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GRINDING MACHINERY

GRINDING
MACHINERY

JAMES J. GUEST

WITH 200 ILLUSTRATIONS

LONDON

EDWARD ARNOLD

1915

PREFACE

THE subject dealt with here is that of grinding as employed in
engineering machine shops, and is one which is, for several
reasons, of continually increasing importance to manufacturers.

The book has been written in response to the frequently
expressed wishes of engineers, works managers, and machine
operators, that I should give them detailed information, often
of a character beyond that which could easily be dealt with
in conversation or by letter. As such readers are familiar
with ordinary workshop practice and tool details, these matters
are as a rule only referred to briefly ; but the nature of many
of the inquiries addressed to me for advice — not on grinding
only, but on many other questions as to plant and methods of
production — has led me to the conclusion that the subject of
grinding could not be adequately presented without some brief
treatment of various topics connected with it.

The book has been planned so that the whole subject is
presented as systematically as possible, and so as to lay bare the
reasons underlying the various matters. Upon a knowledge of
these depends a sound judgment as to what is suitable plant,
of the possibilities of the process, and concerning the best mode
of using the machinery. The Table of Contents fully indicates
the arrangement of the book.

I have treated the vexed subject of work speeds first from
the point of view of the best modern practice, and then intro-
duced my theory of grinding. This was first published in a
paper before the British Association for the Advancement
of Science in September 1914. It dispels the current belief
in a standard work speed, but offers in return an explanation
of the phenomena encountered, and supplies the best methods
of meeting the various difficulties.

The machines illustrated have been carefully chosen with
regard to the ends in view, and in the selection a preference has
always been given to those of the pioneer firms ; machines of
my own design have, however, only been introduced as illus-
trating special points, e.g. the automatic steady, which could
not otherwise be shown. Machines have throughout been

vi PKEFACE

treated from the point of view of the grinding process, and not
as interesting examples of mechanism, so that unless the detail is
directly connected with grinding the description is as brief as
is compatible with lucidity.

The various problems presented by different classes of
work have been treated in the same manner. The reader will
detect these various phenomena under other guises and, under-
standing the nature of the case, will treat it appropriately.

The feeds used and the errors involved in grinding are so small
that in a number of the illustrations some of the dimensions
are very much exaggerated for the sake of clearness ; in all
cases, however, the fact is quite evident, and can lead to no
misapprehension.

Where the best method of presenting any matter has involved
the use of equations, the results have been also given in ordinary
language so as to be available to any reader.

Where my opinion is expressed, particularly if opposed to
current belief, I have written in the first person.

My thanks for photographs of and information concerning
their products are due to the following firms and their agents :
Messrs. The American Emery Wheel Works Co., Sir W. G.
Armstrong, Whitworth & Co. Ltd., Charles H. Besly & Co.,
Beyer, Peacock & Co. Ltd., The Blanchard Machine Co., The
British Abrasive Wheel Co. Ltd., Brown &Sharpe Manufacturing
Co., The Bryant Chucking Grinder Co., The Carborundum Co.,
The Cincinnati Grinder Co., The Daimler Co. Ltd., Greenwood &
Batley, Ltd., A. Harper, Sons, & Bean, Ltd., The Heald Machine
Co., Alfred Herbert, Ltd., John Holroyd & Co., The London
Emery Works Co. Ltd., Lumsden Machine Co. Ltd., The
Newall Manufacturing Co. Ltd, The Norton Grinding Co., and
the Norton Co., Pratt & Whitney Co., Hans Eenold, Ltd., K.
Sterne & Co. Ltd., Walker Grinder Co., Willmarth & Morgan,
and more especially to Messrs. The Churchill Tool Co. Ltd. and
the Landis Tool Co., who made a number of drawings especially
for this volume.

The beautiful microphotographs of Figs. 2 to 8 were kindly
made for me by Mr. 0. F. Hudson, Lecturer in Metallurgy at
the University of Birmingham. I am further obliged to the
authorities of the Municipal Technical School, Birmingham,
for the loan of the apparatus with which I made the microphoto-
graphs of Figs. 13 to 15.

J. J. G.

LEAMINGTON, 1915.

CONTENTS

CHAPTER I
GRINDING AND MANUFACTURING

Grinding, Polishing,and Lapping
Mechanically guided Grinding .
Modern manufacturing
Physical necessity for accuracy .
Allowances. Tolerances and
Limits .

PAGE PAGE

1 Hole and Shaft basis for

2 Limits .... 6

3 The action of a Grinding Wheel . 12

4 Grade. . . . .14
Basis of the accuracy of Grinding 15

CHAPTER II

THE ABRASIVES AND THE WHEEL

Natural Abrasives . . .17
Silicates and Grindstones . 17
Emery and Corundum . 20

Artificial Abrasives . . 21

Carborundum . . .21
Alundum ... 22

Grits . . . . . 24

Bonds and Grade ... 25
Vitrified. ... 26

Elastic .... 27
Silicate . 28

Strength and Surface Speed . 28

Strength and Bond-. . . 29

Wheel Speeds ... 31

Mounting Wheels .

Balancing .... 35

Truing Wheels . . .37

Wheel Dressers . 37

Diamonds . . . 38

Setting Diamonds . . 39

Diamond Laps . .. . 40

CHAPTER III

THE WHEEL AND THE WORK

The material ground and various

Abrasives . . . .42

Size of Grit and quality of Finish 43
Adherence of Grit to Work

Surface .... 44

Grade and its selection . . 45

Wheel Speeds . . . 48
Work Speeds — former and

current practice ... 49

Finishing Speeds ... 50

Theory of Disc Wheel Grinding . 52
Number of cutting points on

Wheel Surface 53

Chips in Grinding ...
Normal velocity of the material
How the Chip is formed . .
Contact in Grinding . .
Chips and the normal velocity
of the material . . .

The controlling facto

57
59
61

65
67

Maximum output — vt . . 68
Magnitude of the quantities

involved .... 69

The forces at the Grinding Point 70

Temperature rise — Fused Chips . 7 1

Vlll

CONTENTS

Grinding hardened Steel .
Effect of length of arc of contact
Area of contact proportional to

power ....

Alteration of Work Speed to

meet difficulties .
Work surface speed to depend

on WTork Diameter

PAGE

72
73

74
76

Slender work and work of large
diameter *

Changing width of Wheel .

Changing Grade used

Effects of Wheel velocity and of
traverse ....

Cup Wheel Grinding

Normal velocity and Feeds .

PAGE

77
78

79
81

CHAPTER IV

THE WORK AND THE MACHINE

Development of Machine

Grinding . . . 84

Dry Grinding ... 84

Protection against Grit . £ 5

Wet Grinding and solutions 85

Distortion in Dry Grinding . 87
Longitudinal expansion

and Spring Tailstocks . 88
Temperature effects and

change of Axis . . 88

Advantage of Dead Centres . 89

Effect of initial internal stresses . 90
Their distribution and

magnitude ... 90

Case of bright drawn Steel 92

Remedy ... 93

Necessity for truth of Wheel and

its preservation . . 94
Rate of traverse of Main

Slide .... 94

Double copying principle . 96

Pause or Tarrv 90

Grinding up to a Shoulder. 97
Vibrations . . . . 98
Free vibrations . . 98
Damping ' . . . 102
Forced vibrations . . 103
Balancing . , . . 105
The Universal Grinder — descrip-
tion . . . .110
Travelling Work or Travel-
ling Wheel . . .112
Tapers by swivelling the

Work Table . . .113
Types of slide fitting . .115
Precision of the reverse . 116
Tapers by swivelling the

Cross Slide . . .117
The Cross Feed . .119
Provision for Wet

Grinding . . .120
Steadies . . .120

Arrangement of the Drive . 120

CHAPTER V
DETAILS OF PARTS

The Wheel Spindle and Bearings 1 23
Spindles for Cup Wheels and

End Thrust . . .128
Spindles for Internal Work —

Ball Bearings . . .134
Wheel Collets; Cup Wheel

Chucks 145

The Wheel Spindle Drive . . 148

Wheel Truing Arrangements . 150

Guards, Pumps, and Nozzles . 152

The reversing mechanism . 155

The Cross -feed mechanism . 162

Steadies . . . .172

Machine Bodies . . .178

CONTENTS

CHAPTER VI
PLAIN GRINDERS AND EXTERNAL WORK

of the Plain

Development

Grinder .-.-..

Table Sections and Water

Guards ....

The Work Head and Centre

Grinding Head .
Driving arrangements

Rapid speed-changing de-
vices ....
Dead Centre Gears .
Machines with Work Drive

self contained
Self-contained Machines .
The Work — preparation ; Centre
Holes ....
Work from the black
Allowances in Turning
Case-hardening ; Turning ;

Casing; Hardening
The Work— in the Machine
Centres .

PAGE PAGE

Driving and Balance . 218

180 Mandrils ; Tubes ; Live-

centre work . . . 220

181 Setting the Stops and details 221
Getting Work to taper or

189 parallel . . .221

190 Wheels— truing Wheels . 222
Work Speed and travel . 222

192 Correction of Wheel troubles 223

197 Formed work . . .225

Auto -travel and ad just -
199 ment of Cross-feed . . 225

201 Work defects . . .226

Work not round . . 226

213 Chatter and Steadies . 227

214 Slender Bars . . .229

215 Crank Shafts and corner radii . 231
Economy . . . .235

216 Quantities and two handlings 235
218 Times— estimating . . 236
218 Costs . . 237

CHAPTER VII
INTERNAL GRINDERS AND THEIR WORK

Economic production of

accurate Work . . .239
Internal Grinders and Cylinder

Grinders . . . .239

Internal Grinders . . .241

Travelling Work Machines . 241

Travelling Wheel Machines 243

Dry or Wet Grinding . . 243

Cylinder Grinders . . . 245

The Wheel Head and

Feed 245

Travelling Work and
travelling Wheel . . 252
of the accuracy of the
Machines . . , .255
Setting Work for Parallel

Grinding . . . .257

Holding the Work . . . 258

Gaars . . . .259

Width of Wheel . . .260

Work Speeds and regime 263

Times . . 268

CHAPTER VIII
THE UNIVERSAL GRINDER AND ITS WORK

Travelling Wheel Type . . 270
The Swivelling Cross Ways and

Head .... 275

Double Taper Work. . 275

Facing Shoulders
The Work Head and
Spindle
Flat work

live

277

278
280

CONTENTS

CHAPTER IX
SURFACE GRINDING

Disc Wheel Machines — Planer
Type . . -.

Lathe Type . . .

Work Speeds .
Cup Wheel Machines . *

Work sliding .'

PAGE

285
289
291
292

Work rotating . *
Magnetic Chucks
Grinding Metal Slitting Saws
Disc Grinders.

With two Heads

PAGE

295
297
301
306
312

CHAPTER X

SHARPENING CUTTERS AND TOOLS

Types of Cutters . . . 315

Principles of Cutter sharpening 317

Clearance . . 319

Secondary clearance . 319

Parallel Cutters . -. . 320

Tooth Rests ... .322

Setting for Clearance with Disc

Wheels . . .324

In Universal Grinder . 325
In Cutter Grinders . .331
Setting can be simplified . 333
Sharpening End Mills . 334

Limiting Diameter of

Wheel . . .336

Setting for Clearance with Cup

or Dish Wheels . . 338
Chart of Settings . . 341
Setting can be simplified . 343
Gear and Formed Cutters ; Hobs 344
Universal Cutter Holders . 349

Twist Drill Grinders . . 350
Lathe Tool Grinders — Mechan-
ically guided . . .353

CHAPTER XI
FORM GRINDING AND CURVED SURFACES

Mechanically generated Cups
and Cones .... 356

Form Grinding — short parts . 853
Collars, Cups, and Cones . 359
Castellated Shafts . . 361
Gears and Worms . .361

Generated Gears . . . 364
Worms . . .368

Cams and Links

Manufacturing Machines . . 376
Grinding Shafts, Rods, and Balls 380
Jigs, construction . . . 383

CHAPTER XII
POLISHING AND LAPPING

Polishing Lathes and Belt

Machines .... 384

Lapping . • 387

Grading fine Abrasives . 387

Charging Laps . . 388

Lapping Machines for Flat

Work . . 389

Principles of Lapping . . 389

Allowances for Lapping . . 390

Surfaces which can be Lapped . 391

Flat Work . . . .391

Cylindrical Work . . .394

Accuracy attainable . . 395

CONTENTS xi

CHAPTER XIII
MEASURING AND ITS BASIS

PAGE PAGE

Ultimate Standards — The Yard 398 Determination of the

The Metre . . . 398 Measurement . . 403
Natural Standards . . 399 Standard Gauges . . .406

Temperature Effects . . 400 Micrometers . . . 407

Subdivision of the Standard . 400 Limit Gauges ; External . 411
Line and End Measure . 400 Internal — Cylindrical and

Measuring Machines . . 401 other . . ... 412

Determination of Contact . 402 Conclusion . . . ". . 416

APPENDIX

PAGE

MISCELLANEOUS EXAMPLES OF GRINDING TIMES . . . 418
TABLES

I. Limits for Cylindrical Work, Metric — Newall system . .423

II. Limits for Cylindrical Work, English — Newall system . . 424

III. Limits for Cylindrical Work, English — Browne & Sharpe . 425

IV. Allowances and times . . . ...?.. . 426

V. Comparison of Wheel Grades of different firms . . 427

VI. Wheel selection . . . . . , . . .428

VII. Wheel selection . .430

VIII. Grinding Wheel speeds ~. .431

IX. Work speeds .432

X. Clearance setting for Cutters — Disc \\heels .... 434

XI. Clearance setting for Cutters — Cup Wheels .... 435

XII. Decimal and Metric equivalents of fractions of an Inch . . 436

XIII. Metric-English conversion ...... . • 436

XIV. Tapers . ... ... .437

Miscellaneous notes . . . . . . • 438

INDEX . 439

GRINDING MACHINERY

CHAPTEK I

GRINDING AND MANUFACTURING

Grinding. — In modern machine-shop practice the term ' grinding '
has now acquired a definite meaning, and is confined to the
shaping of material by means of rotating abrasive wheels of
practically rigid substance. The shaping may be done by hand,
as in sharpening a lathe tool on a grindstone, or may be a me-
chanically guided operation, as in the truing-up of a hardened
steel mandril in a grinding machine, but owing to the im-
portance of the latter work the term ' grinding,' or more definitely
' precision grinding,' as an operation, is practically confined to
it. As opposed to turned or milled work the quality of ground
work which first makes itself appreciated is fineness of surface ;
this, however, is surpassed by that of polished work, which
does not possess the first characteristic of ground work —
namely an accuracy considerably surpassing that of work
produced by ordinary cutting tools.

Polishing and Lapping. — Polishing consists in removing
the small inequalities of surface by rubbing the work with
soft material charged with abrasive powder. By using succes-
sively finer powders the material is removed by smaller and
smaller amounts with a corresponding improvement in the
quality of the surface. To do this work rapidly the soft
material is made into bobs or belts and run at a very high

2 GRINDING MACHINERY

rate of speed, but as this soft material follows the larger
irregularities of the surface of the work, the result is that
accuracy is not a feature of the process.

The accuracy given to certain work by machine grinding
can be improved by lapping (Chapter XII), which consists
in making a lap (or piece of metal, or other material softer than
the work) to envelop the work, charging it with abrasive, and
working the two together until a better fit is obtained. This
is a slow process, and demands much care. It consequently is
only used in those operations for which the accuracy of form
or the quality of surface given by grinding is insufficient.

Both grinding and lapping are really cutting processes
when closely looked into, and in the heavier kinds of grinding
chips which can be handled are produced.

Although the use of grinding or abrasive processes is
of primeval antiquity, and grinding machines have long been
in use, it is only of recent years that machine grinding has
become one of the recognised shop operations. At first applied
to the manufacture of gauges, hardened steel spindles, and
to the cutters and mandrils of the shop, now all the more
accurate parts of engines, motor cars, machine tools, sewing
machines, and machinery in general are ground, and the use
of the process is extending to pieces in which the precision
is not of such importance.

A number of causes have combined to effect this rapidly,
and a review of these will assist in the formation of a broad
judgment of the possibilities of the process, of its nature,
and of its limitations.

Mechanically guided Grinding. — It is not so long ago that
turning was a mechanically guided operation only in so far
that the work was carried between centres, as the slide rest dates
back only to Maudslay ; yet now the art of turning metal by
hand exists as a commercial process in very few trades — such
as axle box making — and almost all manufacturing machines
using steel tools have them mechanically guided.

That this substitution of mechanically guided for hand
guided tools has taken place is, by the nature of commercial
progress, due to the fact that it results in a cheaper product,

GEINDING AND MANUFACTUKING 3

and this economy is due to the comparatively unskilled labour
which can be employed, and to the opportunity it offers of
speeding-up the process. After mechanically guided tools
became usual, the appreciation of accuracy became more
possible, and so a way was opened for the employment of
grinding as a productive method. The replacement of a steel
tool by a grinding wheel was first adopted to deal with the
problem of hardened work — the correction of distortion due to
the process of hardening ; in France grinding machines are still
termed ' Machines a Eectifier.' In its early days the process,
although it gave more accurate results than turning, and
produced a superior surface, was so tedious that it was con-
fined to those cases where the requirements warranted the
expense, e.g. the spindles of machine tools. Single point
diamond tools were sometimes used on very small hardened
work, but the expense and difficulties encountered were great.

Modern Manufacturing. — Following the development of
the steam engine and machine tools, with the resulting spread
of the facilities for making machine parts, came the develop-
ment of modern mass production, involving the use of special
small tools of advanced accuracy. This called again on the
use of mechanically controlled grinding for the purpose of
finishing and sharpening these tools, and for the production
of the gauges simultaneously required. The old process of
making a reamer, for example, necessitated several careful
annealings and operations removing little metal, and a then-
satisfactory reamer was an inferior and expensive tool compared
with those finished by the grinding operations of to-day.

These demands resulted in the production of machines — the
universal grinding machine and the cutter grinder — for the
manufacture and sharpening of the special tools, and the
production of gauges and other hardened parts. The capa-
bility of dealing with hard steel (due to the very much harder
nature of the abrasive particles of the wheel and their freedom
from heat effects), and the adaptability to precision work (due
to the sharp edges of the particles taking a very fine chip
with little normal force), are the properties which render the
grinding process especially suitable to the requirements of

4 GKINDING MACHINEKY

tool manufacture. From this footing in the tool-room, the
process of grinding has extended, aided by improvements
in both wheels and machines, until to-day mechanically
guided grinding machines have a place in all manufacturing
shops where accurate work is required, and not on hard steel
parts alone, but on many classes of material. This could
not be so unless the grinding machine produced work of certain
required accuracy or of other desired qualities, at a cost un-
mistakably less than it can be produced at by other processes.

It would be premature to discuss here the question of the
advisability of adopting the process and installing the machinery
in any special case ; knowledge to this end is to be gathered
throughout the book, and the matter is again referred to in
the conclusion, after the nature of the process, the trend of
modern development, and the reaction of this art upon other
manufacturing methods have been considered.

For reasons which can be easily understood, the process
of grinding is more accurate than that of turning, and less
accurate than that of lapping under proper conditions, and
the surface produced corresponds fairly with the accuracy.
When using these three processes within limits of accuracy
easily attained by them, the cost is generally least in the
roughest process — that is, with the single point cutter — and is
greatest with lapping ; but as any particular limit of accuracy
is made finer the cost of finishing by the rougher processes
increases very rapidly. Hence if we are fixed to certain
limits of accuracy it will prove to be cheaper to finish by
grinding than by turning, or by lapping than by grinding,
according partly to what these limits are, and partly to the
character and condition of the machines and appliances avail-
able. Speaking generally, therefore, work necessarily of a
very high degree of accuracy should be first turned, then
ground, and finally lapped.

Accuracy is compulsory. — The limits of accuracy required
are therefore of primary importance in determining what
processes should be used in the production of a part of a
machine, and whether grinding is desirable or necessary.

In order to be satisfactory, to run and wear well, machinery

GEINDING AND MANUFACTURING 5

demands in its construction certain accuracies, due to properties
inherent in the nature of the materials employed, the use
to which they are put, the oil to be used in the bearings, &c.
These are the primary factors which enforce limits upon the
dimensions of machine parts. These limits may be very liberal,
and attainable by mere careful casting or forging, or they may
be very narrow, and require very accurate workmanship to
meet them. Of the former, many loom and agricultural
machine parts are illustrative : and as an example of the
latter we may take the case of a forced fit, where a cylindrical
piece is forced by a press into a hole slightly smaller in
diameter than itself — say a wheel and axle which rotate to-
gether. Consider this case more closely.

Supposing that the female part or hole is made first, it
is necessary that the plug should be made a certain amount
larger in diameter than the hole, else it will be loose, or at
any rate insufficiently tight when forced in : on the other hand,
it must not exceed it by a certain (other) amount (dependent
on the external and internal diameters of the female piece
and the material of the parts), else it will be impossible to
force the plug into the hole, or damage will result in doing so.
These considerations determine certain dimensions between
which the diameter of the plug must lie ; the stresses in the
parts of the forced fit, and the force necessary to press the
parts together, or to turn the plug inside the hole, will depend
upon the particular diameters to which the parts are formed,
but their amounts must be within a satisfactory range. The
margin of diameter or the limits are therefore determined
for any particular case by the elastic properties of the material
used.

Beyond this, the quality of the surfaces, and the nearness
of the material surface to the ideal geometrical surface (if one
may express it so), affect the problem ; more so, however, in
cases of running fits where there is wear than in the forced
fit example which we have taken. In all cases, however, a
certain maximum and minimum difference of size is entailed
by the physical properties of the materials.

Limits, Tolerances, and Allowances. — When the problem

6 GKINDING MACHINERY

is extended from the production of a single shaft for one
particular hole to the case of manufacturing these parts in
quantity, the matter becomes a little more complicated, as
the holes will vary in diameter amongst themselves in what-
ever way they are produced, and it is very desirable that
manufactured parts should be interchangeable.

Our physically controlled limit of difference of fit has
then to be divided into two parts applicable to the two parts
of the fit. From the point of view of manufacturing one
particular fit, the division of the allowable margin (between
the male and female parts of a fit) should be such as to make
the cost of manufacturing the particular parts of that fit in
quantity a minimum ; but for manufacturing reasons the
margin is divided according to broader considerations, with
the result that it has become possible to make ' limit ' gauges
for the different classes of fit commercial articles.

It should be observed that owing to the difficulty of working
close to the actual size of a gauge, parts — whether male or
female — made to limit gauges come regularly well within the
limits, so that when a physically determined margin is divided
between two sets of limits, a little may safely be added to its
amount.

We have considered the hole to have been produced first ;
if a shaft had been required to be a running fit in the hole it
would have been made to a somewhat smaller diameter than
a shaft to be a press fit, so that it would rotate easily and
provide room for oil. In quantity manufacturing the holes
would all be made the same size within the small limit allowed,
but the shafts would have different diameters (each with its
limits) according as they were to be press or running fits. It
would, however, be a matter of indifference whether the holes
or shafts were actually made first.

The sizes in this case are said to be on the hole as a basis, and
there is one set of limit gauges for the holes for whatever
purpose they are intended ; the variations for the various
types of fit being made on the shaft, there being different sets
of limit gauges for the shaft according to the purpose of the fit.

The Hole and Shaft Basis. — This is shown in Fig. 1, in

GEINDING AND MANUFACTURING 7

which the proportions are distorted for the sake of clearness.
There is here one gauge A for the hole, the nominal size of

Gives Greatest Driving Force.
Gives- Smallest Driving Force.

C. External Limit Gauge for Drive Fit

Internal Limit
Gauge -One only

LIMIT GAUGES

HOLE BASIS.

/Half Tolerance

Half Allowance
B. External Limit Gauge for Running Fit A.

Half Tolerance V g „

a- -\\—

Thinnest Oil Film
Thickest Oil Film.

FIG. 1. — GAUGES ON THE HOLE BASIS

which is 1 J inch. To be satisfactory the hole must be such that
the long end of the gauge, 1-250 inch in diameter, must go into

8 GKINDING MACHINERY

the hole, while the short end, which is 1-251 inch in diameter,
must not go in. The hole is made of a size within these
limits, whatever the purpose for which it is to be used.

Shafts to be a running fit in the hole are made to the flat
gauge B, the large end of which, 1-2485 inch across, must
pass over the shaft, and the smaller end, 1-2475 inch across,
must refuse to do so.

The shaft is drawn inside the hole, the sectioned circle
showing the smallest shaft which will pass the gauge, and the
circle just outside it the largest ; the largest hole is shown
in a part which is sectioned, and the smallest hole which will
satisfy the gauge indicated by the circle just inside it. Thus
the cross-hatched portion shows the oil in the case where the
fit is the closest ; if the fit were the slackest which would
pass, the two clear rings will also represent oil. Actually the
fit will not be near these extreme cases.

The difference between the two ends of a gauge is called
the ' tolerance,' being the error allowed in the work. For
example, the tolerance on the Internal Limit gauge is here
1-251 — 1-250 inch, or 0-001 inch. The difference between the
size of the hole and of the shaft is called the ' allowance ' for
the particular purpose of the fit.

The upper External Limit gauge C represents the gauge
for a shaft to be a driving fit, necessitating a press to force
it into the standard hole. Here the widths across the gauge
faces are 1-252 inch and 1-253 inch respectively, and the shaft
will be on the average 0-002 inch larger than the hole. On the
left the two full circles indicate the limiting sizes of the hole,
and the broken circles the extreme diameters (greater) of the
shaft which is to be forced into the hole.

Here the shafts are made of different sizes for different
purposes, while a hole of the same size is used for all purposes.

The shaft may, however, be used as a basis ; in which
case all shafts would be the same size (within the invariable
limit), and the holes would vary between different limit ranges
according to the type of fit required.

Opinions are divided as to the merits of the two systems.
As the great majority of holes are conveniently produced

GEINDING AND MANUFACTUKING 9

close to size by reaming or broaching, and as the cost of extra
sets of these tools for producing the holes, of mandrils to
cope with the various diameters required by the shaft-basis
system, and the difficulty of storing them is considerable,
the hole-basis is initially the less expensive, and I consider
it the more suitable for firms manufacturing in moderate
quantities. To meet the requirements of such customers, the
firms making a speciality of the production of limit gauges
are inclined towards the hole-basis system. It is initially
convenient, which leads to its establishment, and hence to its
permanent use.

For very large quantities the shaft-basis presents the
advantage that tools made originally for the larger holes
(i.e. the running fits) can, when worn, be reground for the
smaller allowances (e.g. a press fit), which is a saving, and
the initial expense is not of such serious import with the
quantities. As regards the effect on design, there is little
difference in the systems ; the shaft-basis makes less machining
with a little more trouble in fitting. Limit gauge sets are
rather cheaper to make on the hole-basis.

While many engineering firms work upon the hole-basis
system, the shaft-basis has received the seal of the approbation
of the Engineering Standards Committee, who have carefully
considered the opinions and practice of many firms. They
have issued a list of allowances for the various running fits.

Some years ago Messrs. The Newall Engineering Co., Ltd.,
then of Warrington, but now a branch of Messrs. Peter Hooker,
Ltd., compiled from general British and Continental practice
the sets of limits given in Table I and II, pages 423-4, which
result in satisfactory fits on the English and Metric systems.
They should be compared with Table III, which represents
Messrs. Brown & Sharpe's practice. I have ventured to
rearrange the form of the matter which these firms courteously
allowed me to use. I have used the limits given by the Newall
Engineering Co. for much of my manufacturing work, and
have found them to be satisfactory.

Practically for manufacturing purposes specially fixed limits
have often to be used, and also the two systems may be

10 GEINDING MACHINERY

combined when appreciable advantage is to be obtained
by it. For example, the hole-basis system may be used in the
manufacture of a machine, and the shaft-basis for the counter-
shafting.

In working to these or such limits, various gauges arid
measuring contrivances are used, and it must be borne in
mind that these gauges and the tools used must possess a
higher degree of accuracy than that of the limits themselves.

The limits and tolerances • are fine, running into fractions
of the thousandth of an inch — this being rendered necessary,
as explained above, by the elasticity of steel, the thickness
of the oil film in the bearings, &c.

The fineness of these commercially necessary limits tends
to make good machine work expensive, and puts a premium
on the use of machines and tools which have initially high
accuracy, and in which it will not be impaired with undue
rapidity in use. These machines and gauges make the capital
cost of plant for interchangeable manufacturing very high,
but it is to be remembered that accuracy of parts to limits
materially reduces assembling costs. It is cheaper to make
to a fine limit, using a gauge, than to a wider one and trying
the actual parts to fit, so that the product may be not only
superior but cheaper. The controlling factor in these cases is
the quantity of the repetition work.

It will be seen that these naturally (physically) enforced
limits are such as tend to make work expensive when the finish-
ing is done by turning, assisted by filing and the use of emery
cloth for finishing. As shafts and external work, however,
within these limits can be easily produced very economically
by grinding, now that the principles underlying the successful
employment of the process are becoming understood, and
wheels and machines made in accordance with them, the
grinding machine finds an increasing field of usefulness In
soft metals such as mild steel and cast iron, holes within the
limit can be cheaply produced by reamers and broaches ; when
the material is very hard, grinding frequently proves more
economical, while holes in hardened steel must be ground where
truth and economy are requisite. It is essentially the demands

GRINDING AND MANUFACTUEING 11

for these degrees of accuracy, and for the corresponding quality
of surface involved, which is extending the use of the grinding
machine so rapidly, since it here shows economy over lathe
work.

As accuracy is the first quality looked for in ground work,
it follows that fine workmanship is essential in a grinding
machine. To explain what is meant by fine workmanship is
impossible in a book, and to this extent any literature on
the subject is bound to be defective. Appreciation of it is
not attained by every one in the shops. The accuracy of
the work produced by any machine depends upon the design,
material, and workmanship, condition and the handling of
the machine ; and to produce work economically the machine
must possess such accuracy in itself and be such as to perform
the work with little trouble. Apart from the requirements
of accuracy, grinding machines have to meet the question
of protection against grit, the problem of high spindle speeds,
and other difficulties, so that the selection of grinding machines
requires particular care.

The substitution of a rotating abrasive wheel for the tool
in a lathe produced the first form of grinding machine, and
such a substitution is still useful in many cases, although machines
specially designed for grinding produce better work much
more rapidly. Let us now see what conclusions can be arrived
at by comparing the action of a rotating wheel with that of
a single-point cutter in removing material from the work.

The grinding wheel may be regarded as consisting of a
number of very small tools held in position in the wheel by a
cement. The wheel is ' trued ' by means of a diamond tool,
so that the points of a very large number of the small tools
lie on the wheel surface. By the rotation of the spindle
the particular particles in use are brought into action, and
each takes a cut on the metal of very small depth and width.
The length of the cut depends on the length of the path of
the particle in contact with the work. Thus in external grind-
ing the length is short (say jfa inch or TV inch) ; in internal
grinding it is usually longer (say up to £ inch), while if a cup
wheel is used, grinding upon its flat face, the length of cut is

12 GKINDING MACHINERY

considerable and may be several inches. Photographs of the
small chips produced by these fine cutting points are shown
in Figs. 14 and 15, and resemble the larger swarf from lathe
tools.

The Action of a Grinding Wheel. — The particles of abrasive
are bonded or cemented together indiscriminately in the wheel,
so that the angle at which the cutting surface of a particle
meets the work — which corresponds to the top rake of a tool —
varies over a wide range, instead of being correctly suited to the
material, as a shaped tool can be. It is the same with the angle
of clearance behind the edge of these cutting points. On the
whole, therefore, the cutting edges of the particles are presented
to the work at most unfavourable angles. In the truing of
a wheel by means of a diamond tool, the projecting edges of
the abrasive particles are turned off, so that, regarded as cutting
tools, their rake angles are unaltered by the process, but their
clearance angles are made zero.

The net result of this is that it requires much more force
per given area of cut, and therefore much more work, to remove
the metal by grinding than by turning, planing, or milling. This
difference of the amount of work is further increased by the
very small chip taken in grinding (as a chip of small area requires
relatively more force than a chip of larger area) and by other
causes. The work represents that part of the cost of the
operation which comes in the power account, and these costs
are difficult to allocate. When, however, it is a question between
roughing off a large quantity of metal by ordinary tools and
finishing by grinding, and doing the whole operation from the
rough by grinding, such as producing parts from the forging,
this cost is to be borne in mind, as it may turn the scale in favour
of the double operation.

In the case of finishing work by grinding, this extra cost is
very slight, and need not be considered.

Although the cut is very fine, as there are a number of
cutting points in action at once, and as the speed of the cut is
so high (about a mile a minute), the power which must be
supplied to a grinding machine intended to give a rapid pro-
duction is very high ; but with sufficient power the time taken

GRINDING AND MANUFACTURING 13

— and hence the total cost — need not be unfavourable to the
grinding machine.

The edges of the particles, being very keen (see Fig. 5,
page 19), will take a very fine cut, and the cut can only be very
fine, as it is controlled ultimately by the size of the particles
of the abrasive in the wheel, and their bondage in the wheel ;
and this fineness enables dimensions to be obtained accurately,
not only by its own nature, but also because the total force of
the fine cut is small, and therefore less force is put on the piece
of work and on the machine than where a cut of greater sec-
tional area is taken by an ordinary cutting tool at a very much
slower speed. This taking of a very large number of very
fine cuts, enabling accuracy of size and quality of surface to be
obtained, and the comparatively small cutting force in action,
are the features which lie at the base of precision grinding. The
particles of grit are so keen that they will cut steel when the
depth of cut is of the order of a hundred thousandth, and work
can be ground to the ten-thousandth part of an inch.

The rapidity of working will depend upon the number of
cutting points in action per minute, and accordingly high
wheel speed is of great advantage, for the number of small cuts
made per minute depends directly on the speed. It is, therefore,
customary to employ as high speeds as are consistent with
safety. The number of cutting points also depends directly
upon the width of the wheel, and this reasoning leads to the
employment of wide wheels, and arranging that as much as
possible of the width of the wheel shall be in use.

As the depth of cut is so small (of the order of yoVo mcn
usually), in order that there should be a large number of cutting
points coming into action as the wheel revolves, the wheel must
be turned very true on its axis, for which purpose a diamond
tool is necessary. A diamond is so hard that it cuts the particles
of abrasive across while the cement or bond retains them in
position. For making a wheel sufficiently true for rough
purposes a 'wheel- dresser' (see Fig. 11, page 37) — which acts
by dislodging the outstanding particles of abrasive from the
wheel — is cheap and effective. Soft cup wheels may also be
trued by its use or with a piece of hard carborundum block.

14 GRINDING MACHINERY

For wheels working on the edge a diamond tool is essential
when good work is requisite.

Continuing the comparison with a single point cutting tool,
we next observe that the chip in a lathe, whether it breaks
off short or forms a long spiral, usually has no difficulty in finding
room to dispose of itself in ; room must also exist for the chips
in the case of grinding, and unless there is room trouble must
result. One of the great improvements in wheels has been the
reduction of the amount of bond necessary so that the space
between the particles of abrasive is not filled up, but the wheel
is open and porous, affording space for the chip as it is
produced.

Grade. — As the edge of a lathe or other cutting tool gradually
becomes blunt, so do the edges of the particles of abrasive
which project slightly from the geometrical surface of the
wheel, and act as cutting points. Although the material of
these is extremely hard and uninfluenced by any temperature
attained, the keenness of the small parts is gradually lost,
and the force at the cutting point necessary to take the chip
increases, not only owing to loss of keenness, but since the area
of the chip section for a given depth of cut consequently in-
creases. If the amount of bond or cement is suitable, the
increasing force dislodges the cutting particles from the wheel,
and as this takes place all over the surface of the wheel, new
cutting points take the place of the worn ones, and the action
of grinding proceeds. If. however, the particle is held in the
wheel more firmly, the forces involved, the power required, and
heat produced continue to increase until the work is burned, or
other trouble occurs. It is evident that the amount of the bond
or cement which holds the small cutting particles together,
and the corresponding hardness of the wheel (called its ' grade ')
should vary with the nature of the work.

Grit. — As mentioned above, the depth of cut possible with a
wheel depends upon the size of the particles of abrasive of which
the wheel is composed ; this is termed the ' grit ' of the
wheel, and is usually the same throughout the wheel, though
for some purposes a mixture is used. The large grits suitable

GEINDING AND MANUFACTUKING 15

for heavy cuts are distinguished by low numbers, and the
small grits which yield fine finish by means of light cuts, by
higher numbers. It is not essential, however, to use fine grits
to secure a satisfactory and fine surface, as by carefully truing
the wheel — which is equivalent to shaping the cutting points
into ' broad cutting ' tools — a fine finish can be obtained with
very coarse grits.

Basis of the Accuracy of Grinding. — As the work proceeds,
the wheel loses particles from its surface and wears down,
and it is sometimes asked how it is possible to produce straight
parallel work with a wheel which is continually losing its size
by disintegration.

Suppose that the wear of the wheel alone affected the result,
and that everything else was ideal in the case of grinding a
piece of work round and straight in a machine such as is shown
in Fig. 29. The travel of the work would be exactly parallel
to its axis, and the result would be that the work could be
ground true within any limit which could be assigned, however
small. For after the wheel has passed over the work and the
cut for the next travel put on, the wheel cannot wear down by
more than the amount by which it has been fed forward, as if it
wore down this amount it would no longer touch the work.
So that by reducing the cross-feed as the work is ground nearly
to size, the amount of want of parallelism, being less than
the final amount of the cross-feed, can be made as little as is
desired.

This finishing of the work surface by an exceedingly fine
cut which produces an insignificant amount of alteration in
the shape of the wheel, is one of the fundamental points of
precision grinding. Further, the cut being very fine, it produces
little force, so that the errors due to springing of the work are
small.

For example, a hole might be ground out by a wheel taking
a deep cut and fed once slowly through ; this would not
make the hole parallel or to the taper for which the machine
was set, for the wheel would wear in the process — and the
work would also distort with the removal of the metal. On
some external work, where the wheel is large compared with

16 GKINDING MACHINEKY

the amount of metal ground off — so that the wear of the wheel
is small — traversing is dispensed with, without the loss of
commercial accuracy.

At these fine feeds (say j^o ^nc^ on ^e work diameter) the
amount of wear on the wheel is very slight, and the effect on
the work is commercially unnoticeable. In fact, when a
number of pieces have been rough ground to within a thousandth
or two of an inch of size, they may often be finished to size
without any apparent wear on the wheel ; the number depend-
ing upon the area of the surface to be ground.

It is not always possible to arrange matters so that the
wear of the wheel has no effect on the work shape, sometimes
for reasons of productive economy, but in general the method
of working should be arranged with that point in view.

These considerations of the nature and requirements of
the process of grinding lead on to the methods by which they
are met in the manufacture of the wheels and in the construction
of the machines.

CHAPTEK II
THE ABRASIVES AND THE WHEEL

As the distinctive feature of grinding machines is the wheel,
it is well to consider the properties and mode of action of it
first.

From the earliest days tools and weapons have been made
and sharpened by grinding, at first by rubbing on flat stones,
and later by the use of rotating wheels ; also fine particles of
hard materials have been used for purposes of abrasion.
Most of these natural abrasives are composed of either silica
or alumina.

Natural Abrasives. — Among those stones and abrasives
which owe their hardness to silica may be mentioned mill-
stones and gritstones, quartz and quartz sands, tripoli, and
pumicestone. The hardness of crystalline silica is 7 on Mohr's
scale, which is rather harder than Fe3C, the cementite of carbon
steels. Crystalline alumina is much harder, being 9 on Mohr's
scale (see page 438), and furnishes the natural abrasives known
as Emery and Corundum. The diamond, which is crystal-
lised carbon, is 10 on Mohr's scale, but the difference in
hardness between Corundum and the diamond is very great.
This step in the scale is considerable compared with the others.

Silicates. — The effective abrasive stones consist of silica
particles held together by a cement of carbonate of lime, and
occur in great variety. The finer are used as hones, and the
coarser, used as grindstones, hold their place in many manu-
facturing processes. The principal hone and oilstones are the
German, Washita (of various grades), Turkey, Canadian, and
Arkansas ; they are expensive, and seldom used except for
smoothing the edges of tools. Some of the abrasive wheel
makers have placed artificial oilstones on the market, and

17 c

18 GRINDING MACHINERY

they possess advantage over the natural stones in their
convenient shape, uniformity, and freedom from flaws. For
producing a fine smooth edge on workshop tools such
as scrapers I have not so far found anything better than
Arkansas stone, which, however, is unfortunately very ex-
pensive and also needs care in selection. The principal sources
of grindstones in this country are Yorkshire and Derbyshire,
from the quarries of which qualities suitable for mill- or
grind-stones are produced. Stone of a finer grit is suitable
for woodworking tools, the most famous quarries being
at Bilston, which are unfortunately now beginning to be
exhausted.

Grindstones. — In Fig. 2 is shown the grit of which a Bilston,
and in Fig. 3 that of which a Derbyshire, stone is composed.
They are magnified 20 diameters so that they may be
conveniently compared with the photographs of other abrasives
shown in the corresponding figures.

For manufacturing purposes gritstones, compared with
artificial wheels, are at a disadvantage in that the grit itself
is comparatively soft, and in that their smaller tenacity renders
it dangerous to run them at surface speeds such as those
which a modern abrasive wheel will safely withstand. They
are, however, comparatively very cheap, and have a ' grade '
particularly suitable for some work, and which the manu-
facturers of abrasive wheels have only recently been able to
produce with success.

The stone is soft when quarried and hardens somewhat
on exposure to the air. Owing to the mode of natural
formation, grindstones may contain soft spots and be otherwise
irregular in structure; in the work for which they are em-
ployed this is usually of little moment. Mounted grind-
stones tend to come to rest regularly in a certain
position, so that one portion may be immersed in water
for long intervals ; this should be avoided, as it softens that
part of the stone.

The stones from the same district vary very considerably
in hardness ; the sand grains in some are closely bonded
together, and the stone is so hard that it is also used as building

THE ABRASIVES AND THE WHEEL

material. From this the hardness varies until there is so
little cementing material that the stone can be easily disinte-

FIG. 2. — BILSTON GRIT.

20 DIAMETERS

FIG. 4.— EMERY, No. 60.

20 DIAMETERS

FIG 3. — DERBYSHIRE GRIT,

20 DIAMETERS

FIG. 5. — CORUNDUM, No. 60.

20 DIAMETERS

grated by the pressure of the fingers. Where the work consists
of parts with delicate edges or points (e.g. razors and needles),
such stones are used, the harder stones being used on the
rougher work.

20 GRINDING MACHINERY

A surface speed of 800 or 900 feet per minute, circum-
ferential speed, is suitable for grindstones, although in manu-
facturing processes they are frequently run very much faster.
In these cases they must be held in a strong mounting, such as
is shown in Fig. 10. This compares unfavourably, in the light
of what has previously been said about the advantage of high
speed, with the corresponding 3500 to 7000 feet per minute
at which artificial wheels are run.

As particles of crushed emery are so very much harder
than the sandstone grit, it would appear to be an easy matter
to produce artificially very much more effective wheels than
those of natural stones, especially as with a strong cement or
bond a much higher speed could be used. That particular
quality of softness of the natural stone, considered as a whole,
in virtue of which the particles of grit are torn from the stone
directly they become slightly blunt, so that the face of the
wheel always contains sharp grit ready to cut, proved to be
difficult to imitate.

Emery. — Until recent years the principal abrasive used
for wheels was emery, an impure form of corundum, that
having the highest reputation coming from the Island of Naxos.
Other sources occur in Smyrna, in the Pfalz district (Vosges),
in Massachusetts, and in Ceylon. Naxos emery contains from 55
to 65 per cent, of corundum ; other emerys from 30 to 55 per
cent., usually about 40 per cent. only. About two-thirds of
the impurities consist of iron (magnetite), and the remainder
of tourmaline, of which the hardness is 7-5 (Mohr). The emery
is obtained in masses, either shaly or having no definite structure,
and without definite planes of cleavage. It is not only hard
but also close grained and tough; the iron gives it a black
colour. When crushed the particles retain these characteristics.
The excellency of the Naxos material and the small source of
supply resulted in the supply being ' cornered ' about the
middle of last century ; the Greek Government now work
the mines, and make considerable reductions to their National
Debt as the result. Since the discovery in Canada of large
deposits from which nearly pure (90 per cent, or more) corundum
can be obtained, the importance of Naxos emery has rapidly

THE ABEASIVES AND THE WHEEL 21

declined, although the price of the corundum is about two and
a half times that of the emery.

Corundum. — In Fig. 4 is shown emery and in Fig. 5 Canadian
corundum grit, both being of size No. 60, and magnified 20
diameters. The emery particles appear to be somewhat
smaller than the corundum — due to the mesh of the sieve
having actually smaller spaces than in the case of the emery.

Corundum is crystallised alumina (A1203), and when crushed
the particles have semicrystalline appearance and sharpness.
Pure crystalline alumina is colourless ; the natural corundum
usually has a faint yellow tinge, but when the clear crystal is
coloured by nature with certain metallic oxides, the result is
a gem, and such are the ruby, sapphire, and topaz. The
turquoise also is mostly alumina.

The density of emery varies according to the impurities —
from 3-65 to 4-05 ; pure corundum has a density of 4. The
Canadian Corundum Company state that their product is
practically pure, as they allow 2 per cent, of impurity only.
This is an extraordinarily perfect refinement, and a much less,
say 5 to 10 per cent., might be expected.

As corundum is practically colourless, wheels made from
it are coloured by the bond only, and are of a light colour :
if emery be used in admixture the wheels are of darker shade,
darker in proportion to the amount of emery, and the dark
particles can be easily seen. As corundum is the natural
product which stands next to the diamond in hardness, and
as emery contains 35 to 65 per cent, of impurity, it seems evident
that an admixture of emery will not improve the cutting
properties of the wheel ; it should, however, considerably lessen
the selling price.

Artificial Abrasives. Carborundum.— In 1891, by the use
of the electric furnace, Acheson first commercially prepared a
new abrasive, which was christened Carborundum, and chemi-
cally was carbide of silicon (SiC), the weight analysis
being Si = 69-10 ; C = 30-2— impurities 0'64 per cent. It had
previously been prepared in the laboratory by Moissan, without
its value being recognised. It is produced by mixing in the

22 GRINDING MACHINERY

furnace, carbon 50 per cent., silica or aluminum silicate 25
per cent., and common salt 25 per cent, by weight, fusing and
then allowing the mass to cool. On the resulting mass being
broken it is found to consist of crystals of a purple blue colour,
formed on the hexagonal system. The sp. gr. varies from
3-171 to 3-214, and the hardness lies between 9 and 10 on Mohr's
scale, so that it stands next to the diamond. It is, however,
brittle, while corundum is comparatively strong and tough.
Acheson has made numerous improvements in the furnaces
for producing the material, and considerable quantities are now
produced by the Carborundum Company at Niagara, where
advantage is taken of the low cost of electric power. Car-
borundum is now also produced in France, Germany, Austria,
and Canada, and for trade purposes sometimes masquerades
under other names.

When the crystals are crushed into fine particles for wheel-
making and other purposes, the fragments are irregular in form,
partly of a glassy and partly of a crystalline fracture, and very
keen edged, so that with its special hardness carborundum
would seem to be an ideal abrasive for the formation of wheels.
In practice the wheels made of it are the most efficient for work
on cast iron. The glassy smooth surface of carborundum
makes it difficult for the bond to adhere to it, and hence wheels
made of this abrasive are apt not to be so regular in the grade
as those of other abrasives. Particles of 60 grit are shown in
Fig. 6, magnified to 20 diameters : larger grits are more prismatic
and irregular in shape.

Alundum. — The electric furnace has since been employed
in the manufacture of artificial corundum, denominated
Alundum, by the Norton Manufacturing Co., who manufacture
considerable quantities. Artificial corundum has been made
in a small way for nearly a century, and for some years artificial
rubies have been manufactured by a building-up process, and
were placed on the market as gems without reference to their
origin. The curious fact that in the rubies offered from
certain sources the flaws were all spherical, while generally
they are of distorted shapes, led to the tracing of the former
to an artificial source. Alundum is produced from bauxite —

THE ABRASIVES AND THE WHEEL

a pure form of clay. It is said that traces of chromium can be
introduced into artificial corundum and render it harder than
the naturally produced material. Corundum and alundum
almost always contain traces of iron, which renders it much
tougher than if it were purer ; the pure crystals are colourless
and rather brittle. In their endeavours to improve the
quality of their products the British Abrasive Wheel Co.
have experimentally purified some of their artificial alumina ;
but it is questionable whether it is as good an abrasive as
crystals of usual impurity. In Fig. 7 is shown alundum size

Fia. 6. — CARBORUNDUM, No. 60.

20 DIAMETERS

FIG. 7. — ALUNDUM, No. 60.

20 DIAMETERS

No. 60 grit and magnified 20 diameters, for convenient com-
parison with Figs. 2 to 6 showing other abrasives. The fracture
is similar to that of carborundum, but the fragments are
rather less angular. Like carborundum, alundum is sold
under other names.

Abrasives differ in hardness, in tenacity, in angle of natural
crystallisation, in fracture, in specific gravity, in resistance to
high temperatures, and also in their purity. It is necessary
that they should be unaffected by high temperatures, not only
that the fine edges of the fragments should withstand the heat
produced by metal cutting, but also that they may not be
injured by the temperature (about 3000° F., or 1650° C.)

24 GKINDING MACHINERY

necessary to fuse the bonds employed in the vitrified process —
which produces the wheels most generally useful in precision
work. The specific gravity affects the speed at which the
wheels can safely be run, but on these points there is so little
variation between abrasives that the toughness and hardness
of the material and the type of fracture of the particles are the
important differences.

Grits. — After the abrasive is crushed into small particles
they are separated into sizes, first by the usual rotating sieve
process, and afterwards by rocking sieves, and the pitch of the
mesh of the sieve gives the name to the particles which pass
through it, but which did not pass through the one size smaller
mesh. For example, the particles which passed through a
sieve with 36 wires to the inch but which did not pass through
the preceding finer mesh is called 36 grit, No. 36 emery or
carborundum as the case may be, and a wheel madtf of that size
abrasive is said to be of 36 grit. The illustrations of grit (magni-
fied 20 diameters) show No. 60 grit, that size being selected as one
in general use for many purposes. This method of sizing is not
a very definite one, as the diameter of the wires of the sieve is not
specified, and larger particles pass if the wires are thin than if
they are thick, either originally or from wear. Also the arrange-
ment of the wires in the mesh gets out of shape, thus altering
the size of the particles which pass through.

The crushed abrasive is separated into grits varying from
No. 6 to No. 250, beyond that finer particles are separated
by the time they take to settle in a liquid, as explained in
Chapter XII ; for commercial purposes a stream of water is
used. The very fine grits are distinguished by letters F,
FF, &c., and 'flour.' The sizes usually employed in wheels
used on grinding machines run from 24 to 80, but as coarse
as No. 6 is used for some purposes, and No. 250 is employed
on glass work. The size of the grit controls the sectional
size of the small chips which can be produced by the wheel,
so that wheels of the coarser grits grind more quickly, and
wheels of fine grit produce a higher finish. Some wheels
are made with a mixture of grits termed ' combination,' with
a view to combine the features of rapid cutting and fine finish.

THE ABEASIVES AND THE WHEEL 25

It is, however, to be noted -that good workshop finish is obtained
easily with the coarser wheels, provided the machine and
wheel are in good condition. Commercially very fine finish,
such as requires wheels of 80 grit, is only needed in special
cases ; accuracy, within the limits considered in Chapter I, is
usually the chief consideration.

Bonds. — In a wheel these particles of abrasive are joined
together by a cement or bond. Originally shellac or some
gum was used, but the bonds now chiefly in use are the vitrified,
silicate, and vulcanised, though others of various natures are
employed by some firms.

Usually a wheel is of uniform grade throughout, which is
attained by very complete mixing of the wheel substance
before moulding the wheel shape and careful after-treatment.
That disc wheels are often considered to be softer towards
the centre is partly due to their circumferential speed diminish-
ing as they wear down, and partly to the same amount of
work necessitating a greater radial wear, since the circum-
ference over which it is distributed is less.

For some purposes a wheel with different grades is required ;
for instance, if it is important that a disc wheel should keep
the corners sharp and free from roundness, the sides of the
wheel may be made with more bond than* the intermediate
portion.

Grade. — The greater the amount of bonding material the
more firmly are the different particles of abrasive held together,
and the greater the force required to detach them from the
wheel. When in use the particles get blunt gradually, and
as they do so the force of the cut they take increases until it
becomes so large as to dislodge the particle from its hold.
The property of the wheel by which this disintegration takes
place is termed its ' grade.' It depends on the amount of
bonding material, the more there is the harder the nature
of the wheel is. The ' grade ' of a wheel must be such that
in use the disintegration of the wheel only just takes place,
and different grades are necessary for wheels to be used on
different materials. The grade is usually denoted by a capital
letter, the early letters of the alphabet being usually used

26 GKINDING MACHINERY

for the soft grades and the later ones for the hard grades ;
this is not, however, the invariable practice, though it is to be
hoped that it will be universally adopted. A chart showing
the relation of the grades is given on page 427.

The grade of a wheel is not a very definite quality. The
properties of a wheel depend partly on the abrasive and
partly on the bond and its amount, so that, for example,
wheels of tough corundum and harder, but brittle, carborun-
dum, if made with equal amounts of the same bond, would
not behave in the same manner when used on mild steel.
The amount of the impurity in the abrasive also affects
the matter : for example, emery is corundum with an equal
amount of impurity, and accordingly is softer than corun-
dum. Wheels are tested for grade by ascertaining the force
which is necessary to dislodge the particles at the surface ;
this is done by using the end of a file or hardened screwdriver,
pressing it on the wheel surface and then pushing it until
some particles are broken out of the surface. The grade is
estimated by the amount of force required. If the force
were measured it would determine the tangential effort
necessary to disintegrate the wheel surface, and this may
be considered as approximately deciding the grade of the
wheel. But the actual behaviour of a wheel in use depends
also on other factors — the rapidity with which the particles
become blunt, for example.

The desirable properties of a bond are that it should have
a high tenacity, should resist the action of water, soda water,
oil, or other fluid used in grinding, should be easily controlled
in quantity and distribution in the wheel, and should not be
subject to atmospheric influences.

Vitrified Process. — The wheels most usually employed in
machine grinding are made by the vitrified process, in which
the bonding material is a felspar or kaolin. This is mixed
with the crushed abrasive into a wet mass, and moulded to
shape. After the wheels are dry, they are rough turned and
stacked in a kiln, which is fired. When the bond has fused and
run, the whole is allowed to cool slowly. The bond is of the
nature of porcelain, and very little is necessary to cement the

THE ABRASIVES AND THE WHEEL '27

particles together firmly enough to give the requisite hold on
the particles for producing the useful grades. This gives a very
open nature to the wheel, the bonded particles having much
free space between them, as can be seen in Fig. 8, which is a
photograph of awheel of alundum No. 60 grit, such as is shown
in Fig. 7, magnified also 20 diameters. The wheel has been

FIG. 8. — VITRIFIED WHEEL SURFACE, TRUED. 20 DIAMETERS

trued and the surfaces of the particles as cut by the diamond
can be traced. The wheels are turned true after vitrifying,
and the centre holes lined with lead in the larger sizes.

Wheels of this bond cut very freely, and are unaffected by
any of the fluids used in grinding. They are the most generally
useful for machine grinding, presenting the cutting points
openly, and holding the particles with the minimum of bond.

Elastic Wheels. — Wheels made with elastic or vulcanised
bonds are about twice as strong as those with the vitrified
bond, so that where a thin wheel is necessary or where side-
thrust is likely to come upon the wheel, this bond should be
selected. The bond is rubber, masticated, and the wheels are
shaped, pressed firmly, and vulcanised. The process produces
wheels with the material close up, which lack the porosity of
the other bonds and cut best when worked hard.

28 GRINDING MACHINERY

Silicate Wheels. — Silicate wheels, in which silicate of soda
is used as the bond, require more bond than in the vitrified
wheels to cement the particles together so as to constitute the
same grade, so that they are not so open in texture. Also for
an equal degree of safety they must not be run so fast as the
vitrified wheels. Where soft grades are required, as in surface
grinding with cup wheels, this bond is very suitable, as there is
not then too much bond to hinder them cutting very freely,
but there is sufficient to secure a fair hold on the particles,
and the correct grade can be accurately obtained. This is
important, as with such wheels a very little difference in the
grade leads to rapid disintegration if it is too soft, or to
glazing if it is too hard.

Larger wheels can be made by the silicate than by the
vitrified process, owing to the manufacturing risks of the latter.

Some silicate wheels are affected by atmospheric influences,
and lose their strength in course of time.

The material of a wheel consists of particles of abrasive
held together with certain forces by the bond, and alters as these
are changed. Many bonding materials have been tried — those
given above being in general use. The vitrified bond is used for
free-cutting wheels of moderate dimensions ; the silicate where
soft wheels are required, the extra amount of bond holding the
particles uniformly, but not being of sufficient amount to clog
up the wheel ; and the vulcanised for wheels where greater
strength is requisite. Experiment may yet lead to better
bonds ; the amount of hold which a certain proportion of bond
should have, depends ultimately on the hardness and toughness
of the abrasive. The vitrified and silicate bonds are well
suited to the present abrasives, but elastic bonding offers
opportunity for improvement.

Strength and Surface Speed. — Upon the strength of the
bond and its amount depends the speed at which a wheel can
safely be run, and upon the wheel speed depends the output
of the machine, so that the strength of the bond is a factor in
grinding efficiency.

It can be proved that the stress in wheels depends upon the
square of their circumferential speed (provided we disregard the

THE ABKASIVES AND THE WHEEL 29

small variation of density due to the different bonds and their
amount), so that for any allowable stress in the wheel there is
a corresponding definite circumferential speed. Wheels should
usually be run up to this speed, and hence the revolutions per
minute at which a wheel should be run is inversely proportional
to its diameter.

To ascertain the manner in which the size of a wheel affects
the permissible speed of running, consider the case of similarly
shaped wheels, that is wheels whose external and internal
diameters and width of face are all proportional. Let o> be the
permissible angular velocity for a wheel of outside radius r,
(so that (ar is the peripheral speed), then o> will depend upon r,
upon the strength/ per unit area of the material of which the
wheel is composed, and also upon its density p. That is, we
have —

where I, m, n, and a are constants, and 2 indicates that the
sum of a number of terms may have to be taken. If L, M, and
T are the dimensions of length, mass, and time, we shall
have —

.*. n = — and m — — 1

or c*r=a A/ *

Thus, the limiting value of the circumferential speed (a>r)
is proportional to the square root of the permissible stress (/)
if we regard the density as constant ; and conversely the
stress in a wheel depends on the square of its circumferential
speed — and not on its diameter.

Tenacity and Bond. — As the tenacity of a wheel depends

30 GRINDING MACHINERY

upon the amount of bond, and the greater the amount the harder
and stronger the wheel, a greater stress can safely be allowed
in a hard wheel than in a soft wheel, and therefore a higher
circumferential speed can be permitted. It is usual, however,
in practice to neglect this, and to consider that the safe circum-
ferential velocity of all disc wheels is the same, and this is
taken to be from 5000 to 7000 feet per minute. Cup wheels,
however, especially if silicate, should be run at a lower speed ;
from 3500 to 4500 feet per minute is suitable.

For wheels which have not the same ratio of inside to
outside diameter the size of the hole has an effect, but as
the wheel has to be driven by flanges holding it on the two
sides, this effect also is usually not considered.

The best makers test all their wheels before dispatch by
running them at a high speed (usually 9000 feet per minute
peripheral velocity), and in this connection it is to be noted
that if under test a wheel is run at double the speed at which
it is to run in use, it has been subjected to four times the
working centrifugal stress, and if to two and a half times the
speed to over six times the working stress.

In Table VIII, page 431, will be found the number of revolu-
tions per minute at which wheels of different diameters must
be run in order to attain various circumferential speeds from
3000 to 7500 feet per minute.

A number of experiments upon the strength of wheels
have been made by professors of engineering both in America
and on this side of the Atlantic. Unfortunately the grade of
the wheels is never stated, so that the results are of little
value ; a firm desiring a test strikingly in their favour as
regards wheel safety might make wheels of a very hard and
useless grade for the purposes of the experiment. The strength
chiefly depends on the grade, but to some extent on the grit
of the wheel as well.

The tensile strengths of the material of vitrified wheels
is approximately as below for various bonds of 60 grit. The
amounts are in pounds per square inch.
Grade H I J K L M N

Strength 600 800 1200 1350 1500 1750 2000

THE ABRASIVES AND THE WHEEL 31

The amount of variation with the size of grit runs about
as below —

M Wheels— grit . . . . 60 46 36
Strength— pounds per sq. inch . 1750 1550 1450
Q wheels— grit . . .8 12 14 20 24
Strength— pounds per sq. inch 1150 1400 1550 1750 2000

so that for equal factors of safety the circumferential speeds
in feet per minute should be as follows—
Grade H I J K L M N

Circumferential) 350Q 4Q()0 5000 525Q 55Q() 6000 6500
speedj

The stress may be found from the equation—

where v is the circumferential velocity in feet per minute
and dlt dz the diameters of the wheel and flange respectively.
In deducing the formula, the density of the wheels has been
taken as TO lb. Per cubic inch, and in the absence of any know-
ledge ^ has been taken to be the value of <r (Poisson's ratio).
Calculation of the stresses will show that the factor of safety
is rather over three, which is sufficient in machines of this class.

Wheel Speeds.— In use, a disc wheel gradually wears down,
and as its diameter decreases so the circumferential speed falls.
As the limiting factor to the circumferential speed is the
safety necessary, the rate of rotation should be increased as
the wheel wears, otherwise the wheel will appear to be of a
softer grade owing to the ratio of work speed to wheel speed
increasing, and if the diameter is much lessened without in-
creasing the number of revolutions per minute, the wheel
will wear away rapidly.

In order to be able to raise the rate of revolution as the
diameter decreases, so as to keep the circumferential speed
nearly the same, some speed variation device, such as a pair
of step cones, should be included in the drive. The number
of speeds which should be provided depends upon the amount
the wheel is intended to be worn down. In precision grinders

32 GRINDING MACHINERY

the hole in the wheel has usually to be of considerable size, so
that the wheels can be held in collets for the purpose of changing
them rapidly and without loss of wheel substance, and in this
case a reduction of the wheel to two-thirds of its diameter is
about as much as is obtained : two or three speeds are then
sufficient. In some machines, such as ordinary tool grinders,
where the wheel is not changed until used completely or to
some arranged diameter, the hole in the wheel may be com-
paratively small. Owing to the prices at which these machines
are usually sold, step cones cannot reasonably be looked for
in the drive, although they would be a good investment for
the user. Where the speed can be increased so that the fastest
speed would give so high a circumferential velocity to the largest
wheel used as to be dangerous, some arrangement should be
included to prevent the fast speeds being used when large
diameter wheels are on the spindle. The best method of
all is to use simple single speed machines, and as the wheel
wears down transfer it successively to machines with faster
running spindles : this method is, however, only available in
few cases.

Mounting Wheels. — In mounting a wheel upon a spindle
it is very essential that it should go on easily but without
appreciable play, and for this end the holes of all wheels but
the smallest should be brushed with lead, which can be quickly
scraped if necessary so as to allow the wheel to fit easily. If
the wheel be forced on the spindle or collet, bursting stresses,
similar to those due to rotation, are caused, and there is con-
siderable risk that the cumulative effect will render the wheel
unsafe.

Before mounting a wheel it should be examined for cracks,
and tapped lightly with a hammer, so as to judge by its ring
whether it contains an unperceived crack. Even then a new
wheel should be started with care, as it is not absolutely certain
that a flaw will be detected.

It may be noted that at the speeds employed the bore of
pulleys expands so that unless they are originally a very close
fit they may be loose when running. For this reason collets
should have a taper fit on the spindle; they are then tight

THE ABRASIVES AND THE WHEEL

when running and can also be easily removed. The amount of
this enlargement of the bore at a given speed can easily be
calculated from the elastic properties of the material of the

FIG. 9. — WHEEL MOUNTING

collet, and the correctness of the amounts found have been
confirmed by direct measurement on the expansion of the
holes in steam turbine rotors.

Wheels should be mounted between flanges arranged to bear
on the wheel near their circumference only. If the flanges are
flat, tightening the nut to close them tends to make them a

34 GKINDING MACHINEKY

trifle concave, which would be dangerous ; they should there-
fore be distinctly recessed towards the centre, and sufficient
flat bearing area provided at the outside. Machines of the better
class are all fitted with collets designed on this principle, and one
such is illustrated in Fig. 35, page 126. For the sake of clear-
ness the mounting of a wheel is also shown in Fig. 9, where the
flanges A, B, bear on the outer part only, and are recessed at
C and D towards the centre.

Between the wheel and the flanges, washers E, F, of soft

FIG. 10. — INSERTED SEGMENT WHEEL

material, such as blotting paper or cardboard, should be placed,
so as to distribute the pressure, where the wheel is gripped.
Some makers send out their wheels with stout paper washers
already fixed to the sides, which is a great convenience.
Preferably the flanges should be keyed.

If the wheel is likely to receive sidethrust, the flanges should
extend to as near the edge of the wheel as is practicable.

Cylinder and cup wheels are mounted in recessed flanges,
and held by plates, between which and the wheel washers of
soft material must be placed, or they may be held in special

THE ABEASIVES AND THE WHEEL 35

chucks. Examples of the construction are given in Figs.
37 and 38. Cylinder and cup wheels are expensive, and for
large work, such as surfacing armour plate, chucks with inserted
segments are used. Such a chuck is shown in Fig. 10, in which
the segments A, B, are secured by the wedges C, which bind
the segment on three faces, and thus hold it securely.

Segments of artificial material are very expensive, and those
of natural grit stone much cheaper, even when due allowance
has been made for the greater amount of work done by the
artificial material. Accordingly in these machines the natural
stone is used, and its softness enables the cutting to be done
rapidly.

Balancing. — The circumferential speed of wheels being about
5000 feet per minute usually, the rate of rotation of the wheel
spindle is very high, and hence the centrifugal effects of any
want of balance and truth in the wheel or spindle are very
considerable, and form the cause of some of the difficulties
encountered in grinding.

The wheel spindle itself and all the rotating parts attached
to it must be in balance and run steadily by themselves ; if,
when the wheel is mounted, vibration then occurs on running
it, the trouble lies in the wheel.

The amount of these forces can be judged from the force
necessary to prevent a mass of one ounce, at a distance of
3 inches from the axis, from flying outwards when it is
moving round the axis at 1900 r.p.m. (the rate for a 10-
inch wheel). This force is almost 20 Ib. weight.

The expression for the effect of want of balance is —

where n is the number of revolutions per second, m is the mass
of the out- of -balance part (the difference from uniformity),
r the effective radius in feet at which it acts, and g the acceler-
ation due to gravity, which is 32' 2 feet per second per second.

The effect is equivalent to a periodic permanent force of this
maximum amount, and under certain conditions it can enforce
vibrations of the same frequency as the revolution of the wheel,

D 2

36 GEINDING MACHINEEY

or a simple fraction thereof, on the machine and on the work,
causing chatter. This subject is referred to more fully later.

Some makers balance their larger wheels before passing
them for delivery by adjusting the lead in the central hole,
and this is convenient initially. As the want of balance is some-
times caused by want of uniformity in the material of the wheel,
this is not a perfect arrangement, and a wheel of such a nature
will go out of balance as it wears down. Small amounts of
want of balance are quite unavoidable, and the best way of
meeting them is to make the wheel head so heavy that the
effects are reduced to insignificant amounts. Where there are
sufficient machines to warrant it, the wheels may be balanced
periodically on parallel ways.

In the machines constructed by the Landis Tool Company,
the collet is made with a groove containing movable weights,
which can be adjusted until balance is obtained. To give a
correct dynamic (as opposed to a static) balance, these weights
should be in the plane of the wheel ; they are placed as close to
it as constructive details will allow.

Besides the usual disc and cup shaped wheels a number of
shapes are used, suited to the various purposes for which the
wheels are employed. Most of the wheel makers give drawings
in their catalogues of the shapes they supply, and will make
wheels to such shapes as are desired. Wherever possible disc
wheels should be used, as they are the cheapest form, and also
cause less delay in delivery.

Silicate wheels take a few days in making, but the vitrified
wheels take several weeks, and there is also the chance that
after that time just what is desirable is not obtained, so that
care is necessary in ordering wheels for any particular purpose.

In specifying a disc wheel the diameter, face, hole, abrasive,
bond, grit, and grade should be stated ; with seven different
factors varying, a great number of wheels are necessary to meet
possible requirements. Machine makers are tending to use
wheels of fewer combinations of diameter, face, and hole, but
the recognition and adoption of a uniform system would be
advantageous, and it could be revised at such intervals as
progress might dictate. One of the difficulties is that in cases

THE ABRASIVES AND THE WHEEL 37

where the requirements of the work necessitate the changing
of the wheel, collets are used, so that the collet with the con-
tained wheel is changed. This necessitates a larger hole in the
wheel than if it is to be mounted directly on the spindle. To
meet the case it might be arranged to make the hole in wheels
of a particular diameter of one of two sizes according to the
purpose for which the wheel is needed. I have suggested*
the following series —

Wheel Diameter (inches) 6 8 10 12 14 16 18 20 22 24

Size of Hole (inches) either J | f 1 1J 1J If If 2 2

or 2 3 4 5 5 7 8 8 8 10

Truing Wheels. — To render the working portion of a wheel
true enough to be serviceable in precision grinding it must be
turned true by use of a diamond, which in almost all cases must

FIG. 11.— WHEEL DRESSER

be mechanically guided. The diamond is so very much harder
than the abrasive materials that it cuts the particles of the
wheel across without dislodging them from the bond, so that
they become — as remarked earlier — small tools without
clearance. The chip taken is so fine, however, that this does
not matter. ' Wheel dressers ' of various kinds have been
invented, consisting of discs with plane or corrugated edges
which rotate when in contact with the wheel, and so dislodge
the projecting particles ; they cannot, however, cut them,
and do not produce a wheel surface comparable with that
produced by a diamond, and not good enough for regular
grinding work except in the case of soft cup wheels. A typical
wheel dresser is shown in Fig. 11. A more effective one is
provided by mounting a sharp -edged hollow steel washer on
the end of a spindle mounted on ball bearings. The disc
rotates freely as the friction is so small, and presented properly

* Inst. Automobile Engineers, 1911.

38 GRINDING MACHINERY

to the wheel disintegrates its surface easily. For truing
grindstones a similar but more substantial tool is useful, and
the rotating disc here is usually hollow, and its axis nearly at
right angles to that of the stone ; or the end of a tube is used,
the tube being rolled by hand along the rest set close to the
wheel. A piece of hard carborundum block is very effective
in truing ordinary wheels, and in removing glaze from small
wheels by hand.

