turning moment which will be
impressed upon the worm wheel,

a c

Mi ~ W

Where W is the maximum weight on one front wheel; a, the
distance between the centre plane of the wheel and the steering
pivot; b, the length of the knuckle arm and c, the length of the
steering arm. Hence we may write

a c

W D2 p

b
Data on hand shows that in modern pleasure car practice

\W a c

D = J X

\ ^nn h *

(72)

600 b p
and in motor trucks fitted with solid tires

/ W a c

D = J X

\ i ?no h f>

(73)

1,200 b p
Six pitch teeth are usually employed in pleasure car steering

gears, and four pitch teeth in gears for heavy trucks. The worm
is made with from two to four threads. Equations (72) and (73)

422 THE STEERING GEAR.

are useful as an indication of the capacity of different gears.
They are intended to be used only in connection with mechan-
isms comprising a full wheel; when a sector is used the centre
distance for a certain capacity should be made somewhat greater,
as with no means for compensating for wear of the teeth it is
advisable to reduce the wear by keeping down the unit tooth
pressure.

We will now illustrate the design of a worm and wheel steer-
ing mechanism by the example of a gear for a medium sized
touring car with a maximum weight of 750 pounds on one front
wheel and a distance of 2^4 inches between the centre plane of
the wheel and the pivot axis. We may assume that the steering
arm and knuckle arm are of equal length. If the pitch of the
teeth is to be 6, then the required centre distance of worm and
wheel is

'J75° 2^5 =2.57 rn^s-
600 ^ o . 52

Now suppose that the worm has three threads and an angle of
lead of 14 degrees, so as to be slightly reversible. Then the
worm pitch diameter will be

3X0.5236 =2.o67 inches,
3.1416X0.242 _^

A wheel with 21 teeth would give a reduction of 7 to 1 and
would require a little over one complete turn of the steering
wheel to turn the steering arm 60 degrees. Such a wheel would
have a pitch diameter of

21 x 0-5236 = 3>6o5 inches

3. 1416 X 0.9703
The centre distance then would be

2.067 + 3.605 = 2>836 inch€Sf

This is a little more than the centre distance required according to
equation (72). If the centre distance had come ®ut a little too
small we could have chosen one or two more teeth for the wheel
and made the calculation over.

The included angle of the wheel face is usually made between
45 and 60 degrees.

It is somewhat difficult to arrive at a basis for dimensioning
the steering gear, since the forces which the different parts
are called upon to transmit are indeterminate. These forces,
of course, increase directly with the weight on each front
wheel, and substantially as the distance between the centre
plane of the wheel and the steering pivot axis. The forces

THE STEERING GEAR. 423

also increase with the maximum speed of the car, but rather
than to introduce the speed into formulae for the dimensions
of the gear it will be advisable to use different constants in
such formulae for gears intended for different classes of vehi-
cles. The author has found that in average pleasure car
practice the torsional strength of the worm wheel shaft at the
elastic limit of the material is about seven times greater than
the product of the weight on each front wheel into the dis-
tance between the centre plane of the wheel and the steering
pivot axis, and in truck practice three and one-half times
greater. These coefficients will serve as a basis for portion-
ing the worm wheel shaft, the steering arm and the drag
link. The proper size of the worm wheel shaft can be deter-
mined first, and the other parts enumerated can be made of
such size that they are strained to their elastic limit when the
shaft is strained to this point.

The usual formula for the torsional strength of a round
shaft is

T = 0.196 d5 S.

If the shaft is square at one end for fitting the steering arm
its strength is reduced to about

T = o.i4 da S.

If now we make 6" equal to the elastic limit of the material
then for pleasure cars,

7 ^0 = 0.14 d3 S
and

50 Wa . .

Y~ (72)

while for motor trucks

(73)

These formulae are to be used only for the conventional con-
struction, as they would fail if the steering pivot were in the
centre of the wheel.

The worm wheel shaft is preferably forged integral with the
wheel, owing to the fact that space in the direction of the
axis of the worm wheel is limited, at least if the shaft is
mounted in plain bearings, as is usually the case, and it is
therefore difficult to secure the worm wheel or sector rigidly
by keying or otherwise.

424 THE STEERING GEAR.

Bearings. — Each of the two parts of a worm and wheel steer-
ing gear is subjected to both thrust and radial loads, the thrust
load on the worm being particularly great. Ball thrust bearings
are nearly always provided on the worm shaft, whereas the
radial load on this shaft is generally taken on plain bearings,
though in some instances cup and cone bearings are used to take
both the radial and thrust load. This applies to both the worm
and the wheel. The cup and cone bearing would seem to haye
special advantages in this case, and it is somewhat surprising
that it is not more extensively used. In the majority of cases the
wheel shaft is mounted in plain bearings and has plain thrust
washers of bronze or hardened steel. In gears for the cheaper
grade of cars the shaft of the worm wheel or sector is generally
supported in one bearing only, but this is not as satisfactory as
bearings on opposite sides of the wheel. The total bearing length
of the worm wheel shaft is made from three diameters in the
case of a single bearing to as high as six diameters in the case of
two bearings. From four and one-half to five diameters is good
average practice. It is very essential that proper provisions be
made for the lubrication of the shaft bearings, as excessive wear
due to want of lubrication is common and very annoying.

In order to provide means for adjusting the mesh of the worm
and the wheel, eccentric bearing bushings are sometimes placed
on the wheel shaft, which can be turned in the hubs of the hous-
ing and secured in any position. Such an adjustment permits of
compensating for errors in machining the housing, but not for
wear of the worm and wheel.

Steering Shaft. — The steering shaft to which the worm is
secured presents quite an engineering problem. The size of
the worm limits the external diameter of this hollow shaft, and
its internal diameter is limited by the fact that it must contain
three concentric members, viz., a stationary tube which supports
the sector on which the spark and throttle levers move, the
throttle control tube and the spark control shaft, together with
bearing bushings for the latter two. Yet, the steering shaft must
have an appreciable wall thickness because the worm and the
steering hand wheel have to be keyed or otherwise rigidly se-
cured to it.

The worm calculated in the foregoing example, which had
a pitch diameter of about 2^ inches and a bottom diameter of
about Hi, is about as small a worm as it used in steering

THE STEERING GEAR.

425

gears. The largest diameter of steering shaft that this will
take is about il/% inches outside diameter. If the control
shafts are to be placed concentric with the steering shaft the
largest possible wall diameter of the latter is one-eighth inch.
The different concentric 'members could then be made of the
following dimensions: Spark shaft, five-sixteenth inch diam-
eter; throttle control shaft, one-half inch o. d. and three-
eighth inch i. d.; stationary tube, three-quarters inch o. d.,
five-eighths inch i. d.

JT31

FIG. 277. — WORM AND WHEEL STEERING MECHANISM WITH ONE
PART CASING.

In steering gears of large size, where the worm diameter
does not limit the outside diameter of the hollow shaft so
closely, a tube with a three-sixteenth inch or even thicker wall
is used, which permits of securely keying the worm and hand
wheel to it, and the middle portion of the tube is turned
down in the lathe for weight economy.

For fastening the worm to its shaft the best plan would
seem to be to broach it out and mill, say, four grooves into
the outside of the steering shaft, but the most common plan
seems to be to use a single key.

426

THE STEERING GEAR.

Steering Gear Cases — There are three general types of
steering gear cases. These cases may be cast in a single
piece, with a separate end plate, as shown in Fig. 277; they
may be split in the plane through the worm axis and per-
pendicular to the wheel axis, as in Fig. 278, gr in the plane
of the wheel axis and perpendicular to the worm axis, as in
Fig. 279. The tendency in American practice, especially in
the low priced class, seems to favor the first construction.
The worm can be introduced either from the top or bottom,
and the wheel, of course, is introduced from the side. One
of the thrust bearings rests against the wall of the case and

FIG. 278. — WORM AND WHEEL STEERING MECHANISM WITH VER-
TICALLY DIVIDED CASING.

the other against a threaded bushing screwing into the
casing. This bushing is made slightly larger in diameter than
the worm, and is locked in position by a clamp screw which
contracts the neck of the case. The casing, as well as the
removable end plate, is cast with a bearing hub. which is
properly strengthened by ribs. The thrust on the worm wheel
shaft is taken up on thrust washers.

These cases are generally made of malleable iron, with a
wall thickness of three-sixteenth inch. The gears and bear-

THE STEERING GEAR.

427

ings are lubricated by means of grease contained in the case,
and a plugged hole is provided in the case for replenishing
the grease supply therein at intervals. However, the bearings
should preferably be provided with separate grease cups, par-
ticularly the top one.

Housings split in one of the centre planes are somewhat
neater in appearance, but involve more machine work. The
halves must be doweled, and, of course, several more bolts
are required for the joint than where only an end plate has
to be secured. This construction also facilitates assembling,

FIG. 279. — WORM AND SECTOR STEERING MECHANISM WITH CASING
DIVIDED THROUGH THE SECTOR Axis.

as the steering post can be completely assembled before the
housing is put in place, and, besides, the latter can be made
somewhat more compact, as it is not necessary to introduce the
worm and thrust bearings from the end.

Fig. 279, which shows the housing divided in a plane per-
pendicular to the worm shaft, also illustrates the use of a
sector instead of a complete wheel. Where a sector is used it
is customary to provide set screw stops, limiting the motion
of the sector, which makes steering stops on the front axle
unnecessary.

428

THE STEERING GEAR.

Screw and Nut Type Steering Gears — The screw and nut
steering gear consists of a multiple square threaded screw
and a corresponding nut, with trunnions on its outside,
carrying square trunnion blocks located in slots in the arms
of a forked lever, which is keyed or otherwise secured to the
steering arm shaft, or made integral therewith. The size
of the screw depends somewhat on whether the control shafts
are to be concentric with the steering post or outside of it.

FIG. 280. — SCREW AND NUT TYPE STEERING GEAR.

Let us call the distance between the screw and steering arm
shaft axes a. Then if the steering arm is to swing through a
maximum range of 60 degrees, or 30 degrees to either side
of its central position, the motion b of the nut along the
screw from the central to one of its limiting positions must be
such that

— = tan 30° = 0.577
a

Thus, if 0 = 3 inches, then

b = 3 x 0.577 =1,731 inches

THE STEERING GEAR. 429

and the total motion of the nut along the screw is twice this.
or 3.462 inches. If the screw be given a lead of 2^ inches
then the steering hand wheel will have to be turned through

2.5

in order to turn the front wheels through their entire range.
Now, suppose the screw has an outer diameter of 2 inches.
Then the angle of the thread at the circumference will be
such that

tan 6 — - ^ - = o. 398
2X 3-1416

6 = 21° 42'.

With a lead of 2.5 inches and quadruple thread the thickness
of the tooth will be

X 0.929 — 0.29 inch.

8
The depth of the thread is usually made equal to the width.

Double Screw Adjustable Gears — It has been attempted to
overcome the difficulty encountered in cutting the thread in
the nut by casting a babbitt thread in a steel sleeve provided
with holes to insure a good hold for the babbitt. Some of the
gears based on this principle have proven failures, probably
because the thread contract surfaces were too scanty. Of course,
even a slight amount of wear in the steering mechanism is ob-
jectionable, because it entails a very considerable play in the hand
wheel. Various schemes have been tried for taking up wear in
steering mechanisms, but most of them are either too expensive
for commercial work or else are objectionable for other reasons.
A very neat mechanical solution of the adjustment problem
is embodied in the double screw type of the Gemmer Mfg.
Co., illustrated in Fig. 281. Secured to the steering shaft D
is a steel shell C, which is provided with a left hand square
screw thread on its outer surface and a right hand thread on
its inner surface, the pitch of both threads being the same.
When shaft D is turned right handedly, sliding member B is
moved down and sliding member E up. These two sliding
parts press against opposite ends of a double armed lever F
secured to the steering arm shaft and cause the latter to turn
in its bearings, the power being transmitted through sliding
member B when shaft D is turned right handedly, and

430

THE STEERING GEAR.

through sliding member E when shaft D is turned left hand-
edly. Any wear on the threads can be taken up by screwing
the bushing A further into the housing.

Another combination often used in steering gears is a screw
and nut, together with a rack and spur wheel sector, the rack
teeth being cut on the outside of the nut.

FIG. 281. — DOUBLE SCREW TYPE STEERING GEAR.

Bevel Gear Steering Mechanism — Other mechanisms for
reducing the steering motion include a bevel pinion and sector,
a spur pinion and sector, a spur pinion and rack and a planetary
set. All of these gears are completely reversible, and with a
car fitted with any of them it is impossible for the driver to
take his hands off the wheel while in motion, and he feels the
road shocks more than with the type of gear previously de-
scribed. These steering mechanisms, therefore, are suited only
to cars of moderate speed capabilities or those having such an
arrangement of the steering pivots that practically no motion
can be transmitted from the wheel to the steering mechanism.

THE STEERING GEAR.

431

Owing to the reversibility of these gears the gear reduction
should be made as large as space limitations permit.

Fig. 282 illustrates the Reo steering gear which is of this type.
The thrust of the bevel gear sector is taken up on a steel roller,
and the steering motion is limited in a very simple manner by
leaving a portion at each end of the sector without teeth. Bevel
gear type of steering mechanisms have less need for housings
than the worm and wheel type, but some designers enclose them
also.

Support of Steering Gear. — If the knuckle arm to which
the drag link connects is below the front axle the steering

FIG. 282.— REO BEVEL STEERING GEAR.

arm can be placed inside the frame member — a construction
found on a considerable number of European cars. Where
the knuckle arm is above the axle this arrangement is impos-
sible, because the front spring would interfere with the drag
rod.

In this connection it is to be remembered that with the drag
link outside the frame it limits the possible steering motion to-
ward the side on which the steering gear is located, as the front
wheel will rub against the drag link before touching any other
part. This disadvantage may be overcome by placing the drag
link crosswise of the frame. In motor trucks having the motor
located underneath the driver's seat the steering mechanism

432

THE STEERING GEAR.

naturally comes in the right position for a transverse drag link,
and in touring cars it can be brought into the proper position by
giving the steering post a large inclination. In any case, the
aim in laying out the steering connection should be to minimize
the effect of front spring action on the steering gear. With a
transverse drag_link the link should be substantially horizontal
when the car carries a normal load, whereas with a fore-and-aft
drag link, with the car under normal load, the axis of the drag
link produced should pass through the centre of the front spring
eye — supposing the front spring to be pivoted to the frame in
front and shackled at the rear.

In touring cars the steering gear housing usually comes in
a rather cramped position between the engine and the frame.
It may be so placed that the worm wheel shaft passes either
through the web of the frame channel, above the channel
or below the channel. In most cases the shaft passes right
through the frame member. The housing is generally bolted
to the frame side member, being provided with a bracket
which fits into the opening of the channel. Again, the hous-
ing may be bolted to the top of the side member, to an
engine arm or to a cross member of the frame. A rigid

support is necessary ; and, besides,
it is well to remember that holes

g-F^H^I-R— \ rffr^Jtn through the flanges of a frame

7/^xpjy f^TTI channel greatly reduce its strength,

whereas holes through the centre
of the web have practically no
weakening effect.

Steering Arm — The steering
arm in a touring car is generally
from 7 to 9 inches long. The
knuckle arm in most designs is
made as long as the location of
the front springs permits, and the
steering arm the same length or
slightly longer. In a worm and
complete wheel type of steering
gear the steering arm is always fit-
ted to the squared end of the
wheel shaft, so as to permit of
turning the wheel through a quar-
ter circle. The hub of the arm is
split and clamped on the shaft, the

FIG. 283. — STEERING ARM.

THE STEERING GEAR. 433

clamping bolt passing slightly beneath the surface of the shaft.
When a worm wheel sector is used and the housing is
divided in the plane through the sector shaft the steering
arm and shaft may be forged integral, with a flange sector
on the shaft to which the worm wheel sector is bolted. Oc-
casionally, the steering arm is bent so that, although its hub
is located inside the frame, its connection to the drag link
comes outside the frame, so as to avoid interference with the
spring. A typical design of steering arm, with the usual pro-
portions, is illustrated in Fig. 283. It will be found that if
this arm is made of the same material as the wheel shaft it
is of substantially the same strength as the squared portion
of the shaft. When a worm wheel sector is employed instead
of a complete wheel the steering arm usually is secured to its
shaft with a tapered joint — a Woodruff key and castellated nut
being used.

Drag Link and Connectors — The drag link, which in tour-
ing cars usually extends directly fore-and-aft and in motor
trucks and cars of the raceabout type crosswise of the frame,
is usually made of the same cross section as the tie rod. This
practice is logical, at least if the tie rod is located back of the
axle and the drag link is of about the same length. However, if
the highest weight economy is desired the proper size of this tube
can be calculated by means of Rankine's formula for columns,
proportioning it so that its material will be strained to the elastic
limit when the rod is subjected to a thrust equal to the quotient
of the torsional strength of the steering arm shaft by the length
of the steering arm. In the better grades of cars, particularly
those provided with non-reversible steering gears, it is customary
to introduce cushion springs in the drag link joint so as to relieve
the shock. A length of tube of enlarged diameter is
screwed over the end of the tube forming the main part of
the drag link, or is pinned to it. As shown in Fig. 284, in-
serted into this connector housing are the following parts
in the order named : A coiled spring, a spring block with a
spherical depression, the ball end of the steering arm, an-
other spring block, another coiled spring and a screw plug
secured by a cotter pin. In this design the ball is passed
through a hole far enough to the end of the connector hous-
ing so that the ball can never get opposite it after all the
parts are in place. Sometimes the slot in the housing through
which the steering arm passes extends entirely to the end
of the housing, in which case a screw cap is used instead of

434

THE STEERING GEAR.

FIG. 284. — BALD AND SOCKET SPRING CUSHIONED CONNECTOR.

a plug to close the end of the housing. The spring cushioned
joint is generally placed at the steering gear end of the drag link,
the joint at the opposite end being made similar, but without the
springs. Both joints are generally enclosed in a laced leather
boot which is filled with grease.

Fig. 285 illustrates a front end connector of English design.
It is of the ball and socket type, but entirely different in prin-
ciple from the connector shown in Fig. 284. The ball is held
between two steel blocks, which are inserted into a fitting of the
general form of a chain link. The blocks are held between one
end of this link and the end of the connector rod, which latter

FIG. 285. — DRAG LINK FORWARD CONNECTOR.

THE STEERING GEAR.

435

passes through a hole through the hub at the opposite end of
the link. The chain link and connector rod are secured together
by means of a gland nut with differential threads, the thread on
the hub of the link being much coarser than that on the rod.
Thus, when the nut is screwed over the threads on the rod and
the hub, although both are right-handed threads, the link will be
moved relatively to the rod, and. thus the socket blocks will be
forced against the ball. When they have been properly adjusted
the nut is locked by means of a split pin.

Universal joints are necessary at both ends of the drag
link, because the steering arm moves in a vertical plane and
the knuckle arm in a horizontal plane, but instead of ball

FIG. 286. — FORKED CONNECTOR.

and socket joints, forked joints are sometimes used. These
are somewhat simpler in construction, and larger bearing
surfaces can be obtained than with ball and socket joints,
but they are not so easily enclosed in a grease filled, laced
leather boot, and are generally lubricated by means of a
special grease cup. The grease cup may be screwed into the
cross piece, as shown in Fig. 286, or into the end of the horizontal
pin.

Steering Wheel — Steering hand wheels are made 14 inches
in diameter for very small cars, 16 inches for medium sized
cars, 18 inches for large touring cars, and as high as 20 inches
for heavy trucks. The rims are made of either hardwood or
hard rubber. The section is generally oval, ixi^ inch and
il/ixil/2 inches being common sizes. The spider is made of brass

436

THE STEERING GEAR.

or aluminum, with either three or four spokes — generally four.
In commercial vehicle practice malleable iron spiders are used.
The spokes of brass and malleable iron spiders are mostly made
of oval section, but the spokes of aluminum spiders are made of
channel section or of T-section with large fillets to facilitate
buffing. For a 16 inch wheel with brass spider the spokes are
made about l^xfys inch near the hub and tapering down to
y%K$s inch near the rim. In an aluminum spider for the same
diameter wheel, the spokes, if of channel or T-section, are
made about ?/£ inch deep near the hub and y^ inch near the rim.

FIG. 287. — STEERING WHEEL WITH ALUMINUM SPIDER
AND BENT WOOD RIM.

There are two general designs of wood rims. The most
commonly used type, illustrated in Fig. 287, is secured to the
arms of the spider by means of wood screws. The other form,
used more particularly abroad and in the higher grade cars in
this country, has a ring cast integral with the spider, which is
let into a groove turned in a part of the wooden rim (see Fig.
288). The rims are made in different ways. In one construc-
tion, illustrated in Fig. 287, the whole rim is made of a single
piece of wood. First a solid piece of wood of square section

THE STEERING GEAR.

437

and the requisite length is sawed out, and its ends are cut with
wedge-shaped teeth about y^ inch wide and I to 1^4 inches deep.
It is then turned down to a circular or oval section, steamed
and bent to a circle of the right size to bring the pointed tenons
together, when they are glued and firmly pressed together in a
special clamp in which the rim is left until dry. Specially flexible
woods are used for this construction, as most woods do not al-
low of bending to such a small radius. Instead of making the
entire rim in one piece, it may be made in halves, with joints of
the type above described. A quarter inch dowel pin through the

FIG. 288. — STEERING WHEEL WITH LAMINATED WOOD RIM AND
OVAL ARM SPIDER WITH INTEGRAL RIM.

centre of the joint makes it more secure. Fig. 287 shows two
methods of securing the rim to the spokes of the spider.

Another method of making the rims consists in building them
up of segments. For the more expensive cars, rims of mahogany,
walnut or ebony are extensively used. As a rule, three layers of
segments of four or six to the circle are used, six being pre-
ferable, as there is not so much end grain where the segments
are joined together. After the segments are sawed out they
are glued up three deep into rings, and are then turned up in a

438

THE STEERING GEAR.

lathe. They are secured in the lathe either by being glued to a
wooden face plate with a sheet of newspaper between, or else
by means of a number of screws. Of course, if the spider is
cast with an integral ring, the final turning up of the rim has to
be done with the spider in place.

Vulcanized rubber steering wheel rims are coming into ex-
tensive use. The rubber is vulcanized onto a ring cast in-
tegral with the spider, and is provided on the inside with de-
pressions to fit the fingers, and on the outside with small

FIG. 289.— HARD RUBBER RIM WHEEL.

evenly spaced projections, so as to enable the driver to ob-
tain a firm grip of the wheel. A typical hard rubber steering
wheel is illustrated in Fig. 289.

In pleasure cars the steering shaft is generally enclosed in a
brass tube of iV inch wall thickness. Referring to Fig. 290, this
tube is set into a recess formed in the adjusting nut at the top
of the steering gear and usually forms a tight fit in a bracket se-
cured to the dashboard or to the toolboard. At the top it receives
a bushing for the steering shaft, or it may extend into a

THE STEERING GEAR.

439

recess turned in the hub of the steering wheel, in which case
the hub holds the casing concentric with the shaft and no bush-
ing is required. In some designs the steering shaft case ex-
tends down to the dash bracket only, and in commercial vehicles
it may be entirely omitted.

There is a great deal of variation in the inclination of the
steering column, depending upon the relative location of the

FIG. 290. — STEERING COLUMN.

steering mechanism and the driver's seat. In standard touring
car practice it is usually inclined about 45 degrees, and in the
more rakish types of cars, such as raceabouts, about 60 de-
grees. In order that the driver may be able to easily enter his
seat the steering wheel rim should not come closer than 8 inches
to the front edge of the seat cushion.

Adjustable Steering Column— Owing to the fact that
drivers vary a great deal in stature, some manufacturers con-

440 THE STEERING GEAR.

sider it expedient to make the rake of the steering column ad-
justable. This practice is particularly prevalent in England,
where bodies are built to purchasers' specifications, and it is
possible that this is another reason for providing adjusting
means, as the relation of the seat to the column determines the
comfort of the driver to a large degree. To make the steering
column adjustable, the bearing hubs of the steering gear case
are mounted in trunnion supports on the frame and the column
passes through a slot in the dashboard or toeboard, clamping
means being provided to secure it in different positions.

CHAPTER XVI.

CONTROL.

Spark and Throttle Control — The conventional location ot
the spark and throttle control levers is on top of the steering
column. A sector of hardened steel is secured by screws to a
double armed brass bracket which is fixed to a stationary tube
concentric with the steering post. Usually the bracket is clamped
to the tube, though some makers fasten it by means of a screw.
The spark lever is usually secured to the central rod by pinning,
and the throttle lever to the tube surrounding this rod by clamp-
ing.

The angular extent of the sector may be anything from about
75 degrees to a complete circle. The former size of sector is
used if the connections from the lower ends of the spark and
throttle shafts are to be made direct by levers and links. This
is the simplest construction, but it is obvious that a much finer
control is possible if the range of the finger levers is greater,
and for this reason a reducing gear of some kind is usually in-
troduced in the control mechanism at the bottom of the steering
column. In American touring car practice it is customary to
use a sector of 180 degrees or slightly less, whereas in European
practice 90 degree sectors are very common. The 180 degree
sectors are so placed that the ends of the sector lie in the fore
and aft direction, the sector extending to the right from the
steering post. Forward motion of the levers advances the spark
and opens the throttle.