Diamonds. — Diamonds are of two very different kinds,
crystalline and amorphous, both being allotropic forms of
carbon, as is also graphite. They are natural products, the
crystalline being found principally in South Africa, Australia,
and Brazil, a few only now coming from India. The amorphous
diamond, carbonado, or carbon, is found in Brazil. Diamonds
have been produced artificially, but so far only in very small
sizes and at excessive cost, and larger diamonds have not been
produced from smaller ones in the manner in which artificial
rubies are made. The crystalline diamond is of the octohedral
system, and, when pure, is transparent and colourless. It
can be split by means of a sharp blow on the back of a knife, the
edge of which is held against the crystal, along the planes of
cleavage, and by this means splints suitable for diamonds, to be
used as small tools, are made. Sometimes diamonds are tinged
with a yellow or brown colour, and rarely with blue or red,
which latter colours enhance their value as gems. The
crystalline diamonds used as gems and for manufacturing
purposes are of the same nature ; the latter simply have such
defects as spoil their value for decorative purposes. The
crystalline diamonds, then, which are offered for commercial
purposes, all have defects, and the question of their suitability
and comparative value is of importance in their selection,
and can only be judged after experience. Those with
incipient cracks should be avoided, while an elongated shape
renders setting easier and more secure. While those of a
good crystal shape generally give the best service, they are
also the most expensive. Diamonds appear to vary con-
siderably in hardness. I have a preference for those from
Brazil. It is advisable to supply at first tools containing cheap

THE ABEASIVES AND THE WHEEL 39

small diamonds (say J ct.), as the stones sometimes fall or are
ground out of their setting and are lost ; when this risk is
reduced by experience, larger diamonds should be used, as
they are more economical, although the price per carat is
greater. Diamonds weighing 1 ct. are suitable for wheels up to
about 2 inches wide. As a diamond cannot be inspected well,
nor weighed when it is mounted into a tool, it is well to buy
the diamonds loose and mount them afterwards.

The amorphous diamond or carbonado is black and opaque,
and shows no structure under the microscope. It is very
considerably harder than the crystalline variety, but it is
also more expensive. When the wear and cost are taken
into account I consider that the crystalline diamond is the
more economical.

When a wheel is to be trued straight across (as a disc
wheel trued cylindrical, or a cup wheel, flat) the position of
the corner of the diamond which operates is of no importance,
but if a complex shape (e.g. a gear tooth space) is to be pro-
duced accurately on a wheel for reproduction on the work, the
position of the working corner is very important, and it is
difficult to adjust it accurately. In such cases a carbonado
should show to its best advantage.

Setting Diamonds.— For use diamonds are set at the end
of a cylindrical rod of steel or brass, thus forming diamond
tools, and precision machines are provided with means for
clamping the tool to the work table in order to true the wheel
parallel to the main ways of the machine. The axis of the
diamond tool should be presented to the wheel face at an
angle, and not normally, so that when a flat is worn on the point
of the diamond, a fresh corner may be presented by turning
the tool round in the clamp.

It is to be noted that setting the diamond off the axis of
the tool, or bending the tool, has not the same effect.

There are several ways of mounting diamonds for the
purpose of tools, some of which are shown in Fig. 12. I have
a preference for setting them as at A, using a brass holder and
solder (preferably hard) as the operation is easily and quickly
performed, and there is no risk of injuring the diamond. A

40 GKINDING MACHINEEY

bit of swarf dropped in the hole keeps the diamond up while
soldering. Brazing into a steel holder is more troublesome,
and although it makes a stronger setting, hard solder is amply
strong enough for the purpose. In the holder C, the diamond
is held by the screwed cap, and in that shown at D by the cross
screw springing the split holder.

In truing the wheel plenty of water should be used. The
action of the diamond cuts the particles of abrasive across,
but in doing this the edge of the diamond gradually gets
worn away and blunt. If too great a flat is worn on the
diamond and presented to the wheel, the particles are no
longer cut across, but are splintered and dislodged bodily, and
the truing is no longer satisfactory. When this occurs the
diamond has to be reset. In the initial setting the diamond

FIG. 12. — DIAMOND TOOLS

is presented in the most satisfactory manner, so that resetting
does not make matters as favourable as they might be. Again,
in setting, the diamond should not be presented to the wheel
with the planes of cleavage parallel to the wheel face, as it
may break; so that the amount of resetting is limited, and
diamonds should be treated carefully from the beginning.

In Fig. 8 the wheel surface shown has just been trued with
a diamond tool, and the surfaces where alundum particles
have been cut across and the small splinterings are visible.

Diamond Laps. — In internal grinding the problem of the
wheel and of the method of holding it on the spindle increases
in difficulty as the diameter of the hole decreases, and for small
holes wheels are replaced by diamond ' laps.' The lap is made

THE ABKASIVES AND THE WHEEL 41

of soft steel, and, as it is necessary that it should run very
true, it should have a taper fitting to the spindle. It is
charged with diamond powder by rolling it with the powder
and oil between hardened steel plates. The diamond powder
is made by crushing up small diamonds : the resulting powder
is mixed with oil, and the particles separated into various sizes
by the time they remain in suspension. In rolling between
the hardened plates the soft steel is penetrated by the particles
which remain embedded in it, and project very slightly from
the steel. The lap, after being charged, should be tapped and
brushed to remove the particles not firmly embedded. Laps
charged with the coarser particles — those first deposited from
the oil emulsion — naturally cut the most rapidly.

When the lap is rotating and brought to the work, the
diamond points projecting from the lap cut the work in exactly
the same manner as the particles of emery or corundum pro-
jecting from the surface of a wheel do, so that the process is
really a grinding and not a regular lapping (see Chapter XII)
operation. The speed should be as high as possible, and the lap
should run perfectly true. The cut can only be exceedingly fine
from the nature of the lap : it must not be forced ; the diamond
powder, however, is so very much harder than any other abrasive
that these laps cut fairly quickly and last a considerable time.
The truth of the lap depends upon its original form : it cannot
be ' trued.' Neither could a wheel made of diamonds (if they
could be manufactured cheaply) be trued, so that, without
the discovery of a very much harder substance for truing
them, they would be of little use in precision grinding.

CHAPTEK III

THE WHEEL AND THE WORK

The Material of the Work and the Various Abrasives.— To deal
with the various materials used in engineering manufacture
and construction, and to grind them efficiently and to a desired
quality of surface, there is a choice of four variations in the
nature of the wheel : the nature and size of the abrasive grit,
and the nature of the bond and its amount.

The abrasives may be divided into the Oxide of Aluminium
(A1203) group and the Carbide of Silicon (SiC3) group. Of the
former emery is now little used in machine shop grinding, as the
amount of impurity lessens its value as a cutting agent con-
siderably, and the cost of making it up into wheels being the
same as that of making up the purer materials, the wheel cost
is not lessened much, although the natural abrasive is much
cheaper. The grading is also affected by the impurity. There
remain natural corundum and its artificial equivalent, alundum,
which is also sold under other names. Although one is inclined
to prefer a manufactured material as being more under control
as to quality, there seems little difference between these
abrasives.

Corundum and alundum are the best abrasives for working
on steel, whether mild, high tension, or hardened, and on brass.
They are also used for grinding bronze, rubber, celluloid, and
such materials.

Carborundum (also sold under various trade names), the
carbide of silicon abrasive, is the best for grinding cast iron,
whether soft or chilled ; and it is also used for grinding bronze
castings, glass, &c.

Carborundum, from its hardness, is the best abrasive for
use on materials (e.g. cast iron, hard rubber and fibre, glass, &c.)
which are not strong enough to fracture it, but the toughness

THE WHEEL AND THE WOKK 43

of the alumina abrasives renders them the more suitable for
those materials which only yield under a high shearing stress
(see 'Phil. Mag.' July 1900, and < Engineering,' July 8, 1908), or
in which there are constituents of such different hardnesses
as ferrite, cementite, austenite, and martensite, arranged in
dimensions (as will be seen later) comparable with the section
of the chip taken in grinding.

Quality of Finish and Size of Grit. — The number of the grit
(or the size of the particles to which the abrasive material is
crushed) which should be used depends partly upon the nature
of the material to be ground and partly on output or the finish
required. The tougher the material the coarser the grit which
will be suitable.

The rate of removal of material increases regularly with
the coarseness of the grit, so that generally in manufacturing
coarse grits are desirable.

The quality of surface produced, while it depends upon the
fineness of the grit, depends to a far greater extent on the con-
dition of the wheel and the machine, and for engineering purposes
an entirely satisfactory finish can be obtained with wheels of
from 24 to 80 grit, the finer grits being used on the smaller work.

In ground machine parts two qualities are looked for —
accuracy of surface and smoothness of finish. If the surface
be examined closely it will be seen to be covered with a
multitude of small scratches, which are the marks of the cuts
made by the particles of abrasive in the wheel. If these marks
are uniform, clear and sharp as if made by a keen cutting point,
it implies that the force of the cut has been small, and hence pro-
bably the work is round and otherwise true, and accordingly this
finish is to be regarded as that of a good ground surface. This
class of finish can be obtained from wheels of the above-
mentioned grits by carefully truing the wheel. If the marks
are too deep or conspicuous for the purpose in view, the next
finer grit should be selected ; with 60 to 80 grit, however, the
surface obtainable is good enough for workshop gauges. By
slightly polishing the wheel after truing it a smoother surface
can be produced — a small piece of hard carborundum oilstone
is convenient for the purpose ; it mnst be used very lightly,

44 GEINDING MACHINEKY

or the polishing will be overdone. One half-thousandth of an
inch is the most which should be left on the diameter of the
work before smoothing the wheel for this finish.

If smoothness of surface as well as precision is necessary—
as in fine gauges and important bearings — the work may be
touched-up with some very smooth emery cloth, or, what is
much better, lapped a little as described in Chapter XII.

Possibility of Grit being embedded in the Work.— It is occa-
sionally stated that emery (and I suppose other abrasives) are
retained in the surface of ground shafts, and destroy the
bearings in which they run. This objection is the same as
that which used to be raised to cut gear teeth — it often
means that the objector has not got a grinding machine, just
as it used to mean that he had not a gear cutter.

A piece of abrasive is cemented into a wheel, and cuts a
piece of steel with its projecting point ; the point wears a
little, and then the cut is wider. The force of the cut thereby
is increased, and tilts the piece of abrasive from its setting,
and it falls away. The particle of abrasive cannot get em-
bedded in the steel unless it is forced in. The easiest way
to do this is to roll it in ; if the wheel itself were used to do
this the force necessary would destroy the wheel face first,
as the bond is only sufficient to withstand the force due to a
very fine cut. As there is no other way of embedding the
particle, it may therefore be concluded that abrasive material
cannot be retained in the ground surface. It is not too easy
to roll the very fine abrasive into the soft steel of ' diamond
laps/ using hard steel plates for the purpose. I have examined
ground parts for embedded abrasive, using a microscope, but
have never found any, and chemical analysis has been applied
with the same result.

The only case which seems possible is with such cast iron
as contains open pores in which fine abrasive dust might
lodge ; the best safeguard against the possibility is to grind
with plenty of water, and to rinse the work in clean solution
afterwards before it dries. The finer particles remain sus-
pended for a considerable time in a fluid, and so would not
have settled to the surface.

THE WHEEL AND THE WOEK 45

Turning now to the nature of the bond, three choices are
open : the vitrified, the silicate, and the elastic.

Uses of the Various Bonds. — For general purposes the
vitrified bond is the most serviceable : it is strong though
brittle, and very little of it is necessary to hold the particles
together, so that the wheels are porous and open-grained,
allowing plenty of room for the chips and solution, and so
cutting freely.

The bond in silicate wheels is weaker, so that more of it
is necessary to hold the abrasive particles together with the
same strength ; this makes the harder wheels too compact
to cut freely in machine grinding, but the soft wheels are very
satisfactory, and they have the advantage that the desired
grade can be secured more exactly in their manufacture than
in the case of the vitrified wheels.

They are therefore to be considered for cup wheels and
for the small wheels for internal grinding. The manufacture
of the latter by the vitrified process appears to present some
difficulty, as small wheels made out of fragments of larger
vitrified ones always seem to work better, although nominally
of the same grit and grade.

Another advantage attaches to the silicate process — namely,
that wheels can be produced by it in a short time, while vitrified
wheels of usual size require two or more weeks in the making
alone.

When a wheel is likely to be called upon to encounter
unusual forces in its use, as when a disc wheel is used upon
its side near the edge, or when a thin wheel is necessary,
elastic wheels should be used, as they are much safer
under such circumstances, owing to their greater strength.
Their elasticity also makes them useful in grinding very thin
work.

Grade. — Whatever bond is used the grade of the wheel
depends on the amount of the bond used, but the working
of wheels of the different abrasives, or of the same abrasive
of different purities (corundum and emery), varies, although
the kind and amount of bond is the same in each. In use the

46 GEINDING MACHINERY

projecting points of the particles in the wheel gradually become
dull — the forces on them then increase ; the amount of bonding
material used must be such as to hold the particles in the
wheel until they are worn a suitable amount, and not to be
capable of retaining them there much longer.

The desirable amount of bond varies with the material
on which the wheel is to be used, and how it is to be used.
With hard materials the particles should only lose their edge
slightly before they are released from the wheel, but with
softer materials they should be retained longer, partly for
economy, and partly because the very sharp particles cut the
work very easily and produce a rather scratchy surface. Thus
wheels with little bond, and which are therefore ' soft,' are
to be used on hard materials, and the harder wheels on the
softer materials. Wheels are therefore classed according to
their softness or hardness, and separated into ' grades,' usually
distinguished by letters of the alphabet.

The grade of a wheel may be judged by the force required
to dislodge the particles of its substance, using the end of a
file ; with a little experience the grade of a wheel can readily
be ascertained in this way. The behaviour of a wheel in use,
however, somewhat depends on the purity of the abrasive,
so that this method cannot be entirely relied upon in selecting
a wheel for a particular purpose, although it depends upon the
force required to disintegrate the wheel — which is the meaning
of grade.

Unfortunately different wheel-making firms express the
same grade by different letters, and even in opposed sequence.
Probably the ' Norton ' system of grading is most used. It
is used throughout in the text of this book, and it is to be
hoped that it will be soon recognised as the standard, and
accepted by wheel makers generally.

In this method of grading the early letters of the alphabet
represent the softest wheels of the Vitrified and Silicate grits,
and the later letters are used successively as the hardness
increases. For Elastic wheels numbers are used, the number
increasing with the hardness. This is shown in the following
table—

THE WHEEL AND THE WOEK 47

WHEEL GRADES — NORTON SYSTEM

HARDNESS. j VERY SOFT | SOFT | MEDIUM

| HAUD

Vitrified and Silicate
Wheels

EFGHIJKLMN

0 P Q

Elastic Wheels .

I 1 I* 2 2* 3 3J

4 5

Suitable for ,-

Pace Work. Hardened Mild Steel.
Steel. Cast Iron.

A comparative table (No. V) of the grading by several
firms is given on page 427, to meet the difficulty of the present
disorder. It is particularly misleading that the Carborundum
Company use the early letters of the alphabet for the harder
wheels, reversing the usual system.

The British Abrasive Wheel Company's grading is identical
with that of the Norton Company. Many firms prefer to
make wheels of their own special bonds and grades to suit the
particular requirements of each case, no particular grade being
stated, but a reference being kept for future use. Some engineers
used to make threads of peculiar pitch and shape long after
the Whitworth standard was accepted, the taps being preserved.

Selection of the Grade. — For external work on wrought
iron and mild steel (0-15 to 0-40 % carbon) grades L and M
are most suitable, M generally, and L for large diameters of
work and rigid machines ; as the hardness of the steel is
increased L becomes generally the correct grade. On
hardened steel K is to be used generally, but where accuracy
and very high finish is required a J wheel of a finer grit is
better. For cutter sharpening J and K grades work well on
carbon steels, but even softer can be used on high-speed
tools. For brass and bronze L is usually right. For cast
iron of customary hardness L and M grades are best, but
for chilled cast iron the much softer wheels H or I. For
internal grinding wheels of slightly softer grades are desirable,
as the contact of the wheel and work extends over a longer arc.

For cup wheel grinding, where the contact is over a con-
siderable area, still softer wheels have to be used, G and H
being usual grades, and at the same time a coarse grit is used.
For work on the same material, however, wheels of two or three
grades are necessary, as the area of contact here depends

48 GEINDING MACHINEEY

on the width of the work, and the greater this is, the softer
the wheel which must be used. The grade of the wheel in
cup wheel grinding must be carefully chosen, as if the wheel
be only just too soft it wears away rapidly, while if it be too
hard it refuses to cut.

The increase of the power and rigidity of machines has
made the selection of grade of wheel an easier matter than
it used to be, for the permissible range is extended in both
directions. If a wheel giving trouble on a light machine
by being on the point of glazing be transferred to a more
rigid and .powerful machine, the cut can be made heavier,
which will stop the glazing tendency ; but on the other hand
a soft wheel which works satisfactorily on a rigid machine,
may, if transferred to the same work on a light machine, have
its surface disintegrated by the vibration.

Selection of the Wheel.— Table VII, page 430, shows the
various grits and grades of wheel suitable for work on a number
of materials. In selecting from it the influence of the machine
and quality of work required should be borne in mind. Usually
as soft a wheel as is consistent with the requisite finish should
be used, for with a given power the output is then greatest.

Wheel Speeds. — The speed at which the wheel should be
run is the highest consistent with a proper factor of safety :
and this leads to the rule that they should run at a certain
circumferential velocity, which varies according to the strength
of the wheel material, so that it is higher for hard wheels than
for soft, and for elastic than vitrified or silicate bonds. Elastic
and vitrified wheels of L and M grit can be run safely up to 7000
feet per minute, though a rather slower speed is usual ; K
wheels up to 6000 and J up to 5000 feet per minute. Soft
silicate wheels, G and H grade, can be run at 4000 feet per
minute. Some silicate wheels have a brass wire mesh inserted
in them in the process of manufacture with a view to safety,
but I cannot speak from experience with regard to them.

It should not be forgotten that the wheel should be examined
and tested, by tapping it with a hammer, for cracks before
mounting it, and that the spindle should be started slowly and

THE WHEEL AND THE WOKK 49

the wheel watched, as occasionally, though very seldom, they
run dangerously out of truth.

When a wheel glazes, it is frequently recommended that
its circumferential speed be lowered ; this tends to check the
glazing, but it can be checked in other ways, and then if
these are insufficient the wheel can be changed.

In turning the speed of cutting is limited by the heat pro-
duced, which draws the temper of the tool and spoils it. In
grinding there is no such limit, as the cutting particles can
withstand the temperatures produced, although it may fuse
the metal being ground. As the wheel diameter lessens by
wear the surface speed unavoidably drops, until it is possible
to use the next faster spindle speed ; but otherwise it should
not be reduced except in the case of trouble from vibration.

In circular grinding, external or internal, the work and
wheel should run to meet one another, otherwise the wheel
may drive the work at intervals, producing a bad surface.

Work Speeds. — The question as to what is the best speed
for the work in circular grinding is one upon which there are
many and conflicting opinions. It appears to be invariably
accepted that the work surface speed is the controlling feature,
and that if, for a particular material, a satisfactory surface speed
is found for any diameter of the work, then that surface speed
will be correct for all diameters — provided that no trouble
arises from the slenderness of a particular piece of work, or such
causes. This corresponds to lathe work, where the surface
speed at which a particular tool will cut continuously for a
reasonable time, is a mark of the quality of the tool. Some
little time ago Messrs. Brown & Sharpe stated that a some-
what slower surface speed should be used on large diameters
than on small, but in their latest notes they return to the
previous point of view, and advocate the same surface speed,
whatever the diameter be.

Formerly it was the practice to run work at surface speeds
from 150 feet per minute upwards to twice that amount or
more. To-day the 'speeds used are much lower, but are very
varied, some authorities advocating speeds from 10 to 20
and others from 60 to 70 feet per minute. The intermediate

50 GEINDING MACHINEKY

portion of that extreme range is that which is most usually
used.

The following firms, who manufacture and use grinding
machines, recommend the work surface speeds given —

ATTTTTORTTY WORK SURFACE SPEED

IN FEET PER MINUTE.

Brown & Sharpe 35-65

The Churchill Tool Co., Ltd. 35-70

Greenwood & Batley 25

Alfred Herbert, Ltd. (Mr. Darbyshire) 25

The Landis Tool Co. 25

This idea of a constant work surface speed (i.e. independent
of the work diameter) I consider, for reasons which I give
later, to be incorrect. For moderate diameters (say 2 inches
to 4 inches) I think that speeds of 30 feet per minute with
24 to 36 grit wheels, and 40 feet per minute with the finer
grits, are suitable for mild steel ; for cast iron 40 and 50 feet
per minute respectively in the same cases ; but my views are
given fully later.

Table IX, page 432, gives the number of revolutions
per minute at which work of various diameters is to be run
in order that the work may have a selected surface speed.

The first part of the grinding operation is to remove the
metal left on in turning for the purpose primarily of ensuring
the work being properly ground, and the second part consists
in securing an accurate and well-finished surface. With
regard to the removal of stock, it is not to be immediately
concluded — though it has not unfrequently been regarded as
self-evident — that the higher the work speed the more rapid
the grinding ; later considerations will show that the reverse
is more nearly the case, and it will be noticed that the firms
making the heavier machines recommend the lower work

Finishing Speeds. — When the work has been rough ground
to within a thousandth of an inch or so on the diameter, it
becomes a question of finishing, and whether the work speed
should be changed, and, if so, whether it should be increased

THE WHEEL AND THE WOKK 51

or diminished. On this point again there are diametrically
opposite opinions.

Where the quantities are small it is not usual to change the
work speed, unless the machine in use is provided with a
quick-change device so that no time is lost, for the work can
quite well be rough ground and finished at the same speed.
Where the quantities are large (25 or more, but it depends
upon the size and the allowances) it is advisable to put the
work through the machine twice, and in this case a different
work speed should be selected for finishing.

With the very fine cut of finishing grinding, it is evident
that the quality of surface primarily depends upon the number
of the cutting points of the wheel which have gone over any
portion of the work surface. Hence the time taken simply
depends upon how long it takes a certain amount of wheel
surface to pass the work ; that is, the time taken does not
depend at all on the surface velocity of the work, but only
on that of the wheel. At these small finishing cuts no difficulty
occurs in either increasing or diminishing the work speed as
regards the behaviour of the wheel ; increasing the work
velocity, however, distributes any errors better, and should the
wheel be worn to a (very slight) curve it lessens the faint
spiral mark which is seen (Fig. 27), and considerably reduces
the effect. With the higher finishing speed, moreover, a surface
of sufficiently good quality may be produced in less time. The
sole objection to the higher speeds for finishing appears
to be that they are more likely to cause vibration troubles ;
but with the slight cuts used these very seldom occur if they
are absent in the rough grinding.

Where then a different work speed can be used for finishing
it should be higher than for the roughing out ; from 25 to
75 per cent, increase is reasonable, but I believe that still more
may frequently be used with advantage and without introducing
troubles from vibration. With this view I believe that most
authorities agree, but I would mention that others (Mr. Darby-
shire, of Messrs. Alfred Herbert's, and Mr. Edge, of the British
Abrasive Wheel Co., among them) advise a 25 per cent,
reduction of the work speed for finishing.

52 GKINDING MACHINERY

Difficulties and Change of Speed. — After starting the work,
trouble may occur in the grinding, which necessitates a change
of work speed. If the wheel glazes, increasing the speed of
the work may prevent it ; and, on the other hand, if the wheel
wears away too rapidly, the work speed should be reduced.
Vibration may occur between the work and the wheel, causing
chatter marks (see page 104) ; the work speed should then be
changed. If it is due to a synchronous effect a slight altera-
tion, either increase or decrease, of the speed may stop it.
Generally a decrease is advisable. The vibration is usually
originated by a want of truth or balance in the wheel, which
should be trued with a diamond before restarting the work.

As the time taken in the actual grinding of a part
consists of two parts — that of removing the allowance left
on the work for grinding, and that of finishing to the requisite
degree of accuracy and quality of surface — a machine may fail
in efficiency in either of these two divisions of the work. To
turn out work quickly, it must be convenient to manipulate ;
to finish accurately and well, the machine must be sufficiently
rigid and accurate and in good condition ; while for removing
the stock left on from the turning rapidly it must have a
sufficiency of power and weight, with rigidity enough to corre-
spond to the forces involved.

The rate of removal of the stock also depends very largely
on the wheel and on the speeds and feeds used. They should
be selected so as — if possible on the particular piece of work —
to use the machine to its full power capacity.

Theory of Grinding. — I have mentioned that I do not
consider the work surface speed in cylindrical grinding to be
independent of the work diameter. The theory which I
advance (Brit. Ass. Report, 1914) is that the controlling factor

is vz j_ t, where v is the surface velocity of the work,

D and d the diameters of the wheel and work respectively,
and t the diametrical reduction of the cut. For internal work
the wheel diameter is to be considered to be negative. If the

quantity v2 —. — t exceeds a certain amount, the wheel dis-

THE WHEEL AND THE WOEK 53

integrates too rapidly, failing to size the work properly, and
wasting away ; if on the other hand it is less than another
certain quantity, the wheel surface glazes, and it fails to cut.
The range between these quantities is that in which grinding
can proceed satisfactorily.

Number of Cutting Points on a Wheel.— To arrive at this
result it is necessary to consider the action of the wheel on
the work closely. The wheel surface consists of a large number
of cutting points, which take chips of very small section at a
very high speed. Behind these points lie other arrays gradually
taking up the action as the former are broken off or get worn
down and finally dislodged from the wheel. As an increase
in the depth of the cut brings more points into play, and as
truing the wheel increases the number it previously had, the
number of points ' on ' the surface of a wheel is a rather
indefinite number. Taking a 60-grit wheel I estimate the
number of cutting points at about 1500 per square inch. This
estimate may be objected to, the more especially as the Norton
Company estimate the number at 3300 points for a wheel of
this grit. If the particles which have passed through a square
mesh the spacing of the wires in which is ^j inch, but had failed
to pass one of ^V inch spacing, were neatly and compactly
arranged side by side, the number of points would be not so very
much more than the latter estimate ; but an examination of
a wheel shows that the particles are attached together in a
very open architectural style (see Fig. 8), giving plenty of free
space. Also in use a particle gets dislodged from the wheel
before it is much worn, and this leaves an empty space. By
glazing a wheel slightly the points on or near the surface can
be counted ; or they can be counted from a record of the surface
such as is shown in Fig. 13, A and B.

The depth of the cut which a point takes is very small,
much smaller than the one or two thousandths of an inch
which is usually regarded as the thickness of the chip taken.

The number of points depends on the size of the grit, being
inversely proportional to the square of the average linear
dimension. Hence the number of points per square inch
varies as the square of the number of the grit ; e.g., if

GRINDING MAOHINEBY

FIG. 13. — CUTTING POINTS ON WHEEL FACE

THE WHEEL AND THE WOKK 55

there are 1600 with 60 grit there are 1600 X (|£)2 or 256
with 24 grit.

If the wheel be trued, the projecting points are turned off
the particles, the diamond being so hard that it cuts the
corundum or other fragments right across ; this brings more
points up to the wheel surface, so that there are more active
points on a wheel when it has just been trued than there are
after it has been in use. Also the width of the trued points
is. much larger, and there is no clearance behind the edge.
When a wheel glazes the same occurs, and the glazed points are
smoother. In Fig. 13 at A is shown the particles on the wheel
face of a 46-grit wheel after it has been trued with a diamond,
and the result of use of the wheel on the number of effective
particles is shown by the corresponding view at B. At A
there are not only very many more particles effective, but
the areas presented by the various particles are greater as the
projecting edges are trued off. This is »well seen at C, which
gives a view of the trued surface magnified fifty diameters,
and the fiat, trued-off facets are of definite area. The joining
of the particles is the bond, which is also trued off flat. At D
is shown a used wheel surface magnified also fifty diameters.
The grit in all these cases is 46 alundum. At E is shown
a carborundum wheel surface, 36 grit, turned with a diamond
and magnified to the same extent. The diamond cuts the
abrasive grit across, splintering it slightly with the alundum,
but considerably in the case of the carborundum. In A and
B the grit particles are black for sake of clearness ; in C,
D, E they show as white, and the recesses of the wheel face
as black.

The Chips in Grinding. — The chips produced by a cup
wheel, with plenty of water, can easily be seen and handled ;
though of very small cross section they may be some inches
long, and in heavy work collect in the separating channels
of the machine as a kind of steel wool. Such chips are shown
in Fig. 14 ; they resemble turnings closely. The chips pro-
duced by a disc wheel in circular work are very short, but
are thicker than those from a cup wheel. If the work is
done dry the chips are ignited by the heat, and are mostly

GKINDING MACHINERY

consumed as sparks. With a good flow of water, however,
they can be collected, though some will be found melted into

FIG. 14. — GRINDING CHIPS, CUP WHEEL. 50 DIAMETERS.

FIG. 15. — GRINDING CHIPS, Disc WHEEL. 50 DIAMETERS.

round globules. In Fig. 15, which is a photograph of the
chips from a plain grinder, the swarf, fused globules, and some

THE WHEEL AND THE WOEK

broken abrasive can be seen. The magnification is 50
diameters. These chips present just the appearance of the
larger chips taken by a lathe tool, but it is curious that the
grinder chips from hardened steel resemble those from a
tough mild steel instead of from a hard and brittle material ;
probably this is accounted for by the high temperature
produced at the cutting point.

Normal Velocity of the Material. — Now consider a small
area on any wheel face at which grinding is taking place.

FIG. 16. — VELOCITIES OF WHEEL AND MATERIAL

This is shown at ABCD in Fig. 16, and may be regarded as a
space across which a large number of cutting points travel
with a high velocity V in the direction shown. The material
of the work here fits the space ABCD and has a velocity there,
which we will suppose to be of the amount v, and in the direc-
tion shown. Suppose this velocity split into three velocities, v±
normal to the area ABCD, v2 parallel to it and to V, and va
parallel to the area and perpendicular to V. Now if v2 alone
existed, the work would just move along the surface of the
wheel without getting ground away ; and the same if v3 alone
existed. All that v2 would do would be to make the particles
of the wheel appear, as viewed from the work, to move faster

58" GKINDING MACHINEEY

(or slower) than V by the amount vz. As shown, it would be
faster, as v2 and V are opposed in direction. Similarly all that
vs would do would be slightly to increase the apparent amount
of V to v/(V + v2)z + v32, and to alter (slightly) by angle

tan"1^-^ — - its direction as viewed from the work. This leaves

v1 alone as the effective velocity, and upon this normal velocity
of the material of the work into the wheel face the grinding
action must depend. If a steel rod were placed with its end on
the surface of a wheel, and with its length perpendicular to the
wheel face, and then pushed lengthways slowly into the wheel,
it would be ground away and have normal velocity only.

As the particles of the wheel passed the grinding space they
would be taking cuts, and the depth of these cuts would depend
upon the rate vl and on the time since a cutting point passed
nearly enough along the same path. This time — very small —
would be equal to the average distance between the following
cutting points divided by V, their velocity. The depth of the

cut would therefore be equal to ^. p, where p is this average

distance, which is evidently proportional to the size of the grit
of the wheel.

Now the force exerted by and on the cutting point depends
upon the section of the chip, and therefore — in a certain wheel
run at a definite surface velocity (V) — it depends upon v^
When this force reaches a certain amount it is sufficient to
break or dislodge the particle, and hence the disintegration
of the wheel face depends upon the normal velocity v± of the
material. Hence v^ must not exceed a certain amount.

If v^ were very small the points of the particles would become
worn down by the rubbing action before there was enough
metal projecting over them to enable them to cut. Thus to
have v1 very low tends to make the wheel glaze. These two
quantities — the force on the cutting points and the amount of
rubbing — control the breaking up and glazing of the wheel face,
and they depend on vl9 the normal velocity of the material.

If we alter V we shall somewhat alter the force necessary
to take the same cut ; experiments on the variation of cutting

THE WHEEL AND THE WOEK 59

force with speed in lathes show that it rises with the speed, but
only slightly. It is therefore best to make V as high as is
reasonably safe, as the output is thereby increased, since vlt and
therefore v, is in proportion to V.

Disc Wheel Grinding. — To illustrate more fully what is proved
here and just how the chip is formed, suppose that A, B, C
(Fig. 17) are three points on the circular surface of a disc wheel,
and that they follow one another along the path CBA. This
path is really curved, but it is supposed to be magnified so
highly that the small piece of it at which we are looking is
practically straight. AD, BE are two particles following the
same track with velocity V. Now let the work in contact
with the wheel face along A, B, C be fed into it with the velocity

FIG. 17. — FEED AS IN Disc WHEEL

and in the direction v, which is inclined at an angle 6 to V,
and we will suppose this angle 0 small as sketched, and the re-
solved part of v perpendicular to the wheel face, only 1 per
cent, or less of V. Directly A passes the point at which it
is sketched, and moves off, the point A of the work moves along
AF, and meets the cutting particle EB which has come up
to the position E'B' at F. If this takes the small time t,
then BB' = Vi, AF = vt, AG = v2t, and GF = vj, where v±
and v2 are the components of v along and parallel to V, since
AFG can be taken to be the triangle of velocities. Since
GB' must be a small quantity compared with AB, we can con-
sider that AB = AG + BB' = v2t + V*, and .-. * = TrA,B

V -f- v2'

Hence the thickness of the chip which the tooth E'B' is taking

(which is FG) = v, .— — —

V + v2

That is, the thickness of the chip depends on vlt since AB

GRINDING MACHINERY

evidently depends on the size of the grit only, and vz is only
a small fraction of V ; that is, the thickness depends on the
normal velocity of the material into the wheel face. This
confirms the previous proof.

Face Wheel Grinding.— As another illustration, consider
work fed into the face of a cup wheel ; we shall again find that
the size of the chip depends on the normal velocity of the work.
This is shown in Fig. 18. Here ABC is again the wheel face,
and the work is feeding into it with velocity v in the direc-
tion shown, but the cutting points are moving upwards from
the plane of the paper with velocity V. The work which passes
the point A of the particle AD feeds along AF until it comes

UPWARDS

FIG. 18.— FEED AS IN FACE WHEEL

to the particle BE which cuts it and passes on upwards. The
work continues to feed on until the next particle comes up along
the path of BE, and in that time feeds into its path a distance
FF', which is vt, where t is the time taken for the second
particle at BE to follow the first. If px be the pitch of the
particles this way, then ^ = Vt. The area of the chip, shown

shaded, is then FF' x FG. We have FF' = vt = v^. Also

FG = AF X -, since AFG is the triangle of velocity for v and its

components along the wheel face ABC and perpendicular to it.
Hence if AF = p2, the pitch of the particles the other way, we
have for the area of the chip the value

The expression p^z evidently depends on the grit in the wheel

THE WHEEL AND THE WOKK

only, and therefore again the chip section depends on vlt the
component of the work's velocity normal to the wheel face.

The cutting particles are distributed very irregularly in the
wheel face, and some take deeper chips than others, but the
above shows what happens in a case we may regard as typical
of the average, although the action of the points of particles
below ABC is not considered. In both of these cases the
size of the chip depends on the normal velocity Vi of the

FIG. 19. — CONTACT IN EXTERNAL WORK

work to the wheel face, and therefore the force on the cutting
particle and the disintegration of the wheel face depend upon it.

Theory of Disc Wheel Grinding. The Arc of Contact—

Keturning to the case of a disc wheel used to grind circular
work, consider what happens where the wheel touches the
work. The contact is an area or surface, with a breadth
equal to that of the wheel and a certain length, small it is
true, but still to be considered. It is sometimes referred
to for convenience as a line, but if it were merely a line
no metal could be removed in the grinding process. Every-
where along the arc of contact except on the line joining the

GEINDING MACHINERY

centres of work and wheel, the work has a normal velocity to
the wheel face. In Figs. 19 and 20 is shown the nature of the
contact, Fig. 19 showing it for external and Fig. 20 for internal
grinding. The corresponding parts are indicated by the same
letters, so that one description applies to the two cases. The
wheel ABCD, whose centre is at E, grinds the work FBCG,whose
centre is at H, and the broken line CKL shows the work surface
as it would have been if the wheel had not ground it, so that BK

Fia. 20. — CONTACT IN INTERNAL WORK

is the depth of cut. The directions of rotation of the wheel and
work are shown by the arrows, and the depth of cut is particu-
larly exaggerated for the purpose of making matters clear.
The arc of contact is BC, and the area of contact has a length
BC with a width equal to the acting width of the wheel.

The wheel and work surfaces run to meet one another, and
owing to the closeness with which the particles of abrasive
follow one another owing to the high speed, the part FBKL
of the work above the line of centres EKBH is ground almost
entirely away, and contact only takes place below, along

THE WHEEL AND THE WOKK 63

BC. Since the work rotates in the direction of the arrow the
cut begins just above the point B, so that the length of cut
can be taken as BC, though it is a little more, and the length of
the chip is rather shorter, as it is compressed while being made.
To obtain the length of BC, let D = 2R be the diameter
of the wheel, d = 2r that of the work, and t the amount
being ground off the diameter of the work, so that BK = |£.
Then calling the angle HCM, where M is on the prolongation
of EC, a, we have by the trigonometry of the triangle HCE —

HE2 = HC2 + CE2 ± 2HC . CE cos a
where the minus sign refers to internal grinding, "Fig. 20.
Or (r ± K^p)2 = r2 + E2 ± 2r E cos a

or cos a = 1 -- ==- — . — since — is so small.

rK 2 8

Or expanding cos a, by trigonometry, it being a small angl

••—

Now if angle HEC be ft, we have —
sin y8 sin a
HC = = HE

Sin's

and / . fi = , since both a and 0 are small angles,

and/. arcBC = K3

D.d.t

or -

r ± R 2 (d ± D)

So that the length of BC depends on the diameters of both
wheel and work, upon the depth of the cut, and whether the
grinding is external or internal. To illustrate the actual
lengths involved, a few cases are given in the following table

GKINDING MACHINERY

for different diameters of wheel and work. The depth of the
cut has been taken as TWO" mcn °n the work diameter.

LENGTH OF ABC OF CONTACT FOB

INCH ASIDE CUT

EXTERNAL.

INTERNAL.

Diameter of
wheel

14 in.

18 in.

1 in.

3 in.

Diameter of
work

lin.

6 in.

2 in.

12 in.

Hin.

2 in.

3£ in.

5 in.

Length of
contact .

0-0306

0-065

0*0425

0-085

0-095

0-045

0-145

0-087

FIG. 21. — CONTACT IN FACE WORK

The arc of contact is thus longer than it is usually assumed
to be, and is much longer in internal than in external grinding.
If the depth of the cut in the internal cases be reduced to
^oVo mcn on the diameter (that is, to a quarter of the previous
amount), the length of the arc of contact is halved, so that
they are 0-0475, 0-0225, 0-0725, and 0-0435 respectively, or
about the same average as the external examples given.

As a contrast, the case of the face wheel is shown in Fig. 21,
which is a plan view supposing the wheel spindle to be vertical.
The wheel ABCD shows in section as a ring, and the grinding
takes place mainly over the area marked with broken circular
marks at AB, though a little is done on the opposite side of

THE WHEEL AND THE WOKK

the wheel. The length of the cut AB is now considerable,
being rather longer than the width of the work. To secure
flat work the work must not be much larger than the diameter
of the inside of the cup wheel, the limit being the diameter of
the highest circle of cutting points when the wheel has worn a
little. The cutting points are indicated in the figure by the
broken arcs, and the work is shown travelling under the wheel

FIG. 22. — FORMATION OP CHIP BY Disc WHEEL

in the direction of the arrow. The marks of the grinding on
the work are also indicated.

The chips produced in the two cases are shown in Figs. 14
and 15 respectively.

Normal Velocity of Material. — Now consider how the
chip is formed. In Fig. 22 is shown a figure like Fig. 19, but
to it are added lines showing the formation of the chip. The
cutting point X has just moved over the arc BC, and the point
Y is following it. Immediately X has passed any point P on
the arc BC, the material at P begins to move along the arc

66 GKINDING MACHINEEY

PQ of a circle with centre H ; and if t be the time after which
Y follows X, then PQ will be 27rntHP, where n is the r.p.m.
of the work. Thus B will get to S, where BS = 27rntHB, and
C to R, where CK = 27rntHC in the shorfc time t. The cutting
particle Y will meet the metal very nearly at SQK, and its
extreme point will move along BPC, so that the shape of the
chip will be of the curved triangular shape shown shaded.
The particle Y never touches S, and T is the nearest point
it gets to it. The distance of T from BS, however, is so small
as to be practically immeasurable.

Now if v be the velocity of the surface of the work, CR = vt,
and if RU be drawn perpendicular to PC, then UR = v-J, where
v1 is the component of the work velocity at the point C, which
is normal to the face CP of the wheel there ; v is along the
arc CK, and v^ along the line MCE, hence v-L== v sin HCM =
v sin a = va — -J Va? = va (very nearly).*

* The values of the expressions for s and v± can easily be proved geo-
metrically, a method which appeals more to engineers than the algebraic
one given in the text. In Fig. 19 draw CX perpendicular to HE, and let
Y and Z be the ends of the diameter BEY, KHZ. In any circle the product
of the segments of intersecting chords are equal (see Euclid III. 35), so
that —

XC2

XBXY

and

-+-}

XY^XZ/

But where, as in our case, BK is only a few thousandths of an inch and
XY and XZ several inches, we may take XY as equal to BY or D and XZ
as d ; and in the same way BC and XC are exceedingly nearly equal, so
that we can consider that XC is equal to BC or s, and hence--

dOt

= 2(J+DJ

Now draw HM perpendicular to CM ; then the sides of the triangle
OHM are perpendicular to the directions of v and its components vx and v2,
and therefore —

vt HC
v ~HM

THE WHEEL AND THE WOEK 67

).2* .' (1)

The thickness of the chip depends on vlt but as the cutting
particle takes a chip the width of which increases with the
breadth — and in proportion to it — unless the cutting point
has been turned by a diamond tool so as to cut at once over
a comparatively considerable breadth, the area of the chip
will depend on v^2 ; and as the force tending to dislodge the
particle varies nearly as the area of the chip, therefore- it varies
as Vj2, or, since we can drop the constant 2, as —

The Controlling Factor. — Also, if s = BC, we have—
/~rE 7_^i Kr

:v jr+rr =?*r+R

so that ^ is proportional to s, and hence the v^ at any inter-
mediate point P is proportional to 5, the arc up to P measured
from B. Hence the total disintegrating action must be
dependent on the maximal normal velocity at C, so that in
reckoning up all the action along the arc the total effect

depends on vz . ^ . t.

The first part of the action from B towards P has no tendency
to disintegrate the wheel; it tends to glaze it, as the normal
velocity is so small, and is zero at B. The action in this early
part of the arc is the same as in finishing with a small cut BZ.
When the particles of a wheel are glazed a little they tend to
push the work away during the early part of the arc BC, and so
increase the rubbing and glazing further unless it be checked.

It can be checked by increasing v2 . _ . t — that is, by
But HM . EC = 2 x area of triangle HCE = XC X HE

2s(d+T>)

s(r + K - ¥) d + D

HM = - = s . (very nearly)

and .*.

v dD

/ dDt 4(d+D)2_ /d+D

V 2(dTr» ' d*D* = VV ~dD~ '

68 GKINDING MACHINEKY

increasing either v or t, but it is to be noticed that increasing v
is far more effective than increasing t : for example, if v be
increased 30 per cent, the effect is increased 69 per cent., and
it would require that increase of t to produce the same effect.

Conversely to check wasting of the wheel vz . ^ . t must be

i d\j

lessened, and it is more effective to reduce v than t. There will
be in different cases a more or less wide range over which the
quantity may vary, and yet the wheel work reasonably ; it is
best that its value should not be near either the glazing or wast-
ing points, else a little difference anywhere may cause trouble.

Since vz . ~T . t contains both v and t it can be varied

by changing either quantity ; hence we see that the actual work
surface speed is not definitely controlled by this quantity, and
therefore may vary over a considerable range.

Maximum Output. — Now the two quantities v and t can
be arranged, while keeping this factor constant, to meet some
other condition. As \vt is the rate of removing material,
and since this is ultimately limited by the power which can be
taken by the machine for unit width of wheel face we have

vt = c . . . ;' . (2)

as the condition for reaching the greatest output. Hence
the most rapid output would be obtained by decreasing v and

increasing t, in such a way as to keep v2 . — TFT~ • t constant.

Pushed to its limit with a machine having indefinitely great
power, this would indicate that the most rapid method of grind-
ing is to remove the material at a single traverse, using a slow
surface speed and a heavy cut. Besides other difficulties,
however, this would be directly opposed to that fundamental
principle of grinding which secures accuracy, although the work
may change its shape slightly (see page 93), by taking a number
of finer cuts. It is in any actual machine definitely limited
by the fact that vt is (nearly) proportional to the power supplied
to the machine per unit width of wheel face, and this is the
deciding factor, so that the limit is expressed by equation (2)
above.

THE WHEEL AND THE WOKK 69

We then have for a given machine and width of wheel face
vt = c, a constant, and for a particular kind of wheel and

material v2 . - — — . t must lie between two limits which we will
dD

call at and a2 ; then by dividing we see that v . ~^— must I*6

between — and — , which gives the limits for the efficient surface
c c

velocity. If we find some value b between a± and a2 as actually
the best, then we shall have —

as the best surface velocity.

We notice that it depends immediately upon the power
factor c, and the higher this is the lower the values of the best
surface velocity. The tendency to reduce work speeds of
recent years is thus shown to be (in part) a direct consequence
of the greater power factor of the machines.

Magnitude of the Quantities involved. — It will also be
noticed that the best value of v depends upon the diameters
of both work and wheel, but before considering this more
closely let us consider the magnitudes of the various quantities
involved in the action. These can easily be estimated in a
particular case. As an example, suppose that the wheel be
14 inches diameter by 1 inch face, of 36 grit, and be running
at 5000 feet per minute circumferential speed ; and the work
be 2 inches diameter running at 30 feet per minute surface
speed, with a depth of cut of -nyoo inch on the diameter.
The rate of removal of material = J vt

= 0*18 cubic inches per minute.

The length of the arc of contact = '

= 0-0296 inch

(rather less than -^ inch).
The maximum normal velocity of the material v±

= 12* 3 inches pef minute.

70 GKINDING MACHINEKY

The number of cutting points per square inch we will take
as 600, though it is not a very definite number. The shape of
the chip will be a wedge on a base which we may take to be
roughly rectangular with an average width of n times its depth.
Its length will be 0-0296 inch, or -g^ inch. If its depth be x
and width nx the average volume will be J . x . nx . ^ = ^ nx2.
There will be 600 X 5000 X 12 chips taken, and their volume
will amount to rfg. nx2 . 600 . 5000 . 12 cubic inches, which must be

the same as 0-18 cubic inch. So that nx2 = ^— — — — r-r —

c>Uu X oUuu X J. £

0-0000003^ cubic inch. If we take n = 3, then x = 0-00033 and
nx = 0-001, so that the base of the chip would be one-thousandth
of an inch wide and one-third of that amount deep. If n were
larger the chip would be wider and thinner. If we had — still
taking n as 3 — calculated the depth from the maximum normal
velocity, we should have arrived at the same figures. The
average ' pitch ' of the consecutive cutting points on the wheel
face would be about 1 J inches.

The Force at the Grinding Point.— Several machines use a
wheel 14 inches by 2 inches, and they are arranged to take, and
do take, about 5 h.p. Of this a portion is used in driving the
machine parts and absorbed in the belting, the remainder
alone reaching the cutting point. Probably more than 1 h.p.
is absorbed in the belts, friction, &c., but assuming that that
amount only is absorbed, it leaves 2 h.p. per inch of wheel
face at the cutting point, so that (as 99 per cent, of this goes
through the wheel) the force at the edge is 13 lb.

This force is the tangential force ; the normal force tending
to separate wheel and work is very small, but its ratio (about
one-eighth) to the tangential force depends on the condition
of the wheel particles, and is higher if they are glazed.

The area of contact is 0-0296 square inch, and therefore con-
tains usually 18 cutting points, so that the force on each averages
0-72 lb., and the final force on each T45 lb. Experiments on
cutting tools in a lathe show that the force per square inch
of chip section increases as the area of the section diminishes.
Taking some experiments by Prof. E. H. Smith, an average
value of the cutting force on a chip of 0-001 square-inch section

THE WHEEL AND THE WOKK 71

was 290,000 Ib. per square inch, which would give about 0-llb. on
a 0-00000034 square-inch area, while the average rate of increase
of force per square inch of cut as the area of the cut diminished
would increase this to 0-35 Ib. This force would be that on
a properly shaped cutting point presented correctly to the
work ; the shape and presentation of the edges of the abrasive
particles would very considerably increase this value, so that
within the limits of our knowledge the forces on the point
calculated from the opposite points of view agree fairly well.
Nothing is known as to the effect of taking the cut at so high
a rate as 5000 feet per minute, instead of at a hundredth or
even a fiftieth of that amount.

Judging from the stress strain curves, the high speed would
make little difference in the case of hard materials, but might
reduce the work on tough metals, e.g. copper and bronze.

The chips in Figs. 14 and 15 were made with coarser grit
wheels, but bear out the above calculations as to the size of
section. In cutting steel the cutting point has to meet alter-
nate layers of ferrite (soft) and cementite (hard material) in
the pearlite, and these layers are of a thickness about that of
the chip taken in grinding. The distribution of martensite
and austenite is of a similar order of size. The changing
force on the cutting point, exceedingly rapid though the
variation is, may be one reason why the harder carborundum
does not work so well on steel as the softer but tougher
alumina abrasives.

Temperature Rise. — In considering the temperature effects,
it does not matter whether we deal with the chips individually
or in bulk, and taking the latter view as the simpler, if H be
the horse-power expended at the grinding point, m the number
of cubic inches of metal removed per minute, and supposing
that half the heat goes into the chip, then the temperature
rise of the chip in degrees Fahr. is —

H X 33,000

2 J kpm

where fc is the specific heat of the material, p its density, and
J, Joule's mechanical equivalent, which is equal to 778 ft.-lb.,
For steel fc = 0-113 and p = 0-284 Ib. per cubic inch. So that

72 GKINDING MACHINEEY

if H = 2 and m = O18 as in our example, we have for the

temperature rise 2 x 778 x^-nfx °0°284 X 0-18 or 7250° F'
As the metal melts at 3250°, this temperature would fuse it
easily.

Fused and Ribbon Chips. — In dry grinding the metal is
ignited and burns as sparks, but in wet grinding the water
carries away the heat and keeps the temperature down. In
Fig. 15, which represents chips from a heavy plain grinder, it
will be noticed that most of them are fused somewhat, and some
have been melted completely and then chilled by the water
into small globules.

The temperature rise depends directly on the power used,
and inversely as the rate of removing metal, so that it is greatest
with hard wheels. It is higher with fine grit wheels owing
to the extra force per square inch of chip section as the size
of the chip diminishes, and also higher with the harder steels.
By combining these factors ' ribbon ' chips can be produced,
in which the chips are fused together and come from the
machine as a ribbon of steel.

Grinding Hardened Steel. — The heat produced cannot be
lessened by any application of cooling water ; the latter
simply carries away the heat produced, and so reduces the
temperature to which the metal rises at the cutting point.
In grinding hardened steel there is thus considerable risk of
drawing the temper of the metal at the surface if the work
is hurried ; so that just at the surface the steel would be
softened, although remaining hard inside, owing to the mass
of metal absorbing the heat with a less rise of temperature.
Thus the temper could only be drawn for a few thousandths
of an inch deep, but this is sufficient to spoil a hardened surface,
and this must be avoided by taking light cuts, and using
plenty of water applied right at the grinding point when
removing the last few (five is sufficient) thousandths from the
diameter of the work.

The above estimation of the quantities in a particular case
puts us in a position to consider another point with regard to

THE WHEEL AND THE WOKK 73

the derivation of equation (1) — namely, the effect of the length
of the chip ; for if the chip were indefinitely long, as it might be
supposed to be if we took a cup wheel and fed it parallel to its
axis into some stationary work, there would finally be no room
for the swarf, and the wheel would clog. With the dimensions
of the chip found, it is now clear that nothing of this nature will
take place. In modern open texture wheels there is abundant
room for the length of the chips in circular grinding, especially
when it is remembered that their greatest thickness is only
a fraction of a thousandth of an inch. In using cup wheels for
surface grinding, the length of the chip is considerable — some
inches it may be — but if the area of the chip be fine enough
trouble seldom arises.

Effect of Length of Arc of Contact.— A question may also
be asked as to what is the effect of a longer or shorter arc of
contact in these cases, and more particularly in internal grind-
ing, where it is considered to have a very undesirable effect.
The action, however, is similarly distributed in all cases. We
have —

^r— . 2t and s = \/

so that, eliminating t —

Vi_ d+~D

That is to say, the normal material velocity at any point P
(see Fig. 22) of an arc of contact is proportional to the length
BP ; hence whatever the history of a cutting point, whether it
goes a greater number of times over a short arc or a fewer
number over a longer one, it gets just the same amount of
each kind of action. A cutting point as it passes along the arc
BPC encounters the material at grazing incidence at B, and
rubs and glazes : then as the normal velocity increases along
the arc it cuts. As the wheel rotates the particle makes a
succession of cuts, gradually getting blunter until it is finally
fractured or torn out of its bond by the force of the cut. The
particle, however, comes into action before it becomes, as the
wheel wears, one of the prominent surface particles ; near the

74 GKINDING MACHINEKY

centre line HBE it does not cut ; later it begins meeting the
material first at almost grazing incidence. If the arc were
longer, with the same final normal velocity vlf practically the
same would happen, all in proportion ; but the arc being longer,
the particles would require proportionally fewer turns before
they became blunted and dropped out of the wheel.

Area of Contact is proportional to the Power.— Now, taking
the same equations for ^ and s, let us eliminate d instead of t ;
D also goes out, and we have —

/ dl^t /t y*.2t _ vt

V V " P

This shows us that whatever the diameters of work and
wheel, the length s of the arc of contact is proportional to vt,
or to the amount of power supplied per unit width of wheel
face.

Now in our case of a machine with a certain wheel and a
certain amount of power available at the wheel face, vt is con-
stant, and has been taken to be c : so that in all cases derived
from the conditions (1) and (2) the arc of contact has the same
length.

Hence, if we base a series of work speeds for different
diameters upon the formula of equation (3), the arcs of contact
will all be of the same length, and the action at each point of
these arcs will be the same ; while the fact that the power at
the wheel face is the same, tells us that the total force on the
work will be the same in each case.

Alteration of Speeds to check Wear of Wheel and Glazing.—

Before considering the work speeds based upon equation (3) it
will be convenient to consider what is to be done if, after a work
speed v has been selected, trouble occurs.

Suppose that the wheel wears unduly. To prevent this,

the quantity v2 . — tr- . t, or, since jl is a constant, as we

have our work and wheel in the machine, the quantity vH is
to be reduced. At the same time vt is to be kept constant — that
is to say the maximum output is to be still obtained. To do
this we must reduce v and increase t in the same proportion ;

THE WHEEL AND THE WOKK 75

this will keep the output vt as before, but will reduce the
normal material velocity which is disintegrating the wheel
surface.

As an illustration, consider the case previously taken, and
suppose the wheel so soft that it wore badly under the speed
(30 feet per minute), and the cut (y^o- inch on the diameter).
The normal material velocity was 12-3 inches per minute.
Now, if the speed be reduced to 15 feet per minute, and the
cut put up to TWO mca on the diameter, the rate of removing
stock will be the same, but the destructive normal velocity
is reduced to 6-15 inches per minute, which the wheel will
probably withstand.

Conversely, if the wheel be glazing, the work surface velocity
must be increased, and the depth of cut decreased ; this
increases the normal material velocity, and disintegrates the
face of the wheel faster, preventing glazing.

The simplest way to reduce wheel wear is to reduce the
cross-feed ; when, however, this has been reduced sufficiently to
check the wheel wear satisfactorily, the possible output from
the machine has been very much lessened. It has gradually
been found from experience that it is better to reduce the work
speed than the cross-feed, but this also lessens the output
possible. The correct method is that given above — to reduce
the work speed far more than is sufficient to regulate the wheel
wear, and to increase the cross-feed simultaneously.

The normal material velocity, v V/ . 2£, which is

possible is a function of (i.e. depends on) the nature of the
wheel and work material only ; it may be said to express the
grade of the wheel. It is not an exact quantity — a wheel dis-
integrates, and it is a question whether it is doing so too rapidly
for economy. The amount in the example, 12 inches per
minute, is suitable for a 36 K wheel ; with 16 inches the wheel
face usually loses too much to be satisfactory, but with 3846 K
alundum wheels Messrs. Brown & Sharp e run at 20 inches
satisfactorily. For economy a wheel must disintegrate, and
the best rate is a matter of the ratio of wheel and labour
cost.

GKINDING MACHINEEY

Deduced Work Speeds. — Now, considering equation (3), we
have v = - . , =r and taking the example given as satisfactory

C Cv ~\~ U

we obtain the quantities in the following table as corresponding.
WORK SPEEDS AND FEEDS IN CIRCULAR WORK

Work diameter — inches

Surface velocity — feet per minute
Cross-feed — thousandths of inch
on diam. . . » .
KP.M. . . .

8-3

3-6
63-5

1-87
61

1
57'4

53'3

•57
50-6

87-7

•34
42

128

•23
30-6

Surface velocity — feet per minute
Cross -feed — thousandths of inch
on diam
R.RM. . . .

8'2

3-66
62-7

15-6

1-92

59-7

28-6

10-5
54-7

49'

•61

76'3

•39
36-5

106

•28
25-2

In this table I have taken a very wide range — in practice
such different diameters as J inch. and 16 inches would be
done on very different machines — in order to show where
difficulties arise in carrying out the natural formula of equation
(3). The table shows the speeds and also the corresponding
feeds for the various work diameters with a 14-inch wheel,
and again with it supposed worn down to 10 inches diameter.
The difference of wheel diameter has not very much effect.

It will be noticed that the r.p.m. are much more nearly
constant than the surface speeds ; further considerations will,
however, make an alteration.

Changes to meet Vibration of Slender Work.— Work of
| inch diameter according to the above table runs at 8-3 feet
per minute, which is within the limits of modern speeds, but
the amount of cross-feed — 0-0036 inch on the diameter — is very
high, and the slender work would vibrate under the cut, the
force due to which is the same in all the series of diameters.
To check the vibration and chatter the force of the cut must be

reduced, and hence vt must be made smaller. But v2.

=-
a I)

must be the same, so that v is to be increased and t diminished.
As an example, suppose that the force be halved : the velocity
must be doubled and the cross-feed reduced to one quarter,

THE WHEEL AND THE WOEK 77

so that they would be 16 J feet per minute and ToVo in°h or
less on the diameter. The tendency to vibration here limits
the output and not the power which is conveyed to the machine.
To what extent the velocity has to be raised and feed reduced
depends on the length of the part and the efficiency of the
steadies. Thus on small diameter work the speed usually has
to be raised above the speed given by equation (3), and it is
done at a sacrifice of the rate of removing material.

Effect of changing Width of Wheel Face.— At the other end of
the scale we have a different set of conditions — the work speed
is very high and the depth of cut small, and this is also the case
with internal grinding. Now high work speed may mean trouble
from vibration, due to the work being out of balance ; also such
fine cuts as those indicated are the finest for which a machine is
usually arranged, or less still, and with a slender internal spindle
difficult to use for other reasons ; it is, therefore, desirable to
be able to use less work speed and deeper cuts. Keeping
to the same grit and grade of wheel, there is only one way
to do this, which is by increasing the value of vt ; then v can
be reduced in just the ratio in which vt is increased, and t can

b c2

be increased in the square of the ratio, since v = - and t = r

c o

and c is increased. Now the maximum power delivered to
the machine is fixed, and hence the only way to increase vt is
to decrease the width of the wheel used, as vt is the power per
inch width of wheel face. So that for large diameter work
a narrower wheel should be used than for medium sizes.
Again considering our example, if we used a wheel of 1 inch
face instead of 2 inches, the work speed to suit it would be
44 feet per minute for 8-inch work and 64 for 16-inch diameter
work, and the cross-feeds 1 J and 1 thousandth on the diameter.
The disintegrating effect is just as before, and the power
employed and the output are similar. The total force of the
wheel on the work is the same, but it is concentrated along
one inch length instead of along two inches. The cross-feeds
would now be of amounts suitable for use ; while the previous
small amounts could only be employed advantageously as
the accuracy of the work was improved by the grinding.

78 GEINDING MACHINEKY

The effective width of wheel face in use is that of the
traverse per revolution of the work, so that the power used
per width of wheel face may be increased by using a slower
travel. In the next chapter, however, it is shown that the
traverse should be between f and | of the width of the wheel
face, and it is seldom that more than one such rate is available ;
and I have accordingly, for the sake of simplicity, taken the
effective width as proportional to the actual width of the wheel
face, in the above considerations.

The influence of wheel diameter change, due to wear or
actual change, on the correct work speeds and on the desirable
width of wheel face, is little in external grinding, but becomes
very important in the case of internal work. In Chapter VII,
accordingly, the matter is dealt with more fully.

Effect of Change of Grade. — Another way of overcoming
the difficulty is to use a softer grade wheel ; by this the value

of vz 1" . 2£ is lowered, as a less normal material velocity
aD

is suitable. This is not the only effect, though, of a change
of grade, as for the same h.p. supplied the value of vt — twice
the material removed — increases ; so that a change of grade
is effective in a double way, and the variation of a single
letter in the grade makes a considerable difference. Since vt is
now increased the output is increased.

This is generally the effect of changing the wheel for one
of a softer grade. The normal material velocity must be less,
and also vt is increased, giving a double effect in lowering the
correct surface speed. If by means of a more powerful machine
we further increase vt, the surface speed is lowered further
still. The depth of cut and the output are increased by
both alterations ; the particles of abrasive do not do quite
so much work, and more are used. This has been the trend
of development of wheels and machines for some years ;
the correct surface speeds have therefore been considerably
lowered.

From the output point of view soft wheels of a coarse grit
should be used ; if the work is to be finished with the same
wheel, the quality of surface desired controls these points.

THE WHEEL AND THE WOKK 79

If the wheel wastes away the work speed is to be lowered, and
the depth of cut increased. Lowering the work speed alone is
effective, but it sacrifices output, which can be maintained by
lowering the speed more and simultaneously increasing the
depth of cut. The converse is to be done if the wheel glazes.
For finishing, the work speed should be increased if the amount
of grinding warrants the change, as here the depth of cut is
small, and the tendency to glaze increases. This increase is
an advantage in finishing work, but a considerable increase
of speed is permissible, as the depth of cut is so small. Work
of small diameter usually necessitates a reduction in the
rate of removal of material, even if it be well steadied. On
large work, to secure cross -feeds of amounts which can be
reliably maintained, softer or narrower wheels are to be used ;
the same applies to internal grinding and also to flat surface
grinding with a disc wheel, which is the same case with d
made very large indeed.

My conclusion then is that no correct work speeds can be
given when the material of the work and kind of wheel alone
are specified, as the power supplied and diameter of the work
affect the matter very considerably.

The attention now paid to particular work surface speeds
and the advocacy of certain rates is due, I consider, to a mis-
apprehension of the real nature of disc wheel grinding and
to a desire to bring the practice into line with lathe work, to
which it is only superficially akin. The adverse criticism of
the high surface speeds used in the past is mistaken ; men were
just as capable then as they are to-day, and it can be taken
as certain that they adopted the speeds most suitable for the
appliances available. The generally accepted views of what
are suitable speeds -to-day are given earlier in this chapter, but
are based upon the prevailing idea that there is one suitable
work surface speed.

With the understanding of the principles elucidated above,
readers should not have much difficulty in arriving at the
best speeds after knowledge of the particular machine in use
has been acquired. Figs. 199 and 200 will be useful.

Though the normal material feed will have certain limits

80 GKINDING MACHINEEY

between which it must lie, it is best to work well away from
them — alterations being made when an indication is shown that
the speed is near one of the margins. Neither glazing nor
wasting occur at once, and can usually be checked by atten-
tion ; it takes more to break up a glazed wheel surface than
to check it from glazing. Neither is it well to run too near
the limit of the power supplied by the belt to the machine ;
it may hasten matters for a time, but invites trouble, e.g. if the
machine slows so much as to check the water supply, the work
may be spoilt.

Effect of Wheel Velocity. — The wheel velocity simply
enters into everything — except vibration effects — as a ratio ;
if it is increased or decreased all velocities and outputs change
in the same ratio. The fall of wheel velocity as its diameter
decreases has not the same effect as speeding the machine
differently. The power delivered to the wheel is the same, so
long as the belt is on the same steps of the cone pulleys, and
the output possibility is not altered, but feeds would need
modifying to meet the lessening of V — and hence the normal
material velocity — while vt was constant. To lessen V has
the same effect as increasing v ; it should therefore be done
only to meet troubles due to synchronous vibration.

Effect of Traverse. — So far we have merely considered the
work to rotate ; the sideways traverse introduces the velocity
v3 of Fig. 16, as is shown in Fig. 23, where along Ox at the lower
edge OA of the area of contact OABC the normal velocity
is Vj ; vz is very nearly equal to the surface velocity, and v3 is
the travel velocity ; the latter produces very little effect, as
its value is so small compared to V, which it alters relatively

to v/V2 + t?32. •

The grinding at the point here depends on t^ — the effect
of v2 and v$ is to present surface of the work to the wheel.
The extent of ground surface depends upon the vz, and the
volume of material removed on vlt while vs, the travel, merely
serves as a mechanical device for continuing the action. If
v3 acted alone a hollow flat would be ground along the circular
work ; the shape of the edge of the wheel would wear to a
shape which would give a feed corresponding to that described

THE WHEEL AND THE WOKK

in Fig. 24 as relating to a face wheel, the feed to' which takes
place as below.

FIG. 23. — FEED IN CLYINDRICAL WORK

Cup Wheels. — In grinding with a cup wheel, the work is
simply fed to the face of the wheel parallel to the face itself,
either by a slide or rotatory motion. If the wheel axis is per-
pendicular to the slide, the work is flat, and the wheel face is
frequently considered to be flat, as its defect from flatness does
not produce marks similar to the visible helical marks produced
on cylindrical work when the wheel wears slightly round.
Actually the wheel face is slightly curved, as is shown in an
exaggerated manner in Fig. 24, where the material is feeding
with velocity v, parallel to the line AB touching the wheel face.
The outside AC of the wheel face does most of the work, and
wears to such a shape as that shown, while the inner face AD

GKINDING MACHINEKY

wears a little, as some grinding always takes place along EB.
At any point then the velocity v can be resolved into vz along
the wheel surface and v{ normal to it, which latter controls the
cutting. The whole curve AC is very shallow, as CF is the
depth of the feed, which is only a few thousandths of an inch,
so that Vj is very small indeed. The width of the work which
can be ground flat is AB, which is a little more than the inside
diameter of the wheel. The area of contact which is the
width of the work by AC, can be anything up to AB X AC, and
is very considerable, and contains a very large number of
cutting points, necessitating a very small chip for each of them,
else an unpracticably large driving force would be required.

P^£'£

v/;.y.:v •:;..'

*?•• . • : '. „•' .-' .'

'•':''• '••.'•'.'••'•' ;'.'-

^H-'r';.v.y.i>

', • ^ • ' _^^^^

rj*"*f^
fa A

^-^

FIG. 24. — FEED IN CUP WHEEL WORK

In disc wheel work the grazing incidence of the cutting points in
the first part of the contact, BP in Fig. 22, tends to glaze the
particles, and this is corrected by a suitably high normal velocity
at the point C ; in the plane ABC this grazing incidence does
not occur, but the unavoidably small normal velocity over the
whole surface makes the wheel likely to glaze. The wheels
used therefore must be of soft (about H) grade, and they should
be of coarse grit, so as to keep the number of cutting points
small, so that the share of the driving power which each point
gets is as large as possible.

For simplicity the section in Fig. 24 is supposed to be
taken through the axis of the wheel spindle, and the velocity of
any point on the section CAD of the wheel face is normal to
the paper, as in the case sketched in Fig. 18. At other parallel
sections the cutting particles have a velocity inclined to the
paper surface, giving a lesser component perpendicular to that

THE WHEEL AND THE WOKK 83

surface and a component parallel to v. The value of v± is thus
affected indirectly, being the velocity of the material normal
to the wheel face. It decreases continually (at any radius) as
the point we are considering departs from the section taken ;
when it reaches the plane at right angles to that its value is
zero. This variation of the action, however, makes no difference
to our ultimate conclusions, which must be similar to those
deduced for disc wheel grinding.

By using cup wheels with thin walls the number of cutting
points is kept small, but a limit is soon reached in this direc-
tion, owing to risk in making and using the wheels. In any
particular case the wheel may be bevelled on its cutting edge
to reduce the number of points and prevent glazing, but so
wasteful a measure should only be resorted to under necessity.

The wheel surface has less power per square inch of contact
when the work is wide, so that it is least under control in that
case, and the wheels need then to be softer and coarser than are
suitable for narrower work.

The rate of removing material is btv, where b is the breadth
of the work and t the depth of the cut : for example, on work
10 inches wide, with a depth of cut of 0-002 inch, a work velocity
of 50 inches per minute would remove a cubic inch in that time.
If AF were then f inch (say for a wheel having walls 1 inch

•002

thick), the normal velocity would be 50 X —==• or 0-133 inches

* i o

per minute, or only gV of the rate in the example of circular work
taken. If the grit were 24 with about 250 points per square
inch, and the wheel speed 4000 feet per minute, there would be
250 X 4000 X 12 chips taken in that time, so that their sec-
tional area would be about 1 2 o 0*0 o o o square inch, which is much
less than the section of the chips taken by the smaller grit
wheel on circular work in the previous example. An examina-
tion under the microscope of such chips as are shown in Fig. 14
shows them to be of this order of size, but usually rather larger
in section, which indicates that fewer cutting points are in
action than has been estimated.

CHAPTEK IV

THE WORK AND THE MACHINE

The Development of Machine Grinding. — The difficulties which
had to be overcome in order to make the success of the modern
grinding machine, come into two classes : those inherent in
the process of grinding, and those involved in the necessary
mechanism of the machines to attain the desired ends — •
accuracy, finish, and quantity. Some of the difficulties of the
process and the ways of overcoming them have been described
in the preceding chapters ; others will be best illustrated in
connection with the consideration of the development of the
machines and of the details involved.

As the process of machine grinding was first applied to
work of circular section, such as shafts and spindles, and as
these still form the most important application, we shall
consider the process principally from that point of view.

The earliest grinding machines consisted of lathes with a grind-
ing head and spindle mounted on the slide rest and driven from
overhead. This is a practice still followed occasionally, either
by reason of its small initial cost as plant, or for the advantage
of performing lathe and grinding operations at one setting of
the work. Its advantages are most apparent in the case of
small work, such as is done in watch lathes, when several
opaertions can be performed on a piece of work without re-
setting by means of attachments (such as grinding spindles)
to the lathe, or by transferring the work by interchangeable
quills from one machine to another. The highly finished surface
of watch lathe beds and parts enables them to be kept fairly
free from grit, which sticks to and rapidly ruins the oily ways
of an ordinary lathe. Hence dry grinding is not so detrimental
to these small tools, and can be commercially used on them.

Dry Grinding. — In such arrangements and in some of the

THE WOEK AND THE MACHINE 85

earlier machines which followed them the work is ground
dry. This makes it necessary to use wheels with comparatively
narrow faces, and to employ light cuts, otherwise untrue work
results from the effects of the heat produced.

As the grinding head in lathe grinding is carried on the
compound rest, it has several sliding surfaces between it and
the bed, which is not a suitable arrangement to withstand
the tendency of the spindle to vibrate ; for this reason, and
because the fine adjustments desirable in a grinding machine
are not provided on lathes, it is not easy to obtain first-rate
work quickly in this manner.

Furthermore, the dust from dry grinding consists partly of
exceedingly fine particles which float in the air, and are carried
to all parts of the machine and lodge on them, especially
if these parts are oily. Bearings can be very effectively
guarded from the grit, but sliding surfaces are far more difficult
to protect. Examples of guarding are seen later, but the best
practice is to extract the air and dust away with an exhaust
fan (see Fig. 122), and thus protect not only the machine
but the operator from the ill-effects of the grit-laden air.
Where the amount of dry grinding is considerable, suitable
provision for dust extraction must be made to meet the require-
ments of Factory legislation.

Protection against Dust.— With these points in view it is
evident that the first call in a grinding machine is for the
protection of its parts from the waste abrasive. For other
reasons modern manufacturing grinders work with an abundant
flow of water, or some other fluid, over the cutting points of
the wheel ; this at once simplifies the problem of protection
very considerably, and in many machines practically perfect
protection is obtained. In the case of small machines which
work dry, such as small internal grinders and cutter grinders,
the difficulties are considerable, but unless they are carefully
considered and met in the design, the machine can preserve
its accuracy for a short time only.

Wet Grinding.— Wet grinding meets the dust difficulty, but
its employment is essentially due to the need of keeping the

86 GEINDING MACHINERY

temperature nearly constant; and so permitting the work to
be ground accurately far more rapidly than if done dry, and
to its lubricating properties, which enable a fine finish to be
obtained quickly. In dry grinding the temperature rises very
considerably, and trouble is caused by the work changing
its shape, and causing inaccuracies in the product. Actually
the material can be removed more quickly by dry grinding,
but as the accuracy and finish are lost the process is without
its chief merits, and is uncommercial.

Grinding Solutions. — The solution used must be thin, and
may be either plain water, water with soda dissolved in it,
or a solution of soluble oil, or one of the preparations now on
the market for this special purpose. For cast iron and for
hardened steel work the soda solution is to be used, but the
soluble oil or special preparations give the best finish on softer
steel work. For the soda solution, sufficient soda must be
used (1J to 2 oz. of soda to the gallon of water) to leave an
efflorescence when the solution evaporates ; this solution is
quite ' thin,' and the wheels cut freely when it is used. So
with soluble oil just sufficient is to be used to prevent the
parts or machine from rusting. The great disadvantage of
plain water is that it rusts the machine and the work (the
latter unless it is oiled immediately it is taken from the machine),
and for that reason I consider it uncommercial and undesirable.
However, there are advocates of its use, chiefly urging that
the grit contained in a solution pumped over the work con-
tinuously, and the gradual rise of temperature, affect the work.

As the first requirement is dust protection, so the second
is the provision of arrangements for dealing with an ample
supply of liquid. The use of solutions involves the use of a
pump, and the provision of a tank (which is frequently formed
in the body of the machine) ; the apparatus used, nozzles,
and systems of guarding the working parts from the solution,
are described later on, as they vary somewhat in different
machines.

Beyond the dust difficulty, the chief one encountered in dry
grinding is that of the effects of the heat produced, and with
the early hard wheels it was greater than with the modern free-

THE WOEK AND THE MACHINE 87

cutting wheels. Further, the grinding machine was then used
for work on hardened steel almost entirely, and a piece of
hardened steel is practically never straight. In grinding it
between the centres much more would be ground off one side
than off the other, and when the work was finished it would
be straight and true, but its temperature would be unequal,
one side being much hotter than the other, and as the work
cooled and the temperature became equalised, the contraction
of the side previously the hotter would bow the work, making
it concave on that side.

In the absence of cooling liquid, the solution of the difficulty
is to take plenty of time over the work, or to let it have frequent
intervals of rest, which is not an economical course. In order
to distribute the cutting, and so the heat produced, as uniformly
as possible over the work longitudinally, and thus to minimise
these bad effects, the work was rotated rapidly (about 150 to
250 feet per minute, circumferential speed), and a narrow-faced
wheel used. This practice has endured long after the difficulty
it was intended to overcome had been removed by the free
use of water, although for heavy cutting slower speeds are
advantageous, as previously shown.

Distortion in Dry Grinding.— The amount of bowing is
very conspicuous when the accuracy aimed at in ground work
is considered. Suppose, for example, a piece of work f inch
in diameter by 9 inches long be ground, and that when it is
finished the temperature varied uniformly across the piece,
one side being 60° F. hotter than the other ; then when cold
this side will be shorter than the other side by 9 X 60e inches,
where e is the coefficient of expansion of the material (see
Notes, page 438). The result would be that the piece would
warp, as it cooled, into an arc of s, circle, and the eccentricity

i I2te , 92.60.e
at the centre would be J — =- = J — - —

For steel, for which e is about 0-0000065, this is rather more
than g^o inch.

If I be the length, d the diameter of the piece, and i the difference of
initial temperature of the two sides, the difference of contraction is lie,,

88 GBINDIKG MACHINEEY

and this results in the part cooling to an arc of a circle of radius R, where

R = — , since the inside circumference is then shorter than the outside
te

circumference, in the ratio of the sides of the cooled work. An arc of
this radius of length I is bowed an amount

(1A2 JZ ]2 fe

ZR or &n which is equal to * ~ir

Work Expansion and Spring Tailstocks.— Besides this bowing,
the work, if the temperature rose uniformly or irregularly
in it, would expand longitudinally as a whole. To prevent
this giving rise to large axial forces the tailstock barrel
was arranged, to be held up to its work by a spring, and
not clamped, so that the expansion would press the barrel
back. This construction is now employed as the best, although
water is used ; for heavy work the tailstock barrel is usually
clamped, and occasionally released and re- tightened.

When water was first introduced to keep the temperature
of the work low or constant, it was applied in a small stream,
and the above difficulties were reduced, although they were
not entirely overcome, for the heat produced caused effects
during the grinding as well as afterwards.

« Change of Axis.' Temperature Effects.— When a piece of
work, particularly if of hardened steel, is placed in a grinding
machine, it will not run true, and as it revolves and traverses
past the wheel some parts of the skin will be ground before
others. These parts will then be the hotter, so tha if they occur
along one side of the work that side will expand, and the
work as a whole will be bowed, that side becoming convex.
The result is that this side will be ground still more, and the
other side will not be touched. As the temperature equalises
itself by conduction through the work, the work tends to become
straighter, and then the opposite side of the work, which so
far has not been ground, becomes the farthest from the axis,
and is consequently ground. The work then is not round.
Later the two parts at right angles to the line joining the parts
first ground will be ground. Thus the grinding proceeds
irregularly and unsatisfactorily as to accuracy of work

THE WOEK AND THE MACHINE 89

When any such irregularity in grinding occurs the attention
should first be paid to the centres.

Advantage of ' Dead ' Centres.— If the work head centre
is live, as in a lathe (and as is used for convenience in some
grinding work), it may run out of truth, thereby throwing a
previously truly turned piece of work out of truth at that end.
In grinding machines, to prevent such irregularities both
centres are made dead wherever it is possible, and the work
driven by means of a dead centre pulley or gear, revolving
round one of them, as is illustrated in Figs. 69 and 117. In
that case, if the centres and centre holes in the work are
properly shaped, and free from dirt, any defect in the round-
ness of the work must be due to some change of the shape of
the material as the grinding goes on.

So, when such an irregularity occurs, it is best first to
examine the centres themselves, and then to clean the centre
holes (see Fig. 87, page 214), and try whether the effect is then
removed. If it is not, and the water supply is as full as is
provided on the machine, the cut must be reduced and the
work done more slowly. If the wheel is not cutting quite
freely it should be changed for one of a softer grade, or if one
is not available, the width of the face of the wheel reduced.

If it is the bowing or * change of axis ' of the work which
causes this effect, it is most conspicuous at the centre of the
length, and the position of the greatest irregularity is a guide
as to whether the trouble is due to ' change of axis ' or is
connected with the centres.

This trouble is accentuated in thin hollow work, as then
the heat generated has to be conducted round the circum-
ference through the thin metal instead of through the whole
section when it is solid, thus it takes longer. In grinding
thin work it is well to go slowly, and not rough out with a
heavy cut.

The energy brought to the grinding point (about 99 per
cent, coming through the wheel spindle) is turned into heat
as the metal is removed ; this heat immediately raises the tem-
perature at the point to a very high degree, so that the ground-
off particles bum as sparks and the spot on the work becomes

90 GEINDING MACHINERY

very hot. The chief function of the water is to cool this spot
promptly and carry away the heat before it has time to spread
by conduction into the body of the material, and so distort
it ; hence the fluid should be applied as directly to the grinding
spot as is possible. This presents no difficulty in external,
but is not so easy on internal, work.

When the grinding is dry the ground-off metal is sometimes
entirely burnt away, only abrasive dust being left ; even
under a heavy flow of water some of the small chips are burnt
as sparks or fused into spherical globules.

Effect of Internal Strains. — The abundant water supply
used on modern machines and the free-cutting wheels have
almost eliminated this change of shape due to temperature,
but a similar effect, though it is less in amount, is due to
another cause — the existence of internal stresses in the material
of the work. Such stresses are produced and left in the
material by any mechanical treatment severe enough to
produce permanent set. Upon the results of this cause no
water supply or grade of wheel can have any effect, as they
are due to the removal of material which carried stress, and
so kept the work in its original shape.

Neither the temperature effect nor the relieved stress effect
occur until turning marks are ground out, and both are most
conspicuous at the centre of the length, so that they are difficult
to distinguish, and also the latter may induce the former.
The stress effect is to be suspected if the work is from the
unturned bar, particularly if it is bright drawn.

Distribution of Internal Stress and its Magnitude.— To

illustrate the manner in which relieved internal stress produces
its effect, let us consider a rectangular bar which happens to
be bent (say into the arc of a circle), and is then free from
internal stresses and strains. Now straighten this bar by
bending it very slightly beyond the straight line (the opposite
way to which it was initially bent), and then releasing it, so
that its elasticity restores it to the straight line, and it remains
there. This bar has then internal stresses in it. What they
are and their distribution depends upon how much bent the

THE WOEK AND THE MACHINE

bar was at first, and its particular cross-section. If the bar
was originally bent to any degree exceeding a small amount,
the internal stress left on the outside is compressive stress
on the side where the bar was previously concave. Fig. 25
shows a typical case, and gives the stresses in a rectangular
bar. It is drawn to scale for a square bar 3 inches by 3 inches
section and 2 feet long, originally bent so as to be y\ mch
out of straight (i.e. the distance between the hollow of the
concave side and a straight-edge placed across the end is
fV inch). The material of the bar has a yield-point at 40,000 Ib.

STRAIN STRESS.

FIG. 25. — STRESS IN A STRAIGHTENED BAR

per square inch. The figures are supposed drawn on a line of sec-
tion of the bar — that is, ABC is a line across the bar, and the
length QE represents the stress at that point ; abc is the same
line, and pm the strain, extension or contraction. When the
bar is bent for straightening, just before it is released, the
stresses are given by the broken line DEBFG, the corresponding
strain line being dbg ; that is, the stress is zero at the centre
of gravity of the section — here the centre — and increases both
ways till it reaches 40,000 Ib. per square inch at one third the dis-
tance out, and then remains the same to the outside. After re-
lease the stress left in the bar takes the figure HKLBMNP, and
the strain the line hbf ; that is, the stress is zero at the centre,

92 GKINDING MACHINEKY

runs up to 20,778 Ib. per square inch at J inch from the centre,
then diminishes to zero at a little over 1 inch from the centre,
and then is of the opposite nature and increases to 17,778 Ib.
per square inch at the outside. In mild steel the state of stress
left is symmetrical. The more the bar was bent initially the
greater these stresses are at the skin ; they do not in a bar
of rectangular or circular section approach the yield-point
stress of the material. Calculation shows that in a rectangular
bar the maximum amount is half the yield-point stress, but in
a bar of cruciform section the stress can reach the yield-point.

Now suppose that we mill a piece off the side of this bar
in which there is a compressive stress. The bar will shorten
as a whole — but this will be a very small matter and will not
concern us — and will bend up, this side becoming concave.
If on machining the machined side becomes convex, it will
show that it had internal tension in it before machining.
The whole distribution of stress alters on machining ; for
example, the zero stresses are not afterwards at the same
points of the material as before. The amount such a piece
of work may buckle depends on its length and thinness, and
upon the yield-point of the material; as an example, some
cold rolled strips 32 inches long by 0-2 inch thick, machined
on one side to -£% inch, buckled, when released from the miller,
into an arc If inches high.

Usually the amount of distortion can only be small, but
it is very perceptible in grinding. If a round piece of work
contained such stresses as above described, and the side with
the compressive stress touched the wheel first, the bowing
would make it tend to shrink away from the wheel ; when the
side with the tensional stress was ground it would tend towards
the wheel, so that effects in grinding would be somewhat
similar to those due to heat effects.

Type of Stress frequent in bright Drawn Steel.— If, however,
the whole of the outside circumference initially had tensile
internal stresses, and the interior compressive, the longitudinal
results balancing, immediately any part of the bar was ground
it would bend towards the wheel and be ground more, and

THE WOBK AND THE MACHINE 93

when the bar was so reduced that another part of the
circumference was ground, the bending would take place in
that direction. This is the state of stress which occurs in
bright drawn steel when drawn with a heavy reduction; and
renders grinding difficult. The initial states of stress in bright
drawn steel have been found experimentally to run up to
50,000 Ib. per square inch tensile and 54,000 Ib. compressive,
and such amounts render the distortion as grinding proceeds
very conspicuous.

I have found that reeled bars and hot worked bars grind
without any trouble from this source. The reeled bars have
internal stresses ; it is the screw symmetry of the distribution
of the stress caused by the rotation in reeling which causes
this freedom from trouble.

Both temperature and relieved stress effects are due to
the elongation (or contraction) of the length of parts of the
material. Under a rise of temperature of 100° F. a steel bar
expands 0-00065 of its length, and about the same elongation is
produced by a stress of 20,000 Ib. per square inch, which is less
than half the yield-point stress of regular mild steel. The
distortion effects due to the relief of stress are, however, much
the smaller, as they are due to the removal of a small portion
only of the material.

Remedies. — The greater part of the change of shape takes
place the moment the material is removed, and is permanent,
but there is a small after-effect which takes place very slowly.
The easiest way to meet this difficulty is to rough grind first
and allow an interval before finish grinding, but where very
precise work is required (e.g. machine tool spindles) the most
satisfactory method is to anneal them slightly. Very little
is necessary (boiling for a short time in water I consider is
sufficient); so that the hardness will not be affected. It has
been shown that the crystalline structure of overstrained mild
steel reforms itself when annealed even in this slight manner,
but further investigation into the subject, especially as regards
hardened steel, is desirable.

Although a piece of work may show irregularities in the
grinding, it does not always mean that there is any real trouble ;

94 GEINDING MACHINEEY

errors are shown up so conspicuously in a good grinding
machine that the amount involved is apt to be over-estimated.
If the work grinds regularly it may be taken to be right ; if
there are slight irregularities it is a question of the particular
requirements whether they are sufficient to be of importance.

Necessity for True Wheels.— In the early machines the
width of the wheel used was small, chiefly for reasons of the
heat effects, but with the provision of good water supplies
and the improvements in wheels, the width employed has been
much increased, with the advantages of bringing a larger
number of cutting points into action. To bring the width of
the wheel effectively into action it must be trued so that
where it touches the work it is parallel to the surface it is
producing, otherwise the traverse of the work as it rotates
will produce a screw thread mark down the work, and part
of the wheel may not come into action at all. As the depth
of cut is only a few thousandths of an inch at most, and in
finishing is very small indeed, the diamond tool for turning
the wheel true should be mechanically guided, so as to have
the same movement relatively to the wheel as the work has ;
this is most perfectly attained by simply attaching the diamond
tool to the work table, whether the machine be for external,
internal, or surface work. It should cut the wheel as near as
possible to the place where the wheel cuts the work, otherwise
— if the wheel spindle be not parallel to the line of travel of
the work — it will not true it quite as correctly as it ought to
be done (see pages 150-2).

Rate of Travel. — After the wheel has been turned true
in this manner, when it is brought up to the work (supposed
rough ground), it will cut right across its face. In order to
keep it cutting right across its face as the work rotates and
travels across the wheel, the travel must be such that one
revolution of the work brings an entirely new portion of the
work to the wheel face. The traverse movement must not
be such as to leave any portion of the work unground, and in
order to have a margin the travel per revolution should be
decidedly less than the width of the wheel, say f of it at most.

THE WOEK AND THE MACHINE

If the travel per revolution is small compared to the width
of the wheel face, as is shown in Fig. 26 at A, the leading edge
of the wheel does the principal work. The spiral line is drawn to

FIG. 26. — RATES OF TRAVERSE

indicate the track of this leading edge, but this track will not be
marked on the work. The work is supposed to be travelling to
the right (or the wheel to the left), and the left-hand portion
of the wheel is doing the cutting, and the remainder, at most,
just grazing the work.
As a result, the left
side wears ; on the re-
verse travel the right
side of the wheel face
wears, with the result
that the wheel face
wears into a curve as
shown. This curve is

very shallow ; the amount of curvature could not exceed
the depth of the cut, say ToVcr> but a fraction of this
amount (0-00005 inch) will produce conspicuous travel marks

FIG. 27.— SPIRAL MARKING

96 GEINDING MACHINEEY

such as are shown on a ground bar in Fig. 27, where the
optical effect is striking.

Therefore, in order to keep the wheel as flat as possible,
the traverse should exceed half the width of the wheel, as is
indicated at B in the figure, where the spiral line indicating
the (unmarked) track of the leading edge shows a traverse
movement CD of about | of the wheel face. The part CD of
the wheel is now doing the work, and wearing ; on the reverse
traverse the corresponding part EF wears, and the wheel
tends to keep flat. The travel then should be between f
and f of the wheel face.

For the finishing travel or two it is best to travel less, by
increasing the rate of rotation of the work without altering
the travel speed ; the wear under the finishing travel is
infinitesimal, and the effect of any slight rounding is minimised.

This applies also to internal grinding and to flat grinding
when the curved edge of the wheel is used (see machines in
Figs. 121 and 124), but in the cases in which the flat face of a
cup or cylinder wheel is used for surface grinding this arrange-
ment is impossible, and the cutting face of the wall of the
wheel wears to a curve. This curve is so slight, only one to
two thousandths of an inch in depth, that the wheel face is
usually considered to be flat, but trial shows that it is curved
to this extent.

Double Copying Principle. — In a lathe, where the traverse
of the tool per rotation of the work is small, the truth of the
work may be regarded as a direct copy of the truth of the
lathe bed, but in grinding, where large traverses per rotation
of the work are used, there is a double copying principle in-
volved. The truth of the ways is first copied on to the wheel
face, and then series of the wheel face copied on to the work,
using the truth of the ways for the formation of the series, as
in broad-cutting with single tools. The exactness demanded
makes it necessary that the wheel face truth is derived directly
from the machine ways.

Pause, or Tarry. — In Fig. 26 the wheel at B is shown up
against a shoulder of the work. If, with this large traverse,

THE WOKK AND THE MACHINE 97

the reverse took place promptly on the shoulder being reached,
a certain portion of the work, CGH, and the corresponding
portion on the other side of the work, would remain untouched
by the wheel. It is advisable then for there to be a pause or
tarry at the reverse of the motion of the table. If this pause
lasted for half a revolution of the work, there would be only
one quarter as much surface left unground ; this part is
shown shaded at CKH.

These unground portions are shown developed in the lower
part of the figure : LM is the work and NP the shoulder ;
the shaded part QES shows the unground part for no tarry,
and TUV for a tarry of half a revolution. KW is half the
traverse per revolution of the work.

To leave no portion of the work untouched the tarry should
continue while the work makes a complete revolution, but it
is not advisable that it should last so long, as there being little
material opposed to the wheel towards the end it then is apt
to cut a little deeper.

If the machine is not fitted with a tarry mechanism — most
are not — it is well to throw the traverse motion out at the
shoulder now and then to avoid the accumulating effect of
the unground parts.

Where there is not a shoulder no tarry need be used ; the
edge of wheel should be set to run beyond the end of the work
by about half the width of the wheel, so as to produce the
same effect.

In internal grinding there should be no tarry, and the wheel
should not be run so far out of the work, as there is a tendency
for this to produce ' bell mouthing ' in the hole, owing to the
spring in the spindle and supporting sleeve.

Grinding Parallel close to Shoulder. — Sometimes it is
very essential that the diameter of the work should be uniform
right up to a shoulder, and free from the slight effect of rounding
of the wheel face. This can be secured by throwing out the
cross-feed at the other end of the work and feeding at the
shoulder end only. This throws the wear on the other (left
hand, as shown) edge of the wheel as at X, and keeps the side

98 GEINDING MACHINERY

towards the shoulder flat. The feed may be heavier than is
normal at the shoulder end, and little or nothing at the other.

Vibration. — Besides the general truth of the work produced,
there is a truth of surface which is necessary — that is, the
surface of the ground work must be free from blemishes,
particularly from series of regular marks known as chatter.
These are due to vibration of the parts of the machine and of
the work. The actual modes of preventing these defects are
described later, but as vibration is a phenomenon much more
frequent, and of greater importance in grinding machines than
in other machine tools, its nature is here of particular interest.

The characteristic of a vibratory motion is that it repeats
itself after a certain interval of time (known as the period),
and the motion may be either the same in all particulars, or
its magnitude (termed the amplitude) may gradually increase
or diminish. The period or time taken to go completely
through the motion once may be many years, as in the pre-
cession of the earth, the second or two of the swing of a clock's
pendulum, or the inconceivably small time of a such a vibration
as constitutes light. In grinding, the important period is
that of the rotation of the wheel, varying from TV to 3^0 of
a second ; in this small time there must take place all the
changes of force and resulting small movements, due to any
want of balance in the wheel. The movements must be small,
but the forces involved may be large, and that they almost
certainly will be large when any conspicuous vibration takes
place can be ascertained by calculating the values of the

(2 \

47r2n2r— or — . — ) for a few cases.
9 r g/

Free Vibrations. — If we support a weight by a spring, and,
after it has found its position of rest, give it a vertical blow,
it will oscillate up and down through a greater or less space
(the amplitude), according to the strength of the spring and
the amount of the blow. When the weight is at its farthest
distance, either up or down, from its position of rest, the
spring is extended or compressed (from the configuration of
rest), and has stored in it a certain amount of work or energy,

THE WORK AND THE MACHINE 99

and just for the instant the weight is at relative rest and has
no kinetic energy. As the weight approaches its central
position it gains velocity and kinetic energy, while the spring
is less extended or less compressed, and the energy stored in
it becomes less, until at the central position it becomes zero.
Its energy has now been transferred to the weight as kinetic
energy. If the strength of the spring is slight enough in
comparison to the weight, the motion will take place slowly
enough to be easily observed, as the period may be made
some seconds. If the spring were stiff and the weight small,
the rate of vibration would be rapid. Such an interchange
of the form of the energy is typical of vibratory motions such
as we have to consider. The amplitude depends on the amount
of energy involved, but the period in which the whole motion
takes place does not depend on the amplitude (unless it in-
creases to a large amount), or on the blow originally given to the
weight. After a time, chiefly owing to the resistance of the air,
the extent of the vibration will be found to have lessened, and
finally the weight will come to rest. Such damping resistances
are proportionate to the velocity of the weight at any time.

The force with which the spring acts in accelerating or
retarding the motion of the weight is (by Hooke's law) propor-
tional to the distance the weight has moved from its position of
rest.

If the weight consisted of a heavy central part of a steel bar,
and the springs of slender ends to the bar, the same kind of
vibration would take place if the bar were placed between the
centres of a grinding machine and struck a blow. The ampli-
tude of the vibration would now be small, and the period prob-
ably too small for the motion to be satisfactorily observed ;
the elastic restoring force would, however, be again proportional
to the displacement of the heavy part from its position of rest,
and the period would not depend upon the amount of the blow.
The movement would be damped out quickly.

Similar vibrations take place in uniform bars and in masses
of metal, which vibrate elastically and change shape (very
slightly) during the vibration. The restoring forces, which
depend on this distortion of shape, cannot be expressed so simply

100 GEINDING MACHINEKY

as they can in the examples above taken, and in considering
the character of a vibratory motion we shall treat of such
examples for the sake of simplicity.

Vibrations of a weight or a bar struck and left to itself are
termed ' free ' vibrations, in contrast to other vibrations, which
may be caused by alternating forces continually acting on the
parts, and which are termed ' forced ' vibrations. In order to
' force ' a body to oscillate, the disturbing forces must them-
selves be regularly repeated and periodic ; they may, however,
be gradually applied or abrupt. Considering the bar previously
mentioned, if it were set to rotate, and a wheel somewhat out of
truth were brought up to grind it, such disturbances would be
caused. In reckoning these the average cut can be taken as a
uniform smooth effect, while the forces above and below the
average would be an alternating disturbing force. It would be
periodic, the period being that of a revolution of the wheel, but
would vary irregularly, and not according to a simple rule, like
the spring in our previous case did.

However such a periodic disturbing force or disturbance
varies, smoothly or abruptly, it can be built up (as was proved
by Fourier) by the Addition or superposition of a number of
constituent disturbances, each varying with the time accord-
ing to a simple sine or cosine law — that is, in the manner in
which the position of the vibrating weight above-mentioned
would change in the absence of resistance. The period of
each of these constituents is a simple fraction — the half, third,
fifth, &c. — of the period of the total disturbing force, here
the period of the rotation of the wheel. Thus each constituent
can be expressed in the form Pn cos rikt, where t is the time
reckoned from when a particular point of the wheel touches

the work, -=- is the period of revolution of the wheel, Pn is

the greatest value of this constituent disturbing force corre-
sponding to the number n, and n is successively 1, 2, 3, 4, &c.
Beckoning the time t in seconds (that is, in fractions of a
second), if the wheel be making 1400 r.p.m. (suitable for a
14-inch wheel), the wheel period would be yf o second, and k
would be 146'5. The value of Pn cannot well be found in

THE WORK AND THE kjACHlNE ''101

this particular case, but from our point of view that is not a
matter of importance. These constituents are usually termed
harmonics, from their importance in sound vibrations.

The effect of such a disturbance on a part which can vibrate,
is best considered by writing down the fact that the acceleration
is produced by the forces acting on the body, as an equation.
This takes the form —

m J+a^+te=2PBcosnfc( . (1)

where x is the amount the part we are considering has moved
from its undisturbed position in the time t. The first term
expresses the acceleration forces, the second the damping
resistances to the motion ; the third term is the force which
tends to restore the body to its undisturbed position, and the
right side of the equation represents the disturbing forces,
the symbol £ being prefixed to indicate that we must add
all the simple constituents together — or take as many of them
as matter for our purpose. The second term is the velocity
multiplied by the damping constant a, and the third the
movement x multiplied by the force which, acting alone on
the body, would move it through unit distance (usually 1 inch),
or, if the body would only move a small distance, a hundred
times the force required to move it one hundredth of the unit
(rJu- inch).

The advantage of expressing the relation of the acceleration
and forces algebraically lies in the fact that if the equation
be solved, we then know just what the resulting motion is,
and can ascertain what happens, and can trace the causes of
the results. Without such aid vibration effects are difficult
to consider accurately. The result of solving the equation
gives us —

- —
x = Ae 2m sin

/ /~b a^ \

( \/ . _ t _|_ a\

* ra 4m2 /

COS

^ V (b -

The movement therefore consists of two portions, which are
added together to give the value of x at any time ; each of

102 GRINDING MACHINERY

these portions is a vibratory motion, as each involves a sine
or cosine of the time, and therefore repeats itself at intervals.

The Damping out of Free Vibrations.— The first term

_ at_ / /fo a2 \

Ae 2m Sin^ /^/ 2. tf -f a ) is an oscillating motion which

has an amplitude Ae ~2m ; this is not constant, but gradually

diminishes, for as t gets larger e " 2™ gets smaller, unless a is
exactly equal to zero, when it remains equal to unity. As
there is always some damping resistance, a cannot be zero,
so that after a time the vibration represented by this first
term dies out, however large A may be. This is the chief
effect of the damping ; it damps out the vibration represented
by the first term of the solution of the equation. It also
slows the rate of vibration somewhat, and makes the vibration
lag behind the force. Bearing this in mind, we will first
consider a to be very small, and omit it, and the solution then
takes the simpler form —

x = A sin( \/^-.( + a}+ 2 ^— ~ %79 • cos nkt (3)
m b — mn2k2

Suppose that the disturbing forces P did not act, then the
solution would represent the motion without them — that is
to say, the ' free ' vibration. Hence the free vibration has an

amplitude A, and will repeat itself when \/ ~ .t-{-a has increased

ffi

by four right angles, or after a time Tx = 2 TT A/ i • This is the

period of the free vibration, and depends only on m and b —
in our first example — the weight (m), and the strength of the
spring (b). The factor A depends on the amount of the blow
which started the motion, and a on just when the blow was
struck.

Our damping factor e- 2m tells us that the free vibration
dies out, however large A is — that is, however large the original
free motion may be, and a trial shows us that with the parts
of a machine these vibrations die out very rapidly. After
this free vibration has died out we are left with only the second

THE WOKK AND THE MACHINE 103

term on the right in equation (3), which represents the effect
of the periodic disturbance — in the case we have mentioned,
an untrue grinding wheel.

Forced Vibrations. — In considering the effect of any con-
stituent PM of the disturbing force, it is to be first noticed

that the period of the vibration which it enforces is —7- —

rik

that is, its own period, and not the natural period of free vibra-
tion of the part affected. Secondly, the amplitude (or magni-
tude) of the forced vibration due to the various constituents Pn
are not directly proportional to the values of Pn, but to those

values divided by - — n2/c2. Hence, although in practical
wi

cases the values of P« get smaller, as n is made successively
1, 2, 3, 4, &c., their effect in enforcing vibration will not neces-
sarily do so, and will not do so if '=- \/ -- is nearly a whole

K in

number ; for in that case some value of n2k2 will be small,

and the resulting amplitude large. Now 27rA/ — and — p are

v b nk

the periods of the free vibration of the part, and of the con-
stituent Pn of the disturbing force, and if they are nearly
equal the forced vibration produced will be large.

There are then two causes of considerable vibration, a
very large periodic disturbing force, and a near approximation
of the period of a constituent of a periodic disturbing force to
that of a free vibration of a part. The first is easily detected
and removed, but the latter is more difficult to deal with.

It might be thought that if perchance nzk2 = — that the

vibration caused would at once be exceedingly great, but this is
not the case. From the equation point of view the solution
fails, and has to be taken to a closer value, with the result that

the expression for the forced vibration becomes —

p
x = -5- * • sm nki

104 GKINDING MACHINERY

Again the period is the same, but the amplitude „— T- * starts

by being very small, and increases gradually but continuously
as t increases. The chatter and vibration caused eventually
becomes so great that the cause has to be remedied before work
can be proceeded with.

With sound vibrations the effect is known as * resonance,'
and this term is now applied to such phenomena generally,
whether of sound, electricity > or mechanics.

The importance of these constituents of quicker period than
that of the actual total disturbance is now clear. These quicker
periods are the |, J, J, &c., of the total period, and practically
these are more likely to coincide nearly with a free period than
is the full period of the disturbance. The free period may be
either one of the machine or of the work : if the work be stiff
it will be a period of the machine, if thin it may be either.

When vibration and chatter occur, the source of vibration —
a flapping belt or untrue wheel — should first be ascertained, and
the cause removed. This is equivalent to making the term P
zero in the equation. Then some period in the machine or
work should be altered, so as to change this nearness of the
period of the forced and free vibrations. As the period of the
effective constituent of the disturbance is frequently J or J
of the full period, only a moderate alteration is necessary or
desirable.

Supposing that the chatter marks on a bar are due to vibra-
tion enforced by irregularities in the wheel, their pitch indicates
which of the constituents is the effective one. For, supposing
that the work surface speed be 40 feet per minute, and that the
wheel speed is 1400 r.p.m., the wheel period is 14100 min. (Tfo
sec.), and if the chatter marks were due to the first term they
would be spaced by the distance which the work surface would

40 X 12
move through in that time, or inch, or about f inch. If

J.4UU

they were due to the second term containing cos 2 U, they would
be spaced half this distance apart ; if to the third term, one-
third of the amount, &c.

Transverse vibrations of the work itself are checked by

THE WOEK AND THE MACHINE 105

steadies ; except on slender work the period is very rapid, and is

I2
given, in seconds, by the expression , where I is the length

and d the diameter in inches of a steel bar supported by the
centres only. As an example, the period of a bar 4 feet long by

48 X 48

1 inch diameter placed between the centres is (= 0-029)

oOuuU

of a second, or rather over 2000 vibrations per minute. A mass,
such as a piston, at one end of a bar, will reduce the rate of
vibrations to about one half.

Summing up, then, we see that to produce continuous vibra-
tion there must be some cause of a periodic nature, which
enforces the vibrations by reason of a relation of its period
with that of some natural period in the machine or work.
When the action starts, free and forced vibrations of nearly
equal period are produced ; the free die out, but as they do so
the movement then arranges itself, so that the accelerations
and forces satisfy equation (1), and the forced vibration assumes
a permanent condition. When such happens the periodic effect
is to be removed if possible, and also some periods altered to
prevent recurrence of the action.

Balancing. — One of the chief causes of vibration is want
of balance in the wheel, its spindle, or other parts of the grinder,
including even the count ershaf ting, and the problem of
balancing is further of interest in much of the high-speed
machinery the parts of which are produced by grinding.

A machine is said to be ' balanced ' when its parts are so
made and arranged that it is free from the dynamic effects
of the movements of its parts, but the term is applied in two
ways. In machinery, such as steam engines, containing
parts moving in straight lines or oscillating through angles,
many of the undesirable dynamic effects may be eliminated
by a careful arrangement and proportioning of the parts in the
original design. In this procedure the materials are supposed
uniform and the construction perfect ; the ' balancing ' is
here done before the machine is made. When simpler spindles
are run at very high speeds, however, the effects are so great
that even defects of density in the materials are of importance,

106 GKINDING MACHINERY

and a spindle may be out of balance although in design it is
symmetrical about its axis. This is the case which is of
interest in grinding, and by ' balancing ' is then meant the
addition of small weights (or the making of other adjustments)
so that the spindle will run without vibration.

Suppose that a spindle is itself perfect in every way, but
that when a thin wheel is mounted thereon it runs out of
balance. The error must be due to one part of the wheel
being heavier than another, and as an illustration suppose
that the wheel contained a part having extra mass ra situate
at a radius r ; the * centrifugal ' force at a speed of n revolutions
would be 4:7r2n2rm, which would be balanced by that of a
mass m, placed at a radius r, at all speeds, provided only that
m1 were selected so that m^r^ = mr. It does not matter what
the value of rx is, so that the balancing may be done by replacing
a little of the wheel material near the hole by some lead. This
is the method adopted by manufacturers who balance those
of their wheels which happen to have such error. In course
of wear the irregular part of the wheel may be used up, so that
it is again out of balance and requires correction in the same
manner. Plenty of mass in the wheel heads of grinders is
very desirable, as it reduces the effects of small unavoidable
errors of wheel balance.

The simplest method of testing for such want of balance
and of correcting it is to mount the wheel on a parallel spindle
known to be in balance, and to place it to roll on parallel ways.
If it rolls so that one part of the wheel always tends to rest
at the bottom, that part is the heavier, and correction is made
by adding weight to the other side until the spindle comes
to rest indifferently in any position. The wheel is then in
' static ' balance, and when mounted on a true spindle will run
steadily. As the forces due to high-speed rotation are greater
than those due to gravity in the ratio AirWr to g (where n =
revs, per sec., r = radius at which mass is in feet, and g =
32-2, so that the ratio for a mass at a radius of 2 inches
running at 1000 r.p.m. is 57), static balancing must be very
carefully done to be dynamically efficient, and hence wheels
are often balanced dynamically.

THE WOEK AND THE MACHINE

107

If, however, the part which is out of balance is not thin
like a disc wheel, static balance may fail dynamically in another
manner, and it may even make the vibration worse. This is
illustrated in Fig. 28, where a perfect spindle ABCD is
supposed to be supported in a horizontal position in bearings
at A and D. Suppose that a mass m be fastened to the spindle
at C : the spindle will tend to turn round and set itself with C
as low as possible. It could be balanced statically by placing
a mass equal to m anywhere along the line at the bottom,

FIG. 28.— BALANCE OF SPINDLES

opposite either to B, to C, or to any other point in BC. If
the spindle with the mass m at C where the radius is r were

rotated at n revolutions per second, a force 4?r2n2r- , indicated

9
by the broken line with an arrow head, would be exerted

by the fastening to prevent m flying off ; this force would
be transmitted by the shaft and produce reactions P and Q
at the bearings A and D respectively — P and Q bearing the
inverse ratios of the distances of C from these forces. Now if
the spindle were balanced statically by a mass m placed opposite
to B, on rotation, the forces produced at the bearings, although
(as the figure is drawn) opposed to P and Q, will not be equal

108 GKINDING MACHINEEY

to them in magnitude owing to the different distances of
C and B from the lines of P and Q ; thus the spindle will not
be in balance nor run steadily. It will only be in balance if
the position selected for the balancing mass be exactly opposite
to C, and in an actual spindle the position of this mass variation
(here m at C), which renders the spindle out of balance, is
unknown.

Now suppose that in addition to the mass m at C the spindle
carried a mass M at E on a plane AED different from ACD. In
rotation there will be additional forces, indicated by X and Y,
at the bearings. Combined with P and Q these give S and T
as the resultant reactions, the planes APSX and DQTY being
perpendicular to the axis AD ; so that S and T will be the
rotating reactions at the bearings. It will be noticed that
these forces have a lead and lag on the positions of the masses
m and M. No single mass placed anywhere on the spindle
can balance these non-parallel forces, and two masses must be
used. Although an actual spindle will not be out of balance
in so simple a manner as this, the same conclusions are true ;
two masses are necessary which may be placed at predetermined
distances along the length of the spindle, but their angular
position must be correct.

The problem of actually ascertaining this correct position
and the amount of the balancing masses is no easy one. In
cases of built-up masses intended to rotate at a high speed,
such as the rotors of steam turbines and dynamos, want of
dynamic balance is to be expected. Flanges are frequently
provided for the reception of the necessary masses, but both
the amount and the angular position of these masses must be
determined from experiments on the shaft rotating in its
bearings. These are suspended or mounted so as to be capable
of horizontal side movement, controlled (usually) by springs,
and observations are taken on the amount of movement of
the bearings and the corresponding angular position of the
shaft, from which the position for the correcting masses can
be deduced.

As the shaft rotates, the want of balance sets up vibrations,
which may be of two types, corresponding to the side movement

THE WOKK AND THE MACHINE 109

of the shaft as a whole (and will not exist if the shaft be in
accurate static balance) and to its angular movement. At
two corresponding critical speeds there will be greatly increased
vibration, owing to the period of natural vibration of the
shaft as it runs, approximating to the period of the force
causing vibration — that is to the period of revolution. In
experimenting, the observations are naturally taken at one
of these critical speeds, as the phenomena are then the most
conspicuous. To ascertain the angular positions at which
the correcting masses should be applied, a scriber is adjusted
just to touch the shaft (usually at or near a bearing), leaving
a short mark on surface previously coated with raddle. The
shaft is then rotated in the opposite direction at the same
speed, and another mark scribed. These marks will be found
to be at different portions of the circumference, and the angular
position at which the correction is to be made is taken to be
half-way between them.

The preceding section indicates that considerable errors may
easily arise here, as the angle between the scribed mark and
the position of the correction to be made, varies rapialy with
changes of velocity near the critical value. In equation (2) , page
101, the angle between the displacement x and the alternating

force is found to be tan"1- — - _7 - . If a were zero, no angular

difference of position of the scribed marks would occur ; this
damping coefficient — due to friction at the bearings and air
resistance — always exists, so that the numerator of the fraction
always has some (small) value, and hence there is always
angular lag. The denominator depends upon the difference
of the squares of the periods in question, and this is very
small in the neighbourhood of the critical speeds, so that at

them, although the damping is small, the angle tan'1^— — — =

o — win k

approaches a right angle, and a little difference in the rate of
revolution in the two directions will make much difference
to the position midway between the two marks.

These various difficulties lead to a method of trial and error
in the balancing of high speed rotating parts, the shaft being

110 GKINDING MACHINEKY

tried and balanced, and then tried again until a sufficiently
accurate running balance is attained.

The Universal Grinder— Description.— From the lathe fitted
with a grinding head on the slide rest to modern manufacturing
grinders has been a long development, first resulting in grinding
machines, termed Universal, and capable of dealing with very
varied work, for the tool room, and later in machines for more
specialised purposes. As the Universal Machine was developed
first, and presents many typical features, it will be well to con-
sider it first, taking as illustrative of modern practice Messrs.
Brown & Sharpe's machine, No. 1 size, which is illustrated in
Figs. 29 and 30. This machine is capable of grinding external
work, parallel and of any angle of taper, internal work, flat
work held on a face-plate or in a chuck, and of sharpening
certain classes of cutters. In Fig. 33 outlines of the machine
and countershafting are given, showing the arrangements for
driving the various parts.

The development, it is seen, has produced a machine with
practically no resemblance to a lathe, carrying a grinding
head ; this is accounted for by the very different forces involved,
and the special need in grinding for accuracy, freedom from
vibration, dust protection, for dealing with a large water supply,
and general convenience.

The illustrations show the machine arranged for external
grinding. The work is carried between the centres A, A' of the
workhead B and the tailstock C, and is rotated by means of the
dead centre pulley E, which is driven by the belt uf. The tail-
stock C carries the diamond tool by means of the clamp D,
which holds it firmly while the wheel is being trued.

The tailstock barrel is held up to the work by a spring
having an adjustable tension, and can be withdrawn from the
work, to free it for removal, by the lever C '. For the purposes of
face-plate and chuck work, when the pulley F is used for driving,
the headstock spindle is rotated in bearings (see Fig. 117,
page 279) but for work between centres the spindle is locked by
the plunger G, and the pulley E revolves upon the fixed spindle.
The accuracy of the roundness of the work thus depends upon
that of the centres themselves only. These can easily be ground

112 GRINDING MACHINERY

up true by swivelling the workhead B over on its base B' to the
correct angle, as indicated by the graduations, putting the centre
in the centre hole of the spindle, and driving the latter by the
pulley F. The headstock BB' and tailstock C are carried on a
table H, which swivels about a vertical stud at its centre, upon
the main slide J, the angular adjustment being controlled by
the knob K. Two plates K', K", hold the table to the main
slide, and the plate K' carries a divided plate giving the amount
of the angular adjustment. The main slide J slides on the body
L, L', which, for convenience, is made in two parts, the upper L
containing the feed mechanism, while the lower L' is fitted as a
tool cupboard. The work is thus carried, as it rotates, to and
fro in front of the wheel, which is stationary.

Travelling Wheel and Travelling Work.— In the lathe it
is the tool, and the grinding wheel where that is substituted
for the tool, which is traversed over the work. Geometrically
it does not matter which is traversed relatively to the other,
and grinding machines are manufactured on both systems ;
one in which the wheel traverses is illustrated in Fig. 110,
which is a view of the No. 3 Universal Grinder of the Landis
Tool Co. The parts are lettered to correspond with those of
the machine now being described, and some further reference
to them will be found on page 270.

Practically each system has its advocates, both among
manufacturers and among users, and which is the better is an
undecided point, or perhaps a matter of personal preference. My
preference is for the moving work type for all but very large
work : partly because I consider it better to have the position
of the cut stationary, so that one can watch it if need be without
oneself moving, and because I prefer to have the cross-feed
handwheel and gear in one fixed position ; partly because
I think that the accuracy of response of the wheel to the move-
ment of the cross-feed hand wheel and ratchet is more accurate
if it is not subject to the stresses involved in the reversal of
movement ; partly because vibration arises more frequently
from the wheel than from the work, and that therefore the
less freedom it has the better ; and partly because, according
to my calculations, wear, provided the design is correct,

THE WOKK AND THE MACHINE 113

produces less inaccuracy in the work. On very large machines
the travelling work type, however, is more expensive to con-
struct, and it also occupies much more shop room. As
representing the other point of view, the arguments are, first,
that the work is supported directly on the body of the machine,
as the work table, even when swivelled, has no overhang,
and is practically solid with it, and secondly, that there is
considerable saving of floor space. Also occasional very long
work can be ground, supported by external temporary fittings.
Strenuous advocates of the system further claim that the
weight of the moving parts being fixed, the reversals are
more accurate (for reversing, see page 116), and also it does
not overstrain the reversing mechanism, as the slide carries a
constant load ; that the design ' favours a heavy main and
cross slides to reduce vibration of the wheel head ' ; and
that unequal wear on the main slide is avoided.

Taper Work by Swivelling Work Table.— The headstock
BB' and tailstock C are adjustable along the table H to suit
work of various lengths, and are guided by tongues in a T
slot, so that the axes of the centre points lie on one line. For
taper work the table H is swivelled on the main slide J, and
this setting of the axis of the work at an angle to the line of
travel produces the taper of the work, whether the work or
the wheel has the traversing motion. This is shown in plan
in Fig. 31, where the wheel is supposed stationary, and the
work to be moved parallel to the line of the main slide — the
lowest line on the figure. This shows how the taper is pro-
duced, and as the motion is a relative one between the work
and the wheel, it is clear that this applies to either of the two
cases — the work or the wheel actually travelling. This device
of swivelling the table keeps the centres in line with one another,
which is necessary to avoid trouble in attaining the accuracy
desirable.

If the machine were required for parallel (i.e, straight)
work only, still it would be necessary to have a fine adjustment
for parallelism ; for on moving the headstock or tailstock,
microscopic particles of grit might lodge on the aligning surface,
and thus disturb the position on clamping. Any error would

114

GKINDING MACHINEKY

be doubled on the diameter of the work, and hence the necessity
for a fine adjustment to correct for this. On large machines,

FIG. 31.— TAPERS BY SWIVELLING THE WORK TABLE

designed for parallel work only, this adjustment is made (as is
usual in lathes) by fitting the tailstock to set over.

For taper work the wheel has to grind the work at a point

THE WOEK AND THE MACHINE 115

' level ' with its axis, else errors similar to those produced
by setting a lathe tool below the centre on taper work are
produced.

Where the machine is designed for quite small work the
table may be swivelled, if provided with a suitable fine adjust-
ment to the movement, to 45°, and so all degrees of taper
ground. On larger machines this would involve much over-
hang and liabilityto vibration, so that the more abrupt tapers
are obtained by swivelling the wheel slide, as described later.

The ways by means of which the body L carries the main
slide J consist of a vee M and a flat M', as can be seen in the
view in Fig. 33, and also in Figs. 75 and 76. While main slide
ways are often of other types (see Fig. 105), this is a very
convenient one. There are no gibs, and the surfaces are kept
in contact by the weight of the parts only, with the result
that the slide runs freely, and is not subjected to the forces
which are liable to be introduced by the adjustment of a gib.

Types of Ways — Slide Fitting.— For precision work the
ideal method of producing a slide is by the simple intersection
of two planes ; on scraping up these a straight line way is
produced, accurate to the degree of accuracy of the planes.
This construction, if suitably arranged for a grinding machine
main slide, would present difficulties in the lubrication, and
accordingly the vee and flat is preferable. On small hand-
operated machines, where the pull of the work belt may lift
the table and main slide, the latter is best gibbed. Whatever
be the actual type of ways, it is upon the perfection of them
that the straightness (i.e. uniformity of diameter if parallel,
or straightness of generator if taper) of the work depends.
In this machine the length of ways on the body and slide are
nearly the same, which causes the least trouble from wear in
the smaller machines ; on large machines it is best that the
body ways should be relatively longer. In the machine shown
in Fig. 84 the body ways are very much longer, being nearly
double the length.

The table motion is derived from the speed cone N, which
drives a bevel gear reversing mechanism in the case P, and so
ultimately the table by means of a pinion and a rack fastened

i 2

116 GKINDING MACHINEKY

to the main slide. For setting the work the table is operated
by the hand wheel Q, which is connected through gearing
to the table when the knob K in its centre is drawn out ;
when this knob K is pushed in the hand wheel Q is free, and the
automatic feed is connected with the table. The movement
of the main slide J is reversed by the action of the dogs S, S',
whose position is easily adjusted — and which contain in them-
selves a fine adjustment — operating the reversing lever T, the
movement of which acts on a ' load and fire ' mechanism, which
shifts a clutch in the reversing mechanism at P. The action
of such a mechanism is shown later (see Fig. 52, page 157).

Precision of Reverse. — As most work has shoulders upon
it, and it is desirable to go close up to them in the reversing
when grinding, the precision of the reverse is important.
The variation of the position of the main slide at reverse
is to be divided into two parts, one due to the reversing
mechanism, and the other affected by the momentum of the
main slide and what it carries. The latter depends on the
table velocity and on the lubrication of the ways. Just after
the clutch ceases to drive, the table is free and runs on a dis-
tance x given by the equation JM-y2 = jjMgx, where M is the
mass of the table and all it carries, v its velocity, //, the co-
efficient of friction of the ways, and g the acceleration due to

v2
gravity. Hence x = ^ — and does not depend on the weight

of the slide or table, or of the work. If v = 60 inches per minute
and yu, = 0-035 inch, then x = 0-037 inch, or about -fa inch. In
actual running at any speed this will only vary as //, varies,
owing to the variation in the lubrication of the ways ; but if the
speed be altered to 80 inches per minute the new over run would
be 0-065 inch, or TV inch, so that the table would run 0-028 inch, or
nearly ^ inch farther. It is wise, therefore, if the reverse is
close to a shoulder, to make it a little earlier (by using the
fine adjustment of the stops) before increasing the speed
of the traverse. In the illustration it will be seen that
the stops are located by a rack ; this prevents their slipping
when moving the reversing lever over, which happens if the
stops are held by a frictional lock and the operator forgets

THE WORK AND THE MACHINE 117

to tighten it. If, however, such a lock is well designed, very
little tightening will secure it against the risk of slipping.

Turning now to the wheel head, we see that the spindle
is arranged to carry either a wheel U at the centre, or one
overhung at one end of the spindle at U'. In the case of Universal
machines the position between the bearings enables certain
taper work to be done more easily, and it also (very slightly)
reduces the effect of the oil film in the bearings. The over-
hung wheel is far easier to change, and in plain machines for
external grinding it is practically exclusively used. In this
machine the spindle with its bearings complete (see Fig. 34,
page 125) can be removed from the machine by unclamping
the caps V, V, and after the wheel has been changed it can be
replaced without distortion, as the outer cases of the bearings
have spherical seats. The wheel head W which carries these
bearings is adjustable on the plate X, which swivels on the
cross slide Y. The lower ways Z of the cross slide can in
turn swivel on the body of the machine ; this adjustment is
graduated, and is that used in grinding abrupt tapers on work
between the centres.

Quick Tapers. — In Fig. 32 is shown a plan of the wheel
head with the cross slide thus set over grinding a taper of
45° aside on work between the centres ; the movement for
traversing is in the direction of the cross slide travel as shown
(parallel to the face being ground), and is operated by the
cross-feed mechanism.

In grinding tapers by this swivel adjustment of the cross-
ways the traversing is done by the regular cross-feed motion,
which is very slow, and the cut is put on by the hand wheel,
which in regular use traverses the main slide. The angle of
the cross-ways is set as closely as possible by eye, but the exact
taper is finally got by the use of the swivel adjustment K to
the work table.

The wheel head is here shown swivelled on the cross slide,
so that its axis is parallel to the cross slide ways. This is
not necessary, but it is desirable, as otherwise all end play must
be taken out of the spindle.

When the taper work (external or internal) is held in a

118

GRINDING MACHINERY

chuck or on a face plate, the upper part B of the work head is
swivelled, not the cross-ways. In this case the work is traversed
by power, as the main slide is employed and the cut put on by

FIG. 32. — TAFERS BY SWIVELLING THE CROSS-WAYS

the regular cross-feed. This avoids the inconvenience of
traversing by use of the fine cross-feed, and the difficulty of
putting on the cut properly by tapping the main traverse
hand wheel.

THE WOKK AND THE MACHINE 119

Without altering the setting of the cross slide the parallel
portion of this piece of work could be ground, using the main
traverse of the machine. In this case the reduction of diameter
does not correspond to the graduations of the cross slide, but
is less than these by the factor sin a, where a is the angle
(aside) of the taper, which is shown as 45° in the figure. For
example, at 30° the actual feed of the wheel normal to the
surface of the straight portion of the work would be only half
that indicated by the graduations, and at 14° 30" it would be
only a quarter. This is sometimes taken advantage of in
grinding gauges where a fine cross-feed is desirable.

In all setting of the machine for tapers and back again for
parallel work, the adjustment should first be made on the
graduations as closely as possible by eye, but the final test has to
be the fit to a gauge, or the measurement of the ends, and to
make the final adjustment the knob K is used. As the accuracy
aimed at is a fraction of a thousandth of an inch, setting by
eye is not only hardly precise enough, but the result may be
vitiated by the accidental presence of a particle of grit between
the headstock or tailstock and the aligning ways of the table.

As the wheel head is used in various angular positions the
spindle pulley has flanges. The cross slide is gibbed, as the
tension of the belt driving the wheel head is in some positions
considerable ; accurate response to the movement of the cross-
feed disc is very desirable, and it is essential that the lubrica-
tion be not neglected, and the slide should be moved now and
then over its whole range. The motion from the cross-feed
hand wheel a is transmitted through a worm and worm wheel,
through a vertical shaft along the axis of the swivelling adjust-
ment of the cross-ways, and operates the cross slide by a pinion
and rack.

The Cross-feed. — The cross-feed is arranged with an auto-
matic feed, which is operated at the reversing of the table,
through the cross-lever &, which by means of a ratchet and wheel
turns the cross-feed shaft. The smallest amount of the cross-
feed, which corresponds to one tooth of the ratchet, is the
8-0*0 o of an inch movement, representing ^-oV o~ °^ an mc^ on *^e
diameter of the work, which is a convenient amount in view of

120 GRINDING MACHINERY

the limits required by the conditions previously considered. An
automatic throw-out consisting of a shield, which prevents the
ratchet from action, is fitted, and its position is easily adjust-
able, both for considerable differences of position and for the
small amounts corresponding to the wear of the wheel. On
external work, where the size of wheel is not limited by the size
of the work as it is in internal grinding, the wear of the wheel is
in many cases negligible and, if the cross-feed mechanism sizes
correctly, repetition work can be ground rapidly to size with
hardly any time spent on measuring. Cross-feed mechanisms
are referred to in more detail in a later chapter.

Provision for Wet Grinding. — The grinding fluid is circulated
by means of a centrifugal pump c, having a vertical spindle,
driven by the belt r' over the idler pulleys d, d' ; it is delivered
on to the work at the grinding point by the pipe e and the nozzle
/, and then is drained away by the guards g to the channels and
tray, whence it flows back into the tank h, in which the pump is
placed. The guards g — which are shown loose in Fig. 29—
consist of a number of joggled loose parts, which are built up on
the table to suit any particular length of work, in the manner
shown in Fig. 30. At the rear are two removable guards j, j', to
catch the spray and splash.

Steadies. — When slender work is being ground, although the
force of the cut is small, it is apt to vibrate, which leads to chatter
marks ; to prevent this, and also to enable such work to be
ground quickly, it has to be supported by steadies. Two of
these, k, k', are shown in position in Fig. 30, and on the floor in
Fig. 29. They are adjustable, so as to support the work under-
neath and opposite to the wheel, and by their use the work can
be sprung if desirable, as it sometimes is.

When the machine is used for internal grinding the work is
done dry, all the water fittings being removed. The dead centre
pulley is replaced by the chuck or face plate, and the wheel
head by the counterhead I and internal grinding spindle and
bracket m, all of which are shown on the floor in Fig. 29.

Arrangement of Driving Mechanism.— The machine is
driven from the source of power by means of the fast and

THE WOEK AND THE MACHINE

121

loose pulleys n, n', on the first shaft. This drives the grinding
wheel by way of the step cones p, p', and the pulley q on the
second shaft and the belt q', thus providing two speeds for
the wheel spindle. This second shaft also drives the pump
by means of the pulley r and belt r'.

FIG. 33. — BROWN & SHARPE No. 1 UNIVERSAL GRINDER. ARRANGEMENT

OF THE DRIVE

The first shaft drives the work by means of the step cones
t, i' , and the drum u on the second shaft and belt u'. An addi-
tional belt is shown on the left-hand hanger carrying the drum
shaft, which is for use with the small size dead centre pulley,
which is shown on the machine in Figs. 29 and 30. The step
cones provide four work speeds, but the number is increased
by the provision of two dead centre pulleys of different

122 GEINDING MACHINEKY

diameters. The step cone t is engaged by means of a friction
clutch operated by the shipper bar and slider v'. This shipper
bar is operated by the handle w, conveniently placed on the
machine body, through the connecting rod (pipe) w'. After
taking the friction clutch out of action, the continued move-
ment of the lever w brings a friction brake x into play, and
stops the rotation of the drum quickly, and prevents it having
a tendency to start rotating while the work is being measured.
The third (drum) shaft carries at its end a step cone y, which
drives the traversing mechanism of the table through the
belt y' and step cone N.

It will be noticed that here the work is driven by a belt
which moves along a drum as the work traverses ; in the case
of machines in which the wheel head traverses, it is the belt
to the wheel head which moves along a drum. Here the change
of speed for the wheel and the work are both obtained by
shifting belts on step cones in the countershafting, but in
Chapter VI some alternative arrangements are shown, which
aim at rendering the change of speed easier and more rapidly
effected. This Universal machine has been steadily developed
to its present perfection by Messrs. Brown & Sharpe, and is
intended for tool-room use. It should be compared with the
Landis Universal Grinder (see Chapter VIII), which is designed
for the same purpose. A knowledge of these - types forms
a convenient point from which to survey the trend of develop-
ment of the modern manufacturing grinders.

Several of the arrangements on this and similar machines
have been designed and developed to meet the particular
needs of grinding machines, and these we will now proceed to
examine more minutely, noting the variations produced by
the modern trend towards the employment of machines of
more limited scope, and towards the external, internal, and
flat work being done on different machines.

CHAPTEK V

DETAILS OF PARTS

The Wheel Spindle. — The quality of the work produced by a
grinding machine largely depends upon the wheel spindle.
Compared with the work spindle of a lathe, the wheel spindle
runs at an exceedingly high velocity, but the direct forces
applied to it are comparatively small ; compared with other
fast-running spindles (such as steam turbine shafts), the fit
in the bearings has to be very close. In the design the pro-
tection of the bearings against the entrance of grinding fluid
and grit, the lubrication, and adjustment must be efficiently
provided for, and the material and workmanship must be
of high quality.

In Figs. 34, 35, 36, and 37 are shown typical spindles,
.which illustrate modem practice, being the spindles of
Messrs. Brown & Sharpe's No. 1 Universal, Messrs. The
Churchill Machine Co.'s Plain, the Landis Tool Co.'s Universal,
and Messrs. Pratt & Whitney's Vertical Surface Grinder. In
the first three the edge of the wheel is almost always used ;
in the last the face alone. In all these the journals are parallel,
and few makers use conical type bearings. One is illustrated
in Fig. 38, the spindle of the Blanchard Surface Grinder. In
the parallel type the side and end adjustments are quite
independent, and when the wheel is used upon its edge, the
play (side) of the spindle possible is only that due to the thick-
ness of the oily film. If the journals are conical, the longitu-
dinal expansion (differential only as it sometimes is) affects
the side play, and difficulties in obtaining a high finish to the
work are apt to occur ; also the distribution of the oil in
the film is adversely affected by the centrifugal effect, which
tends to force the oil to the large end of the taper, and so out
of the bearing. Constructionally parallel journals present the
advantage that they can be properly lapped, while the conical

123

124 GKINDING MACHINEKY

type cannot be lapped so efficiently (see page 391). Practice
differs as to whether the spindle should be hardened (as it is
in the spindle of Figs. 34 and 36), or simply of heat-treated
spindle steel. The former undoubtedly requires more care
"in the manufacture, but the hardened surface is very much
harder, takes a better finish, and has a longer life, so that I
consider it decidedly to be preferred. If the spindle is of
hardening steel, the threaded parts must be made true after
hardening, so that the parts where they occur must not be
hardened, or must be softened afterwards, as the whole spindle
must run very exactly true ; if the journals are case-hardened
(which I prefer), this difficulty does not arise, but the case-
hardening must be properly conducted, otherwise surface
defects may develop. It is often alleged against hardened
spindles, particularly if of hardening steel, that the material
tends to distort in course of time ; if proper precautions
(see page 93) are taken, this tendency is exceedingly slight,
and the number of hardened spindles which are giving entire
satisfaction in use is an answer to the argument. The journals
should be lapped after grinding to make them as perfect as
possible, and to remove the small marks of the grinding,
which tend to cut the bearings. Some makers form oil
grooves in the spindle, but regular practice is opposed to this,
as are the phenomena displayed by oil in bearings in such
experiments as those of Mr. Tower.

Wheel Spindle Bearings. — In the designs of Figs. 34 and
35 the bearings (bronze) are taper on the outside, and split
through at one side ; to adjust for wear, the nut A at the
large end of the bearing is slackened, and then the bearing
is drawn into its taper seat, and so closed to the spindle, by
tightening the nut B at the other end. Finally, the adjust-
ment is secured by locking with the nut A. The second bearing
— in which the letters correspond but are marked with a dash —
is adjusted in the same manner. In Fig. 35 the split in the
bronze is dovetail shape, and the adjustment of the bearing
further secured by tightening the dovetail clamps, LM, L'M',
by the screws shown at NP, NT'.

Wheel spindle bearings should run warm, and the tempera-

DETAILS OF PAETS

125

ture attained is a convenient check on the correctness of the
adjustment. The finer the finish desired on the work, the

closer should be the adjustment of the bearings, and the
warmer they should run. This design of bearings renders ad-
justment very convenient, and lends itself well to lubrication

126

GEINDING MACHINEEY

arrangements. The split bushes with taper outside, I also
consider as very suitable for the bearings of spindles for

DETAILS OF PAETS

127

internal work, but the particular arrangements of the nuts
above illustrated cannot well be employed.

128 GKINDING MACHINEKY

In the spindle of the Landis Tool Co.'s Universal
Machine, Fig. 36, the side adjustment is made by removing the
screws A, taking out the liner B, scraping its surface, and then
replacing and tightening up the screws. This type of adjust-
ment is used frequently in the smaller machines, and the packing
liner is often made of wood, or even hard felt, which can be com-
pressed— in which cases the adjustment is controlled by second-
ary screws acting as a check and lock upon the closing screws,
an arrangement which can be seen in Fig. 170. In the Pratt &
Whitney Vertical Surface Grinder the bearings are of white
metal, and are of the cap type. The same type is employed
(see Fig. 127) in the Walker Single Stroke Grinder — also a
vertical spindle cup wheel machine.

In both the Universal Machine spindles, Figs. 84 and 36, the
bearings are self-aligning, the outer cases C, C' of the bearings
proper, D, D' in Fig. 34, having spherical seats, where they are
held by the caps E, E' to the wheel head body F. By releasing
the caps the spindle, bearings, and cases can be removed for
changing the central wheel, and on replacement the bearings
align themselves, and so do not strain the spindle. When
removing the spindle and bearings for this purpose, it is very
essential that no grit be allowed to get into them, and every care
should be taken to prevent it — particularly at the bearing at
which the end thrust is not taken, as it is free to slide along the
journal when lifted out of position. In the Landis design the
spherical seats C, C' are formed on the bearings D, D' themselves,
which are drawn on to the wheel head surfaces by suitably
arranged bolts E, E'.

In plain grinders the bearings D, D' are usually drawn
into tapers formed in bushes C, C' let into the wheel head E,
as in the Churchill design, Fig. 35, but Messrs. Greenwood &
Batley employ a self-aligning type, somewhat similar to that
of the Landis Tool Company, but with the bearings pulled
up to spherical seatings opposite to the contact of wheel and
work. In Fig. 63 the nuts of the bolts are to be seen.

Design for End Thrusts. — Ideally the end thrust should be
taken up over a short length only, as at F in Fig. 35, and
also in Fig. 36, but if it is taken over the whole length of a

DETAILS OF PABTS

129

bearing, as at over D
in Fig. 34, and pro-
vided with suitable
collars, the result has
always, so far as I
am aware, been satis-
factory. IntheLandis
design, Fig. 36, the
thrust is taken by
a stationary collar,
which is provided with
a fine longitudinal ad-
justment by means of
a graduated sleeve; by
this means the wheel
spindle can receive a
fine movement in the
direction of its length,
for the purpose of
grinding snap gauges
and such work, using
the side of the wheel.
In this case the end
thrust must be taken
up so as to leave no
play, but in work
where the curved face
of the wheel is used,
a slight degree of
end freedom is best
allowed ; it produces
no effect if the spindle
is parallel to the main
ways of the machine.
In machines where
the flat face of the
wheel is employed,
such as cup wheel

FIG. 37. — SPINDLE OF PRATT & WHITNEY
VERTICAL SURFACE GRINDER

130 GKINDING MACHINERY

surface grinders, the provision for takingl the \ end \ thrust
is very important, and it should be taken up as close to
the wheel as is possible, so as to minimise the effects of
temperature change. This is so arranged in the Pratt
& Whitney vertical surface grinder spindle, Fig. 37 ; the
direct thrust is taken on a ball-bearing thrust washer A, and the
end play is taken out by another ball and thrust washer B at
the rear of the main bearing ; this is held up to position (and
also thereby holds the main thrust in position, when there is no
end thrust from work on the spindle) by means of ^a set of springs
at C. This eliminates the effect of temperature on the amount
of end play and — except so far as the initial tension in the springs
is concerned — does away with the need of adjustment for end
thrust. The spindle driving pulley D is carried on an indepen-
dent bearing E, as is customary in good practice in belt -driven
drilling machines, so that the belt pull does not come on the
spindle and its bearings. The spindle is driven indirectly from
the pulley through the collar F, and slides through the upper
bearing, as the head H, carrying the lower bearing K, is adjusted
vertically to suit different thicknesses of work, or for feeding.

In Fig. 38 is shown the spindle of another surface grinder,
the Blanchard, in which the whole spindle head is carried on the
vertical slide, and moves as a unit. The spindle A is carried in
a taper bearing B at its lower end, and by a ball bearing C at its
upper ; the direct end thrust of the wheel is taken on a ball
thrust bearing at D as near to the wheel as possible ; the com-
pletion of the thrust bearing is at the upper end of the spindle
by the spherically seated ball thrust washer E, which is held
to its seat by the springs F, which thus keep the lower ball
thrust D tight up, as in the previously described design.

The main bearing here is a taper bearing, and is adjusted
to the spindle by the nut G : the raising of the bronze bush
making it fit the spindle more closely, as the spindle A is held
endways by the thrust at D. The centrifugal effect here
carries the oil up the bearing, so that it aids the circulation of
the oil, which follows the course indicated by the arrows. In
this case the main journal here has an oil way cut in it. General
views of these vertical surface grinders are given in Figs. 125, 126.

DETAILS OF PAKTS

131

Lubrication. — Grinding spindles not only run at a high speed,
but the fit of the bearings to the spindle is very close, so that the

FIG. 38. — WHEEL HEAD OF BLANCHARD VERTICAL SURFACE GRINDER

arrangement of the lubrication is important. In Fig. 34 the
oil supplied through the hole GG' at the top runs round the
bearing bushes D, D', and is distributed along the length of the
bearing by the capillary action of pads H, H' in the slot, which

132 GEINDING MACHINEEY

is here arranged to be at the bottom of the bearing. It is
prevented from flowing out by means of the wood strips J, J^

In the Churchill spindle, Pig. 85, oil. wells are provided,
into which lubricating rings Q, Q' dip and carry the oil to the
top of the journal. After lubricating the spindle the oil is
returned to the reservoir by the passages shown. By means
of a neat but simple device of arresting the sideways motion
of the ring by a suitably placed point, the rings are caused to
twist slightly at each end of a sideways traverse. This twisting
causes them to traverse axially over the width of the oil chamber,
and so distribute oil over that length of the top of the journal.
On reaching the end, and meeting the projection there, the ring
is twisted so that it travels back again. In the sectional
views, the spindle K, bearings D, D', bearing bushes C, C', and
the wheel head E are shown, and also the holes E, E' for ascer-
taining that the oil reservoirs are filled correctly, and the holes
S, S' for emptying them. The open slot of the bearings is here
seen at the top. Shallow screw threads, shown at T, U, T',U'
in the sectional view, prevent the escape of oil at the ends of
the bearings.

In the Landis design, the oil supplied through the hole G
at the top runs round the circumferential groove H to the
longitudinal grooves J, J' at the bottom of the spindle K, and
so is distributed along the journal.

In the spindle design of the Pratt & Whitney machine, the
oil for the main bearing is fed through an ordinary lubricator,
and slowly passes through felt washers L, Fig. 37, into the
longitudinal groove M. The upper spindle bearing and pulley
bearing are lubricated in a similar manner, but felt washers
are not employed.

In some cases I prefer direct oiling by means of sight feed
lubricators, an arrangement which is seen on the Landis head,
Fig. 36, and on Messrs. Greenwood & Batley's, Fig. 62. The
oil can then be supplied at any desired rate continuously, and
it is clean oil, provided the sight-feed lubricator itself is dust-
proof ; as such lubricators are usually intended for other
purposes, and are subject to the conditions of competitive
manufacture, such is not always the case. Grinding conditions

DETAILS OF PAETS 133

require such accuracy that the cutting of a wheel is affected by
the addition of oil to that already in the lubricating system, so
that the rate of supply of oil must be uniform. If necessary
the supply may be stopped while finishing a part.

Although the spindles are a very close fit in the bearings,
there is some space between the surfaces which the oil occupies ;
the spindle when running does not set itself exactly central,
but the oil film varies in thickness round the circumference of
the bearing. Varying forces, such as caused by vibratory
jerks of the belt, or due to want of balance in the wheel, make
the spindle alter its position in the bearing, the thinnest oil
space changing its position. The result is a series of chatter
marks on the work.

The spindles require good lubrication, as they run at a high
speed, although the load is low ; and the oil used should be
light, so that the space between the spindle surface and
the bearing may be as small as possible. When a perfect
oil film exists, it is not of uniform thickness all the way
round, but the spindle sets itself so that the film is thickest
on the intake side — that is, before the line where the result-
ant force on the spindle axis cuts the bearing. The pressure
in the oil film also varies, and is a maximum behind this point
where the resultant force on the spindle axis cuts the bearing,
and the pressure diminishes from the centre towards the
edges of the bearing. If a hole is drilled in a bearing to a
point of high pressure, oil will flow out, and it is impossible to
lubricate a spindle at such a point unless the oil is supplied
at a head exceeding that which corresponds to the pressure.
Thus the selection of the points at which oil is fed into bearings
is very important, and should be made upon the principles
mentioned above, founded on the researches of Mr. Tower
(' Proc. I. M. E.,' 1883, 1885, and 1888), Prof. 0. Reynolds, and
Mr. Lasche. In these experiments, however, a half bearing only
was used, and the fit was not close like that of a machine tool
spindle. The first experiments were on slow speed bearings,
but those by Mr. Lasche (' Traction and Transmission,' Jan.
1903) extended to the speeds used in grinding machines.
The effect is most enhanced in the high speed bearings of

134 GKINDING MACHINEEY

spindles for internal grinding, where, if it be attempted to
feed oil to the bearing at a high pressure point, it refuses to go
near, and if the spindle be oiled when stationary the oil is
promptly pumped out as the spindle gains speed.