Some means must be provided for automatically holding the
control levers in any position in which they are placed. The
most common arrangement consists in providing the steel sector
with ratchet teeth on both edges, and the finger levers with a
spring pressed pawl which engages with the teeth on the sector.
The ratchet teeth are cut with an angle of about 90 degrees, so
that if a tangential force is applied to the lever arm the pawl will
slide freely over the notched sector. A typical design of control
levers is shown in Fig. 291.

441

442

CONTROL.

In another design of control levers an arm of spring metal is
riveted to a brass hub and provided with a hard wood or hard
rubber knob on the outer end. In this case the flat side of the
steel is placed vertically, and the under and upper edges are
notched, wedges secured to the levers by means of rivets engag-
ing with these notches. Probably a somewhat neater design
would be obtained by saw slotting the lugs on the lever centres,
placing the spring steel arms in the saw slot, and countersinking

FIG. 291.— RATCHET CONTROL.

the holes for the rivet heads. In the design shown in Fig. 292
the throttle lever must be pressed down and the ignition lever
raised up in order to move them easily. By using two sectors it
is possible to arrange the levers so that both of them can be
released by pressing on them, which method of operation may be
considered preferable, for the reason that the weight of the hand
naturally rests on the levers. The ratchet teeth should not be
over ^s inch deep, so the lever can be moved with as little noise
as possible.

CONTROL.

443

Fig. 293 illustrates a design of friction levers. On top of the
stationary tube in the steering column is mounted a cylindrical
brass box. with a horizontal slot on one side through which the
control levers extend. An extension of each lever arm to the
opposite side of its axis carries a friction segment which is
pressed against the inner wall of the cylindrical housing by a
coiled spring. The pressure of this spring can be adjusted by
means of a nut and lock nut.

FIG. 292. — SPRING LEVER CONTROL.

Ball Wedge Locking Device. — Fig. 294 illustrates a mechan-
ism widely used on European cars for securely holding control
levers in any position in which they may be set. The mechanism
consists of a stationary housing A, which is usually part of the
bracket by which it is supported. E is the control lever and B
the operated lever. Formed integral with lever E are two lugs
F F, extending between the wall of the housing A and a cam C
on the shaft of lever B. In the recess between the two lugs F F
are located two steel balls with a coiled spring between them.
The cam surface and the inner wall surface of the housing are
eccentric, and are so spaced relative to each other that the steel

444

CONTROL.

balls do not quite contact with the lugs FF when no pressure
is being exerted on the lever E. The wedging effect of the balls
between the two non-concentric surfaces securely locks the lever
B in place. It will, moreover, be seen that lever B is locked
against motion in either direction, each ball locking it against
motion in one direction. If lever E is turned in a particular
direction, one of the lugs FF presses against the ball near it.
slightly compressing the spring, and the other lug then abuts'
against the arm of lever B, so that any further motion of lever
E entails a corresponding motion of lever B. One of the pre-
cautions to be observed in the design of the device is to see that

FIG. 293. — FRICTION CONTROL.

the clearance between the balls and the lugs FF, when lever E
is not under pressure, is slightly less than the clearance between
these lugs and the arm of lever B. The inner wall of the hous-
ing and the cam surface are grooved to fit the contour of the
balls, so as to distribute the pressure over a larger surface and
prevent injury to the balls. The condition necessary that the
lever may be locked securely is that when the ball is in the locking
position the tangents at its two points of contact make with each
other an angle which is less than twice the angle of friction.

When applied to a control gear on top of the steering column,
lever B in Fig. 294 is replaced by a small lug on cam C, with

CONTROL.

445

which the lugs F F may engage, and cam C is fastened to the
central shaft by which the motion is transmitted. This locking
device is used even for such important parts as the emergency
brake lever, but where the effort to be transmitted is consider-
able two or three pairs of balls are used and a cam with three
cam surfaces.

Owing to the fact that the control levers have a motion of
about 150 degrees, whereas a lever arm transmitting motion
through a link does not work advantageously beyond a range
of about 90 degrees, the motion of the control shafts has to be
reduced in some way, and this is now generally accomplished
by means of a pair of small bevel gears or bevel gear sectors
at the bottom of the steering column. As shown in Fig. 295,

FIG. 294. — BALL WEDGE CONTROL LOCK.

the bevel gears or sectors are secured to the lower ends of
concentric vertical shafts carried in a bearing which is gener-
ally clamped to a bracket cast integral with the steering gear
housing. Sometimes the bearing bracket is formed integral
with the bottom plate of the steering gear housing to which the
stationary tube carrying the finger lever sector is fixed. Where
there are several concentric shafts, as in this case, if they are to
be prevented from rattling, it is necessary that a bearing bushing
be provided for each shaft, rather than to rely upon the fit of
one shaft in the other.

Instead of a bevel pinion and sector, a pair of screws and
nuts may be used for transmitting the control motion at the
bottom of the steering gear housing. The more elaborate de-

446

CONTROL.

signs provide a screw, nut and trunnion mechanism of the same
type as used for steering cars, the whole mechanism being
inclosed. In the simpler designs the nut and its trunnions are
dispensed with, a pin projecting laterally from a lever arm ex-
tending into a spiral slot cut yi a cylinder secured to the con-
trol shaft.

Bowden Wire Mechanism — The Bowden wire mechanism,
which is used to some extent for the control of the throttle and
the timer, more particularly in England, consists mainly of two

295. — CONTROL REDUCING GEAR.

parts, a closely coiled and practically incompressible spiral wire,
constituting what is termed the outer member, and a practically
inextensible wire cable threaded through the above, and known
as the inner member. The principle of the mechanism is illus-
trated in Fig. 296. A is the actuating lever; B, the operated
lever; C, the inner member; D, the outer member; E, an adjust-
able stop ; F, a lock nut, and G, the abutments or brackets. It is
obvious that since the outer member is incompressible and the
inner member inextensible, if the lever A is moved around its

CONTROL.

447

fulcrum, the end of lever B will be moved with relation to the
abutment G.

Control Levers on Steering Post. — Fig. 297 illustrates a
construction in which the control levers are mounted on the
steering post underneath the steering wheel. This design is used
more particularly on commercial cars and the lower priced pleasure
vehicles, being probably the simplest possible arrangement of the
control. The shafts for the spark and throttle are arranged con-
centrically and are supported in bearings secured to the steering
column. A sector is also cast integral with the top supporting

FIG. 296. — BOWDEN WIRE MECHANISM.

bearing, and the control levers are pressed into contact with the
sector by means of a coiled spring surrounding the power part
of the central control shaft, the spring pressing the tubular
shaft upward and the solid shaft downward. Lever arms are
secured to the lower ends of these shafts, and connection to the
throttle and tinier is made by links direct. The sector on which
the levers move extends over an angle of about 90 degrees, and
is usually placed in front of the steering column, as this location
is most convenient for making connections from the lower ends
of the shafts.

448

CONTROL.

FIG. 297. — CONTROL LEVERS ON STEERING POST.

FIG. 298.— CONTROL JOINTS.

CONTROL. 449

Control Joints. — In the connecting linkage, if two lever arms
to be connected swing in the same plane a forked connector is
employed, and a standard for such connector yokes and eyes has
been worked out by the Society of Automobile Engineers. If
the two arms do not swing in the same plane, as is often the
case, a ball and socket type of joint is used. The links of the
control mechanism are generally made of cold rolled steel, seven-
thirty-seconds or one-quarter inch in diameter, and one part of
the joint is screwed over the end of the rod. In cars sold at
a very low price the end of the rod is sometimes bent at right
angles and passed through a hole of slightly greater diameter
in the end of the arm, a split pin being passed through the end
of the rod. This type of joint rattles more or less, and is not
very satisfactory. Fig. 298 shows three types of ball and socket
joints for carburetor and spark connections. The one shown at
A consists of a brass socket and a steel ball, the brass socket
being bored out and having the edges spun in after the ball is
in place. A well designed type of joint is shown at B. This
resembles a steering drag link joint, except that only one spring
is used whose object is to firmly press the socket blocks against
the ball. No play can develop in a joint of this type, and there-
fore it remains free from rattle. The joint shown at C is similar
except that the spring is missing and D shows the simple joint
above referred to.

In cars which have two independent ignition systems it is neces-
sary to make connection from the spark control to the two
timers, and this is often accomplished by securing a bell crank to
the top of the short vertical shaft shown in Fig. 295. On the other
hand, many cars have been built in recent years, particularly
abroad, without manual spark advance, and in that case only a
single control lever has to be accommodated on the steering post.

Usually at least one of the devices that must be connected to
the control levers is located on the opposite side of the chassis
from the steering column, and tfie connection to it must then
pass either around or through the engine. A short shaft may be
carried in bearing brackets secured to the forward side of the
dashboard, or to uprights rising from the sub- frame, but some
manufacturers pass a shaft transversely through the engine base
underneath one of the crankshaft bearings, thus eliminating un-
necessary linkage. Great care is latterly exercised by designers
to make the control linkage as simple and unobstrusive as pos-
sible. Thus, in the Fiat car the connecting link to the timer is run
inside the sub-frame channel.

450

CONTROL.

Accelerator Pedals— Most modern cars are fitted with both
hand and foot control of the throttle. The throttle foot control
device, generally referred to as the accelerator, assumes different
forms, and three designs are illustrated in Figs. 299 and 300.

FIG. 299. — ACCELERATOR PEDALS.

The one shown at A, Fig. 299, is a pedal of the piano type,
being pivoted to a bracket secured to the dashboard. At B, Fig.
299, is shown an accelerator which has a motion around a vertical
axis, and is operated by a sideward motion of the forward part

CONTROL.

451

of the foot, with the heel resting on
the footboard. The bearing bracket
for this lever is also secured to
the dashboard, but in a much lower
position than that for design A. In
the design shown in Fig. 300 a
foot button is used, together with
a bell crank carried by a bracket
secured to the under side of the
toe board. All three designs have
their adherents and all give satis-
factory results.

Throttle Linkage. — The method
of connecting up the throttle with
the hand and foot controls is illus- FIG. 300. — ACCELERATOR
trated in diagram in Fig. 301. In FOOT BUTTON.

this figure A represents the lever at the bottom of the steer-
ing column. Through the boss at the outer end of this lever
passes a rod which joins to the throttle arm. It will be noticed
that arm A contacts with a collar on the control rod on one
side and with a coiled spring on the rod on the opposite side.
The accelerator pedal B connects with the throttle lever through
a control rod with an oblong hole at one end through which
passes a pin extending laterally from the arm of the pedal. The
accelerator pedal is normally held in the off position by a coiled
spring anchored to a stationary part of the car.

The hand control mechanism is so arranged that by moving
the throttle lever on top of the steering column through its entire
range the throttle valve is only about half opened, and the

Fir,. 301. — DIAGRAM OF THROTTLE CONTROL LINKAGE.

452

CONTROL.

throttle can only be fully opened by depressing the accelerator
pedal B. Operating the hand lever does not affect the position
o.f pedal B, because the control rod connecting the pedal to the
throttle arm has a sliding connection with the pedal. If the
throttle is fully opened by means of the accelerator pedal and
the driver then removes his foot from the latter, the throttle
will return to the position for which the hand lever is set. The
spring around the control rod which connects arm A to the,
throttle arm permits of fully opening the throttle by means of
the accelerator pedal, even though the hand throttle lever may
be set in the position corresponding to closed throttle.

FIG. 302.— GOVERNOR THROTTLE CONTROL (AUTOCAR).

Motor trucks generally have their motors fitted with gov-
ernors and require a special control mechanism. Two separate
throttle valves may be used, arranged in the intake passage one
above the other, one connected with the governor, the other con-
nected to hand and foot controls, or simply to a hand control.
The throttle controlled by the governor will remain fully open
until the motor attains the speed for which the governor is set,

CONTROL. 453

when it will begin to close. A simpler and more common method
is to use only a single throttle valve to which the governor is
connected by a slotted link. Fig. 302 shows the mechanism em-
ployed on the Autocar light truck. The engme is ordinarily
under the control of the governor, but the driver may close the
throttle independent of the governor.

Clutch and Brake Pedals — What may be called the conven-
tional arrangement of the control for cars fitted with sliding gear
transmissions, comprises two pedals located on opposite sides of

FIG. 303. — TYPES OF CONTROL PEDALS.

the steering post, the one on the left being the clutch pedal and
the one on the right the brake pedal. The accelerator, if one is
provided, is placed either between or to the right of these pedals
for operation with the right foot.

Where a unit power plant is used the pedals are sometimes
carried on the clutch housing, but the more common plan is to
provide a tubular shaft extending partly or entirely across the
frame, which is carried in bearing brackets secured to the frame.
One pedal is secured to this shaft, and the other is free upon it
or is secured to a hollow shaft telescoping over the other one.

There are two general types of control pedals, the straight
and the bent type, as illustrated in Fig. 303. The pedals, of

454

CONTROL.

course, have to pass through the toe board, and if they are
straight they require a long slot in this board, whereas if they
are bent, like the one shown at A, they require only a compara-
tively small hole to pass through. The straight pedal is lighter,
but the bent pedal is now usually used because there is an ad-
vantage in having the driver's compartment closed off from the
engine compartment as far as possible, so that a minimum of heat
and noxious gases from the engine will reach the occupants.

Pedals vary in effective length from 12 to 16 inches. They are
generally drop forged, and the section is made either I or T
shaped, oval or rectangular, the I and oval sections predominating.

FIG. 304. — ADJUSTABLE PEDALS.

A 14 inch pedal usually has a section modulus near the hub of
0.10 to 0.12, while near the pad the section modulus may be re-
duced to one-fourth this value. Usually the dimension of the
section in the plane of greatest stress is made equal to about
twice its other dimension, but if the pedal is much off-set side-
ways, as is sometimes the case, it must be made stronger later-
ally. The inclination of the toe board in American touring cars
varies from 35 to 45 degrees and this approximately deter-
mines the location of the big end of the bent pedal in the position
of rest. The lighter end of the pedal should approximate an arc
of a circle with the pivot axis as a centre, but usually it is turned
so the pad comes somewhat higher.

CONTROL.

455

when it will begin to close. A simpler and more common method
is to use only a single throttle valve to which the governor is
connected by a slotted link. Fig. 302 shows the mechanism em-
ployed on the Autocar light truck. The engine is ordinarily under
the control of the governor, but the driver may close the throttle
independent of the governor.

Adjustable Pedals — Considerable attention has been paid
in late years to the problem of comfort for the driver, and this
has led to the introduction of adjustable pedals. It is evident

FIG. 305.— PEDALS ADJUSTABLE AT THEIR HUBS.

that a pedal suitably located for a tall person is quite incon-
venient for a person of short stature, and vice versa. These
adjustable pedals are usually bent at a right angle. Fig. 304 shows
four different designs. In design A the pad is secured to a
round rod fitting in a hole through the upwardly turned part of
the pedal proper. The rod is drilled with a number of transverse
holes, and may be secured in any one of several positions by
means of a through bolt. In design B the shank of the pad
is threaded and is clamped in the hub of the pedal by means of
two nuts. In design C the pedal itself is made of I section, and
the pad is made with double shanks fitting into the hollows in the

456

CONTROL.

s'des of the I, the two parts being clamped together by two
through bolts, which may be passed through different holes in
the pedal. This is one of the neatest designs of adjustable pedals,
since the small end of the pedal may have the usual curvature and
the section where the parts are joined is rectangular. In design
D the shank of the pad is threaded and screwed into the drilled
and threaded portion of the pedal, which latter is slotted and
clamped tight on the shank.

Control pedals may also be adjusted at their base, and two
methods of accomplishing this are illustrated in Fig. 305. In
either case there are a free and a tight hub. In design A the

FIG. 306.— PEDAL PADS.

tight hub has two lugs with coaxial set screws, between the
points of which is located a lug projecting laterally from the
pedal. In design B the tight hub is provided with a slotted sec-
tor, cut with radial grooves on one side, to which the pedal can
be clamped in different positions.

Pedal Pads— Pads are either secured rigidly to the pedal or
hinged thereto. In the former case they are usually made con-
vex toward the rear, so that as the pedal turns around its ful-
crum a section of the pad always fits squarely against the sole
of the driver's shoe. On the other hand, if the pad is hinged to
the pedal it is made either plane or slightly concave, and in the
higher grades of cars a spring is provided to hold the pad in

CONTROL. 457

position when the foot is removed, so as to prevent rattling.
Generally, however, the swiveled pad is allowed to hang in posi-
tion under its own weight. Various means are resorted to in
order to prevent slipping of the foot on the pad, the most com-
mon being the formation of diamond shaped points by forming
V-shaped grooves on the surface of the pad diagonlly in two
directions, these grooves being either formed in a drop press or
cast on. (See A, Fig. 306.) Another method consists in provid-
ing the pad with either one or two ears, and several models in
the higher priced class are provided with rubber covered pads.
(B, Fig. 306.) These rubber coverings are used together with
ears on the sides of the pad, and are evidently intended to pre-
vent slipping of the foot in the direction of motion only.

There is absolutely no uniformity with regard to the form and
dimensions of the pads. They are made square, rectangular, oval
and round. If ears are provided on both sides the pad should be
at least 3^ inches wide, but if no ears are used it is sometimes
only 2l/2 inches wide. Some pads are larger in the fore and aft,
others in the transverse direction.

Most clutches are disengaged by drawing them to the rear,
and in the case of such clutches the pedal shaft is located on top
of the clutch shaft. However, some forms of clutches, like the
inverted cone clutch, are disengaged by a forward motion, and
in this case it is more convenient to have the pedal shaft run
underneath the clutch shaft. The latter arrangement has a
further advantage in that if the service brakes act on the rear
wheels the brake arm on the pedal shaft has to extend upward
and comes in a more convenient position if the shaft is located
lower. It is generally endeavored to place the clutch collar and
pedal shaft in such relative positions that the shipper arms on
the pedal shaft may connect directly to the clutch collar, but if
this is not possible a pair of links may be interposed between
the shipper arms and the clutch collar. The leverage of the
clutch pedal is made between 4 and 6, depending upon the clutch
spring pressure and structural considerations.

Interconnection of Clutch and Brakes— Formerly it was
customary to interconnect both brakes with the clutch, so that
if either brake were applied the clutch would first be disengaged.
The idea which first led to this construction was, undoubtedly,
that if the driver wants to stop quickly he should simultaneously
disconnect the engine and apply the brake, so the driving effort
of the engine ceases and no braking effort need be expended in
dissipating the energy stored in the flywheel. The intercon-

458

CONTROL.

nection is usually accomplished, in the case of the foot brake,
as illustrated in Fig. 307, a projection on the hub of the brake
pedal engaging with a projection on the clutch pedal whenever
the brake pedal is moved to apply the brake. In the case of the
hand brake the connection is made by means of a link connect-
ing arms on the clutch pedal shaft and the brake lever shaft, re-
spectively, with a sliding joint at one end so that the clutch
can be disengaged without applying the brake. One disadvantage
of interconnection is that with this scheme it is not possible to
use the engine as a brake and use the mechanical brakes at the
same time. For this reason the interconnection was first limited

FIG. 307. — SERVICE BRAKE INTERCONNECTED WITH CLUTCH.

to one brake and is now generally dispensed with altogether.
As a matter of fact, with the clutch and brake pedals in the
usual position, it becomes second nature for the driver to press
on both of them simultaneously if he wants to make a quick
stop.

Single Pedal Control— In several makes of cars the clutch
and service brakes are operated by a single pedal. The first mo-
tion of the pedal releases the clutch and a continued motion
applies the brake. This necessitates a special operating mechan-
ism for the clutch. One arrangement, involving the use of a

CONTROL.

459

FIG. 308.— SINGLE PEDAL CONTROL, TOGGLE TYPE.

FIG. 309.— SINGLE PEDAL CONTROL, CAM TYPE.

460 CONTROL.

toggle mechanism, is illustrated in Fig. 308, and another involving
the use of a cam mechanism is shown in Fig. 309. In the former
case the clutch collar is moved relatively rapidly during the first
motion of the pedal and more slowly as the motion of the pedal
proceeds. With a cam mechanism the motion of the clutch
collar stops entirely after the clutch is fully disengaged, that
portion of the cam coming last under the cam follower being con-
centric. In order to prevent an unduly large release motion of the
clutch bands it is well to provide a sliding joint at the forward
end of the brake rod (Fig. 308). This combination of clutch and
brake control in a single pedal works very satisfactorily, but, of
course, the pedal must have a somewhat greater range of motion
than when it operates either the clutch or brake alone. The two
pedal control has however practically become standardized and it
is likely that single pedal control will disappear entirely.

Pedal Shaft Assembly. — In some designs of cars employing
a housing for the clutch, the clutch pedal is supported by this
housing and the brake pedal by a bracket secured to the frame
side member. In cars with a sub-frame the pedal shaft bearings
can- be secured to this frame, whose top surface is usually 1 to 1J4
inches above the clutch axis. Some designers secure these bear-
ing brackets to the front side of a frame cross member and
others to the inside of the frame side channels.

Right, Left and Centre Control.— Formerly the steering
column was nearly always placed on the right side of the car, and
the hand levers for operating the change gear and emergency
brakes were located just outside the driver's seat on the right.
Lately, however, more and more cars have the steering post on
the left hand side and the hand levers in the centre. Centre con-
trol may also be combined with right hand drive, and left hand
control with left hand drive. The argument in favor of left steer-
ing is that with the rule of the road compelling drivers to keep
to the right, they can much better gauge the clearance when
meeting other vehicles, if they are seated on the left side. On
the other hand, the driver is at a disadvantage when overtaking a
vehicle or drawing up at the curb, as he is then on the "off"
side. The advantage of control levers on the left side is that if the
vehicle is drawn up alongside a curb both the driver and front seat
passenger can get into the car without first walking half way
around it. However, if the levers are on the left hand side they
must be operated by means of the left hand, which usually is not
as dexterous as the right hand. This is one of the reasons for

CONTROL.

461

the increasing popularity of centre control. Another reason is
that if the change gear lever is located at the centre it may be
mounted directly on top of the change gear box, thus doing
away with superfluous connections. Finally, if the gear and brake
levers are in the centre the outside of the body is smoother or
"cleaner."

FIG. 310.
THUMB LATCH LEVER.

FIG. 311.
SPOON LATCH LEVER.

Control Levers. — Brake and change gear hand levers are
generally drop forged with a rectangular, oval or I section, but
cast steel or bronze levers are also used. In pleasure cars the
length of these levers generally varies between 20 and 24 inches,
depending upon the height of the seat The maximum pressure
which a driver is ever likely to exert against these levers is 100

462 CONTROL.

pounds. Thus, if the length of the lever from the axis to the
middle of the handle be 20 inches, the bending moment at a dis-
tance of 1 inch from the axis is 2,000 pounds-inches. Now, let
us suppose that the section is to be rectangular, with a height
twice the width. Then, for a stress in the material of 15,000
pounds per square inch, the equation of moments is

b d* d3

15,000 = 15,000 — = 2,000

6 12

<f = 1.6

d = 1.17— say, 1 3/16 inch

b = 19/32 inch
An elliptic section of twice the height as the width has a sec-

ds
tion modulus of — approximately, and the necessary height d

for the above case figures out to 1.385 — say, \Y% inches. For
light cars the section of the levers can be calculated on the basis
of a maximum pressure of 50 pounds, because on these cars less
effort is required to operate the gears and brakes and the driver
knows that he cannot expend his whole strength on the levers.

The change gear lever of selective type change gears moves
in an H sector or gate, and does not require a latch to hold
it in position. However, a latched lever is always used with
the progressive gear control, and the emergency brake lever is also
provided with a latch. There are two general types of latch
levers, illustrated in Figs. 310 and 311, respectively. The former
is known as the thumb latch and the latter as the spoon latch.
The operation of these latches is self-evident and need not be
described. Both levers illustrated are designed as brake levers,
and it may be pointed out that if the lever is a "push lever, '
applying the brakes as the driver pushes it away from himself,
the latch spoon must be on the forward side of the grip, whereas
if it is a "pull lever" the latch spoon must be on the back. The
hand grip is generally made of circular section, and often it is
covered with a brass tube which is screwed or welded on. Plating
the grips has proven unsatisfactory, as even a heavy coat of plate
soon wears off. If no brass casing is used the handle is gener-
ally made tapering, with the largest diameter at the top. For all
except the smallest cars the handle can be made $4 mch in
diameter if parallel, and from ^ to ^ inch if tapering.

The two levers are generally arranged to turn about a com-
mon pivot axis, and the brake lever is the one farthest away
from the driver. Near its big end it is provided with a central

CONTROL.

463

FIG. 312. — SLIDING LEVER SELECTIVE GEAR COVT

464 CONTROL.

slot through which passes the ratchet sector. Ball ended change
gear levers are now used to quite an extent. In England balls
of hardwood are sometimes forced over the top ends of the
levers and held in place by screws. The levers are often bent
laterally because of the bulging form of the body and in order
that there may be plenty of clearance between the grips of the
two. It is also a good plan to make the brake lever of such
length that its grip comes somewhat higher than that of the
gear lever.