Protection against Grit. — It will be noticed that in Fig. 34
the adjusting nuts are curved in towards the spindle at their
sides ; in Fig. 35 the headstock has a groove formed in it,
which is covered by a projection of the wheel collet, and in Fig. 36
the wheel collet is deeply recessed, and the bearing projects into
it, so that the bearing is protected from the entrance of gritty
fluid. In the latter cases, Figs. 35 and 36, the end thrust bear-
ing is completely enclosed. Similar arrangements are used on
the spindles for internal work, shown in Figs. 42 and 43.

Position of the Wheel.— The central position of the wheel
between the bearings, as in Fig. 34, makes it possible to grind
some cases of taper work between the centres more easily ;
the effect of the oil film is also minimised, as there is no multi-
plication by the leverage of the overhang. The advantages,
however, are so slight that it is generally considered that the
convenience of easily changing a wheel at the end of the spindle
without disturbing the bearings in any way, outweighs them,
and in plain grinders, at any rate, the position of the wheel is
so arranged.

Spindles for Internal Grinding. — Turning now to the spindles
for internal grinding, we find very severe limitations and condi-
tions are imposed on the design by the nature of the case. To
produce a desirable circumferential speed at the wheel the rate
of revolution of the spindle must be very high, and requires
6350 r.p.m. for a 3-inch wheel and 19,000 r.p.m. for a 1-inch
wheel to give 5000 feet per minute to the wheel edge. Usually a
somewhat lower speed is used, but still it is a very high one. As
the wheel has to grind a hole, either the spindle must project
from its bearings and carry the wheel considerably overhung,
or else the support for the bearing at the wheel end must be
small enough to go down the hole, which arrangement allows
little room for the bearing and adjustment. In all but the
smallest sizes such a supporting sleeve carrying a bearing near the

DETAILS OF PAKTS 135

wheel is desirable, as the amount of play at the wheel is then that
due to the wheel end bearing, and is not intensified by the amount
of overhang. There seems to be an ' impression ' that the
sleeve is a stiffer construction in itself, but this is not the case —
a solid spindle of the sleeve diameter must be the stiffer, as
splitting it up into sleeve and spindle would increase the
number of degrees of freedom. The stiffness in any particular
case can be calculated.

Whatever may be the opinion as to the desirability
of hardened steel for the larger spindles, there seem to be
few objectors, at any rate among the users, to its employment
for these small spindles. The bearings are almost always of
phosphor bronze.

Typical designs of internal spindles are shown in Figs. 39,
40, 41, 42, 43, 44, and 45, of which Figs. 39 and 40 are by
Messrs. Churchill, Fig. 41 by Messrs. Brown & Sharpe, and
Fig. 42 by Messrs. Heald, while Figs. 43, 44, and 45 represent
two of my designs, given as illustrating special points.

In Fig. 39 the spindle A is supported close to the wheel
by a bearing C, which is carried in the sleeve D ; and as it
wears the bronze bush C is closed by pressing it into the taper
recess of the sleeve by means of the nut E. The other, en-
larged, end F of the sleeve D, is gripped in the supporting
bracket, and in it is carried the support G for the rear bearings
H, K, of which there are two, on opposite sides of the driving
pulley J. By removing the support G from the tube, and the
cap L, the bearings H, K can be adjusted by the nuts M, N
respectively. The chief force on these small spindles is that
due to the wheel belt, particularly as the tightness of the
belt is adjustable by the operator of the machine. Carrying
the pulley between two bearings distributes the effect of the
tension over them, and this construction is used also in the
spindles of Figs. 29, 40, and 42. There is, however, in this
construction a little more difficulty in the dust proofing, and
the added difficulty of making three bearings collinear. A
way out of this last difficulty is to make the pulley spindle
co-axial with, but separate from, the wheel spindle, and
to connect them with a flexible coupling ; a simple form of.

138 GEINDING MACHINEKY

approximating to this is illustrated in Messrs. Brown &
Sharpe's spindle, Fig. 41. Here the internal spindle proper B
has a reducing projecting end centred in the pulley spindle C,
and is driven by a tongue and groove. Here the rear bearings
—those of the pulley spindle — are the regular ball journal
bearings D, D', and the larger is within the driving pulley,
and thus takes the pull of the belt.

The front bearing E is of the outside taper type, and is
adjusted by being pressed into the female taper of the sleeve
F by the thrust of the collar H, when the sleeve F is screwed
in — the collar H being prevented from moving by the inner
tube G. This operation first takes out all the end play, and
then closes the bearing E. The sleeve F is knurled on the
outside so that it can be turned easily. When this has been
adjusted, the sleeve F is unscrewed sufficiently to free the
collar H, and make it a running fit. This sleeve F which
supports the wheel end bearing is carried in the bracket, and is
clamped after adjustment.

In both designs, Figs. 39 and 41, the wheel bearing is oiled
from the bracket, the fluid travelling up the inside of the
sleeve. Where the bearing is so close to the wheel, too much
oil should not be given to the bearing, as a drop getting on
to the work causes the wheel to choke, and hence delay. In
the design of these spindles, there is a bearing close to the
wheel, and the spindle is small there, but in Figs. 40, 42, and
45 are illustrated spindles in which the wheel is overhung
from its bearing by the length greater than the depth of the
hole.

Fig. 40 shows Messrs. Churchills' ' Adapter ' spindle, which
is a heavy hollow spindle A of such dimensions that wheel
holders B of various lengths and diameters can be fitted to it,
and so that the projecting part of the spindle may be suitably
stiff for the work being done. The wheel holder B is drawn
to the taper seat C by the draw-in rod D running through
the spindle A. The limitations on the bearing construction,
which are enforced by the allowable size of the sleeve in Figs.
38 and 40, here do not apply, and the type of bearing is that
previously described in connection with the larger spindles

DETAILS OF PARTS 139

of Figs. 34 and 35, and has the advantages of easy adjust-
ment and independence of the side and end play. It will be
noticed that the pulley has a taper fit to the spindle, and
is held by a nut. The end thrust is taken on the rear
adjusting nut of the back bearing, and is entirely enclosed
by the cap.

The Heald ' Style A 1 ' internal grinding spindle is shown
in Fig. 42, where the spindle A is supported by three bearings
B, C, and D, and carries the wheel E, overhung from the nearest
bearing B, by the reduced part F of the spindle itself. The
bearings are all of the parallel inside, taper outside, split type.
The wheel end bearing B is carried in the sleeve G, and is
adjusted by the nut H, the turning of which moves the bearing
B both into and out of the taper of the sleeve G positively,
the bearing and nut being connected axially, as the shoulder
K of the bearing lies in the recess L in the nut H, and is held
there by the retaining nut M. When the bearing B has been
correctly adjusted it is locked into the taper of the sleeve G
by the taper wedge N expanding the slot, on the screws P, Q
being tightened, as in the bearings of Fig. 35. The sleeve
G is screwed firmly into the bracket R, which supports the two
rear bearings C, D, one on each side of the driving pulley.
The lubricating oil is distributed over the journals by the wicks
seen at S, and in the other bearings.

The spindle of Fig. 40 is fitted with wheel collets, so that
the collet and wheel may be removed together. In Fig. 39 the
wheel is carried on the plain part P of a screw, which fits the
spindle nose by a plain part Q, and so is supported firmly.
In neither case is the wheel put on the spindle nose itself ;
this should never be done, as small wheels cannot be held firmly
against slipping, and if that occurs when the wheel is on the
end of the spindle, the latter is worn away.

Reference can be made to Fig. 102, in which can be seen the
spindle of Messrs. Healds' cylinder grinder ; this is an altogether
longer spindle, but the construction is similar to that of
Fig. 42, there being three bearings, one close up to the
wheel, but the driving pulley is (necessarily) overhung at the
rear.

140

GEINDING MACHINERY

Supporting the Wheel Bearing in the most rigid manner. — In

order to call attention to one or two points, a drawing is given
in Fig. 43 of the wheel end of the larger internal grinding
spindles of my design.

Here the bearing A is closed for adjustment by the nut B,
and should the adjustment be carried too far, it is slackened by
unscrewing the nut B slightly and pressing the bearing out by
means of the collar G, the end adjustment of the spindle being
released for the purpose. The oil is carried to the bearing A

M N
FIG. 43. — GTTEST INTERNAL GRINDING SPINDLE

down the independent oil way D, and is delivered to the central
recess E of the bearing, and hence to the slot filled with a felt
pad, the location of which, in regard to the point of the cut,
is carefully arranged. The wheel collet has a conical fit to the
spindle, and protects, in conjunction with the nut B, the bearing
from the grinding fluid and grit. The nut has a projection
which is turned up (instead of down as in the design of Fig. 34)
so as to form a channel guiding the drops of gritty water away
from the bearing. The inside of the nut B is just clear of the
spindle, and has a shallow screw thread cut along it, so that
the rotation of the spindle tends to take out any oil which gets

DETAILS OF PAKTS

141

there, and so prevents the ingress of any grit. The adjust-
ment is locked by the nut F. The plan and end view show
that the sleeve differs from those previously described, in that
it is considerably eccentric to the spindle ; GH is the axis of
the spindle, while JK is that of the sleeve.

Before internal grinding was a manufacturing method, it might
be held that the stiffest sleeve which could be used on a parti-
cular hole and the largest wheel were obtained when the wheel
was nearly the size of the hole, and the sleeve just a trifle smaller.
This, however, is
not a commercial
arrangement, as it
allows for no wear
of the wheel. If
we arrange for a
reasonable wear
of wheel and then
consider how to
provide the utmost
rigidity, we are
led to a sleeve in
which the spindle
is carried off the
centre of the
sleeve. Suppose
that ABCD, centre
P, Fig. 44, is the

smallest hole for which the spindle is intended ; AEF, centre Q,
the initial size of the wheel shown just grinding the work ; and
AGH, centre E, the size of the wheel when worn to its small
limit, also shown just grinding the work. The adjusting devices
and sleeve, if concentric with the spindle, must then all fall
inside the circle AGH ; but if the sleeve be not concentric,
although the adjusting nuts will still have to fall within the
circle AGH, the sleeve body can extend from A to J, where K J=
PC. Then the sleeve, when the full-sized wheel was in use, would
just graze the work at C. Giving a little clearance, L J, we arrive
at AKLM, the circle indicated by section lines as the size of

FIG. 44. — ARRANGEMENT OF GUEST ECCENTRIC
SLEEVE

142 GEINDING MACHINEKY

the best circular section sleeve. The centre is atS, offset a distance
KS from the wheel centre. This is larger than the concentric
sleeve, as indicated by the shaded portion outside the smallest
wheel AGH. Its relative stiffness is very much greater than the
difference suggests to many, for the rigidity depends on the
moment of inertia of the section, and therefore is approximately
as the fourth power of the outside diameter. With practical
dimensions, allowing for the water way, it is about three times
as rigid as a concentric sleeve. Advantage is taken of the
facility offered for forming the water supply way in the metal
of the sleeve ; very little rigidity is sacrificed, as the position
of the hole causes its sectional area not to have much effect on
the moment of inertia of the total section. The water way in
the sleeve is shown at L, the water is delivered through it to a
nozzle, M, Fig. 43, which carries it round along NP and delivers
it on to the work (not the wheel) at T in Fig. 44, and the direction
of delivery is such that it runs along the work surface to the
grinding point.

Ball Bearings. — Ball bearings have frequently been used
for grinding machine spindles, but for the larger sizes are not
desirable, except for thrust bearings and for polishing heads.
They save power, and need less oiling, but this is of little moment.
The best work, which is the chief consideration, is obtained
with uniformity from parallel plain bearings. Where, however,
the rotation is very rapid, as in spindles for small internal
work, the quality of the work is less affected by the use of
ball bearings, and they are justifiable. In Fig. 45 is shown
my design for the bearings of these small spindles, in which
certain difficulties arising in earlier types I constructed
are avoided. In careful hands the previous type was
quite satisfactory, but the design illustrated is proof against
mal-adjustment. The bearings are of the three-point type,
and the spindle A is one piece only. The wheel end cup B is
fixed, the pulley end cup C slides, and is forced to position by
the spring D. This keeps the balls at this end up against the
cone E of the spindle, forcing the spindle to the left, and so
keeping the cone F and balls at that end in position. There
is no adjustment provided to be tampered with, and should

DETAILS OF PAETS

143

any temperature rise occur, its
effect is taken up by the action
of the spring. The pulley is
overhung, which makes the dust-
proofing easy. Though a sepa-
rate collinear en(J drive might
be preferable, it would be far
more expensive.

However an internal grind-
ing spindle for small holes is
constructed, no unreasonable
life should be expected from
it and its bearings. A spindle
carrying an inch wheel, if the
circumferential wheel speed be
the same, makes as many
revolutions in six months as
the spindle of a 14-inch wheel
does in seven years, and this
fact is often overlooked. To my
mind the best solution is — pro-
vided dust-proofing and lubrica-
tion are satisfactory — simplicity
of design, and such that the
wearing parts are of inexpen-
sive construction. It will be
noted that the wearing parts of
the bearings in several designs
illustrated are very simple and
cheap to replace.

Condition for slipping in a high
speed Ball Bearing. — In Fig. 46
is given a sketch of a ball bear-
ing. The spindle whose axis is
AB has the cone CD formed upon
it, and EFGH is the ' cup.' A
three-point bearing is shown, in
which the ball touches the

-CQ

144

GKINDING MACHINERY

cone at L and the cup at M and N. It is frequently stated
by writers in engineering books and periodicals that unless
the tangent to the ball at L, here CDB, meets the axis AB

FIG. 46. — SLIP-IN BALL BEARINGS

in the same point that MN meets it, there will be side-slipping
of the ball on the cone at the point L, though not at M and N ;
this, however, is not the case— there is no side slipping of the
ball in three-point bearings at slow speeds. If OLD and MN
do not meet the axis at the same point B, all that happens is
that the ball has spin round the normal LK at L just as it

DETAILS OF PAKTS 145

always has at M and N. In a high speed bearing, however,
the ball may slip on the cup and cone surfaces at all three
points L, M, and N, by rotation round an axis perpendicular
to the plane of the paper. The condition for slipping is to
be found as follows from the couple necessary to change the
axis of spin of the ball as it runs round. The cup is supposed
fixed and the ball centre K to run round its track with
angular velocity H. Let a = angle ABM, r be the radius
of the track of ball centre, fl' the angular velocity of the ball
round BMN, and mk2 its moment of inertia. Then, in the
lower figure, if P be the ball centre, draw PS perpendicular
to the spindle axis OB, and PO parallel to MN, to meet it
in 0. After a short time Bt let the ball centre get to Q. To
do this and then to be rotating about OQ, that is not to slip,
it must have angular acceleration co round QP, hence OPQ is a
triangle of angular moments, and we have —

~~ OP ~~ r cosec a

and .*. w = fl . fl' . sin a.

Hence from the upper half of the figure we have—
2 JJL Fa = mk2cb = HIV sin a . mk2

2 u. F = - . £l2 . sin a . mk2

^ -i-i / . IIVIH O9

or S F = r sin a . XI2

. ao

where 2 F is the sum of the three normal forces at the points
L, M, N ; a the radius of the ball ; b the length of the per-
pendicular from K on MN ; and /JL the coefficient of friction.
If XI exceeds the value given by this equation the balls
will slip on the bearing surfaces. Putting the equation in
revolutions per second and F in pounds weight —

2 F — -= — . 7r2n2rm

Wheel Collets. — As one particular grit and grade of wheel is
not suitable for all the work which may be required, the wheel
may have to be changed frequently. If this is the case several

146 GKINDING MACHINEKY

wheel collets should be provided, and the collets with the wheels
in them changed, and not the wheel only, as is necessary if a
single collet is used. This saves time and wheel material, as
with a collet the wheels come up so true when put on the spindle
that only a light cut with the diamond is necessary. It is
equally important that small machines, such as cutter grinders,
should be provided with spare collets, as on these machines the
wheels are changed 'very frequently. To ensure a fit free from
shake the collets for the disc wheels should have a taper fit to
the spindle, and preferably the central portion of the bearing
area should be removed, as shown in Fig. 35 at V. With the
correct amount of taper no key is really necessary, though one
is fitted in this case. On the larger machines the collet
should have an inside thread, as shown at W, Fig. 35, so
that it can be drawn off the spindle by screwing a recessed
threaded plug down the collet until the inside of the plug
meets the spindle nose and withdraws the collet from the
spindle.

The collets should grip the wheel close to the edge of the
flanges only, as is shown in Figs. 9, 35, 36, &c., and washers
of some yielding substance, such as blotting paper, put between
the wheel and collet flanges to distribute the pressure, or the
collet may be lined with white metal for the same purpose.
Wheels are now usually supplied with washers fastened to
them ready. It has been pointed out that the wheel must be
an easy fit, so as not to cause any bursting strains in its
material by forcing it into position.

In Fig. 36 the wheel is shown reduced where the collet grips
it, and the collet flanges are flush (or nearly so) with the sides of
the wheel. This entails the necessity of using specially shaped
wheels, which frequently take some time to procure, and so have
to be ordered well ahead of requirements, but in some cases
their use is very desirable. In crankshaft work, for example,
a wheel has to reach a long way down to grind a pin, and recess-
ing the wheel so that the collet flanges are below its sides
enables a wheel of much smaller diameter to be used. In such
collets the collet flange is tightened up to grip the wheel by
four screws, as shown at LL', more conveniently than by

DETAILS OF PAKTS

147

the single nut, shown in Fig. 35, securing the collet flange
there.

Holding Cup Wheels. — Chucks or collets for cup or cylinder
wheels are either mounted on a taper, as in Fig. 38, or screwed
nose of the spindle, as in Fig. 37, or — what minimises the distance
from the grinding edge to the thrust bearing — attached directly
to a flat collar formed on the spindle itself. The chuck shown
in Fig. 37 (the ' Pratt & Whitney Surface Grinder) is typical.

FIG. 47. — BESLY CUP WHEEL CHUCK

In mounting, the wheel is first placed on the plate N (removed
from the face plate for the purpose), and secured there by
shellac melted in position. It is then clamped down by the
ring P, with leather pads between the metal and the wheel, and
finally bolted to the face plate Q. The water supply in this case
is carried through the spindle, which is hollow, and receives the
supply from the tube, seen in Fig. 125, at the top of the spindle.
In Fig. 38 the water is supplied also to the interior of the wheel
by the passages shown at K and L. The wheel is secured by
cement at M to the plate N, which again is mounted on the face
plate Q. Owing to the porous nature of the wheels used, the

148 GEINDING MACHINEKY

inside of them is waterproofed with beeswax. In Fig. 37, close
to the edge of the wheel is a metal band, which can be
tightened on to the wheel by screws in its fastening ; this
should be set a short distance from the grinding edga of the
wheel, and acts as a safety device.

Chucks are on the market in which the wheel is gripped a
short distance from its working edge, and adjusted forward
when worn. They are more complicated than a simple mount-
ing, as described above, and, I consider, no more effective — in
fact, the average overhang from the thrust bearing is much
more. They have the small advantage of requiring no rear
wall or projection. One such, illustrated in Fig. 47, is the
pressed steel chuck of the Besly Grinder. As the wheel B
wears it is adjusted forward by the flange B, which is threaded
on D, and is then gripped by drawing the split ring A into
its taper seat in the chuck body C, by means of the screws
shown.

If the wheel is more of a cup shape — that is, has more wall at
the back — the fixing with shellac or other cement can be omitted,
but in large wheels the value of this extra piece has to be con-
sidered, as it cannot well be used on a Plain or Universal Grinder
as a disc wheel, as the grade generally necessary in a cup wheel
is much too soft for cylindrical work. For very large face
wheels, such as are used for grinding armour plates, wheels built
up of segments (either of natural or artificial stone) are used ;
the cost is less and the breaking-up of the wheel face enables
them to cut better. Such a wheel is shown in Fig. 10 ; the
segments are held in position by means of wedges, and can be
adjusted as required.

Driving the Spindle. — In Figs. 84, 40, and 45, the driving
pulley has a taper fit to the spindle, but the parallel fit shown in
Figs. 35 and 36 is more usual. If the fit is a parallel one the
pulley should be a light drive on the spindle, which should be
designed to be withdrawn from its bearings without disturbing
their adjustment. At the high speeds at which small internal
grinding pulleys run, the centrifugal effect expands the hole
in the pulley so that it floats on the spindle when running, and
I consider that a conical fit is here much the better type.

DETAILS OF PARTS 149

For the usual proportions of diameter between pulley and
wheel (0'35 to 0*45), the belt speed has not much effect, but when
the pulley has the same or a larger diameter than the wheel
(as in the case of some internal and cup wheel machines, see
Figs. 45 and 37), the centrifugal effect affects the tension. In
these cases the belt must be initially tight to pull well, but the cen-
trifugal effect lessens the pull on the bearings as the spindle
acquires speed. The effect is still further increased in the case
of internal spindles, where the speed of the belt runs up to
5000 feet per minute. At high speed the belt must be wider
than it need be at low speeds to give the same driving torque on
the pulley, and to last well the belt must be pliable, as it has to
run round a small pulley. The practical effect of running a
belt at 5000 feet per minute is to add a tension in it of 125 Ib.
per square inch for the ordinary density of leather ; if run at
'2500 feet per minute the added tension is one quarter of this.
The effect then is very considerable, and leather belts for
driving internal spindles should be at least twice as wide as if
calculated without allowing for the centrifugal effect.

Link beltings are so heavy in comparison with the working
tension that they are of no use for driving wheel spindles,
though their flexibility and being endless suggest their use.
The centrifugal effect is easily calculated by integrating round
the pulley, the relation between the tensional stresses fpl and p2

in the slack and tight sides being ^ — — 2= eA*e, where p is the

m-f*>*

density and v the velocity, using feet and seconds as the units.
Belts fitting on the sides of a vee groove are sometimes
used for driving internal spindles : they run well, but I have
no records of how they wear. Steel chains are used by Mr.
Hans Renold for driving some of the grinding machines (both
wheel spindles and feeds) in his factory. The wheel spindles
are driven by ' silent ' chains, as is shown in Figs. 183 and 124,
which illustrate a rod grinder and a surface grinder respectively.
The sprocket wheel need not be so large in diameter as a belt
pulley, so that the chain would not run so fast as a belt. As
a chain sprocket is really a many-sided polygon, the velocity
transmitted by a chain is not quite uniform ; the difference

150 GEINDING MACHINEEY

from this is, however, so small that no chatter marks are
produced on the work thereby.

As a disc wheel wears down its circumferential velocity
diminishes, and as the behaviour of the wheel and its factor of
safety depends upon it and not on the diameter, this circum-
ferential velocity should be kept constant by increasing the
rate of revolution of the spindle. This is usually provided for
by means of step cones in the countershafting, as shown in
Pig. 33, where cones with two steps are shown.

If, however, an idler pulley be arranged on the wheel belt,
as shown in Fig. 97, the speeds can be obtained by means of a
step cone on the wheel spindle only. The driving pulley in
the countershafting is then a flat-faced pulley only, and the
spindle speed is easily changed by merely changing the belt
from one step of the spindle cone to the other, and the tension
idler takes up the belt difference. This arrangement has the
further advantage that the tension in the slack side of the belt
is controlled by this tension idler (the tension in the tight side
is dependent on the power which is being taken), so that no
great difference is made, as the wheel head moves in and out
with the cross slide. The bearings then run under good condi-
tions, and the slide itself need not be gibbed, but ways similar
to those of the main slide used, and the wheel head kept down
by its weight alone.

The spindle of Fig. 35 is driven in this manner, and the
ways of the wheel head are as shown in the figure at X and Y,
and the general arrangement of the drive is shown in Fig. 62.

In Figs. 79 and 82 are shown tension and idler arrangements
on a self-contained machine. These general arrangements are
more fully described in Chapter VI.

In face wheel grinding machines, the diameter of the
grinding face does not decrease, and when one diameter of
wheel only is used, one spindle speed only is necessary. Where,
however, it is necessary to use cup wheels of other diameters,
other suitable speeds must be provided, and this increases the
range of usefulness of wheels of any particular grade.

Wheel Truing Arrangements. — It has been pointed out
that in such cases as we are now considering the diamond

DETAILS OF PAETS 151

or wheel truer should be attached to the work-carrying part
of the machine, so that the relative motion of wheel and work
will true the wheel correctly. In Figs. 29 and 30 the diamond
tool is carried in a bracket on the tailstock. In this machine
(Brown & Sharpe) the bracket shown is arranged to carry
a tool for truing the side of the wheel, by aid of the cross-
feed motion. Similar arrangements are shown in Fig. 77
and in Figs. 78 and 85, which represent the designs of
the Churchill and Norton machines respectively. In all
these the wheel is trued above the centre line, which is a
matter of indifference if the spindle be parallel to the main
ways, but if it be not it produces a slightly curved surface,
so that the wheel does not cut over its whole face. To avoid
this the Landis Tool Co. adopt the arrangement shown in
Fig. 64, for holding the short diamond tool, which is here
level with work centre. Although the arrangement does
not appear so direct and substantial as when the diamond
tool is held in a clamp on the tailstock, the diamond tool is
here backed up by the work, as shown. The fitting is shown at
D, in Fig. 110, detached from the machine. In the Cincinnati
grinders, Fig. 112, the diamond tool is set ' level ' with
the axis by being put through the centre itself. Although
these devices secure a theoretical point, I prefer supporting
the diamond as rigidly as possible, with a minimum of overhang.
The drawings show the axis of the diamond tool square with
the face of the wheel, but it is rather better if arranged to be
at a small angle (10° or 15°) to the normal to the surface, as
the end is not worn flat so quickly.

It is not so necessary to use diamond tools on wheels for in-
ternal grinding and face grinding. In the former the wheels have
frequently to be trued at short intervals, and it is easy to touch
them up with a hard piece of carborundum where they are seen
to be glazed, and it saves the time of bringing up the diamond
tool. On the internal grinders of my design the diamond tool
is provided with a fine adjustment, so that when one piece of a
repetition lot is completed, the diamond point can then be set
to the wheel, and serves as a kind of gauge, which prevents the
hole being ground over-size, besides being always ready for use.

152

GRINDING MACHINEKY

The act of truing a wheel brings a large number of facets
into action, and makes the wheel more likely to glaze when it
is on the point of doing so, than it is if trued by a rougher
method. The best method is to have the wheel of the correct
grade for the work, use the diamond tool, and the full face
of the wheel ; but as broken wheels have frequently to be
used up on internal work this is not always possible, and wheels
which are rather too hard have to be made to work, although
the spindle is too springy to maintain the requisite disinte-

FIG. 48. — STEEL WHEEL GUARD — CHURCHILL

grating cut. Also owing to the exigencies of manufacture,
small wheels made to an ordered grade are frequently some-
what too hard. Whenever possible water should be used on
the diamond when truing the wheel. Where it is necessary
to true a wheel to a particular shape to ' form ' grind work,
the diamond tool must be carried by a special mechanism,
of which examples will be given later.

Wheel Guards. — Wheels may burst if run at excessive
speeds, such as can be caused by the engine racing, or by
mounting a wheel on a spindle speeded for a much smaller
one. Forcing on too large a collet or an accidental injury

DETAILS OF PAKTS

153

may also cause a wheel to be unsafe. In machine shops doing
accurate work such causes are infrequent, but the results are
in any case to be guarded against, and the cast iron wheel
guards employed are usually substantial. While the strength
and inertia of such a guard are sufficient for wheels of moderate
size, large wheels should have guards of wrought iron or
mild steel. One such
is shown in Fig. 48,
which gives a closer
view of the wheel head
of the machine by
Messrs. Churchill, of
which Fig. 80 gives a
general view.

To increase the
capacity of steel wheel
guards to take up the
energy of a bursting
wheel, the sheet is
frequently bent into
corrugations, as in the
tool grinder by Messrs.
Harper, Sons, & Bean,
which is shown in
Fig. 49.

Pumps and Nozzles.

—The best type of
pump for the circula- FlG. 49.-CoRRUGATED STEEL WHEEL
tion of the water is a GUARD — HARPER, SONS, & BEAN

centrifugal with its axis

vertical, so that the bearings are above water-level. The flow is
radially outwards, the water going into the pump disc at its
centre, and being delivered at the increased pressure due to the
rotation at the outer edge, and hence flowing to the delivery
nozzle. The head against which a centrifugal will deliver de-
pends (nearly) on the square of its velocity, and this makes
it advisable that the speed should be constant, otherwise
there is apt to be undue splashing at the delivery. The best

154

GEINDING MACHINERY

arrangement of the piping is shown in Figs. 58 and 78, where the
nozzle can be quickly swung out of the way, so that the
work can be measured in comfort, and the nozzle then easily
replaced in position.

The section of a pump is shown in Fig. 50. Here A is the
body, B the paddle, and C the vertical spindle driven by the

FIG. 50. — CENTRIFUGAL PUMP

pulley D. The water-level must be well below the bottom E
of the spindle bearing, but well above the top of the paddle.
The fluid enters the paddle at the centre, and receives velocity
by the rotation. It is delivered into a channel F of gradually
increasing section, and finally delivered at the space G to the
vertical pipe H. Pumps which require packing or have a
definite contact in the working parts are rapidly ruined by
the grit in the grinding fluid.

DETAILS OF PAETS 155

The simplest effective nozzle consists of a pipe cut off at
about 45°, as is shown in Fig. 36 at L, and used with the lip
nearest to the wheel. The pipe may be flattened towards the end.
In small machines this is entirely satisfactory ; larger machines
usually have a special fitting, as shown in Figs. 57 and 58,
or have an adjustable flap to the nozzle so that it can be spread
as desired. It is very important that the fluid should be
directed right on to the grinding point ; the cutting points
of the abrasive material ought to work in water, so that the
heat produced is partly absorbed at once in the fluid. A certain
velocity is needed in the jet to accomplish this, as the wind from
the wheel blows the water about.

The speed of the wheel throws the water off as spray, the
finer parts of which float as a kind of mist, and make such
guards — as are shown at j, j' in Fig. 30, and in other illustrations
— desirable. To reduce the spray to a minimum, traps for it
are sometimes cast in the guards, as in Messrs. Churchills'
machine on page 171, Fig. 58.

The Reversing Mechanism. — Two types of reversing
mechanism are common in grinding machines : the trigger
release and the plunger trip, which is usual in automatic slot
drills. Of these the former requires less force, and has less
wear. The chief cause of small variations in the reversing
position is due to the momentum of the parts reversed, pro-
vided the trip mechanism is well arranged. The trigger
release is shown in Fig. 51, which is a drawing of the reversing
box of the Cincinnati Grinder, shown later in Fig. 112. The
drive is through the pulley A seen on the left, which is fast
on the shaft BC, on which the clutch D is keyed to slide. The
shaft BC is enlarged where D slides, and two keys are shown
fitted. The clutch D is alternately engaged with bevel pinions
E and F by the clutch teeth on their faces ; so that these
alternatively drive the bevel gear G — indicated by its pitch
circle — into which they both mesh, and thus give it, and through
it the table of the machine, motion in alternate directions.
When the top H of the reversing lever HJ is moved to the
right, it moves the slider L on the bar MN to the left, carrying,
by means of the springs P, Q, the bar with it, which thus moves

156

GBINDING MACHINERY

the clutch D by means of the fork E, which is connected to
it by means of a second bar, into engagement with the clutch
teeth on E. The trigger S then falls with its tooth U behind
the collar T, which is fast on the bar MN, and thus retains
the clutch teeth in mesh. The table then runs towards the
left, and when the stop moves the top H of the reversing
lever to the left, the lower end J moves the slider L, which is

FIG. 51. — TRIGGER REVERSING MECHANISM — CINCINNATI GRINDER Co.

loose on the bar MN, to the right, compressing the spring Q.
The rod MN cannot move, since the collar T is prevented
by the tooth U of the trigger. The spring is compressed until
the foot V of the reversing lever, after engaging the trigger S,
lifts it so that the tooth U comes out of engagement with the
collar T, and the spring then carries the rod MN, and with
it the rear rod (which is connected to it), the fork R, and
clutch D to the right, taking the clutch D from engagement
with the bevel pinion E, and engaging it with the bevel pinion
F ; the tooth Y of the left-hand trigger then falls behind the

DETAILS OF PAKTS

157

collar Z, and so retains the clutch D in mesh with the right-
hand bevel pinion, and the table now runs towards the right.
If the motion is well made the moment of reverse is determined
by the trigger edge, moved very directly from the table,
passing the collar edge.

The arrangement is perhaps more clearly seen in Fig. 52,
which is a photograph of the apron of a Guest No. 0 Grinder,
taken during the erection of the machine. In designing, I

FIG. 52. — TRIGGER REVERSING MECHANISM — GUEST

hold accessibility a cardinal virtue, and the removal of the
apron cover accordingly exposes the whole reversing mechanism.
The parts are lettered in the same manner as for Fig. 51, and
the same description applies, except that here the fork E is
carried directly on the rod MN to save shock. The step -cone
A is driven from the step-cone a at the rear of the machine ;
the bevel gear G drives the rack g (and so the main slide)
through intermediate spur gearing.

So far as the bevel pinions, gear, and clutch are concerned,
the plunger type is the same ; reversing is done by means of a

158 GKINDING MACHINEKY

plunger with a vee top which works against the foot of the
reversing lever. This is illustrated in Figs. 53 and 96, where the
reversing lever AB is shown with its top A to the right. The
table is travelling to the left, and as the stop moves A over to the
left, the bottom of the reversing lever B moves to the right, and
in doing so forces the plunger D down, compressing a spring
in the bracket E. When the bottom point of the lever has
passed the vee of the plunger D, the latter rises and forces the
reversing lever quickly over. The clutch F, which engages
the bevel pinions G, H alternatively, is connected to the reversing
lever through the lever J and bar K. This has two studs L, M,
which the reversing lever AB moves, and there is a little slack
between the lever and the studs, so that the clutch teeth keep
in gear until the point of the reversing lever has passed the
point of the plunger D, and then the reverse takes place rapidly.
The sliding clutch F is slowly withdrawn from the bevel pinion
clutch it is in engagement with till the moment of reverse, and
is then quickly moved into engagement with the opposite bevel
pinion. Once there the plunger retains it in engagement until
the next reverse. The motion can be reversed by the lever
N, which moves the rod K ; by centralising N the clutch F can
be centralised, and thus the travel motion thrown out of action.
The motion from the bevel pinion is communicated to the table
by means of gearing, the final movement to the table being
given through a rack bolted to it. In small machines the
small torque due to a screw and nut motion to the main slide has
been found to produce inaccuracies in the work.

In the arrangements of various designers there are differences
of construction in the reversing mechanism, but if the action
is understood, any small matter getting out of order can be
easily set right. One cause of failure to reverse in the trigger
type may be noted, however — a trigger failing to fall owing
to dirt or tightness due to any cause. The result is that,
at the following reverse, as the spring is compressed, it slides
the clutch out of engagement with one bevel pinion, without
taking it over into the other, and the traverse motion stops ;
and as the defect is at the opposite side to the parts operating
at the moment of failure, some time may be spent in locating

DETAILS OF PAKTS

159

160 GEINDING MACHINERY

it. In these machines the reversing lever is operated by
dogs seen at a, a' in Figs. 51 and 54. In the Cincinnati machine
the stop bodies are clamped on to the vee bb', and operate
a fixed projection c of the reversing lever by means of swing
pieces d, d'. These have a fine adjustment by means of the
screws e, e', and can be swung up so as to miss the projection
c, so that the slide can be run beyond the reversing points
when desired for gauging. On returning the table the pro-
jection c lifts the swing piece, which then falls into acting
position again. In Messrs. Churchills' machines the stops
are seen in Fig. 96, which is a view of an Internal Grinder, in
which the traverse and reversing motions are the same as in
the Universal and Plain machines. Here the stop bodies a, a'
slide along a rack W, and have a fine adjustment by means of the
screws e, e', the flanges of which engage the rack. The stops
operate on the withdraw pin c of the reversing lever, and by
drawing it out against a spring the slide can be run beyond the
reversing points. On returning the incline dd' pushes back the
withdraw pin c. The engagement of the screw flanges with the
rack makes it impossible for a stop to slip, although the operator
may omit to clamp it.

Stops fitted to a rack are also used in Messrs. Brown &
Sharpe's machines (see Figs. 29 and 54, in the latter of which
the lettering is similar to that of Figs. 51 and 96) ; they are
simply held by a clamp in the Norton Co.'s design, in which
supplementary stops (see Fig. 56) for limiting the run of
the table beyond the reversing points for gauging purposes
are also fitted.

This direct connection between the main slide and the
reversing mechanism is impossible where the main slide carries
the wheel head, unless the machine were worked the wheel
side of the machine. In machines for very large work this is
probably the better arrangement, but in smaller machines it
would be very inconvenient, and the mechanism for setting the
reversing points is then provided on what is normally the front
of the machine. The arrangement in the Landis machine is
clearly seen in Fig. 98, which illustrates an Internal Grinder.
The stops a, a" here are adjustable round a worm wheel W, and

DETAILS OF PAKTS 161

are given a fine adjustment by means of small worms c, c',
which are in gear with the worm wheel. By lifting the small
worms out of gear, the stops can be rapidly adjusted to the
approximate position. The worm wheel is geared directly
into the main slide rack and turns with it, making here nearly
one complete revolution for the full main slide traverse — as is
seen by the internal gear teeth at M on the worm wheel — which
occupy nearly the whole circumference. The main slide is
moved by hand by the wheel /, the shaft of which carries a
pinion meshing, with the internal gear dd.' A similar arrange-
ment is seen in the front view (Pig. 62) of the Greenwood &
Batley Plain Grinder.

In plain grinders a pause or tarry device inserted in the
gearing between the reversing mechanism and the main slide
is an advantage : it should be adjustable as to the amount,
and capable of being thrown out of action when required.
For my machines I used a single-tooth clutch, which could be
inserted more or less deeply in a clutch having steps of different
height ; this is an effective but simple device, as is desirable
in mechanism which is enclosed.

The hand wheel for traversing the table should be geared
so that its top moves in the same direction as the table moves.
The action of throwing the automatic traverse into action
should, on the larger machines, throw the hand wheel out of
gear — for the hand wheel motion being geared down con-
siderably to the table motion, its rim velocity is high when
connected with the running table, and the momentum change
at reverse causes severe forces on the gear teeth. I consider
it to be advantageous if the movement of the throw-out motion
normally causes the throw-out to take place at the next reverse,
instead of immediately ; thus the operator does not have to
watch for that moment when he wishes to stop the wheel at
the end of the work for gauging purposes.

The use of wide wheels and the recognition of the principle
that the traverse per revolution of the work should exceed
half the width of the wheel has led to rapid rates of traverse.
The dynamic effects are the more considerable in the machines
for work of small diameter. Although the main slide speeds

162 GKINDING MACHINERY

are small compared with those of planing machines, the
precision of reverse and absence of shock are so desirable
that cushioning is being tried. The machine (Norton,
3 inches x 18 inches) of Fig. 85, has a cushioned reverse. The
Greenfield Manufacturing Co. make a machine in which the
main slide is driven hydraulically, the motion being controlled
by a two-way valve, and in this they have the same end
in view.

On all but the smaller machines it is desirable that an
adjustable safety slip motion be fitted in the main slide drive,
so as to allow the slipping to take place instead of serious
damage. Such a slip motion is shown at P in Fig. 53, and
consists of a flanged coupling between the shafts of the motion,
driving by friction only. In this illustration (Fig. 53), it
will be seen that the drive for the table traverse comes through
a change speed box Q of the Hendy type, through the shaft E
and friction P to the reversing box ; S is here the hand
traverse motion, and T the throw-out lever.

The Cross-feed Mechanism. — The lower end of the reversing
lever in Figs. 29 and 51, the lower end of the plunger in some
machines, and in Fig. 53 a rocking lever operates the respective
automatic cross-feed mechanisms. These all consist of a ratchet
wheel, operated by a pawl, to which a variable stroke can be
given. A typical design is that of Messrs. Brown & Sharpe,
shown in Fig. 54, and has been referred to on page 119.

The mechanism is operated by the vee point A at the
bottom of the secondary lever Be, which, acting on the roller
C, presses down the lever D to a definite position at
each reverse of the table. After the point has passed the
roller, the spring E pulls the lever D up until the end of
one or other of the adjustable stops FG meets the curved
arc B, near the bottom of the secondary lever. This limits
the extent to which the spring pulls the lever up, and so
the extent of movement of the ratchet H, which is operated
through the link K ; and this determines the number of teeth
of the ratchet wheel L which the ratchet H will take at each
reverse. The amount of feed is set by adjusting the position
of the stops F and G, and can be arranged to be different

DETAILS OF PAETS

163

at the two ends of the stroke, which is useful when it
is desired to grind a diameter right up to a corner, as is de-
scribed on page 97. The cross-feed is thrown out of action
by putting the ratchet H out to the position IT, in which it is

FIG. 54. — CROSS-FEED MECHANISM — BROWN & SHARPE

retained by the spring latch M. The wheel can then be run
back by hand freely. As the feed takes place it carries round
with the ratchet wheel KL, which is graduated and fixed to
the hand wheel N, the shield P, which eventually comes under-
neath the ratchet H, and prevents it from acting, thus auto-
matically throwing out the feed. This shield P is carried
round by the arm Q, which is held in any desired position on

164 GKINDING MACHINERY

the ratchet wheel by the plunger ratchet at E ; it can be
rapidly slipped round, moving it clockwise, and is provided
with a latch adjustment ST. By squeezing ST together the
part T containing the plunger ratchet E is approached to the
grip S by an amount rather greater than the tooth space, carry-
ing the tooth of the ratchet with it ; on release it slips back
over the next tooth, so that the result is that the shield has
moved back through the space of one ratchet tooth.

Such a mechanical throw-out to the cross-feed action will
trip the motion, so that the cross-feed disc is practically in the
same position every time, and if the connecting mechanism
to the wheel head is correctly designed and well made, work
can be duplicated by such a device to an accuracy which
is commercially satisfactory. The moment of the throw-out
of the cross-feed movement may, however, be controlled from
the size of the work itself, and the work size will then be inde-
pendent of the wear of the wheel. Messrs. Pratt & Whitney
and myself have independently brought out such devices ; in
both cases the control was electrical, the diminishing size of
the work operating a lever which made an electrical contact
when the work was to size, the resulting current energising
an electro-magnet, which threw the feed out. Messrs. Pratt &
Whitney employed a single diamond point to eliminate the
effect of wear. In my arrangement the work was measured
across a diameter by a lever caliper with hardened surfaces,
and arranged to swing a little ; this eliminated the effect of
vibration, and made an accurate throw-out, although vibration
was present. Electrical contrivances, however, make their
way very slowly in workshops, and in connection with grinding
machines there is the disadvantage that all wires and connections
have to be very carefully protected from the soda water or
oily solution used, as it is most destructive to the insulation.

To work satisfactorily any cross-feed must receive attention ;
the ratchet wheel and mechanism must be kept clean, and
the cross-slide oiled and run to and fro over its full range
occasionally.

In grinding one piece, after the work has been got parallel,
the shield is set just short of the pawl H, and the automatic

DETAILS OF PAKTS 165

feed then takes off a thousandth or so, and is thrown out by
the feeding up of the shield. The machine is allowed to run
a few traverses more, and the diameter of the work is then
measured, and the amount which it is over-size ascertained in
quarter thousandths of an inch. The grips ST are then pinched
once for each quarter thousandth of an inch the work is over-
size, and the machine started again. The automatic feed is
allowed to throw itself out, and. the machine to take a few
more traverses, and the work should then be to size except
for the wear of the wheel. In most cases this is negligible,
but if the work is large and the wheel has worn so that the
work is still over-size, the grips ST are again pinched once
for each quarter thousandth of an inch remaining, and the
process repeated.

For repetition work, the ratchet H is thrown back from
the wheel to the position H' indicated by the broken line,
and the wheel run back from the work one or two turns of
the hand wheel. The next piece of work is then inserted in
the machine, and the wheel brought up until it cuts, when the
automatic feed is thrown in, and the machine left to its work.
The position of the shield at which the wheel first cuts should
be noted, so that the wheel may be brought rapidly up to it
as the succeeding pieces are placed in the machine.

While the machine is grinding, the centres of the next
piece should be cleaned and a carrier placed on it in readiness —
two carriers are desirable for this purpose in small repetition work.
In machines in which the accuracy of the cross-feed can be
relied upon, when the automatic feed has been thrown out,
and a few traverses more taken place, the piece of work may
be removed without measuring it, and the next substituted,
and the machine started. The piece removed can then be
checked for size. If it is over-size beyond the limit, the cross-
feed is at once compensated to take what may be allowed off,
so that the piece then in the machine will be to size. After
it has been finished the over-size piece can be returned for
finishing.

Much work has one or both ends reduced for a short dis-
tance to take a wheel, or collar, or serve as a journal, and this

166

GRINDING MACHINERY

distance is too short for traversing the table. The wheel
is then fed in by hand, and to limit the cross-feed movement
in this case a stop U is provided, which can be drawn forward
by the handle V when required, and forms an abutment
for a projection on the shield arm Q. This enables the diame-
tral size of the short lengths to be duplicated easily ; com-

FIG. 55. — CROSS-FEED MECHANISM — GUEST

pensation for the wear of the wheel is made in the same manner
as before.

In Fig. 55 is shown my design of cross-feed mechanism,
illustrating some points which I regard as desirable. It is
operated by the lever A, the other end of which is pressed down
by an edge of the reversing dogs ; by running the dog screw
well out, the cross-feed action is thrown out at that reverse.
The lever A rocks the arm B, pivoted concentrically with the
spindle, so that the point C of the ratchet CD reaches a definite

DETAILS OF PAKTS

167

point each time. The amount of the return of the ratchet
is controlled by the position of the end E of the arc EF, which
is adjusted and locked by the knurled nut G. The graduations
of this adjustment, seen at F, give the amount of cross-feed
on the work diameter. The ratchet CD is shown retained in
its out-of-action position by its end D. The,, ratchet is finally

" i

FIG. 56. — FEED MECHANISM — NORTON

thrown out of action by the stop H, carried by the graduated
disc J ; the throw-out takes place when the zero graduation
reaches the fiducial mark K, so that the reading at any time
gives the amount which the machine will feed before the
throw-out takes place — as shown it is 3J thousandths of an inch
on the work diameter. This enables the wheel to be brought
rapidly into action in repetition work on which the grinding
allowance is known. The knob L compensates for the wear
of the wheel by shifting the disc J back on the ratchet

168 GKINDING MACHINEKY

wheel (not visible, and which is keyed to the shaft) one
tooth at a time. The mechanism is enclosed to protect it
from the grit.

The chief differences in the cross-feed mechanism consist in
the driving of them. The Norton feed mechanisms are seen
in Fig. 56 : the drive is from a rocking lever A, through a sliding
rack B and pinion C ; this gives a considerable movement to the
ratchet D, so that it first falls into engagement with the ratchet
wheel E, then moves it, and then moves back to the position
shown. This permits the wheel to be run back from the work
at any time except when the ratchet is actually feeding, without
the operation of throwing the ratchet out of engagement. The
compensation for the wheel wear here is by a small pinion F,
which meshes with the ratchet wheel, which is cut as a gear
wheel for the purpose. The pinion is turned by the handle G,
which has a plunger and a locating hole in the plate H corre-
sponding to each tooth of the pinion ; thus the movement from
one locating hole to the next moves the shield back one tooth of
the ratchet wheel, corresponding in this case also to 0-00025 inch
on the diameter of the work. This is a positive device, and the
position of the shield on the ratchet wheel cannot be moved
without withdrawing the plunger arid turning the handle G :
it takes some time, however, to move the position of the
shield far.

To adjust the amount of the cross-feed at each reverse, more
or less movement is given to the sliding rack B by adjusting the
position K, at which it is connected to the rocking lever A.

In the small Norton grinding machine shown in Figs. 85 and
86 a differential gear is included in the cross-feed mechanism,
so that the usual movement through a ratchet tooth space is
replaced by the larger one indicated by the notches at Q.

Where the wheel head and cross slide are the traversing part
of the machine, the derivation of the speed motion has to be
different, but the mechanism connected with the ratchet wheel
is generally similar. In Fig. 57 is shown a side-view of the
wheel head of a Landis Plain Grinder with automatic feed ;
here the ratchet wheel A, ratchet B, and the compensation
latch C for the wear of the wheel, are clearly seen. The ratchet B

DETAILS OF PAETS

169

is operated by the shaft D, which receives its motion from the
lever E. At the reverse the plate F rises, pushes up the weight
G, and feeds the ratchet ; on the return of the plate, the weight
G falls, carrying the ratchet back with it. The amount of
return, and hence of the feed, is adjusted by the screw H.
In Messrs. Greenwood & Batley's Plain Grinder (see Figs. 62 and
63), which is of the travelling wheel type, the attachments to the
ratchet wheel are well enclosed, which is always a desirable

FIG. 57. — LANDIS PLAIN GRINDER, END VIEW

point in a grinding machine. The feed motion is arranged to
operate at the end of the stroke, during the pause before re-
versing, by means of end movement of the main slide rack. The
mechanism is carried on the main slide, so that the hand wheel
and auto-gear do not move in and out with the cross slide.
This is a desirable feature, particularly upon the larger sizes
of machines.

It is very desirable that the movement given to the ratchet
wheel corresponding to the minimum cross-feed should be an
easily visible amount ; also the operation of the ratchet wheel
by the ratchet with certainty requires a reasonable pitch of

170 GEINDING MACHINEKY

tooth. This comparatively large amount of motion has to be
reduced in a very large ratio to give the small movement
(usually g-oVo inch) of the cross-feed, corresponding to a tooth
space of the ratchet wheel.

This reduction is made by means of a worm and worm
wheel in almost all machines, the final movement of the slide
being produced by a rack and pinion. While this is undoubtedly
convenient in the case of Universal grinders, I have a strong
preference for a plain screw feed in the case of Plain grinders,
though Messrs. The Norton Manufacturing Co.'s machines are
the only machines, I believe — save those of my design — so
fitted. Backs and pinions can be cut fairly accurately, but
screws can be lapped to a very high degree of accuracy, as is
described in a later chapter, and most measuring machines
employ a screw as the final means of subdivision of the inch.
The accuracy of the response of the wheel movement to the
indications of the cross-feed disc is most important in manu-
facturing grinders, especially in repetition work where less
skilled operatives are employed.

A cross section of the Churchill Plain Grinder, showing the
arrangement of the cross-feed, is given in Fig. 58. The ratchet
wheel A is fast to the pinion B, which is in mesh with the gear C,
which is loose on the worm shaft DE. The worm F meshes with
the worm wheel G, which is on a horizontal shaft carrying also
a pinion H, which gears with the bull wheel, and this engages
the rack L, fixed to the cross slide M. The backlash is taken
out by the weight N, which holds the wheel head back from the
work by means of the chain PP'. It will be noticed that the
worm is fitted with ball thrust washers to lessen the friction,
and runs in an oil box. The pinion E is keyed to slide on the
shaft DE, and when moved to the right engages the gear C by
means of the single-tooth clutch seen. The movement of the
ratchet wheel A then operates the cross slide, the worm and
worm wheel supplying the principal part of the reduction ratio.
When K is in the position shown, it is out of gear with the
automatic movement (but is always in mesh with the lower
gear), and the wheel head can then be run rapidly to and fro
by the hand wheel S, an indicator at T showing the movement.

DETAILS OF PAKTS

171

This is very convenient when the work has considerable steps
on the diameter, and also for truing the wheel.

In Fig. 53 the front view of this mechanism is shown :
U is the hand wheel for rapid movement of the wheel head, V
the indicating slide, and W the hand wheel for fine movement
of the wheel head. At X is an arrangement similar to that in

172 GRINDING MACHINERY

Fig. 56 for compensation for the wear of the wheel. The wheel
head cross slide is not gibbed, but consists of a vee and a flat,
as can be seen in Figs. 35 and 48.

In Universal machines, where the lower cross-ways swivel
round a central point, this particular arrangement cannot
be used ; the only difference is that the worm wheel G then lies
in a horizontal plane, and its vertical shaft is concentric with
the stud about which the cross- ways swivel ; the pinion at the
upper end of the worm wheel shaft meshes directly with the
rack. Many Universals have no arrangement for taking the back
lash out of the rack and pinion, as a loose weight with its
chain would be troublesome when the cross-ways were adjusted
to an angle. Such an arrangement is very desirable, as precise
correspondence of the cross slide position with the indications
of the cross-feed wheel is very important in repetition work.

The arrangement of the mechanism between the cross-
feed hand wheel and the rack in the Landis machines can be
seen in Fig. 36. As shown, the cross-feed is not automatic. The
feed disc M operates a worm shaft, the worm of which and the
corresponding worm wheel lie in the casing N. The worm
wheel shaft, the axis of which, PQ, is vertical, carries a pinion E
on its lower end, which is in mesh with the rack S, which is
bolted to the main slide of the machine by the screws shown.
Here the feed motion moves with the wheel head. In Fig. 57
the part F operating the cross- feed automatically is seen to be
elongated, so that it operates the feed in whatever position
the wheel head happens to be. Here the slide is of the vee
type, gibbed as shown at TT' in Fig. 36. The cross-slide is
here held back from the work by a spring enclosed in the case K,
Fig. 57 ; the spring is helical, and used in bending (by twisting
round its axis), so that its tension can be adjusted easily.

Steadies. — Another feature peculiar to grinding machines,
though for Plain and Universal machines only, is the steady ;
of these a pair are shown at 7c, 7c' on the floor in Fig. 29, and in
position on the machine in Fig. 30. A line drawing of this
steady is shown in Fig. 59, and is Messrs. Brown & Sharpe's
design, used on all their machines.

Spring Type.— The object of steadies is to prevent vibration

DETAILS OF PAKTS

173

of the work and hold it firmly against the cut of the wheel. As
the diameter of the work decreases by the grinding a little at
each stroke of the main slide, steadies for grinding machines
cannot be set once for all like a lathe steady, but must be
arranged to keep in contact with the work continuously as its
diameter decreases. Two types are in general use — those

FIG. 59. — STEADY, SPRING TYPE — BROWN & SHARPE

adjusted by screws, and those held up to the work by springs ;
the steady of Fig. 59 is of the latter type.

Here the steady body A is clamped to the machine table
B by the screw C ; at D is shown a water guard, and at E a
piece of work. A lever F is pivoted at G to the steady body, and
is forced inwards by a spring H, the tension of which can be
adjusted by the nut J ; its forward motion is limited by the
fine pitch screw K. This lever forces forward a sliding piece L,
supported on a roller at M so as to move freely, and carrying
a shoe which bears on the work at N and P. In order that the

174

GEINDING MACHINEEY

shoe should touch the work at both N and P it is pivoted to L
at the vee Q, and adjusted by the screw K, the point of which
bears on the rear part of the shoe. The nut S, in which the
screw K works, is free to slide in the recess in L, and is kept down
by the spring T, the tension of which is controlled by the
nut U. The screw K controls the size of the work, and the

FIG. 60. — STEADY, SCREW TYPE — LANDIS

screw E adjusts the shoe so that it touches the work at the
two points ; both movements are spring controlled. When
the work is to size the screw K is in contact with its stop and
the nut S at the bottom of the chamber ; while the work is being
ground the shoe is forced into contact with the work at P and N
by the combined action of the springs, neither the screw K
nor the nut S being in their final position.

The shoes, though they are metal, wear as a number of
parts are ground, and the screws K and E are adjusted to
compensate for this wear. The screw K requires to be adjusted

DETAILS OF PAKTS 175

carefully, as it ' sizes ' the work ; thin work is sized at its
ends by the cross-feed of the machine, the table being set
correctly parallel first, but the intermediate parts are sized by
manipulation of the steadies, using the screw K.

Screw Type. — In Fig. 60 is shown the steady of the Landis
machines ; here the shoes A and B are adjusted by the screws
C and D respectively, which feed the screws up positively. The
upper screw C is the more important, as it directly controls
the work diameter : it acts directly on the sliding part E to
which the shoe A is fixed. The shoe is moved positively by
the screw C, but is pressed forward beyond the positive position
by the spring F, the tension of which is adjusted by the
screw G.

The shoe B is held by the bell-crank lever H, pivoted at J ;
it is operated positively forward by the screw D, the forward
motion of which is limited by the adjustable nut K and with-
drawable stop L.

Above the steady is the section of the rod on which the
sheet steel water guards hang ; the arrangement can be seen
in Figs. 64 and 82.

In the Norton grinding machines the steady shoes are
adjusted positively by screws, but no springs such as shown at
F, Fig. 60, are employed ; rollers are used to make the motion
more sensitive. A series of steadies are shown in position on a
machine in Fig. 66.

In these positively adjusted screw steadies the shoes are
of wood ; this supplies a certain degree of elasticity, which is
desirable when the work is forced to the wheel by a hand opera-
tion. Should the force exerted be too great the wood yields
and wears, while metal would present a firm support, and
force the wheel to cut.

Brass or bronze shoes soon wear to a bearing on the work,
and for repetition work are very desirable. When, however,
the quantities are very great hard steel shoes are the best,
and accurate stops should then be fitted. Occasionally brass
shoes mark the work with a trace of colour, but it can easily
be removed in finishing.

The shoes must bear as shown in Fig. 60 — the shoe A

176

GRINDING MACHINERY

opposite to the wheel, and B almost vertically beneath the
centre of the work, but somewhat towards the wheel. After
a little time the shoes wear at the contact points and provide
bearing area ; but there must always be a clear space between
these areas, and when the shoe is in .one piece, as in Fig. 59,
this condition must be observed.

In machines of British manufacture (see Figs. 58 and 62)
the simple screw steady without springs seems to be generally
adopted. There is considerable difference of opinion as to

FIG. 61. — STEADY, AUTOMATIC — GUEST

what the pitch of the screws should be. If it is fine there is
no sensitiveness to the touch — that is, the force with which the
work is pressed cannot easily be felt when handling the steady
screw. If the pitch is coarse, then the most minute amount of
turn of the screw moves the steady block a very considerable
(according to grinding accuracy) distance, and reliance has
to be placed on the estimation of the force ; as the effect of
the force varies with different lengths and diameters of the
work, each job requires a little practice.

The screw steadies need continual attention and adjustment,
keeping the operator fully occupied. They are, however, very
much easier to set up than the spring type.

DETAILS OF PAETS

177

Automatic Type. — The steady shown in Fig. 61 is one which I
brought out and fitted to my machines (initially in 1904) : it is
arranged to work automatically. The main part is the rocker
which swings in the top vees : as it swings forward one of the shoes
(here pieces of rod adjustable for different sizes of work) touches the
work, the second is then adjusted to touch it also, by means of a
fine pitch screw bearing on the heel of the steady block holding the
two shoes. As there is a ' change point ' in the mechanism the
moment the second shoe touches, this position is at once perceived,
and the adjustment is very easy. The weights of the parts are so
arranged that the shoes are pressed on to the work, but with a force
of only a few ounces, so as not to spring it.

A steel ball is then placed in the inclined vee groove cut in the rear
part of the rocker, and rolls down it until it touches the still more
inclined surface above the vee groove, and takes a position as shown
at x. Immediately a little has been ground off the work, the balance
of the rocker causes it to move forward and to keep the shoes in
contact with the work. The ball, however, acts as a continuous
ratchet, and prevents the cut of the wheel forcing the work away.
Although the whole steady is rigid, and metal to metal from work to
machine table, the sensitiveness of the arrangement is such that no
trouble occurs, though the shoes are metal. The swing latch at the
back is to keep the rocker up and the steady block out of the way
when inserting work. The action of the steady has proved to be
sensitive and accurate.

The following records of tests indicate the degree of sensitive-
ness of this steadv : —

Test.

Maximum variation
of diameter.

No. 1
2
3
4
5

Work \" x 9^'— Bright drawn steel— 3
measurements over 6J" — 1 steady . .
Work \" x 9|"— Bright drawn steel— 3
measurements over 6£" — 1 steady . .
Work \" x 9£"— Reeled steel— 3 measure-
ments over 6£" — 1 steady
Work if" x 24" — Turned M.S. — 8
measurements over 20" — 3 steadies .
Work -if" x 24" — Turned M.S. — 8
measurements over 20" — 3 steadies .

0-0003"
0-0002"
0-0001"
0-0003"
0-0004"

In these tests the steadies were adjusted to the work at the
start, and not touched afterwards.

The steadies in position on a machine can be seen in Fig. 68. The
block- ad justing screw is at K, and the block at M, while at L is the

178 GKINDING MACHINERY

sizing screw for sprung slender work. Messrs. Pratt & Whitney more
recently (patent of 1908) have brought out a similar, but not so
sensitive, arrangement.

Follow Rest. — When work has already been ground nearly to
size — within O'OOl inch — it may be steadied for finish grinding
by a steady fixed at the wheel. The steady may be carried
on the wheel head or on the body of the machine, if the wheel
head does not traverse. As the steady is fixed at the wheel
it is very efficient in preventing chatter, and highly finished
accurate work can be obtained by its means. It can be used
for parallel work only, and is best suited to large quantities
of slender work of high accuracy.

In grinding rods and shafts a steady of this type is used ;
the rod is rotated and fed through the steady once only, the
wheel being wide enough and of such grade and grit as to
finish the work at a single pass. Such a machine is shown
in Fig. 183 ; very fine adjustments are fitted both to the
wheel and to the steady, and the latter is of hardened steel.

Machine Bodies. — It has been pointed out that the forces
at the grinding point are very small compared to those occurring
when cutting tools are used, but it will have been observed
that the bodies or main frames of modern grinding machines
are very massive, when compared with the bed of a lathe for
work of the same size.

This is partly to meet the requirements of accuracy and
partly to check vibration. To ensure the maintenance of
accuracy of the ways the modern practice is to provide three
feet to the machine body, and upon these it is to rest, and the
remainder of the space beneath is to be clearance ; the body
is scraped and the slides fitted when it is resting thus, so that
the machine works under the same conditions as it is manu-
factured. The feet are shown at U, V in Fig. 58, and also
the clearance space between the rest of the machine and the
floor. The machines are not to be bolted down, they merely
rest by their own weight, which is arranged to be quite sufficient
for the purpose.

When the machine is very long this method is not adopted :

DETAILS OF PAETS 179

a good concrete foundation is prepared, and the machine
levelled upon it, supported by adjustable taper wedges. These
can be easily seen in Fig. 83, which gives a view of Messrs.
Nortons' largest machine. The wedge moved by means of
a screw gives a very fine adjustment, so that the machine
may be set true in itself and kept true, although the foundation
may sink or distort. While rigidity in the vertical longitudinal
plane is important, it is more so in the vertical plane perpendi-
cular to that, and in the horizontal plane, although these
rigidities appear to be sometimes slighted by designers.

Although these rigidities are always to be considered,
in the bodies of the machines of my design, attention
was especially paid to the breaking up of the vibrations
by placing the stiffening ribs of the correct shape in suitable
positions. By a suitable design both aims can be secured
by the same metal correctly located, so that the machine
while not increased in weight will be less subject to vibration
troubles. The mechanical principles upon which vibrations
depend are those given in treatises on dynamics, and are
obtained from the general laws by neglecting, as far as is
possible, the squares of small quantities. A brief treatment
adapted to the scope of this work has been given in
Chapter IV.

CHAPTER VI

PLAIN GRINDING MACHINES AND EXTERNAL WORK

Development of the Plain Grinder. — As the Universal Grinder
was steadily developed, it gradually became evident that
much of the unhardened steel work, previously completed
in the lathe, could be profitably transferred to the grinding
machine for the finishing process — that is, not only was the
finish obtained of a higher quality, but that it often at the
same time cost less. This opening up of the process of finishing
by grinding as a manufacturing method naturally led to
the construction of simpler but more powerful machines, for
external work only, which machines hence acquired the name
of Plain Grinders.

Compared with the Universal Grinder, work capacity for
work capacity, the Plain Grinders are fitted with wider wheels,
usually of greater diameter, have a more copious water supply,
more rapid feeds, and generally are more stiffly built, and
take much more power. The cross-ways, wheel heads and
work heads have no swivelling adjustment, and in the larger
machines, which are intended for parallel work only, the
work table also does not swivel ; the parallelism is then secured
by use of a set-over tailstock.

The comparative simplicity has given the opportunity for
certain improvements. In the Brown & Sharpe Universal
Grinder, Figs. 29 and 30, the table H is flat on the top,
which presents advantages in some work which these
machines are occasionally called upon to do, but it does
not offer a corresponding advantage for plain — that is
straight or slightly taper — work done between the centres;
and as a table section somewhat of a triangular or L section
has a greater rigidity, and yet does not increase the height
of the work from the main ways, such a section has become

180

PLAIN GE1NDEES AND EXTEENAL WOEK 181

usual in Plain Grinders. In some designs the system of
protecting the table by means of short pieces of telescopic
guarding — as shown in Figs. 29 and 30 at g — which require
arranging for each different length of work, also gives
place to protection by arrangements requiring less attention.
Where the wheel head travels there is more inducement to
retain the flat- topped table which does not travel, and so can be
easily made deeper. This is the case in the machines shown in
Figs. 62, 63, and 110, which are a Plain Grinding Machine
by Messrs. Greenwood & Batley, and the No. 1 Universal
Grinder of the Landis Tool Co. respectively, in both of which
the wheel traverses. The guards consist of sheet steel pieces
bent to the requisite shape and hung from a rod, reaching from
one end of the table to the other. The top of the table in
these machines is flat, and the centres are aligned by the
vertical scraped edge D (Figs. 62 and 63), against which the
headstock and tailstock are pulled by the action of the bolts,
the heads of which lie in an inclined tee slot, as is seen
best in Fig. 64, which shows the section of the table in the
Landis Plain Grinders, and the mode in which the parts are
fitted to it. The parts are lettered to correspond.

The Table Section. — The table A has a flat top B, on which the
tailstock C rests, and a vertical edge D, against which the aligning
edges of the headstock and tailstock are pulled by inclined bolts
E, E' — the slot F for the bolt heads being correspondingly in-
clined. The sheet steel guards G, H, K are shown, hanging round
the horizontal rod J. These parts are also seen in Fig. 57, where
LM is the flat top of the table, the slot in which is marked N.
Two sets of graduations at P will be noticed. This is useful
and customary, the graduations being in degrees and in inches
per foot taper. Where the table, for the sake of rigidity
primarily, is given a shape having a somewhat triangular
section, the detail can be arranged — after providing suitable
guiding edges for the headstock and tailstock — to assist in
carrying off the water. In the case of small machines the
headstock and tailstock may be of the ' swan neck ' type,
and overhung from ways on the side of the table farthest from
the wheel, as is shown in Fig. 65, which gives the table section of

184

GKINDING MACHINEKY

Messrs. Brown & Sharpe's No. 11 Plain Grinder. Here the
ways A, B which support and guide the headstock and tailstock
are well protected from grit and splash by the sheet metal
guard C. This guard with the inside DE of the table forms
a surface off which the water runs to the channel F of the main
slide G. In larger machines it is desirable that the supporting

FIG. 64. — HEADSTOCKS, TABLE, AND GUARDING — LANDIS TOOL Co.

parts for the work should have as little overhang as possible, and
more rigid designs are adopted, Messrs. Brown & Sharpe then
using the slip guards described above.

Mr. Norton's design can be well seen in Fig. 66. Here the
upper ways A, B are protected by the vertical projection C,
and the lower way 1) has the sheet steel guard E jutting out
over it. The tailstock leg and foot F is doubled round the
sheet steel plate E to rest on its way D. The groove G is
merely for the heads of the clamping bolts to fit in, and it is a

PLAIN GBINDEKS AND EXTEKNAL WOKK 185

matter of indifference that the water flows on to it. The head-
stock and tailstock are bridged across from one way to the
other by these curved legs, and the swan neck type of overhang
is avoided.

Footslock

FIG. 65. — HEADSTOCK, TABLE, AND GUARDING — BROWNE & SHARPE

In Fig. 67 is a sketch of my design of table section and of
method of protection of the ways. Here the guards consist of
three pieces of sheet steel, one, ABCD, fastened to the table and
reaching the whole length between the headstock and tailstock
when separated to their limit, and pieces EF and GH about

186

GRINDING MACHINERY

half that length — the former carried by the headstock and the
latter by the tailstock. These three guards telescope as the
headstock and tailstock are adjusted, and protect the table
completely in all positions ; to allow of this telescoping the

FIG. 66. — NORTON PLAIN GRINDER, END VIEW

guard ABCD is joggled at the centre, the piece AC running
towards the headstock and through it, and the piece BD to-
wards the tailstock and beyond it. The object in enclosing the
table so completely along the bottom edge at DF is to prevent
the wind from the wheel blowing the gritty liquid round the
guards to the grinding way. For work of large diameter these
guards are easily removed ; the table must then be cleaned

PLAIN GRINDERS AND EXTERNAL WOEK 1ST

up before replacing them. For purposes of rigidity the guards
pass through a curved slot KL in the headstock, so that overhang
is avoided. The tailstock is slightly inclined, to allow the lower

FIG. 67. — HEADSTOCKS, TABLE, AND GUAEDING — GUEST

FIG. 68. — GUEST PLAIN GKINDER, END VIEW

188

GRINDING MACHINERY

parts of the guards to pass it. The appearance of a table so
enclosed is seen in Fig. 68, which is a view of an 8-inch by 48-inch
machine, and in which the lettering corresponds. A number

of steadies are
shown in posi-
tion.

In machines
where the table
ways are well
protected, a
little attention
is nevertheless

necessary, as
spray floats in
the air and
settles on sur-
faces, finally col-
lecting into
drops. These
must be occa-
sionally wiped
up. Also a
shoulder on the
work or a key-
way may cause
splashing if the
water supply has
a slightly too
high velocity.

In the ma-
chines of Messrs.
The Churchill
Machine Tool

Co., the table is of a triangular section which carries off the flow of
water easily, but no attempt is made to protect the table ways
from fluid and grit except that drain gutters are cut across
the lower ways. The table is quite open, and can be got at
without difficulty for wiping up when the position of the

FIG. 69. — PLAIN GRINDER, WORK HEAD — CHURCHILL

PLAIN GRINDEKS AND EXTEKNAL WOKK 189

headstock or tailstock is changed, as can be seen in Figs. 58
and 80.

The Work Head. — As Plain grinders are intended to be used
for work between the centres only, there is no necessity for the
work-head spindle to be fitted into bearings, as all it has to do is
to support the centre, which is dead. Accordingly the head-
stock in these machines is simply a bracket into which the
spindle, carrying the dead centre pulley and centre, fits tightly :
and this construction has the further advantage that there is
now no oil film round the spindle to produce its effect on the
work. Fig. 69 shows the construction of the headstock of
Messrs. Churchills' smaller machines. The table section is
shown at ABCDEF, AB being the surface where it fits the main
slide, CD the upper guiding way, and F the lower, and E the
clamping edge, whereby the bolts GH, G' clamp the headstock
J in position. The spindle K is a tight fit in the headstock,
and is drawn in by the nut L : it is bored through so that the
centre M can be easily removed for sharpening. The dead
centre pulley has a bronze bush, and rotates easily on the
spindle ; and a protection plate is screwed on to the front
of it. It is surrounded by a fixed protecting casing with belt
apertures ; at the side is shown the driving pin, which can
be adjusted to any convenient distance from the centre.