Selective Control. — There are three general systems of se-
lective control. The first of these comprises a sliding shaft
to which the control lever is rigidly secured and which at its
inner end carries a downwardly extending arm which is adapted
to engage into a slot on one or the other of the sliding bars.
A typical control of this type is illustrated in Fig. 312. The gear
control lever A is clamped to the hollow shaft B which at its
opposite end carries the arm C, whose free end is adapted to
engage into slots on the slider bars DE. Lever A moves in the
sector. When it is in the slot nearest the car frame, arm C con-
nects with slider bar E which controls the first speed and reverse
gears. Moving the hand lever to the rear gives the first forward
speed, and moving it to the front the reverse. When the hand
lever is in the slot farthest from the car frame, arm C connects
with slider bar D, and moving the lever forward gives the inter-
mediate speed, while moving it backward gives the high speed or
direct drive. Arm F controls the locking bar G, shifting it in the
direction of its axis the same distance as the tubular shaft B is
shifted by means of levers A. The slider bars are provided with
a slot on their under side which allows the locking bar to pass
when they are in the neutral position. The locking bar has a slot
on its upper side, and when this slot is underneath a slider bar it
allows that bar to be moved in the direction of its length, while
the other bar is locked in position. A spring-pressed ball engages
with conical holes in the slider bars, to help the driver find the
position of correct mesh.

The second type of selective gear control, known as the swing-
ing lever control, is illustrated in Fig. 313. The control lever
is pivoted to a hub which is free to turn on the control shafts.
At the sides of the control lever there are two short levers,
which are fast upon concentric control shafts. Each of the con-
trol shafts carries an operating arm inside the frame member,
each operating arm being connected to one of the slider bars.
The upwardly extending arms are provided at their upper

CONTROL.

465

end with lugs bent at right angles, between which lugs the con-
trol lever engages when it is pressed in the direction of the par-
ticular short lever. The control lever is normally held in the
neutral position by two flat springs secured to the two short
levers, respectively. Thus, when the control lever moves in one
of the slots of the quadrant it is connected to one of the short
levers and turns the control shaft to which that short lever is
secured. Vice versa, when the control lever moves in the other
slot of the quadrant, it operates the other short lever, and, con-

FIG. 313. — ROCKING LEVER SELECTIVE GEAR CONTROL.

sequently the control shaft to which that lever is secured. The
slotted ends of the short lever arms may extend right into the
H quadrant.

The third type of gear control is represented by the ball-
supported lever class of which the Reo, illustrated in Fig. 314,
was the prototype. This is used exclusively for centre con-
trol as the gear level is mounted in a tubular projection cast
on the cover plate of the gear housing. The lever has a ball
support on two rings of bearing metal of which the lower is
fitted against a shoulder in the tubular projection and the

466

CONTROL.

CONTROL. 467

upper is held in place by a sheet metal cap drawn down by
coiled springs anchored to the cover plate.

The lower end of the lever is of flat cylindrical shape and is
adapted to engage into slots in the sliding bars .A A. Trans-
verse holes are drilled through these sliding bars at that part
where the slots are, and each hole contains a steel plug B.
This plug is reduced in diameter at the middle of its length
and a pin C, shown in dotted lines, !s put through the sliding
bar in such a position that it passes through the depression
of plug B and prevents the latter from falling out when the
sliding bar is handled separately, as in the repair shop. Lock-
ing bolts D D are located in bosses cast on the cover plate
and are forced by coiled springs toward the sliding bars. The
reduced inner end of these locking bolts is of the same dia-
meter as the hole in which the plug B is located. With the
gear lever in the central position, as shown, both sliding bars
are locked and the lever, therefore, cannot be moved in a fore-
and-aft plane. If the ball handle of the lever is swung to the
right the lower end of the lever will force the plug B entirely
into the left sliding bar, forcing the locking bolt out of it,
whereupon the sliding bar may be slid forward or backward
to engage the gears. Meanwhile the right sliding bar is se-
curely locked against endwise motion. It will be noticed that
the shipper levers are screwed over the sliding bars for pur-
poses of adjustment.

While all the different designs of selective control may be
classed under one of the above heads, there are numerous vari-
ations in detail. Thus, the swinging lever, instead of being pivoted
at its end, may have the pivot at some distance from the end,
and the end may be connected to a sliding shaft adapted to engage
with one or the other of the slider bars. In some designs a con-
trol lever is pulled by a spring in the direction of the outer slot
in the quadrant, one advantage of which is that there is little
danger of inadvertently engaging the reverse gear when chang-
ing from low to second, or from high to second.

In the past considerable trouble has been experienced in the
operation of cars because of the lack of uniformity in the ar-
rangement of selective gear quadrants, that is, the relative
arrangement of the different gear positions. This made it awk-
ward for a driver accustomed to one make of car to drive
another with the gear positions differently arranged, and even
involved an element of danger. In order to do away with this
state of affairs the Society of Automobile Engineers undertook

468

CONTROL.

FIG. 315.— S. A. E. GEAR LEVER
POSITIONS.

FIG. 316. — REVERSE SLOT BLOCK.

the work of selective gear quad-
rant standardization and
evolved the preferred arrange-
ment shown in Fig. 315. The
brake lever is usually pulled to
the rear in order to apply the
brake, although there is also
some variation from this prac-
tice.

In selecting this quadrant
one point that was kept in mind
was that it is desirable to have
the gear lever in the high speed
position far removed from the
brake lever in the off position,
so that there is no danger of
accidentally getting hold of the
gear lever when wishing to
stop quickly in an emergency.
Further, with control levers in-
side the body, it is desirable to
have them close together in the
lateral direction when the gear
lever is in the high gear posi-
tion (which it is most of the
time) so there will be the least
interference with lap robes, etc.

Reverse Lock- Out. — In

order to obviate the possibility
of accidentally engaging the
reverse gear, a block is provided
which blocks the slot corre-
sponding to the reverse until
after a latch bolt has been
drawn out of place. Such a
block is illustrated in Fig. 316.
The change gear lever is pro-
vided with the usual thumb
button, which, however, is not
pressed as long as the driver
wants to drive in the forward
direction. This thumb button

CONTROL.

469

connects with a short double armed lever pivoted on the side of
the gear lever, with a down turned forward end which abuts
against a raised portion on the H quadrant as the gear lever is
about to enter the reverse slot. The operator must then press on
the thumb button before the reverse gear can be engaged.

Clutch and Change Gear Interlock — In order to prevent
shifting of the gears while the clutch is engaged, some designers
provide an interlock between the gear sliding and clutch operat-
ing mechanism. This may be so arranged that the gear
cannot be shifted unless the clutch is out, and the clutch can-
not be engaged unless the gears are in full mesh. Of course
the former function is the most important and some interlocks

FIG. 317. — CLUTCH AND GEAR INTERLOCK.

are designed for it alone. A diagram of one arrangement is
illustrated in Fig. 317. A sector is. secured to the gear lever
shaft and has a slot across its face parallel with the shaft into
which a latch bolt engages when the gear lever is in the neutral
position. This latch bolt is operated by means of a linkage from
the clutch pedal shaft. It will be seen that with the latch bolt
in the slot on the sector the gear lever cannot be moved into
any of the slots of the gate.

In pleasure cars the range of motion of the brake lever handle
should not exceed 16 inches, and the gear lever motion should
be less for the sake of convenience in operation. Selective gear
control levers generally move only about 8 inches. Control shafts
and other parts of a large car should be designed to have a
resisting moment of 2,000 pounds-inches, with a stress of about

470

CONTROL.

15,000 pounds per square inch for low carbon steel. English
designs generally make their gear quadrants in the form of a
box, the object being to protect the selector mechanism and its
bearing from mud, etc.

FIG. 318. — TURNBUCKLE ADJUSTMENT FOR BRAKE ROD.

Brake and gear control shafts are generally arranged con-
centrically, though occasionally they are carried in separate bear-
ings parallel and close together. When arranged concentrically
the brake control shaft is mostly the inner one, though the reverse
arrangement is also met with.

Brake Rod Adjustment. — Fig. 318 shows a turnbuckle ad-
justment for brake rods which is provided with a handy locking
device. The ends of the two rods connected are threaded right
and left respectively. A clamp made of sheet brass is hinged

FIG. 319.— SCREW ADJUSTMENT FOR BRAKE ROD.

to the buckle and its opposite end is forced over^a flattened por-
tion of one of the rods, thus preventing unscrewing of the
turnbuckle. Another form of adjustment, seen particularly on
French cars, is shown in Fig. 319. The rod is shown screwed
through the pivot pin, but it may also be held between two nuts
on opposite sides of the pin. It is customary to make the
diameter of the trunnion equal to twice the diameter of the rod.

CHAPTER XVII.

THE FRAME AND ITS BRACKETS.

Automobile frames are almost exclusively made of pressings
from sheet steel. Laminated wood and armored wood frames
are used by a few manufacturers of pleasure cars, and rolled
section steel frames by some makers of commercial cars.

Materials. — Originally pressed steel frame members were
made of cold rolled Bessemer steel, with a carbon content of
about 0.10 per cent. Bessemer steel has since been discarded
in favor of open hearth steel, and while cold rolled sheets are
still used in most cases, hot rolled stock has also come into
use. Frames are also made of chrome-nickel steel. Alloy
steel frames are now always heat treated, it having been found
that without heat treatment the gain in elastic limit hardly war-
rants trie additional cost of the special steel.

The most widely used frame material at the present time
is open hearth carbon steel of about 0.20 per cent, carbon
content. In the annealed condition such steel has an elastic
limit of about 35,000 pounds per square inch. Steel with a
somewhat higher carbon content, about 0.25 per cent., is also
used, and has a somewhat higher elastic limit, but is not as
malleable as the low carbon product. The chief reason for
using cold rolled steel is because of the natural bright finish of
this steel as it comes from the mill.

On page 473 are given the physical properties of three steels
recommended for use in pressed steel frames by the Society of
Automobile Engineers. Two of these are carbon steels and the
third is an alloy steel.

Sheet steel for frames is measured by the United States
sheet metal gauge, and is furnished in thicknesses of 0.125, 0.156,
0.187 and 0.250 inch.

Frame Sections. — The side rails of automobile pressed steel
frames are invariably made of channel section, with the open

471

472

THE FRAME AND ITS BRACKETS.

vx\

THE FRAME AND ITS BRACKETS.

473

side turned inward. Most of the cross members employed are
also of channel section. The side rails are the most important
parts, they being subjected to the greatest unit stress and con-
stituting the bulk of the weight. The height of the section
is constant over a certain portion at the middle of the rails,
generally about one-third the whole length, and decreases
uniformly toward both ends. Straight side rails are by far
the cheapest to produce, and are generally used for low priced
cars, but in the larger size vehicles it is necessary to narrow the
frame in front in order to enable the car to turn in a circle of
reasonably small radius, and to give it a single or double drop, or
a "kick up" over the rear axle, in order to bring the centre of
gravity down low without inordinately reducing the clearance
between the frame and axles required for proper spring action.

S. A. E. FRAME STEELS.

Chemical and physical properties recommended as embody-
ing current practice minima:

Chemical

Elastic
Limit, Lbs.
Per Sq. In.

Reduction
of Area,
per cent.

Elongation
in 2"
per cent.

S. A. E. Steel
1020
Carbon Steel
(.15-.25 Carbon)

Natural

35,000

•*. A. E. Steel
1025
Carbon Steel
(.20.30 Carbon)

Heat
Treated Natural

40,000

60,000

S. A. E. Steel
3230
Nickel Chromium
(.25-.3S Carbon)

Heat
Treated

85,000

Insweep and Drop. — The insweep of the frame at the front,
to reduce the turning radius, confronts designers with a diffi-
cult problem, as it imposes a twisting moment on the frame
bar at the bend, and a light channel section has very little re-
sistance to twisting strains.

474

THE FRAME AND ITS BRACKETS.

When pressed steel frames narrowed in front were first used
the "insweep" was generally in the form of a compound curve
of very short radius. This greatly weakened the frame and often
led to trouble. At present it is customary to extend the insweep
over a great length and to increase the width of the flanges
at the frame. Several designs of frame bars inswept in front
are shown in Fig. 319A. In design A the inner edge of the flange
runs parallel with the longitudinal axis of the car up to the end of
the offset, whence it runs in a straight line to the rear end, where
the flange is made as wide as at the front end. In design 7?
the inner edge of the flange runs parallel with the car axis to a
point just beyond the intermediate cross member, beyond which
the flange is of the same width as in front. In design C the
flanges are widened only at the offset.

FIG. 321. — INSWEPT FRAME REINFORCED.

Fig. 320 shows side views of four types of side rails, A
being the ordinary straight rail ; B, a rail with a single drop ;
C, a rail with double drop, and D, a rail with a kick-up over the
back axle.

The greatest offset in the front part of the frame side rails
is probably required in taxicabs, whose frame must be very
narrow in front in order to admit of turning around in an
ordinary city street without backing, and comparatively wide
in the rear so the rear seat will accommodate three passengers
without crowding, This problem is sometimes solved by

THE FRAME AND ITS BRACKETS. 475

using channel section reinforcements in the side bars at the
front end, which extend to a cross member somewhat to the
rear of the bend in the frame, as shown in Fig. 321.

To obviate the weakening effect of offset rails and still have
the frame narrow in* front the side rails may be made straight and
set so as to approach each other toward the front.

Calculation of Side Rail Section— Each frame side rail con-
stitutes a beam which is supported at four points, the points
of spring attachment, as oiiown in Fig. 322. The reactions R
at opposite ends of each spring will be equal, and the re-
sultant of these two reactions acts on the frame midway be-
tween spring eyes or directly above the axle. In a pleasure
car of standard design the weight on the frame is distributed
more or less uniformly from a point substantially above the
front axle to a point a little behind the rear axle, and, there-
fore, we will not be far wrong in considering the frame side
bar a beam supported at two points, directly above the axles,

A A A A i i 1 II . til 1 11 1 1 1 1 1 n 1 l 11

2* 2R,

FIG. 322. — DIAGRAM OF LOAD AND REACTIONS ON FRAME RAIL.

and carrying a uniformly distributed load between points of
support.

Let / = the distance beween supports (wheelbase), and W
the weight carried by each frame rail, then the maximum
bending moment, which occurs midway between supports, is

— . It is evident that the modulus of the section at the

point of maximum bending moment should be proportional
to this moment. Calling the necessary factor of safety /, then
Wl ZZ
8 = f,

where Z is the section modulus and L the elastic limit of the
material. Just what value should be given to / cannot well
he determined from first principles. The above equation may
be transposed to read

z-WJLL

- 8Z
The weight W on one frame rail is proportional to the total

476 THE FRAME AND ITS BRACKETS.

weight of the car with load (Wi). Hence we may write
_ a W^lf laf\ W^ I
8 L = \TJ L

Denoting the expression ( — ) by c we have

W*l

Z=c £

In frames for pleasure cars built up to 1910 the average value
of c was 0.12. However, when the fore-door type of body came
into use considerable trouble was experienced from cramping ol
the front doors. These are located not far from midway be-
tween the points of support of the frame, where the deflection
is the maximum. To obviate this cramping, the constant r is
now made equal to about 0.16 for carbon steel and as high as
j.2o for alloy steel, in the case of high powered cars. For low
powered cars, especially those of short wheelbase, like 20-25
ftotse power runabouts, a frame rail whose section modulus gives
a value of 0.10-0.12 to the constant c is amply strong. Therefore,
to sum up for pleasure cars :

Z^C^i (74)

J^f

c = 0.10-0.12 for low powered small cars;

c = o.i6 for high powered cars with carbon steel frames;

c = 0.2,0 for high powered cars with alloy steel frames.

The fore-door body has made stiffness of. the frame an im-
portant factor, and from this point of view the use of alloy steel
offers little advantage.

In the above the frame rails have been considered as simple
beams subjected to bending stresses and shear only. As a mat-
ter of fact, the rear springs usually are located outside the frame
-ind the reaction at their points of attachment imposes a tor-
sional stress on the side rails. However, very little torsion oc-
curs, because the cross members take up these stresses. With
the usual three-quarter elliptic rear springs the quarter eli^tx
members are often bolted directly to extensions of the rear
cross member, and only the reaction at the forward spring
shackle can produce trosion in the side rail. It, therefore, is not
essential to consider the torsional moment of outside springs in
the calculation of the frame section, but cross members should
preferably be placed as close to the point of spring attachment to
the frame as possible.

In motor trucks the bending moment on the frame rails fol-
lows a somewhat different curve, for the reason that usually the

THE FRAME AND ITS BRACKETS.

477

load considerably overhangs the rear axle. C. F. Cleaver in the
Automobile Engineer of August, 1912, published a diagram of
bending moments and shear in the frame of a 4 ton truck of
standard design, which diagram is herewith reproduced (Fig.
323). Of course, the weights of the individual parts of the
mechanism are generally not accurately known when the frame
is designed, and sufficiently close results will be obtained by as-
suming the total weight of truck and load and using a formula
of the same form as (74) but with a different coefficient, be-
cause of the different weight distribution, speed and type of tires,
as compared with pleasure vehicles. Commercial vehicle data

nding Moment

FIG. 323. — DIAGRAM OF BENDING MOMENTS AND SHEARING FORCE
ON MOTOR TRUCK FRAME RAIL.

in the author's possession shows that in average modern practice

W\l

Z = o.og —jT- « (75)

This equation is to be used only if the load overhangs the rear
axle as much as in Fig. 323. If the overhang is much less a
somewhat greater coefficient should be used.

The Society of Automobile Engineers has been endeavoring
to standardize pleasure car frames and recommends the fol-
lowing practice:

478 THE FRAME AND ITS BRACKETS.

-4

FIG. 324. — FRAME MEMBERS.

A — Amount of drop between top of side rail and front spring
bolt:

4" or 4%" drop for 3" side rail
4%" or 5" drop for 3%" side rail
5" or Sy2" drop for 4" side rail
5%" or 6" drop for 4%" side rail
6" or 6%"' drop for 5" side rail
6%" or 7" drop for 5&" side rail
7" -or 7%" drop for 6" side rail

B — Represents radius of curve of bottom flange of side rail
at front end:

8", 12", 16", 20" and 24"

C — Rear-end rise — amount of difference between level of
frame at rear and top flange of side member:

2", 3", 4" and 5"

D — Radii of combined curve in bottom flange .of side mem-
ber to make rise at C:

10", 20" and 30"

E — Side rail offset to commence at least 10" back of rear
end of front end taper.

CROSS MEMBERS

F — Recommended widths of gusset plate ends — 4", 5" and 6".
G — Radii of curved gusset plates to be 3" and 4". Straight
gusset plates to be cut at angle of 45°.

Members with straight drops could be made to have drops
vary in multiples of %", adopting a constant angle for the
dropped portion.

H — Top of subframe to be on line with inner side of lower
flange of side rail.

I — width between bars for flywheel clearance to be 17",

and 18".
J— Recommended width of all engine bar flanges to be iy2".

THE FRAME AND ITS BRACKETS. A.

WIDTH OF FRAME

30" for front end of frame, the width in rear to vary with
side rail offset.

Hot Riveting

Diameter Spacing Distance

Diameter of Rivet Drilled Hole Between Centres

5/16" 11/32" 1%"

3/8" 13/32" iy2"

RADIUS OF FILLETS

3/16" for sections below 5"
^4 for sections 5" and above.

MISCELLANEOUS

Length of straight centre sections of side rails to be designed
in multiples of 2".

Taper of side rail ends to be 1/16" to 1". This taper coin-
cident with centre sections in multiples of 2", will produce a
depth of section at extreme ends of side rails varying in mul-
tiples of %".

TABLE IX— SIDE RAIL SECTIONS.

Variable

Outside

Dimension.

Desig-

Flange

Punch

Using

nation.

Width.

Size.

o. 125

o. 156

0.187

0.250

!n.

In.

1 54

254

3 1-16

3/2

1/2

3/4

3/2

3 9-i6

35A

I}4

3 11-16

3 15-16

41-16

4 3- it

4/4

1/4

4^6

4 7-i6

4 15-16

5/8

5/2

5 7-i6

5/4

55/8

Iti

S7/s

5 15-16

6Ji

This completes the specifications of side rails. It will be ob-
served that standardization of this part has been carried farther
than that of almost any other automobile part. Makers of auto-
mobile frames took an active interest in this work of stand-
ardization, as it enables them to turn out a great range of
frames with a minimum investment in dies.

480

THE FRAME AND ITS BRACKETS.

Following are the section moduli of these sections:

TABLE X— SECTION MODULI OF FRAME SECTIONS.

3.000
3.5oo
3.062
3-9375

4-375
3-625
4.000
4.062
4-437

4.375
4.500
5-375
4.937
4.187
5.875
5-437
4.625
5.000
5-937
5-500
6.000
5.125
5.625
6. 125

• 5
•5

• 5

• 5
•5
-5
-5
-5
•5
•5
-75
•5
•75
•75

• 5
•75
•75

• 5

• 75

• 75
•75
•7.5
•75
•75
•75

0.125
0.125
0.156
0.125
0.155
0.125
0.187
0.156
o. 187
o. 156
0.125
0.187
0.125
0.156
0.250
0.125
0.156
0.250
0.187
0.156
0.187
0.187

0.250
0.250
0.250

0.66
0.81
0.86
0.98
i. 08

1.18
1.26
1.40
1.47
1-53
1.56
1.67
1.84
1.87
.1.90
2.06
2.16
2.17
2.19
2.45
2.78
2.86.
3-26
3-70

Following are the dimensions and constants of standard rolled
steel channels sometimes used for truck frames :

TABLE XI— PROPERTIES OF ROLLED CHANNELS.

Depth.
5 • • •

Thickness
of Web.

O.IQ

Width

of Flange.
i . 75

Weight
Per Foot
(Pounds).
6.5

Moment
of
Inertia.

Section

Modulus.

i 89

8 o

6 .

o. 20

i . 92

6 .

O 44

2 l6

? 8

7 ...

0.21

2.09

9 • 75

6 o

, . O.44

2. 3O

I4 75

2 26

2 is

6't- 5

8 .

. . O.4O

2.AA

16.2*

7Q .O

TO.O

The moment of inertia and section modulus as given in the
above table apply to a neutral axis perpendicular to the web at
the centre.

Cross Members. — Cross members are made of widely different
forms, according to the parts they have to support, etc. At the
ends they are made of an outside height equal to the inside height
of the side rail section at that particular point, so as to fit into
the side rail channel. In pleasure car frames there are usually

THE FRAME AND ITS BRACKETS.

481

four cross members, one in front, one at the rear and two inter-
mediate ones, though if a sub-frame is used there is generally
only one intermediate cross member, back of the change gear
box. The front cross member usually comes underneath the
radiator, being dropped to accommodate the latter, and also car-
ries the bracket for the starting crank. The two intermediate
cross members generally support the change gear and they often
have to be dropped to pass underneath the gear box or the drive
shaft, arched to pass over the top of the box or shaft or made of

FIG. 325. — REAR GUSSET.

comparatively large height at the middle and with a hole through
which the drive shaft passes. The rear cross member can gen-
erally be made straight, and it is customary to use a specially large
gusset at the rear corner of the frame in order to prevent any
tendency to distortion. A popular design of rear corner gusset is
shown in Fig. 325. In England tubular cross members are used
to quite an extent, and cross members of cast steel and man-
ganese bronze are also in use.

Sub=frames — Sub-frames on which the engine and change
gear are supported are still used to a considerable extent, al-
though not as much as formerly. These, too, are generally made
of channel section pressed steel, and are riveted to the forward
and an intermediate cross member, being so placed that the top
of the sub-frame comes flush with the inner side of the lower
flange of the main frame rail. A typical sub-frame construction
is shown in Fig. 326.

In designing drop bars, the radii of the outlines should be made
as large as possible, as short curves are hard to draw. The width
of the flanges should be made equal, or at least nearly so, and the
ends of the bar should preferably be so designed that the flanges

-'.32 THE FRAME AND ITS BRACKETS.

are trimmed to the same length. Stock will be economized if an
integral gusset is provided for on the lower flange.

Frame Joints — The individual parts of pressed steel frames
are joined by riveting, either separate or integral gussets being
used (A and B, Fig. 327). Two methods of riveting are in use,
viz., cold riveting and hot riveting. In testing a hot riveted joint
under tension in the plane of contact, as the tension assumes a
certain definite value, there is a sudden increase in extension.
This is due to the fact that up to this point the tension is re-
sisted by the contact friction which in a hot riveted joint is very

—

FIG. 326. — SUB-FRAME CONSTRUCTION.

considerable, because the -rivet in cooling draws the two parts to-
gether with great force, and to the further fact that the rivet, also
because of its contraction in cooling, does not entirely fill up the
hole. With cold riveting the hole is completely filled by the
rivet, but, on the other harid, the surfaces are not applied to each
other with as great force. It seems that hot riveting, on the
whole, has proven the most satisfactory and is now in general
use. Two sizes of rivets are used, 1% and ^ inch. The holes
for hot riveting for these two sizes are made M and £| inch,
respectively, and are spaced about il/2 inches. In riveting
brackets to frame members, three rivets are often used. All
rivet holes weaken the frame, but the weakening effect varies
greatly with the location of the holes. A hole at the middle of
the web has but little effect, but the opposite is true of a hole
in one of the flanges. In this connection it is well to remember
that the lower flange is under tension and the upper under com-

THE FRAME AND ITS BRACKETS.

483

pression, the unit stress being the same in both, and since the
compressive strength of frame materials is somewhat greater
than their tensile strength, it is advisable to put rivet holes in the
upper rather than in the lower flange, where this can be done
just as well.

At the New York automobile show in 1906 the Darracq Auto-
mobile Company of France exhibited a complete sheet metal
frame in one piece which aroused a great deal of curiosity at the
time. It was undoubtedly made from separate stampings by
means of the oxy-acetylene welding process which was then

FIG. 327— TYPES OF GUSSET PLATES.

in its infancy. The frame was highly polished and showed abso-
lutely no evidences of joints. While it is quite possible to make
rivetless frames in this way the advantages secured do not war-
rant the cost. In fact, a well made riveted pressed steel frame,
of ample section for the load to be carried lasts well and gener-
ally gives very little trouble.

Underslung Frames — An underslung frame — that is, a frame
located underneath the axles — is sometimes used because of the
low centre of gravity it gives. By means of a raised sub-frame
the engine and gear box are placed at about the same distance
from the ground as ordinarily, because to lower them would
mean reducing the ground clearance; but the frame, body and
passengers are materially lowered, which lowers the centre of
gravity of the whole car and increases its stability. Specially
large wheels are employed in connection with underslung frames,
which increases the ground clearance and incidentally tends to
give a straight line drive. The frame is usually the lowest part
of the car and has a ground clearance of 9 to 10 inches.

484

THE FRAME AND ITS BRACKETS.

FIG. 328. — UNDERSLUNG FRAME RAIL.

Fig. 328 shows the general form of the side rail of an underslung
frame.

Wood Sill Frame. — The H. H. Franklin Manufacturing Com-
pany uses a frame made of wood sills. Each sill is made of three
laminae of second growth white ash, which has been air sea-
soned and kiln dried in the plank, the laminae being glued and
screwed together, and so arranged that the grain in adjacent ones
runs at a slightly different angle. The built-up sill is kiln dried
at a somewhat lower temperature than the lumber, and is then
shaped to the exact size required. Thin strips are then glued
along the top and bottom edges to cover the
joints in the main portion of the sills, so as
to keep out moisture. Next, two side sills
are placed in their proper relation to each
other and connected by cross-pieces. The
rear corners are metal bound and provided
with 4 inch gusset blocks. The attachment
of brackets, painting and varnishing complete
the frame.

A wood sill of selected material and prop-
erly proportioned is stronger in a vertical
plane than a steel frame rail of the usual
proportions and of equal weight. Thus, ac-
cording to tests made by the engineers of the
Franklin Company, a pressed steel side rail
having a section of 4^x1 ^xfs inch, and a
FIG. 329. — SECTION weight per linear inch of 0.408 pound, has a
OF FRANKLIN resisting moment of 114,830 pounds-inches,
WOOD SILL. whereas an ash sill measuring 124x6 inches

and weighing 0.266 pound per linear inch
has a resisting moment of 142,275 pounds-inches. That wood sill
frames are not more generally used is probably due to the diffi-
culty of securing really faultless wood and to the very careful
handling the wood requires in the process of manufacture, which
makes the frame rather expensive. Besides lightness, it is
claimed for the wood sill frame that it absorbs shocks and muffles
noise.

THE FRAME AND ITS BRACKETS.

-.00

Wood sills reinforced with steel flitch plates and square tubes
filled with wood have also been used, especially abroad, but have
been practically entirely discarded in favor of pressed steel.

Frame Trusses— Frame trusses in the past frequently were
used as last resorts in cases where the frame was found to be too
light for the load after the car had been built. It may be that
this brought them into disrepute, for at present they are prac-
tically never used on pleasure cars and only on a few motor
trucks. The use of trusses in railway cars is universal, and their
use on motor trucks should permit of a considerable saving on
the weight of the frame. The only objection that can be raised
to a properly designed truss is, that if it should be improperly
adjusted by an incompetent driver it would give trouble. Trusses
are known as two panel or three panel, according to whether
one or two struts are used. With a two panel truss the strut is
preferably located midway between anchorages, and with a three
panel truss the distance between anchorages should be divided
into three equal parts by the struts. Probably the chief reason
that trusses are now seldom used on motor trucks is that the
bodies of these trucks usually overhang the rear axles to such an
extent that the bending stress in the fidme directly over the rear
axle is as great as at the point of maximum bending moment be-
tween axles. Trusses,- of course, are of particular value in
vehicles of very long wheel base and with comparatively little
overhang. The best anchorage points are the points at which
there is no bending moment, which is some distance inside the
axles.

The tension in the truss rod and the compression in the^strut
can be easily calculated. Suppose that the load on the frame be-
tween the points of anchorage is evenly distributed and that the
truss is so adjusted that it relieves the frame at the point where
the strut is secured to it of all bending stress. Then (Fig. 330)
calling the total weight on the frame between truss anchorage W,
the compression on the strut is W/2 and the tension in each truss
rod is W/(4 sin a). Since the load on the truss is a dynamic one,

FIG. 330.— DIAGRAM OF FRAME TRUSS.

486

THE FRAME AND ITS BRACKETS.

a safety factor of at least 4 should be
allowed in both the truss rod and the strut.
The stress on the strut depends merely
upon the weight carried by the frame, but
the tension in the rods is less the greater
the height of the strut or struts and the
shorter the length of the end panels.

Some means of adjustment must be pro-
vided. Either the ends of the truss rods
may be threaded and provided with nuts;
a turnbuckle may be inserted in one-half
of the truss rod, or the strut may be so ar-
ranged that it can be lengthened or short-
ened. Fig. 331 illustrates a design of
trussed frame for a motor truck.

Spring Brackets — The chassis frame is
carried on the springs through the in-
termediary of spring brackets. At the
front semi-elliptic springs are used, as a
rule, which require a bracket at either
end. The forward bracket is generally
made in the form shown in Fig. 332. It
tits into the downwardly curved forward
end of the frame channel to which it is se-
cured by one rivet in the vertical plane at
the extreme forward end of the channel,
and three or more horizontal rivets. In
the cheaper cars and in commercial vehi-
cles this bracket is usually made in the
form of a plain forked connector, but in
the design illustrated the spring eye is
surrounded by a shroud which extends a
little below the axis of the spring bolt and
completely encloses the spring eye. This
makes for a neater appearance than an open
forked bracket. The eye bolt can be held
from rotating in the bracket either by a
small pin extending into its head from
underneath and into the prong of the fork,
or by a small key.

The rear ends of semi-elliptic front
springs are connected to the frame brackets
by shackles, and these shackles may work

THE FRAME AND ITS BRACKETS. 43?

FIG. 332. — FRONT SPRING FRONT BRACKET.

either under compression or under tension, the brackets being
designed accordingly. Simplicity of construction is in favor of
shackles under compression, and these are now generally used,
even on the most expensive cars. Fig. 333 shows two forms of
front spring rear brackets for shackles working under compres-
sion. That shown at A does not require any rivets through the
flange of the frame rail, and therefore may be considered the
better construction, although at this point of the frame rail the
strain on the material usually is not very great.

The rear springs at their front end are either pivoted or
shackled to their brackets. Two designs of brackets for this part
of the car are illustrated in Fig. 334. The one shown at A is a
plain fork and is secured to the frame by three rivets, one of
which passes through the lower flange. The design shown at B
is of the shrouded type, which gives a somewhat neater appear-
ance if the front end of the rear spring is exposed to view.

FIG. 333.— FRONT SPRING REAR BRACKETS.

488

THE FRAME AND ITS BRACKETS.

Generally, however, it is covered with a shield, and an open type
of bracket is used.

The bracket for the rear spring front end is sometimes com-
bined with a bearing for the brake shaft and also with a bracket
for the forward end of the radius rod. For instance, the bracket
may be made with a follow stud surrounded by the hub part of a
shackle forging, and the brake shaft extend through the hollow
stud.

If semi-elliptic springs are used at the rear the frame rail
may be curved downwardly, the same as in front, and provided

°)

_^— J

FIG. 334. — REAR SPRING FRONT BRACKETS.

with a bracket similar to that shown in Fig. 332. A bar is then
run through the eyes of the bracket on opposite sides of the
frame, whose ends, somewhat reduced in diameter, serve as the
spring shackle bolts. This practice is more or less prevalent in
Europe. An alternate construction consists in the use of long
spring brackets of the general form shown in Fig. 335 at A.
Brackets of this type are riveted to the bottom flanges of the
side rail and rear cross member and also to the web of the latter.
The short members of three-quarter elliptic springs may be
secured by bolts or clips to brackets riveted to the side rails near
their rear ends, or may be clamped between extensions of the
flanges of the rear cross member, as illustrated in Fig. 335 at B.
In the design shown the spring plate has three holes drilled
through it, the forward one of which is for the usual spring

THE FRAME AND ITS BRACKETS.

489

centre bolt, which holds the leaves together, and the outer two
of which are for clamp bolts. Five bolts are used by some de-
signers. At C in Fig. 335 is shown a bracket for the cross mem-
ber of platform springs which is riveted to the rear cross member

FIG. 335.— REAR SPRING REAR BRACKETS.

of the frame. In order to prevent twisting of this frame mem-
ber it is well to run diagonal braces from the side rails to the
middle of the rear cross members, as shown. French designers
usually make this bracket of an inverted box shape, which gives
it a neater form but interferes with riveting at the centre of

490

THE FRAME AND ITS BRACKETS.

the base. Sometimes this bracket is of considerably greater
length than here illustrated, while one designer dispenses with
it by giving the frame rear cross member a rearward curve at the
middle and clips the spring to it directly.

Spring brackets for motor trucks differ from those for pleasure
cars on account of the difference in frame construction and be-
cause neat appearance is not such an important factor. Fig. 336,
illustrates two designs of truck spring brackets. That shown at
A is a front bracket and is riveted to the front corner of the
frame. However, the tendency in American design is to have
the frame overhang the springs in front, so the bracket comes

...L.i. I ^/ J

K
['

r ,H

L_j..j_

™ — ^.s \

22! \

FIG. 336. — MOTOR TRUCK SPRING BRACKETS.

underneath the frame. A bracket of the type shown at B is used
at the rear end of the front springs and also at the shackled end
or ends of the rear springs.

Radiator Brackets. — Radiators may be secured either to the
front cross member or to the side rails. Owing to their rela-
tively frail construction it is desirable that they be so supported
that distortion of the frame will not strain them seriously. The
simplest arrangement consists in securing brackets to the sides
of the radiator which are bolted down to the top flange of the
side rails (A, Fig. 337). This, of course, does not protect the
radiator against frame distortion. A better plan consists in pro-
viding the radiator with trunnions which are supported in bear-
ings secured to the frame rail (B, Fig. 337). The top then is

THE FRAME AND ITS BRACKETS.

491

braced or steadied by the water return pipe to the top of the
engine and sometimes by a rod connecting to the dashboard.
Still greater protection against frame distortion can be secured
by slipping bushings with spherical seats over the trunnions.

In the case of commercial vehicles special precautions have to be
taken in designing the support for the radiator. It must be pro-
tected from both road vibration and strains due to distortion of
the frame. The radiator is insulated against road vibration by
supporting it from the frame through the intermediary of springs,
coiled compression springs being generally employed and flat
springs in some instances. Strains due to distortion of the frame
are guarded against by flexibly supporting the radiator at three
points. It is carried upon springs on opposite sides, and either

FIG. 337.— RADIATOR BRACKETS.

the top or the bottom is braced by a rod to some part of the
frame or body. Sometimes this brace is also spring cushioned.
Fig. 338 illustrates the Dayton truck radiator support which pro-
tects the radiator against both frame distortion and road vibra-
tion, the radiator being hung on coiled springs by brackets se-
cured to the front of the engine housing.

Fig. 339 illustrates a bracket used for flexibly supporting the
gear box, engine or unit power plant at three points. It is se-
cured to a frame member by three bolts and is provided with a
forked connection which joins by a pivot bolt to a lug on the part
to be supported. This arrangement affords a universal support,
which protects the supported part against any distortion of the
frame.

Truck Bumpers — Motor truck frames generally are provided
with a bumper in front which will receive the shock of a collision

492 THE FRAME AND ITS BRACKETS.

FIG. 338.— TRUCK RADIATOR SUPPORT.

Top View.

Side View.

FIG. 339— UNIVERSAL BRACKET FOR THREE POINT SUSPENSION.

THE FRAME AND ITS BRACKETS.

493

and transfer it directly to the frame, thus protecting frail parts at
the front of the car, such as lamps, radiator, etc. These bump-
ers are made in many different forms. One manufacturer bends
the frame side rails inward in a curve so they meet at the middle
of the car where they are joined together by a plate riveted to
them. Another uses a sort of arch formed of angle iron which
is riveted to the side frame rails. In Fig. 340 is shown a tubular
bumper carried by brackets extending forward from the frame

FIG. 340.— TRUCK BUMPER.

FIG. 341. — FENDER BRACKETS.

side rails. It is desirable that no part of the truck project ahead
of the bumper, and for this reason the engine starting crank is
often hinged so it can be swung out of the way.

The brackets supporting the front fenders should preferably
be secured to the frame in such a manner that the fenders can
be quickly removed, for the reason that the latter generally inter-
fere considerably with any important work on the engine. A
method of securing the brackets which insures this quick re-
moval is illustrated in Fig. 341. A small bracket is reamed with
a taper hole to receive the fender hanger. It is apparent that

494

THE FRAME AND ITS BRACKETS.

with a bracket of this kind the fender can be quickly taken off.
The same type of bracket may be used for the searchlight, and,
in an inverted position for the running board hangers. Rear
fender brackets are generally riveted to the frame, but can be
made detachable at very little extra expense. The design for
such a detachable bracket is also shown in Fig. 341. Fender
irons often are bolted to lugs formed on radiator or spring
brackets.

Fig. 315 illustrates a design of step or running board hanger
of which it is customary to use three on each side in pleasure
cars and two in trucks. This hanger is made of pressed steel
and has a channel section which varies with the load. The one

X) O O'
A

FIG. 342. — STEP HANGER.

here shown is secured to the frame by three rivets all in a line.
Another plan consists in making the base flaps of substantially
rectangular section and using four rivets.

Starting Crank Bracket—In many cars the bracket for the
engine starting crank is secured to the frame front cross mem-
ber, as illustrated in Fig. 343. Instead of the hub of the bracket
being on the under side of the cross member it may be so located
that the shank of the starting crank has to pass through a hole

THE FRAME AND ITS BRACKETS.

495

FIG. 343. — STARTING CRANK BRACKET.

in the cross member, the bracket being riveted to the web of the
channel either in front or in the back. The crank and bracket
show provisions made for automatically holding the former in
the upright position when disengaged.

Lamp Brackets — Of the different lamps carried on an auto-
mobile the head and tail lights are usually supported by brackets
secured to the frame. Fig. 344 shows two designs of head light
brackets and one tail light bracket At A is shown a drop
forged bracket which fits with a taper joint into a bracket riveted

FIG. 344. — LAMP BRACKETS.

496 THE FRAME AND ITS BRACKETS.

to the frame side rail. One designer places the frame bracket
inside the channel, passing the shank of the lamp bracket through
a hole in the top flange, which makes for neat appearance. In
the headlight bracket design shown at B the prongs are bolted to
the shank, which makes the distance between prongs adjustable.
Headlamp brackets have been standardized by the Society of
Automobile Engineers. Three standard sizes are recommended
for the forked type of head-lamp support, the forks having cen-
tre-to-centre widths of 7]/4, &/4 and 9% in. The upper ends of
the supports are to be Y2 in. diameter, with y2 in. S. A. E. threads
and machined shoulders not less than ^ in. diameter. The dis-
tance from the upper face of the shoulder to the last full thread
on the end of the support should not be less than \l/2 in. where
no tie-rod is used, or ll/2 in. plus thickness of rod where a rod
is used. The use of nuts and lock washers for locking the lamp
to the fork is standard practice.

An adjustment should be provided for the support to allow

a change of the vertical angle of the lamp without bending any

part of the support The lugs attached to the lamp shells should

have bores of 17/32 in., the bores being \l/2 in. long. The center-

f the hole in the lug should be not less than 9/16 in. from

arest point of the shell. The clearance between the lower

f the bracket and the lamp should not be less than 9/16 in.

CHAPTER XVIII.

SPRINGS.

Automobile frames are supported on the axles through the in-
termediary of steel springs. Leaf springs, built up of a number
of leaves or plates of different lengths, are used almost exclusive-
ly, though coiled springs have been used on low priced cars.

Classification of Springs — The simplest form of automobile
spring is the half elliptic spring illustrated in Fig. 345 at A. It
is made up of one master leaf whose ends are formed into an eye
for connection to the spring brackets or shackles, and a number
of shorter leaves, the lengths of the leaves decreasing uniformly
with their distance from the master leaf, except that in springs
for heavy loads the leaf or leaves nearest the master leaf some-
times extend to the ends of the latter and even enwrap the
spring eyes. ' The various leaves of a spring are held together
by a centre bolt.

All other types of springs are made up wholly or in part of
half elliptic springs. At B, Fig. 345, is shown the three-quarter
elliptic spring, which consists of a quarter elliptic top member and
a half elliptic bottom member, the two members being joined by a
bolt at one end. At C is shown the elliptic spring, consisting of
half elliptic top and bottom members which are joined by bolts at
both ends. D shows the three-quarter scroll elliptic, consisting of
a quarter elliptic scroll top member and a half elliptic bottom
member, joined by shackles at one end. E shows the scroll el-
liptic (one end) spring, consisting of a half elliptic top member
with a scroll at one end and a half elliptic bottom member, joined
at one end by a bolt and at the other by shackles. The spring
shown at F is known as the scroll elliptic (both ends) ; it con-
sists of a half elliptic top member with scrolls at both ends and a
half elliptic bottom member, the two being joined by shackles at
both ends. At G, Fig. 346, is shown a platform spring (three
point suspension), which consists of two half elliptic side mem-
bers and one half elliptic cross member, the side members being

497

498

SPRINGS.

FIG. 345— BODY SPRING TYPES.

SPRINGS. 409

joined to the cross member by shackles. At H is shown a three-
quarter elliptic platform spring consisting of two three-quarter
elliptic side members and one half-elliptic cross member, the side
members being joined to the cross members by shackles. / shows
an auxiliary spring consisting of a half elliptic spring with plain
ends.

346.— BODY SPRING TYPES.

In Fig. 347 is shown a half elliptic cantilever or floating canti-
lever type of spring. This is mainly used for rear suspension of
pleasure cars. It is a 'half elliptic spring which swivels on the car
frame at its middle, is shackled to the frame at the forward end
and connects to the axle at its rear end. Quarter elliptic springs,
which are also classed as cantilever springs, are used for both
front and rear suspension on light cars. The heavy end of these
is secured to the frame and the light end to the axle.

500

SPRINGS.

FIG. 347. — GRANT CANTILEVER SPRING.

Spring Material. — The common spring material which has
long been used for carriage and railway springs is a carbon steel
containing about I per cent, of carbon. The S. A. E. specifica-
tions for this carbon spring steel are as follows :

0.95 CARBON STEEL.

Carbon 0.90101.05% (0.95% desired)

Manganese 0.25100.50% (0.35% desired)

Silicon o. 10 to 0.30%

Phosphorus, not over 0.035%

Sulphur, not over 0.035%

The natural sources of the above steel are the basic open
hearth, crucible and electric furnace. This grade of spring steel
is suited for the most important springs, as with proper heat
treatment it will give very good results. The heat treatment of
the spring plates after they are worked to shape consists in
quenching in oil at a temperature of about 1,400 degrees Fahr.,
reheating to about 500 degrees Fahr. and cooling slowly. The
temperatures are given for purposes of illustration only. The
physical qualities of the completed spring will greatly depend
upon them, and the best quenching and reheating temperatures
are usually worked out by experiment in each shop.

The carbon steel above specified when tempered will have the
following physical properties, according to the heat treatment:

Tensile strength 120,000 to 180,000 Ibs. per sq. in.

Elastic limit 70,000 to 95,000 Ibs. per sq. in.

Elongation in 2 inches 9 to 10%

Reduction of area 14 to 16%

Besides carbon steel, chrome-nickel steel, chrome-vanadium
steel and silico manganese steel are used in the manufacture of
springs. The S. A. E. specifications of silico manganese spring
steel are as follows:

SPRINGS. 501

SILICO-MANGANESE STEEL.

Carbon 0.45 to 0.55% (0.50% desired)

Manganese o . 60 to o . 80% (o . 70% desired)

Silicon i . 90 to 2 . 20% (2% desired)

Phosphorus, not over 0.04%

Sulphur, not over 0.04%

The following heat treatment will probably give good results:
Heat to 1,600-1,750 degrees Fahr., quench, reheat to about 800
degrees Fahr. and cool slowly. The best reheating temperature
should be carefully determined by experiment. The elastic limit
will be about 150,000 pounds per square inch.

Krupp's silico manganese spring steel is claimed to have the
following physical properties when spring tempered :

Tensile strength 250,000 to 255,000 ibs. per sq. iw

Elastic limit 206,000 Ibs. per sq. in.

Elongation 3-5%

Chrome nickel and chrome vanadium steels vary in composi-
tion and different heat treatments result in different physical

-1

/'~ s \

> .y

FIG. 348.

qualities, but either steel properly spring tempered should have
an elastic limit upward of 150,000 pounds per square inch.

Theory of Leaf Springs— The simplest form of leaf spring
is that containing only a single leaf. Such a spring may be con-
sidered either as two cantilever beams loaded at their ends or as
a simple beam loaded at the middle. Fig. 348 represents such a
spring in diagram. If we consider each half of the spring as a
cantilever and denote the load on one end of the spring by P, the
half length of the spring by /, the width by b, the thickness by t
and the coefficient of elasticity by E, we have for the deflection of
the end of the spring

d= i PI* 4/V3
3 El ~ Ebi*>

(See cantilever beams in any textbook on mechanics.) The
bending moment at any distance x from the end of the spring is
P x and the stress in the material at that point is

bcf

502 SPRINGS.

Hence, with a single leaf of uniform section over its whole
length the stress due to the bending moment varies from nothing
at the end to a maximum at the middle of the spring. There-
fore, if a single uniform section leaf were used the material
would be very poorly utilized, and one of the objects in using
a multiple leaf spring is to make the stress substantially uniform
in all parts of the spring. Now suppose we took a number of
equal leaves and assembled them as shown in Fig. 349. Then,
if loads were applied to the top leaf, all of the leaves would be
deflected the same amount. If there are n leaves the deflection
would be the same as in the case of a single leaf subjected to a

load . . Therefore the deflection of a spring like that shown in

n
Fig. 321 should be

4-Pf

Enbt3
-1 *-

FIG. 349.

However, in a multiple leaf spring there can be no deflection
without one leaf sliding over another, which introduces the factor
of friction. As a leaf of the spring deflects there are two forces
at work, viz., the force due to the load P carried, and the force
due to the internal strains. The former force is constant, but the
latter increase from nothing at the moment the deflection begins
to the value of the former when it attains its maximum (in a
single leaf spring). In a multiple leaf spring the friction between
leaves is opposed to the deflection and, therefore, assists the in-
ternal forces or those due to the strains in the material. While
the spring is deflecting the difference between the force due to
the load on the spring and that due to the internal strain is
available for overcoming the frictional resistance, and it is ob-
vious that when this difference becomes equal to the frictional
force the deflection ceases. Hence the deflection will be re-
duced and an allowance must be made for leaf friction. This
reduction varies with the number of leaves, but the allowance
may be placed at 15 per cent, for practical cases.

SPRINGS. 503

In an actual vehicle spring the leaves are of gradually decreas-
ing lengths, and since the outer end of any leaf is not supported
by leaves below it, the deflection will be greater than in a spring
of the form shown in Fig. 349. Reuleaux has calculated that if
the lengths of springs decrease uniformly, as in Fig. 350, the
multiplying factor will be 1.5. That is, a spring of the type
shown in Fig. 350 will deflect 50 per cent, more for a given load
than a spring of the type shown in Fig. 349, both being of the
same dimensions. However, in automobile springs the second
leaf often extends out as far as the centre of the spring eye, and
in heavy motor truck springs even two or three leaves support
the main leaf at the eyes, in which case the multiplying factor is
smaller. From the value of this factor for the extreme cases,
Figs. 349 and 350, viz., 1 and 1.5, its value for any intermediate
case can be closely approximated. For commercial springs it
probably never drops below 1.25. Hence, taking 1.25 and 1.5 as

FIG. 350.

the extreme values of this factor in actual practice, and taking
into account the effects of both shortening of the leaves and of
friction between them, we have for the deflection of vehicle leaf
springs

(1.25 to 1.5) (1 — 0.15) 4PP
d= -

Enbt3
which may be simplified to read

_ (76)

E n b r
The larger coefficient is to be used when the length of any leaf is

less than that of the preceding one by — ; the smaller if several

of the longer leaves are substantially equal in effective length.

Equation (76) covers the case of a spring with leaves of equal
thickness. If the thickness t differs we may substitute for n t* in
the denominator, ^3 + 1? + t£ ................. .... . /n3, or 2 t'A,

which gives

504 SPRINGS.

The bending moment at the middle of the spring is equal to
PI. In a spring having n leaves of equal thickness t, this bending

p J

moment is equally divided and that on each leaf is — . Since

the section modulus of the leaf is , the unit stress is

6
PI

n 6 PI

bt* "~ nbt2

If we divide the elastic limit of the material by this stress we ob-
tain the factor of safety, which in well designed springs is usually
between 2.5 and 2.75. Therefore, calling the elastic limit of the
spring material L, the maximum safe load on the spring with
a safety factor of 2.5,

W=Lnbt\ (78)

In case the leaves are of unequal thickness we can calculate the
strain in each from the fact that the elastic curves of all leaves
at the middle must be alike. Under these conditions the moment
coming on each leaf is proportional to its moment of inertia.
The bending moment on the heaviest leaf (of moment of inertia
/) then will be

and the unit stress in this leaf will be
Pit?

s-™=*r,± (79)

bt? b Z tA

In the design of the springs the designer has to deal with a
considerable number of variable factors, viz., the length, width,
thickness and number of leaves, and the elastic limit of the ma-
terial. Of these the first two are generally determined by em-
pirical rules based upon experience. Longer springs make for
an easier riding car, because with a greater length a greater de-
flection can be obtained for a given change in load without in-
creasing the stress in the material. Thus, the stress will remain
the same if

t~t2
and under these conditions

SPRINGS.