The Centre Grinding Head. — Since the work-head spindle
does not rotate, a separate small running head is provided in
Plain grinding machines for the purpose of receiving the
centres and rotating them for grinding their points true. It is
common practice to make these small heads with their axes
at a fixed angle of 30° with their ways, so that when placed in
position on the grinding machine table they sharpen the centre
to an included angle of 60° when the table is straight ; they
may, however, be made adjustable, or at any angle to suit
particular work.

Although the centre grinding head is a small attachment, it
is an important one ; the taper hole for receiving the centre
must be run dead true, otherwise when the centre is placed in
the main headstock it will be out of line, which will create
trouble continuouslv.

190 GEINDING MACHINEKY

The Driving of Plain Grinders. Belt Drives only. — In the

headstock just described, which is typical of the headstocks of
small Plain grinders, the dead-centre pulley is driven by a belt
from a drum overhead, as is shown in Fig. 70, which gives the
general arrangement of the whole of the drives for this machine
—the Churchill 6-inch Plain Grinder — and may be compared
with Fig. 33 giving the corresponding arrangement for Messrs.
Brown & Sharpe's No. 1 Universal Grinder, both of which
machines are of the travelling work type. Here the fast and loose
pulleys A,B for the main belt are on the first shaft CO', on which
is also the pulley D which drives the wheel spindle. There are
two speeds provided for the wheel spindle, obtained by moving the
belt at the wheel head, and one two-step pulley EE' only is used.
The belt runs as shown under a tension idler F, which compen-
sates for the difference of diameter of the steps on the wheel-
head pulley, and also for the variable position of the spindle
in and out, preserving a requisite tension on the slack side of
the belt. Thus the adoption of a tension idler adds consider-
ably to the life of the wheel spindle bearings, besides rendering
the change of its speed easy.

The first shaft CO' drives the second shaft at the rear by
means of the pulleys G, H, so that it runs at constant speed.
From the second is driven the drum for the work, the pump, and
the feed : the pump from the pulley J, the feed by means of
the step cone K on the second shaft and L on the machine,
and the drum shaft by means of the step cones M, N, the latter
of which is connected to the drum shaft P by means of a friction
clutch Q. This is operated by the lever K on the machine
through the connecting-rod S ; the brake is shown at T. The
drum P drives the dead centre pulley.

It will be noticed that the traverse is driven from a constant
speed shaft (by. the cone pulleys K and L), while in Fig. 33 it is
driven (through the pulleys y and N) from the shaft of the
drum which drives the work. In the latter case the traverses
therefore are a definite amount per revolution of the work,
and this possesses the advantages illustrated in Fig. 26 (page 95).
Plain grinders, however, generally have the traverses driven
independently, and the makers give various reasons for the

PLAIN GEINDEBS AND EXTEKNAL WORK 191

192 GEINDING MACHINEEY

arrangement ; one, however, does not appear to have been
referred to — namely, that high rates of rotation must be provided
for work of small diameter, and a traverse of nearly the wheel-
width per revolution then gives so high a velocity to the main
slide that the shock of the reverse must be cushioned, or will
lead to trouble if used. If the traverses are independently
driven, a limit of speed suitable to the machine and its gearing
can be easily arranged.

Rapid Speed Changing Arrangements.— This drive is nearly
the same as that shown for the Universal ; it has added a
tension idler to the down wheel belt, which permits the wheel
speed to be changed easily, and adds some other advan-
tages. Where speeds have to be changed frequently in manu-
facturing machines it is desirable that it should be an easy
and quick operation, and on the larger grinding machines it
is now customary to fit such arrangements, and is beginning to
be so on the smaller sizes. They usually take the form of gear
boxes of either the Hendy, the spring key, or sliding gear type,
such as are in favour in modern machine tool practice. The
operator of a grinding machine is continually making measure-
ments to a fraction of a thousandth of an inch, and welcomes
any convenience which makes it unnecessary for him to handle
a greasy belt, so that the obtaining of the various speed changes
by the movement of a lever has a secondary gain, besides that
of the time directly saved.

As regards the change of work speed, there are two very
different arrangements : according to the first, the speed of
the belt to the dead centre is changed by a gear box through
which the drive goes ; while in the second the gear box is on
the work head itself, and the work is driven by a dead centre
gear. The former type is used not only on Plain machines,
but also on Universals, and is hence better illustrated by taking
an example from among the latter. Fig. 71 shows the general
arrangement of the drive of the Cincinnati Universal Grinder,
in which the speeds are obtained by gear boxes carried at the
rear of the machine. Here the main drive is to the pulley A on
the first shaft BC. This shaft drives the wheel spindle pulley
D by means of the pulley E, giving one speed only, and the

PLAIN GEINDEES AND EXTERNAL WORK 193

gear box pulley F by means of the pulley G. From the left hand
part of the pulley F the pump is driven by a belt to the pulley H
and then through gears. The gear box is shown in Fig. 72.
The pulley F drives the top shaft which, by means of the

FIG. 71. — ARRANGEMENT OF DRIVE — CINCINNATI GRINDER Co.

clutches J, K and the gears LL', MM' gives two speeds to the
middle shaft N. For each of these speeds the lowest shaft
P can have any of six speeds by means of the nest of gears
Q, Q, Q, any one of which may be made the driver of the lower
gears Q, Q, Q by means of the spring key R controlled

194

GKINDING MACHINERY

by the rack sleeve and gear S, S', the gear being operated
from the front of the machine. The lower shaft on which
are the fixed gears Q, Q, Q carries the pulley T, which drives
the main slide traverse pulley A in Fig. 51. The middle
shaft is carried through to a second speed box U on the

FIG. 72. — CHANGE SPEED Box — CINCINNATI TOOL Co.

left of the machine, containing a nest of gears controlled
by a spring key operated in a similar manner to the other
from the front of the machine. The secondary shaft —
the upper one — carries a pulley V, which drives a pulley W
on the drum shaft XY, and from this the work is driven in
the usual manner by the belt Z. The countershafting is now
very simple, and all the speed changes are controlled by two

PLAIN GRINDERS AND EXTERNAL WORK 195

levers in the front of the machine, and both work and traverse
can be stopped by a movement of the lever, which operates
the clutches in the first speed box. The work spindle is belt
driven, which gives a smooth motion, and is not liable to cause
chatter marks. The drive shown gives one speed only to the
wheel head, but it could easily be arranged for more.

The advantage of having all the work and table speed

FIG. 73. — NORTON PLAIN GRINDER, 10" X 36"

changes on the machine — instead of being obtained by shifting
belts in the countershafting itself, or from the countershaft
to the machine (Figs. 33 and 70) — has caused the use of this
type of drive to extend rapidly. Messrs. Brown & Sharpe
have adopted it on their Plain grinders, using speed boxes
similar to those on their milling machines, except in the
smallest size, where an adaptation of the Sellars friction drive
is used. In Fig. 97 it is shown adapted to an internal grinder
by Messrs. Churchill.

o 2

196

GRINDING MACHINEKY

When the mechanism for changing the speed of the work
is carried on the headstock itself, the arrangement is generally
only suitable for a Plain Grinder ; the spindle could be either
live or dead, but the change over from dead centre to chuck
work would be a little troublesome if both were fitted. Figs. 73
and 74 show a 10-inch by 36-inch electric drive Norton Grinding
Machine, and in this the change of speed for the work is got

FIG. 74. — NORTON PLAIN GRINDER, 10" X 36"

by moving the belt A from the drum to one or other of the
steps of the cone pulley B, the shaft of which drives the dead
centre gear in the casing C by a pinion. The shaft is carried
in a swing frame about the spindle axis, so that the belt from
the drum can be made tight, whatever the size of the step it is
on. The tension is put on the belt A by the lever D — attached
to the swing frame — which is locked when the belt is tight.
The belt A passes through a guide E, which slides along a bar
F, and can be located correctly for the various steps of the
cone B. As a step cone driven from a drum cannot have a

PLAIN GKINDEKS AND EXTEENAL WOEK 197

very wide range of speeds, the drum has two speeds, by counter-
shafting pulleys with friction clutches. The feed is driven in a
similar manner — shown in Fig. 56 — the belt L which runs round a
weighted tension idler drives the pulley M, the speed depending
on the step of the cone upon which the belt is set. Here the
range of speeds given by the cone pulley M, which is driven
from a drum at the back, is increased by the gearing at N. To
avoid handling the belt, the change of the position along the
cone is made by the sliding fork P, the cones having inclined
parts Q, Q' between the steps, so that the belt L moves up and
down the cone easily.

The more usual method is to drive a gear box on the work
head by a constant speed belt from the drum, and obtain the
whole range of speeds by the gearing. Examples are shown
in Fig. 75 of a machine by Messrs. The Churchill Machine Co.,
where the gear box is of the spring key type, and in Figs. 62
and 63 of Messrs. Greenwood & Batley's machines, in which
the gearing is of the Hendy type, but the design avoids the
irregular slot opening of the Hendy box, and affords very
complete protection.

Geared Dead Centre Drives. — In these cases, where the
work is driven through a dead centre gear, there is always a
possibility, of the gearing producing surface marks on the
work. The dead centre gear should be as large as possible,
and the teeth numerous, cut spirally and of an overlapping
width. Even then marks are sometimes produced in the
work. They may also occur when the work is driven by a
worm and worm wheel. In such designs as that of Mr. Norton,
where the dead centre gear is driven by a pinion carried in
a swinging frame, the frame may be unlocked for the finishing
traverses — the weight alone makes a sufficient tension in the
belt — and by its yielding produces a smoother surface on the
work. It is frequently stated that gearing does not produce
surface marks on the work, but so far as my experience goes,
wherever a gear drive has been replaced by a belt drive, the
quality of surface produced has been improved. For much work
the surface marking, which is of very small depth, is not a matter
of importance, and the dead centre gear drive is then satisfactory.

198

GRINDING MACHINEEY

These improvements in Plain grinders to meet manufacturing
requirements have made them continually more complicated,

and the trend now is towards reducing the number of belts to
the machine, and finally towards self-contained machines. The
movement, commenced with the larger machines, has extended

PLAIN GEINDEES AND EXTERNAL WORK 199

to the smaller, and now Messrs. Nortons' smallest machine
(3 inches by 18 inches, Figs. 85, 86) is built self-contained.

By driving the work from the body of the machine itself
the countershafting is reduced to a single shaft, and by
arranging the wheel drive on the machine it then becomes

PLAIN GEINDEES AND EXTEKNAL WOKK 201

self-contained ; as these points are independent, machines
which illustrate both are selected as examples.

In Figs. 75 and 76 are shown views of Messrs. Churchills'
machine with self-contained work drive by means of a belt :
the drive is from the pulley in the rear, round the two centrally
situated idler pulleys, then round the work head idler pulleys
and main pulley, and finally by the idler pulleys at the tailstock
end of the table back to a central idler pulley and the driving
pulley. One of the idler pulleys is made to keep the correct
tension on the belt. In this arrangement the table may be
swivelled on the central stud without affecting the running of
the belt.

Another arrangement of the drive is seen in Messrs. Churchills'
large self-contained machine of Fig. 77, in which the work drive
is by means of a horizontal front shaft, a vertical shaft, and an
inclined horizontal shaft to the work head. In both these
machines the change of work speed is made by a gear box in
the head itself.

A similar drive is used on Messrs. Nortons' large self-con-
tained machines, Figs. 78 and 79, where the horizontal shaft
is inside the body of the machines and drives the horizontal
shaft, carried by the table and work head, by an inclined shaft.
The work table in this case cannot be swivelled, and the tailstock
has a set-over adjustment for securing exact parallelism.
The change of speed is obtained by a cone drive similar to that
previously described, and carried on the body of the machine.
The machine shown is fitted with a gap to accommodate such
work as pistons fixed to their rods.

The drive to the wheel spindle on these machines is similar :
the wheel spindle itself is driven from a countershaft carried at
the rear of the work head and adjustable — in Messrs. Churchills'
design by sliding, and in Messrs. Nortons' by swinging—
for the alteration in belt length ; and this countershaft is
driven from below by a belt at the side of the machine. A
weighted tension idler pulley is contained in this drive, so
as to allow the cross movement of the wheel head to take place
without affecting the drive to the wheel. The direction of
the belt pull is here almost directly away from the work, but
this cannot be avoided on self-contained machines. Two belts

204

GKINDING MACHINERY

are used, but the drive can be arranged with one only, as can
be seen in Fig. 82, which shows a very large machine by the
Landis Tool Co. There are here two idler pulleys used, the
belt to the wheel spindle being bent the reverse way in its

FIG. 80. — CHURCHILL PLAIN GRINDER, 30" X 20' 0".
ELECTRIC DRIVE

SELF-CONTAINED

circuit ; it has the advantage, however, of being a much longer
belt than those of the system first described.

These machines are entirely self-contained, and are driven
by a single pulley or a motor suitably placed. Where the size
of machine is still greater, the arrangements for transmitting
the motion to the work become cumbersome, and the work head
is then most conveniently driven by an electro-motor, so that
two or more independent electro-motors are employed in the

PLAIN GRINDERS AND EXTERNAL WORK 205

driving of the machine. The greater the amount of power
required at any point, the more suitable does the employment
of a separate motor at that point become, so that the larger
and more powerful the machine the more profitable is the
employment of separate motors for the various movements.

In Messrs. Churchills' 30 inches by 20 feet Plain Grinder,
Fig. 80, two motors are employed — one to drive the work and
the other driving the wheel and other motions. The machine
is of the travelling table type although the length is so
considerable, and is generally of much the same design as this
firm's smaller machines which have been previously illustrated.
The work head motor is set with its axis at right angles to
the work axis, so that any want of balance there may be in the
armature does not produce direct effects on the work. The
arrangement of the cable conveying the current to and from
the work head motor as it moves can be easily seen. The
wheel guard in this machine is of rolled steel instead of the
usual cast iron.

A machine of the same capacity, 30 inches by 20 feet, by the
Landis Tool Co. is shown in Figs. 81 and 82. It is driven by
three motors. The wheel, 30 inches diameter, is driven from a
variable speed motor, controlled from the front of the machine,
by a belt running round two idler pulleys, as can be seen in
the rear view. This grinding wheel motor is not carried
on the main slide, but runs on the track seen at the rear of
the machine, and receives the current from, and delivers it
to contact shoes which run on the wires at the rear of the
body of the machine. The grinding head cross slide has a
rapid power movement controlled by the lever seen alongside
the hand cross-feed ; this is in addition to the usual fine auto-
matic cross-feed.

The motor at the work head end of the machine serves
the double purpose of revolving the work and traversing the
main slide, the speed changes being by change-speed gear
boxes. The third motor is used to drive the pump, and is
seen at the right-hand end of the machine, with its armature
spindle vertical.

It will be noticed that in this machine the wheel slide is

208 GEINDING MACHINEKY

^ik

not gibbed down, but is guided by a vee and a flat way. The
reversing stops are fitted on a rod at the front of the machine
and tripped by contact with the travelling wheel and mechanism,
which is moved in unison with the wheel by means of the screw to
be seen just above the rod on which the reversing stops are fitted.

A very large roll grinding machine, taking work up to 50 inches
by 17 feet, by the Norton Grinding Co., is shown in Fig. 83.
Here the wheel head travels, and the motions are controlled
from the wheel side of the machine, which is the best arrange-
ment with work of large diameter. Here five independent
motors are employed : a 40-h.p. motor for driving the wheel,
one of 15-h.p. for revolving the rolls, and three 2-h.p. motors
for moving the work headstock and tailstock along the ways
to the different positions required, and for driving the pump.
The wheel is 24 inches in diameter by 8 inches face, and weighs
200 Ib. ; the small crane seen at the wheel head is for lifting
the wheel and its collet. The centre seen in the tailstock is
6 inches in diameter, but is not used for the work seen in
the machine, which is ground supported in pillow blocks.
The total weight of the machine is 100,000 Ib.

In their largest machine, shown in Fig. 84, Messrs. Churchill
have adhered to the travelling work type. This machine
has a capacity of 50 inches by 25 feet, and takes wheels up to
50 inches by 5 inches. Its weight is well over 100,000 Ib. and
its bed is 50 feet long. It is driven by two electric motors, and
the controlling mechanism and operating levers are brought
to the front of the machine. The general details of the
mechanism follow the lines of the smaller machines, but the
rapid movement of the wheel head is power driven — by means
of the open and crossed belts on the pulley to the right of
the operating mechanism. When in use the lower part of
this mechanism is covered and protected by a steel platform,
above which only the lever handles and the hand wheels
project. The mirror, carried on the steel wheel guard, gives
a view of the approach of the wheel to the work. The staging
carrying the conductors of the current to and from the wheel-
head motor, which is of the variable speed type, is seen at
the rear of the machine.

irm

PLAIN GEINDEKS AND EXTEENAL WORK 211

The large machines illustrated above, which have been
built in recent years, and their* commercial success, show that
there is a growing reliance in the suitability of grinding for
work of large size, and a belief in its economy. All these
machines are fitted with easily operated speed and feed controls,
as on such sizes it is a necessity ; on the smaller machines
such fittings are a great convenience, but they are expensive
features when the total cost of the machine is considered,
and this renders their acceptance into current practice slow.
That they are becoming regular features of the machines
indicates that it is now recognised that the handling time is
worth saving.

As illustrating the extension of the fitting of such con-
veniences to small machines, views are given in Figs. 85 and
86 of the smallest machine made by the Norton Grinding
Co. The main drive of the machine is at A (Fig. 86) and
from the main shaft the belt B drives the pulley C on the
wheel head countershaft, the correct tension being maintained
by the spring-controlled idler pulley D. The countershaft
pulley E drives the wheel spindle itself by a belt running
round the tension idler F. The table feeds are driven from
the pulley G on the main shaft, which drives the cone pulley H
(Fig. 85). This in turn drives the cone pulley J, the various
table speeds being obtained by shifting the belt along it.
From J the table is driven in the manner adopted in the
larger machines. The work is also driven from the main
shaft through the double Hooke's joint telescopic shaft K and
gears, the speed changes (4) being obtained by the cone pulleys
L and M, the latter of which drives the dead centre gear by
a pinion. The control rod for this motion is seen at N, the
handle being in front of the machine. Below this is the
handle P operating the main belt fork. The cross-feed contains
a differential gear, so that the spaces seen at Q giving the
minimum cross-feed movement are wide ; a substantial dead-
stop is provided at E. The settling tank S is pivoted at its
lower inner corner for convenience in cleansing. As the table
movement on small work (the machine takes 10-inch by 1-inch
wheels) is rapid, the reverse is pneumatically cushioned.

212

GEINDING MACHINEEY

Such machines as described above indicate the develop-
ment of the art of grinding as a manufacturing process. In
the progress from the Universal Machine of the tool room,

FIG. 85. — NORTON PLAIN GRINDER, 3" X 18". SELF-CONTAINED

the desire for increased production was first met by the use
of greater power by more rigid machines, and this has been
followed by the employment of rapid speed changing and
handling devices, while at the same time continual efforts
have been made to improve the protection of the various parts
against grit, and to increase the useful life of the machines.

PLAIN GKINDEKS AND EXTEKNAL WOKK 213

From the machines we now turn to the work, and the
actual process of the use of the machines.

Preparation of the Work. Centre Holes. — External cylind-
rical wrork is done between dead centres wherever possible,
as it eliminates errors due to a live centre running out of

FIG. 86. — NORTON PLAIN GRINDER, 3" X 18". SELF-CONTAINED

truth. In the preparation of the work the centre holes are
important, and should be of the shape shown in Fig. 87, the
centre hole A being drilled well beyond the vertex B of the
taper C, and for this Slocomb centre drills are useful. The
end of the work at D in the neighbourhood of the hole should
be faced if there is much work to be done on the part, as other-
wise the hole may tend to wear to one side.

214

GRINDING MACHINERY

For repetition work, if there are tapers or shoulders on the
work, the centre holes in all the pieces should be drilled to the
same depth, as the tapers can then be sized by the automatic
cross-feed, and no readjustment of the reversing stops is
necessary.

The angle of the taper is usually 60°, but some firms prefer
to work with 75° ; this is the greatest angle used in work to
be ground. The diameter of the hole desirable depends upon
the work : centre holes suitable for lathe work are large
enough for grinding. When the part has no lathe work on it
the centre holes should be as large as would be used on lathe

work, if output be the
consideration, but if it
be precision they should
be smaller. For gauge
work £ inch on medium
size and -f$ inch diameter
on larger gauges is suf-
ficient for the large end
of the taper ; and in
work of this precision the
holes should be lapped a
little after hardening.

Key -ways may be filled with wood if they cause a tendency
for the water to splash.

In some cases it is more profitable to grind direct from the
rough, whether black bar, forging, or casting, than it is to turn
first. In these cases care should be taken that the allowance
is as little as is consistent with the work always cleaning up.
Black bar should be reeled : -^ inch is sufficient allowance for
diameters up to 1 inch by lengths up to 4 feet. While it is
impossible to give a general rule, shafts in which the ratio of
length to diameter is 30 or more are usually economically
ground from the black. The more slender the part and the
harder and tougher the material, the more difficult the turning
is, and the more likely it is that grinding from the black will
prove economical. It may be noted that if the shafts be of
tool steel for the sake of hardness they should be turned first,

FIG. 87. — CENTRE HOLES

PLAIN GRINDEKS AND EXTERNAL WORK 215

as the surface may have been decarbonised to some extent in
the processes of manufacture, and requiring a diametral •£$• inch
or so to be removed.

Automobile crankshafts and many other parts are frequently
ground direct from drop forgings. The primary consideration^
here is the quantity, as the cost of dies is considerable. The
forgings can be produced regularly within ^ inch of size, and
closer should it be desirable. The amount to be ground
off is further increased by the allowance of 5° taper aside at
shoulders and some other flat parts which is necessary, in
order that the work may leave the dies readily.

Allowances for Grinding. — In preliminary turning a smooth
quality of surface is not desirable ; the ridges left from the tool
are very rapidly ground off, and help to keep the wheel in good
condition for rapid work.

The amount allowed for grinding in the turning is governed
by the necessity for the work invariably finishing to size, and
should be such as to leave no doubt in the mind of the grinding
operator as to whether it will do so. The lower limit is fixed
by this consideration, and an upper limit arranged so as to give
such a margin that the turning can be done rapidly. As the
finishing from 0*020 inch over-size takes only a little longer than
from 0*015 inch over-size, the lathe limit should be wide with the
aim of total economy on the whole of the work. The limits should
be closer where the work is done on a capstan than on a centre
lathe, as the cost of working to the finer limits is then smaller.

The practice of Messrs. Brown & Sharpe is to allow
0*008 inch to 0'012 inch on the work diameter for all sizes of
work. This is an allowance only suitable for repetition
manufacturing in quantity ; for general work the allowance
should be larger, otherwise too much time will be taken in
the turning.

The Landis Tool Co. recommend the allowances given in
Table IV, but do not suggest the limits.

The allowance given should depend not only on the size
of the part, but also on the rate at which it is to be turned,
and the purpose for which the part is intended. If the part
is intended for strength, particularly against fatigue, and the

216

GEINDING MACHINEKY

turning rapid, not less than O'Ol inch for capstan or 0*015 inch
for centre lathe work should be allowed, as it is important
that all the material over-stressed (and perhaps therefore
containing incipient flaws) in turning should be ground off.
^Reasonable regular tolerances (to be added to the minimum
allowance, are 0*004 inch to 0*006 inch for capstan and O'Ol inch
to 0*015 inch for centre lathe work.

Case-hardened Work. — For hardened work the limits can
only be fixed after experience with the particular steel used,
and depend on the shape of the part also. When work is
desired to be hard in some places and soft in others it is usual
to case-harden it on those parts only which are to be hard.
Case-hardening for grinding cannot be done by ' potashing '-

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FIG. 88. — TURNING FOR CASING AND HARDENING

that is, by making the work red hot and rubbing the surface
with ferrocyanide of potassium, which fuses on the surface and
carbonises the iron there into tool steel — as the effect of this
only extends to a depth of a few thousandths of an inch from
the surface. To case-harden to a depth suitable for grinding,
the part must be heated in contact with carbonaceous matter
or gas for several hours. To prevent the parts which are
desired to be soft from becoming carbonised, they may be
covered with clay — which is unreliable — or copper-plated
(the whole is copper- plated and the plating afterwards polished
off the parts to be hard), but preferably only the parts to be
hard are turned, the whole cased, then the casing turned off the
parts to be left soft, and finally the part hardened. This is
illustrated by the sketch of a spindle shown in Fig. 88, in which
the bearings AB, CD, and the face DE are required to be hard
and the rest of the spindle soft ; also suppose that the spindle
is to be hollow as shown. The depth of the casing and the

PLAIN GRINDERS AND EXTERNAL WORK 217

allowance for grinding will vary with the size of the spindle ;
for a length between one and two feet a depth of ^ inch to
•fa inch of carbonising is sufficient, and a suitable grinding
allowance is 0*020 to 0'025 inch on the diameter.

The stock is cut off and the ends faced so that the part is
fV inch or J inch longer than the finished spindle — suppose
it J inch over-length. The bearings AB and CD are then
turned with the allowance above mentioned for grinding,
and a little is left on the face DE, so that the part has
the shape of the broken outline. It is best to turn off
the skin of a bar ; it is apt to be hard after carbonising.
It is then carbonised by heating in contact with charred
leather, granulated bone, or other suitable compound, at
a temperature of 900° C. for about five to six hours. There
are a number of mixtures on the market for the purpose of
carbonising, but most of these are supplied in a state of fine
powder, which is undesirable, as the carbonising is actually
performed by the gas given off. Granulated bone contains
phosphorus, and it is better to avoid it. Sulphate of barium
mixed with the leather accelerates the process, but whether
the result is as good as with charred leather alone is doubtful.
The amount — percentage — of carbon absorbed in the steel
depends on the depth from the surface, so that the depth of casing
is not an exact figure, though a fracture shows a well-marked
ring. The depth, which depends on the time of heating, may
be anything desired — up to several inches in the case of armour-
plate. As it takes time for the heat to penetrate the box and
carbonaceous material, it is advisable to put small test pieces
in the box of parts to be cased. These may be withdrawn
hardened and broken, so that the actual depth of casing can
be ascertained at various times, and the correct amount
secured in the parts.

When the depth is sufficient the parts are allowed to cool
slowly. Then the spindle is rough-turned to about 0*025 inch to
0*05 inch over -size, and the ends faced to size, and it is ready to
be reheated and hardened. As all the outside of the part which
was carbonised has been turned off except at the bearings AB,
CD, and the face DE, these alone become hardened. The

218 GKINDING MACHINEKY

object of leaving so much on the ends is to make sure that the
carbon does not reach a part to be machined in a lathe after
the hardening process, and it should not be forgotten that
deep centre holes should be drilled out before hardening, as
the spindle is to be hollow.

In casing the part should be quite clean and free from oil.

When hardened steel has to be straightened, its temperature
should be raised as much as possible without drawing the
temper, and the straightening done at that heat.

Generally a little warping takes place, but the allowance
given should cover the distortion in spindles of the length given,
and over 1 J inch in diameter. Trial with the particular part is
the only way to fix allowances, and once fixed the kind of steel
used should be adhered to.

In grinding hardened work it is best to use a soda solution
(not oil), so that the wheel cuts as freely as possible, and to use
light cuts when within 0-005 inch of size (diametral), otherwise
the surface hardness may be impaired (see page 72).

Specially Accurate Work. — Generally speaking, grinding
should be the last process done upon any part required to be
accurate ; turning and milling operations, and particularly
key-waying, are apt to distort the material. For particularly
accurate work such as machine tool spindles the finish grinding
should be done without removing the part from the centres, as
there is always a chance of a minute particle of grit in the
centre holes slightly altering matters.

Machine Centres. — The centres of the machine must be kept
in good condition ; they should be dead hard near the points.
For work smaller at the last diameter than the centre is, it is
most convenient to use a half centre in the tailstock barrel, so
that the wheel can be run off the work without being run
back. Female centres should be used on work (such as twist
drills) where the centre hole must not be left, as the finished
shape is definite as to length, and removing a tit is quicker than
grinding the material away until there is no hole.

Driving the Work. — The carriers used for driving small work
should be of the balanced type, and should fit the work nearly,
as any out-of-balance effect may show itself in the work ; for

PLAIN GEINDEKS AND EXTEENAL WOKK 219

holding finished work carriers drilled and reamed to the size and
split are useful. A sketch is given in Fig. 89.

When the machine is gear driven there is a chance of the
teeth producing marks on
the work ; to minimise this
effect a piece of rubber tube
or leather may be put round
the driving pin, or between
it and the carrier.

When work is parallel FIG. 89.— CARRIER FOR FINISHED WORK

from end to end (or parallel

except that one part is a push fit and the rest is a running fit) it is
best to grind the length at one operation, and then a carrier cannot
be put on the work, but it is driven from the end either by a
running square centre or by a special dog. For the first method

FIG. 90. — DRIVING WORK FOR GRINDING AT DOG END (BROWNE & SHARPE)

a secondary head is used, in line with the regular dead centre
work head, but containing a live spindle fitted with a square
centre, and driven from the dead centre pulley in its rear.
The angle of the square centre should fit the hole in the work,
and for sharpening it, if the angle is 30°, the head should be
set at an angle of 22° 12'.

220'

GKINDING MACHINEKY

In Fig. 90 is shown a dog arranged to drive shafts so that
the wheel may pass over the whole cylindrical surface. Two
holes have to be drilled (extra operation) in the end of the
shaft. Two steadies are shown in position.

Mandrils. — The mandrils for holding hollow work are
ground to a small taper, so that one end just fits, while the other
is a very tight fit, and drives the work by friction. The correct
taper depends on the ratio of diameter to length of the work ;
to meet the generality of work they are usually ground to a taper
of 0-003 inch per foot. The centre holes should be formed and
the ends recessed, as shown in Fig. 87 ; the large end should have
a longer reduced part than the other end has, so that they can
be at once inserted in the work in the correct way. The size

FIG. 91. — HOLLOW WORK HELD BY CONES

should be stamped on the reduced part so that it cannot be cut
and effaced by the work slipping.

Hollow Work. — Hollow work is best held between cones,
the ends of the work being bored to the angle ; one cone is
solid on a mandril, which goes freely through the work, and the
other screws on it and is tightened to the work. If centred
plugs are driven into the work, they may distort it, and the first
one is difficult to remove. A sketch illustrating the arrange-
ment is given in Fig. 91 , and illustrates a case where the work
can be ground completely at one operation.

When the work is thin, for example a tube or drum, the cut
must never be forced ; any appreciable rise of temperature
distorts the work, which causes untrue grinding, and finally
loss of time. As soft a wheel as possible should be used.

With an ample water supply the work does not rise in
temperature appreciably as a whole, and so does not expand
lengthways, and it is accordingly customary to clamp the
tailstock barrel, since rigidity of the parts opposes vibration.

PLAIN GEINDEKS AND EXTEKNAL WOEK 221

The barrel should be released and retightened at intervals,
so that should there be slackness between the centres and centre
holes, it will be corrected by the tailstock spring forcing the
centres up to the work.

The centre holes should always be wiped and both oiled
before putting the work into the machine : error produced by a
particle of grit may not be detected until the piece is practically
to size and it is too late to remedy it.

The tailstock barrel is held up to the work by a spring,
and provision is made for adjusting its tension. When
placing the work between the centres, it should be ascertained
that the tension is suitable for the size of the work ; a con-
siderable amount is desirable for heavy work, but slender
work will stand a light end force only.

Setting the Stops. — After putting the work between the
centres the stops are set by running the main slide to the position
at which it is required to reverse, then the reversing lever is
pushed over until the trip takes place, and the stop moved
up to it and clamped. The fine adjustment screw should then
be set out a little further and the reverse tested automatically
to see that it is correct, and the position finally adjusted.

Shoulders. — In grinding to a shoulder the reverse can be
set close to it, and the wheel brought right up to grind the
shoulder by hand. If the machine is not fitted with a tarry
motion the travel may be occasionally thrown out at .the
shoulder end, while the work makes two or three revolutions.
If it is important that there should be no slight taper near the
shoulder due to the wear of the wheel, the feed at the other end
of the stroke may be thrown out, so as to throw the wear of the
wheel upon that side.

When preparing work in the lathe the corners may be
nicked in, as shown at B, C, and D in Fig. 88. It must be
remembered, however, that any such nick very considerably
weakens the shaft. Where strength is the consideration no
nicking is permissible, and a radius corner is desirable, parti-
cularly when the value of the stress varies.

Setting for Parallel and Taper Work. — In setting the table

222 GEINDING MACHINEEY

for taper work, or for parallel work after taper, it is first set
over to the correct position, as shown by the graduations on the
plate ; but this does not secure the correctness of the work,
partly because of the difficulty of seeing to such degrees of
accuracy as are aimed at, and partly from the chance of grit
under the headstock or tailstock affecting the centre line posi-
tion. The final appeal must be to the ground work itself, either
by gauge or measurement by a micrometer, the former being
best for taper work and the latter for parallel work. In
adjusting the swivelling screw the amount of movement should
not be overdone, as there is always a little slack in the fitting,
and it is quicker to keep it in one direction.

Advantage should be taken of the fact that adjusting the
taper screw does not move the work in the neighbourhood of
the swivel pin much to or from the wheel.

Where long work of a particular length has to be done at
intervals a bar of the same length as the work with short
portions of equal diameters — rather larger than the rest of the
shaft — at each end, is useful for setting the table accurately
and quickly.

The Wheel.— The wheel for the particular work is to be
selected according to the material and shape of the work, and
data for facilitating the choice are given on pages 42-8,
and in Tables VI and VII. A new wheel should be started
slowly to make sure that it is not excessively out of truth.

In truing the wheel plenty of water is to be always
used on the diamond, and the setting must be examined
occasionally.

The wheel should be trued at the speed at which it is to
be used ; if the spindle speed be considerably reduced, with
the object of saving the wear of the diamond, the wheel may
run very slightly out of truth when at the grinding speed.

Speeds and Feeds. — The speed for the work is to be selected
on the principles given in Chapter III and the data of pages 432,
433, and the rate of speed of the main slide is to be adjusted
so that the travel per revolution of the work is from f to | of
the width of the wheel face.

PLAIN GRINDERS AND EXTEKNAL WORK 223

Loading. — Very occasionally in grinding mild steel, but more
frequently in grinding copper and soft bronze, the particles
of metal become embedded in the wheel surface instead of
falling freely away. The wheel is. then said to be loaded, and is
unable to cut ; it is best in such cases to change the wheel,
but if that is inconvenient the surface should be redressed, and
a finer cut used. A high wheel speed lessens the tendency.

I have proved in the chapter on the wheel and the work
that there is no definite correct work surface speed, but that
its best value depends not only upon the material of the
work and wheel, but also upon the diameters of each and
upon the machine used. Thus the work speed selected may
easily be incorrect and, if it be much out, the wheel will
wear unduly or glaze ; the speeds and feeds must then be
corrected.

Checking the Wear of the Wheel. — If the wheel wears away
too rapidly it is not at first evident unless very excessive.
The diameter of the work should be measured and the cross-feed
reading taken. After the work diameter has been reduced
somewhat, the amount should be compared with the wheel
movement as registered by the difference of the cross-feed
readings ; the difference gives the wear of wheel diameter, and
should be very small.

When the quantity is sufficient for two handlings, the wheel
wear should be quite appreciable in the roughing, else the
grinding will take longer than is necessary ; but if it is too
great, not only is the wheel wasted, but it becomes untrue, and
so time is lost. Eapid wheel wear is often accompanied by
chatter and vibration ; a want of balance may then be sus-
pected, as it causes a wheel which is wearing a little to become
untrue, and then chatter and waste commence.

The most obvious method of checking the wheel wear is
to reduce the cross -feed ; experience, however, has shown that
it is better to reduce the work speed instead, as a better output
is secured. This is regarded as the best modern practice.
The correct method, however, is to reduce the work speed
considerably more than is sufficient to stop the undue wheel
wear, and to increase the cross-feed correspondingly. This

224 GKINDING MACHINERY

method (see Chapter III) stops the waste, but does not sacrifice
output, as the previous methods do.

Checking Glazing. — When, on the other hand, a wheel
glazes, the speeds and feeds are to be changed in the opposite
direction : the work speed raised and the cross-feed reduced,
which is rendered necessary, as it is here supposed that the
machine is already taking its working horse-power.

When a wheel face is thoroughly glazed it is difficult to
break it up and to restore it to the proper condition, and it
is frequently necessary to re-true it. At the first intimation
that the wheel is glazing a good cut should be put on by hand
to check it, and then the work speed increased and the feed
reduced.

If the speed and feed alterations do not stop the glazing,
more force must be used per inch of wheel face, which is done
by reducing the width of the face. The effective width may
be reduced by decreasing the traverse, but the wheel face
then tends to wear convex.

The final resource if wheel wear or glazing persists is to
change the wheel.

On any particular machine work of small diameter should
run at a slower surface speed and with a deeper cut than is
correct for work of moderate diameter ; if the force of the
cut is too great a higher velocity and less cross -feed should be
employed. When the work is of large diameter, the surface
speed should be higher and the cross-feed less ; if the cross-feed
thus becomes undesirably small, a narrower or softer wheel
(see Chapter III) must be used. Either alternative will permit
a heavier cross-feed and a slower work speed to be used (see
Chapter III and page 264).

After experience with any particular machine, the correct
work speeds should be selected without difficulty, as the variation
of the size of the wheel as it gradually wears down produces
no great effect. The influence of this factor is discussed in
the next chapter, as it is of importance in internal work.

Fig. 199 is drawn to assist the determination of correct
work speeds. In it the E.P.M. of the work is plotted against
the ratio of work and wheel diameters by use of the formula

PLAIN GEINDEKS AND EXTEKNAL WOEK 225

deduced in Chapter III. The factor for the diagram has to
be determined by trial for the particular machine in use.

Output. — After the work speed and cross-feed are satis-
factory, trial may be made — by reducing the former and in-
creasing the latter — to increase the output. The work speed
must not, however, be so far reduced as to produce defects in
the accuracy of the work.

For finishing — the last few traverses when the quantity is
small, or the second handling when it is large — the work speed
should be increased, as the cross-feed is now small. The re-
straining factor here is the greater tendency of higher speeds to
produce vibration, and the speed should not be raised so much
as to approach that which would produce vibration.

The rate of travel may be reduced, but there is little
advantage in it except to minimise a travel mark.

Form Grinding. — Diameters of short length, frequent on
the ends of shafts, are most quickly ground by feeding the
wheel directly in without using the traverse ; if the length is
greater than the wheel face, the wheel should be fed in twice,
the outer side being done first and not quite to the full depth.
After feeding in, the work is traversed off the wheel by hand,
securing uniformity oi diameter. With a reliable cross-feed it
is not necessary to measure the work until it is finished, and
a dead stop to the cross-feed is here useful, as it saves
watching the graduations closely. This method of work may
be termed ' form grinding,' as it can be used in the production
of work other than of straight section. For accuracy reliance
is placed on the wheel truth.

Cross-feed. — Traversing by hand tends to produce an
illusive impression of greater rapidity of work, and generally
both the automatic traverse and the autocross-feed are to be
used : the latter should be adjusted as above, but it should not
be such as to be close up to the limit either of the wheel or
machine. Working near to any limiting conditions is not
economical in grinding : the wheel face is not a permanent
surface, but alterations in it are constantly taking place ; if
for any reason trouble arises, as it probably then will, the loss of

226 GEINDING MACHINEKY

time more than effaces the gains previously made. What is
to be aimed at is a steady condition which can be maintained
in the face of unavoidable small variations, and not a condition
of grinding a few parts in the minimum time with the maximum
stress on the machine and operator. The most satisfactory
adjustment of the cross-feed is to have it on the low side ; it can
be increased by hand, at any time when the work is being done,
easily.

The water supply must be directed right on to the work at
the grinding point, and the flow must be steady, as irregularities
in it may cause irregularities in the work.

Errors of Roundness. — Troubles may occur either in the
accuracy of the work shape or in the quality of its surface.
The former takes the shape of want of roundness of the work.
This is occasionally, but seldom, due to an unsuitable wheel, and
the cause is generally to be found in the work itself.

If the error is at the ends of the work the centres or centre-
holes are to be suspected ; if at the centre then a heat or re-
leased strain effect. In the former case, it should first be noted
whether the centres are right up to the metal of the work ;
if they are not this should be rectified, and another trial made.
If they are, the work should be taken out and the centre
holes carefully wiped and oiled, and it should be seen that their
shape is correct, as in Fig. 87 ; another trial should then be
made. If the centres themselves are worn, they must be
reground.

Such trouble may also be due to want of balance in the work
or carrier. If this is the case the work should be balanced
and the carrier changed, but the effect may be considerably
lessened by reducing the work speed, as want-of-balance effects
vary with the square of the speed.

In the second case — where the trouble is due to heat effects
— attention should be given to the water supply, and the rate
of grinding should be reduced. If the cause, however, is the
release of internal stress, nothing can be done except mildly to
anneal the material.

If the work is not a straight parallel or straight taper,
the defect is in the main ways of the machine, or may be due

PLAIN GEINDEES AND EXTEKNAL WOEK 227

to forcing the rate of work. It is easily ascertained whether
the latter is the case by taking more time in finishing. In work
which is not too stiff this want of straightness can be corrected
by manipulation of the steadies; when the work is too stiff
the only method is to let the wheel traverse over the high
parts and so reduce them. Appreciable error due to want of
truth in the main ways should, however, never occur.

Vibration and Chatter. — The most serious defect of quality
of surface is due to chatter, which causes a series of small
flats on the work. This is due to vibration, which may arise
from several causes.

The wheel spindle belt runs at a high speed, and a heavy
lacing or fastener is quite sufficient to originate the vibration ;
the belt should preferably be an endless one, or if not, the
lacing should be either a belt lace (without large knots) or
else of the wire hook type. The belt may oscillate as it runs ;
if this happens it is probably due to insufficient tension in it,
and the belt should be taken up.

The wheel spindle should run very nearly metal to metal
with its bearings, and in satisfactory running the bearings are
quite warm, and the motion of the spindle smooth. The correct
adjustment of the bearings is best ascertained by their
temperature rise, so that those bearings which can be adjusted
while the machine is running, or at any rate immediately
the spindle is stopped, are the most convenient. To produce
a very fine surface on the work the bearings should run hotter
than is necessary for ordinary work ; they will not, however,
have so long a life when set up closely. If, after these points
have been attended to, the wheel head vibrates when the spindle
is run without doing work, the wheel is out of balance. It
should be trued and tried again, and if still out must be re-
balanced. Occasionally wheels are so much out as to be
unusable. If the work progresses satisfactorily for some time,
and then chatter gradually begins and a kind of rumbling
noise, due ultimately to irregularities in the wheel face, sets in,
the depth of cut or the work speed is too great, or the wheel
too soft. Immediately this occurs the work should be stopped
and the wheel, as it will have lost its true shape, redressed,

228 GKINDING MACHINERY

taking a fairly good cut over it : the work speed or cross speed
should be reduced, and a fresh start made slowly so as to get
rid of the marks on the work.

Vibrations set up in a machine from any cause, travel all
over it, both through the body of metal and along surfaces, and
are reflected from junctions or at variations of the section.
In a thick, heavy section the vibration may not be apparent,
as the movement will be so little, but the conveyed energy
may make a slighter part vibrate conspicuously. Waves
travel to and fro, and may reinforce or annihilate the effect of
one another ; it is only when the former occurs that the effect
becomes conspicuous. The velocity with which a wave travels
is independent of its size (amplitude), so that by varying the
rate of the production of waves, the result may be very different,
and very little difference may be necessary to prevent effects
accumulating. Accordingly a simple change of work speed
may be effective in stopping chatter.

As regards the work's part, marks may be due to irregularities
in the drive if a dead centre gear is used. To prevent this,
the driving pin may be cushioned by a bit of leather or rubber.
The dead centre gear teeth should be spiral, but of not too
acute an angle. Worm drives also may cause marks on the
work. In either case, as a preventative measure, the teeth
should be numerous. Probably the chief cause of chatter is
vibration of the work itself, or the supporting centres, under
the forced vibration of a heavy, irregular cut. The object
of steadies is to prevent this, and whenever the work is of
such dimensions as to render it likely that vibration will occur,
they should be used. While a steady may permit a short, fairly
stiff piece of work to be ground a little more quickly than it
can be without one, the time of setting up and using the steady
is to be taken into account, so that for small and moderate
quantities steadies are not much used except where there is a
suspicion of chatter. This is chiefly due to the continual atten-
tion and adjustment the present designs of steady necessitate,
and which are not required by an automatic stea(ty. The
value of the use of steadies increases with the length of the work
and also with the quantities ground at a time. The action of a

PLAIN GE1NDEKS AND EXTEKNAL WOKK 229

steady consists in resisting vibratory motion of the work at the
point of application of the steady blocks. If the steady block is
held in contact with the work positively, by means of a screw
or otherwise, the steady itself will have to spring if the work
is to vibrate there. If it is held up into contact by a spring,
the work is strained by the force of the spring and the vibration
time greatly quickened, and the amplitude (amount) reduced ;
in the latter case there is always contact, and the blocks should
be metallic, while in the former case unless the steady is con-
stantly attended to there may be slack, and to prevent this
wood blocks are used which yield elastically, and so take up
small amounts of slack. For large quantities of repetition
work steady shoes of hardened steel are the best ; they must,
however, be accurately made. In these cases dead stops to
the steady movement are very convenient.

Steadying by Straining. Grinding Springing Work. — Between
the steadies the work is free to vibrate, considered as fixed
where steadied. The period of vibration is then very much
shorter than that of the work as a whole, and the amplitude
correspondingly reduced. Usually this checking of the vibra-
tion is sufficient, but in the case of thin work it is not so, and
chatter marks occur between the steadies, though they are
absent near them. In this case the period of vibration of
these intermediate parts can be shortened by springing the bar
so that it is bent into an arc. If a thin bar be placed between
the centres and struck with the hand in the centre, it springs
and vibrates easily. If then steadies (say two) be placed along
it and set up to it, it will be found that an equal blow is resisted
much more solidly, and the rod vibrates through a much less
distance — the vibrations are much faster and die out more
quickly. Now adjust the steadies so as to spring the bar
upwards, and it will be felt that the resistance to a downward
blow is again considerably increased and the vibration effects
diminished. This is the state to be aimed at when long, thin
bars are to be ground. If vibration occurs between the steadies,
they are adjusted to spring the bar, until it feels nearly rigid
at the intermediate points. The lower shoe of the steady should
get well round the work, as at M in Fig. 60, for example.

230

GRINDING MACHINEEY

When ground so sprung the section at any point will be
circular and the bar straight (if previously free from internal
stress) when released. To grind it parallel the steadies must
be manipulated. In springing the bar it should be sprung
nearly vertically upwards, but slightly outwards away from
the wheel, and to effect this the lower shoe must reach beyond
the centre. This is shown in Fig. 92, where A is the section
of work near the centre, and the broken circle B indicates the

section of the bar when
it is sprung. Places
should be ground for the
steady blocks before ap-
plying them. On start-
ing to grind the ends
alone are ground first, as
the effect of the steadies
has been to draw the bar
away from the wheel, and
the bar is then larger at
the centre than at the
ends ; the steadies are
then adjusted as the
grinding proceeds so as
to push the bar into the
wheel — as shown at C in
Fig. 92 — and to grind it
there to the same diame-
ter as it has at the ends. The diameter of the bar at its
ends is then obtained by the use of the cross-feed, the table
having previously been set parallel so that the two ends are
the same ; the diameter is made the same at each steady by
using the adjustment, which moves the blocks towards the wheel.
When these diameters are correct, those at intermediate points
along the bar will be the same within insignificant amounts.

Thus the bar is first sprung up in the direction PQ and
then pushed in towards the wheel along the line ES. The
direction PQ should be slightly away from the vertical ; that
of ES is not of importance.

FIG. 92. — SPRINGING SLENDER WORK FOR
GRINDING

PLAIN GKINDEES AND EXTEKNAL WOEK 231

The being out of balance of work or carrier always pro-
duces an effect ; whether it is noticeable or not depends on
the amount of the want of balance and the stiffness of the
work ; and what is noticeable depends on how closely the
work is examined and on what the requirements are.
Defects of roundness are not visible from the optical ap-
pearance of the shaft (as traverse marks are), but a little
lapping will show very conspicuously defects which cannot be
detected with certainty by a micrometer, but which are of

FIG. 93. — METHOD OF DRIVING CRANK SHAFTS — LANDIS

importance in journals. The application of steadies decreases
the effect of this want of balance very considerably, and generally
to very trifling amounts.

Crank Shafts. — Crank shafts are particularly springy, and
liable to suffer from out-of-balance effects. For grinding the
pins they are best held at the ends in collar grips and driven
simultaneously from both ends, so that the shaft is stiffened
in the same way as a column is, by fixed ends as against
pin joints. The application of a steady to the part being ground
then holds the whole shaft firmly, so that want-of-balance
effects are reduced to as little as possible. The arrangement
is shown in Fig. 93 ; the face plate carrying the jig with a

232 GEINDING MACHINERY

throw adjustment and dividing plate is gear driven from the
splined shaft seen in front. The other head is driven from
this shaft, an adjustment being provided in the gearing for
setting the heads in unison.

The pin of a crank shaft is an example of ' form grinding/
A wheel the width of the pin, shaped to the required radius
at the corners, should be used and fed directly into the work.
If the wheel is rather less in width the corners are not ground
so easily, as they produce considerable side-thrust on the wheel.
To reach down the webs to the pin in multiple throw cranks
requires a very large wheel, even when the collet holds it by
recesses so that the collet and its flange lie between the side
surfaces of the wheel, and machines have usually to be specially
fitted to give the correct speeds to the size. If possible the
wheels for particular shape pins should be used for them only,
and kept mounted in their collets, for to alter the radii, and
especially to turn the wheel flat right across, is most wasteful.
The roundness of crank pins can be tested by lapping with a half
lap or bearing ; for other parts a half lap is sufficient for
testing the roundness and removing the cut marks from the
surface, though a complete lap such as is shown in Fig. 187,
page 394 is advisable — if it can be used — in order to obtain
the best results. Unless ftie marks of the grinding cut are
removed by a lap or smooth emery cloth the smalls-sharp
ridges may damage the bearing.

To true the wheel and form the round corners accurately
the motion of the diamond tool must be controlled by a special
jig. Such a radius truer is shown in Fig. 94, and is that fitted to
the crank shaft grinding machines of Messrs. Churchill. It is
arranged to bolt on the top of one of the steadies. Here the
diamond A is carried on the pivoted arm B and moved by the
handle C, so that its point describes a circle about the axis DE
of the pivot. To enable it to be set at the correct distance
from this axis DE, the arm B is hollow, and a stepped gauge
F can be pushed along the axis DE until the step of the desired
radius comes opposite the diamond A, which is then adjusted
by means of the screw G just to touch the gauge surface. The
amount of angular movement of the diamond and lever C is

PLAIN GEINDEES AND EXTEENAL WOEK 233

limited by stops at H, so that the corners of the wheel and its
face can be dressed by continuous movement of the diamond,
as is indicated by the broken line KLM indicating the wheel.

FIG. 94. — RADIUS TRUER AND STEADY — CHURCHILL

The fitting of the radius truer to the steady is shown at N.
Ideally the diamond should work level with the work centre,
but the error involved in the small displacement shown is
insignificant owing to the large diameter of the wheel used.

The section of table adopted by Messrs. Churchill, the
mode of clamping the steadies to the table, and the method of

234

GKINDING MACHINERY

adjusting the steady shoes, are clearly shown in this illustration.
The steady shoes P, Q, are adjusted positively forwards and
upwards respectively by means of the screws K and S, and
no springs are used.

Fig. 95 shows a crank shaft in a Landis Crank Shaft Grinder,
and the radius truer in position for work.

After obtaining satisfactory accuracy and finish, output

DIAMOND SETTING GAUGE

GAUGE CLAMPING SCREW

SCAIZ Of DIAMOND SETTING GAUGE
METRIC EMWJSH

FIG. 95. — RADIUS TRUER AND CRANK SHAFT — LANDIS

is to be looked for. If it is evident from the running of the
belts that the machine is taking as much power as they can
supply, the only way to increase the output is to use a softer
or coarser wheel, so that the same amount of power will remove
the material more rapidly. If the wheel be changed for a
softer one, the work surface speed should be reduced and the
depth of cut increased at the same time, but after some experi-
ence the correct wheel will probably be selected. If the belts
are not delivering as much power as they can be expected to,
the work speed should be reduced and the cut increased but

PLAIN GEINDEES AND EXTEENAL WOEK 235

limitations as to accuracy and quality of surface must be
borne in mind. Such trials take some time, for the results
of small changes to improve matters already good are only
slowly apparent ; hence for small quantities it is not economical
to be over-anxious to make the actual grinding time the
minimum, as the changes may easily run up the gross time
taken, so that the net result of this is a loss.

Repetition Work.— In quantity work (say fifties or more
according to the size) it is best to put the parts through the
machine twice, for rough and finish grinding, and the best speeds
should be ascertained.

Where each operation is done quickly, two or more carriers
should be used ; while one piece is being ground the piece
previously ground is checked for size, and if correct, the
carrier removed to an unground piece, and the centre holes
cleaned and oiled ready for the machine. When the cross-feed
has been automatically thrown out on the part being ground,
two or three more reverses (always the same number) should
be allowed before stopping the work. The wheel should
never be stopped unless it is necessary.

The wheel is then run back one or two complete turns
of the cross-feed wheel, the work removed without measure-
ment, and the next piece put between the centres and started.
The wheel is then brought rapidly up to the work until the
position corresponding to the maximum grinding allowance
is reached, when it is moved more slowly. One advantage
of a rough lathe finish is that the cut of the wheel shows
when the tops of the ridges are touched, and when considerably
more feed can be well put on without damage to work or wheel.
The automatic cross-feed is then thrown in and the piece left
to the machine.

If when measuring the piece, after removing it from the
machine, it is large owing to the wear of the wheel, the cross-
feed is adjusted by the compensation device, one movement
of which usually corresponds to 0-00025 inch reduction on the
diameter. In roughing the piece need not be returned to the
machine, and in finishing it should not occur. Usually small
pieces should be rough ground to within 1 to 1J thousandths

236 GKINDING MACHINEEY

of a inch of finished size : this will be sufficient to enable them
to be finished with certainty.

If the grinding is close to size, and the wheel can be run off
the work at the tailstock end, it need not be run back for
finish grinding ; and if the wheel is correct a considerable
amount — say a square yard, but it differs with the grit and grade
of the wheel — of work surface should be finished without
readjustment.

Time Required. — The question of how long should be
allowed for the grinding of a piece of work depends on the
particular work, on the finish required, very greatly on the
quantity to be done, on the machine, and on its operator. I
have devised the following formula which will enable reasonable
times for plain, straightforward work to be rapidly estimated.
It is intended for quantities of from 10 to 20, and for normal
skill in using the machine, and includes the time for setting up,
measuring, truing the wheel, and to give a rate which can be
maintained all day. This is the kind of estimate which I
believe to be of most interest. The allowance for grinding is
supposed to be 0-020 to 0-025 inch on the work diameter.

If d be the work diameter and I the length, in inches, of the
portion to be ground, then the time in minutes is —

* = k (J <ft + I + d)

where To is a factor dependent on the quality of the work and on
the machine. For a machine such as Messrs. Brown & Sharpe's
No. 2 Universal the values of k would be J for running fits and f
for push fits. For more powerful machines the factor would
be reduced — to about 0*4 and 0*55 respectively for machines
using wheels of 2-inch face.

If the work is to be ground for a finish only and not to a
limit size, two-thirds of the time derived from the above
formula should be allowed.

The formula is based on the following considerations. The
proposition is to grind so much off the surface and to give
a certain finish to it. Now slender pieces of work cannot
sustain so great a force at the grinding point as stiffer pieces can,
and to allow for this, we may consider the effective diameter to
be d + x instead of x : and as short pieces take relatively a

PLAIN GEINDEKS AND EXTEKNAL WOEK 237

little longer than larger parts, except when ' formed/ we
may take the length as I -f- y instead of I. Now the time taken
on both roughing-out and finishing will depend on the product
of these, which is (d + x)(l + y) or dl -f- xl + yd + xy. The
formula must be very simple to be of any use, and of the simple
numbers practice makes 2 as the most nearly correct figure for
x and y — so that the time is proportional to dl + 2? + %d -f- 4 —
and we may neglect the number 4 for simplicity, arriving at
the expression —

The values given for k are from practice, and suitable for the
purposes named above.

The time taken in the actual grinding is very much less, and
it can be greatly reduced if the quantities are large. In con-
trasting the times derived from this formula with those done
as ' exhibition ' times, or with those resulting from continuous
experience in grinding one article, this must be borne in mind.

A collection of ' times ' taken on a variety of work is given
on pages 418-21. These are selected from a quantity of data
kindly furnished by Messrs. Brown & Sharpe and the Landis
Tool Co. They represent the result of considerable experience
in the particular piece of work, and such times must not be
expected to be obtained without it. For varying work the
times given by the above formula will be found to be reasonable
over a wide range of diameter and length.

Costs. — The cost of grinding must be taken as inclu-
ding the cost of the wheel material and power used as well as
the labour charge, and this apart from dead expenses and
establishment charges. The wheel cost in external grinding
depends greatly on the management of the grinding ; in
roughing-out the wheel should wear, otherwise it will be found
that the labour and power charges will be high, but it should not
wear away too rapidly and waste. No fixed rules can be given,
for the ratio of wheel and power cost to labour cost should
evidently depend on the size of the machine, the larger machines
taking the greater power and using wheel substance more
rapidly.

The cost of the power is usually — one might say invariably

238 GEINDING MACHINERY

— neglected. It is difficult to ascertain, but a grinding machine
requires so much more power than most machine tools of similar
capacity that it should be debited with the cost, or part at
least. Taking power at f d. per electrical unit, a h.p. hour will
cost C'65d. If we take a machine using 5 h.p. for half the time
(that is, it takes 5 h.p. while roughing-out and very little the
rest of the time), this then is about a quarter of the average
rate paid for labour. With soft wheels the wheel cost is
greater than with hard wheels, but at the same time the
power required is less. Hence work can be done faster on
a given machine with soft wheels ; this lessens the labour
charge, which is the highest charge. Soft wheels, therefore,
provided that they are run in a manner which does not waste
them, prove on the whole economical.

CHAPTEK VII

INTERNAL GRINDING MACHINES AND WORK

CAUSES, similar to those which have placed the plain grinder
in the manufacturing shops, have more recently led to the
development of internal grinding machines. The progress
made is slower, as the quantity of work is less, and the process
more difficult.

Economic Production of Accurate Holes.— For the accurate
sizing of holes in hardened metal the internal grinder is necessary,
and from this its scope has gradually extended. In the softer
metals small holes can be sized within very close limits, and
inexpensively by the use of reamers. As the diameter of the
hole increases the cost of the reamer increases very rapidly,
and the number of holes representing the life simultaneously
diminishes, since the number of teeth cannot be increased
in proportion to the diameter ; so that as the diameter in-
creases, the advantages of grinding gradually make themselves
felt. With the high tension steels the life of a reamer is
shortened — in some cases to only a few holes — so that here
reaming is expensive, although it follows in train with the
preceding lathe operations. Broaching, where the quantities
are large enough to warrant the expense of the tools, is satis-
factory on the high tension steels : both broaching and grinding
mean a second operation, transferring the work to another
machine. For blind or slightly taper holes of accurate diameter,
grinding usually offers considerable advantages.

Two Types— corresponding to Lathes and Boring Machines.

—Internal Grinding Machines are divided by their general
arrangement into two classes — corresponding to lathes and
boring machines respectively — which have received the titles
of Internal Grinders and Cylinder Grinders; In the former
the work rotates, while in the latter it does not, although

239

INTEENAL GRINDING MACHINES AND WOKK 241

it may receive the travel movement, and have other adjust-
ments. When the work is unwieldy or very large, the second
class are advantageous, but for other work the lathe type is
usually the better, and on them taper work is easily done,
while it is impossible on the usual machines of the other type.

The arrangements of the parts in Internal Grinders may
be made in a variety of ways — either the work or the wheel
head traversing — and either of them receiving the cross-feed
movement, the various arrangements having their particular
advantages.

Internal Grinders. Travelling Work.— In Fig. 96 is shown
Messrs. Churchills' Internal Grinder, in which machine the
work receives the travelling motion, and the wheel head the
cross-feed adjustment ; and in Fig. 98 is shown the Landis
Internal Grinder, in which the wheel head receives both the
travelling motion and the cross-feed adjustment — as in their
Plain Grinders. In some machines (Messrs. H. W. Wards'
for example), the wheel head receives the travelling motion,
and the work the cross-feed. In Fig. 96 the work head / can
swivel on its base g through a large angle, and work of any
taper can be ground. The whole head can be adjusted to
any convenient position along the table h, which also carries
the three-pin steady ;, and which receives the fine adjustment
for the taper by means of the handle /c. The main slide I is
provided with stops a, a' and with a traversing and reversing
mechanism, the same as that fitted to the Plain Grinders of
the same firm. This machine is also fitted with their change-
speed gear box, of which the handle m changes the rate of
revolution of the work, and the handle n controls, independently,
the rate of travel of the main slide, while the handle p stops
both motions simultaneously. The arrangement of the drive
is shown in Fig. 97. The fast and loose pulleys A and B are
on the first motion shaft CD, which drives the speed counter
head E on the cross slide by the large pulley F ; the pump,
when wet attachments are fitted, by the pulley G, and the change-
speed box by the pulley H. The power is received at the
change-speed box by the pulley K ; the main slide is driven
by the shaft L, and the work driven from the final pulley M

242

GEINDING MACHINEEY

of the change-speed box. This pulley M drives the pulley N
on the drum shaft PP, and so the work spindle pulley Q. The

whole machine is stopped by the belt slipper K, while the work
and table alone are stopped by the lever k.

This drawing shows clearly many of the features of the

INTEKNAL GKINDING MACHINES AND WOEK 243

machine, and attention should be paid to the bridging of the
cross slide ways over the main slide and table ; this is the most
rigid method of supporting the cross slide, and at the same time
it aids the protection of the parts. The device of mounting a
secondary counter head on the cross slide is, it will be noticed,
practically invariable practice ; the belt to the cross slide then
does not run at the very high speed at which it is desirable that
the internal spindle belt should run, so that the construction
avoids the vibrations which these high-speed belts are wont to
set up when they are long.

Travelling Wheel Type.— The Landis Internal Grinder, Fig. 98,
corresponds closely to the lines of their Plain machines : here
the work head A swivels on the base B, which is integral with the
table BC, and not adjustable along it. The fine adjustment for
the taper is obtained by swivelling the whole table BC by the
screw D. The graduations are clearly seen here, on the vertical
edge of the table. The traverse motion, power E, and hand /,
the stops a, a', the friction gear change speed G, and the cross-
feed details H are the same as on the Plain Grinders ; the wheel
slide has end covers K instead of the roller protection, as the
stroke is short. The driving arrangements are similar to the
Landis Universal Machine (page 272).

The machine is fitted for wet grinding, the supply being
through the nozzle L ; the pump and tanks are seen in the
foreground. This machine is fitted with a split chuck operated
pneumatically. The compressed air is conveyed to the machine
through the piping NN.

Dry and Wet Grinding.— There are many advocates of
dry internal grinding as opposed to wet, and some think
that a small quantity of water is satisfactory. Except for
small holes I advocate wet grinding, with an ample supply
of water directed on to the cutting point, as is usual in
external work, and consider that the water supply must be
so efficient as to keep the wheel quite clean, or that there
should be none, and the work ground dry. When the
amount to be ground out is large, it is sometimes best to rough
out dry and finish wet, so as to eliminate temperature errors ;

244

GKINDING MACHINEEY

when the work is ground dry for sake of quickness it must be
cooled before finishing, as the expansion of the diameter due to

the rise of temperature can easily be half a thousandth of an
inch per inch of diameter of the hole. There is a certain loss
of time in changing over from the dry to wet work owing to the

INTEENAL GRINDING MACHINES AND WORK 245

contraction of diameter, so that even with large grinding
allowances there is no certain gain to rough out dry and finish
wet. When the hole is practically to size the water may be
turned off, or very nearly so ; the wheel then tends to retain the
loose abrasion particles and to glaze, and so gives a smooth
finish to the work surface. In dry grinding a spot of oil on the
wheel in the final finishing will produce the same effect.

The water pipe should be carried down the spindle on the
side farthest from the grinding point and then brought over
and directed on to the work, so as to flow to the place of wheel
contact. It is usually carried down on the same side of the
spindle as the grinding takes place upon, but the water does
not then reach the grinding area properly owdng to the wind
from the wheel.

The water may be fed over the outside of the work, but
this does not meet the case effectively if the work is thick or
irregular in shape, and is useless if the ground surface is to be
dead hard, since the heat is not carried off before it has time to
affect the body of the work, as it is when the water is supplied
at the grinding point. Further, a small quantity of water is
liable to get on to the wheel as it comes just out of the work at
the reverse, and this spoils its cutting properties.

In my design (see Fig. 99) ample provision is made for the
use of water, which is carried down a passage in the eccentric
sleeve and delivered on to the work by a nozzle, as illustrated in
Fig. 43. The nozzle is visible at A, Fig. 99, and the wheel B is
seen to be placed eccentrically with regard to the sleeve C.
The guard D is carried on the machine body, and the guard E
on the main slide ; these move telescopically while grinding is
going on, and on running the work back make an open space
for gauging conveniently.

The Cylinder Grinder. — Turning now to Cylinder Grinders,
which correspond to boring or drilling machines, we see that
the work does not rotate, and that the wheel spindle, in addition
to its own rapid rotation, must at the same time be carried round
another axis (corresponding to that of the boring bar or drill),
so that the envelope of the wheel (i.e. the curve which it always
touches) is a circle — namely, the section of the hole being ground

246

GEINDING MACHINEKY

out. Also some convenient means must be arranged whereby
the size of this circle can be increased little by little, and so the
cut of the wheel put on and the hole ground to size. This action
is shown in Fig. 100, where the grinding wheel spindle A, rotating
rapidly on its own axis, is itself carried round the main axis B,

FIG. 99. — GUEST INTERNAL GRINDER. 16" x 10"

so that the wheel takes successively the positions indicated by
the circles C, C, C. These all touch the inside of the circle
DD, whose centre is at B, and this circle represents the hole
which is being ground out. If the distance BA is increased, as
is shown at BE, the diameter of the corresponding circle FF
is increased : this increase of the distance BA then puts on the
cut and increases the size of the hole ground. It also compen-
sates for the wear of the wheel and for different sizes of wheels

INTEENAL GRINDING MACHINES AND WOEK 247

and holes generally. Thus it corresponds to the cross-feed of
an internal grinding machine.

Usually the wheel used in grinding a hole bears a larger
ratio to the diameter than that shown in Fig. 100 ; but it is
drawn small in this figure, partly for the sake of clearness,
but also to indicate how some fixed external cylindrical work,
such as locomotive connecting rod pins, may be ground in

FIG. 100. — MOVEMENT AND FEED IN CYLINDER GRINDER HEAD

position. The successive circles C, C, C showing the positions
of the wheel in its motion round the axis B, not only touch
the inside of the circle DDD, but also touch the outside of the
smaller circle, which thus represents a fixed pin ground exter-
nally in a machine of this nature.

Constructionally the rotation round the axis B is obtained
by carrying the whole mechanism in bearings concentric with
B — the wheel, its spindle, and pulley are all carried by the main
spindle whose axis is B, as is also the mechanism for varying

248

GEINDING MACHINEKY

the distance AB. The usual construction is indicated in Fig. 101.
Here A is the axis, and BCD the bearing of the main spindle.
This main spindle is bored eccentrically for the second spindle
EFG, whose centre is at H, so that the eccentricity is HA. This
second spindle is also bored eccentrically at KLM to take the
wheel spindle and its bearings, whose axis is at N, so that this
second eccentricity is HN. By rotating the second spindle

FIG. 101. — CONSTRUCTION OF WHEEL HEAD OF CYLINDER GRINDER

EFG inside the first, BCD, the axis N of the wheel spindle is
made to move round the broken circle QNAP, whose centre
is H and radius HN ; thus the distance AN changes as this
rotation is made. Usually HN is made the same as HA, so
that N passes through A as it travels round the circle NAPQ,
and its greatest distance from A is then twice HA.

As the main spindle revolves, the wheel spindle N is carried
round the circle NKS, thereby grinding the hole as already
described ; and the cut is put on by altering the radius AN of
this circle, by turning the spindle EFG relatively to the main

INTEENAL GEINDING MACHINES AND WOBK 249

spindle ; and practically it is necessary to make this adjustment
while the two rotations are taking place. This construction
is simple and rigid : to make it convenient a mechanism must
be added whereby the second spindle can be rotated inside the
main spindle, while the latter itself is rotating, and while the
spindle N is also rotating. Such a mechanism and the details
of the whole arrangement are shown in Fig. 102, which is a
drawing of the head of Messrs. Healds' cylinder grinder, of
which Fig. 103 gives a general view.

The main spindle AAA' revolves in the bearings BB',
CO', which are of the capped type, as can be seen in Fig. 103,
and are lubricated by felt pads as shown at D, D'. The end
thrust is taken over the rear bearing CC' between the flanged
end A' of the main spindle itself and the driving gear wheel E,
which is adjusted by the nut F. The gear wheel E, which is
keyed to the spindle, is driven by the pinion G which derives
its power from the pulley H, while a hand wheel H' serves for
turning it by hand. The second spindle J J is fitted eccentrically
in the spindle AA ; the front bearing consisting of a taper hole
KK in the spindle AA itself, and the rear bearing is parallel,
the bush LL being taper on the outside, and adjusted by the
nut M. The end adjustment is by means of the nuts NN',
while the nut P at the front end of the spindle, besides taking
the end thrust, secures the correct fitting at the front taper
bearing KK.

This second spindle JJ carries — eccentrically — at the front
end the sleeve QQ of the internal grinding spindle, and at the
rear end the rear bearing E of this spindle. The sleeve QQ
is fitted to the second spindle JJ by a taper seat. The internal
grinding spindle 8^283 is very long and is provided with three
journals — at Si near the wheel, S2 in the rear of the sleeve QQ,
and S3 at the bearing E in the rear of the second spindle JJ.
The construction of these bearings and the fittings of the
spindle generally are easily understood from the drawing, and
may be compared with Fig. 42, page 137, which illustrates a
simpler spindle by the same firm.

The rotation of the spindle JJ within the spindle AA — by
which the feed of the wheel is controlled — is effected by means

INTEKNAL GKINDING MACHINES AND WORK 251

of a worm wheel T keyed to the spindle JJ, and operated by
a worm U carried in a casing fixed to the main spindle AA.
The worm shaft VV has a squared end on which a handle
can be placed for rapid adjustment, and is rotated automatically
by the shaft W through the gears at X. The shaft W is turned

FIG. 103. — HEALD CYLINDER GRINDER

by a star wheel Y of many teeth, through the space of one of
which it is moved by contact with a curved plate at each revo-
lution of the main spindle A. The curved plate is seen in
Fig. 103. This can be thrown in or out of action by the
handle seen a little to the left of it. The knurled head Z
gives a hand fine feed adjustment.

The movement of the second spindle inside the main
spindle takes place — unless controlled by hand — at every

252 GEINDING MACHINEKY

revolution of the work. In some designs, such as that of
Messrs. Brown & Sharpe, the feed is made to take place at each
end of the traverse, as is done in Universal and Plain Grinders.
This is probably the more convenient arrangement, but as in
internal grinding wheels wear much more quickly than in
external work owing to their small diameter and face, the
advantage is not very great.