505

The usual lengths of different kinds of front and rear springs in

pleasure cars are given in the following table taken from a

book on Leaf Springs, compiled by David Landau, and published

by the Sheldon Spring and Axle Co. The loads referred to in

the table are those which the springs will carry when the car

is loaded with its rated number of passengers, and the lengths

are those which the springs will have when so loaded.

TABLE XI— PLEASURE CAR SPRINGS.

FRONT SPRING, SEMI-ELLIPTIC.

Load on One Spring,

Length,

Width.

Pounds.

Inches.

350 to 400 ....

33 to 34

1/2

400 to 500

35 to 36

500 to 550

36 to 37J4

600 to 800

37l/a to 40

800 to 1,100

40 to 42

2*A

REAR HALF ELLIPTIC SPRINGS.

Load on One Spring,

Length,

Width,

Pounds.

Inches.

450 to 550

46 to 48

55U to 650

49 to 50

700 to 850

51 to 52

900 to 1,000

52 to 55

2J4

i.ooo to 1,350

55 to 57

2*A

1,350 to 1,550

57 to 60

2J4 t02j4

RE,

IR SPRINGS, THREE-QUARTER ELLIPTIC.

Semi-Elliptic Length of Scroll

Load on One Spring,

Element, (Link to Bolt),

Width,

Pounds.

Inches. Inches.

Inches.

450 to 500

45 to 47 18 to 19

500 to 650

47 to 49 18 to 19

rtf

650 to 775

47T/2to 51*6 ig Y2 to 22

775 to 900

S*J/2 to 52 22J4 to 23

to 2J4

S2*/2 to 53^ 23 to 24

to 2J4

1,000 to ,150

$3l/2 to 54 24 to 25

tO 2J4

1,150 to ,250

54 to 54^ 25 to 25^

to 2*A

1,250 to ,350

5454 to 55 25^ to 26

to 2M

i,35^ to ,450

55 to 56 26 to 26j£

'A to zya

1,450 to ,550

56 to 58 26^2 to 27

2^4 to zy*

1,550 to ,650

58 to 60 27 to 27}^

2V* tO 2J4

FULL ELLIPTIC SPRINGS.

Load on One Spring,

Length,

Width,

Pounds.

Inches.

500 to 700

800

1,000

2J4

1,100

,200

2Y4

300

,400

,500

2V*

.600

506

SPRINGS.

THREE-QUARTER PLATFORM SPRINGS.

Load on

One Side Spring,
Pounds.

500 to 550 .

600 to 700 .

900 .

,000 .

,100
,200
,300
,400
,500

Length of

Side Spring,
Inches.

45 to 47
, 47 to 49
, 51 to 53
, 53 to 55
. 55 to 57

57^

58^

Length of
Cross Spring,

Inches.
39^
39^

39^ to 40
39l/2 to 40
39J4 to 40
40
40
40
40

Width,
Inches.

2 to 2yA

2Y4

2Y4
2Y*
2Y*

The author has compiled the following figures on the average
lengths and widths of springs used on motor trucks :

TABLE XII— MOTOR TRUCK SPRINGS.
FRONT SPRINGS, HALF ELLIPTIC.

Load Capacity, Length, Width,

Tons. Inches. Inches.

3/4 ' 38 to 40 2

1 38 to 40 2J4

11/2 40 to 42 2*/2

2 42 to 44 2V*

3 44 to 46 2Y2 to 3

4 46 to 48 3

5 48 to 50 3

REAR SPRINGS, HALF ELLIPTIC.

Load Capacity, Length, Width,

Tons. Inches. Inches.

3/4 48 to 52 2

1 48 to 52 2Y4

\y2 so to 53 2y2

2 50 to 53 2l/2

3 52 to 54 3

4 52 to 55 3

5 54 to 56 $y2

PLATFORM SPRINGS, SIDE MEMBERS.

Load Capacity, Length, Width,

Tons. Inches. Inches.

3^ 44 to 48 2

1 44 to 48 2*A

1 J4 46 to 48 2 J4

2 46 to 49 2Yz

3 48 to 50 3

4 48 to 51 3

5 50 to 3^

Width and Thickness of Leaves. — It has long been custom-
ary to make spring plates according to the Birmingham or Stubb's

SPRINGS. 507

gauge, and the following table gives the sizes employed, together
with the cubes of the thickness, for convenience in calculating de-
flections and maximum safe loads :

No. Thickness (Inch). t3

oo 0.380 0.05^9

0 0.340 0.0393

1 0.300 0.0270

2 0.284 O.O229

3 0.259 0.0174

4 0.238 0.0135

5 0.220 0.0106

6 0.203 0.0084

Owing to the non-uniform variations in thickness in the Stubb's
gauge some manufacturers are having plates rolled varying in
thirty-seconds of an inch.

Thickness (Inch). t5

0-375 0.0527

0.344 0.0407

0.312 0.0304

0.28l O.O222

0.25O 0.0156

O.2I9 O.OIO5

0.187 • 0.0065

Spring plates are made in the following standard widths : For
pleasure cars: il/2, 1^4, 2, 2% and 2,l/2 inches. For commercial:
2, 2J4, 2l/2t 3, 3^, 4 and 4^ inches.

Flexibility — The flexibility is a most important quality, as an
insufficiently flexible spring makes the car hard riding, while a
spring too flexible will cause the chassis frame to strike the axles
and is liable to break. Spring makers rate or gauge springs by
the load required to deflect them one inch. From the automobile
designer's standpoint the most important factor is the deflection
caused by the maximum dead load the springs will have to bear.
This total deflection should increase with the length of the spring,
because, on the one hand, long springs are used on high pow-
ered, luxurious vehicles which are naturally expected to be easier
riding than small cars, and, on the other hand, a greater deflec-
tion can be obtained with the larger springs without increasing
the stress in the material. Since the length, width, etc., of the
springs are empirically chosen, it is obvious that thare can be no
rational relation between the length of the springs and their de^
flection under their maximum dead load, but data on hand shows
that in practice the two factors mentioned vary substantially in
direct proportion.

508 SPRINGS.

The deflection should also increase somewhat with the elastic
limit of the material. Of course, if we make two springs of ex-
actly the same dimensions, the one of ordinary carbon spring
steel and the other of alloy spring steel, they will deflect equally
under equal loads, because both steels have substantially the same
coefficient of elasticity. But that is not the proper way to use
alloy steel. Wherever alloy steel is substituted for carbon steel —
except in cases where the original design proved far too weak —
the weight of the part is reduced. Therefore, with alloy steel in
place of carbon steel we would use thinner leaves, which would
deflect more. The higher elastic limit of the alloy steel enables
it to withstand this higher deflection. Viewing the subject from
another standpoint, if it were not possible to secure better riding
qualities there would be little object in using alloy steels for
springs. A spring can be made adequately strong of carbon steel,
but designed mainly with a view to strength, such a spring is apt
to be rather hard riding.

As spring steel is a rather expensive material the weight of
steel required for the springs is an important item. It will be
shown further on that for a given deflection and a given stress
in the steel the same weight of steel is required whatever the type
of spring used. However, the more complicated types, like three-
quarter and full elliptic, are more likely to be used when large
deflections are wanted, and vice versa, the simplest type, the
quarter elliptic, is most likely to be selected when it is desired
to keep down the cost of the springs.

The following table shows the deflection ranges with the dif-
ferent types of springs.

TABLE XIII. RANGE OF DEFLECTION UNDER DEAD

LOAD

Half Elliptic front 1^4—2 inches

Half Elliptic rear 3V2— 5V2 inches

Three Quarter Elliptic rear 4 — 6% inches

414 — gi/, incluv;

Truck Half Elliptic front 2*4— 3% inches

Truck Half Elliptic rear 2%— 3% inches

Truck platform 3&— 4% inches

It will be seen that the half elliptic front springs of pleasure
cars deflect less than half as much as rear springs of the same
type. One reason for thus limiting the play of the front springs
is the desire to minimize its effect on steering. Another is that
it permits of lowering the frame, since not so much clearance be-
tween frame and axle is required. As regards the various types
of rear springs, it is obvious that the greater the relative length of
the spring the greater the deflection under full load can be made;
that is, a three quarter elliptic or platform spring will deflect
more than a half elliptic, and an elliptic spring most of all.

SPRINGS. 509

As far as pleasure car rear springs are concerned, the initial
deflection under load to be allowed for is chiefly a commercial
question. The greater the initial deflection — load and quality of
spring steel being the same — the greater the weight of the springs
required, and the higher their cost. The greater deflections given
in the tabulation are therefore found on the higher priced cars.
Eccentrated Springs — The formulae for deflection and maxi-
mum safe load developed in the foregoing apply directly only to
half elliptic springs. It is obvious that the deflection of an elliptic
spring under a given load is twice that of one of its half elliptic
members under the same load. In three -quarter elliptic and plat-
form springs the case is slightly more complicated. If the axle
were secured to the middle of the length of the half elliptic or
side member, the ends of the spring would deflect unequally,
which would cause the axle housing to constantly rock around its
axis under the play of the springs, or the spring saddle to rock

FIG. 351. — ECCENTRATED THREE-QUARTER ELLIPTIC SPRING.

on the axle housing, both of which are objectionable. In the
above case there are two quarter elliptic springs in series on one
side of the axle, while there is only a single quarter elliptic on
the other side, and the combined deflection of the two quarter
elliptics would be twice that of the single elliptic. In order to
overcome this defect, the half elliptic or side spring is usually
"eccentrated ;" that is, the centre of its support on the axle is at
unequal distances from the spring eyes. That end of the half
elliptic or side member which is shackled to the frame must be
so much longer than the other end that under a given load it will
deflect as much as the other two quarter elliptics together. The
proper amount of eccentration can easily be calculated for a three
quarter elliptic, provided the two rear quarter elliptics are of equal
length. Since the width, thickness and number of leaves of each
of the three-quarter elliptics in Fig. 351 are the same we have by
equation (76).

510 SPRINGS.

11=^2J2^ 1.264

For practical purposes a coefficient of 1.25 would be sufficiently
close, which makes the two lengths as 4 to 5. If the springs are
thus arranged the deflection can be calculated by assuming that the
longer end of the half elliptic member carries one-half the total
load and calculating its deflection under this load, which will be
equal to the deflection of the whole spring. In a platform spring the
length of the cross member is independent of that of the side
member. In order to find the proper eccentration for the side
member of a platform spring proceed as follows : Assume one-
quarter of the total load on the rear springs to be supported
by one-half of the cross member, and by means of equation (76)
calculate its deflection. Denote this by ds. Now, denoting the
deflection of the long end of the side member by d\ and that of
the short end by d*f we have

di = d* + d*
According to equation (76).

5.1 P /x3 5.1 P h5

E n b t* E n b t*
E n b f
h3 — I? =

5.1 P
We also have /t _j_ /8 = L

These two simultaneous equations can readily be solved after
the arithmetic values are inserted in the right hand terms.

Front half elliptic springs also are sometimes eccentrated, the
object being to increase the wheelbase without increasing the
length of the car.

Number and Thickness of Plates—The deflection of a
cantilever loaded at the end is given by the equation
, W*

and the maximum stress in the material of such a lever is

Wlc Wit

s=s-r~rr

Hence

—

and

SPRINGS. 511

Placing the coefficient of elasticity E at 28,000,000 this reduces to

42,000,000 d

The gauge thickness closest to the result obtained should then
be chosen, and if the result should come midway between the
thicknesses of two gauge sizes, the length of the spring could
be varied slightly and the calculation made over. After t has
been determined the necessary number of leaves may be deter-
mined by a transformation of equation (76) as follows :
«
— (82)

Sample Calculation — To illustrate the use of the formu-lae
derived in the foregoing, we will calculate the springs for a five
passenger touring car in which each of the half elliptic front
springs has to carry 650 pounds and each of the three quarter
elliptic rear springs 850 pounds. From Table XI we find the
proper size of front springs to be 38x2 inches and the proper
size of the rear springs, 52 x 2 + 23 x 2 inches.

We will assume that carbon spring steel, with an elastic
limit of about 135,000 pounds per square inch, is to be used
for the front springs, so that a stress of 50,000 pounds per
square inch can be figured on. The deflection of the springs
under full load would be about 1% inches. Then, inserting
values in equation (81) we find for the necessary thickness of
plates.

50,000 X 102

t = = 0.286 say 0.284 inch

42,000,000 X 1.5

Inserting values in equation (82) we get for the number of
leaves required

5.1 X 325 X 193

n = = 5.92

28,000,000 X 1.5 X 2 X 0.284s

Therefore, six leaves would be chosen. The actual deflection
then would be equation (76)

5.1 X 325 X 198

d = «= 1.48 inches

28,000,000 X 6 X 2 X 0.284s

and the actual stress

42,000,000 X 1.48 X 0.284

8 = = 48,900 Ibs. p. sq. in.

192

The rear springs, we will assume, are to be made of alloy
spring steel, which will sustain a stress of 75.-000 Ibs. per

512

SPRINGS.

square inch. The deflection of the rear springs under load may
be chosen at 5 inches. The long end of the half elliptic mem-
ber will be 52 — 23 = 29 inches long. Inserting values in
equation (81)

75,000 X 292

t = = 0.300

42,000,000 X 5

Inserting in equation (82) the number of leaves figures out to
5.1 X 425 X293

= 7.05

28,000,000 X 5 X 2 X 0.3003
Therefore seven leaves would be used. -

Comparison of Spring Types. — The load on each end of a half
elliptic spring is generally denoted by P and the half length by /.
The total load on the spring then is

W = 2 P

and this is the reaction on the support, if we neglect the weight
of the spring itself. Now suppose the same spring to be used as a
floating cantilever. The reaction on the support is the same as
before, viz., 2 P, but in this case the whole load comes on one end
of the spring. The reactions at the middle and the forward end
of the spring can then be easily found by taking moments (Fig.
352) ; they are 4 P and 2 P respectively. Hence, since the load

FIG. 352.

at each free end is twice as great as in the case of the half elliptic,
each end will deflect twice as much with relation to the center
and the stress in the spring will be twice as great.

Stress in and Deflection of Cantilever Springs. — The expres-
sion for the unit stress in a half elliptic spring is

6 P I 3 W I

n b f n b i~

and since the stress in a cantilever spring is twice as great we
have for it

SPRINGS. 513

6 W I

M b f

With the half elliptic spring the reduction in the opening of the
spring is the same as the lowering of the frame, but this is not the
case with a cantilever spring. Since the forward end is constrained
to maintain the same level relative to the middle, the deflection
of the forward half will result in a slight rotation of the spring
around its center support and the rear half will deflect twice as
much with relation to the frame as it does with relation to the
middle section. Since each half of the spring deflects twice as
much as a corresponding half elliptic, it is obvious that the lower-
ing of the frame is four times as great as with a half elliptic
spring. The equation for the deflection of a half elliptic spring
is

(4.25 to 5.1) P F (4.25 to 5.1) W ?

E n b f 2E n b tz

where W is the weight supported by the spring, and since a
cantilever spring deflects four times as much under a given load
as the same spring used as a half elliptic, the deflection of a can-
tilever spring is evidently given by the equation

(8.5 to 10.2) W P

d —

E n b t3

It is obvious that since a certain spring gives a deflection four
times as great when used as a cantilever as when used as a half
elliptic the same spring could not satisfactorily be used in both
ways for a certain definite spring load. For a given load the
cantilever spring would have fewer and thicker leaves and be
shorter than the half elliptic. We will now assume springs of
the two types respectively, designed for the same load. The
stresses in the material should be the same in each case, as
should the deflection under load, as this latter factor determines
the riding qualities. We will designate the dimensions of the
cantilever spring by means of primes. The weight of a vehicle
spring is closely proportional to the product of its length, width,
number of leaves and thickness of leaves. It is then to be deter-
mined what is the relation of this product for the cantilever
spring to that for the half elliptic spring.

Since the stresses in the material of both springs must be equal
3 W I 6 W I'

n b f n V C

514 SPRINGS.

and since the deflections are the same

4.25 W I3 8.5 W I'3

2E n b t3 E n' b' t'3
From this we get
/3 4/'3

= - - (83)

n b f n b' t'3

We may similarly simplify the equation of the expression for
the stress and get

/ 21'

Squaring n b f n b' t''2

r 4r-

— (84)

n2 b2 t4 n'2 b'2 *"

Dividing equation (83) by equation (84) we gel

n b f n b' t'3

n2 b2 f4 n'2 b'2 t'4

which when reduced gives

nb I t = n b' I' t'

Hence the weight of a cantilever spring will be the same as that
of a half elliptic if the deflections under load and the stresses in
the material are the same, respectively.

The same relation holds between any other classes of springs.
With the same weight of spring material stressed to the same
degree the deflection per 100 Ibs. is the same, and conesquently
the riding qualities should be the same. The choice of spring
types,, therefore, is not so much a question of riding qualities de-
sired as of convenience in mounting and of the use of springs for
purposes other than body suspension, such as the transmission
of the driving thrust from the axle to the frame and taking up
the torque reaction.

Mountings of Cantilever Springs. — As originally designed the
cantilever spring took neither the driving thrust nor the torque
of the rear axle, a pair of links from each side of the frame to
the axle serving this purpose. The rear end of the spring rested
on a roller mounted underneath the axle housing. Thus the axle
was securely tied to the frame, and breakage of the springs would
not cause it to come adrift. Floating cantilever springs in sev-
eral instances are used to take the driving thrust. In one con-

SPRINGS.

515

struction the rear end of the spring is secured to the spring perch
by means of a pressure block of special design, as illustrated
in Fig. 353, and clips. In another design a bolt is passed through
the end of the master leaf and the rear flange of the spring perch,
and a clip over two or more leaves and through the front flange
of the perch.

( ( C

) ) ) )

FIG. 353.— WESTCOTT CANTILEVER SPRING.

The Hotchkiss drive is also being used on commercial vehicles
•and in this application of necessity requires particularly rugged
construction. In Fig. 354 is shown the construction of the Per-
fection Spring Company, which embodies what is referred to as
a three point shackle. The shackles are mounted on a spindle
extending from a bracket.

• j

1 j- J

J LL

^=i

FIG. 354.— PERFECTION THREE POINT SHACT-T-.

516

SPRINGS.

The master leaf of the spring is formed with an eye surround-
ing a bolt extending from this bracket. The second leaf is formed
with an oblong eye through which passes a bolt carried in the
shackles and another bolt carried by the shackles ties the four
longest leaves together as it were.

In order that the springs may be able to protect the car frame
and body from road shock, adequate clearance must be allowed
between the frame and axles. This clearance should be slightly
greater than the total deflection of the spring under dead load.
If the clearance is thus limited the spring can never be stressed
to more than a little over twice its normal stress, so that danger
of breakage is almost eliminated if the elastic limit is from 2.5
to three times the normal stress. A rubber bumper is usually
attached to the spring at the centre which eliminates shock if
the spring closes up completely.

Centre Bolts and Centre Bands — The separate leaves of
leaf springs are held together by means of a centre bolt and nut.
An objectionable feature of the centre bolt is that it materially
weakens the spring, and breakages through the centre bolt holes
are not rare. Some spring makers have attempted to overcome
this defect by using in place of the centre bolt a pair of beads
formed on the spring leaf at its centre, nesting in depressions in
the leaf below. While this does not hold the leaves together, it
keeps them in their proper relative positions longitudinally as
well as transversely. However, the use of centre bolts is well
nigh universal and the S. A, E. Standards Committee on Springs
has recommended the following sizes for these:

FIG. 355.— CENTRE BOLT.

Pleasure cars —
Inches.

A.
Inches.
5-16

B
Inches

Inches.

2 54 to 2 yi

Commercial cars —

2 .

. 5-i6

2y4 to 2y2 ....................... . ^ H 54

3 to 3y2 ......................... 7-16 M X

4 to 4% ........................ ** 54 H

The bolts are to have S. A. E. standard threads, and hexagonal

nuts are usually employed. Where two beads or nibs are used

SPRINGS.

517
inch diameter

the committee recommends that they be made of
and spaced at 94 inch centre distances.

Heavy truck springs are held together by shrunk centre bands,
as shown in Fig. 356. These are made of very soft iron and of
the following dimensions (according to the Springs Division of
the S. A. E. Standards Committee) :

FIG. 356. — CENTRE BAND.

Load Capacity

of Truck,

Tons.

Inches.

25*

3
3

Spring Arch. — Spring leaves are made from rolled stock, and
after they have been cut to the right length are tapered and bent
to form an arc of a circle. That is to say, the majority of
springs, which are said to have a true sweep, are thus bent ;
truck springs are occasionally given a double sweep, the ends
curving in the opposite direction to the middle portion. The
difference between true sweep and double sweep springs is largely
one of appearance. In a half elliptic spring the distance between
a line joining the centres of the eyes and the bottom of the
shortest leaf (or the top of the main leaf) is known as the arch.
It is appare it that the necessary arch is dependent upon the
clearance required under full dead load and on the design of the
spring brackets and frame. A relatively small arch is preferable,
because with it a certain increase in load will give a greater
deflection. This can easily be seen by reference to Fig. 357.
The bending moment at a distance / from the spring eye is equal
to P I cos a, and this is a maximum when a = O, that is, when
the spring is straight. However, some arch is generally neces-
sary in order to insure the required clearance when the spring is
under load. As the value of the cosine does not drop much

SPRINGS.

FIG. 357. — DIAGRAM SHOWING EFFECT OF ARCH ON DEFLECTION.

below unity for the first 10 degrees, this does not have much
effect on the deflection. Foreign pleasure cars are sometimes
provided with nearly flat springs.

Clips and Spring Perches. — Half elliptic and quarter elliptic
spring members are secured to the spring seats or perches by means
of box clips. These are made of very low carbon steel, which will
not easily become brittle under vibration, or preferably of nickel
steel. The shank is made of a diameter equal to one-quarter the
spring width and is cut with an S. A. E. standard screw thread.
Hexagonal head nuts are used on these clips, which can be
locked by means of spring washers, check n..ts or cotter pins.
Generally the ends of the shanks are slightly upset, so the nuts
cannot be lost. The distance between the two clips is made as
small as the design of the spring saddle permits, because that
part of the spring between clips is inactive ; it is generally about
1.5 times the width of the spring. A pad of some soft material
has to be placed between the spring and its seat. Leather and

FIG. 358.— Box CLIP.

SPRINGS.

519

wood have been used, but the best results are obtained with two
Jayers of 8 ounce duck soaked in white lead. Fig. 358 shows a
box clip fitted in place. However, heavy washers are now used
and the units are made two diameters high.

If the rear springs take up the torque or brake reaction their
perches must be securely fastened to the axle housings by rivet-
ing or otherwise. Else the perches swivel on the axle tube
between shoulders, as shown in Fig. 359 at A. The perch is made
in two parts, joined in a horizontal plane and held together by
two square head bolts whose heads are sunk into the spring seats.

FIG. 359. — SPRING PERCHES.

Some designers form the upper part of the spring perch with
lugs to which the radius rod connects.

Undoubtedly the best mounting for a spring perch is that illus-
trated in Fig. 359 at B. A sleeve with a spherical outside sur-
face is riveted to the axle tube, and the perch, which is made in
two parts, is bored out to fit this sphere, so as to give a uni-
versal connection. With the ordinary form of spring mounting
if one rear wheel, say, rises over an obstruction, both rear spring;
are subjected to torsional strains, which they are ill adapted tc
withstand, and this is avoided by using spring perches with
spherical seats.

520

SPRINGS.

FIG. 360.— TIM KEN ADJUSTABLE SPRING PERCH.

Front and rear solid axles usually have the spring seats
forged integral with them. However, a great many motor truck
axles are manufactured by parts makers, and it is then practically
impossible to provide in the dies for integral spring seats, be-
cause of variations in the width of the frame in different designs
of trucks of substantially the same capacity. Fig. 360 illustrates
the manner in which the Timken-Detroit Axle Company get
around this difficulty. A spring block is placed on top of the
axle and the spring secured in place by means of two clips or
four bolts whose lower ends pass through cleats on the under
side of the axle.

Instead of having the box clips bear directly upon the spring
leaves, a pressure block is sometimes inserted between them. As

FIG. 361.— SPRING PRESSURE BLOCK.

SPRINGS.

521

shown in Fig. 361, this is made with grooves for the clips, with
a hole or socket for the head of the centre bolt and with a
curved under surface. This curved under surface obviates local-
ization of the stress at the end of the spring seat and renders the
whole length of the spring available for elastic deflection.

Rebound Clips and Reverse Leaves. — When the wheel
strikes an obstacle in the road the spring near it is compressed,
whereby energy is stored up. Immediately after the compression
has ceased the spring distends again, and if the blow to the
wheel was a heavy one the rebound will carry the body far
beyond its original position of rest relative to the axle. The
main leaf of the spring will thereby be curved in the reverse di-
rection, and as it is not supported by the other leaves in this
direction, it is apt to be stressed beyond the elastic limit by the
rebound.

FIG. 362. — REBOUND CLIP.

There are several methods of preventing such injury to the
main leaf. The most common consists in the use of rebound clips
by which part of the load will be transferred during sharp re-
bounds from the main leaf to the second and third leaves. As
shown in Fig. 362 the rebound clip is preferably riveted to the
end of the shortest leaf which it surrounds, and a tubular spacer
is slipped over the bolt to prevent the leaves being clamped
between the ends of the U-shaped clip, whereby their free play
under ordinary running conditions would be hampered. There
is also another simpler form of clip, known as the clinch clip,
which is simply a piece of flat steel bent into rectangular form,
with the joint at the middle of one of the long sides. This form
of clip is used mainly near the spring eyes, which hold it in
position.

Another method of limiting the rebound consists in placing a
couple of reversely curved leaves on top of the main leaf, as illus-
trated in Fig. 363. These reinforce the main leaf during the
rebound and prevent its breakage. Finally, quite a number of
makers now connect the frame at the rear with the axle tube by
rebound straps, one on each side, which limit the rebound motion.

522

SPRINGS.

Alignment— Although the clips at the centre of a spring tend
to hold the leaves in alignment, they alone are not sufficient, and
some means of preventing lateral motion of the leaves must be

FIG. 363. — REVERSE LEAVES.

provided at their ends. One of the most common plans is to
raise a central longitudinal rib on the leaves for a certain dis-
tance from the end, the rib on one leaf entering a corresponding
gutter on the next. This method is quite successful, but un-
fortunately it does not permit of the use of clips on the leaves.
Another widely followed plan consists in providing the ends of
the leaves with lips, by drawing out the leaf stock laterally in the
forge and bending the lips at right angles, as shown in Fig. 364.
A third method consists in slotting the end of the leaf longi-
tudinally and raising a nib on the leaf below it. The first and
third methods are illustrated in Fig. 365, which figure shows all
of the different spring points in use. The most common forms
of points are the egg-shaped ; round, short French ; round end ;
slot and bead; ribbed and square, and tapered points.

Spring Eyes, Bolts and Shackles — The eyes are either
turned in or out, or are in line with the main leaf, as illus-
trated in Fig. 366 at A, B and C, respectively. In-turned eyes
are the most advantageous, as they are easier to make than
the central eyes, and there is less danger of their opening up
under the pressure of road shocks than with out-turned eyes.
According to S. A. E. specifications, the width of the leaves
at the eyes must be within 0.005 inch of the nominal size. In

FIG. 364. — SPRING LIPS.

all high grade work the spring eyes are bushed with either
phosphor bronze or steel. In case the latter material is used
a seamless steel tube cut to the right length is forced into the
eye and reamed out. With phosphor bronze bushings the bolt

SPRINGS.

523

FIG. 365.— SPRING LEAF POINTS.

preferably should be case hardened and ground. The object
of bushing, of course, is to provide means for readily renew-
ing the wearing surface when that becomes necessary. The
S. A. E. committee recommends bushings of one-eighth-inch
wall thickness.

Truck springs occasionally are provided with elongated
eyes, known as box eyes, which slide on rollers over the
spring bolts; they are also made without eyes at either one
or both ends, the ends sliding in combined wear plates and
guides.

Some means must be provided for effectively lubricating
the shackle bolts, as they are working continuously and will
quickly wear out if they are allowed to remain dry. Small
grease cups, with one-eighth inch pipe threaded stems, are

FIG. 366.— SPRING EYES.

screwed into the heads of these bolts, or the bolts are made
with integral grease cups. Both methods are illustrated in
Fig. 367. In the cheaper cars oil cups are provided instead
of grease cups, or even only oil holes. In platform springs

524

SPRINGS.

the side springs are connected to the cross springs by means
of double or universal shackles, as illustrated in Fig. 368.
These should be made as short as possible, especially in the
case of pleasure cars, as there is always an unpleasant sway-
ing of cars fitted with platform springs when driven at speed,
which is one of the chief reasons why platform springs were
largely given up for three-quarter elliptic on pleasure cars.
These springs are now used to quite an extent on motor trucks
of the speedier class. In this class of work the double shackle
usually consists of two substantially U-shaped members which
are hooked together, the same as used on horse trucks, so
there are only two pivot joints to each double shackle.

FIG. 367. — SPRING SHACKLES AND SHACKLE BOLTS.

The distance apart of the spring brackets should be fixed
so that when the spring carries its normal load the shackles
stand vertically, whether they be in tension or compression.
This arrangement gives the greatest assurance that the shackles
will never come into a position parallel to the ends of the main
leaf in which the spring is locked. To prevent the reversal of
shackles due to excessive rebound they are now often made
of substantially U-shape, as shown in Fig. 369, which limits
their angular motion. These are known as non-reversible
shackles.

Inclined Springs. — Front half elliptic and full elliptic springs
occasionally are set so that the line connecting the two spring
eyes is not horizontal, but slants upward in the forward direc-
tion. The reason for this is that the direction of the worst
shocks on the spring is not vertical but slightly inclined to
the rear, and it is, of course, advantageous to have the direc-
tion of heavy shocks coincide with the direction of spring

SPRINGS.

525

FIG. 368. — DOUBLE SHACKLES FOR PLATFORM SPRINGS.

play. This inclination can be obtained with semi-elliptic
springs by placing the eye of the rear bracket slightly lower
than the eye of the front bracket, and with full elliptic springs
by suitably inclining the seat of the spring bracket on the
frame. Full elliptic and three-quarter elliptic springs are
sometimes clipped to the under side of the axle in order to
lower the frame, and are then said to be underslung.

Torsion and Thrust on Spring — In a few cars the torsion
due to the rear axle drive, the driving thrust of the rear
wheels, and the torsion and thrust due to the action of the

FIG. 369. — NON-REVERSIBLE SHACKLE.

526

SPRINGS.

FIG. 370. — AUXILIARY TRUCK SPRING.

brakes are taken up by. the springs. Since only the main
leaf connects the axle to the frame it is on this leaf that mos»
of the extra strain due to these forces comes. This makes it
necessary to use leaves of comparatively little arch and to
provide spring clips. Engineering opinion regarding this practice
is divided; some regard it as crude and unsatisfactory, while
others claim to be highly advantageous.

Auxiliary Springs — Auxiliary or jack springs are used on
motor trucks to take up part of the load when the truck is
heavily loaded. They are generally secured to the top of the
half elliptic springs, and their ends come in contact with
wear plates on the under side of the frame side rails after
the main leaves have compressed a certain amount. Another
plan is to secure the jack spring to the under side of a frame
cross member and let its ends bear against wear plates on
the rear axle. (Fig. 370.)

Lubrication— Although friction between leaves is desirable
to an extent, because it dampens the rebound, yet it is neces-
sary to keep the leaves lubricated where they bear one against
another. The common plan is to pry the leaves apart in
some manner and introduce lubricant between them with a
table knife. To enable the leaves to hold the lubricant they
are now rolled of the section shown in Fig. 371, so as to
form a grease retaining space between them. Lubrication of

FIG. 371.

SPRINGS. 527

the leaves is necessary mainly because without it there is an
objectionable squeak, though, of course, it also results in
reducing frictional losses.

Some makers in designing their springs take account of the
fact that the torque reaction of the motor increases the load
on the springs on the right side of the car and decreases that
on the springs on the left side (for a motor rotating right
handedly) by making the right hand springs slightly stiffer,
but this effect is usually neglected.

CHAPTER XIX.

ROAD WHEELS.

There are essentially three types of wheels used on motor
cars, viz., artillery wood wheels, which are used on the great
majority of all vehicles; steel wire wheels, which are used on
some pleasure cars, and cast steel wheels, which are used on
lieavy trucks. Disc wheels made from pressed steel are also
being used, but only in rare instances.

Artillery Wheels. — Wood artillery wheels consist of a set
of spokes turned from some very tough wood, generally hickory,
which are clamped at their inner end between flanges on a metal
hub and at their outer end are tenoned into a wooden felloe,
which later is surrounded by a steel band or ring. The spokes
are turned to an elliptic section, and great pains must be taken to
get the fibre to run exactly in the direction of the spoke length.
The spoke billets must be split and not sawed.

Spoke and Felloe Material. — The spokes and felloes of ar-
tillery wheels are made from well seasoned or kiln dried hickory,
which is used because it combines strength, toughness and elastic-
ity in the highest degree. Hickory grows in many parts of the
United States, but the best qualities are said to come from the
Ohio Valley and from the northern portions of the country.
Second growth stock and stock from the lower portion of small
trees yield the best parts. The wood should preferably be cut
when all the sap is out of the tree, which makes the cutting sea-
son in the southern part of the country exceedingly short. Hic-
kory is mostly cut by mill men operating portable saw mills, who,
when the supply in a certain district is exhausted, move their
plant to another part. These mill men sell their stock to the
wheel makers.

Wheel Diameters. — It is now the universal custom in pleasure
car design to use wheels of the same diameter in front and rear,
because with equal sized front and rear tires only a single spare
need be carried. The most common wheel diameters for pleasure

528

ROAD WHEELS. 5^

cars are 32, 34 and 36 inches. Wheel diameters vary with the
wheelbase substantially as follows :

Inches.

Less than 100 inch wheelbase 30

100 to 110 inch wheelbase 32

110 to 120 inch wheelbase 34

115 to 135 inch wheelbase : 36

It will be noticed that the wheelbase ranges for 34 inch and
36 inch wheels overlap. For wheelbases between 110 and 120

FIG. 372. — SPOKE AND FELLOE ASSEMBLY OF PLEASURE CAR WHEEL.

inches 36 inch tires are used on the more expensive cars and 34
inch on the lower priced. Outside wheel diameters are always
expressed in even numbers of inches, except when the so-called
mongrel tires are used ; that is, a tire of a given width on a rim
designed for a tire one-half inch narrower. A few makers have
used wheels of 40 and 42 inches diameter, but such cases
are rare. One reason for using such large wheels is the desire

530

ROAD WHEELS.

to secure ample ground clearance in underslung cars. Large
wheels, of course, improve the riding qualities of the car and add
to the life of the tires, but these advantages are at least partly

offset by their increased cost. They also greatly increase the
stress in the axles, as the leverage of a lateral shock to the
wheel is proportional to the wheel diameter.

ROAD WHEELS. 531

In motor truck work 34 and 36 inch wheels are used almost
exclusively, irrespective of size, except that the rear wheels of
5-ton and over trucks sometimes are made as large as 42 inches
in diameter. In this connection it may be pointed out that in
motor trucks the front wheels are frequently made of somewhat
smaller diameter, since, until recently, solid rubber tires were not
made so they could be interchanged by the driver, and, therefore,
there v:as no advantage in interchangeable front and rear tires.

The diameter of the wood wheel is less than the nominal
wheel diameter by twice the height of the tire and rim. For solid
tired wheels the dimensions have been standardized by the
S. A. E. and the standard specifications will be found in the ap-
pendix to this volume. Standardization of pneumatically tired
wheels along similar lines is now under way.

Number of Spokes — Front wheels of pleasure cars are made
with either 10 or 12 spokes, rear wheels of pleasure cars with 12
spokes. For motor trucks the numbers of spokes are made sub-
stantially as follows:

Load Capacity. Front. Rear.

One ton or less 12 12

il/2 to 2l/2 tons 12 14

2l/2 to 4l/2 tons 14 14

Over 45^ tons 14 16

Proportions of Spokes — Until quite recently it was the uni-
versal practice to make spokes of an elliptic section, the width
of the spoke averaging three-fourths its depth in the direction of
the wheel axis. Lately, however, spokes of square or rectangular
section have come into extensive use for truck wheels and bid
fair to oust the elliptic spoke entirely for that purpose, since the
rectangular spoke is stronger in proportion to weight than the
elliptic spoke. The width of the spoke is generally made con-
stant from end to end, but the depth or thickness (dimension in
the direction of the wheel axis) tapers about l/% inch from hub
to felloe. However, in heavy truck wheels, which, on account of
their dual and even triple tires, require very wide felloes, the
thickness of the spoke is sometimes made increasing from the
hub toward the felloe. Improved turning lathes have recently
been introduced in wheel manufacture which allow of obtaining
two opposite tapers in one operation.

Ine tenons, which are forced into holes drilled in the felloes,
are made equal in diameter to about one-half the depth of the
spoke. One wheel maker says that they should be made of such
length that they extend entirely through the felloe and bear up

532 ROAD WHEELS.

against the steel band. This causes the pressure of the load to
be transferred directly from the spokes to the steel band and
prevents splitting of the felloe through the tenon holes. The
length of the mitre or head of the spoke held between flanges
should be at least 1.25 times the depth of the spoke. The throat
of the spoke, or that portion intermediate between the barrel
and the mitre, is drawn to a radius of about 2 inches and so
that the throat circles of adjacent spokes intersect at ^ inch
from the hub flange circle, while the curved edge of the face of
the mitre comes l/% inch from the hub flange circle.

Spoke Dimensions. — It is found that the greatest strain on
artillery spokes is the result of lateral forces due to skidding.
The wheels must be made strong enough to withstand any such
shocks which are proportional to the weight upon them. The
resistance of the wheel to withstand lateral shocks is proportional
to the number of spokes, to the section modulus of the spoke and
inversely to the diameter of the wheel. That is,

n Z

Calling the depth or thickness of the spoke (dimension between
flanges) d and the width b, the section modulus of an oval spoke
b d2 b d'2

is approximately and that of a rectangular spoke .

10 6

Hence n b tf

But b varies substantially in proportion to d, and therefore we
may write

n d*

and D

Also, since it is customary to use spokes of the same size for
front and rear wheels, notwithstanding the fact that they carry
different maximum loads, we will take for W the total weight
of the car and load. The author's data shows that the average
value of c in pleasure car practice is 14. Hence

1 \W D

d = r4S/— (85)

In the case of truck wheels, since the ratio of width to thick-
ness of spokes varies considerably, it is best to introduce the

ROAD WHEELS.

533

width in the formula. Also, a separate equation should be given
for spokes of rectangular section. Since the spokes of front
and rear wheels are often made of different thicknesses, it is
best to introduce in the formula the weight w on the front and
rear axles, respectively. The author finds that in modern prac-
tice

ivD

1,000

for oval spokes ................................ (86)

and

w D
1,500

for rectangular spokes ...................... (87)

FIG. 374.— PLEASURE CAR FRONT HUB.

Wheel Hubs — The hubs of artillery wheels are made either
of cast steel or of malleable iron. Fig. 374 shows a typical
design of pleasure car front hub, and Fig. 375 a design of truck
rear hub. The general form of the hubs is largely determined by
the dimensions of the bearings and their necessary distance
apart. The outer hub flange is generally made integral with the
hub casting, while the inner one is free, being slipped over a

534

ROAD WHEELS.

machined cylindrical surface so as to be accurately guided.
Some manufacturers round the inner inside edge of the movable
flange, but wheel makers say that this practice is to be con-
demned. If the flange has a fairly sharp corner and meets the
hub barrel at 90 degrees the clamped surface of the spoke mitre
is considerably longer and the spoke is held so much more se-
curely. Nearly all trouble with artillery wood wheels is due to
shrinkage of the spokes, causing looseness in the hubs.

FIG. 375.— TRUCK REAR HUB.

There is much variety in respect to the number of flange
bolts used, and the manner of locating them. The most extensive
practice is to use one bolt for every two spokes and to place it
between the mitres of adjacent spokes. However, some manu-
facturers use a bolt for each spoke, placing it between adjacent
spokes, while still others pass it right through the centre of the
mitre.

Securing Sprockets and Brake Drums— Where a brake
drum is secured to the rear wheel it is sometimes fastened only
by the regular hub flange bolts, the pressed steel drums serving
also as the loose flange of the hub. In this case, naturally, the

ROAD WHEELS.

535

integral flange is made of considerable diameter and the flange
bolts are placed as far out as possible. Other designers, how-
ever, use two circles of bolts, one passing through the integral
flange, spoke and brake drum, and the other, outer one, through
the spoke and brake drum only. In the latter case the spokes
are generally enlarged where the bolts pass through them,* as
shown in Fig. 376 at A. Instead of securing the brake drum
by means of bolts, some designers provide clips, as shown in the
same figure at B. Where brake drums are directly secured to
wheel spokes it is desirable that the flat of the spokes at the
joint with the drum be equal to the greatest width of the spoke,
as otherwise a sharp angle is formed at the joint, in which dirt
collects.

A/V\

FIG. 376. — BRAKE DRUM FASTENINGS.

In order to strengthen the spoke assembly at the centre the
Schwarz Wheel Company makes the mitre of the spokes inter-
locking, as illustrated in Fig. 377, and some other manufacturers
provide keys between the mitres of adjacent spokes.

Hub Caps. — Wheels are held in place on the axle spindles
by nuts on the ends of the latter, which bear against the inner
race of the outermost anti-friction bearing and which are locked
against unscrewing by split pins or similarly effective means.
However, the hubs are provided at their outer ends with screw
caps, in order to retain the lubricant in the bearing and exclude
dust and grit, as well as for the sake of appearance. These hub
caps are provided with a comparatively fine thread, and screw
up against a shoulder formed on the hub barrel, the thread being
either on the inside or outside of the barrel. As loss of hub
caps is a very annoying thing, they are often locked by the

536

ROAD WHEELS.

familiar spring wire ring locking device, while the hub caps of
motor trucks, which, on account of the greater vibration on solid
tired vehicles, are particularly apt to shake loose, are sometimes
made with a small drilled lug and wired to one of the spokes to
prevent their loss. In order to make it possible to conveniently
remove them, the hub caps of pleasure cars are generally pro-
vided with a hexagonal outer portion to which a monkey wrench
can be applied, or with a slotted flange taking a special wrench.
A good scheme in connection with large truck hub caps is to cast
them with four square lugs on their outer plane surface, between
which a pry bar can be inserted.

FIG. 377.— SCHWARZ INTERLOCKING SPOKE.

Owing to the difficulty of unscrewing a cap with a thread 3 to
4 inches in diameter, some makers secure the hub caps by means
of cap screw bolts. It is a common practice to cast the name of
the manufacturer or his trade mark on the hub cap. For light
cars the caps are sometimes made of sheet metal.

Dished Wheels — Front wheels, as well as rear wheels of
those shaft driven cars which have an arched rear axle are gen-
erally dished; that is, the spokes are set at an angle with a plane
perpendicular to the axis of the wheel. In standard American
practice the dish is made 2 degrees. This must be provided for
in turning the hub flanges. Dishing greatly adds to the lateral
strength of the wheel, because it distributes the stress due to any
lateral shocks over a considerable number of spokes. Wheel
makers who have been accustomed to dished wheels all their
lives — these wheels being used exclusively for horse vehicles —

ROAD WHEELS. 537

also maintain that dishing adds to the beauty of a wheel. The
dish of the spokes and the set or camber of the axle should
preferably be alike, as then the bottom spokes, which carry the
load, will stand vertical.

Manufacture of Wheels — At the wheel manufacturing plants
the spoke billets and felloe strips arrive in the green state, and
the first operation consists in kiln drying them. They are packed
in the kiln, which is now generally heated by steam, and the best
results are said to be obtained by starting with a low heat,
gradually increasing it to a maximum and then decreasing it
again. After this process has been completed the billets for the
spokes are placed in eccentric turning machines and the barrel
portion of the spokes is turned substantially to size, whife the
head end is left in the rough state. The spokes then go back
for another drying treatment in the kiln, after which the head
ends are mitred and faced, and the spokes are equalized and
sanded.

The felloe stock as it arrives from the saw mill is steamed in
both exhaust and live steam, and is then bent to the proper curva-
ture, after which it is placed in the kiln and dried for from 20 to
30 days. Upon the completion of the drying treatment, the
felloes are planed, bored, rounded and sanded. The felloe of a
wheel is always made in halves, and the next operation consists
in assembling each half felloe with its spokes, the tenons of the
spokes being forced into the felloe. Next, the two halves of the
wheel are inserted in a screw press and forced on to a dummy
hub. They are then equalized; that is, reduced to the same
height, and the wheel is then reduced to the proper diameter for
the steel band. The latter is heated before being applied to the
felloe, and after being put in place is compressed on it by means
of an hydraulic press. The dummy hub is then taken off and
the wheel is sanded and primed or oiled, and the hub and other
metal parts are fitted to it. The two halves of the felloe are
joined together by means of steel plates extending across the
joint and secured to the felloes by bolts.

Wire Wheels — Wire wheels were used in this country to a
considerable extent in the early days of the automobile, but,
probably on account of too light construction, gave a great deal
of trouble and were soon discarded. They were reintroduced by
an English manufacturer about 1908, and are now widely used
abroad, and also'being taken up again in this country. The chiet
advantage of the wire wheel is that, as compared with a wood
artillery wheel, it has a much greater lateral strength in pro-

538

ROAD WHEELS.

FIG. 378.— SECTIONAL VIEW OF RUDGE-WHITWORTH WIRE SPOKK

ROAD WHEELS. 539

portion to its weight. This makes it possible to use wheels of
smaller weight, which are easier on tires, and some comparative
tests made by the London Taxicab Company are said to have
shown a remarkable tire economy in favor of the wire wheel. An
objection to the wire wheel is that it is not as easily kept clean
as an artillery wood wheel.

FIG. 379. — SIDE VIEW OF WIRE WHEEL.

At present wire wheels are generally made of the demountable
type, these wheels abroad being provided with a hub in the
form of a comparatively thin steel shell formed with serrations
on its inner circumference, which is slipped over the regular
hub on the axle and secured in place by means of a clamping
nut. The Rudge-Whitworth wheel, illustrated in Fig. 378, is of
this type. Such a wheel serves the same purpose as the demount-
able rim generally used in this country, one or more complete

540 ROAD WHEELS.

extra wheels being carried on the car, and in case a tire puncture
or other tire defect is suffered, the wheel carrying the damaged
tire is removed and one of the spare wheels with its tire already
inflated is substituted therefor. In the McCue, a wire wheel
made in this country, the hub of the wheel is driven by a num-
ber of pins secured into a flange of the inner hub and extending
through holes in the outer hub.

The so-called triple spoke construction, illustrated in Fig. 37S,
is generally employed for automobile wire wheels. One-half of
the spokes in the outer row extend tangentially in one direction
and the other half in the opposite direction. The inner row of
spokes and the intermediate row also extend in opposite direc-
tions, respectively. Owing to the fact that the thread at the
outer end of the spokes reduces their effective cross section and
that that portion of the spoke near the head is subjected to bend-
ing stresses in addition to the tension on it, it is customary to
swage down the middle portion of the spoke so as to make it
substantially equal in strength to the threaded portion, thus
eliminating unnecessary weight. In order to secure the neces-
sary lateral strength the hubs must be made of considerable
length and the spoke flanges placed as far apart as possible.

As regards the necessary size of spokes, it may be said that a
touring car of recent design, weighing with load approximately
5,000 pounds, han, 36 inch wire wheels with 56 spokes each,
swaged down at their middle portion to ik inch diameter.

Cast Steel Wheels — Probably the greatest amount of trouble
with artillery wood wheels has been experienced with those used
on heavy trucks. Owing to the very thick spokes required in
these wheels, a comparatively slight proportional shrinkage of
the spokes causes them to loosen in their hubs, and the rather
severe jarring of the wheels due to the use of solid tires then
has a very destructive action. For this reason cast steel wheels
are latterly being used to an increased extent in motor truck
practice. These wheels were first used in Germany, and the
greatest amount of experience with them has been gained in that
country. We show herewith (Fig. 380) a sectional view of the
cast steel rear wheel, as specified for German military trucks.
These trucks are designed for a maximum total load of 5^
metric tons on the rear axle, and the rear driving wheels are to
be fitted, with dual solid tires of 41 inches outside diameter, 5.6
inches width and 3.6 inches depth, the cast steel portion of the
wheel being 34 inches in outside diameter. It will be seen that
the wheel is provided with a hollow spoke of about 3 inches

ROAD WHEELS.

541

FIG. 380.— CAST STEEL REAR WHEEL OF GERMAN MILITARY TRUCK.

542 ROAD WHEELS.

minimum depth, the wall of the spokes as well as the inner
wall of the rim being a shade below l/4 inch in thickness. These
wheels are provided with plain parallel bearings, in which re-
spect they differ from cast steel wheels used in this coun-
try, as it is customary here to use anti- friction bearings. In
the majority of cases the spokes are made cross shaped, which
makes the molding a good deal easier, but the hollow round
spoke is neater in appearance and also has the advantage with
respect to lateral strength, at least in the case of trucks of large
capacity.

Floating Bushings — Abroad the road wheels of motor trucks
are frequently fitted with floating bushings instead of with
antifriction bearings and the Government specifications for
military subsidy vehicles 6f some countries specify these bush-
ings. One of the advantages of this construction is that with
it the wheel can be quickly removed and replaced in case of
tire trouble. Except when starting from rest, a plain bearing
with floating bushing offers not very much more resistance
than an antifriction bearing.