Arrangement of Machine with Travelling Work. — In Fig.
103 the general arrangement of the machine is easily seen.
The head a already described is mounted on a bridge b
over the main ways : the work, or jig for it, is bolted to the
table c, which has a cross adjustment on the main slide d, which
slides on ways formed on the knee, which itself is fitted to
slide vertically on the body of the machine. The reversing
motion, which is controlled by the stops on the front of the
main slide, is contained in the case g, and the whole knee,
main slide, cross slide, and work, can be raised by the handle
h operating the screw 7c. The rate of traverse for the main
slide is controlled by the change speed box /, the motion from
which is transmitted to the reversing box g through the double
Hooke's joint connection seen in front of the machine. At m
is the change-speed box for the rate of rotation of the main
spindle, the motion being transmitted through the belt n to
the pulley H and then through the pinion G and gear E of
Fig. 102. The wheel spindle pulley p is driven from the
countershaft through a speed counter which swings, since the
position of p varies as it is being carried round by the rotation
of the main spindle, and a spring is arranged to act on the
swinging link and so keep the belt driving p at the correct
tension.

By means of the cross and vertical adjustments to the
table c, a series of parallel holes can be ground in a piece of
work — e.g. the cylinders of a monobloc petrol engine — and for
this purpose such a machine is very conveniently adapted.
Single cylinders for such engines, however, are preferentially
ground in the former type of Internal Grinder, as in that type
the slight taper (which is about 1 in 1000, and is desirable, so
that the cylinder is parallel when the head end is hot as it is in

INTEENAL GKINDING MACHINES AND WOKK 253

use) can easily be set and ground. Taper holes cannot be
ground in machines of the boring type, although some have
been made with arrangements for the purpose. This introduces
further complications into the mechanism, and the results have
not so far, I believe, been encouraging.

The increase in the distance AN between the axes of the
main and wheel spindles (see Fig. 101) is not proportional to the
angular movement of the second spindle EFG in the main
spindle BCD — that is, it is not proportional to the change
of the angle AHN, or to the amount of turns of the worm
wheel, and hence to the amount of turn of the worm.* The
amount of cut put on then is not proportional to the movement
which puts the cut on, but depends upon what angular position
the second spindle then has with the main spindle. Although
with practice the amount of metal being removed can be judged,
this is not very reliable except where a number of parts are
done under exactly the same circumstances, in which case
the amount removed can be fairly well estimated by the time
taken if the appearance of the grinding be kept uniform. The
difficulty of estimation is greater with wet grinding than with
dry.

When the feed is proportional to the movement producing
it, as is the case with internal grinders of the first type, the
wear of the wheel alone affects its sizing properties, and although
in internal grinding the wheel wear is sometimes as much as
the increase of work diameter, it can be allowed for, and the
proportional cross-feed is a good indication as to the increase
of the size of the hole, and is a desirable feature, provided in
attaining it the simplicity and rigidity of the above type are not
lost. In Fig. 104 is shown the line drawing of an arrangement
giving a proportionate feed.

In the line drawing it will be seen that the main spindle H
is bored through at an angle to the axis ; the secondary spindle
J fits this bore, and can be adjusted lengthwise in it, but is
prevented from turning by means of a key. The grinding
wheel spindle is carried in the secondary spindle, and in the

* AN = 2 AH sin \ &, therefore 8 . AN = AH . cos $ 0 . S0, so that cut
varies as worm turn and cos £ 6.

INTERNAL GRINDING MACHINES AND WORK 255

bracket E bolted to it, and its axis is parallel to the main
spindle ; adjustment of the secondary spindle along the
inclined hole in the main spindle then alters the distance
between the main and wheel spindles, and so adjusts the cut.
The adjustment is simply performed by the screw mechanism
shown at N, and is proportional to the movement producing it.
The actual construction is practically more difficult than that
previously described. The screw N does not rotate ; it moves
endways only, carrying the main spindle H with it ; as the
secondary sleeve J cannot move endways it has to move trans-
versely, and so puts on the feed.

Arrangement of Machine with Travelling Wheel Head. — When
the work is small it is best that it should travel, as there is
then less tendency to vibration, but with large machines the
wheel spindle is frequently arranged to travel. This type of
internal grinder is made up to large sizes, and one such machine
is shown in Fig. 105. Here the wheel head traverses and
the work remains stationary ; the main ways consist of two
flats and two vertical surfaces, and are protected by roller
blind devices at the wheel end. The arrangement of the
mechanism in general can be traced in the illustration.

The Bases of Accuracy. — The accuracy of the work from
both types of internal grinding machine, depends immediately
upon the straightness of the ways of the main slide and upon
the perfection of the main spindle and its bearings, together
with the distance apart of the latter and the closeness of their
adjustment. The uniformity of size of a parallel hole, or
the straightness of side of a taper hole depend on the perfection
of the main ways and upon the correctness of the wheel
' height,' while the roundness of the hole depends upon the
truth of the main spindle and its bearings.

In both types there is overhang, the work from the main
spindle bearings in the lathe type and the wheel from the main
spindle bearings in the boring machine type ; so that as regards
this point of view, supposing that the bearings are equally good
and far apart, the two types of machine may be regarded as
equally good. Generally speaking, however, the lathe type is

INTEBNAL GETNDING MACHINES AND WOKK 257

the better as regards these points. In machines for special
purposes, and in which the work rotates, where the work is
comparatively small, it can be arranged to be held inside the
main spindle, and so this overhang avoided, but for machines
for general use this is impossible.

Setting the Work Head Parallel. — When the work revolves,
if its axis be set at an angle to the line of the main ways, the
hole will be taper. This is shown in Fig. 106, where the taper is
small. The work axis is AB and the line of the main slide is
CD, making an angle 0 with AB. The wheel grinds the side EF
parallel to CD so that the work is ground to a cone of included

FIG. 106. — SETTING INTERNAL WORK PARALLEL

angle 20, with the greater diameter to the right in the
illustration.

The angle at which the wheel spindle happens to be set
makes no difference, but unless it is parallel to the main ways
all end play should be taken out. If it be not, the spindle
will move in its bearings at each reverse, and the cut will then
be heavier when the traverse is in one direction than in the
other.

If the wheel in Fig. 106 is moved over to grind the work on
the opposite side of its diameter, the relative movement will
now be along the broken line GH parallel to CD, and the wheel
will cut at K and be clear of the work at L. If the lines AB
and CD be parallel, however, the hole will be parallel, and the
wheel when moved over will cut equally all along the side GH ;

258 GRINDING MACHINERY

this is a delicate test for parallelism, and is useful in setting the
work head to the parallel position.

There is no corresponding adjustment in machines of the
boring type, and the work -from them is parallel. Should the
axis of the main spindle be out of line with the main ways
the work is still parallel, but its cross section is not circular.
The error is very small, however, since the principal component
of it is proportional to the product of the width of the wheel
and the angle between the axis of the main spindle and the
line of the main ways.

The straightness of the parallel hole or the taper depends on
the straightness of the main ways geometrically ; practically
it is affected by the spring of the slender spindle and the oil
films, tending to produce ' bell-mouthing.'

Holding the Work. — For internal grinding work can be held,
as for turning, in three or four jaw-chucks or on face plates,
but as the work has already been machined there is a wider field
for the use of collet chucks and fixtures. Ordinary chucks
cannot be expected to be very accurate, as they are manu-
factured under competitive conditions to meet the requirements
of lathes for which their precision is almost always ample. The
jaws of a concentric chuck can easily be ground out true
for any particular diameter. When doing this it is best to
grip a piece of material in the chuck in the rear part of the
jaws, so as to force the jaws into the holding position. Work
such as gears can be held in a chuck with independent (prefer-
ably four) jaws, and set true. Cutters may be held in the
same manner, but usually holding to a face plate is preferable.
Work which is likely to be pressed out of truth by the force
of the jaws should be held to a face plate, or — if it is circular
on the outside — may have a fairly thick split collar slipped
over it for the chuck jaws to grip upon. Holding work tightly
in an ordinary chuck will distort it, with the result that the
ground hole will go out of shape when the work is released
from the chuck.

Where the quantities warrant it split chucks and holding
fixtures are very desirable, as they reduce the time of setting so
considerably. If a piece is to be ground both externally and

INTEKNAL GEINDING MACHINES AND WOKK 259

internally, it is frequently best to put it on a mandril and rough
grind the exterior first ; on putting it into a collet chuck the
inside, which was in contact with the mandril, now runs true,
which lessens the time of internal grinding. It is finally put
on another mandril, and the exterior finished.

Gears. — It is a matter of varied opinion as to how hardened
gears should be held ; generally it is considered that they should
be located by the points on the pitch line, which is rather indefinite
in some cases. I think, however, that it is preferable to hold
by the bottoms of the tooth spaces (always machined at the

FIG. 107. — HOLDING SPUR GEARS — HEALD

same time), as defects in the grips and grit produce less errors
in the averaging of the distortion due to hardening. At least
six equally spaced (or nearly so) grips should be used. Fig. 107
shows a suitable arrangement given by Messrs. Heald, but here
only three spaced gripping points are used.

Jigs should be made to locate the previous machining of
the hole to be ground as accurately as possible, and should be
arranged to hold the work without distortion. For example, a
jig for petrol engine cylinders should hold the cylinder by the
ring and face (machined at the same time as the cylinder was
bored), by which it is held to the base plate, and it should be
fastened in the same way. It is quite free elsewhere, and free
from holding strains. Quicker gripping devices can easily be

260 GKINDING MACHINEKY

arranged, but not with so perfect a location and freedom from
strain.

Jigs for thin work should hold it by compression on the
ends, so as not to spring it across any diameter.

Belts. — The belt to the wheel spindles for internal grinding
usually runs at a very high speed. Considerations of the
centrifugal effect in leather belting as it runs round a pulley
shows that a belt transmits most power at a speed of about
5000 feet per minute, and in this case the pulley would be the
same size of the wheel, or rather larger, as the wheel surface
speed is usually somewhat below that amount, as the spindle
speed is so high. My practice used to be to run the belts to
internal grinding spindles at this speed, with the easily remem-
bered rule that the wheel used was not to exceed the pulley
diameter. With these high speeds it is necessary that the
belt should be endless : raw hide or orange tan belting is best
for all but the smallest size spindles, for which cotton belts,
woven endless, are most suitable.

Water is to be used in quantity or not at all ; the wheel
must be clean, and a meagre water supply tends to choke it.

Width of Wheel.— The width of the wheel must be less
than that for external grinding for the same power delivered
to it. This is explained in Chapter III, but as the difference
is considerable in internal grinding, I refer to the subject
again.

The relation between the work speed and the depth of cut
which must hold in order that the wheel face may neither glaze

nor disintegrate too rapidly is that v2 7^ t should lie be-
tween two limits, and preferably it should have a certain
value, which depends on the nature of the wheel (which is
supposed to be run at a fixed speed) and the material ground
only. To get the output of which the machine is capable, we
also have vt having another constant value, dependent on
the machine and wheel. From these we get the values of
v and /.

Now vt is to be reckoned per unit (i.e. per inch) width of

INTEENAL GRINDING MACHINES AND WORK 261

wheel face, and we can increase the value of vt for any machine
by decreasing the width of wheel face. If in any case we have
obtained the values of v and t and find them unsuitable, we
can alter their values by altering vt for the case — that is, by
altering the width of wheel.

If , taking a case of grinding which gives good results in external
grinding, and using the same values of the above, we consider a
case of internal grinding for which the values of the diameter of
wheel and work are different (and the negative sign in the
formula is to be taken), we find that very much higher work speeds
and very fine depth of cuts are requisite. Now fine depths of
cut are undesirable or even impossible with a small spindle,
supported at best by a bearing in a sleeve which can easily
spring. We must therefore increase the depth of cut, and to
meet the wheel condition we must decrease v to an extent

which makes v2 —ypr- 1 the same as before. This will increase vt,
dD

and to do this we must reduce the width of the wheel. Taking
the same power and using it on a narrower width increases vt
at the wheel face.

This does not mean that we are going to lose output,
which depends on vt : it alters neither the output nor the
total force on the work, nor yet the final force on the wheel
particles tending to dislodge them from their setting. What
it does is to increase the length of the arc of contact, keeping
the average force the same, but since the width of the wheel
used is less the net result is the same. Generally speaking,
the output is proportional to the length of the arc of
contact multiplied by the wheel face, or to the area of
contact.

Consider the same example as was taken in Chapter III,
page 69. Here in external work, where d = 2 inches, D =
14 inches, v = 30 inches per minute, and t = O'OOl inch on the
work diameter, the grinding was satisfactory. If our internal
work were 3 inches diameter and the wheel 2J inches, we
should then find that v = 257 feet per minute, and that
the corresponding cut would be O000115 inch on the work
diameter.

262 GKINDING MACHINERY

Suppose that we increased the feed to one thousandth of
an inch on the diameter, then the corresponding velocity would
be v, where —

^ 2572X 0-000115

lOUO

or v = 257 Xx/6-115"

= 87 feet per minute

The value of vt would now be increased in ratio 3-15, so
that we should have to reduce the wheel face to J inch.
Actually if the same power were delivered to the machine
we should have to reduce it further, as less of the power reaches
the wheel in internal than in external grinding, owing to the
greater loss in the belting and journal friction. The spindle
bearing also is to be considered, and hence less power is usually
delivered to the machine.

Treated thus, wheels of the same grits and grades will suit
internal, as suited external work, but considering that the
wheel is not supported so rigidly, a slightly softer wheel is
desirable for internal work. The cubic amount of wheel wear
should be the same, but as it is distributed over a much smaller
circumference and width the effect is much more conspicuous,
and leads to the impression that the wheel material does less
work.

The wheel must not be too soft, otherwise it tends to pull
into the work and have its substance wasted. This action is
probably due to a gyroscopic effect. Suppose the spindle
AB, Fig. 108, is running free in the bearings with an oil film
round the journals, and that the force P of the cut acts at the
point C of the wheel B and acts upwards, the spindle running
in direction DC. Then if the spindle can bend or move about
the point A, the force P produces a moment P . AB about
the line AX, in the sense indicated by the arrow ; which com-
bines with la) round AB to make the axis of rotation move
towards C, as shown by the broken line, and so carries the
wheel into the work. This increases P and tends to continue
the motion of the wheel into the work with increasing rapidity,
until it reaches a point where it quickly destroys the surface

INTEENAL GEINDING MACHINES AND WOKK 263

of the wheel. This will not happen if the wheel is near to the
glazing point, as the normal force then checks the action.
With springing spindles, therefore, the speeds and feeds must
be more nearly what is just correct.

Work Speeds and Wheel Action. — Excessive wheel wear
and glazing are to be checked by the same methods as have
been given for the case of external grinding, but speeds
and feeds are much more difficult to select correctly, and
require much more manipulation than in external grinding.
This is due to the influence of the changing diameter of the

FIG. 108. — SPINDLE ACTION — PULLING IN

wheel as it wears down in use, which is here very great, while
in external grinding it is very small.

Suppose that a piece of work 4 inches in diameter is being
ground externally with a 36 K wheel, 14 inches in diameter,
taking 2 h.p. per inch of wheel face, and that a work surface
speed of 30 feet per minute with a feed of 1J thousandths of
an inch (mils) on the diameter is found to be the most perfectly
satisfactory. The corresponding work surface speeds for
wheels of different diameter can be calculated from equation (3),
page 69. By setting off the various wheel diameters along OA
in Fig. 109 and the corresponding work surface velocities
parallel to OB, we obtain the broken curve OCD, which shows
at a glance the effect of any change of wheel size. As the

264

GKINDING MACHINERY

INTEKNAL GKINDING MACHINES AND WOKK 265

wheel diameter decreases the work surface speed should also
be lowered, but the effect of wearing the 14-inch wheel down
to 10 inches would cause only a small fall of the best work
velocity from 30 feet to 27 -5 feet per minute. If the wheel were
changed for one of 6 inches diameter the best work surface
velocity would fall to 23, and if a 24-inch wheel were used it
would rise to 33 feet per minute. However the wheel diameter
were increased the corresponding work speed would never
rise above the value 38*6, indicated by the broken horizontal
line to which the curve CD is asymptotic. The corresponding
feeds are shown by the broken line T in the lower part of the
figure, and are obtained from the fact that vt is constant.

It will be seen that wheel wear has no practical effect on
work speeds or cross-feeds in external work.

If the h.p. per inch of wheel face were doubled, we should
obtain the full line curve OEF giving the work velocity, and
the feeds would be given by the full line curve below. This
shows the influence of increased power in slowing work speeds.

Now suppose that the work be internal instead of external.
The wheel diameters are set off to the left along OA' and
the corresponding work surface velocities parallel to OB',
while the feeds are in the remaining quadrant of the diagram.
The curve OGH giving the natural work speeds is a continuation
of the curve OCD, but its inclination is very different, and
for wheels not much less than the size of the hole the work
speed is very high, and the corresponding feed, given by the
curve A'WV so very low, as to be unusable. This, as explained
previously, necessitates the use of a narrower wheel, using
more power per inch of face. Suppose that the wheel face
be halved ; the work speeds are then given by the full line
curve OKLM, which is a continuation of FEO, and the feeds
by the curve A'X. Thus a work surface speed of 65 feet
per minute (the point L), with a feed of O'OOl inch (the
point X) would be the best for a wheel just over 3 inches in
diameter.

This condition allows certain margins, and may be departed
from on one side until the wheel glazes, and on the other until
the wheel wears unduly. Both these conditions are expressed

266 GEINDING MACHINERY

by different values (ai and a2, page 69) of the quantity b in the

equation v -= — = -, so that by drawing further curves
d\j c

of a similar nature (rectangular hyperbolas) to those already
drawn, we shall obtain the limiting lines on the figure. If
the work speed were reduced by a particular amount it will
cause glazing ; the broken curve ONP, drawn for a ratio of
one-half, indicates this condition. The original curve OGH
represents a condition of wheel waste at this amount (4)
of h.p. per inch of wheel face, and the dotted curve OQR
will represent one of excessive wheel waste.

Accordingly the area of the figure in which grinding can
proceed is that between the curves ONP and OGH, and this
I have shaded.

Suppose that a speed of 65 feet per minute be selected
for the work, which gives a feed of O001 inch on the work
diameter. This is represented by the line PLGQ on the dia-
gram, and we see that the largest wheel which could be used is
3 1 inches diameter, and that it is just on the point of glazing.

As the wheel wears down its action improves, until at
the point L, which is on the full line curve FEOKM, it would
be at its best, the diameter then being just over 3 inches.
Further reduction of diameter would make it wear more
rapidly, and at the point G, 2J inches diameter, it would be
wasting unduly.

If the use of the wheel be continued further, using the
same work speed — that is to Q — the cross-feed must be reduced
and the output sacrificed.

The short length of the line PLG (and for clearness wide
margins have been taken) in which the wheel successively
glazes, works well, and wastes, shows that the regimen in
internal grinding is not constant — as it practically is in external
work — and that the difference between the diameter of the
wheel and of the hole has a great effect. With the limited
number of work and speed changes on a machine it is impossible
to obtain any particular speed and feed desired, but what is
to be aimed at is to start with a wheel just on the point of
glazing, and it is then known to be on the curve ONP. When

INTEENAL GRINDING MACHINES AND WOEK 267

a condition corresponding to the point G is reached the work
speed is to be lowered, and if it were lowered so as to reach
the point N (15 feet per minute) it would then again be on
the point of glazing.

In external grinding a 14-inch wheel, using 2 h.p. per inch
of wheel face, was at its best when the work velocity was
80 feet per minute and the cross-feed 0*00125 inch ; if we
take the same velocity for internal work (the point U) at
the same h.p., we shall find by drawing UV vertically upwards
that the feed (the point V) is the same as in the external work.
For this to be the case the particular wheel diameter would
be only 1*75 inch, and so not suitable for a 4- inch hole.

So far the wheel surface speed has been supposed to be
kept constant, while in practice the wheel spindle speed would
probably be constant. The effect of this is still further to
reduce the range over which the wheel can be used without
altering the work speed. It can be easily shown that by
drawing a rectangular hyperbola PZY through P to OA' and
OB' as asymptotes, the limiting diameter of the wheel is given
by the point 2 on the curve OUGZH, and the wheel diameter
is then 2| inches instead of 2J inches, as it would be if its
surface speed were kept constant.

In grinding holes, then, we see that comparatively narrow
wheels must be used, and from the nature of the case a wheel
of a diameter somewhat approaching that of the hole must
be used. The work should then be started with as high surface
velocity as is consistent with a workable cross-feed, the wheel
being bevelled at its edge if necessary to stop glazing. This
gives the best starting condition. After the wheel has worn
down a certain amount it will begin to wear away too fast,
and the work speed should then be lowered — which permits
an increased cross-feed — and this restores the wheel action
to the conditions in which it tends to glaze, and so the cycle
begins afresh.

I have drawn Fig. 200 with a view to assisting in the
selection of work speeds, the revolutions per minute obtained
from the formula being plotted against the ratio of wheel to
work diameter. It is to be observed that the regimen has

268 GKINDING MACHINEEY

a gradual change as the wheel wears down, and that this is
to be counteracted by altering the work speed. The wheel
speed should be kept constant so far as the arrangements
of the machine permit.

It will be gathered that conveniences for easily changing
the work speed are especially desirable on internal grinders.

The wheel should be trued with a diamond tool mounted
on the work slide. It is convenient to have a fine adjustment
to the diamond tool so that it can be set just to graze the
wheel when the work is to size, thus serving as a gauge to
prevent the work being ground over-size.

The stops should be set so that the reverse at either end
takes place before the wheel gets more than half clear of the
work, otherwise bell-mouthing is apt to occur.

As small wheels (an inch or so in diameter) seem to be
regularly harder than their supposed grade, it is customary
to make them out of larger wheels worn down or accidentally
broken. These always seem to me to work better than those
supplied to the size. The pieces of large wheels can be drilled
with an old three-square file and turned up by a boy, at a frac-
tion of the cost of the equivalent small wheels from the wheel
factory.

Times for Internal Work. — Times on internal grinding
depend on many factors. Setting the work takes little time
with good appliances — e.g. spring collet chucks for ordinary
work and special jigs for such work as motor cylinders, &c.,
but for work which requires to be set closely when held in a
chuck or strapped to a face plate, some time is necessary. For
such work as cutters or hardened steel gears five to ten minutes
or even more is reasonable setting time, the amount depend-
ing on the size of the work and the accuracy required.
Cutters are far more easily set on the face plate of a vertical
internal grinder than on a horizontal spindle machine. Apart
from this the time depends on the amount to be ground out of
the hole, the material, and on the machine and the spindle.

On small holes especially it is desirable that the spindle and
sleeve should be so large in diameter as only to allow a good
initial clearance and reasonable wear for the wheel, and the

INTEKNAL GKIND1NG MACHINES AND WOKK 269

less overhang from the support the better. An unsuitable
spindle greatly increases the time required to grind the hole ;
a wheel of unsuitable grit and grade has a like effect.

The wheel should not come far out of the work, for much is
apt to produce bell- mouthing ; the time for gauging is usually
small compared with the actual grinding time, and may be
taken as proportional to it, so that the time may be written —

T = Mil + a

where d = work diameter, I = length of work, t the allowance
on the diameter for grinding, and a is a constant allowing for
attention to the machine, setting, &c., and fc a constant varying
with the spindle. For work which requires small time in
setting, if d and I are in inches and t in thousandths of an inch ;
the time in minutes will be obtained if a = 5 and ft is taken as
follows for spindles reasonably suited to the following holes —

Up to a diameter of I" 1J" 2J" 2f" 3J" 6"
fc = -4 '3 -2 -15 -125 -1

The length is supposed not to be so long as to cause trouble
from excessive spindle vibration.

The times thus calculated are suitable for work on hardened
steel ; for cast iron or bronze the time will be shorter, a little
so on the small work increasing to one half or more on the larger
sizes. For example, automobile cylinders from 2| inches to
3 1 inches diameter and from 5 inches to 8 inches long are
usually ground in from 10 to 25 minutes, depending on the
size, the allowance, and the quality of the cast iron. As in
external work, carborundum is the most satisfactory abrasive
for cast iron. A few examples of times, kindly supplied by
the firms mentioned, are given (page 422) later.

CHAPTER VIII

THE UNIVERSAL GRINDER AND ITS WORK

Travelling Wheel Type. — ' Universal ' grinding machines are
arranged to be^able to do both external and internal work, and
are usually able to do some other work in addition. The
Brown & Sharpe Universal Grinder is illustrated in Figs. 29, 30,
and 33, and described in Chapter IV ; the description there
and also the lettering in general fits the Landis Universal
Grinder, illustrated in Fig. 110, which is of the opposite type, in
that the wheel head with its cross slide is mounted on the
main slide and traverses. The principal details of the machine
have already been noted. The diamond tool holder is seen at
D on the floor, and a drawing of it in action is given in Fig. 64.
The speed variation for the rate of travel of the main slide is by
means of friction wheels in the case N, their position being con-
trolled by the lever N7. In the Landis Internal Grinder, Fig. 98,
this controlling lever is at the friction box, and the friction wheels
are of the concave recess type, with the leather-covered friction
wheels arranged to swivel to give the speed alteration. In this
internal machine the main slide movement is short and the
main ways are protected by cast iron covers, but in the Univer-
sal, where the movement is longer, a spring roller blind cover,
shown at J', is used. The countershafting is shown in Fig. Ill ;
the wheel head is driven from it by means of a belt q' from a
large high-speed drum qq, along which the belt travels to and
fro, following the movement of the main slide. The work head
is driven by^a belt u' from a short drum u, so as to allow for
different positions of the head BB' along the work table H.
The fast and loose pulleys n, ri, cone pulleys p for driving the
wheel drum qq, cone pulleys t, tf for driving the work drum,
and the pulleys r and y for driving the pump and traverse

270

THE UNIVEKSAL GKINDEK AND ITS WORK 271

respectively are all lettered in accordance with the description
in Chapter IV.

The Cincinnati Universal Grinder is shown in Fig. 112, and

the arrangement of the drive which was brought out by
this firm has been already described in Chapter VI, and
is being adopted on other machines owing to its convenience,

THE UNIVEESAL GEINDEE AND ITS WOKK 273

as the countershafting is simple, and all speeds of the work
and table are obtained by the manipulation of handles on
the machine itself.

Speed change boxes carried on the machine itself are also
a feature of Messrs. Alfred Herberts' large Universal Grinder
(24 inches by 12 feet capacity) shown in Figs. 113 and 114.
Various differences of arrangement are noticeable, which adapt
the machine to larger universal work and to such as is done in

FIG. 112. — UNIVERSAL GRINDER — CINCINNATI GRINDER Co.

Messrs. Alfred Herberts' shops. The work head is driven by
spiral gears set at 45°, so that in moving the head through 90°
the belt is stretched as little as possible, as the headstock pulley A
changes its angular position. The headstock and tailstock fit
the table by means of a vee B and flat C ; the vee is gashed
at intervals to permit the grinding solution to flow away, and
the table is open and not protected. The headstock and tail-
stock are traversed along the table by means of the wheels D,
the shafts of which terminate in pinions meshing with the
rack E. The guarding of the main ways is effected by sloping

274

GKINDING MACHINEEY

sheet steel guards F, G, after the same manner as in the Norton
machines. The vee G of the main slide is here at the side of
the ways nearer to the operator, an arrangement which was
also adopted on the earlier Norton machines. My preference
is for the vee on the inner side, as is the practice of Messrs.
Brown & Sharpe, Churchill, &c. The steadies H are arranged
so that the three shoes used bear at points on the work circum-

FIG. 113. — HERBERT UNIVERSAL GRINDER, 24" x 12' 0"

ference which are well apart. The speed change boxes J, K
are controlled by wheels L, M at the front of the machine.
The automatic throw-out to the cross-feed contains a number
of independent plates at N, so that several different diameters
can be duplicated on work without removing it from the centres.
The wheel head carries the internal grinding spindle bracket
integral with itself, and also a separate countershaft P for
driving it, with an eccentric mounting to the shaft so that
the belt from its pulley to the internal spindle can be easily
tightened. The backlash is taken out of the wheel slide by

THE UNIVEKSAL GKINDEK AND ITS WOKK 275

means of a secondary rack, capable of sliding but held up to
its pinion by a spring ; the tension in the spring is adjusted
until its force moves the wheel slide with certainty along its
ways — which are of the vee and flat type. The adjustment
of the cross slide to any desired angle is made by the lever Q
at the rear of the machine, which operates the pinion above it
through a ratchet.

The Swivelling Cross-ways. — The work of the Plain Grinder

Ifl

FIG. 114. — HERBERT UNIVERSAL GRINDER, 24" x 12' 0"

is limited to tapers of slight angle, the maximum amount of
which depends on the size of the machine, being 6° or 7° only
in the larger machines, but much more in the small machines.
The complementary taper can also be ground by traversing
the wheel with the cross-feed. The cross slide in Universal
grinders is arranged to swivel - as a whole, so that tapers of
any angle can be ground on work between the centres or
held in a chuck. The arrangement is described in Chapter IV,
and illustrated in Fig. 32.

Double Taper Work. — Occasionally it is convenient to be
able to grind two tapers on work at a single setting, and the

THE UNIYEESAL GEINDEK AND ITS WOKK 277

method of doing this is illustrated in Fig. 115, which shows a
plan view of a Landis Grinder arranged for the work. The
table AB is first set over to the angle a so as to grind the slight
taper C, the included angle of which is 2a ; and the cross slide
is then set over as shown to grind the abrupt taper. To do
this it has to be set over to the angle a + /3, where 2/3 is the
included angle of the abrupt taper. The taper C is ground,
using the automatic feeds, but for the abrupt taper the wheel has
to be traversed over the work by the cross-feed motion. The
wheel head E is shown swivelled on the top of the cross slide F
to about its usual position. The spiral spring which takes up
the backlash of the cross-feed in these machines is contained in
the case G. All the cross slide and its mechanism is carried
on the main slide H, and the roller protecting guards for the
main ways are seen at J and K. Although quick tapers in
internal work can be done by swivelling the wheel slide, it is
better to do them by swivelling the work head, as then the
automatic feeds can be used. When it is desirable to grind
two tapers at one setting on work held in a chuck, the cross
slide is swivelled as above described for work between the
centres.

Facing Shoulders. — For facing shoulders, the swivel
adjustment of the wheel head on the cross slide is useful.
Suppose that a collar has to be faced square on a parallel
shaft, as shown in Fig. 116. At X is shown the case of a plain
grinding machine, where the wheel axis AB is parallel to the
work axis CD. The edge of the wheel grinds the work along
EF, and the side of the wheel the shoulder along FG. To
prevent untruth or want of squareness of the side of the wheel
grinding the shoulder out of truth it is advisable slightly to
recess the side of the wheel, as indicated by the broken line H J.
At Y is shown the same case, but the corner of the wheel has
been rounded by wear, the amount being much exaggerated :
to keep the corner square it is usual to recess the work slightly
in the lathe, as indicated at KL : or sometimes as at MNP
in the figure Z. Such recessing cannot, however, be done
when the strength of the shaft is of importance : in such
cases a filet corner should be employed. In the figure Z

278

GRINDING MACHINEEY

the wheel axis QE is shown slightly inclined, so that only the
corner of the wheel touches the shoulder on the work, and
touches it along a line in the plane of the paper, and not along
an arc at right angles to it as in the figure X with the wheel
recessed. The edge of the wheel touching the shoulder is
trued and the shoulder ground by traversing the wheel out
by the cross slide in the direction indicated by S ; this produces

FIG. 116. — GRINDING SHOULDERS

a true conical or flat (according to the setting of the cross slide)
surface of much better quality than that produced by the
method shown at X.

When the wheel spindle is thus set inclined slightly to the
main ways, it is important to take the end play out of it, and
the diamond when truing the wheel should be as nearly ' level '
with the axis as possible.

The Work Head and Running Spindle.— Since the work
head spindle is used for chuck work it is fitted to rotate
in bearings, and since it is also used for dead centre work it

280 GKINDING MACHINEKY

must be capable of being locked, while the dead centre pulley
rotates loose upon it. Messrs. Brown & Sharpe's design is
shown in Fig. 117. For chuck work the spindle is driven by
the pulley A, between the bearings B and C, which are bronze
bushes split along one side, and are closed by the caps D, E,
and are prevented from closing further by wedges in dovetail
slots. The spindle nose has a parallel part and a thread for
receiving chucks and face plates, and also the dead centre
pulleys shown in position. The outer pulley F can be removed,
leaving the smaller one G which will give a higher speed to the
work. An adjustable driving pin as shown at H is a con-
venience. When the dead centre is used the spindle is locked
by the plunger J engaging a hole in the pulley. The whole
upper part K of the head has a swivel adjustment on the
base L, so that taper and flat work can be done.

Dead centre pulleys have non-adjustable parallel bushes
which are cheaply replaced. They are not to be expected to
have a very long life, as it is difficult to protect them perfectly
against the fluid, and the best way to meet the difficulty
is to adopt a design with the wearing parts as simple as
possible.

Collet Mechanism. — The spindle is hollow, and Universal
machines are usually supplied with a draw-in collet mechanism
as is shown in Fig. 118, and is very useful for holding washers,
saws, and other parts to be ground upon the face. The work
is placed upon the split collet C, which is expanded by the
screw B until the work is gripped tightly. The screw B works
in the sliding sleeve D, which is prevented from turning by the
pin E, and by turning the rear hand wheel A this sleeve is
drawn into the face plate, and carries the collet C and the work
with it, and draws the work up against the face plate F. The
face plate can easily be ground in position, and so the two faces
of the finished work will be true with one another.

Flat Work. — The best flat or nearly flat work is done by
swivelling the work head through a right angle and using the
automatic feeds. It must be remembered that as the feed is
indexed as a certain amount measured on the diameter of the

THE UNIVEKSAL GEINDEE AND ITS WOEK 281

work, the actual movement of the wheel head and amount ground
off a collar in this method is only half that shown on the
graduations. A diagram of the arrangement is given in Fig. 119,
where the wheel A takes successively the positions shown at
B and C relatively to the work DEPF, whose axis is PQ. The
surface produced is here a male taper, and the wheel cuts from
E to P and then becomes clear of the work towards C. If the
work head is swivelled so that the axis takes the position PE,
then the surface ground would be a hollow cone, and the wheel
would cut into the work in the position C, as the surface of the

FIG. 118. — COLLET MECHANISM OF UNIVERSAL GRINDEF. — BROWN & SHARPE

work would be that indicated by the broken line PG, so that
the corner of the wheel must not be traversed beyond the
centre. If the work axis PS were exactly perpendicular to
the wheel travel EP, then the wheel would continue cutting the
same when in the position C, and so an even light cut of the
wheel over both sides of the work — particularly at the circum-
ference E and H — indicates that the work is flat, and furnishes
the best method of setting the work head axis perpendicular
to the main ways of the machine. The final adjustment
of this is made by the aid of the screw K (Figs. 29 and 110),
which swivels the work table and the work headstock which
it carries.

GEINDING MACHINEEY

Work can be ground similarly by keeping the work head
axis parallel to the main ways, and setting the wheel head round
through a right angle. In this case, however, the wheel has
to be traversed over the work by the cross-feed and the cut
put on by the main slide motion, both of which are inconvenient ;
the work, however, is more easily set in the machine and is

FIG. 119. — FACE WORK IN UNIVERSAL GRINDER

easily seen. When such work is needed in quantity one of
the machines illustrated in the succeeding chapter is more
suitable.

Flat or nearly flat work may also be produced in a Universal
grinding machine by the use of a cup wheel, the face of which is
brought up against the work. If the work revolves, as in the
above cases, the work will be flat when the axes of the wheel
and work are parallel ; the quality of the surface produced
is not so good as that produced by the method previously

THE UNIVEKSAL GEINDEK AND ITS WOKK 283

described. Machines specially adapted for the purpose are
described in Chapter IX. Cup wheels can be used to
produce flat work, such as square and hexagonal shafts, knife
edges, &c., in a Universal Grinder by suitably mounting the
work and using the traverse motion. Fig. 120 shows a Landis
grinding machine set up for grinding a square shaft. The table
is first set so that the work is parallel to the main ways and then
the wheel spindle set square with the work, or rather very

FIG. 120. — GRINDING SQUARE SHAFTS — LANDIS

nearly square, so that it cuts at one side only. If it is set
decidedly off the perpendicular position the sides of the square
are ground slightly hollow. On the left is to be noticed the
index plate and plunger for locating the sides of the work
correctly. When the side of the square is less than the diameter
of the tailstock it is necessary to use a long centre as shown,
otherwise the wheel will foul the tailstock. A steady is shown
supporting the long centre.

It is convenient to be able to sharpen large cutters in a
Universal Grinder, as they are frequently beyond the capacity

284 GEINDING MACHINEEY

of the regular shop cutter grinder. For any parallel cutters
all that is needed is an adjustable tooth rest such as is seen on
the floor in Figs. 29 and 110 ; but for face and angular cutters it is
necessary to have an auxiliary wheel head which can be in-
clined and adjusted vertically. Such a head as fitted by the
Landis Tool Company is shown in Fig. 162 ; it takes the place
of the bracket for the internal grinding spindle, and is adjusted
to grind the clearance on the cutters according to the principles
explained in Chapter X.

CHAPTER IX

SURFACE GRINDING

NEXT to work of circular section the production of flat surfaces
is of most importance in engineering, and such work may be
produced by grinding in several ways, each having work to
which it is best suited. These methods may be divided into
two classes, employing the edge and face of the wheel respec-
tively, and these subdivided further according to the method
of producing the flat surface.

Edge Wheel Machines— Planer Type. — In Messrs. Brown &
Sharpe's No. 2 Surface Grinder, Figs. 121 and 122, the edge of
the wheel is used and the work traversed beneath it. At the
end of the stroke the work is traversed sideways for the next
cut, so that the surface is produced in a manner geometrically
that of a planing machine. The surface produced is one
parallel to that containing the lines of the main and cross
slides, and its accuracy, so far as geometry goes, depends solely
on the straightness of these two lines.

The main slide ways consist of two vees, but cannot be seen
well in the views ; the cross- ways are of similar type, and are
clearly seen in Fig. 121. The main slide A can be traversed by
the hand wheel B or by power, the reversing being done by
stops, one of which is seen at C, acting on a plunger trip
mechanism. The main slide is carried on the cross slide D,
the movement of which is controlled by the hand wheel E,
and can be operated automatically by the gearing shown at F.
This cross- feed is rapid, as the cross slide must be quickly moved
through a space from f to f of the width of the wheel at each
reverse, so as to keep the wheel face flat, as explained in con-
nection with cylindrical grinding (page 95) ; it involves much
more strain on the mechanism than the small amount of cross-
feed of the machine we have previously considered. The wheel

285

286

GRINDING MACHINERY

spindle G is horizontal, and is supported by a bearing close up
to the wheel ; the whole wheel head H has a vertical adjustment
by means of a screw J, the nut of which is rotated by the hand
wheel K through bevel gearing. The ways of the vertical
slide, which are of a very unusual type, are clearly seen in the

FIG. 121. — BROWN & SHARPE No. 2 SURFACE GRINDER

illustrations. The machine is driven from an overhead counter-
shaft by means of a belt running round the pulley L, then round
the wheel spindle pulley, and finally round the pulley M to the
overhead driving pulley ; the pulleys L and M are carried by
a swing frame N, which is pivoted at P, and the weight of which
preserves a suitable tension in the belt. In Fig. 122 the
machine is shown equipped with a dust extractor ; the machine

SURFACE GEINDING

287

is used dry, and the grit-laden air drawn away by an exhaust
fan. Much of the dust and grit can be caught on a wet belt
running slowly on the side of the machine towards which the
wheel runs as it cuts.

In larger machines of this planer type, the wheel head

FIG. 122. — BROWN & SHARPE No. 2 SURFACE GRINDER

may be carried between two uprights, as is the tool in regular
planing machines, or it may be carried as in Fig. 123, giving
an open-sided machine. The machine shown in this illustration
is by the Norton Manufacturing Co., and has a capacity of
15 inches by 8 feet by 17 inches, and takes a wheel
14 inches diameter by 6 inches face. The sheet guards
A, A' protecting the main ways, the reversing stops, and
mechanism are similar to those on the plain grinders by

288

GEINDING MACHINERY

SURFACE GEINDING 289

the same firm. The bed is supported on a series of taper
wedges B, B, so that the effects of settlement of the founda-
tion at any time can be corrected. The wheel head is
carried on a horizontal slide C, and has a rapid cross
movement by the hand wheel D — no automatic movement
is provided ; the width of the wheel necessitates considerable
cross movement in surfacing, and this is left to be operated by
hand. There is at E a second hand wheel — geared into the
shaft of D by means of a worm and worm wheel — whereby a
slow cross motion can be given to the wheel for truing it. A
large supply of water is arranged for, delivered by the pipe F,
and guards at G and H are provided to deal with the spray.
Power is provided to raise and lower the vertical slide J, and
fine adjustment for setting is provided at K. The machine
is self contained, the countershafting being within the machine
body, and requires 15 h.p. for regular work. The width of
the wheel enables formed straight work to be ground, up to
6 inches wide ; for such work special arrangements are necessary
for mechanically guiding the diamond tool in truing the wheel.

In neither of the machines of Figs. 121 and 123 can the wheel
be inclined in a manner corresponding to the setting of a planer
tool-box ; should pieces of material require to be ground in such
a manner on these machines, the work has to be set up as
necessary, or suitable jigs made. The efficient driving of a
wheel spindle which can be inclined and moved in such positions
is somewhat difficult, and although it has been tried the other
method is preferred. Undercut surfaces, such as the vees of
ordinary machine slides, have not been ground with commer-
cial success.

The same observations apply to the use of water in surface
as in circular grinding, but small machines are seldom fitted
for wet grinding. As only one side of the work — instead of
all sides as in cylindrical grinding — is ground at a time,
temperature effects are large in dry surface grinding, and the
wheels used must be very soft so as to minimise the effect.

In Fig. 124 is shown a special Surface Grinding Machine
constructed by Hans Eenold, in which again the edge of a
disc wheel is used in the grinding, but the surface produced

290

GKINDING MACHINEEY

in a different way — namely, by rotating the work round an
axis, here vertical, and traversing the wheel across by a slide

FIG. 124. — SUBFACE GRINDER — HANS EENOLD

at right angles to the axis. This corresponds to face work
on a lathe or vertical boring mill, and the accuracy obtained
depends geometrically on the straightness of the cross slide,

SUKFACE GKINDING 291

and the perfection with which its line is perpendicular to
the axis of rotation. If this angle is not a right angle the
work is ground conical, either male or female ; and as this
is sometimes useful — in such work as metal slitting saws —
a small adjustment of the angle is provided for in such
machines, usually by tilting the work spindle and face plate
round a horizontal axis. The work is fed up to the wheel
and the cut put on by the vertical movement of the work,
which is controlled by the hand wheel at the front of the
machine.

The wheel spindle is driven by a ' silent ' chain running from
overhead ; the chain wheel B is so long that, as the wheel slide
moves to and fro automatically, it only slides through the
chain which is driving it. The wheel head C slides horizontally,
and the rack D with the reversing dogs are seen at the front
of the machine with the reversing mechanism in the box G
below them. The feeds and work are all driven by the chain
E, and from this motion the chain F drives the reversing box G.
The vertical work spindle carries a magnetic chuck H for
holding the work ; its speeds are obtained through the change-
speed gear box U, which is controlled by the lever E, the
motion being transmitted through the gearing at V. The
cut is put on by raising the work spindle and magnetic chuck
by means of the hand wheel S. The pump, driven by the
sprocket T, is on the far side of the machine with the water
tank ; at W is the control switch for the magnetic chuck, and
the lamp seen is inserted in the circuit to reduce the current
by means of its resistance. The driving of such machines
by chains is unusual but illustrative. The corresponding
machines, placed on the market by the Churchill Machine
Tool Co., and other firms, are all belt driven.

This method of grinding flat work corresponds exactly
with chuck work done by setting the work head round
(page 281), so as to be square with the main ways in a
Universal Grinder.

Work Speeds. — In these cases, where a flat or nearly flat
surface is ground by the edge of a disc wheel, the arc of con-
tact is small and is equal to 2\/Dft, where D is the diameter

292 GKINDING MACHINEKY

of the wheel, and h the depth of cut. This value can be ob-
tained from the formula of Chapter III, by putting |£ = h,
and making the diameter of the work infinite, or it is at once
evident from the geometrical relation that the products of
the segments of chords in a circle are equal. The limiting

velocity and depth of cut depend on v2 ^ (to which v2 "jl t
reduces on making d infinite), and the best velocity on =- (to

which v reduces). Hence we see that the table speed

should be diminished as the wheel wears smaller, and the
depth of cut increased proportionally. As the wheel approaches
the centre of the work as the table rotates, it is desirable that
the rate of rotation of the work be increased, so as to keep the
work surface velocity at the wheel edge constant, but this is
seldom done.

Cup Wheel Machines. — Until comparatively recently cup
or cylinder wheels of a nature suitable for accurate work
were difficult to obtain, but with their development the progress
of machines employing them has been steady and rapid. Owing
to the very large area of contact the grit used must be large
and the grade soft, and truing is usually done with a piece
of hard carborundum block, as if the wheel is carefully trued
with a diamond tool it is more apt to glaze. For such reasons
the surface produced is marked, more or less deeply, by the
circular marks of the cut, and is not of so high a quality as
that produced by the edge of the wheel.

Large cup wheels are very expensive, and wheels built up
of suitably shaped pieces of grit stone, held in a chuck, are
used on large work. Artificial abrasive slabs are also used
in such chucks, but for this work the gritstone at present is
holding its position, for the cost is very small compared with
that of the artificial material.

As the arc of contact — see Fig. 21 — increases with the width
of the work, the grade of the wheel should be softer the wider
the work, and it is necessary that the grade should be right
to prevent glazing or wearing away ; hence it is necessary to

SUEFACE GKINDING 293

keep wheels of various grades mounted ready for use, even
although one kind only of material is ground.

The power required to drive a wheel effectively with such
areas of contact is very high, although soft wheels are used,
and the water supply must be plentiful to carry away the heat
correspondingly generated. Soda water is to be preferred to
a soluble oil mixture, as owing to its * thinness ' the wheels
cut with rather greater freedom. Also the total amount of
grinding solution (and the tank) should be large, otherwise
its temperature rises undesirably when the work is continuous.
In Fig. 125 is shown a view of the Pratt & Whitney Vertical
Surface Grinder, which uses a cup wheel 14 inches diameter
with a 1 J-inch wall, so that work up to 12 inches wide (see
page 64) can be done. The work is carried by the main
slide A under the wheel B, so that the geometrical accuracy
of the surface depends upon the straightness of the main
ways, and on the accuracy with which the wheel spindle is
set perpendicular to them. The wheel is fed to the work
by the use of the vertical slide C, so that the machine is
simple, in that it only contains two slides and a spindle as the
main parts. Mechanically it corresponds to a Face Milling
Machine. The table has power feed, with two speeds,
34 inches and 102 inches per minute, with reversing mechanism
operated by the stops, and one of which, D, can be raised, so
that the table can be run beyond the stops for examining
the work. At E is the hand traverse motion for the main slide.
The vertical feed, which puts the cut on, is operated auto-
matically by the usual type of mechanism, or by the hand
wheel F, which gives the fine feed ; rapid adjustment of
position can be made by the hand wheel G. The movement
of the vertical slide is by rack and pinion, and the wheel head
is held back by its weight being over counterbalanced by the
chain H and a weight, the force being applied by the chain.
The design of the spindle is shown in Fig. 37, page 129 ;
it will be noticed that the spindle itself is relieved from the
heavy pull of the driving belt, which is 4 inches wide, as the
pulley runs on an independent bush, as is usual in drilling
machine practice. The spindle is hollow, and the water is

294

GKINDING MACHINEKY

supplied by the pipe J through the spindle to the inside of
the wheel. Owing to the porosity of the wheel, the water
can be forced through it and spun off by the centrifugal effect,

FIG. 125. — VERTICAL SURFACE GRINDER — PRATT & WHITNEY

and to prevent this the inside of the wheel is coated with
bees'-wax. The water supply through the pipe shown at K is
useful for washing grit and swarf from the table when setting
work.

When in use the guard shown at L is placed in front of the

SUKFACE GRINDING 295

machine, and slides up and down in the slots M, N. When
it is down work can be conveniently set, and when raised it
catches the spray from the grinding.

The machine is shown fitted with a removable rotating
table P, driven from the shaft Q. For flat, circular work this is
desirable, and it can be tilted so that metal slitting saws can
be hollow ground. For general flat work, for which the machine
is essentially designed, a magnetic chuck fixed to the table is
very desirable, as it saves a considerable amount of time in
setting most work.

In Fig. 126 is given a view of the Blanchard Surface Grinder,
in which the work is carried on a rotating magnetic chuck A
and ground by the cup wheel B. The magnetic chuck, with
its spindle and bearings, are arranged to slide under the wheel,
but merely for purposes of convenience in setting and examining
the work, and not for traversing it. The water guards have
been removed for sake of clearness and to show the measuring
device C, which consists of an Ames Indicator suitably mounted,
and by which the thickness of the work is indicated at any
time during the grinding, as it passes on the face of the
magnetic chuck outside the wheel. The wheel spindle, shown
in detail in Fig. 38, with its pulley and bearings, is carried on
the slide D, which is adjustable vertically by the handle E,
and can be fed by power through the change-speed box F. At
G is the change-speed box for the rotation of the magnetic
chuck, and above it at H and K respectively the valve handle
for the water supply to the inside of the wheel, and a demag-
netising switch. The belt for driving the spindle is a 5-inch
double belt, the pulley being 14f inches diameter, and runs at
1000 r.p.m for a 16-inch diameter wheel ; a 20 h.p. motor is
recommended.

Machines using very much larger cup wheels are used for
grinding armour-plate which has been hardened, but have
few features of interest other than their size. The largest
size in use takes up to 80 h.p. The wheels used are of the
inserted segment type (see Fig. 10) and natural stone is
employed.

InFig. 127 is shown the Walker Single Stroke Surface Grinder;

296

GKINDING MACHINEEY

in this the work is carried on a rotating magnetic chuck
and ground by simply bringing the cup wheel down to it by
means of the slide. When the surface is to be flat its accuracy
depends geometrically upon the parallelism of the axes of the
wheel and the work. As in other machines the work head,
which is here carried in the lower knee, can be set at a small
angle to the wheel spindle, as it is pivoted by screws to the
knee and adjusted about this axis by means of an adjusting

FIG. 126. — BLANCHARD VERTICAL SURFACE GRINDER

screw. In this machine only one slide is actually necessary ; the
wheel can be raised by the lever, the work set in position,
and the grinding done by simply bringing the wheel down upon
it ; but in order to make the machine into a more efficient
manufacturing machine, the magnetic chuck with its spindle and
tilting arrangement is carried on a second slide. In working,
the wheel head is always brought down to one position denned
by a fixed stop : it is raised for removing the work and setting
the next piece and then again brought down, grinding the work,
to the same position. The knee carrying the work is adjusted

SUEFACE GEINDING 297

vertically, by a graduated hand wheel, to suit the thickness
of the work and to compensate for the wear of the wheel ;
the work spindle pulley is driven from the vertical drum at
the rear, and is made long for the purposes of driving in all
positions of this vertical adjustment. The movement of the
wheel head by the lever always takes place over the same range,
and controls the current magnetising the chuck, making it
as it descends and breaking it as it rises. It also controls
the rotation of the chuck by means of a linkage, which
clutches the drum on to the rotating vertical shaft by
means of the clutch as the slide descends and withdraws
the clutch as it rises. Thus a single movement of the lever
alone is necessary to magnetise the chuck, set it rotating, and
bring the wheel down until the work is ground to a definite
size. The wheel pulley is driven by a belt from the pulley
on the rear shaft. In the linkage is a stop, by moving
which the clutch is not thrown out when the head is raised ;
the magnetic chuck then continues to rotate, and can be
easily cleaned. The water tank, the supply nozzle, and
discharge can be clearly seen. The machine illustrated is
fitted with a ventilated magnetic chuck, the blower for which
is driven by the small electric motor.

Magnetic Chucks. — For the purpose of surface grinding,
parts may be held in vices or by any of the devices which
are usual in planer or shaper work, but for much work the
most convenient method is by means of magnetic chucks,
as previously mentioned. These hold the iron or steel by a
magnetic pull to the face of the chuck, and all else that is
needful is a stop to prevent it moving in the direction of the
cut. The pull takes place on to the surfaces round the gaps
wherever the work is there in contact with the chuck ; the
pull is considerable, and unless the side of the work towards
the chuck is true, thin work is apt to be sprung towards the
chuck.

When a magnetic chuck is set on a machine with its face
true, or ground in position, work can be taken off and replaced
with practically perfect accuracy and no trouble, and parts
can be duplicated as regards thickness with little difficulty.

298

GKINDING MACHINEEY

The chief matter of importance is that the face of the chuck
be swilled and wiped clean from grit before the work is set
on it. The resulting saving of time is so great that a surface
grinder for general use can hardly be considered to be com-
plete without one, and in some machines, such as shown in
Figs. 124, 126, and 127, a magnetic chuck is built in as an
integral part of the design.

Fundamentally, a magnetic chuck is merely an electro-
magnet with suitably shaped
pole pieces. In Fig. 128 is
an explanatory sketch of a
magnetic chuck. The current
enters the chuck by the wire
at A, circulates round the cen-
tral part B as indicated in the
plan view, and leaves by the
wire C ; a switch for making
and breaking the current is
shown at D. When the cir-
cuit is made, a number of
closed lines of magnetic force
arise in circuits, as indicated
by the broken lines in the side
view, up the central part B
and along the top F, across
the gap GG, down the sides
H, H, and across the bottom
to the central part again.
The irregular shaped top FF,
and the correspondingly shaped top of the sides H, H, form the
two poles of the magnet. The gap GG is filled up with non-
magnetic substance, usually white metal, so that the top
of the chuck is continuous. If the chuck rotates the leads
have to be carried to rings, and the current brought to them
through brushes, similar to those of a small dynamo or motor.
Any piece of steel put across the two poles is attracted
to them, and forms an easier way for the magnetic lines than
the non-magnetic gap does, PO that the number of lines con-

FIG. 127. — WALKER ONE-STROKE
GRINDER

SUEFACE GEINDING

299

siderably increases as the way becomes easier. The pull on
the steel part depends on the number of magnetic lines passing
through it.

Iron and steel can only accommodate a certain number
of lines per square inch, so that if the part be very thin (say
less than -fa inch) the number of lines through it may not create

FIG. 128. — DIAGRAM OF MAGNETIC CHUCK

sufficient holding force ; hence thin pieces are more difficult
to hold than thick, and may necessitate chucks of special
design with narrower and more numerous gaps.

The shape of the gap GG varies in different chucks accord-
ing to the work for which they are intended ; circular chucks
may have the gap arranged in many ways — it may be a series
of radial lines connected by arcs, or a number of circles arranged
concentrically or otherwise.

800 GEINDING MACHINEKY

The coil of the chuck has to be wound to suit the voltage
of the electric supply ; too high a voltage would overheat
the coil in a chuck designed for a lower voltage, and might
fuse the wires. Continuous current is almost always used ;
chucks can be made for alternate current, but are more com-
plicated and do not hold so well ; hence if the current supply
is alternating, it is better to run a small continuous current
dynamo to supply the chuck current. Very little current is
needed, so that the low efficiency of the small dynamo is not
a matter of much moment.

There is a considerable amount of energy involved in
the production of the system of magnetic lines, and some
precaution is needed in breaking the circuit ; a secondary
resistance should be fitted, or at any rate the switch should
be of the quick break double pole type. As the magnetic
lines rapidly decay on the electric circuit being broken, they
produce an electromotive force round the wire circuit, which
tends to generate a powerful but temporary current.

High voltages should not be used, as the operator's hands
are usually wet, and shocks are then severe.

Soda water and oil are very destructive to (electrically)
insulating materials, and it is necessary that the chuck should
be quite waterproof, and no holes, tapped or otherwise, should
lead to the interior, other than that necessary for the leads
(wires conveying current to and from the chuck). The leads
should be encased in a tube or lie within the machine, protected
against injury from grinding solution or accident.

In Fig. 129 is shown a magnetic chuck by the Walker
Grinder Company ; the interior is ventilated in order to
prevent deterioration of the insulation by the grinding solution.
The machine spindle A carries a chuck plate B, to which
the magnetic chuck C is fastened. The ventilating air passes
through the spindle — which is hollow — at F, circulates in the
chuck and escapes at the holes E, E, which have gauze across
them to prevent the entry of dirt. The current is conveyed to
the chuck coil through the rings G and H, on which brushes
rub. At P is some of the non-magnetic material in a gap in
the chuck face. The forced draught is usually produced by

SUBFACE GEINDING

301

a small blower driven by a motor ; such an arrangement is
shown in Fig. 127.

In chucks of my design — one of which is shown in Fig. 130
— there is no aperture whatever in the chuck face, the central
hole being a blind one and used only for the insertion of plugs
to centre the work. The current is carried to the chuck by
leads through the hollow spindle of the machine, and the slip
rings are two small rings at the rear of the spindle, well away
from grinding fluid and spray.

Hardened steel work which has been held on a magnetic
chuck is apt to remain magnetised. To remove the magnetisa-

FIG. 129. — VENTILATED MAGNETIC CHUCK — WALKER

tion it is necessary to magnetise it in alternate directions
with a gradually decreasing intensity of magnetisation. Instru-
ments for the purpose are called demagnetises, and consist
of an electro-magnet, with a revolving switch for alternating
the current and a resistance which can be gradually increased
to a large amount, so as to reduce the current and the magnetisa-
tion. For small numbers the parts can be simply rotated in
a magnetic field, and then moved away from it while they are
rotating.

Metal Slitting Saws. — The sides of metal slitting saws are
usually ground with cup wheels on machines such as are
illustrated in Figs. 125 and 130, and are made slightly hollow
so that the saw clears itself sideways. This can be done by

302 GKINDING MACHINEKY

using the edge of the wheel as is shown in Fig. 119, page 282,
and adjusting the setting of the work head so that the side
of the saw is ground to the shape of a hollow cone ; the cup
wheel method has some advantages, and the operation presents
some instructive points.

Whenever grinding is being done there is some normal
force between the wheel and the work ; it is slight, but as the
wheel runs off the work it tends to cut a little deeper, as it
is not kept out so effectively as the area of contact lessens ;
thus internal work tends to bell-mouth, and the wheel should
not be run very far out of the hole at either end. So in hollow

FIG. 130. — MAGNETIC CHTICK — GUEST

grinding metal slitting saws with the edge of the wheel, if the
wheel is run off the teeth the slight hollo wness may be lost just
at the edge by the action of this small spring of the wheel
towards the work, so that the saw may tend to bind in the cut
when used. If, however, the wheel be not run off the saw — since
the clearance at the edge depends on the straightness of the
wheel — the result may be the same. When a cup wheel is used
it is brought practically normally up to the face of the saw, and
the grinding is done in that position ; as it is never run off
the edge there can be no rounding, and the relief is obtained
with certainty.

It should be noticed that this small action also affects
such tools as twist drills ; the edge along the flutes is ground

SUEFACE GEINDING 303

and made taper along the length of the drill, the shank end
being a few thousandths of an inch less in diameter than the
lip, so that the drill clears lengthways. In grinding this edge
(clearance is usually milled or ground at the rear of it) the drill
should be rotated so that the rear of the edge strikes the
wheel first ; it tends then to spring out from the wheel a very
little, so that when the cutting edge is being ground it is just
a bit farther from the drill's axis, as there is no time for the
springing to return before the edge has gone past the wheel.
The amount of this action depends on the springiness of drill
and machine : it is always exceedingly small, but drills ground
that way (it is unusual, requiring a left-hand grinding machine
for right-hand drills) cut a little more freely than if ground
using the customary direction of rotation.

If the sides of a saw are ground by the first method, the
angle of the side is constant — that is, a line drawn from the
centre to the outside of the saw surface is straight ; but when
ground by the cup wheel method the line will be a circular
arc. For the same clearance this leaves the centre of the saw
much thicker, which is desirable, and since it removes less
metal the grinding can be done more quickly.

That the shape of the ground surface in this case is spherical
is not difficult to see. Let ABCD in Fig. 131 be the edge of
the wheel face and EF the axis of the wheel spindle, and let
the work axis be FG. In the machines these are in one plane,
and intersect at the point F. Since EF is a perpendicular at
the centre of the circle ABCD, then all the lines FA, FB, FC, &c.,
are equal, and hence as the work revolves round FG all the
lines from F to the ground surface are equal — that is, the
ground surface is a piece of a hollow sphere, and therefore any
plane section, radial or not, of the ground surface is a circular
arc.

The sketch shows FG to miss the circle ABCD, which is
the case of a saw with a raised collar at the centre ; usually
there is no collar, and the wheel is set so that the circle ABCD
passes across the hole in the cutter.

The advantage of this spherical clearance is shown in
Fig. 118, where it is much exaggerated ; the full line PQES

304

GKINDING MACHINEEY

shows a saw with the spherical clearance, and the broken
line from Q a straight (conical) relief. The spherical clearance
gives a greater relief at the edge, and at the same time the
centre of the saw is thicker.

In the figure the saw is shown held on a drawback expanding
collet, which is the best method for the roughing operations.
The saw is first placed on the collet C, and the latter expanded
by the screw B. The collet carrying the saw is then drawn
into the spindle by the screw A, operated from the rear of the

FIG. 131. — GRINDING SAWS, CONCAVE

spindle, until the saw comes against the face plate F. Owing
to the warping in hardening the saw usually will not touch
the face plate all the way round, and it is packed where necessary
with paper, until on drawing the saw up tightly to the face
plate all is firm. After grinding this side is practically true,
and will need no packing when reversed for grinding the other
side. Although the saw is hollow where ground, no packing
piece is really essential, although one is used sometimes.

The resultant cut of the wheel passes fairly close to the
collet, and it acts as a stop. I have ground the sides of circular
cigarette knives 9 inches diameter by yV inch thick, with a

SUBFACE GEINDING

305

f-inch central hole, holding them in this manner firmly under
a heavy cut.

After a saw has been roughed out, the best means of holding
it for finishing is by means of a magnetic chuck. If a magnetic
chuck be used initially the saw must be reversed a number
of times, and a small amount of stock removed at each. For
when a thin untrue piece of steel is placed on a magnetic chuck,
the pull all over its face pulls it flat against the chuck face,
straining it. When the exposed side has just been ground
it is true, but immediately it is released from the chuck it

ntn

FIG. 132. — SECONDABY PIECES ON MAGNETIC CHUCK

springs back, and the ground face becomes untrue. This
repeats itself at each grinding, but the amount gradually
diminishes, so that the ultimate result is satisfactory.

Such precautions are to be taken when magnetic chucks
are used for holding any springing parts for grinding.

Secondary pieces can be set on the top of a magnetic chuck,
and themselves become conductors of the magnetic lines, and
so magnetic. These are frequently useful, for example in
grinding a strip square, as is shown in Fig. 132. Here the
chuck AB carries the secondary piece C, of which the holding
surface is square with its base, set on it, and which holds the
work DEFG by the face DE. Short pieces of wire H should be
placed underneath the work at G. The pull of the piece C
strains the work in a horizontal plane, so that when the piece

306

GEINDING MACHINEKY

is released after grinding the top EP, this surface is still flat,
and can be used for holding the piece magnetically while the
other sides are ground. At K is a stop to prevent side motion.
The piece C should have saw cuts, the ends indicated by the
broken line, to direct the magnetic lines advantageously.

Disc Grinders. — Work of a somewhat lower degree of
accuracy can be done rapidly and conveniently on disc grinders,

FIG. 133. — Disc GRINDER — HARPER, SONS, & BEAN

and one such by Messrs. Harper, Sons, & Bean, is illustrated
in Fig. 133. In these machines the grinding is done by a
sheet of emery cloth glued upon a steel disc, which is rotated
at a very high speed. As steel is stronger in proportion to
its weight than is the material of an emery wheel, the discs
can be run at a higher speed, gaining the advantages so involved.
Peripheral speeds of 7500 to 8500 feet per minute are used.

The surface speed diminishes with the radius, so that the
inner part of the disc is not so effective as the outer portion.
The circles, of cloth or paper, coated with suitable abrasive

SUEFACE GRINDING / 307

material, are glued to the steel disc and kept in a press, which
is a necessary part of the equipment, while the glue sets, so
that the abrasive surface is flat. In coating the fabric with
abrasive more or less glue may be used, as with the bond
in wheels, producing circles of different grades. In use the
circles cut best initially, gradually lessening in efficiency ;
finally they are removed by soaking in hot water.

Generally these circles are coated uniformly with abrasive
of one grit (usually 16 to 24 for cast iron, and 24 to 60 for
steel or brass), but when the work presents a considerable
amount of surface to the grinding disc — and especially if this
surface is unbroken — it is better that the abrasive be distributed
in some pattern, presenting lines of abrasive and free space
alternatively. This reduces the actual area of contact, and
also provides plenty of room for the swarf. The Besly
Company supply discs in which the abrasive is arranged in
a spiral line ; other firms have patterns in which different
abrasives alternate.

Owing to the use of glue in the preparation and mounting
of the circles, water cannot be used in the grinding, which is
accordingly done dry. The heat produced is often considerable,
and may cause the finished work to be objectionably distorted ;
this, however, can easily be avoided by grinding in two or three
operations.

The accuracy of the flat surfaces produced is dependent
on the flatness of the grinding disc, and is of the order of one
thousandth of an inch, while an accuracy of dimension between
one and five thousandths of an inch is to be expected.

The work may be presented to the disc by hand only, or
use may be made of the work tables, such as are shown in
Fig. 133. These are adjustable as to height and as to distance
from the disc, and are balanced. Any work, while it is being
ground, must be moved across the face of the disc, so as to
distribute the wear evenly. This is done by swinging the
work table on the shaft upon which its carriage is mounted ;
the shaft must be parallel to the wheel spindle in order to
secure satisfactory results.

The left-hand table in Fig. 133 can be canted at an angle,

808 GRINDING MACHINERY

so that work can be ground to a bevel easily. The work is
placed upon the table, held in position, and pressed against
the disc by hand only ; this is only suitable for small quantities,
or where little material has to be ground off. When the
work is more severe, the right-hand work table — which is fitted
to slide towards the wheel, and is moved by the lever below
it — is used ; the work is carried on the table, usually in a jig,
and the extent of the grinding is controlled by an adjustable
stop. In Fig. 134 is shown the stop of the Besly Disc Grinder.
The actual stop screw AB is hollow, and can be firmly clamped
by the locking screw C. The screwhead A is graduated, and
the reading is taken against the edge of the plate D. Inside

FIG. 134. — ADJUSTABLE STOP OF BESLY GRINDER

this screw is a second screw EF, which limits the grinding
when its end F comes in contact with the fixed abutment ;
by slacking it back the grinding is allowed to proceed gradually
until the end B of the actual stop screw AB is left in contact
with the abutment, the work being then ground to size.

Disc grinding is usually done from the rough, and the
allowances should be as little as possible. In machining
cast iron it is necessary for the tool to get well under the skin,
especially if the work be not pickled, and accordingly a
machining allowance of ^ inch is given, even on small work ;
for grinding this is unnecessary, and from ^ inch to YB inch
is ample. The same, or less, is satisfactory for brass or bronze
castings. Drop forgings usually need a -^%-mch allowance.
Stampings vary considerably ; frequently, however, the surface
need merely be cleaned up and made true.

SUEFACE GEINDING 309

To reduce the amount of material ground off, surfaces
should be recessed wherever possible ; this makes the grinding
much easier, as room is provided for the swarf, and it may be
essential to the success of the process. The small difficulty
of machining narrow surfaces which occurs in planing does
not here exist ; an extra core is, however, sometimes needed.
The simplest mode of producing a flat surface is to hold
the work to the wheel by hand, allowing it to take its own
seating on the grinding surface. This presents one of the
principal advantages of this system of grinding — namely, that
the surface is cleaned up with the removal of the least possible
material and in the least time, for as the major prominences
are ground off the work reseats itself. In manufacturing so
many surfaces have merely to be cleaned up and made flat
that the point is important.

In Fig. 135 is a drawing of the Besly Vertical Spindle
machine, which takes a disc 53 inches in diameter ; heavy
articles rest upon the surface by their weight only, and being
prevented from moving round, have the lower face ground
flat in the most economical manner. Using a large disc
with surface sufficient to accommodate a large number of
articles, the labour cost of grinding them may be reduced
to little more than that of placing and removing them. The
method is common in optical work, in which the parts are
loaded, as they are light.

In order to secure the abovejadvantage, when work has
to be held in a fixture carried on the sliding work table, the
work holder should be of the floating type. An illustration
of such a jig, by the Besly Company, is given in Fig. 136.
An angle plate is carried on the work table, and carries the
work holder by means of a ball-and-socket joint, so that the
work can accommodate itself to the grinding disc. The ball
is pulled into its socket by a spring, and the work holder
is tilted conveniently by another which forces its lower edge
towards the wheel.

Although the disc grinder affords a convenient means of
doing various work in the tool room and fitting shop, the fact
that no truing is required renders the process suitable for

310 GKINDING MACHINEEY

comparatively unskilled use, and it is well adapted for quantity

manufacturing. The process shows its greatest economy on

SUBFACE GKINDING

311

small parts which can be ground in a minute or less, and
accordingly efficient jig design is essential to obtain the best
results.

As the force on the work is moderate, and is downwards
and outwards from the disc, it is frequently possible to arrange
the jig so that no clamping is necessary, the work being merely
dropped on to the locating points. Where the grinding time
is very short, work carriers, which can be loaded with a quantity
of work, and then placed in the machine, can be arranged for.

JhisPm to prevent Holder tilting too far backward

Set/Aliynna DtUari&S0(&t

Joint

Dotted L ines so Work wilt not tip toward W/ieet

FIG. 136. — FLOATING WORK HOLDER — BESLY

Convenience and simplicity — for there is plenty of grit about
— are the chief considerations.

When the area to be ground, or its over -all dimensions, is
considerable for the size of the machine, the work may be
carried on a rotating work holder, consisting of a spindle
carrying the work by means of a face plate or magnetic chuck.
In order to produce flat work the spindle axis must be set
accurately parallel to the disc spindle. The arrangement then
becomes geometrically equivalent to that of the machines of
Figs. 126 and 127. In Fig. 137 is shown a Besly Disc Grinder
fitted with such a rotating work head.

Thin work may be distorted by being clamped in a jig,

312

GEINDING MACHINEKY

so that after being released the ground surface is not flat ;
in such cases, as in those where the distortion is caused by
temperature effects, the surface may be corrected by being
held lightly against the wheel by hand.

When a considerable amount of metal has to be removed
cup wheels are more economical than cloth or paper discs,
but the work has then to be fed or rocked right across the
edge of the disc. In Fig. 138 is shown a Guest Double Head
Grinder, which illustrates a further point. When two parallel

FIG. 137. — ROTATING WORK HEAD OK
BESLY GRINDER

surfaces are to be produced on the work they may be ground
at one operation by the use of two wheels or discs. The work
is carried by a jig mounted on the table on the front of the
machine, or stretched between the wheels to a similar table
on the other side. In the former case rotating fixtures with
several work holders are convenient, the parts being inserted
at the top, carried across the wheels and out again by the
motion. In the latter case a roughing and a finishing cut can
be given by adjusting the screws seen at the end of the wheel
head, so that the wheel spindles are very slightly out of parallel.
The wheels are fed up independently, so that the wheels cut

SURFACE GRINDING 313

equally, but it is best that the jig should permit the work a
slight lateral movement to ensure this.