In order to ensure satisfactory lubrication, the clearance on
both the inside and outside of the bushing should be from
0.008 to 0.012 inch, for diameters of 3 to 4 inches. If the clear-
ance is too small the lubrication is not so dependable. The
bushings are drilled with numerous oil holes and it is recom-
mended that these be spaced on helical lines. The bearing
surfaces of both the axle and the hub must be carefully ground
and polished, and unless the hub is of a metal showing a fine
texture, it is best to bore it out and force in a steel liner under
hydraulic pressure, which is then either ground or reamed.
The wheel bearings should be so proportioned that the unit
pressure due to the weight and traction effort combined, does
not exceed 400 Ibs. per square inch. If this load is not ex-
ceeded and if the lubricating system is carefully worked out
the bushings will give a very satisfactory life.

APPENDIX

Clutch Spring Table.

The following table permits of readily determining the size of
wire required for clutch springs of certain lengths and diameters
of coil, to exert a certain pressure. D denotes the mean diam-
eter of the coil (from centre to centre of wire), which is equal
to the outside diameter minus the diameter of the wire; d, the
diameter of the wire; IV, the maximum safe pressure a spring
of the particular diameter of coil and diameter of wire will
sustain, and F, the deflection of one coil under a pressure of 100
pounds. It will be noticed that three different values are given
for F for each size of wire and diameter of coil ; these corre-
spond to coefficients of torsional elasticity of 10,000,000, 12,000,000
and 14,000,000, respectively. The maximum safe pressure is cal-
culated on the basis of a stress of 50,000 pounds per square inch.

5/16'

7/16"

= ll/2"

\y&"

154"

l?/8"

2/8"

2 Y*"

2H"

— 204.5

188.5

175.0

163.4

153.1

144.1

136.1

129.0

f.0697

.0882

.1108

.1335

.1643

.1967

.2390

.2751

F^ .0581

.0735

.0924

.1109

.1367

.1639

.1949

.2293

[.0498

.0629

.0791

.0953

.1172

.1406

.1671

.1965

= 389.9

367.3

341.1

318.3

298.4

280.9

265.3

251.3

f.0283

.0358

.0450

.0541

.0667

.0800

.0951

.1102

F-! .0236

.0299

.0375

.0452

.0555

.0667

.0793

.0931

1.0201

.0256

.0321

.0387

.0476

.0571

.0679

.0799

= 663.1

636.8

591.3

551.9

517.4

486.9

459.9

435.7

f.0137

.0174

.0218

.0263

.0323

.0388

.0472

.0542

F\ .0114

.0145

.0182

.0219

.0269

.0323

.0384

.0451

[.0098

.0124

.0156

.0188

.0230

.0277

.0329

.0387

= 1041.

1009.

936.9

874.4

819.8

771.5

728.7

690.3

f.0062

.0079

.0099

.0119

.0146

.0176

.0209

.0246

F] .0052

.0066

.0082

.0099

.0122

.0146

.0174

.0202

[.0045

.0056

.0071

.0085

.0105

.0126

.0149

.0175

= 1636.

1510.

1402.

1309.

1227.

1155.

1091.

1033.

f.0044

.0055

.0069

.0083

.0102

.0123

.0146

.0172

F-i .0036

.0046

.0058

.0069

.0084

.0102

.0122

.0134

[.0031

.0041

.0054

.0060

.0074

.0089

.0105

.0124

543

544

APPENDIX.

545

J
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546

APPENDIX.

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APPENDIX.

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roO\*r>OV£)t>.»^'-i'-i<NCMrciO\ot^OOOCNliO

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i CM CM CM CM CO

I I I I I I I I I I I I I I

iAi^.ivi-vO-.^^CMCMfNCM

548

APPENDIX.

d <r> >o o> 4 N

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tx to *o) o ON oo o o\ oo o* tx oo

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APPENDIX.

*^l/'o»oo

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550

APPENDIX.
S. A. E. Six Spline Fittings.

Permanent fit.

To Slide when not To Slide when Under
Under Load. Load.

l^l^m

r — -

6—1
w =
b =

a =

Nominal

.25 D
.05 D
,90 D

^^m

« — «

6-
w =
h =
a =

.25 D
.0751
.88 D

4
>

1
1

^^
- a

6-
w rr
h =

a =

. •

-c.

.251
.101
.801

1
t

)
)

.750
44 . . .

.675

.188

,750

.638

.188

117

.750

.600

.188

152

.749
.875

.674

.788

.187
.219

109

.749

.875

.637
.744

.187
.219

159

.749
.875

.599
.700

.187
.219

207

.874
1.000

.787
.900

.218
.250

143

.874
1.000

.743
.850

.218
.250

208

.874
1.000

.699
^800

.218
.250

270

.999
1.125

1.124
1.250

.899
1.013

1.012
1.125

.249
.281

.280
.313

180
223

.999
1.125

1.124
1.250

.849
.956

.955
1.063

.249
.281

.280
.313

263
325

.999
1.125

1.124
1.250

.799
.900

.899
1.000

.249
.281

.280
.313

342
421

1.249
1.375

1.124
1.238

.312
.344

269

.1.249
'1.375

1.062
1.169

.312
.344

393

1.249
1.375

.999
1.100

.312
.344

510

1.374
1.500

1.237
1.350

.343
.375

321

1.374
1.500

1.168
1.275

.343
.375

468

1.374
1.500

1.099
1.200

.343
.375

608

1.499
1.625

1.349
1.463

.374
.406

376

1.499
1.625

1.274
1.381

.374
.406

550

1.499
1.625

1.199
1.300

.374
.406

713

1.624
1.750

1.462
1.575

.405
.438

436

1.624
1.750

1.380
1.488

.405
.438

637

1.624
1.750

1.299

1.400

.405
.438

827

1749
2.000

o ._

1.998
2.250

1.574
1.800

1.798
2.025

.437
.500

.498
.563

570
721

1.749
2.000

1.998
2.250

1.487
1.700

1.698
1.913

.437
.500

.498
.563

823

1,052

1.749
2.000

1.998
2.250

1.399
1.600

1.598
1.800

.437
.500

.498
.563

1,080
1,367

2.248
2.500

2 028
2.250

.561
.625

891

2.248
2.500

1.912-
2.125

.561
.625

1 300

2.248
2.500

1.798
2.000

.561
.625

1 688

2.498
3.000

O „._,

2.248
2.700

.623
,760

1,283

2.498
3.000

2.123
2.550

.623
.750

1,873

2.498
3.000

1.998
2.400

.623
.750

2,430

2,998

2.698

.748

2.998

2.548

.748

2.998

2.398

.748

T = 1.000 X 6 X mean R X h X 1 = inch-pounds torque capacity per inch;
bearing length at 1,000 Ibs. pressure per square inch on sides of splines. No allow-
ance is made for radii on corners nor for clearances. ,

APPENDIX.
S. A. E. Ten Spline Fittings.

551

Permanent fit,.

10— A

w =- .156D
h = .045 D

a = .91 D

To Slide when not
Under Load.

10— B.

w = .156 D
h = .07 D
a = .8«D

To Slide when Undejf
Load.

10— C.

w — .156 D
h = .095 D
a = .81 D

Nominal
diameter.

1*4

15*

.750

.683

.117

.750

.645

.117

120

_____

.749

.682

.116

.749

.644

.116

.875

.796

,137

.875

,753

.137

165

______

.874

.795

.186

.874

.752

.186

1.000

.910

.156

1.000

.860

.156

215

.999

.909

.155

.999

.859

.155

1.185

1.024

.176

1.125

.968

.176

1.124 1.023 .175
1.250 1.138 .195

1.249 1.137
1.375 1.251

.194
.215

1.374 1.250 .214
1.500 1.365 .234

1.499 1,364 .233
1.625 1.479 .254

1.624 1.478 .253
1.750 1.593 .273

1.749 1.592
2.000 1.820

.272
.312

1.998 1.818 .310
2.250 2.048 .351

2.248 2.046
2.500 2.275

.349
.390

2.498 2.273 .388
3.000 2,730 -.468

271

336

406

483

566

658

860

1,088

1,343

2.998 2.728 .466

1,934

1.124 .967 .175

1.250 1.075 .195

1.249 1.074 .194
1.375 1.183 .215

1.374 1.182 .214

1.500 1.290 .234

1.499 1.289 .233
1.625 1.398 .254

1.624 1.397 .253

l.,750 1.505 -.273

1.749 1.504 .?72

2.000 1.720 .312

1.998 1.718 .310

2.250 1.935 .351

2.248 1.933 .349

2.500 2.150 .390

2.498 2.148 .388

3.000 2.580 .468

?.998 2.578 .466

T.
183

248
326
412
508
614
732
860

1,302
1.647
2,034
2,929

.750

.749
.875

.874
LOGO

1.125

.608

.117

.607 .116
.709 .137

.708 .136
.810 .156

.809 .155
.911 .176

1.124 .910 .175

1.250 1.013 .195

1.249 1.012 .194

1.375 1.114 .215

1.374 1.113 .214

1.500 1.215 .284

1.499 1 91 _ .238

1625 1.316 .254

1.624 1.315 .253

1.750 1.418 .273

997

1.749 1.417
2.0PO 1.620

.272
.312

T.
841

839

480

545

672

813

967

1,185

1,316

1,720

2,176

1.998 1.618 .810

2.250 1.823 .351

2.248 1.821 .349

2.500 2.025 .390

2.498 2.023 .388
3.000 2.430 .468

< — S.B69

2,998 2.428 .466

T = 1,000 X 10 X mean R X h X 1 = inch-pounds torque capacity per inch;
bearing length at 1,000 Ibs. pressure per square inch on sides of splines. No al-
lowance is made for radii on corners nor for clearances.

»52 APPENDIX.

S. A. E. Four Spline Fittings.

Permanent Fit

w / H

4-A

w equals .241 D
h equals .075 D
d equals 850 D

4-B

w equals .241 D
h equals .125 D
d equals .740 D

}

Norn.
Dia.

D ^

.750

.637

.181

.056

.750

.562

.181

.094

123

.749

.636

.180

.055

.749

.561

.180

.093

.875

.744

.211

.066

107

.875

.656

.211

109

167

.8/4

.743

.210

065

.874

.655

.210

108

1.000

,850

.241

075

139

1.000

.750

.241

.125

219

.999

.849

.240

.074

.999

.749

.240

.124

1.125

.956

.271

084

175

1.125

.844

.271

.141

277

1.124

.955

.270

.083

1.24

.843

.270

.140

1.250

1.062

.301

.094

217

1.250

.937

.301

.156

341

1.249

1.061

.300

.093

1.249

.936

.300

.155

1.375

1.169

.331

.103

262

1.375

1.031

.331

.172

414

1.374

1.168

.330

.102

1.374

1.030

.330

171

1.500

1.275

.361

.112

311

1.500

1.125

.361

.187

491

1.499

1.274

.360

.111

1.499

1.124

.360

.186

1.625

1.381

.391

.122

367

11625

1.219

.391

.203

577

1.624

1.380

.3^0

.121

1.624

1.218

.390

.202

1.750

1.487

.422

.131

424

1.750

1.312

.422

.219-

670

1.749

1.486

.421

.130

1.749

1.311

.421

.218

2.000

1.700

.482

150

555

2.000

1.500

.482

.250

875

1.998

1.698

.480

.-148

1.998

1.498

.480

.248

2.250

1.912

.542

.169

703

2.250

1.687

.542

.281

1106

2.248

1.910

.540

.167

2.248

1.685

.540

.279

2.500

2.125

.602

.187

865

2.500

1.875

.602

.312

1365

2.498

2.123

.600

.185

2.498

1.873

.600

.310

3.000

2.550

.723

.225

1249

3.000

2.250

.723

.375

1969

2.998

2.548

.721

.223

2.998

2.248

.721

.373

To Slide when not under

T equals 1000 x 4 x Mean R x h x 1 equals inch-pounds torque capacity per inch
bearing length at 1000 Ibs. pressure per square inch on sides of splines. No allowance
is made for radii on corners toor for clearance!.

APPENDIX. 553

S. A. C. Standard Lock Washers.

AUTOMOBILE HEAVY (FOR GENERAL USE).

Bolt Lock Bolt Lock

Diameter, Washer Section, Diameter, Washer Section,

Inches. Inches. Inches. Inches.

3/16 1/16x1/16 11/16 y4x*A

y* 5/64x5/64 y* V^A

5/16 *AX# % 17/64x17/64

H y&*y& i 5/16x5/16

7/16 11/64x11/64 1% 5/16x5/16

ya 11/64x11/64 ij4 3/8xy8

9/16 13/64x13/64 iti ti*M

Si 13/64x13/64 ll/3 7/16x7/16

AUTOMOBILE LIGHT (FOR OPTIONAL USE AGAINST SOFT
METAL).

Bolt Lock Bolt / Lock

Diameter, Washer Section, Diameter, Washer Section,

Inches. Inches. Inches Inches.

3/16 1/16x3/64 9/16 13/64x5/32

Vt, 5/64x1/16 ft 13/64x5/32

5/16 Ys^/32 11/16 ^x3/i6

H 5*x-;/32 Y* J*x3/i6

7/16 H/64XJ6 H 17/64x3/16

Y* 11/64x3* i 5/I6XJ4

The outside diameters of lock washers shall coincide prac-
tically with the long diameters of S. A. E. standard nuts, which
are approximately the same as the short diameters of U. S.
standard nuts. The inside diameters of the lock washers shall
be from one-sixty-fourth to one-thirty-second inch larger than
the bolt diameters. The lock washers shall be parallel-faced sec-
tions, and bulging or malformed ends must be avoided.

Temper Test. — After compression to flat, reaction shall be
sufficient to indicate necessary spring power, and on a subse-
quent compression to flat, the lock washer shall manifest no
appreciable loss in reaction.

Toughness Test. — Forty-five per cent, of the lock washer, in-
cluding one end, shall be firmly secured in a vise, and 45 per
cent., including the other end, shall be secured firmly between
parallel jaws of a wrench. Movement of the wrench at right
angles to the helical curve shall twist the lock washer through
45 degrees without sign of fracture, and movement of not more
than 135 degrees shall twist the lock washer entirely apart.

554

APPENDIX.

Light Series of Radial Ball Bearings.

Corner

Radial

No. of

at Bore of

Load

Bear-

— Bore. —

Diameter.

— Width. — Inner Race.

ing.

Mm.

Inches.

Mm.

Inches.

Mm. Inches. Mm. Inches.

Lbs.

200

•39370

i .18110

9 0.35433

0.04

120

201

.47244

1.25984

10 0.39370

0.04

140

202

.59055

1-37795

ii 0.43307

0.04

160

203

.66929

1.57481

12 0.47244

0.04

250

204

.78740

1.85040

14 0.55118

0.04

320

205

.98425

2.04725

15 0.59055

0.04

350

206

. 18110

2.44095

i 6 0.62992

0.04

550

207

•37795

2.83465

17 0.66929

0.04

600

208

.57481

3-14962

i 8 0.70866

0.08

860

2O9

.77166

3.34647

19 0.74803

0.08

9S«

2IO

.96851

3.54332

20 0.78740

0.08

IOOO

211

.16536

IOO

3.93702

21 0.82677

0.08

1 1 60

212

.36221

4.33072

22 0.86614

0.08

1550

213

.55906

120

4.72443

23 0.90551

0.08

1670

214

2.75591

125

4.92128

24 0.94488

0.08

1820

215

2.95277

130

5.11813

25 0.98425

0.08

2130

216

3.14962

140

5-51183

[.02362 3 0.12

2650

217

3.34647

150

5.90554

[.10236 3 0.12

2850

218

3-54332

1 60

6.29924

[ . 18110 3 o. 12

3400

2IQ

3.74017

170

6.69294

1.25984 3 0.12

3750

220

100

3.93702

180

7.08664

1.33858 3 0.12

3950

221

105

4.13387

190

7-48035

1.41732 3 0.12

4600

222

4.33072

200

7.87405

1.49607 3 0.12

5000

Heavy Series of Radial

Ball Bearings.

Corner

Radial

No. of

at Bore of

Load

Bear-

— Bore.—

Diameter.

—Width.— Inner Race.

ing.

Mm.

Inches.

Mm.

Inches.

Mm.

Inches. Mm. Inches.

Lbs.

403

.66929

2.44095

.66929 i

0.04

850

404

.78740

2.83465

.74803 2 0.08

1050

405

.98425

3-14962

2 I

.82677 2 0.08

1320

406

.18110

3-54332

.90551 2 0.08

1600

407

•37799

IOO

3.93702

.98425 2 0.08

1900

408

.5748i

4-33072

.06299 2 O.O8

220O

409

.77166

120

4.72443

.14173 2 0.08

2500

410

.96851

130

5-11813

.22047 2 O.O8

3400

411

.16536

140

5.5"83

.29921 3 o.i 2

3900

412

.36221

150

5.90554

•37795 3 0.12

4400

413

.55906

1 60

6.29924

.45669 3 0.12

4900

414

•75591

180

7.08664

•65355 3 0.12

62OO

4»S

•95277

190

7.48035

.77166 3 0.12

6600

416

3-14962

200

7.87405

.88977 3 0.12

7300

4*7

3.34647

210

8.26775

.04725 3 0.12

8580

418

3.54332

225

8.85830

.12599 3 0.12

IOOOO

419

3.74017

250

9-84256

55 2.16536 3 0.12

11880

420

100

3.93702

265

10.43311

60 2.36221 3 0.12

14,000

APPENDIX.
Medium Series of Radial Ball Bearings.

555

Corner
Mo. of at Bore of
Bear- — Bore. — Diamettr. — Width. — Inner Race,
ing. Mm. Inches. Mm. Inches. Mm Inches. Mm. Inches.

Radial
Load

in
Tbs.

300 10

0-39370 35 J-37795 " 0.43307

0.04

200

301 12

0.47244 37 1.45669 12 0.47244

0.04

240

302 15

0.59055 42 1.65355 13 0.51181

0.04

280

303 17

0.66929 47 1.85040 14 0.55118

0.04

370

304 20

0.78740 52 2.04725 15 0.59055

0.04

440

305 25

0.98425 62 2.44095 17 0.66929

0.04

620

306 30

i. 18110 72 2.83465 19 0.74803

0.08

860

307 35

1-37795 80 3.14962 21 0.82677

0.08

I 100

308 40

1.57481 90 3-54332 23 0.90551

0.08

MS0

309 45

1.77166 100 3-93702 25 0.98425

0.08

1750

310 50

1.96851 no 4.33072 27 1.06299

0.08

2IOO

3" 55

2.16536 120 4.72443 29 1.14173

0.08

2400

312 60

2.36221 130 5.11813 31 1.22047

0.08

2800

313 65

2.55906 140 5.51183 33 1.29921

O. 12

3300

3*4 7°

2.75591 150 5-90554 35 1-37795

O. 12

4000

315 75

2.95277 160 6.29924 37 1.45669

0.12

4400

316 80

3.14962 170 6.69294 39 .1.53544

O. 12

5OOO

317 85

3.34647 180 7.08664 41 1.61418

O. 12

5700

318 90

3-54332 190 7-48035 43 1.69292

0.12

6400

3i9 95

3.74017 200 7.87405 45 1.77166

O. 12

70OO

32O TOO

3.93702 215 8.46460 47 1.85040

O. 12

7700

321 105

4.13387 225 8.85830 49 1.92914

0. 12

8400

322 no

4.33072 240 9.44886 50 1.96851

0. 12

IOOOO

S. A.

C. Tolerances for Radial Ball Bearings.

f\ .1 r»_ ™ T>

W'Hth

Plus Minus Total Plus Minus Total

Plus

Minus

Total

Bearing

Lim- Lim- Lim- Lim- Lim- Lim-

Lim-

Numbers.

its, its. its. its. its. its.

its.

200 to 204

o .0006 .0006 .0002 .0004 .0006

.002

300 to 303

o .0006 .0006 .0002 .0004 .coo6

.002

205 to 215

o .0008 .0008 .0002 .0004 .0006

.OO2

.002

304 to 316

0 .0008 .0008 .0002 .0004 .0006

.002

403 to 411

o .0008 .0008 .0002 .0004 .0006

.OO2

217 tO 222

O .OOI2 .0012 .OOO2 .COO4 .OOO6

.002

3I4t03I9

o .0012 .0012 .0002 .0004 .0006

.002

412 to 416

0 .0012 .0012 .0002 .0004 .OOO6

.OO2

.002

556

APPENDIX.

8888 8888 8888 888

<O«DCO«O oooooooo oooooo

)OOO OOOO

!888 8888 8888 888

§888 888

oooo oooo oooc? oooo ooo

APPENDIX

557

Ill

OOOOOOOO «

8888 8888 8

888 8888 8888 8

•^TfOOOO OOOOOOOO 00(N(N(N M (N N C^ *3

pppp pppp P*-"-;^ '-H'-JI-J^ »-j

OOOOO OOOOOOOO OOOOC^C^l WNNd N

oooo oooo oooo oooo o

S8 882

O^?O*O »-<«Oi-i«O »H«pi-(l
•>t<N>-<a> 00 «D 10 CO <NOO5I

ICIO T}<^Tf<-^ CO

t> o> i-Hco»ot^ O;
eocococo eo

22 2222

558

APPENDIX.

S. A. C. Standard Wheel Dimensions for Solid

Tires.

DEMOUNTABLE AND NON-DEMOUNTABLE RIMS.

Single Tires.

Width of felloe and band, M inch less than sectional size of tire. Thickness
of steel band, J4 inch up to 4J4 inch tire; ^ inch on 4^ inch and larger
tires.

Dual Tires.

Width of felloe and band, twice the sectional size of tire. Thickness of
steel band, ^ inch for all sizes of tire.

Single and Dual Tires.

Inches. Inches. Inches. Inches. Inches.
Sectional size of tire ............. 2 2*6 3 3^ 4

Minimum felloe thickness ........ iJ4 ilA i/4 iJA i$4

Sectional size of tire ............. 4*A S S*A 6 6l/2 and over

Minimum felloe thickness ........ i$4 2 2 2 2%

WHEEL DIAMETER OVER STEEL BAND.
Single and Dual Tires.

Inches,
36
30

Inches. Inches. Inches.

Nominal outer diam. of tires. ... 30 32 34

Wheel diam. over steel band.... 24 26 28

Exact circumference over steel

band; neglecting tolerance 7525/64 8111/16 8731/32 94^

Inches. Inches. Inches.

Nominal outer diam. of tires. ... 38 40 42

Wheel diam. over steel band. ... 32 34 36

Exact circumference over steel

band; neglecting tolerance 10017/32 10613/16 "33/32

Allowable Deviation from Precision in Felloe Bands.

Plus Minus

Inches. Inches.

Tolerance in circumference of band before application.. 1/32 1/32

Tolerance in circumference of band after application 1/16 1/32

Tolerance of thickness of band 0.006 0.006

Tolerance in radius of band after application 1/16 1/16

Tolerance in width of felloe band —

Up to and including 4 inches 1/32 1/32

4 1/16 to 6 inches 3/64 3/64

6 1/16 to 12 inches 1/16 1/16

Variation in trueness of band when placed on surface plate —

Band shall touch at all points within 1/32 inch up to and including 6
inch width. Over 6 inch width within 1/16 inch.

MEASURING CIRCUMFERENCE OF BAND.

In measuring circumference of band, if there is not an allow-
ance on the tapeline itself, a correction amounting to three times
the thickness of the tapeline should be made.

NOTE.— All of the foregoing summary, so far as pertinent, ap-
plies to metal wheels.

APPENDIX.

559

BOLT EQUIPMENT FOR SIDE FLANGES.

All Bolts to Be y2 Inch Diameter.

Outside Diameter

Bolt Diameter

Number Bolt Diameter

Number

Tire Hole Circle.

of Bolts. Tire Hole Circle.

of Bolts.

26 isy2

6, 9 or 18 42 34}4

10, 15 or 30

28 20y2

do. 44 36^

12, 18 or 36

30 22^

do. 46 3Sy2

do.

32 24*/2

8, 12 or 24 48 40}4

do.

34 26y2

do. 50 42}4

14, 21 or 42

36 28y2

do. 52 44y2

do.

38 30J4

10, 15 or 30 54 46}4

do.

40 32H

do.

•

Dimensions of Wrought Iron Pipes.

Nominal

Actual Inside Actual Outside

No.

Diameter,

Diameter, Diameter,

of Threads

Inches.

Inches. Inches.

Per Inch.

, 0.27 0.405

0.364 0.54

0.494 0.675

0.623 0.84

0.824 1.05

1.048 1.315

\\y2

154

1.38 1.66

ny2

154

1.61 1.90

iiX

1.067 2.375

ny>

2J4

2.468 2.875

3.067 3.5

560

APPENDIX.
S. A. £• Steel Specifications.

Spec.

No.

Mn.

P.*

S.*

Ni.

Cr.

V.**

CARBON

STEELS.

1010

.05-.15

.30-.60

.045

.05

1020

.15-.25

.30-.60

.045

.05

1025

.20-.30

.50-.80

.045

.05

1035

.30-.40

.SO-.80

.045

.05

1045

.40-.SO

.50-.80

.045

.05

1095

.90-1.05

.25-.50

.04

.05

1114J

.08-.20

.30-.80

.12

.06-.12

NICKEL

STEELS.

2315

.10-.20

.50-.80

.04

.05

3.25-3.75

2320

.15-.25

.50-.80

.04

.045

3.25-3.75

2330

.2S-.35

.50-.80

.04

.045

3.25-3.75

2335

.30-.40

.50-.80

.04

.045

3.25-3.75

2340

.35-.4S

.50-. 80

.04

.045

3.25-3.75

2345

.40-.50

.50-.80

.04

.045

3.25-3.75

3120

.15-.25

.50-. 80

.04

.045

.00-1.50

.45-.7S

3125

.20-. 30

.50-.80

.04

.045

.00-1.50

.4S-.75

3130

.25-.3S

.50-.80

.04

.045

.00-1.50

.45-.7S

3135

.30-.40

.50-. 80

.04

.045

.00-1.50

.4S-.75

3140

.35-.4S

.50-.80

.04

.045

.00-1.50

.4S-.75

3220

.15-.25

.30-. 60

.04

.50-2.00

.90-1.25

3230

.25-.3S

.30-.60

.04

.50-2.00

.90-1.25

3240

.3S-.45

.30-.60

.04

.50-2.00

.90-1.25

3250

.45-. 55

.30-.60

.04

.50-2.00

.90-1.25

X3315

.10-.20

.45-.7S

.04

2.75-3.25

.60-.95

X3335

.30-.40

.45-.7S

.04

2.75-3.25

.60-.95

X3350

.4S-.55

.45-.7S

.04

2.75-3.25

.60-.95

3320

.15-.25

.30-.60

.04

3.25-3.75

1.25-1.75

3330

.2S-.35

.30-.60

.04

3.25-3.75

1.25-1.75

3340

.3S-.45

.30-.60

.04

3.25-3.75

1.25-1.75

CHROME NICKEL STEELS.

5120

.15-.25

.04

.045

.65-.8S

5140

.35-.4S

.04

.045

.6S-.85

5165

.60-. 70

.04

.045

.65-.8S

5195

.90-1.05

.20-.45

.03

.90- .10

51120

1.10-1.30

.20-. 45

.03

.90- .10

5295

.90-1.05

20-. 45

.03

1.10- .30

52120

1.10-1.30

.20-.45

.03

1.10- .30

VANADIUM STEELS.

6120

.15-.25

.50-.80

.04

.80- .10

.15

6125

.20-.30

.50-. 80

.04

.80- .10

.15

6130

.25-.3S

.50-.80

.04

.80- .10

.15

6135

.30-. 40

.50-. 80

.04

.80- .10

.15

6140

.3S-.45

.50-.80

.04

.80- .10

6145

.40-. 50

.50-. 80

.04

.80- .10

.15

6150

.45-.S5

.50-. 80

.04

.80- .10

.15

6195

.90-1.05

.20-.45

.03

.80- .10

.15

SILICO-MANCANESE STEELS.

9250

.45-.S5

.60-.80

.045

1.80-2.10%

9260

.5S-.65

.50-.70

.045

1.50-1.80% Si

* Not to exceed. fTwo types of steel are available in this class, viz., one
with manganese .25-. 50 per cent, and silicon not over .20 per cent. ; the
other with manganese .60-. 80 per cent, and silicon .15-. 50 per cent. **Not
less than. |Screw stock; the amount of sulphur in this case is to be between
the limits given.

APPENDIX 561

List of Heat Treatments.

A — After forging or machining carbonize at between 1600° and 1750° F.
(1650-1700° F. desired), cool slowly or quench, reheat to 1450°-1500° F.
and quench.

B — After forging or machining carbonize at between 1600° and 1750° F.
(16SO°-1700° desired), cool slowly in the carbonizing mixture, reheat to
1550°-1625° F., quench, reheat to 1400°-1450° F., quench, draw in hot oil at
from 300° to 450° F., depending upon the hardness desired.

D — After forging or machining heat to 1500°-1600° F., quench, reheat to
1450°-! 500° F., quench, reheat to 600M2000 F. and cool slowly.

E— After forging or machining heat to 1500°-! 550° F., cool slowly, reheat
to 14SO°-1500° F., quench, reheat to 600°-1200° F. and cool slowly.

F — After shaping or coiling heat to 1425°-1475° F., quench in oil, reheat
to 400°-900° F., in accordance with degree of temper desired and cool
slowly.

G— Carbonize at between 1600° and 1750° F. (1650°-1700° F. desired),
cool slowly in the carbonizing material, reheat to 1500°-! 550° F., quench,
reheat to 1300°-1400° F., quench, reheat to 250°-500° F. (in accordance
with the necessities of the case) and cool slowly.

H — After forging or machining heat to 1500°-1600° F., quench, reheat to
600°-1200° F. and cool slowly.

K — After forging or machining heat to 1500°-1550° F., quench, reheat
to 1300°-1400° F., quench, reheat to 600°-1200° F. and cool slowly.

L — After forging or machining carbonizing at a temperature between
1600° and 1750° F. (1650°-1700° desired), cool slowly in the carbonizing
mixture, reheat to 1400°-1SOO° F., quench, reheat to 1300°-1400° F., quench,
reheat to 250°-500° F. and cool slowly.

M — After forging or machining heat to 1450°-! 500° F., quench, reheat to
500°-1250° F. and cool slowly.

P — After forging or machining heat to 1450°-! 500° F., quench, reheat to
1375°-1450° F., quench, reheat to 500°-12SO° F. and cool slowly.

Q — After forging heat to 147S°-1525° F., hold at this temperature one-half
hour to insure thorough heating, cool slowly, reheat to 1375°-1425° F.,
quench, reheat to 250°-550° F. and cool slowly.

R— After forging heat to 1500°-1550° F., quench in oil, reheat to 1200°-
1300° F., hold at this temperature three hours, cool slowly, machine heat
to 13SO°-14SO° F., quench in oil, reheat to 2SO°-SOO° F. and cool slowly.

S — After forging or macJiining carbonize at a temperature between
1600° and 1750° F. (1650°-1700° F. desired), cool slowly in the carbonizing
mixture, reheat to 16SO°-1750° F., quench, reheat to 1475°-1SSO° F.. quench,
reheat to 250°-550° F. and cool slowly.

T — After forging or machining heat to 16SO°-1750° F., quench, reheat to
500°-1300° F. and cool slowly.

U — 'After forging heat to 1525°1600° F., hold at this temperature for half
an hour, cool slowly, reheat to 1650°-1700° F., quench, reheat to 350°-5SO°
F. and cool slowly.

V — After forging or machining heat to 1650°-! 750° F., quench, reheat to
400°- 1200° F. and cool slowly.

Heat Treatments For Different Steels.

SPECIF. No. HEAT TREATMENTS. SPECIF. No. HEAT TREATMENTS

1020 A, B and H X 3335 P and R

1025 B and H X 3350 P and R

1035 D, E and H 3320 L

E and H 3330 P and R

1095 F 3340 P and R

2315 G 5120 B

2320 G, H and K 5140 H and D

J330 H and K 5195 P and R

2335 H and K 51120 P and R

2340 H and K 5295 P and R

120 G, H and D 52120 P and R

3125 H, D and E 6120 S and T

3130 H, D and E 6125 T

3135 H, D and E 6130 T

3140 H, D and E 6135

3220 G, H and K 6140 T

H and D 6145 T and U

3240 H and D 6150

3250 M and Q 9250
X 3315 G and

u 01^5 i

D 6150 U

S9250 V

9260 V

562 APPENDIX

1917 American Truck Practice.

* CYLINDER GROUPING.

Cast En Bloc 61 %

Cast in Pairs 36.5 %

Cast Singly 2.5 %

CYLINDER TYPES.

L-Head 83 %

T-Head 12.25%

Valve in Head 4 %

FUEL FEED.

Gravity Feed 82.2 %

Vacuum Feed 13.5 %

Pressure Feed 4.3 %

IGNITION.

Magneto 95

Battery 5

Single System 76

Double Systems 24

COOLING WATER CIRCULATION.

By Pump 79.6

By Thermo-Syphon 20.4

CLUTCH TYPES.

Cone 25

Dry Disc 64

Lubricated Disc . 11

NUMBER OF FORWARD SPEEDS.

Three-Speed 79 %

Four-Speed 21 %

TRANSMISSION LOCATION.

On Engine 52 %

'Midships 47.3 %

On Axle 0.7 %

AXLE TYPES.

Dead Axles 31 %

Live Axles 69 %

TYPES OF LIVE AXLES.

Full Floating 59 %

Three-quarter Floating 7 %

Semi-Floating 34 %

FRAMTS.

Pressed Steel 68 %

Rolled Section Steel 32 %

STEERING GEAR LOCATION.

Left Hand Side 71 %

Right Hand Side 29 %

REPRESENTATIVE TIRE EQUIPMENT.

Capacity.

1 Ton
ll/2 Tons

2 Tons
2]/2 Tons

3 Tons
3l/2 Tons

4 Tons

5 Tons
7 Tons

Front

36 x 4

x 4
x 5

36 x 5
36 x 5
36 x 6
36 x 6

Rear
34 x 4
36 x 5
36 x 6
36 x 4d
36 x 5d
36 x 5d
36 x 5d
36 x 6d
40 x 7d

American Pleasure Car Practice.

CLUTCH TYPES.

1917 1915 1913

Cone 34 % 50 % 54.2%

Disc 66 % 46.2% 42.2%

Others 3.8% 3.6%

NUMBER OF SPEEDS FORWARD.

Two 0.7% 3.8%

Three 89.5% 69.5% 69.2%

Four 9.8% 26.7% 30.8%

GEAR Box LOCATION.

On Engine... 75 % 49.7% 40.4%

Amidships ...14.6% 32.7% 44.6%

On Rear Axle. 10.4% 17.6% 15.0%

FINAL DRIVE.

Bevel Gear... 29.3% 81.9%

Helical Bevel

Gear 68.0% 12.5%

Chain 2.0% 2.5%

Worm 1.9%

Special 0.7% 1.2%

REAR SPRINGS.

1917

1915

1913

Half Elliptic. 29.4%

15.2%

10.6%

Three-quarter

Elliptic ...28.7%

58.2%

69.0%

Elliptic 6.3%

9.3%

9.6%

Platform .... 3.5%

6.0%

8.4%

Cantilever . .29.4%

9.3%

Special -

REAR AXLES.

Semi-Floating.27.1%

20.9%

21.0%

Three quarter

Floating ..24.5%
Seven eighths

26.8%

10.0%

Floating .. . 1.4%

Full Floating. 45.0%

52.3%

69.0%

Dead 2.0%

INDEX.

PAGE.

Accelerator Pedals 450

Alco Drop Forged Axle 246

Axle Housings 233

Axle Tube Bending Moments 239

Axle Tubes 234

Axle Tubes, Methods of Fitting 235

Axle Tubes, Stresses in 237

Axle Weight Formula 214

Axles, Dead 9

Axles, Live 9

Ball Mounted Control Lever 465

Band Clutch 53

Band Clutch, Sample Calculation of 59

Band Clutch, Effect of Centrifugal Force on 60

Band Clutch, Theory of 56

Bevel Gear Bearing Loads 93

Bevel Gear Blanks, Calculation of 219

Bevel Gear Efficiency 278

Bevel Gear Helical 215

Bevel Gear Pinion Bearings, Mounting of 250

Bevel Gears, Straight 232

Bevel Gears, Grinding in 290

Bevel Gears, Strength of 222

Bevel Gears, Manufacture of Helical 231

Bevel Gears, Thrust Loads on Helical 224

Bevel Pinion Blanks, Turning up 291

Bevel Spur Drive 341

Bowden Wire Mechanism 446

Brake Adjustment 377

Brake Dimensions, Determination of 363

Brake Drums 363

Brake Drums, Securing 534

Brake Equalizers 378

Brake Expanding Mechanism 372

Brake Facing Materials 375

Brake Members, Stresses in 369

Brake Releasing Means 366

Brake Rod Adjustment 479

Brake Rod, Adjustment of 380

Brake Shoes, Air Cooled 367

Brakes, Calculation of Band 369

Brakes, Contracting 354

Brakes, Details of Expanding 375

Brakes, Front Wheel 333

563

564 INDEX.

PACK.

Brakes, Location of 358

Brakes, Number of 357

Brakes, Service and Emergency 360

Brakes and Skidding 383

Brakes, Types of 357

Braking Power, Calculation of 360

Chain Adjusting Rods 329

Chain and Sprocket Calculations 325

Chain Cases 336

Chain Drive 323

Chain Pull 327

Chain, Construction of 323

Chamfering Sliding Gears 109

Change Gear Bearing Mounting 112

Change Gear Bearing Pressure 82

Change Gear Bearing Sizes 96

Change Gear Calculation Example 80

Change Gear Intermediate Bearings 98

Change Gear Layouts 76

Change Gear Shaft Dimensions 99

Change Gear, History of 69

Change Gear, Positive Clutch Type 120

Change Gear, Running in of 119

Change Gear, Silent Chain Type 122

Change Gears, Allowable Stress in 78

Change Gears, Manufacture of 107

Change Speed Gear, Purpose of 7

Clutch and Brake, Interconnection of 457

Clutch Brakes 30

Clutch Connection to Change Gear 66

Clutch Disc Lubrication 48

Clutch End Thrust 68

Clutch Shaft Dimensions 65

Clutch Shifting Collar 28

Clutch Spring Inside Shaft 47

Clutch Springs • 27

Clutches, Classification of 12

Cone, Angle of 14

Cone Clutch Calculation 14

Cone Clutch Calculation Chart 19

Cone Clutch Centre 24

Cone Clutch Engagement Springs 22

Cone Clutch, Constructional Details of 20

Cone Clutch, Leather, Pattern for 2J

Cone Clutch Thrust Bearing 25

Cone Clutch, Multiple Spring Type 23

Cone Clutch, Pressed Steel 27

Cone Clutch Types 13

Cone Clutches, Unit Normal Pressure in 16

Cone Diameter 16

Control, Centre 460-465

Control Joints 449

Control, Left Hand 460

INDEX. 565

PAGE.

Control Lever on Steering Post 447

Control Levers 461

Control Ratchet 441

Control, Single Pedal 458

Control, Selective 464

Control, Spark and Throttle 441

Critical Speeds of Shafts 279

Daimler Worm Driven Axle 320

Differential Bearings 256

Differential Gear, Action of 180

Differential Gear, Calculation of Bevel Type 181

Differential Gear, M. & S. Helical 190

Differential, Gearless Type 191

Differential Gear, Spur Type 187

Differential Gear, Purpose of 6

Differential Lock 192

Direct Drive Clutch 102

Disc Clutch Calculating Chart 41

Disc Clutch Constructional Details : 43

Disc Clutch Data 38

Disc Clutch Inner Drum 44

Disc Clutch Materials 38

Disc Clutch Presser 45

Disc Clutch Types 33

Disc Clutch, Calculation of 35

Disc Separating Means 42

Drive, Double Reduction 8

Drive, Single Reduction 8

Drop Forged Rear Axle. . . , 247

Dux Positive Clutch Gear 123

Elliott Type Steering Head 391

Expanding Clutch 62

Fender Brackets 493

Fiat Pressed Steel Axle 243

Floating Bushings 542

Fluted Shafts, Tests of 211

Ford Planetary Gear 138

Ford Pressed Steel Axle 246

Four Wheel Drives 5-351

Frame Cross Members '. 480

Frame In-sweep 473

Frame Joints 482

Frame Materials 471

Frame Rail Calculation 475

Frame Rails, Bending Moments on 475

Frame Sections 479

Frame Sections, Section Moduli of 480

Frame Steel Gauge 471

Frame Trusses 485

Frames, Drop 473

Frames, Purpose of 10

Frames, Underslung 483

Frames, Wood Sill 484

Friction Clutch, Purpose of , 7

566 INDEX.

PAGE.

Friction Disc and Wheel, Dimensions of 153

Friction Disc Drive, Thrusts and Reactions in 158

Friction Drive Efficiency 151

Friction Drive, Types of 147

Friction Drive Materials 150

Friction Lever Control 443

Friction Wheel and Disc, Engaging Means for 156

Friction Wheel Applying Mechanism 157

Friction Wheel Sliding Mechanism 155

Friction, Laws of 38

Friction, Coefficients of 15

Front Axle Section Diagram 389

Front Axles, I-Section 388

Front Axles, Manufacture of 408

Front Axles, Stresses on 386

Front Axles, Tubular and Pressed Steel 408

Front Axles, Weight on 387

Front Mounted Flywheel 199

Front Wheel Bearings 397

Front Wheel Bearings, Mounting of 399

Front Wheel Drive 5

Front Wheel Thrust Loads 398

Gear Box Lubrication 119

Gear Calculation for Strength 77

Gear Carrier 245

Gear Cases 115

Gear Material 72

Gear Motion, Cause of Non-Uniform 215

Gear Reduction Ratios 75

Gear Supporting Methods 118

Gear Teeth, Form of 77

Gear Tester 110

Geared-up Fourth Speed 114

Governor Control Linkage 452

Hele-Shaw Clutch 46

Helical Bevel Gears 215

Hub Caps 535

Internal Gear Drive 348

Jackshaft 340

La Buire Arched Axle 249

Lamp Brackets 495

Lemoine Type Steering Head 394

Levassor Sliding Gear 70

Locking Device, Ball Wedge 443

Maybach's Selective Gear 71

Midland Three Point Support 197

Motor, Location of 3

Panhard Brake 376

Pedal Pads 456

Pedals 453

Pedals, Adjustable 455

Pedal Shaft Assembly 460

Peerless Arched Axle 248

Pitch Line Velocity 78

Planetaries, Calculation of All Spur Type 141

INDEX. 567

PAGE.

Planetary, All Spur Type 131

Planetary, Assembly of All Spur Type 136

Planetary, Assembly of Internal Gear Type 134

Planetary, Internal Gear Type 125

Planetary Gear, Calculation of Speed Ratios 126

Planetary Gear Efficiency 145

Planetary Gears, Bearing Pressures in 138

Planetary Gears, Brakes for 143

Planetary Gears, Constructional Details of 143

Planetary Gears, Gear Stresses in. . 138

Planetary Pinions, Required Number of Teeth in 130

Plate Clutch, Dry 48

Plate Clutch, Three 50

Power Plant, Spring Suspension of 3

Pressed Steel Rear Axles 243

Quadrants 467

Quadrant Designs, Standard S. A. E 468

Quickest Stop, Conditions Insuring the 361

Radiator Brackets 490

Radius Rods, Calculation of 332

Reach Bar or Perch 10

Rear Axle Bearing Adjustment 257

Rear Axle Bearing Pressure 250

Rear Axle Bearing Housings 233

Rear Axle Bearings 249

Rear Axle Braces 277

Rear Axle Thrust 265

Rear Axle Thrust Bearings 263

Rear Axle Torsion 265

Rear Axle Truss 264

Rear Axle, Arched 247

Rear Axles, Dead 338

Rear Axles, Manufacture of 288

Rear Axles, Types of 203

Rear Wheel Drive 5

Rebound Clips 521

Reverse Gear Arrangement 100

Reverse Lock-out 468

Reversed Elliott Type Steering Head 393

Roller Chains, Capacity of 324

Rudge-Whitworth Wire Wheel 538

Schwarz Interlocking Spokes 536

Seitz Friction Drive 148

Semi-Floating Axles, Calculation of Shafts for 213

Shaft Diameters, Calculation of 210

Shaft Joints 211

Shaft Materials 207

Slider Forks Ill

Sliding Gear Efficiency 120

Sliding Gear Locking Dogs 112

Sliding Gear Shaft Front Bearing. 102

Sliding Gear Shaft 104

Sliding Gears, Proportions of 105

Slip Joints . 177

568 INDEX

PAGE.

Spoke Dimensions 532

Spokes, Number of 531

Spokes, Proportions of 531

Sprags 384

Spring Arch 517

Spring Bolts 522

Spring Brackets 486

Spring Calculation, Sample 511

Spring Centre Bands 516

Spring Centre Bolts 516

Spring Clips 518

Spring Eyes 522

Spring Leaf Points 523

Spring Leaves, Alignment of 522

Spring Leaves, Reverse 521

Spring Lengths and Widths, Table of 505

Spring Lips 522

Spring Lubrication 526

Spring Material 500

Spring Perches 518

Spring Plates, Number and Thickness of 510

Spring Play on Bevel Gear Drive, Effect of 270

Spring Play on Chain Drive, Effect of 334

Spring Pressure Blocks 520

Spring Shackles 522

Spring Steel Gauge 507

Springs, Auxiliary . 526

Springs, Cantilever 499

Springs, Eccentrated 509

Springs, Flexibility of 507

Springs, Inclined 524

Springs, Theory of Leaf 501

Springs, Torsion and Thrust on 525

Springs, Total Deflection Constants of L 508

Springs, Types of 497

Sprocket Wheels, Design of 326

Sprockets, Overhanging 328

Starting Crank Bracket 494

Steering Angles, Chart of 418

Steering Arm 432

Steering Column 438

Steering Column, Adj ustable 439

Steering Connectors 433

Steering Drag Link 433

Steering, Four Wheel 5

Steering, Front 4

Steering, Rear 4

Steering Gear Bearings 424

Steering Gear, Calculation of Worm and Wheel 420

Steering Gear Cases 426

Steering Gear, History of .' 411

Steering Gear, Support of 431

Steering Gears, Double Screw Adjustable 429

Steering Gears, General Arrangement of 418

INDEX 569

PAGE.

Steering Gears, Reversible and Non-Reve'rsible 419

Steering Gears, Screw and Nut Type 428

Steering Heads 390

Steering Knuckle Arms 403

Steering Mechanism, Bevel Gear . 430

Steering Mechanism, Theory of 411

Steerings Pivot Bearings, Calculation of 394

Steering Pivot, Inclined 396

Steering Problem, Analytic Solution of 415

Steering Problem, Graphical Solution of 412

Steering Shaft 424

Steering Spindle Diameter 402

Steering Stops 402

Steering Spindle "Set". . . , 401

Steering Tie Rod 405

Steering Tie Rod Connectors 407

Steering Wheel 435

Step Hangers 494

Straight Line Drive 202

Stub Tooth 77

Sub Frames 481

Swiveled Gear Box 201

Three Point Support 195

Throttle Linkage 451

Timken Brake 377

Timken Pressed Steel Axle 244

Torque Rod Supports 276

Torque Rods 274

Torque Tubes 266

Torque Tube Supports 268

Trailer Steering Axle 396

Transmission Axles 199

Transmission Brakes 367

Tread 10

Truck Bumpers 491

Unit Power Plants 193

Universal Joint, Anti-Friction Bearing 176

Universal Joint, Calculation of Block and Trunnion Type 173

Universal Joint, Calculation of Forked Type 169

Universal Joint, Dust Protection of 174

Universal Joint, Lubrication of 174

Universal Joint Sheet Metal Housing 175

Universal Joint, Square Block Type 168

Universal Joints, Leather Disc Type 177

Universal Joints, Proper Angular Relation of Double 168

Universal Joints, Speed Fluctuations in 163

Universal Joints, Types of 160

Weights of Commercial Cars 387

Wheel Base ....*..*. 10

Wheel Bearings 258

Wheel Bearings, Mounting of 260

Wheel Diameters ' cog

Wheel Hubs ' ' S33

Wheel Material, 'Wood '.'. ... '. '. '. '. .............. [ S28

570 INDEX

PAGE.

Wheels, Artillery 528

Wheels, Cast Steel 540

Wheels, Manufacture of 53/

Wheels, Number of 4

Wheels, Wire 537

Worm Driven Axle Design 316

Worm Drive, Advantages of 293

Worm Drive, History of 293

Worm Drive Axle Tube Dimensions, Calculation of 318

Worm Gear Efficiency 298

Worm Gear Efficiency Tests 305

Worm Gear Formulae, Application of 309

Worm Gear, Hindley Type 312

Worm Gear Housings 316

Worm Gear Load Capacity, Calculation of 302

Worm Gear Material 310

Worm Gear Radial Bearing Loads 301

Worm Gear Thrust Bearing Loads 300

Worm Gearing, Theory of 294

Worm Gears, Axial Pitch of 296

Worm Gears, Centre Distance of 302

Worm Gears, Pressure Angle of 295

Worm, Mounting of 315

Worm Top Mounted and Bottom Mounted 314

Worms, Hardening and Polishing of 310

PLATE SUPPLEMENT.

CHANGE SPEED GEAR OF THE PACKARD TWELVE.

571

PLATE SUPPLEMENT.

DRY Disc CLUTCH OF CHALMERS 6-30.

PLATE SUPPLEMENT.

573

BROWN-LIPE DRY Disc CLUTCH
ON CUNNINGHAM CAR.

574

PLATE SUPPLEMENT.

575

576

PLATE SUPPLEMENT.

577

578

PLATE SUPPLEMENT.

BORG & BECK PLATE CLUTCH AND COVERT CHANGE GEAR.

PLATE SUPPLEMENT.

579

TIM KEN TRUCK FRONT AXLE (7,200 LBS. MAX. LOAD),

580

PLATE SUPPLEMENT.

581

582

PLATE SUPPLEMENT.

585

586

PLATE SUPPLEMENT.

FRANKLIN STEERING GEAR.

PLATE SUPPLEMENT.

587

BENZ STEERING GEAR.

588

PLATE SUPPLEMENT.

PEERLESS TRUCK STEERING GEAR.

PLATE SUPPLEMENT.

590

PLATE SUPPLEMENT.

591

PLATE SUPPLEMENT.

;•— '

PLATE SUPPLEMENT.

593

594

PLATE SUPPLEMENT.

595

596

PLATE SUPPLEMENT.

597

o
fc

S
o

598

PLATE SUPPLEMENT.

599

600

PLATE SUPPLEMENT.

»B

PLATE SUPPLEMENT.

601

602

PLATE SUPPLEMENT.

~/) /I r .
U-f

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