The work from disc grinders presents the curved marks
of the path of the cutting particles, and these are sometimes
considered undesirable. They may be polished out or, instead
of a disc grinder, a belt charged with abrasive, or an emery

FIG. 138. — GUEST DOUBLE HEAD GRINDER

cloth band, running over pulleys (see Fig. 184) may be used.
The belt is supported by a flat plate where the grinding takes
place so that the work is flat. Such an arrangement, however,
is not nearly so efficient as a disc grinder.

The time occupied in grinding such work as is suited for
disc grinding depends largely upon the article itself, and no
general rule can be given ; the process should be considered
whenever there are small surfaces to be machined or cleaned
up flat on work which can be easily jigged.

CHAPTEK X

SHARPENING CUTTERS AND TOOLS

In General. — The sharpening of milling cutters and other
tools is an essential part of the work of a manufacturing shop,
and a number of machines are on the market for the purpose.
If the edges of a cutter's teeth become dull they rapidly become
much more so, hence frequent sharpening prolongs the life of
a cutter, very little being ground off each time. Some cutter
makers stamp this advice on their products, considering it
so important. Owing to the diverse forms of the cutters and
various modes of presentation of the edge to the grinding
wheel, a considerable number of movements or adjustments
are necessary in a machine which will meet all demands, and
cutter grinding machines vary from simple forms to sharpen
a few of the more generally used types of cutter to Universal
cutter grinders which, in addition to sharpening all standard
types of cutter, will do external, internal, and surface grinding.
Some machines normally are adapted to sharpen a few types
of cutter, and by the addition of various attachments the range
can be extended as desired ; this is an arrangement alluring
to optimistic small firms, although the initial cost is higher
than that of a simple machine.

The amount of metal removed in sharpening a cutter is
small, as it is only along the edge, either in front of, or at the
back of the tooth that grinding takes place, and as the work
is so small the machines need not be very substantial. It is
this fact apparently which tempts designers into the employ-
ment of unnecessary and very undesirable amounts of over-
hang, which not only tend to inaccuracies initially, but lessen
the life of the machines from wear and the extra difficulty
of the dust protection. It is the best practice that the parts
moved in passing the cutter across the wheel should be as

314

SHAEPENING CUTTEES AND TOOLS 315

light as is consistent with reasonable rigidity, so as to secure
sensitiveness ; the rest of the machine should be substantial,
so as to minimise vibration.

Machines intended to grind the shanks and holes of cutters
and for manufacturing small parts require to be much more
rigidly and accurately built than if intended for cutter
sharpening only ; otherwise they will not size the work easily,
and will lead to various other troubles. It is also desirable
that the use of water should then be provided for, and such
machines conveniently fill a place in factories where little
general machine grinding is done.

For convenience most cutters are ground dry, and as it
is of first importance not to draw the temper of the edge,
the wheel must be of a soft, free-cutting grade. For the same
reason the cut must be light and never forced. The wheel
must be kept clean and never become glazed or smeared with
the thick oil from a cutter. The wheel face used should not
be too wide, as this increases the rate of production of heat.
Cup wheels may be bevelled inside to reduce the width in action.
In cases where water is used the same precautions are still to
be taken, as the use of water does not prevent the heat from
being generated ; it only keeps the work cool by abstract-
ing the heat from the metal. This takes a certain small
time, and if the heat is not conducted away sufficiently
rapidly the temper of the tooth is drawn by the increasing
temperature. Unless the water is guided right on to the
grinding point it is practically useless. Wheels of a soft grade
suitable for cutter sharpening are now easily obtainable, and
trouble arising from hardness of grade is almost a thing of the
past. The use of water, although in several ways inconvenient,
has the advantage that rather harder wheels, which keep their
shape longer, may be used than is possible in dry grinding.

Types of Cutters.— For the purpose of sharpening, cutters
may be divided into two classes : (1) those sharpened on
the back of the cutting edge, so that the clearance is produced
by the grinding, and (2) those sharpened on the front of the
face forming the edge, chiefly in order to preserve a particular

316

GKINDING MACHINEKY

shape of tooth, and in which the clearance is produced by
relieving in the manufacture of the cutter.

The first class may be further subdivided into (1) parallel
cutters with straight or spiral teeth, (2) angular cutters, face
cutters, rose reamers, and end mills. The second class includes
formed cutters, gear cutters, taps, and reamers when sharpened
on the face of the tooth, and also formed tools for lathes—
whether circular or flat.

Clearance. — In Fig. 139 is a sketch of the teeth of these

FIG. 139. — CLEARANCE ON CUTTERS

cutters ; that of the first type is shown at A. The face angle
BAG, where B is the cutter axis and CAD the tangent, is almost
always 90°, although it may be, and generally is, less when
inserted teeth are used ; for reamers it may be a little more.
The clearance angle DAE, at the back of the edge between
the tangent AD and the cutter surface AF, is produced by
grinding the facet AF, the width of which is termed the ' land.'
This should be narrow, and should not exceed J inch on
cutters up to 6 inches in diameter ; for reamers to be used on
steel the width should be about y^ inch, and for those
intended for cast iron or bronze from ^ inch to ^5 inch.
With these small dimensions it is impossible to judge the
angle closely by eye, and to obtain satisfactory results a

SHAKPENING CUTTERS AND TOOLS 317

reliable method of securing the correct angle of clearance must
be employed.

A tooth of the second class is shown at G, and is supposed
to have some particular section which it will produce on the
work in milling. The clearance behind the cutting edge is
here fixed by the curved arc, and is produced in the manu-
facture of the tool. When dull the cutter is sharpened by
grinding the front GH of the tooth. It is usually arranged
that the face of the tooth is ground radial, as the section
of work produced is then easily maintained accurately.
When a tooth gets dull and rubs, the edge is worn away as
indicated by the broken line JKF on the first tooth, and
LM on the second ; it will be noticed that, if there is much
rubbing, in cutters of the second class a very considerable
amount of the face GH has to be ground away to bring the
edge up sharp. The tooth of the first class is not damaged
so seriously. The broken lines indicate the amount to be
ground off in sharpening in the two cases. It is therefore to
formed cutters and gear cutters that the recommendation to
keep sharp particularly applies.

Principles of Cutter Sharpening. — In sharpening cutters of
the first class either the edge of a disc wheel or the face of a
cup or dish wheel may be used, sometimes one and sometimes
the other being the more advantageous. Whichever is used
the clearance must be formed by the motion of the wheel,
and not allowed to be dependent on the shape to which it
wears. The correct methods are illustrated later, but attention
is called here to Fig. 140, in which are shown incorrect methods,
where the clearance obtained depends on the wear of the wheel.
The cutter is supposed to be moved perpendicularly to the
plane of the paper, and the clearance depends both on how
the wheel is trued and how it wears afterwards. At the top
AB is shown the edge, and at the side the face CD, of a wheel
in use, both incorrectly applied. The broken lines indicate
how the wheel wears and the effect on the cutter edge. In
the example of the cup wheel it is the back part of the land
which is chiefly affected ; but if the cutter tooth faced upwards,
or if it were being sharpened at the top of the wheel, it would

318

GRINDING MACHINERY

be the cutting edge which would be rounded. So that the
position shown is the best to use, lest the wheel face at C should
be too wide.

As the clearance on this class of cutter is produced by the

FIG. 140. — SHARPENING CUTTERS — INCORRECT PRINCIPLES

grinding, the ' setting ' of the machine to obtain the correct
amount is important ; for if it is insufficient the cutter does not
work freely, and if it is too much the edge does not stand up
as long as it ought to do. In practice the error is always
made on the side of too much clearance, as too little leads
to immediate trouble.

SHAKPENING CUTTEKS AND TOOLS 319

Hardly any cutter grinders are provided with efficient
means of securing the correct clearance, although sharpening
a cutter at different angles at different times implies that
more is ground off than is necessary to sharpen the cutter.

Amounts of Clearance. — From experience with lathe tools
it is known that 3° is sufficient clearance, but as cutters have
frequently to be fed into the work normally to the surface,
and this feed is equivalent to reducing the clearance, it is
well to regard a cutter as requiring rather more clearance,
say 4° or 5°. The ideal amount would depend upon the
material and upon the particular work. In setting up a
machine to grind the clearance a further allowance must be
made for small errors of adjustment, so that the actual clear-
ance produced may not be too small ; for this reason the ' charts '
of settings which give the amount of adjustment necessary are
usually based upon a clearance of from 5° to 9°. Such a chart
for edge wheel grinding is given in Table X, page 434, with
a corresponding chart for face wheel work in Table XI opposite
to it. Because of the effect of errors of adjustment, it is well
to set small cutters to receive the larger angles of clearance,
and large tools, in which the effect of these errors is relatively
less, for the smaller angles. For face cutters 3° is sufficient.

Secondary Clearance. — Besides this normal clearance im-
mediately at the back of the cutting edge it is sometimes
necessary to grind a second clearance, of an increased angle,
a little farther back, as is shown in Fig. 141. For the width
of the land increases with each sharpening of the cutter, and
as it does so the chance of drawing the temper of the edge
in the operation increases. Before the land becomes large
(say over ^ inch) it is well to reduce its width by grinding this
second clearance of an increased angle a little farther back.
Also in reamers, where the land must be very small — else they
will not cut well — this second clearance is ground. It is
shown in Fig. 141, where A, B, C, D, E, F are points of the cutter
teeth, AG the too wide land, which is reduced to AH by grinding
off the shaded portion HGK by means of the wheel LMHK.

For the sake of clearness the figure is exaggerated, but it
shows that a comparatively small wheel is necessary to grind

320

GEINDING MACHINEKY

this clearance, and yet to miss the next tooth B. This second
clearance or relief can, however, easily be ground by using a
dish wheel, such as is shown operating on the tooth P, grinding
away the part PQR, and reducing the land from DK to DQ
without endangering the cutting edge of the next tooth E,
or it may be ground by the method explained on page 335.
The figure (141) shows the tooth C before grinding and the
teeth E and F afterwards. The angle of the secondary clear-
ance is not important ; after it has been ground the cutter

FIG. 141. — GRINDING SECONDARY CLEARANCE

can be resharpened at the normal clearance angles for a number
of times.

The simplest form of cutter grinder consists of a wheel
head, a cross slide for approaching the wheel and work,
a means of travelling the cutter relatively to the wheel, and a
tooth rest for locating the position of the tooth of the cutter.
With the addition of a tooth rest a Plain or Universal Grinder
will serve to sharpen certain classes of cutters. In some cases
cutters are best indexed round by a division plate on a live
spindle in the work head, but not frequently, and in this case
a tooth rest is not required.

Parallel Cutters — with Holes. — Generally the cutter is

SHAEPENING CUTTEES AND TOOLS

321

traversed past the wheel by means of a slide, but in the particular
case of cutters having a parallel hole they may be traversed by
sliding them along a parallel mandril. This method is only
applicable to cutters of uniform diameter on the outside, for
however the wheel and tooth rest are placed, the distance from
the axis to the ground tooth edge is the same all along the
cutter. The great advantage is that the method produces
parallel cutters without a chance of error in setting, and where
parallelism is important, as it
so often is, the method should
be used. The cutter may
either be moved along a paral-
lel mandril fitting its hole or
may be mounted on a collet
sliding along a bar.

Fig. 142 shows a cutter in
position for sharpening, using
this method, on the Loewe
cutter grinder ; Fig. 143 shows
a parallel inserted tooth cut-
ter being ground on a Landis
Universal machine, the main
slide in this case traversing the
wheel over the cutter, and here
the table must be set parallel
to make the sharpened cutter
parallel.

Parallel Cutters — with Shanks. — Parallel mills with shanks
may be sharpened in a similar manner, the shank being held
in a mandril which itself slides through a hole in a small head-
stock. The face of the tooth being sharpened is kept in contact
with a tooth rest in the usual manner by twisting the knurled
handle of the mandril. A plan view of the arrangement is given
in Fig. 144 ; the cutter A is carried in the shaft BB, which slides
and can rotate in the bracket C ; the shaft BB is hollow so that
the cutters can be easily removed. This arrangement was an
attachment on the cutting grinders which I used to make in Bir-
mingham, but, although it is useful, I have not seen it elsewhere.

FIG. 142. — SHARPENING PARALLEL
CUTTER — LUD. LOEWE

322

GRINDING MACHINERY

Tooth Rests. — To locate the tooth of a cutter in the correct
position and to hold it there, tooth rests, consisting of steel blades,
usually adjustable, are necessary. These may be attached
either to the wheel head, where they are set to act on the cutter
just in front of the wheel, or they may be carried on the
support of the cutter. In the former case they may be used
for all kinds of cutters, but in the latter only for cutters where
teeth are straight. The latter is preferred where it can be used,

FIG. 143. — SHARPENING PARALLEL CUTTER ON LANDIS UNIVERSAL GRINDER

since the cutter tooth does not, in its motion, slide along the
tooth rest as it does in the former case. The construction of
the tooth rests for the two cases is a little different.

Fig. 145 shows a tooth rest carried on the wheel head ; it is
set in front of the wheel AB, and the central part CDE must be
wider than the wheel, and should be quite stiff and rigid. It
is shown swivelled to match the angle of spiral of the tooth of a
cutter GH, which is shown in section above the tooth rest. On
each side of CDE is a strip KL, MN, made thinner than CDE
so as to spring easily ; the top KCDM should be smooth and the
corners slightly rounded. As the cutter edge GH slides over

SHAKPENING CUTTEKS AND TOOLS

323

the top of the rest the grinding takes place ; when H has
got clear of CD on to K (the slide stop being set so that it
does not go beyond it), the cutter can be turned, springing KL
to K'L alongside the wheel as shown in the end view,
allowing the next tooth to come on to the top of the rest,
and not damaging the rest by springing the part ODE into the
wheel. One side, KL or MN, may be omitted, and the cutter
turned when at the other end only.

When a tooth rest is carried on the work table and moves
with the cutter, it will be clear of the wheel when the cutter is

FIG. 144. — HEAD FOR SHARPENING PARALLEL MILLS — GUEST

turned to bring the next tooth into position, and so consists
simply of a strip of steel sufficiently thin to spring easily as the
cutter is turned, but sufficiently rigid to support it firmly when
in action. The blades should be easily replaced, as they are
apt to get damaged by unskilful use, since they go close to the
wheel. Such tooth rests are seen in Figs. 156 and 162. As
the parts are rather close together it is well to traverse the
cutter slowly across before actually grinding, to ascertain that
all is right.

Both types of tooth rest need mounts so that they can be
easily adjusted ; these are seen clearly in Figs. 157 and 162.
The nuts and locking parts should be case-hardened, as an
adjustable tooth rest which will not adjust is dangerous to the

y 2

324

GRINDING MACHINERY

temper — not of the cutter only. In certain cases it is impos-
sible for the simple spring blade to be at once sufficiently
flexible and rigid ; a more expensive hinged blade must then
be used, as is shown locating a gear cutter in Fig. 159.

FIG. 145. — TOOTH REST FOR SPIRAL TEETH

The clearance ground on the cutters of Class A depends as
a rule on the position of the edge of the tooth, and hence on
that of the tooth rest which fixes it. To see how to adjust the
tooth rest position, first consider the case of a cutter ground in
a Plain or Universal Grinder, using a disc wheel as in Fig. 146,
which shows an end view. If A be the axis of the cutter BCD,
of which B is a tooth point and E the centre of the wheel
BFG, then B must be off the line of centres AE, and the

SHARPENING CUTTERS AND TOOLS

325

farther it is from AE the greater the clearance which will be
ground.

Setting for Clearance with Disc Wheels. — The angle of
clearance is the angle at which the edge of the wheel cuts the
circle round the points of the cutter teeth, and this is equal
to the angle EBG. In very simple cutter grinders and in
Universal grinders there is only an adjustment of the points
(lines) A and E towards one another, and the position of B

FIG. 146. — SETTING FOR CLEARANCE IN UNIVERSAL GRINDER

below (or above) AE for a desired clearance depends on both
the diameter of the wheel and of the work. The tooth rest
BH is adjusted vertically and set to keep the tooth point B in
position. This position is usually determined by eye, but the
length of the land is normally so short as to make it difficult
to judge correctly.

For a definite angle of clearance, EBG, the angle EBA is
fixed, and if a gauge be made of this angle, its point would
indicate the correct position of the tooth point B when its
sides passed through A and E respectively. To make it easier
to use, the sides might be stepped back by the radius of the
mandril or work head centre AM, and by the radius EN of

3% GKINDING MACHINEEY

the end of the wheel spindle and the apex B consist merely
of a sharp point, so that the gauge would take the shape of
the figure shown in broken lines. When its edges rested on
the mandril (or centre) and the spindle end respectively, its
point would indicate the correct position for B, and the tooth
rest could be adjusted with certainty. If the point B be made
adjustable, formed on a plate PQB on the gauge plate, it can
be set so that EN and AM have any values, and will therefore
suit any spindle diameter and any mandril diameter.

In a machine with only the movements of a ' Universal '
Grinder, not only is accurate setting difficult, but the tooth
rest must have a different height from the table for each
diameter of cutter ; furthermore taper cutters or reamers
can only be sharpened by using a cup wheel (otherwise the
edge is not straight), and face cutters cannot be ground with-
out special attachments. To meet the requirements of more
easy setting, cutter grinders have an additional vertical adjust-
ment, and usually, to permit cup and dish wheels to be con-
veniently used, an angular adjustment round a vertical axis,
besides adjustments, for making some settings still more
convenient, which vary with particular machines.

The terms ' vertical ' and ' horizontal,' it must be remembered, are
used for the sake of clearness, as in the great majority of cutter grinders
the movements are arranged so that these terms, as used in the text,
are correct. Generally, however, they refer to planes and lines at
right angles.

As illustrating different types of these machines, views are
given in Fig. 147 of the upper part of a Cincinnati Cutter
Grinder, in Fig. 148 of a Brown & Sharpe No. 3 size, and in
Fig. 149 of the No. 1 size of the Universal Cutter Grinder, which
I used to make in Birmingham. In Fig. 147 the main slide
movement is in the line AB, and is operated by the handle C
or lever D, through a vertical shaft ; the cross slide is in
the direction EF, and is operated by the handle G, for the
movement of which a graduated disc is fitted. The vertical
adjustment is made by means of the handle H, which raises
or lowers the vertical piece JK, which carries with it the main
slide and fittings ; the amount of this adjustment is indicated

SHAEPENING CUTTEES AND TOOLS

327

by the graduated disc L. When a cup wheel is to be used,
the whole of the knee M and what it carries is swung round
the vertical column NP, through a right angle, or nearly so.
The work is carried on a table Q — corresponding to the table
of a Universal Grinder — which is swivelled about a vertical axis

FIG. 147. — CINCINNATI CUTTER GRINDER

ST for taper work, and for short work, held on the head E, this
may be swivelled about a vertical axis UV ; the angle of move-
ment is shown by the graduated circle T. In addition it will
be noticed that the head E can swivel about a horizontal axis,
for which movement the graduated circle is that shown at W.
A reference to Fig. 160 will assist in rendering the con-
struction clear. Lines indicating the sliding movements and
angular adjustments are drawn on Figs. 149 and 156 also.

328

GKINDING MACHINERY

In the Brown & Sharpe Cutter Grinder, shown in Fig. 148,
the main slide consists of a cylindrical bar A, which can slide
in bearings, one of which is seen at B, and it is prevented from

FIG. 148. — BROWN & SHARPE CUTTER GRINDER

rotating by a stop which slides in contact with the hardened
steel bar C, the edge of which is set parallel to the bar A. The
cross slide is seen at D and the movement is controlled by
the hand wheel E, which is graduated. The wheel head F is
bridged across the cross slide for purposes of dust protection
and stiffness. The vertical adjustment above mentioned

SHARPENING CUTTEES AND TOOLS

329

is provided for by the action of the knob G, but there is no
swivel adjustment of the whole about a vertical axis, and
hence the regular run of cutters are sharpened with a disc
wheel, and a cup wheel is not used for this purpose. The

FIG. 149. — GUEST UNIVERSAL AND CUTTER GRINDER

swivel head H has an angular adjustment about a vertical axis ;
this corresponds to the swivel adjustment of the table on a
Universal Grinder, and to both the swivels of the table Q and
head E in the Cincinnati Grinder. When work has to be
held between the centres, a rod carrying one fixed and one
adjustable centre is gripped in the swivel head H, set to the
angle of the reamer or tool, and traversed by the main slide.

330 GKINDING MACHINERY

At J and K are seen the grips for the tooth rests, the former on
the work head and the latter on the wheel head ; on the work
head a surface is formed level with the axis above the plane
of rotation of the swivel head, so that the tooth rest carried
on the work head can easily be set level with the centre. The
machine illustrated has a self-contained drive from the motor.
For grinding parallel cutters with holes in them a bar is held
in the swivel cutter head and also at the other end of the machine,
and the cutters are moved along it by hand — either fitting the
bar directly or indirectly by means of a collet — so that they
are ground parallel by the principle described above. When
the main slide is moved a small lever is attached to it for the
purpose, but this is not shown in the figure. Face and end mills
may be sharpened when held in the swivel cutter head, but as
sometimes this is inconvenient owing to interference of the
disc wheel with the next tooth to that being ground, a compound
swivel head, presenting the teeth to the wheel in the method
illustrated in Fig. 152, is generally used.

The Universal Cutter Grinder shown in Fig. is 149 designed for
cylindrical and surface grinding as well as for cutter grinding, and
is shown set up for external work. The main slide A is traversed
by the hand wheel B for regular work, but for fine feeds used for
facing, snap gauges, &c., a fine feed, operated by the hand wheel C,
which is graduated, can be thrown in. The cross-feed is by an
ordinary slide, and is operated by the graduated hand wheel D. The
vertical adjustment is by means of the knee E, the elevating hand
wheel is at F. The swivel adjustment to provide for the use of cup
and dish wheels in sharpening ordinary cutters is here obtained by
swivelling the wheel head G round, but the axis is inclined at the
standard angle of clearance. The effect of this is that in the position
shown the wheel spindle is inclined at the standard angle of clear-
ance, but if the head G be turned through 90° about its axis kl,
in either direction, so as to bring either the main spindle or the
internal grinding spindle into its working position, the wheel
spindles become horizontal. The table H has a swivel adjustment
about the vertical axis ef, and the top of the work head J swivels
about the vertical axis gh, but no extra swivel corresponding to the
graduated circle W of Fig. 147 is fitted, being now unnecessary.
The advantage of making the axis kl inclined is described later. The
machine is shown fitted with self-adjusting guards for wet grinding.

SHARPENING GUTTEES AND TOOLS

331

Simpler cutter grinders than these are made by omitting
one or more of the motions, with a corresponding reduction
of the types of cutter which they are adapted to sharpen,
and with an increase in the difficulties of setting. The great
advantage of a vertical adjustment, accurately graduated,
is that the clearance angle can be obtained by setting from
a table such as No. X, and as the setting depends on the

FIG. 150. — SETTING FOR CLEARANCE WITH Disc WHEEL

wheel diameter (for disc wheels) only and not on the cutter
diameter or angle, the setting is not changed in sharpening
various cutters, but only as the wheel wears.

In Fig. 150 is shown a diagram of the usual arrangement,
lettered in the same manner as Fig. 146. Here the front B
of the tooth being ground (and the tooth rest) is ' level ' with
A, and the wheel centre E is so much higher that the angle of
clearance, EBG, is obtained.

The amount EG by which the cutter axis A is set below the
wheel axis E to secure the angle of clearance, a (— EBG), now
depends on the diameter of the wheel only, and is not affected

332 GKINDING MACHINERY

by the diameter of the cutter. For if A' were the centre of a
smaller cutter BC'D' the same clearance would be ground on
the tooth. Hence, if the machine table, with the headstocks and
centres, is set vertically correctly for one size of cutter it is set
correctly for all. The only adjustment necessary is to and
from the wheel (horizontally) to accommodate the different
sizes of cutters and to put the cut on, and this movement
does not affect the amount of clearance produced. The
alteration of EG need only be made when the wheel has worn
appreciably.

Eef erring again to Fig. 150, since the diameter of the cutter
does not affect the clearance produced, the same amount will
be ground on a taper or angular cutter, as these may be con-
sidered to be built up of a large number of very thin cutters
of varying diameter. To bring the whole edge of the cutter
to be acted on by the wheel, the table carrying the headstocks
is swivelled if the cutter is one carried between the centres,
or the cutter head only if the cutter is held in it. The angle
to which the cutter is ground is here the angle shown by
the graduations of the table or cutter head.

Face cutters and the end teeth of end mills are a special case
of angular cutters for which the angle is 90°, and accordingly
the same method of setting holds good, but these cutters are
more usually sharpened by the use of a cup wheel, as if a disc
wheel be used it has to be of small diameter — especially if the
teeth are cut close up to the centre — otherwise the next tooth is
liable to be scored. The best method of sharpening them when
the teeth go close to the centre is shown in Fig. 152.

In practice to set the machine for the clearance, the centre A
(Fig. 150) is first set level with the wheel centre by means of a
gauge ; the wheel diameter is then taken, and the amount EG
corresponding to it for the angle of clearance desired is ascer-
tained from Table X, page 484. The table (or wheel head in some
machines) is then adjusted vertically through that amount by
means of the graduations on the corresponding hand wheel.
It then only remains to set the tooth rest B level with the centre
A by means of a gauge. Not only should the vertical adjust-
ment be easily made, but the tooth rest should also be set easily.

SHAEPENING CUTTEES AND TOOLS 338

If the cutter have spiral teeth, the highest point of the part
of the tooth rest which is opposite the wheel is the point which
controls the clearance at the edge, and which should be regarded
as the point of the tooth rest to be set if the clearance is
wanted accurately.

When the tooth rest is carried with the work, on the table
or the work head, it can be set permanently level with A.

The distance EG is easily found by drawing a large size
figure to determine the ratio of EG to EB, or by looking up the
value of sin a in tables, and then EG = EB sin a, where EB
is the radius of the wheel in use.

As before mentioned, the terms ' vertical ' and ' horizontal ' are
used, as almost all cutter grinders are arranged so that the adjust-
ments are in these directions. They are, however, only relative
expressions, and if the slides are tipped as a whole in any way
the clearance is unaffected.

In the cutter grinder which I used to make in Birmingham
these setting operations were almost eliminated. The tooth
rest BHK, Fig. 151, was carried on an inclined plane LM
machined on the wheel head, so that its point B moved along
the line ENB, and when the blade was put just outside the wheel
it was in the correct position. All that there was (' is ' would
be more correct, as I believe that every machine is still in use)
to do in these machines was to set the table so that the centre A
was level with B, which was done by adjusting it until a gauge
BPQ touched the top of the tooth rest. When the wheel has
worn down, say to N, the tooth rest point will then lie just
outside it at N, and again the clearance ground will be a =
angle EBG. The tooth rest blade was arranged so that the
position of the centre of its edge was not altered by adjusting
it to suit the angle of a spiral cutter ; and particulars of the
arrangement can be seen by reference to * Engineering,' Dec.
1901, vol. Ixii.

Limiting Diameter of Wheel. — The clearance ground by the
edge of a wheel is hollow, the more so the smaller the wheel
used, and it is well to use as large a wheel as possible, although
the effect of this hollowness is small. A limit is soon reached,
as a wheel above a certain size will encounter the cutting edge

334

GEINDING MACHINERY

of the next tooth and spoil it. The size of wheel permissible
depends on the diameter of the cutter, the number of teeth, and
the angle ; in the case of a face cutter or end mill it depends
on the pitch of the teeth. In this case the pitch varies along
the teeth, being smallest near the centre, and accordingly the
sharpening of small end mills, cut near the centre, presents a
difficulty, which is still further increased when it is desired
to grind a larger secondary clearance (see page 320) to decrease

FIG. 151. — SETTING FOR CLEARANCE WITH EDGE WHEEL ON GUEST
CUTTER GRINDER

the width of land. These cases are more easily dealt with by
the use of a cup wheel, but the best method is that shown in
Fig. 1 52, and is as follows —

1 Sharpening End Mills. — The cutter ABC is here shown
passing by the wheel, the movement to sharpen the edge AD
being as indicated by the arrow in the left-hand view, and
perpendicular to the paper in the right-hand diagram. The
wheel EF is set askew as shown, and looking along the cutter
axis D it appears as parallel to the edge of the next tooth BD ;
this enables the cutter to be moved so far towards the wheel as
nearly to touch the edge in the manner shown in the figure, and
a stop must be used to limit the motion in this direction. It

SHARPENING CUTTERS AND TOOLS

335

thus enables the edge to be sharpened, or the secondary clearance
ground, close up to the axis. That the wheel clears the tooth
opposite to B is seen in the right-hand view, which shows the
way in which the wheel produces the clearance.

The tooth rest GA holds the tooth being ground, so that it is
parallel to the line of motion of the slide. In small cutters
the faces of the teeth pass through the axis as shown, and the
tooth rest is level with the centre. In large mills they are
frequently offset, and then the tooth rest must be adjusted so
that the tooth edge is parallel to the line of travel.

The same arrangement is of use in the case of angular

FIG. 152. — SHARPENING END MILLS AND ANGULAR CUTTERS WITH
TEETH CUT CLOSE TO AXIS

cutters, in which the teeth run close together at the small end.
A diamond tool is sketched on the left in the position — ' level '
with the work axis — for truing the wheel properly.

In practice the wheel is not usually tipped, as shown in
the diagram, Fig. 152, which is so drawn for the sake of
clearness ; the slide and cutter head are usually swivelled
instead.

In sharpening end mills and face cutters it should be borne
in mind that they should be ground slightly hollow on the face
— that is, the edge of the tooth should be slightly inclined to
the axis, so that the teeth cut fully on the outer corners. For
this purpose J° is a sufficient angle to allow. Thi$ renders
sharpening small end mills with a cup wheel awkward, as
when grinding on one side the opposite tooth may be touched ;
hence the preference to be given to the method outlined above.

336 GEINDING MACHINEBY

Direction of Wheel Rotation. — Practice varies as to the
direction in which the wheel should run — whether towards
the edge of the cutter, so that the particles meet it first (as
indicated by the arrow on the wheel in Fig. 150), or the reverse
as indicated in Fig. 146. The former direction produces a
slightly better edge, as it is free from burr, but if the cutter
tooth is not held firmly against the tooth rest the action of the
wheel may make the cutter turn a little, carrying the edge of the
tooth into the wheel and grinding it away. In manufacturing
shops where the cutter grinders are constantly in use the first
method can be safely employed, but otherwise the second
method is preferable. It should be employed if the cutter
edge is to be oilstoned afterwards.

Maximum Size of Wheel. — The largest size of wheel which
can be used on parallel cutters can be found as follows. In
Fig. 153, A is the centre of a cutter, and B, D consecutive
teeth, of which B is being sharpened by a wheel whose centre
is C, and which just grazes D. Then if CBE = a be the angle

of clearance and CAB = -, where n is the number of teeth

in the cutter, and the radii of the cutter and wheel be r and K
respectively, then we have — :

AB BC

sin BCA sin OA13

or K sin (a - — } r = sin -

V nj n

and hence to clear the next tooth K must be less than —

. 7T

sin -
n

. ( TT\

in I a I

\ »/

sin

in the case of parallel cutters. If a = - then a wheel of any

size will clear the next tooth, or a face wheel would clear right
across. So that if the clearance angle be 5°, the number of
teeth in the cutter may be as many as 36 for any wheel to clear ;

SHARPENING CUTTERS AND TOOLS

337

but if the clearance angle be 7|°, the number can only be 24,
and if a = 10°, 18 teeth is the maximum. A wheel of the same
diameter as the cutter will just clear if —

27T

. / 7T\ . 7T

sin { a — I = sin - or a

\ n/ n

or in this case the number of teeth can be double those
previously given.

Angular Cutters. — If, however, the cutter be taper or

FIG. 153. — MAXIMUM SIZE OF Disc WHEEL — PARALLEL CUTTERS

angular, interference occurs with a smaller number of teeth.
This can be seen from Fig. 154, in which the bottom view
is a plan showing the cutter GFANB, whose axis is AH
and vertical semi-angle BHA = 0, and the wheel CB, and
on the cutter's smallest diameter BG is drawn a semicircle
BDG, in which D is the next tooth point to B, so that

2?r
the angle BAD is --. The upper view is taken perpendicular

to the line of movement, or to the edge B of the cutter, and the
cutter section is taken close to the smallest diameter, that is
close to AFG in the plan view. Here in this top view we see

338 GEINDING MACHINEEY

that for the wheel to clear CD must be > E, while from the

bottom view DN = r sin — and BM = BN cos 6 =

( 1 - cos — ) cos 0, and therefore (EB + BM)2 + (CE - DN)2 >
\ n s

E cos a + r(l -cos --J cos 6\ + (E sin a-r sin "—) < E2

n
and hence we obtain —

sin * ( sin2 - cos2 6 + cos2 ^
E< r-

sin a cos - cos a sin - cos 0

1- sin2 -sin2 0

< r-

sin a cot — cos a cos 6

and as 6 increases, cos 6 decreases, and E must increase. For
face cutters put 0 —- 90°, therefore cos 6 = 0, and we have —

. 7T 7T . 27T

sm — cos - r sin —

E< r—*--* or <

sin a 2 sin a

where r is the radius to the small part of the tooth.

Formerly cutters had many small teeth, but the number
has been reduced, chiefly with the object of providing plenty
of room for swarf ; this reduction in the number of teeth
has rendered sharpening much easier, for the above reasons.

Clearance with Cup or Dish Wheels. — Turning now to the
use of the cup or dish wheel, it is first to be noticed that the
surface produced is flat, provided that the ground part goes
across the hollow of the wheel, as is correct practice, and
provided that the travel of the work is at right angles to the
wheel spindle. In Fig. 155 is shown the usual arrangement :
the slides of the machine are set at 90° to their previous position,
and the tooth to be sharpened is canted up or down to secure
the desired clearance. If the grinding takes place level with
the centre of the wheel, indicated by the broken lines, the

SHARPENING CUTTERS AND TOOLS

839

slide must not be quite square with the spindle but set slightly
off, so that the wheel cuts on one side only ; this is necessary
in the case of reamers, as the cut must go smoothly right across,

FIG. 154. — MAXIMUM SIZE OF Disc WHEEI
ANGULAR CUTTERS

FIG. 155. — SETTING FOR CLEARANCE WITH CUP WHEEL

7. 2

340 GRINDING MACHINERY

and so only the side of the wheel nearest the reamer shank
must cut. The land is practically flat. If work is set lower
so as to use the bottom of the wheel, as indicated by the full
lines (or up to use the top), the traverse should be square
with the spindle, and the wheel must be kept hollow so close
to the edge that the tooth passes within the hollow (indicated
by the broken line) ; this gives a very smooth edge to the
tooth.

By grinding at the top or bottom of the wheel, cutters
with a large number of teeth or face cutters can be ground.
If the tooth is set near the middle of the wheel, the wheel may
interfere with the next tooth, and will do so on parallel cutters if
the teeth exceed the numbers given on page 336. To clear angular
cutters they must have fewer teeth. Taking the formula from

page 338, we have sin a cos - — cos a sin - cos 0 equal to

n n

zero, or tan - = tan a sec 6, or the greatest number of teeth is

n = T

tan -1 (tan a sec 6}'

It does not matter whether the edge of the tooth points
upwards or downwards ; this is merely a matter of convenience
in operating. In Fig. 156 is shown a tooth of a face cutter
being sharpened with its edge pointing upwards ; the cutter
is held in a ' Universal Holder,' and the machine shown is
the Le Blond Cutter Grinder. Fig. 157 shows the operation
on a Herbert Cutter Grinder ; the tooth, which is inclined
downwards, is the inserted tooth of a face mill, and is being
sharpened on the side.

In using face wheels the particular vertical position of the
cutter does not affect the angle of clearance, which is regulated
by the height of the point of the tooth BD, B'D' above (or
below) the centre A of the cutter, as the clearance is equal to
the angle BAG, Fig. 155. Thus this height must be propor-
tional to the diameter of the cutter. Tables of the correct
heights for parallel cutters are provided by the manufacturers
of cutter grinders, and such a table, No. XI, is given on

SHAKPENING CUTTEKS AND TOOLS

341

page 435. To use it the tooth rest is set to the height given
above the work axis, and then moved over to the tooth.

Tables of Setting and Angular Cutters.— In the case of taper
or angular cutters from Fig. 155 we see that a small cutter is
ground to the same clearance as a large one if the tooth rest is

FIG. 156. — LE BLOND CUTTER GRINDER. USE OF CUP WHEEL

elevated to a proportional extent ; hence, since an angular cutter
may be considered as built up of a very large number of very
thin cutters, such cutters can be sharpened correctly. In this
connection, however, it must be noted that the tables generally
given apply actually only to parallel cutters : for angular cutters
the setting is different. I have calculated the settings for angles
of 30°, 45°, and 60°, and given them in Table XI, page 435,
in addition to the settings for parallel cutters. For face cutters

342

GEINDING MACHINEEY

the clearance must be obtained by canting the cutter head, as
shown in Fig. 155 on the right, which shows the sharpening of
an inserted tooth face mill. The face cutter must be tipped up
through the actual angle of clearance, which is shown on the
graduated circle provided on the cutter -holding head for the
purpose.

For angular cutters generally, where d is the largest
diameter, the height between the tooth rest and cutter axis

FIG. 157. — HERBERT CUTTER GRINDER. USE OF CUP WHEEL

may be got from the tables for parallel cutters, using d sec 6,
where 6 is the semi-vertical angle of the cutter, instead of d.

In sharpening taper and angular cutters and reamers there
is no danger of getting the edge curved (as with a disc wheel),
since the intersection of two planes — the radial plane of the
tooth face and the ground clearance land — must be a straight
line. It must be noted, however, that the angle (for example)
of a taper reamer sharpened between the centres, is not the
angle through which the table is set — which would be the angle
of a taper gauge.

SHARPENING CUTTEKS AND TOOLS

343

Simplified Setting for Clearance. — In the cutter grinder
(referred to on page 330) which I used to make, all these
difficulties were got over by the simple device of making the
grinding head swivel round an inclined axis BD in Fig. 158, so
that the wheel ACE when set square with the main slide was
inclined to the vertical at the desired angle of clearance a.
Apart from the advantages of turning the head round instead of
the table, slides, knee, &c., the correct clearance was ground on
all cutters, parallel, taper, angular, or face, without any setting—
as the tooth rest had a fixed height level with the cutter axis —
and so located the line from the cutter axis to the tooth that it

FIG. 158. — SETTING FOR CLEARANCE WITH CUP WHEEL IN GUEST
CUTTER GRINDER

was inclined at a, the angle of clearance, to the wheel axis, what-
ever the size of the cutter was. On the right in Fig. 158 is
shown the case of a hollow mill ground to the correct clearance
in the same manner. To meet the single case of face mills with
offset teeth an adjustable tooth rest was provided. This
method also has the great advantage that angular and taper
cutters are ground to the angle of the table setting.

Taper reamers may be sharpened on a Universal Grinder
by the use of a cup wheel, setting the wheel spindle square
with the main ways. The angle of the reamer will not be
that shown on the taper scale of the machine. If, however,
the reamer clearance be obtained by the use of an auxiliary
head, such as is shown in Fig. 162, and this head canted to give

344 GEINDING MACHINERY

the clearance to a tooth set ' level ' with the centre, the angle
of the reamer will be that shown on the scale.

Broaches. — Broaches are tools which have clearance ground
at the rear of the cutting edge, but they are not tools which can
be made well on a cutter grinder even if fitted with attachments
for circular grinding. The cross -feed of the machine on which
they are made must be in good order, as the difference in the
steps is so small — ^ to J of a thousandth of an inch is a usual
allowance. The clearance is obtained by setting the table over
to the angle of clearance, using a wheel narrower than the pitch
of the teeth, and grinding each land to be a taper cone. The
clearance should be very small — 2° is sufficient.

Circular saws can be sharpened on cutter grinders in the
same manner as regular cutters are, but owing to*their large
diameter and thinness they are better held on a flat horizontal
plate, and in some machines provision is made in this manner
for sharpening saws of considerable diameter. When such
saws and band saws are much used, special machines are used
for sharpening them. These present no special features from
the point of view of grinding, but are interesting as examples
of ingenious automatic motions. The wheel used should be
a vulcanite or elastic wheel, as the cut is suddenly applied and
variable.

Cutters Sharpened on the Face of Tooth.— The second class
of tools — namely, those ground on the front of the cutting
edge — chiefly comprise relieved cutters, and to keep the work
shape correct the face ground must (usually) pass through the
axis of the work, or, if the teeth are spiral, a line perpendicular
to the axis must lie on the cutter face. For sharpening these a
dish wheel is usually the most convenient.

Gear and Formed Cutters. — In Fig. 159 is shown a convenient
mode of setting up a gear cutter to be sharpened. It is placed
on a stud A, and the face of the attachment BC is set parallel
to the main slide, a gauge DEF in which EF — equal to the
distance of A from BC — locates the face G of the tooth so
that it will be ground radially by the movement of the slide.
The tooth rest HJ (which has a rigid blade, pivoted at H,

SHAKPENING CUTTEKS AND TOOLS

345

and kept against the cutter by the spring K) is then adjusted
to the back of the tooth, after which the gauge DEF can be
removed. The wheel head should be set a little out of square
as shown, so that the edge only of the wheel cuts.

If a wide formed cutter, of similar type, is to be sharpened,
it is more convenient to place the cutter on a mandril between
centres, in which case Fig. 159 will represent an end view
of the arrangement. The wheel face is now set to pass through

FIG. 159. — SETTING FORMED CUTTERS FOR SHARPENING

the axis, and the movement is perpendicular to the plane of the
paper.

Spirally Gashed Hobs. — Should the teeth be gashed on a
spiral, the wheel must be set to the angle of the spiral, and to
secure a radial cut, the wheel should be turned somewhat conical,
and the grinding line in which the wheel touches the cutter
should be set to pass through the axis of the hob. The tooth
rest in this case must be carried by the wheel head, but the
rotation is sometimes conveniently controlled by a former
or by gearing from the table traverse. A Cincinnati Cutter

346

GEINDING MACHINEEY

Grinder set up for this operation is shown in Fig. 160 ; the
tooth rest A is carried on the wheel head since the cutter is
spiral, and a master form B is used to produce the rotation.
Theoretically in all these cases the cut should be put on by
rotating the cutter round its axis by adjusting the tooth rest,
but as it makes no practical difference, and is much more
convenient, it is put on, as usual, by the use of the cross slide.
If the formed cutter has the gash not parallel, but some

FIG. 160. — SHARPENING A SPIRAL HOB — CINCINNATI CUTTER GRINDER

parts higher than others, it is usually necessary to manipulate
the vertical slide while traversing or sharpen the cutter in two
operations. This trouble can be sometimes avoided by packing
up the head- or tail-stock. Alternately the cutter may be
made in two or more parts and the difference of diameter kept
constant in the sharpening. A cutter for producing a given
form may sometimes be made considerably less in diameter,
or the risk in hardening may be decreased, by gashing in two
or three cuts so that the bottom of the gash is irregular, and
hence the cutter may be much cheaper to make thus. As

SHAEPENING CUTTEES AND TOOLS

347

the trouble of grinding is so considerable, the cutter design
deserves attention.

Taps and the cutting face of reamers may be ground in
the same way, and the wheel may be shaped to the groove. In
these cases the holding is frequently done by use of a division
plate on the head. Small taps are quite satisfactorily ground
by passing them under the wheel, holding them by hand only.

FIG. 16.1. — SHARPENING A TAP — HERBERT CUTTER GRINDER

Fig. 161 shows Messrs. Herberts' cutter grinder set for sharpen-
ing a tap, using a division plate.

In these illustrations the principles of the setting are shown,
and as such can be easily applied to other makes of machines.

As a cutter grinding machine for general work requires
more movements than a Universal Grinder, there is a tendency
to extend the capabilities of the machine by adding arrange-
ments for rotating the work, so that external circular work
may be ground, and a live work spindle, chuck, and internal
grinding spindle in addition to do internal grinding. A vice

848

GKINDING MACHINERY

will equip the machine for surface grinding, so that a much
more ' Universal ' machine than the Universal Grinder is pro-
duced. If the parts are well enough made to be of real service
the cost is not the insignificant matter it would first appear
to be, but such a machine is very useful in a shop which requires
accurate manufacturing tools but has no need for production
grinding.

Automatic feeds are sometimes added, and as the cost

FIG. 162. — CLEARANCE WITH AUXILIARY WHEEL HEAD — LANDIS
UNIVERSAL GRINDER

increases the requirements are sometimes met from the other
end — by adapting the more usual type of Universal Grinder to
do the extra work. This involves replacing the regular wheel
head by a bracket carrying a vertically adjustable (smaller)
head. As this can be set with its spindle either parallel or at
right angles to the main ways, the various kinds of cutter
sharpening previously referred to can be dealt with. Fig. 162
shows a Landis machine so fitted up, with a small auxiliary
head which takes the place of the internal grinding spindle
bracket.

SHAKPENING CUTTERS AND TOOLS

349

Universal Cutter Holding Attachments. — More recently
the vertically adjustable head has been made a more important
feature, and Universal machines are built so arranged. They
are usually fitted also with a ' Universal ' cutter holding
attachment. In Fig. 163 a Universal Grinder of this type,
by Messrs. The Churchill Machine Tool Co., is shown set for
sharpening a face mill, using a cup wheel. The swivel platten

FIG. 163. — TOOL ROOM UNIVERSAL GRINDER — CHURCHILL

on the top of the cross slide here carries a bracket which carries
the wheel head on a vertical slide, and the spindle is driven
directly from overhead. The wheel spindle is elevated by the
screws just visible on the right, operated by the hand wheel
at the top through bevels : various means of holding tooth
rests are seen on the wheel head. The Universal cutter head
is set to cant the cutter up so that the teeth, inclined to the
axis, are horizontal where sharpened.

As cutters with various types and sizes of shank are in
use, collets to suit them are usually required, but several
firms make a universal attachment, such as is shown in Figs. 156

350 GKINDING MACHINEEY

and 163. Any shank, within the capacity of the attachment,
can be conveniently held in the vee by aid of the swivelling
piece Y, which is adjustable by means of the screw above it,
and suits its position to the taper of the shank by swivelling,
holding it sufficiently firmly, but permitting it to be turned
by hand. The rear end of the cutter or its mandril is held up
by a plate (or rod if the shank or mandril be short, as in Fig. 156)
carried on a tail rod. The angular movements are for the angle
and clearance of the cutter, and to compensate for the inclina-
tion of cutter due to the taper of the shank. Such attach-
ments do not hold the cutters for grinding in the same way
as they are held in the milling machine spindle, and so
accidental damage to the cutter shank may affect the grinding,
so that the cutter does not run quite true when in the miller.

Twist Drill Grinders. — Although twist drills can be
sharpened along the cutting edge in such cutter grinders as
are described above, it is afterwards needful to grind away
the material behind this clearance. All that is necessary in
grinding a twist drill is that the lips should be of equal length,
the clearance just behind them correct throughout, and the
angle at the apex approximately right, and that the part
behind the clearance should be quite clear. It requires a
little skill to do it by hand, and as twist drills are so
universally used, machines for sharpening them are manu-
factured. Various devices for giving the clearance to the
edge, and grinding away the metal behind it at a simple move-
ment have been used, almost all needing to be set for the
diameter of the drill. If, however, the movement consists
of rocking the drill round an axis AB — as shown in Fig. 164 —
and grinding it by a flat surface C, while the drill is held by
planes or lines all passing through the point D in which AB inter-
sects the surface C, then all drills will be ground to the same
geometrical shape on their lips when being sharpened. This
is the principle upon which the twist drill grinder I formerly
made was based, and it is also used in the ' Yankee ' twist drill
grinder shown in Fig. 164. In this, the drill is held between
the two planes E and F and by the edge of the lip rest G, all
of which, if continued, would pass through the point in which

SHAEPENING CUTTERS AND TOOLS

351

the axis AB intersects the surface C. The small tailstock
prevents the drill from slipping^ back under the cut of the

FIG. 164. — ' YANKEE ' TWIST DRILL GRINDER

wheel, and serves to feed it up as grinding proceeds. The
surface is produced by the flat face of the wheel, as the drill
holder is rocked round the axis AB. The larger drills are

352

GKINDING MACHINERY

easy to sharpen, but the machine needs to be accurately
made and free from shake to sharpen the small drills correctly.
Fortunately these are easily sharpened with sufficient accuracy
by hand.

FIG. 165. — LUMSDEN TOOL GRINDER

Large drills have a considerable thickness of metal at the
centre for reasons of strength, and the point therefore has
difficulty in entering the metal. To make the drill cut freely
the point is ' thinned ' by grinding small channels up it with
a thin elastic wheel. A vee to lay the drill in for this point-
thinning is convenient, and is fitted to some machines.

SHARPENING CUTTERS AND TOOLS

353

Mechanically Guided Lathe Tool Grinders. — In modern
manufacturing the production of lathe tools has now been
transferred to the tool room, with the exception of the smithing,
and this has been reduced to a minimum. With a tool grinder
such as the Lumsden, shown in Fig. 165, the forged tools or
cut-off bar can be rapidly ground to the desired shapes at the
points when soft, although there may be a considerable amount
to be ground off, so that usually no other operations are
necessary to produce a lathe tool. After hardening and use

FIG. 166. — LUMSDEN TOOL GRINDER. TOOL HEADSTOCK

they can be re-sharpened to the same angles, or slightly less,
so that the tools are sharpened at the edges only.

The motions necessary for grinding can be obtained in
several ways, either by moving the tool or the wheel ; in the
machine shown the wheel oscillates about an axis (near the
floor) parallel to the wheel spindle, so as to grind the facet on
the tool and to keep the wheel surface true.

The tool is held in a chuck capable of presenting it to the
wheel in any desirable position, and which can be swung round
a vertical axis so as to grind a radius on the tool when necessary.
The arrangement of the chuck and adjustments is seen in Fig.
166 ; the chuck has three jaws, and the bottom of the tool is

2 A

354

GKINDING MACHINEEY

placed on the wide top of the bottom jaw. The chuck swivels
round a horizontal axis so that the side clearance can be ground,
and stops are provided for duplicating work. The upper

FIG. 167. — LUMSDEN COMBINATION TOOL GRINDER

horizontal slide is for the purpose of setting the tool for grinding
a radius on it, which is done by swinging it round the vertical
axis shown ; this movement also has adjustable stops provided.
The two lower slides are for adjusting the tool to the wheel and
putting the cut on.

SHARPENING CUTTERS AND TOOLS 355

The use of grinding for shaping lathe and planer tools,
introduced by Sellars many years ago, made its way very
slowly, but small shops now appreciate the advantages to be
obtained, and to meet the requirements of such firms, the
Lumsden Combination Tool Grinder, Fig. 167, has been
designed. The wheel used is of the cup type, and is trued
mechanically by a diamond tool carried in a jig at B. The
tool holder C is fitted to rotate in its bracket D, and can be
set at the desired angle by graduations at the rear, while the
bracket itself can be set to any angle on the graduated arc E.
The traversing movement is given by the lever F by means of
a quick-pitch screw, and the tool is kept up to the wheel by
the lever G. When not needed this mechanism can be swung
up and back to the left, leaving only the lower plate, which
forms a rest inclined to the wheel at the usual angle of clearance.
The machine then becomes an ordinary tool grinder with a
cylindrical wheel. The whole is adjusted towards the wheel
by the knob at H. In this machine, ball bearings are used
for both the journals and thrust of the spindle.-

2 A2

CHAPTEE XI

FORM GRINDING AND CURVED SURFACES

Mechanically Generated Cups and Cones.— In the machines of
the preceding chapters, the surfaces ground are of simple
shape, such as circular tapers of straight axial section and flat
surfaces, but the requirements of engineering now demand the

application of the pro-
cess of grinding, with
the precision and
quality of surface in-
herent in it, to the
production of other
surfaces. The develop-
ment of machines for
such purposes and for
the production of sim-.
pie ground work in
quantities at lower cost
than at present, is the
care of several firms
to-day. Straight shafts
and tapers are pro-
duced in the Universal
Grinder by a double
copying process, the
wheel face being first

' trued,' and thereby made to be a copy of the ways, and then the
surface produced by the wheel face being traversed along the work
by the main ways. The work touches the wheel edge right
across while the grinding is going on, and as the traverse takes
place the ' line ' of contact is maintained. Geometrically, a piece
of a straight line can move along the continued line and

356

FIG. 168. — GRINDING A CONE BALL RACE.
GENERATING METHOD

FORM GRINDING AND CURVED SURFACES 357

coincide with it always. So, geometrically, a piece of a circular
arc can move along a circular arc of equal radius and fit it
always. Mechanically adapting this, such surfaces as ' cups '
and ' cones ' for ball bearings, where the axial sections are
portions of circies, can be ground. Fig. 168 shows the motions
for grinding a ' cone,' and Fig. 169 those for grinding a ' cup ' ;
these are lettered in a similar manner, so that a single description
will apply to both. The work, whose axis of revolution is
AB, has a portion CDEF of its shape of circular axial section :

FIG. 169. — GRINDING A CUP BALL RACE.
METHOD

GENERATING

the wheel, whose axis is GH, touches it along the portion DE.
If J be the centre of CDEF, then if the wheel head, carrying the
spindle GH and wheel DE, have a movement round an axis
through J perpendicular to the plane ABCDEF, the wheel
edge traces out the shape CDEF as it moves, and is always in
contact with it. This corresponds exactly to the grinding of
a shaft of straight taper, and the contact of wheel and work
is maintained throughout the movement. The truth of the
surface produced is dependent on the mechanism and not on
the particular shape of the wheel, initially or after wear, though
these produce an effect on the quality of the surface.

358 GBINDING MACHINEKY

To put the cut on, it is necessary to mount the wheel on a
cross slide, indicated at KLM, and this slide moves the wheel
spindle farther towards the work as the wheel wears. To
true the wheel correctly the diamond — as in the Universal
Grinder — must be supported on the work carrying part of
the machine, and is shown at N. Either the wheel or the
work may receive the movement round the axis at J, corre-
sponding to those cases where the wheel or the work travel in
Universal grinders. In an actual machine arrangements for
properly locating the work axis and the position of the work
on it with regard to J are necessary ; but the essential
matter here is that the truth of the surface is mechanically
produced. Several machines have been brought out for
grinding cups and cones upon these principles.

Taking a larger case, the point of a shell— provided, as is
usually the case, that the axial section is a circular arc — can be
ground in a similar manner, the wheel making contact with the
work over the width of its face, and the work having the
characteristics of the work from a Plain grinding machine.

If, however, the curve to be ground is other than a circular
arc, the lack of continuity of the contact of the work and the
wheel causes irregular wear of the wheel, spiral markings of the
traverse, and other difficulties. When the part operated on is
not too large the wheel may be trued to the desired sectional
shape, and the result produced by simply feeding in the wheel
to the necessary depth, while the work simply revolves or
reciprocates in the plane of the wheel.

Form Grinding. — Such grinding may be termed form grind-
ing ; the accuracy of the product depends directly on the
truth of the wheel shape, as opposed to the cases previously
described, in which the accuracy depends on the mechanical
guidance of the wheel relatively to the work.

Examples of the method have already occurred. The
short ends of shafts on which hand wheels and gears are fitted
may be instanced, and, as described in Chapter VI, page 225,
the most rapid way to grind these is to feed the wheel directly
in to the required depth, then traversing it off by hand.

Collars. — When considering the matter of grinding collars

FOEM GEINDING AND CUEVED SUEFACES 359

on shafts, it was pointed out (page 278), that there was the choice
of two methods : the collar could be ground by bringing the
side of the wheel, previously trued, up to it — as shown at X in
Fig. 116 — or the axis of the wheel spindle having been slightly
inclined, the corner only of the wheel could be used as shown
at Z, and the collar ground by traversing the wheel out. In
the latter method the accuracy is dependent on the mechanical
movement of the slide, and so is to be preferred to the former,
in which errors in the wheel shape have their effect on the
result.

Cups and Cones. — In a similar manner cups and cones
may be ground by truing the wheel to the requisite shape,
and simply feeding it into the work. The truth of the sectional
shape then depends on the form of the wheel, and the surface is
liable to have circumferential marks on it, owing to the pro-
minence of some particular particles in the wheel ; but in
many cases the accuracy is ample, and the marks can be polished
out with fine emery cloth, or they may be avoided by lightly
smoothing the wheel with a piece of oilstone. The simplicity
of the machine necessary is a great advantage.

In cases where form grinding is used, it is very important
that the wheel should be of large diameter compared with the
work ; otherwise the shape turned on the wheel by the diamond
soon loses its accuracy. This is not always possible, for
example in the ball cups of Fig. 169. In these, however,
great accuracy of curve is not needed, and as the cups have
been previously machined all to the same correct curve, the
wheel tends to keep it a good shape by the wear averaging the
same.

Advantage is taken of this in the machine shown in Fig. 170 —
a Guest Hub Grinder — for such work as two -speed hubs. The
work spindle is hollow and carries an expanding collet chuck
operated by the hand wheel at the rear. In front of the
headstock is a slide carrying a running steady, the rotating
part of which is carried on balls, so that it can easily be driven
frictionally by the work. The hub is placed with one race
on the collet, and the slide is moved up by the lever below
until the other end of the hub is held centrally in the taper

360

GEINDING MACHINEKY

hole of the steady, when the slide is locked. The collet is then
expanded and the hub is held firmly. The wheel is dressed to

FIG. 170. — HUB GRINDER — GUEST

FIG. 171. — GRINDING CASTELLATED SHAFTS

Shape freehand, and soon wears to the form of the race as it
comes from the automatic and the hardening.

The radii on crank pins (page 232) form another illustration

FOEM GRINDING AND CUEVED SUEFACES 361

of the method, and the size of the wheel used makes the
retention of the shapes an easy matter.

In these examples the work rotates, but form grinding
may take place where the form is reproduced by linear motion,
as in the grinding of the bottom and sides of the grooves of
shafts for castellated fits, or by helical (screw thread) motion
as in the grinding of worms.

Castellated Shafts. — The former is shown in Fig. 171, in
which the shape of the section of the shaft ABCD A'B' is given
on the left ; the hole in the gear is ground out and the fit is
on the surface BC, B'C', which is form ground by the hollow
face of the wheel, and upon the sides AB, CD, which are
simultaneously ground by the sides of the wheel. To true the
wheel three diamond tools should be used, one for each part,
AB, BC, and CD. They should be carried in a jig supported
between centres, in the same way as the shaft is carried ; the
diamond E, truing for BC, may be set out to the correct distance
by using a gauge, as shown at FGH, and the wheel trued by
rocking the jig on the machine centres. The jig is then fixed
and the sides of the wheel trued by two diamonds, carried each
on its slide, and set out to a gauge. The main slide should
be adjusted at each truing operation, so that the diamond in
use moves in a plane through the axis of the wheel spindle.
The errors involved are thus reduced to a minimum. It is
customary that CD and A'B' should be parallel, but they may
be radial. Only a very simple machine, consisting of a body
having a main slide with a headstock (and division plate on
spindle) and tailstock, and a vertical slide carrying the wheel
spindle, is necessary for this work.

Gear Teeth and Worms. — To meet the requirements of
high speed gearing which has been hardened (or even heat-
treated only), the teeth are sometimes ground, chiefly in motor
car work, and perhaps chiefly as a selling point. Machines for
this purpose may follow the principle of a generating machine,
or of a gear cutter using a formed cutter. In the latter case
the operation corresponds to form grinding, the wheel being
trued to the shape of the space between the teeth and traversed
between them. The earliest machines for the purpose were

GEINDING MACHINEKY

designed for treating cast gears before the days of cut gearing ;
to-day, when practically every gear is cut, it is to the rectifica-
tion of hard gears only that attention is paid. In the early
machines the wheel, a hard one, was simply turned by hand

FIG. 172. — GEAB GRINDING MACHINE — L. STERNE & Co.

to the shape of a template, and it was trusted that the various
irregularities of the teeth would average so that the wheel
would retain its shape for some time. In Fig. 172 is shown
such a gear grinding machine (by Messrs. Sterne & Co.) intended
for treating cast gears. The machine works upon the form-
grinding principle, the wheel, which is 8 inches in diameter, being

FOEM GKINDING AND CUEVED SUEFACES 363

turned by hand to the shape of the tooth space and then
traversed mechanically. The wheel spindle is driven by a
pair of link belts A (see page 149) running round tension idler
pulleys B, B', and the wheel head C is carried on a vertical slide,
to which a reciprocating motion is given by means of a connect-
ing-rod inside the column of the machine. Towards the lower
end of the stroke a dog on the slide encounters the end of the
adjustment screw D, carried on the lever E, the movement of
which is limited by the screw stop F. The gear G is carried
on a vertical stud on the slide K, and is indexed round (using
its own teeth) by the pawl H, which receives its motion from
the lever E. The cut is put on, and the position of the gear stud
adjusted for gears of different sizes (up to 30 inches diameter),
by means of the slide K. This machine was brought out some
thirty years ago, before the days of universally cut gearing,
but recently machines have been made on somewhat similar
lines, but embodying the worm dividing wheel and indexing
mechanism customary in gear-cutting machines, and provided
with mechanical guiding apparatus for truing the wheel. As
these machines are intended for correcting the distortion of
gears caused by heat treatment or hardening, a high degree of
accuracy is necessary if the running of the gear is to be much
improved, and hence the advantage of a jig for guiding the
diamond when truing the wheel. The production of the
desired wheel tooth shape — whether cycloidal or involute—
appears to be a problem of some difficulty. In the movement
of the diamond over the wheel face it is essential that it should
bring one point only of its angles into action, or at any rate
that small variations of the actual working point should have
little effect on the resulting shape of the wheel. In the truing
jig of one machine which I examined this point had been
attended to, but the total motion of the diamond was pro-
duced indirectly by the superposition of two movements (one
controlled by a cam) connected through a large number of
working parts. Such arrangements are very seldom adopted
in machines which aim at any precision. Supposing, however,
that the complete motion of the diamond tool for producing a
gear shape were produced very directly and in a manner free

364

GKINDING MACHINERY

from the errors indicated above, the accuracy of shape initially
given to the wheel would be dependent on the precision of the
lay-out and making of the cam, and upon the accuracy with
which the actual working point of the diamond was set with

FIG. 173. — DAIMLER GEAR GRINDING MACHINE. GENERATING PRINCIPLE

reference to the cam and mechanism. The difficulties will
be appreciated by those familiar with the production of gear
tooth shapes and used to precision work.

These troubles can be avoided by adopting the generating
principle for grinding gear teeth, and this is done in the machine
(Fig. 173) of the Daimler Company. In this machine the side
of the wheel (near its edge) is trued flat, and the tooth shape,

FOEM GEINDING AND CUEVED SUEFACES 365

which is an involute, produced by rolling the gear relatively to
the wheel.

The geometrical arrangement is shown in Fig. 174, where
the teeth of the gear being ground are indicated in two positions.
An involute is the curve traced out by a fixed point, here P,
on a line AB, which rolls upon a fixed circle (centre C) without
slipping ; by this motion P would trace the outline of the

C D E

FIG. 174. — GRINDING GEAR TEETH. GENERATING PRINCIPLE

shaded tooth F. As P at any moment will be moving perpendi-
cular to the position of AB at that instant, a line LPN, drawn
perpendicular to AB at P, will always touch the involute as it
is being traced out by P. Hence by using the wheel LNQ as
shown, it will in its movement always touch the involute side
of F, and will therefore grind the tooth correctly.

Such a movement of a high-speed spindle carrying a wheel
would present practical difficulties (partly owing to gyroscopic
effects), and it is better to fix the line AB, the spindle, and the

366

GEINDING MACHINEKY

wheel, and to roll the circle with its gear teeth upon AB — as
is done in the Bilgram bevel gear generator. The motion,
being relative, produces the same geometrical results.

When the gear centre is at C and the teeth at FGH, the
wheel face DLPN is grinding the point of the tooth F at P.
The gear circle then rolls along AB until its centre goes to E

just beyond D. The teeth

££ A'W*. t^x- are *hen in the position

J, K, indicated by the
broken lines, and the
grinding is finished at the
bottom of the tooth.

It will be noticed that
as the gear rolls the point
of contact with the wheel
is always at the point P,
and hence in grinding the
wheel would wear at this
point only. To distribute
the wear of the wheel a
reciprocating motion is
given to the wheel head,
so that the wheel face
moves to and fro in its
own plane. When the
gear is at JK the wheel
only just reaches to the
bottom of the ^pace, its
position being shown at E
lightly sectioned ; as the
gear rolls the wheel ad-
vances, until, when the gear is in the shaded position FGH,
the wheel is in the heavily sectioned position Q. The wheel is
of the section sketched, and by its movement the wear is thus
distributed over its grinding face.

In Fig. 175 four positions of the action are shown. The
point of contact of the rolling circle with the fixed line is at a,
the centre of the circle at c, the point of contact of wheel and

FIG. 175. — GRINDING GEAR TEETH
GENERATING PRINCIPLE

FOEM GEINDING AND CUEVED SUEFACES 367

gear at p, and the wheel point at I. The suffixes refer to the
different positions, and the movement of the wheel as the gear
rolls is clearly seen.

No movement is given to the wheel parallel to the axis of
the gear in order that it should cover the width of the tooth ;
the wheel used is so large in diameter that this is unnecessary,
the small clearance at the bottom of the tooth space being
sufficient to permit the whole working surface of the tooth to
be ground up. The two faces of the teeth are ground separately,
the gear being reversed on the spindle for the purpose.

No reference has been made to the pitch circle, as it is
only in text books on machine design or when the axes of a
pair have been definitely fixed in position, that involute gears
possess pitch circles.

The action of the machine itself (Fig. 173) can now be
understood. The body A A' carries the wheel B on a wheel
head C, which is arranged to slide parallel to the spindle axis
for the convenience of maintaining the position of the wheel
face constant ; the gib of this slide is seen at C'. The whole
wheel head is then carried on a double cross slide — one part
adjustable to provide for gears of various sizes and for wear of
the wheel as it decreases in diameter, and the other to give the
oscillating movement of the wheel in synchronism with the
rolling of the gear D, which is mounted on the top of a vertical
spindle, and is carried to and fro by the slide EE'. The wheel
face is trued by a diamond tool at F, which is set up to a fixed
stop at H. When the wheel is to be trued, a small cover J in
the wheel guard is lifted, and the slide carrying the diamond
moved forward. The wheel head is adjusted forward a sufficient
amount for the truing by the screw K, and is then dressed ; thus
its flat face is kept always in the same plane.

The vertical spindle L which carries the gear D has a
division plate M, with the same number of teeth as the gear,
operated by hand by the latch N. The pressure being always
one way, the notches are made taper with one side radial, as
is usual in good capstan lathe practice. An adjustment is
provided at P for setting the tooth correctly in relation to the
wheel. The driving pulley for the reciprocating movement of

368 GEINDING MACHINEEY

the slide EE' is at K, the adjustment for the length of stroke
at S, the connecting rod driving the slide at T, and the adjust-
ment for the position of the slide movement at U. The gear is
indexed round by hand, and for this purpose the slide movement
is stopped by the lever V, which takes the clutch out of gear
and applies the band brake, which can be seen immediately
above the lever.

The rolling motion of the gear is produced by means of a
drum W carried on the spindle L, and thus by the slide E, and
forced to turn as it moves by the steel bands X and Y, of which
X is made in two parts so that there is balance of force. One
end of each strip is fastened to the drum W, and the other is
anchored to a bracket, which is carried on the machine body,
and is adjustable in position for drums of different sizes.

The mechanism for moving the head in unison with the
reciprocating rolling of the gear, consists of a cam carried on
the wheel head cross slide and a roller carried on the slide EE',
the wheel head slide being forced up to keep the contact by
means of springs. The water piping, nozzle, wheel, and splash-
guards and other details are customary grinding-machine
practice.

Gears ground by the generating method naturally possess
the advantages inherent in it, and these in addition to those
due to the simplicity of the method of wheel truing in it, as
opposed to the complications mentioned in connection with
the form -grinding method. When the hardening treatment
is careful, gears are little distorted, so that ground gears are a
comparative luxury, the chief desire being usually an improve-
ment in the silence of running. Machines have been made
to improve gears by running them together with abrasive
powder, making a manufacting method of the old crude cure
for noise. Where the desire is for the best, the fact that
grinding on the generating principle is the more expensive may
be disregarded.

In truing the wheel for the purpose of form- grinding a
worm consideration must be given to the question of inter-
ference. The worm may be finished in a lathe by a tool
cutting on an axial plane, and of the shape of the section of

FORM GRINDING AND CURVED SURFACES 369

the worm — which almost invariably consists of straight lines.
It cannot, however, be ground by a wheel trued to a similar
axial section, owing to interference at other points. In Fig. 176

is shown the worm and hob grinding machine of Messrs.
Holroyd, which is adapted for grinding worms either by form
grinding — in which case the wheel covers the whole worm
surface at each travel — or by grinding a small portion of the

2 B

370 GKINDING MACHINERY

worm face at a time, and traversing the wheel down the tooth
face at the reverse after each stroke. The latter process
requires much longer time, but is necessary with worms having
large teeth.

Here the work is carried between centres on the headstock
A and tailstock B, the latter of which is adjustable along the
main slide C, to suit various lengths of work or mandrils, and
the reciprocation of the table, which is by means of a screw,
carries the work to and fro under the wheel ; at the same
time it is rotated by the shaft D in due ratio by means of the
change wheels at E. The drive for this table motion is obtained
from two pairs of fast and loose pulleys (not visible) on the
rear of the shaft F. These are driven by open and crossed
belts, the forks of which are operated from the table by means
of stops on the rod seen in front of the machine. This gives
the reciprocating motion. The table can also be traversed by
the hand wheel on the right. As worms and hobs frequently
have several starts, a dividing mechanism, which can be set to
act at either or both ends of the stroke, is inserted ; the top
of the driving pulley for this is seen at H, the change wheels
at J, the trip mechanism at K, and the handle for hand opera-
tion at L. The action is similar to that customary in gear
cutters. The vertical adjustment of the wheel M is by means
of the hand wheel N, just behind which is an automatic feed
for this movement, so that when the wheel grinds the worm by
feeding down its side, the motion is automatic ; the automatic
throw-out, necessary for this motion, is controlled by the
hand wheel P. The hand wheel Q traverses the horizontal
wheel slide which carries the vertical swivel K, the vertical
slide S, the second vertical swivel T, and the horizontal swivel
U to the wheel head. This cross adjustment serves to set the
wheel centre vertically over the work axis for worm grinding ;
for sharpening hobs the slide has to be run back some distance
to bring the wheel to the correct position. The belt to the
wheel spindle runs over the idler pulleys V, W. The water
supply is shown at X and the spring roller protecting cover
for the main slide at Y.

When the wheel is to be traversed down the side of the tooth,

FOBM GEINDING AND CUKVED SUBFACES 371

the line of motion of the ' vertical ' slide is first set to the angle
of the tooth, and the wheel spindle then set horizontal by means
of the second vertical swivel, but in form-grinding this need not
be done, it being sufficient that the wheel spindle is horizontal.
The horizontal swivel is then adjusted to the angle of the worm
thread, taken on the pitch line (which is not, however, quite
definite unless the worm wheel to be used is settled), and the
wheel adjusted vertically until it is in the correct position for
grinding, and it is then trued. To do this so as to form the
worm face correctly the diamond point is made to traverse
over the (imaginary) desired worm face. This is done by
carrying the diamond tool in a jig between the centres, and using
the automatic motion — previously set up as to the lead of the
worm — so that the point of the tool traces out a helix, which
will in grinding be reproduced on the worm. The diamond is
carried in a slide which is adjusted to the angle of the worm
tooth, and by slowly traversing it down this as the point of the
tool reciprocates helically, the whole surface of (one side of)
the worm will be traced out by the diamond, which will during
this movement turn away all parts of the wheel projecting
across this traced-out surface. The diamond point must be
set so that the slide movement by which it is slowly traversed
at the angle of the worm tooth, would, if it could be continued,
make it pass through the worm axis ; the reciprocating move-
ment need only be sufficient for the diamond to clear the wheel.
Now if the actual worm be placed in position the wheel will grind
it so that none of it projects across the surface traced out by the
diamond tool — that is, it will form-grind it to the correct shape.
The motion traverses the worm past the wheel ; the return
is rapid, and on it the wheel does not cut. If the worm has
more than one start, it is automatically indexed round between
the strokes, the actual stroke set being longer than the length
of the worm so as to allow time for this. Before actually start-
ing the grinding the wheel is raised a little from its ultimate
position, and gradually fed up to it as the grinding proceeds.
By adopting this method of truing, no great difficulty occurs
in setting the diamond so as to true the wheel correctly, though
the truing itself requires considerable time and care.

2 B 2

372 GKINDING MACHINEEY

Complex operations on a wheel whose shape is at best
temporary are difficult to enforce in a shop, and how this
ingeniously conceived method of truing fares in practice I
cannot say, but theoretically it deserves success.

The same machine serves to sharpen hobs in the same
manner, except that here the feed is put on by giving the hob
a slight extra rotation, without simultaneous axial motion,
which feeds its cutting face into the wheel face, previously
trued in the manner just described.

The machine illustrated grinds worms up to 12 inches
diameter by 18 inches long, and takes a wheel up to 7 inches
diameter. It is equipped for wet grinding, but only the
delivery pipe and nozzle are visible (at X) in the view shown.

The employment of ' form ' grinding as a manufacturing
process will increase, as the wheels are employed efficiently and
the machines are of simple construction. The chief essential
is that the wheel should be large in diameter compared with the
length of work surface ground ; the grade of wheel should be
rather harder than would be used for similar work in regular
machine grinding. In some manufacturing, wheels with faces
up to 12 feet in width are used, a small reciprocating motion
being employed to keep the wheel face straight and to reduce
scratch marks.

Some other forms containing ' generating ' lines may be
produced by traversing the wheel over the work and retaining
a width of contact, but these forms are not useful in engineering.

Cam Grinding. — With the employment of hardened cams for
high speed work, such as petrol engines, jigs and machines have
been designed for grinding them so as to secure the advantages
of the resulting accuracy. Small cams, whether separate or
integral with the shaft, can be ground by means of swinging
fixtures in a Plain or Universal Grinder. For cams ground on
the camshaft, the swinging part must take the form of a small
bed carrying a tailstock so as to accommodate various lengths of
shaft. The swinging motion must be derived from the rotation
by means of a master cam. A similar arrangement is sometimes
used for grinding reamers with a convex backing off.

For larger cams special machines are desirable ; one such

FOKM GRINDING AND CURVED SURFACES 373

by Messrs. The Churchill Machine Tool Co. is shown in Fig.
177. The cam spindle is here carried on a cross slide, and its
movement to and from the wheel is controlled by the master
cam, carried on the cam spindle close to the cam which is being
ground, and which is kept in contact with a roller by means
of a weight acting on it through a pinion and rack. The
roller is carried on a lower cross slide, which is slowly fed
towards the wheel by a mechanism similar to that of a Plain

FIG. 177. — CAM GRINDER — CHURCHILL

Grinder, the feed taking place at each oscillation of the upper
cross slide. The wheel has a traverse motion over the face of
the cam by means of an adjustable crank motion, and has a
quick hand motion for withdrawing the wheel from the work.
In thus grinding a cam by means of a disc wheel the precise
shape of the cam is dependent on the size of the wheel, the
cams ground by the machine having a slightly different shape
as the wheel wears down. If the cam has a form such that the
difference becomes important, the diameter of the wheel used
should be kept between certain limits. This difficulty can be

374

GEINDING MACHINERY

got over by using a face wheel, which is equivalent to a disc
wheel of infinite radius as regards this purpose. However,
as the errors involved are usually insignificant, and the surface
produced by the disc wheel is superior, cams are usually ground

T,, ,R

FIG. 178. — LINK AND HOLE GRINDING MACHINE — BEYER, PEACOCK & Co.

by this method. If the edge of the cam is hollow at any point,
a face wheel could not be used, and a limit is at the same time
set on the diameter of the disc wheel which it is possible to use.

Link Grinding. — The grinding of links for locomotives
has been the regular practice for many years, and in Fig. 178
is shown a machine built by Messrs. Beyer, Peacock & Co.,
Ltd., for this purpose. The machine illustrated is a double

FORM GRINDING AND CURVED SURFACES 375

headed combination link and hole grinder, and for the latter
purpose the cylinder grinder method of page 247, which was
first brought out — in 1887 — by this firm, is employed.

Here A is the main spindle, revolving in bearings at B and C,
and carries within it a sliding spindle D, the axial movement
of which traverses the wheel through the work. The spindle
D is bored eccentrically for the feed-adjustment spindle E,
which in turn is bored eccentrically for the wheel spindle F.
This is driven by a belt running over the idler pulleys H,
which are forced to maintain the tension on the belt by a
spring in the case J. The main spindle A is simultaneously
driven by a worm and worm wheel, the worm pulley K being
belt-driven from the pulley L. At M is the hand wheel for
adjusting the radial position and cut of the grinding wheel,
which is done while the spindles are in motion through the
differential gears seen at N. The vertical reciprocating
motion of the spindle is obtained through elliptical gears
in the case P, which drive a slotted disc Q, from which the
motion is transmitted by the connecting rod R. By means
of the handle S, this can be locked to the lever T, which moves
the spindle by a collar connection, and also balances it by
the weights U. The lever T can also be operated by the
handle at its front end. At V is the water supply. The
whole of this mechanism is carried on the head W, which is
fitted to slide in the base X, and can be adjusted to and fro
in it by means of the wheel Y, which operates the screw
through a worm and worm wheel. The whole can be adjusted
on the longitudinal slide of the machine by means of the
hand wheel Z, so that the two heads can be adjusted to any
points of the work, which is carried on the table a in front of
the machine. Holes are ground in the same manner as in a
cylinder grinder, but for links the wheel spindle is not carried
round, the link being held in and moved by the frame b. For
straight links this slides on the table a, and is guided by the
gibs shown in position ; for curved links it is fastened to, and
its motion thus controlled by the radius bar c, which is pivoted
at an adjustable point d carried on a fixed bar e at the rear
of the machine. The radius bar is removed for grinding

376

GEINDING MACHINERY

straight, and the gibs, for curved links. The reciprocating
motion is given by the linkage /, which is driven through
elliptical gears, so that the important advantage of a nearly
uniform motion is obtained.

Grinders with more than two Wheel Spindles.— It is sometimes
necessary that a face should be square wi'th a hole, and it is
then convenient to be able to grind them at one setting. This
can easily be done on some Universal cutter grinders which

FIG. 179. — BRYANT CHUCKING GRINDER

are equipped for circular grinding, and some machines have
been placed on the market specifically for the purpose. If a
machine be fitted with more grinding spindles, and suitable
stops or throw-outs, more complicated work can be duplicated
at one setting, and the machine corresponds more or less to a
capstan lathe.

In Fig. 179 is shown the Bryant Chucking Grinder, in which
three parallel spindles are carried in sleeves, which can be
adjusted axially to their working positions by means of the
three handles seen at the right near the top of the machine ;
the lever seen near the handles locks the sleeves in the arranged

FOKM GEINDING AND CUKVED SUKFACES 377

positions. The whole head carrying these wheel sleeves
traverses, the positions of the reverse being controlled by the
dogs on the front. The work head is carried on a cross slide
which has hand and power feed, and the whole slide is arranged
to swing about a vertical shaft for taper grinding ; the work
spindle is driven by a belt from a drum carried in this swinging
part and driven through bevels from a shaft in the main body.
The spindles carry 10-inch, 6-inch cup and 3J-inch wheels
respectively, and smaller internal work can be provided for ; the
traverses vary from -fa inch to f inch per revolution of the work.

The Churchill Three-Spindle Grinder, shown in Fig. 180,
carries three spindles on a capstan head, by the rotation of
which the spindles — usually carrying wheels for external,
face, and internal work — can be brought into their working
positions. The capstan is mounted in the place of the wheel
head of a Universal Grinder, and not only chuck work but
work between the centres can be done. The spindles are
driven from overhead by a belt, which is shifted from spindle
to spindle as needed.

The capstan type has been employed for as many as six
spindles, an idler pulley being mounted in its centre and
the belt transferred on to it while the capstan is being revolved.
That these machines have been placed on the market is an
indication of the trend of development and trial ; whether
they will hold a permanent place in manufacturing establish-
ments is an open question. It is seldom that it is necessary
that a piece should be so accurate in its various surfaces as
to necessitate grinding them all at one setting ; parallel
surfaces and holes true with them can be ground within very
close limits by the aid of magnetic chucks, and as a general rule
it is cheaper to do work in two operations on simpler machines.

A machine by the Norton Grinding Machine Company
for grinding the outside of ball races in quantity is shown
in Fig. 181 ; it is fitted with an automatic work head, into
which the work is fed down a slide. The wheel is driven from
overhead in the usual manner, and the other motions are
driven from the pulley A. To the left this drives a train
of gears in the case B and so the shaft C, which at the far end

378

GEINDING MACHINERY

FORM GRINDING AND CURVED SURFACES 379

D drives a cross shaft connected with the traversing mechanism,
and at its centre has a cam enclosed in the case E, which
operates a lever pivoted at F, and so the wheel head. From
A the motion is transmitted to the right through bevels to
the inclined shaft GG, and so through bevels at H to the work
head, the speeds of which are obtained through a small gear
box, and the automatic feed motion through a cam. The

FIG. 181. — NORTON AUTOMATIC GRINDER

work is delivered to the machine by the 'slide K, and is removed
after grinding by the travelling chains L. Mechanism for
giving the cycle of motion to the wheel head is shown in
Fig. 182, where the cam Z in the case E and the pivot F of
the lever Y are lettered to correspond with Fig. 181. The
wheel head P is moved by the nut Q, which is fitted with oil
retaining caps R, R'. The screw S receives a reciprocating
motion, giving the automatic movement of the wheel head

380 GEINDING MACHINEKY

for each piece of work, from the rod T, which is moved by
the lever Y. This receives its motion from the cam Z, and its
forward motion is rigorously limited by a stop screw. To
compensate for the wear of the wheel, or to make other
adjustments, the screw S is rotated by its tailshaft T' in the
usual way ; by these means a double -cross slide is avoided.
The rotation of the screw is given by hand through the gears
U, U' from the handle V, and the usual fine adjustment is fitted
by means of the gear W, pinion W with division plate and
latch X.

Grinding Shafts and Rods, &c. — Ordinary shafting and
slender rods, already turned or drawn fairly close to size, can
be best ground by aid of a steady fixed relatively to the wheel,
as described in Chapter V. A machine, suitable for rods
up to | inch diameter, is shown in Fig. 183. This machine was
constructed by Mr. Hans Kenold, and both the wheel and
feeds are driven by chains. The chain to the wheel spindle is of
the ' silent ' type, 2 inches wide, and the chain wheel 4 inches in
diameter ; the wheel is 16 inches diameter and 2 inches face. The
work is rotated and simultaneously fed forward by the head at
the left-hand end of the machine, passes through the steady
and is ground, and then is received by the head on the right-
hand end of the machine, which continues to effect the rotation
and traverse after the rear end of the work has left the other
head. This motion is driven by the chain B, which drives a
shaft in the body of the machine ; from this the chains C and D
run to sprockets on the work heads. The four heads E, F, G,
and H are of similar construction, a worm on the sprocket
shaft driving a worm wheel, upon the shaft of which a convex
disc, J, is mounted. The work is frictionally driven by two
opposed discs J and K, the heads carrying them being vertically
adjustable so as to give a variation of the ratio of traverse
to rotation. In other machines the combined rotation and
traverse is given by the mechanisms used in the roller feeds
of capstan lathes. The rods pass through the tube L to the
central dies N, and are finally delivered from the second heads
to the receiving channel M. The dies are controlled by the
screws at N, and the wheel head is fed up by the hand wheel P

FOKM GRINDING AND CUEVED SURFACES 381

FIG. 182. — NORTON AUTOMATIC GRINDER

FIG. 183. — ROD GRINDER — HANS RENOLD

382 GEINDING MACHINEKY

until an abutment on it meets the end of the micrometer
screw Q, which is adjusted as the wheel wears.

The steady bears for a considerable portion of the circum-
ference on the work, and must be adjusted so as to support
the work on both sides of the wheel without appreciable shake,
receiving the unground work on the left, and passing it on
the right after it is ground to size. The wheel has a coarse
grit on the left hand side for roughing out, and a fine grit
on the right side so as to secure a good finish.

If more than 0'002 inch has to be removed — and this is about
the accuracy to be expected in bright drawn steel — the shafts
have to be passed through the machine twice to secure round-
ness and accuracy, of size. I have examined bars ground on
machines of several makes (in addition to my own) and find
that 0'0005 inch is a limit, both as regards roundness and gauge
size, which can be obtained without difficulty, while 0*00025 inch
or less can be attained. The surface produced is seldom as good
as that of commercial plain grinding, but a high rate of output
is aimed at. Samples of work from the machine illustrated
bear no evidence that the wheel was driven by a chain.

Steel balls are ground by an adaptation of the old process
for making ' marbles.' The rough pieces are placed in a vee
groove in a rotating face plate and operated on by a face
wheel on a parallel, but not concentric spindle. The action
of this, while it grinds the top off a piece, turns it round in
the groove, and so presents a fresh point to be ground, so that
the nearly spherical balls twist over continually as they run
round the vee groove and continually become more nearly
spherical. Steel balls are nearly spherical after hardening,
and in their case the face wheel and the ball face plate are
co-axial ; they rotate in opposite directions, and the balls
are caused to twist so as to present other portions of their
surface to the wheel by the action of a stationary edge bearing
on them, or the groove is spiral, and after travelling along it the
balls are transferred by passages within the grooved plate to
the starting point, and can be examined when on the way.
After grinding the balls are polished in a tumbling barrel.
Boilers are finished in a similar manner.

FOEM GEINDING AND CURVED SURFACES 383

Machines and attachments are on the market for several
special purposes, such as the automatic sharpening of band
and large circular saws, the truing-up of lathe centres in position,
&c., but except as examples of ingenious mechanism these
present no special features. The machines described above
have been selected as illustrating methods of grinding, or as
suggestive of development.

Jigs and Fittings. — In the design of special grinding
equipment and jigs, in addition to the usual considerations,
those introduced by the accuracy aimed at and by the process
of grinding itself must be borne in mind. The work must not
be held in a manner liable to spring it, and usually very little
hold is necessary ; split and magnetic chucks are often suitable.
In important work the geometrical effect of errors in the
alignments and fitting should be reckoned out. All connec-
tions and movements should be as direct as possible, and
backlash taken out wherever possible by springs or weights —
in quickly acting mechanism the former are to be preferred
on account of the lesser inertia effects. Overhangs should be
reduced to a minimum, this often making the difference between
a fine and a poor finish. The effect of the grit is to be
considered, and protection provided to parts when necessary.
All belts, electrical conductors, and switches must be located
well away from the water-supply and spray. If dry grinding is
adopted in a manufacturing process, dust extraction must be
provided for. In most of the machines illustrated the wheel
and work are brought into contact gently, and in automatic
manufacturing operations this should always be aimed at, the
feed being slowed at the moment ; when this is inconvenient
an elastic wheel should be used, or the disc grinding method
adopted.

CHAPTEK XII

POLISHING AND LAPPING

Polishing. — Polishing consists of grinding with a buff, mop,
or belt, charged with abrasive powder ; the elasticity of the
material carrying the abrasive enables it to follow any small
irregularities of the surface of the work, so that a true shape
is not produced, but any surface projections and roughnesses
are smoothed off.

The kind of powder used varies with the material and class
of work ; fine emery for coarse work is followed by crocus
powder, rouge, or lime as the work's surface becomes finer. The
particles of rouge, rotten stone, and Vienna lime vary from a
twenty-fifth to a hundredth of one-thousandth of an inch, or
less, in size.

Whatever the grade of work, high spindle speed and adequate
power are necessary to rapid economic production ; high
spindle speed is also necessary, otherwise mops wear away
quickly, and the speed should be increased as the mop wears
down, or the mop should be changed on to another machine
having a faster-running spindle. A circumferential speed of
5000 to 8000 feet per minute is usually suitable. The cost of
the power (energy) used represents a considerable item in the
total cost.

Polishing Lathes. — The total energy consists in that used
in actually doing the polishing, and that absorbed by the
friction at the bearings, and since the spindle often runs con-
tinuously under a rather tight belt, whether it is actually
being used or not, the latter portion is high. As the work is
not highly accurate, and it is not necessary that the spindle
should fit closely in its bearings, these are usually unduly
neglected, though the cost of reasonable attention is well repaid
in the power saved. The men, machines, and belts usually work

33i

POLISHING AND LAPPING 385

under hard conditions, and it is only recently that dust ex-
tractors have come into general use ; if a machine is to be run
under such conditions it must be simple and cheap, and this
is the reason why the bearings of most polishing spindles are
not provided with such effective lubricating and dust-proofing
arrangements as are really advisable and economic. The
manner in which oil acts in a running bearing is well known,
but it may be briefly recalled here. The diameters of the
journal and bearing differ by a certain amount, and the space
is occupied by a continuously replaced film of oil. If the
surfaces are merely greasy the friction is many times greater
than if the oil film is perfect ; in fact, should the oil film be
broken from any cause the friction instantly increases to a
very considerable amount. Hence for such bearings a well-
arranged lubricating system would soon save its cost in the
power saved.

At starting the oil film is not ready, and the starting effort,
or torque, in a properly lubricated bearing is considerable,
especially if the fit is close; when, however, the oil film has
formed, the effort necessary to keep the shaft turning immediately
drops, and it decreases further as the oil gets suitably warm
and so thinner. The power required to run a shaft must not
be judged from the starting effort. Polishing heads are usually
merely fitted with a Stauffer lubricator on each bearing, while
for power economy they should have a supply of oil introduced
at the right point of the bearing, and be thoroughly dust-
proofed.

Since good ball bearings have become commercial articles,
they have been fitted to polishing heads in order to save this
power loss ; they must be very perfectly dust-proofed, but
have the great advantage of requiring practically no attention.
The power taken is less than for a spindle with ' oil bath '
lubrication, but not so much that it seriously affects the power
bill ; it is of course very much less than for a spindle which is
merely greasy.

Small polishing spindles are often simply spindles with
pointed ends, supported by wooden blocks forced against the
points ; for freehand grinding the same cheap construction

2 c

386

GEINDING MACHINERY

is advantageous where wheels of different diameters must be
used in succession, as the spindle with its pulley and wheel in
position can easily be changed.

Belt Polishing Machines. — Where it is desired to preserve
sharp corners on the work, and in some other cases, a running
belt charged with abrasive is more convenient than a polishing

spindle. Such a machine, by
the London Emery Works Co.,
is shown in Fig. 184, and con-
sists merely of an endless belt,
charged with abrasive, and driven
by power from the pulley A.
At B is a necessary tighten-
ing pulley. The belt is usually
supported at the place C where
the work is applied to it. Three
pulleys are usual, but not neces-
sary— the driver and a tension
pulley are sufficient ; the grind-
ing can be done at or near the
latter, which should be covered
with rubber to make a better
cushion.

Belt polishing machines are
also arranged with a flat support
at C for polishing up flat work

(such as the sides of hexagon nuts), but are not so efficient
for this purpose as the disc grinders previously described.
The speed of the belt cannot be so high as that of a steel
disc towards its edge, and the under-side of the belt rubs
along the support at C, causing friction.

Polishing is a cheap process, and can be sometimes used
to displace machinery operations. Owing to the dust it can
only be commercially conducted in a special department, which
should be fitted with adequate means for extracting the dust
as it is formed.

The Surface Produced. — The surface produced by polishing

FIG. 184. — BELT POLISHING
MACHINE — LONDON EMERY
WORKS Co.

POLISHING AND LAPPING 387

is very bright and to a high degree smooth, but very close
examination shows that, where the material polished consists
of parts of different hardness — such for instance as ferrite (Fe)
and cementite (Fe3C) in steel — the softer parts are rubbed
away and the harder ones stand out. In some cases the softer
parts are spread over the surface to a certain extent, and this
helps to give the uniformly bright appearance ; this action
depends upon the particular polishing powder used.

Burnishing. — A very bright smooth finish is produced by
burnishing, in which the small irregularities are pressed or
rolled flat by a hard polished tool, usually of hardened tool
steel or agate. The work surface is hardened by the process,
but burnishing is seldom used in engineering work, although
the effect is produced incidentally — e.g. by roller steadies.

Lapping. — In grinding the abrasive particles are carried by
being cemented together ; in polishing they are carried by a
soft mop or leather, but they may be carried by being embedded
in a piece of metal, which is termed a lap, and the process of
using it is termed lapping.

The lap may be charged with abrasive powder so fine that it
would be impossible to make it into an effective wheel, so that
lapping is used to give a fine surface to work already ground,
as, for example, the smoothing of the edge of a tool. In certain
cases, by particular adaptation, it can be used also to improve
the geometrical shape, as in the cases of standard gauges.

As generally the process is used on work previously ground,
the abrasive powders need to be very uniform, so as not
themselves to cause scratches in the work. Fine alundum,
carborundum, emery, crocus, rouge, alumina, and diamond
dust are most frequently used.

Grading Fine Abrasives.— The best method of separating fine
particles of a substance according to their size is to mix them
thoroughly with a liquid and then allow it to stand. The larger
particles fall to the bottom first, and the liquid then contains
in suspension no particles above a certain size. It is carefully
poured off and the process repeated, so that the original powder
can be separated into a number of lots of particles, each lot

2 c2

388 GEINDING MACHINEEY

being nearly of the same size. They are denominated as powders
of so long (e.g. ten minutes) suspension in the liquid. This is
very indefinite, as the distance the particles have to fall in the
fluid is a factor. Various oils and paraffin are suitable fluids.
It is this very slow falling of very fine particles which keeps a
cloud of fine water particles suspended in air. The rate of
falling of a sphere in a particular fluid can be calculated
mathematically, the theory having been worked out by Prof.
Stokes, so that the size of .the particles can be determined
should it be desired to know them for any particular object.
This principle of separation was used by M. Perrin to obtain
quantities of similar very fine particles for his microscopic work
on the Brownian Movement, and in this case the rate of separa-
tion of the excessively minute particles was increased by using
centrifugal force in the same manner as a centrifugal separator
hastens the separation of cream and milk, which takes place so
slowly by gravity. It may be pointed out that the particles
will separate out of the emulsion more quickly if it is placed in
shallow dishes, as the particles have not so far to fall.

Charging Laps. — The lap or piece of metal carrying the
powder is charged, or has the powder embedded into it, by the aid
of a piece of much harder material, usually hard steel or stone,
such as agate. The hard steel has the advantage that it can
be formed into a very true roller. When a particle comes be-
tween the hard steel and the softer lap, it is forced into the latter
and remains there, and for this reason the material of the lap
must be softer than the work lapped, otherwise particles will
leave the lap and become fixed in the work. The arbors of old
clocks will be found to have worn by dust becoming charged
into the bearing, and so cutting the steel arbor, which therefore
wears although it is so much harder than the (brass) bearing.

For the best work the particles are to be embedded in the
lap, and those not embedded removed before the lap is used.
Quicker work is done by feeding fresh abrasive to the lap, but at
the expense of quality of the result.

Lead, various white metal alloys, copper, brass, cast iron,
mild steel, and glass are all used as laps. The softer the
material of the lap the larger the particles of abrasive which it

POLISHING AND LAPPING

389

can be charged with, and the more rapidly it will cut. The
quality of the work produced on the other hand improves with
the hardness of the lap and the fineness of the powder.

Lapping Machines for Flat Work.— When a wheel lap—
whether the side or face is to be used — is made, it must be got
very true before being charged, as otherwise the wheel will not
touch the work continuously, for the particles stand out from
the surface so minute a distance. The wheel therefore must
be made true upon the spindle while it is running, and charged
with abrasive, and used
without being removed
from the spindle ; other-
wise the necessary truth
is lost. The material em-
ployed in wheel laps is
cast iron or copper. In
Fig. 185 is shown a ver-
tical spindle machine in
which the flat side of the
wheel is used, and by its
side the roller used for
charging the disc. Lap-
ping of this nature par-
takes of the nature of
grinding, more especially

in a case such as that of the grinding of small holes by means
of a mild steel lap charged with emery (see page 41), in which
case the movement of the work is entirely mechanically guided.
It merely consists in substituting a wheel charged with
abrasive for one composed of abrasive held together by bond.

In what is regarded as more properly lapping, as opposed
to grinding, the work is in contact with the lap over a large
portion of its area — such are the cases of lapping end gauges
on the flat ends and plug gauges on the cylindrical surface.
This area, over which the abrasion proceeds, makes this lapping
much quicker than where the nearly-line-contact of a wheel
edge is used to produce work of so fine a quality.

Principles of Lapping. — The object of lapping in these

FIG. 185. — VERTICAL LAPPING MACHINE —
LTJD. LOEWE

390 GEINDING MACHINEEY

cases is, not only to improve the quality of the surface, but to
attain a higher degree of geometrical accuracy than that
possible in grinding, and the accuracy attainable stands to
that of grinding much as the accuracy of grinding stands to
that of turning. For example, however well a bar may be
turned, if it is placed in a grinding machine and a light cut
passed over it, numerous defects of surface and truth at once
become apparent ; in the same way, if a carefully ground
part be lapped, similar defects of a much smaller amount
immediately make themselves apparent. The defects of the
grinding of round parts which have to slide, such as drilling
machine quills and milling machine arms, are soon shown up
by the rubbing action in sliding ; usually a broad screw thread
appears round such parts, the effect of the traverse of a very
slightly rounded wheel. The depth of such a thread is hardly
measurable, but in certain lights it shows up conspicuously.
I have found that very striking traverse marks are lapped
out when less than TWW inch has been removed from the
work's diameter, so that the depth of such marks is less than
0-00005 inch.

Allowance for Lapping. — We hence see that in grinding
work for lapping sufficient must be left on so that the following
process will take out the marks of grinding — just as the lowest
allowance in turning for grinding is that at which the turning
marks will clean out. As lapping is a very slow process, the
least possible amount should be left on, and the grinding done
very carefully. The amount necessary is from one to two ten-
thousandths of an inch for work up to 3 inches diameter.

Again, in lapping, successive laps may frequently profitably
be used charged with finer and finer powders, so that even
the worst scratches left by one will be removed by the next,
and the surface continually improved.

The surfaces which are best adapted to lapping are
those in which a considerable portion of the surface of the work
keeps in contact with the lap, as they move relatively to one
another — such as flat surfaces or screw threads.

That the results of lapping excel those of grinding as regards
accuracy is due to the errors caused in the latter process by

POLISHING AND LAPPING 391

the oil films and by vibration. In lapping one surface acts
directly upon another, and the effect of the oil film round the
grinding- wheel spindle is eliminated ; if, however, the lap does
not keep contact with the work, errors (such as the ends of a
plug gauge being small) creep in.

Surfaces which can be Lapped. — When two surfaces are in
contact, one element (that is a small portion) of one may move
upon the other in one or more directions, keeping the contact,
according to the shape of the parts — that is, there are two
' degrees of freedom ' possible in the movement of the surface,
but these may be reduced to one, or to none, by the nature of
the surfaces. The last case, where the surfaces are not able
to move along one another, does not interest us ; in the first
case, which includes flat and spherical surfaces, and circular
cylinders (plug gauges), the surfaces can move in two directions
on one another, without losing the surface contact. For
example, a plug gauge can turn round in a ring gauge and slide
to and fro at the same time ; . or one flat surface can slide on
another and turn on it simultaneously. These are the kind of
surfaces which profit most by lapping, and their truth can be
improved in both ways by the process. In the second class,
to which belong conical surfaces and screw threads, the motion
of one surface over the other is possible in only one way ; the
conical surfaces, for example, can only be turned round, but
cannot be moved axially without separation. Lapping in
these cases only improves the corresponding truth of the
parts — that is to say, the lapping of a conical surface improves
its roundness, but not the straightness or angle of its taper,
and lapping a screw improves the uniformity of its pitch and
its freedom from drunkenness, but it does not improve the
shape of the thread — nor can it make the pitch nearer to any
arbitrary standard : it merely averages the errors.

Lapping Spherical and Flat Surfaces.— Keturning to our
first case, the lapping of flat surfaces such as the ends of length
gauges, of micrometer screws, &c. The flat surface is a special
case of a spherical surface in which the curvature is zero.
If a spherical bowl is placed inside another and touches it all
over, the first can be turned round a vertical axis, keeping its

392 GEINDING MACHINEKY

contact complete, and also tilted sideways — that is, turned
round a horizontal axis — also keeping its contact, except just
at the edges. If the first bowl be the work and the second the
lap, moving them together will gradually wear the first bowl
down until it becomes a uniform fit in the second — that is, it
will have a spherical shape. The second bowl or lap will not
wear much as the abrasive is embedded in it ; its shape will,
however, gradually become more spherical, as the higher parts
will do their work first. In ' grinding ' lenses this is the process
adopted ; the lenses are kept continuously in motion while
pressed against a spherical lap, which is convex for the concave
lenses and vice versa, and so the lenses are gradually lapped
to the desired radius.

As the radius becomes larger and larger, the curvature of
the lens or bowl becomes shallower and shallower, and finally
it becomes a flat plane. Still further alteration of curvature
makes the work concave, and the lap will be convex. Such
lapping does not essentially make for flatness : it makes for a
spherical fit, and something further is necessary to secure flat-
ness. This is similar to what occurs in originating surface plates;
two scraped together must be spherical, but the simultaneous
working of a third is necessary to secure flatness. To lap a
surface flat it is best to make use of previously prepared flat
surfaces as a guide ; one surface moving on the other will
keep parallel to itself, and a body carried on it can therefore
be lapped flat by the motion. A convenient jig for lapping
the ends of rods flat is shown in Fig. 186. The part A to be
lapped — here supposed cylindrical and a good fit in the hole
for its reception — is held in the part B, which moves on the
part C, which it touches over the annular area D. The central
part E of the body C is charged as a lap, and by rubbing the
end of A on it in the motion the end of A can be lapped flat.
If the two ends of A are to be parallel, the axis of the hole in
which A fits must be accurately perpendicular to the flat
surface D. This can be secured by grinding the surface D
when the part B is on a true mandril. If the piece A which is
to be lapped is square, the hole in B must be replaced by two
flat surfaces, which are each made square with the surface D.

POLISHING AND LAPPING

393

In this case of lapping spherical and flat surfaces, there is
no question of fit of lap to work ; the surface of the work lies
in contact with the particles embedded in the lap, and is pressed
to it by a suitable force. Free particles of abrasive matter
should be washed off before lapping, so as not to roll loosely
about between the two surfaces. As the material of the work
is removed in very minute portions it is important in all cases
that the surface should be machined — usually ground —

C E

FIG. 186. — LAPPING THE ENDS OF RODS

closely to shape, with as little as possible left on to be removed
by lapping, before lapping is commenced.

Plate glass is now produced so very nearly flat and parallel
that it can be used, when charged, as a lap for flat surfaces.
It has the advantage that its truth of flatness can be easily
tested optically. If two pieces of glass are squeezed together,
bands of colour are seen, formed by the interference of the
reflected light at the surfaces which are placed together.
Actually there is a thin film between them, so that the reflexions
at the very near surfaces interfere. If the bands are uniform
and wide, the surfaces fit uniformly, so that if three fit one
another in this manner they are flat. Such glass plate, charged

394

GEINDING MACHINEEY

with flour abrasive, forms a convenient means of rectifying
the ends of micrometer screws which are worn ; the screw is
set up to the plate so as to hold it very lightly against the anvil,
and the micrometer is then moved to and fro.

Lapping Cylindrical Work. — A lap suitable for parallel
circular work such as bearings and plug gauges is shown in
Fig. 187. It is important to make them very carefully, other-
wise only a small portion of the charged surface will be actually
lapping, and the time taken will be increased. The length

FIG. 187. — LAP FOR EXTERNAL WORK

of the lap should be about equal to that of the work. In
making, it should be bored, split, and fitted up ; then the lap
should be compressed a little by. the screws A, A', and ground
to size when so compressed, and a slight relief given at D.
In use the lap must be set up to the work by means of the
screws A, A', so that there is no play, and the screws B, B' are
then used to lock the position. If there is play the lap will cant
a little as it moves over the work, and tend to lap it small
at the ends. Plenty of oil must be used ; a recess is provided
at C to receive it, and soft wood strips at the outer part of
the slot to prevent its escape there. The lap must be con-
tinually moved lengthways to and fro, as the work rotates
inside it. It should at first have a longitudinal movement more

POLISHING AND LAPPING

395

than its length, and this amount should be reduced as the
work progresses. At frequent intervals it should be reversed,
end for end, on the work.

For purposes requiring less accuracy a half-lap is sufficient,
and it can be applied very easily.

Much inside lapping is done in manufacturing — not for
the perfecting of ground work, but as the cheapest way to
produce the work. Small holes in hardened steel parts when
contracted a little in hardening are quickly lapped to size, while
grinding them is difficult on account of the small diameter.
Carriage axle boxes of small diameter are also commonly lapped,
as, being about 1 inch diameter by 6 inches long, grinding is slow.
They are made of cast iron, chilled on the inside, which is

-3

FIG. 188. — LAP FOR INTERNAL WORK

taper so that the chill can be easily knocked out. The hole
needs to be cleared up and made parallel. For this and similar
classes of work lead laps are the best ; they are quickly made
by casting the lead round a square notched bar which is centred
at the ends, so that the cast lead can be turned to size, and they
take a charge of rather coarse emery easily. For very accurate
work they are not suitable, as they are very soft, and so do
not keep their shape ; neither can they be expanded so as to
fit the hole closely, and so prevent bell-mouthing. A suitable
lap for such work is shown in Fig. 188. The taper mandril
should be ground and the split lap, which is preferably
keyed, ground in position on the mandril. The mandril
taper should be about one per cent.

Accuracy Attainable.— As regards the accuracy of the process
when at its best, it may be noted that standard plug gauges by
first-rate makers have errors of about 5oooo of an inch, while
the flat gauges made by Johansson and others are generally

396 GKINDING MACHINEKY

of a higher accuracy still. These are actual standard length
dimensions ; the accuracy of the surface produced to itself
is higher. In order to ascertain the cause of the force between
flat gauges when wrung together for building up a required
length (see page 406), Mr. Budgett lapped the surfaces he experi-
mented with true within the one-millionth of an inch, as tested
with optical proof planes. He proved that the adherence was
almost entirely due to very fine fluid films between the surfaces
of the gauges.

Internal limit gauges can be ground within ioi00 inch,
but if the conveniences are at hand it is well to lap off the
last one or two ten-thousandths, at any rate at the go-in end,
as the life of the gauge is so much increased by it — there
being more material close to the geometrical surface.

The size of a hole cannot well be measured except by the size
of the plug which will go into it. A plug can be made so
tight a fit in a ring that it can hardly be moved, and a reduction
of a ten-thousandth of an inch makes it an easy fit. A
reduction of half a thousandth of an inch makes the plug
appear to be quite loose in the ring.

The object of lapping a screw is to correct errors of pitch
and drunkenness by averaging them. For the finest work the
same precautions must be taken as in lapping plug gauges.
The lap must be collapsible and must be kept adjusted to
the screw ; its length should be about equal to that of the
screw ; it should have a movement at first of more than its
length, and this should be reduced as time goes on, and it
should frequently be turned end for end. This is very ex-
pensive, and can only be undertaken in particular cases ;
commercially, screws required to be accurate are lapped with
less elaborate precautions, but with useful results. The sizing
feed screws of the principal machines I used to make in Birm-
ingham were lapped, which improved their action considerably.
As regards the accuracy attainable, the screws used for ruling
diffraction gratings present the most perfect results. A screw
9 inches long will rule a grating 6 inches long with lines spaced so
accurately that none of them are a hundred thousandth of an
inch out of position, so that all appreciable errors of pitch and

POLISHING AND LAPPING 397

drunkenness are lapped out of the screw. The mounting of such a
screw introduces errors greater than those in the screw itself ;
and in the use of the ruled gratings, errors of a millionth of
an inch in the spacing are perceptible, provided these errors
are periodic. These screws are lapped in a bath of water kept
at a constant temperature, and the action is arranged to be
automatic, except changes such as reversing the nut.

This accuracy is far beyond what is needed in any com-
mercial work, but it shows the capabilities of the process of
lapping. In lapping for commercial work, tool-room or other,
the progress made can easily be judged by the appearance
of the work, the fine scratches of the grinding cut and other
irregularities gradually disappearing, and the high parts becom-
ing bright first. The lap must be kept a close fit to the work,
so that there is no shake to produce inaccuracy. It is ad-
visable to grind before lapping if it is possible, and to grind
very carefully, leaving a good quality of surface, and an allowance
of one to two ten-thousandths of an inch on hardened steel.

CHAPTEK XIII

MEASURING AND ITS BASIS

The Basis of Measurement. — Modern grinding is essentially
a process developed in response to the demand for increased
precision in the manufacture of parts of machinery ; its success
is due to its meeting the requirements with such readiness as
not to necessitate the employment of exceedingly highly skilled
labour in its use. Apart from the machine, however, there is
the simultaneous necessity of measuring the dimensions of
the parts produced, both by the operator who produces them
and by the viewer in checking them, and the fine limits necessary
have led to the development and manufacture of tools and
gauges specially suitable to such work.

Alternate Standards — the Yard and Metre. — The ultimate
standards to which all measurements and gauges are referred
are the British standard yard and the standard metre. The
British standard yard is defined by Parliament to be the
distance at 62°F. between the centres of the transverse lines on
the gold plugs in a bronze bar 38 inches long by 1 inch square,
kept in the Standards Office ; and the metre is similarly
defined as the distance at the melting point of ice between
the ends of a platinum bar kept in the French Archives. Of
each of these there are a number of very carefully made
copies, and should either original be destroyed it would be
replaced by means of these copies.

Both these standards are quite arbitrary ; they are, how-
ever— which is essential in a standard — very definite and exact.
There has always been a desire for a natural, ultimate unit of
reference, as is evinced by the terms cubit (length of the fore-
arm), foot, hand, and the familiar three barley-corns which
once made an inch. These, however useful in the past, are

398

MEASUKING AND ITS BASIS 399

all indefinite and variable, and hence likely to lead to disputes.
The Eoyal Society took the matter up in the year 1742, and
put forward a standard yard ; a copy was made later by a
Parliamentary Committee, and finally was made the legal
standard in 1824 by an Act. At the passing of this Act, the
question of adopting the length of a pendulum beating seconds
was considered as a possible standard, but wisely rejected.
The Houses of Parliament and the standard were destroyed
by fire in 1834. The standard was then replaced from its
copies, as was provided for in the Act.

^Natural Standards. — Although the metre was intended to
be a natural standard and to be the one ten-millionth part of
a line (meridian) on the earth's surface, reaching from the pole
to the equator, it is now, by law, the length of the bar previously
mentioned. More accurate measurements of the length of
the meridian have shown the former estimate to be appreciably
in error, and in any case it would be a very difficult matter
to compare any particular length with it practically. Sir
John Herschel proposed to adopt the earth's polar axis as
the fundamental unit of length, but like the meridian length
this is slowly changing, and hence not suitable as a standard.
Similar objections apply to the acceptance of the length of a
' seconds pendulum ' as a standard ; its length depends on
gravity, and is very difficult to measure, and further involves
another unit — that of time.

Perhaps, though it is so small, the most suitable natural
standard would be the wave-length of light of a particular
refrangibility (in air at a standard temperature and pressure),
as this is intimately connected with ultimate molecular structure
and the ether. Various measurements of the wave-length
of light of different colours have been made by interference
methods, and it is found that the wave-length varies from

H2 = 3933 to A = 7604 tenth metres (r— -6 of a metre) from

the red to the violet end of the spectrum. The light
corresponding to I>1 (one of the bright yellow sodium lines)
has a wave-length of 0*00005896156 inch, or rather more than
inch. It is true that there is a certain ' width ' to a

400 GKINDING MACHINEEY

line in the spectrum, but the difference of wave-length
corresponding to it is not one part in a million.

Comparisons of the standard metre and yard make the
metre equal to 39*3709 inches, or nearly 3 feet 3| inches. Con-
versely one inch is equal to 2 -539998 centimetres.

By special instruments — comparators — standard scales
such as yards and metres can be compared with one another
to a degree of accuracy of about the one hundred thousandth
of an inch. When working to this degree of precision, the
manner of support of the bar is important, and the effects of
temperature variation would be very considerable if any
appreciable range were allowed. The expansion of hard steel
is about 0 '00001045 of its length per degree centigrade, so that
with even so small a temperature variation as that, a yard
length of hardened steel would expand nearly four ten-
thousandths of an inch. Hence comparisons of scales to the
degree of accuracy desired are made in a room carefully kept
at a constant temperature.

Subdivision of the Yard. — While the yard is the distance
between the points on two exceedingly fine lines, workshop
convenience usually calls for ' end measurements,' such as the
diameter of a shaft, the thickness of a plate, or the distance
between two shoulders. The production of original standard
gauges of an accuracy of a few hundred thousandths of an inch
is very difficult, and involves the use of measuring machines
of the highest degree of accuracy. The standard yard or metre
has first to be copied for the purpose and then subdivided into
smaller portions. There is also involved the problem of making
an accurate transference from the ' line ' measurement of the
standard yard — that is, the measurement of an ordinary scale —
to the end measurement of the distance between the end surfaces
of a flat gauge, or of the diameter of a plug gauge.

End and Line Measures. — Sir Joseph Whitworth subdivided
the yard into feet and then into inches by the production of
end measures which would interchange. The principle used to
compare end and line measurements was to make two end
measures alike, and scribe lines across them close to the centre
parallel to the end surfaces. The equal end measures were

MEASURING AND ITS BASIS 401

placed together with a pair of ends in contact, and the distance
between the lines gave a line measure ; then the two end
measures were placed with the other ends in contact : the
distance between the lines gave a second line measure ; the
mean of these line measures gives the length of each of the
end measures.

These end measures were square bars of hardened steel,
such as is shown in the machine in Fig. 189, with the end
surfaces reduced and carefully surfaced up parallel to one
another. In making such gauges two sides are ground flat
and at right angles; the piece is then held in a right-angled
groove of a jig similar to that shown in Fig. 186, which has an
end surface formed at right angles to the groove, and the gauge
end is surfaced by rubbing on a charged lap whilst the motion is
controlled by the end surface of the jig being on a surfaced
plate. By reversing the gauge the second end is lapped
parallel to the first.

The end measure gauges could be compared by the use of
the Whitworth Measuring Machine, and by having a number
of equal end measures which made up a known measure, then
each of the smaller ones was known to be right to within the
degree of accuracy of the measurements. This process is very
tedious and costly.

Whitworth and other Measuring Machines. — In Fig. 189 is
shown a Whitworth Measuring Machine designed for workshop
use, and measuring to the ten-thousandth part of an inch. For
the origination of his gauges Sir Joseph Whitworth constructed
machines capable of indicating millionths of an inch ; the
principles involved were much the same, but the machine was
more massive, and neither headstock was adjustable. Essentially
machines for end measurement consist of : (1) two surfaces, A
and B, Fig. 189, made very accurately parallel, and provided
with mechanism for moving them to and from each other while
keeping them parallel, (2) means of determining when these
surfaces touch the piece to be measured, and (3) means of
determining the distance they are then apart. In all regular
measuring machines the two surfaces A and B are carried on
bars in poppet heads C and D, one at least of which (here D)

2 D

402

GEINDING MACHINEKY

can be adjusted along the bed. For work to a ten- thousandth
of an inch it is not necessary to have any special means of
determining when the surfaces are in contact, but care must
be taken to keep the pressure light and about the same for the
different pieces measured ; beyond this a more refined method
which will tend to eliminate personal error is necessary. In the
Whitworth machines a ' feeler ' E, which is a thin disc of metal
with its sides surfaced parallel and a light cross handle, is
placed between the flat A of the measuring machine and the

FIG. 189. — WHITWORTH MEASURING MACHINE

flat surface F of the end gauge being measured. The surface
A is adjusted by the wheel G until the feeler will just slide down
by its own weight. This is a very sensitive arrangement, but
is not easily used on cylindrical gauge work. To adapt this
device for convenient use in measuring cylindrical gauges,
Messrs. Pratt & Whitney carry a secondary surface on the
tailstock barrel H, and place the feeler between this secondary
surface and an anvil carried on the tailstock D, using a spring to
force the tailstock barrel H up until the feeler is supported. A
small plug gauge is used as the feeler, and is set with its handle
horizontal ; when the tailstock barrel is forced back a very
slight amount by the gauge being measured, the handle of the

MEASUEING AND ITS BASIS 403

gauge falls to a vertical position, and a little more movement
suffices to allow the gauge to fall out altogether. The one
twenty-fifth of a thousandth of an inch is a difference which
affects promptly the fall of a feeler or secondary gauge.

In the Newall Measuring Machine the tailstock barrel
is forced forward by a spring, and its position in the tailstock
is indicated by means of a lever multiplying gear which tilts
a spirit level ; when the spirit level bubble is at zero, the barrel
is in a certain position, and is pressed forward by the spring with
a definite force, so that the gauge being measured is under this
force.

In the Kogers-Bond Comparator, used by Messrs. Pratt
& Whitney in the origination of their standard gauges, the
poppet barrel is also arranged to slide, and is held up to the
work by a spring, and the end force on the gauge measured is
arranged to be nearly constant, though the exact force makes no
appreciable difference to the measurement. In a machine used
at the National Physical Laboratory contact is considered to be
complete when the barrel is moved so as to make an electrical
contact at its rear end ; this is considered to be sensitive to the
ten thousandth of a millimetre (g-sowo" inch). Thus there are
several effective modes of standardising the contact, satisfac-
tory to the degree of accuracy required.

The third and final function of a measuring machine is to
determine the distance between the measuring faces A and B,
and in this a reference, indirect, to the original standard of
length is necessary.

The first operation in measuring a gauge is to set the tail-
stock in the correct position on the bed of the machine; and
for that two very different methods are in use. The first is by
the aid of standard length end gauges, and this is the method
used in the Whitworth machine. The zero of the graduated
wheel G is set to the fiducial mark on the arm J, and a standard
gauge set up as shown in Fig. 189. The tailstock D is then
moved up by the hand wheel K, operating a screw within the
bed until the surface B nearly touches the end of the gauge,
and then the tailstock is locked in position. The final adjust-
ment of the surface B to contact with the end of the gauge is

404 GEINDING MACHINEKY

made by the graduated wheel L, which moves the surface
B forward by means of a screw, the determination of the correct
setting being effected by means of the feeler E. The surface B
is then set correctly.

The second method is by the use of a scale set in the body
of the instrument and observed by a microscope carried on
the tailstock. This is the method in the Pratt & Whitney
Measuring Machine. The scale consists of a bar in which are
inserted plugs at distances, usually of one inch apart, with very
fine parallel lines marked on the plugs, so that the lines are
spaced at 1 inch apart. The tailstock has a fine adjustment
along the bed of the machine, given to it by means of a screw
carried in a small bracket which can be clamped to the bed
ways. The wheel A is first set to zero ; the surfaces A and B
are then set together so as to release the secondary gauge
previously described, and the cross-hair in the microscope set
to the line on the zero plug. The tailstock and its bracket are
then moved approximately to the desired position, and the
bracket again clamped. The fine adjustment of the tailstock
is then used to move it until the cross-hair of the microscope
coincides with the fine line on the scale, and the setting is then
correct, the surfaces A and B being a definite distance apart,
exact to the accuracy of the scale.

The two methods of setting the tailstock are very different,
the first depending on end and the second on line measurement.
No wear of the scale occurs in the second, while in the first the
setting is made under the same conditions as the machine is
used in.

In both cases the reliance is ultimately upon the accuracy
of the standard end measures or scale of the machine. For
purposes involving high accuracy the errors of the end measures
or scale can be ascertained and allowed for if necessary.

The poppet D and surface B having thus been set to the
nearest unit (inch), the fractional measurement of the size of a
part to be measured is determined by the movement of the
surface A to bring it into correct contact with the piece to be
measured. This movement is produced by the movement of the
graduated wheel G, which is mounted on a screw which moves

MEASURING AND ITS BASIS 405

the part having the surface A ; and the amount is recorded
by the number of complete turns and the fraction of a turn
necessary to give correct contact. When necessary, fractions of
a division of the graduations of G are read to the next decimal
place — the one hundred thousandth of an inch in the Whitworth
machine — by a vernier at J. In this subdivision of the inch
then, reliance for the measurement is primarily placed upon
the accuracy of this screw, both the exactness of its pitch and
its freedom from ' drunkenness.' For very refined work the
errors of the screw can be found, and allowance made for them,
either mechanically or by reference to a table.

Although this is the practice adopted in almost all cases,
the Kogers-Bond Comparator, previously mentioned, employs
line measurement entirely, and compares the end measurement
of any gauge directly with a finely divided line measure. For
gauge work a scale made of hardened steel (so that temperature
may affect scale and gauge equally) is used ; it is ruled by means
of a diamond with fine lines spaced 2500 to the inch. It is
observed by a microscope and subdivision of the graduations is
made in the eye-piece. By means of the finely divided scale and
with a knowledge of its errors, gauges which are fractions of the
unit can be made without the making of the series of inter-
changeable end gauges by which such gauges were first produced
by Sir Joseph Whitworth.

Small differences of length can be compared by means of the
number of wave-lengths of a particular kind of light contained
in this difference. This method is used in the latest Comparator ;
it is, however, a method of measurement not well adapted to
engineering methods.

As described in the preceding chapter, the errors of drunken-
ness and irregularity of pitch can be lapped out of a screw,
so that, provided it is of the correct pitch, it will form a reliable
method of subdividing the unit of the measuring machine. It
will be noticed that in the Whitworth measuring machine the
anvil surface A is formed on the sliding nut and not on the
rotating screw ; this has the advantage that the end surface
preserves its accuracy better — as it does not rotate on touching
the work — and also that subsidiary measuring jaws can be

406 GKINDING MACHINEEY

attached to the barrels H and A, so that snap gauges (such as
shown at C, D in Fig. 1) and cylindrical limit gauges can be
easily measured.

Standard Gauges. — For the production of standard gauges
to be used as references in engineering works such measuring
machines are necessary, for such gauges must be very accurate
— for sizes between 1 inch and 4 inches the error should not
exceed 0 '00005 inch. As the machines are expensive and
require skill in their use it is generally advisable to obtain
standard gauges from firms making a speciality of their
manufacture. Sir Joseph Whitworth first placed reliable
plug and ring gauges on the market ; now there are several
firms, the accuracy of whose products can be relied upon
to be much closer than the figure given above as neces-
sary. For small sizes — less than a tenth of an inch — cylin-
drical gauges are not so convenient as flat gauges, and
recently the employment of flat gauges for larger measure-
ments have come into vogue. The accuracy attained in the
gauges by Johansson and one or two other makers is very high,
being about the one hundred thousandth of an inch. As
several gauges will adhere together when ' wrung ' to one
another, a large number of end sizes can be obtained with
comparatively few gauges, and as the error in each individual
gauge is so small the error in the compound gauge cannot be
of importance. By having the smallest pieces varying in thick-
ness by very small amounts, limit snap gauges can be easily
checked.

Should any doubt arise as to the accuracy of a standard gauge,
it is advisable to requisition the services of the National Physical
Laboratory to report upon its precise measurement.

Gauges — plug and ring and flat end types — of such accuracy
are not intended for use in the shop, but merely for reference. For
actual use copies of these gauges to a lower degree of accuracy
are made in the tool-room or furnished by one of the specialist
firms. For such gauges an accuracy of one ten-thousandth
of an inch (or 0-0025 mm.) for regular engineering work is
ample ; higher accuracy is unnecessary, and adds considerably
to the cost.

MEASUEING AND ITS BASIS

407

Micrometers.— In making these workshop copies of the
standard gauges, or the corresponding limit gauges, while a
measuring machine is desirable, it is not necessary, as the
accuracy can be attained by a good micrometer carefully
handled. This tool appears to have been originated by James
Watt, and although his instrument (to be seen in the Patent
Museum) appears very crude to-day, it represents very high-
grade workmanship for those early days. As a screw gauge
to meet the requirements of instrument makers and wire
drawers, it took somewhat its modern shape ; several detail

FIG. 190. — MICROMETER — SLOCOMB

improvements in its construction have since been made, the
most important being the protection of the screw thread by
Messrs. Brown & Sharpe.

The details of a modern micrometer by the Slocomb Co.
are shown in Fig. 190. The parallel measuring surfaces are
A and B, of which B is fixed, and A is formed on the end of
the measuring screw ODE. The plain parallel part C of the
screw slides through the closely fitting bush F, and the thread
D is never exposed, the rear part being covered by the thimble
G. The nut H is held in the body of the micrometer by a
screw thread J of a different pitch to the micrometer screw D,
so that by turning H wear of the surfaces A and B can be
differentially compensated for. A secondary nut K is forced
away from the main nut H by means of a short spiral spring L,

408 GEINDING MACHINERY

and so takes up any backlash. The thimble G is pressed
tightly on the end of the screw CDE. The thimble is graduated
round the bevelled edge M, so that the divisions represent
thousandths of an inch, the pitch of the screw being 40 per
inch. The whole turns of the screw are read by a scale marked
along the barrel N, the line of the scale being the zero line for
the divisions marked at M round the thimble's edge. Some
micrometers are provided with a spring ratchet movement
to the thimble, so that the ratchet slips when more than a
certain turning force is applied to the thimble, so as to minimise
the ' personal error ' involved in the use of the instrument.
Where the instrument is intended to be used over greater
lengths than an inch, the anvil is formed on the end of an
adjustable bar, and a gauge provided for setting it correctly
for the longer work. A very useful fitting is a split collet, and
a closing nut fitted to the bush F, so that the screw CDE can
be locked in any position, and the instrument used as a snap
gauge. When using it in this manner very little force should
be used ; it must never be forced over any cylindrical work,
as a slight force tending to push it over the work produces
considerable end force on the surfaces AB.

For making workshop gauges it is a convenience if the barrel
N has, in addition to the zero line for the thimble graduations,
a set of vernier lines marked along it ; the decimal fraction
of a thimble division can then be read on the vernier instead
of being estimated.

The accuracy of good commercial micrometers is high, and
they meet the requirements of limit work such as given in
Tables I to III. Work can be duplicated within these limits
with the aid of a good pair of ordinary calipers, but the measure-
ment takes much longer, and for commercial manufacturing
the micrometer is a necessity for economic reasons. If a
limit snap gauge, such as at CD in Fig. 1, be used alone, it
gives no indication of the amount the work is over-size, and so
of what the cross-feed setting should be.

In using a micrometer work should be wiped with the hand
at the points of measuring to remove grit, the anvil B slid
on to the work, and the screw adjusted gently down.

MEASUBING AND ITS BASIS 409

Unless the screw is locked as described above, it should not
be used as a snap gauge ; this is apt to depreciate the micrometer
rapidly, as the end forces produced are great.

Temperature has little direct effect in measuring steel work
in the shop, for the micrometer and work will be practically at
the same temperature, and hence will have expanded the same
amount. If the micrometer be used to compare the work size
with the size of a gauge of the same nominal size — e.g. a 2-inch
running size with a 2- inch standard gauge — which is the best
method of working, care should be taken that the gauge should
acquire practically the same temperature as the work and
micrometer. If the difference of temperature be 10°F. the
error on a 2-inch shaft would be about a ten- thousandth of an
inch, and so would not be often of any importance.

Temperature, however, produces indirectly a much larger
effect, for if the frame of the micrometer be held so that the
inside of the horseshoe frame touches the hand and gets warm,
while on the outside it remains cool, the frame distorts so as
to close the surfaces A and B towards one another. The effect
depends upon the depth of the gap, and is therefore more
conspicuous in the larger sizes ; care must be taken to avoid this
error by handling the instrument properly. In large instruments
the body should be protected by non-conducting material.

The instrument should be checked frequently by bringing the
surfaces A and B together and noting that the reading is zero,
and resetting or allowing for it if it is not so, and by checking
it on a standard gauge of its full capacity.

In measuring work the amount of force used in turning the
thimble affects the reading, for the pitch of the screw is small
(4*0 inch) that a small torque on the thimble produces consider-
able end force at the measuring points, and so strains the body of
the micrometer a little. A slight contact force is all that is neces-
sary, and more tends to wear the surface A, as it twists as it makes
contact ; it is, however, quicker to work with a fair amount of
force. If the method of comparing the work with a gauge is
employed it eliminates this personal error — that is, the difference
of size between the work and the gauge is made to be the same
by different persons, although one will use more force than the

410

GEINDING MACHINERY

other and the actual reading of the micrometer will be
different.

Large work (say a foot in diameter) can be easily measured
by taking the circumference with a thin steel tape ; a thousandth
of an inch on the diameter gives ^ inch on the circumference,
which can easily be appreciated by the naked eye.

Internal work above 2 inches diameter is easily measured by
the use of an internal micrometer. This consists of a micrometer
body A, Fig. 191, into one end of which rods B, B' of various
lengths can be inserted and clamped in definite positions. The

FIG. 191. — INTERNAL MICROMETER — STARRETT

thimble C terminates in the other measuring point D. The
points are slightly rounded. In use the point D is maintained
firmly against one side of the hole, and the end of B is held and
moved about to feel its way through the hole. Dimensions can
be very accurately compared, to within ^V o m°h on holes up to
6 inches. There is the same kind of personal error as referred to in
connection with the external micrometers — a thousandth of an
inch or even more on such a 6-inch hole — but in comparison
of holes this disappears. The particular design shown is that
of the Starrett Company.

The sizes of holes may be taken with ordinary inside
calipers, setting them to the hole and comparing them with an
external micrometer or other gauge, but the time taken is so

MEASUEING AND ITS BASIS 411

much longer that regular internal micrometers should be used.
Messrs. The Newall Engineering Company make an internal
micrometer with three points to touch the work at points on a
circle separated at 120° ; this renders one rocking motion only
of the instrument necessary.

For holes smaller than 2 inches, micrometers are not available,
and calipers or a series of gauges must be used. Vernier calipers
may be used to take the diameter of a hole near its mouth, but
these tools are not generally useful in connection with grinding.

Limit Gauges. — In manufacturing micrometers are used to
give the size of the work as it approaches the limits allowed, but
for the control of the final size and for checking the work, limit
gauges should be used. These practically eliminate personal
error, so that the work can be relied upon to be truly within the
limiting sizes specified.

All limit gauges have two sizes, one which passes over or
into the work, and which therefore is subject to wear, and one
which will not pass over or into the work, and so does not wear.
To distinguish the ends the gauge surface of the latter is made
short, while that of the former is made longer to withstand the
wear. This will be noticed in various types of limit gauge

(Kg. i).

External limit or snap gauges are usually made out of steel
-fs inch to £ inch thick, and take the shape shown at CD in
Fig. 1. A hole, as shown at E, is convenient, as they can be
then hung up on a board in the tool-room. Lightness is a
virtue, and drop f orgings can be obtained suitable for making into
gauges of this type, and for the larger sizes they are desirable.
Large sizes should be single ended only. They may be made out
of steel rod merely bent to a horseshoe shape and the points
hardened and ground to size, but a more formal gauge receives
better treatment and care in the shop, and the cost of the forging
is a fraction only of the total cost of the gauge.

In grinding such gauges on a Universal machine, they should
be supported on the work table with the length of the gauge
Surfaces parallel to the main ways, so that the traverse can be
used for grinding the surface and the cross-feed for putting on
the cut. The flat faces of the wheel, undercut on both sides*

412

GEINDING MACHINEEY

are to be used, and the spindle set square with the main ways,
and all end play should be taken up. The cross- feed in a Univer-
sal Grinder is usually graduated in thousandths of an inch on
the work diameter, so that each of these divisions represents
a one half -thousandth of an inch only in actual movement.
The effect of a movement of one division of the cross-feed hand
wheel may be made still less by swivelling the cross slide, as
explained in Chapter IV.

In use no appreciable force is to be used on these gauges ;
the weight of the gauge itself should be sufficient to take the

FIG. 192. — DESIGN OF GATJGE

large end over the work. A difference of size of 0-00005 inch
is easily appreciable by their use.

For small quantities, where the cost of a special limit gauge is
not warranted, reliance may be placed on the micrometer or on
adjustable limit gauges such as are made by the Newall Machine
Co. A variety of types of variable limit gauges have been
brought out ; in them the chief features to be looked for — after
accuracy and reliability — are simplicity and lightness.

Limit gauges for holes take several forms. For the smaller
holes the type shown at AB in Fig. 1 is most suitable. The
' go in ' end, it will be noticed, is longer than the * not ' end, for
purposes of resisting wear and so that the ends can be dis-
tinguished at a glance. In making these gauges it is well to
lap off the last ten- thousandth of an inch, as it gives a longer life
to the tool.

Some limit gauges of this type have been made with the

MEASUBING AND ITS BASIS

418

end discs ground to a spherical surface. They go into the hole
very easily, as there is no necessity that the gauge axis should
coincide with the work axis. They are more difficult to produce
and wear more rapidly, since the contact with the work is
along a line and not over a surface.

As the size of these internal gauges increases, their weight
increases to an inconvenient amount. They should then have
the end portions recessed and holes bored through, and as

FIG. 193. — LIMIT GAUGE FOR INTERNAL WORK

FIG. 194.— SPHERICAL-ENDED
MEASURING RODS

the size further increases made single ended. A sketch of
such a gauge is given in Fig. 192.

A cylindrical gauge should be used in finally trying holes
for size, but for the larger sizes flat gauges, such as shown in
Fig. 193, with the surfaces at A A', BB', ground cylindrical,
or spherical ended rods as in Fig. 194 are useful. The ends
of the latter are ground to form portions of one spherical
surface, and enter a hole very easily. Both types are very
light. Some expensive jigs for grinding spherical ended
gauges have been described, but all that is necessary is a simple
one, such as is shown in Fig. 195. The hollow spindle AB

414 GEINDING MACHINEKY

revolves in bearings, and the pulley C is driven from the
drum by a belt ; the whole can rotate about the vertical axis
DE, which must intersect the axis of AB. The flat side FG
of the wheel is used, and the axis AB is rocked by hand — using
the lever at H — about DE as the work rotates. On turning
AB round through 180° to grind the other end of the gauge
the belt merely becomes crossed. The wheel spindle should
be set perpendicular to the main ways, and the cross-feed used
for sizing.

Fairly accurate estimation of the excess of the diameter
of a hole over the length of a sharp-ended rod can be made
by holding one end of the latter against one side of the hole,
and noting the amount of movement of the other end necessary
to bring it into contact with the sides of the hole. The amount
varies with the plane in which the rod is rocked ; it is least
when the rod lies in a plane normal to the axis, and this is
the amount to be considered. In Fig. 196 AB, AC are the
two positions of the rod and AD the diameter, so that ABD is a
right angle, and therefore —

BD2 = AD2-AB2

= (AD + AB)(AD-AB)
Hence —

excess of diameter above length of rod = AD — AB

BD2

"AD + AB

2 ,
(nearly)

BC2

8. AD

If the excess be n thousandths of an inch, and fc be the
length of BC in eighths of an inch, and E the radius of the
hole in inches, we have—

1000. fc2 1000 7c2 fc2 .N

n — = _ _._==_ (nearly enough).

64 . 8 . 2 K 1024 E E V

With final reference to the standard yard (or metre), made
indirectly by the use of instruments and gauges such as are

MEASUEING AND ITS BASIS 415

FIG. 195. — GRINDING SPHERICAL-ENDED
MEASURING RODS

FIG. 196. — GAUGING HOLE WITH POINTED ROD

416 GKINDING MACHINEKY

above described, parts can be produced in one factory so as
to interchange with those produced elsewhere, although the
variations from size permissible are those small amounts whose
nature is discussed in Chapter I.

CONCLUSION

The development of grinding as a manufacturing method
is illustrated by the series of machines described above, and
it has influenced and been in turn influenced by other manu-
facturing processes ; it has rendered work which was previously
almost impossible, easy and inexpensive, and has created the
modern view as to what constitutes high-class machine work.
The determination as to whether the process should be adopted
in any particular case will depend not only on what can be
done by its aid, but on what can be done without it.

The principal reasons for the adoption of grinding are (i) the
hardness of the material of the work, (ii) the accuracy necessary,
(iii) the quality of surface required, (iv) the smallness of the
amount of stock to be removed, and (v) the total economy of
the process. Of these (i) and (ii) may render grinding necessary
apart from the matter of cost, and (iii) may leave a choice
between grinding and polishing only, which is a selection easily
made. As regards (iv), the process is always to be considered
as a manufacturing proposition when the part to be made can
be produced nearly to the required dimensions by a cheap or
necessary manufacturing process, or where the part itself is
slight ; it is also to be considered as a final operation to a
roughing process, as in ordinary plain grinding after turning.
The accuracy and cost of the product of modern capstans
and automatics is well known. If the maintainable quality
of their product is satisfactory, grinding is a waste of labour ;
if it is not, it is almost invariably cheaper to rough out the
part in a capstan and finish by grinding than to make complete
in a centre lathe. The makers proclaim that wheels are cheaper
than files (they are much more expensive than tool-steel,
though), but this is a matter of little moment ; the controlling

CONCLUSION 417

factor in the direct manufacturing cost (v) is almost invariably
that of the labour involved, which depends greatly upon the
amount of material to be removed, and hence upon the other
processes in the manufacture of the part.

The correct selection of wheels is important, as the amount
of labour involved depends largely thereon. The action of
a wheel has been described in detail, and when the conclusions
drawn thence have been grasped there should be little difficulty
in arriving at the most suitable grits and grades. There is no
mystery in the matter ; the statements of some wheel makers
that the publication of their grades would do harm is suggestive
of a Delphic utterance. The functions of the abrasive and
bond are quite definite.

The selection of a machine is determined by many factors.
A light machine is usually a cheap one, and such a machine
may do good work if the wheel is in perfect balance, and it
may be sufficient for the purpose in view. Practically it is
generally necessary to do good work rapidly and with wheels
having the small want of balance which is commercially
unavoidable, and, as explained, this implies substantial
machines. Grinding machines of a high class, however, are
so well protected against grit and injury from other causes,
and are built of such good material, that the depreciation is
small if proper attention is paid to them. The accuracy of
construction necessary to give satisfaction is such, and the
alignments involved are so many, that grinding machines —
however good the design — should not be purchased from any
firm whose actions are not honourable.

2 E

APPENDIX

EXAMPLES OF GEINDING TIMES, TABLES, &c;

EXTERNAL GRINDING

TIMES OF GRINDING VARIOUS PARTS,

SELECTED FROM EXAMPLES FURNISHED BY MESSRS. BROWN & SHARPE

PRODUCTION TIMES

Dimensions

(inches)

Time.,

NO. T • -X

Material

iiib Limits

Notes,

Finish, &c.

•Wheel Machine

Dia

m. Length

hrs.

S. Hardened;
M.S.

I 4|
I 6A

317 4

308 Std.-J

The allowances for grind-
ing are those given on

36-4 or 5E No. 11. Plain
64 M. „ 11. „

M.S. ^
M.S.

6TS5

308 Std.-| page 215.
295 £ The work

54 M. „ 11. „
is done in 64 M. „ 11. „

S. Hard. J

e 6|r 148 J batches of 50 or more. 36-4 or 5E ,,11. „

S. Hard. i

* ! Hi

131 | i Most of these parts are 36-4or5E ,, 11. „

M.S.

i 8^s 123 A handled twice, for rough- 54 M. ; ,,11. „

S. Hard. ft llf

91 A

ing and for finishing, &c. 36-4 or 5 E ,11. ,,

M.S.

I o&

88 J

54 M.

, 11. ,,

S. Hard.

I »i

80 1 Std.

Very fine finish 46 K.

, 11. »

M.S. 1
S. Hard. 1

8
1 2|

62 j
60 ! i

Taper — to gauge
Hollow — 1£ in. diam.

54 M.
46 K.

, 11. „
, 2. Univ.

S. Hard. 3

60 1

Hollow — 2f in. diam.

46 K.

,2. „

S. Hard. 1T8« 16

30 |

Very fine finish

46 K.

, 14. Plain

M.S. 3£ 47

30 Std.

54 M.

, 18. „

M.S. 4

J 63|

25 Std.

54 M.

, 28. „

S. Hard.

1 i 24

20 £

Very fine finish

46 K.

, 11. ,»

S. Hard. , 1

r9« 39^

20 1

46 K.

, 14. „

C.I. 2

120 1

46 K.

, 11. „

C.I. 2J i 13f

60 1

—

, 28. „

C.I. 9

40 —

—

, 28. „

Bronze JJ 2M

513 Std.-i

54 M.

, 11. „

M.S. as fig. 3

400 as in fig. Fig. 197. No. 1

54 M.

, 11. „

M.S.

150

., 2

64 M.

, 11. „

M.S.

100

„ 3

64 M.

, 11. „

M.S.

„ 4

54 M.

, 11. »

Soft.

13*

, 6

54 M. „ 14. „

M.S.

17A

, 6

54 M. „ 11. „

M.S.

10^

„

, 7

64 M. "11. „

M.S.

, 8

54 M. , 14. „

M.S.

, 9 64 M. , 2. Univ.

M.S.

,10 54 M,. 14. Plain

M.S.

20J

, 11

54 M. , 11. „

M.S.

3711

17 !

, 12 54 M. , 14. „

M.S.

, 13 54 M. , 16. „

Hard.

, 14 46 K. , 11. „

M.S.

, 16 Lots of 25 64 M. , 14. „

M.S.

, 16 Lots of 25 54 M. , 14. „

M.S.

, 17 64 M. , 16. „

M.S.

70i*s

, 18 54 M. , 16. „

M.S.

, 19 54 M. , 2. Univ.

C.I. „ 8*

•

, 20 Lots of 25 , 2. „

( . I

APPENDIX

419

-?-

19.

—2

tf— •

• 4^" »j

• 7?

. _| _ .

*ist

im
ZO.

Ut^VTS

FIG. 197.

2 E2

420

APPENDIX

EXTERNAL GRINDING

TIMES OF GRINDING VARIOUS PARTS,
SELECTED FROM INFORMATION FURNISHED BY MESSRS. THE LANDIS TOOL Co.

GRINDING TIME ONLY

Dimensions

Allowances in

(inches)

thousandths

Time

Material

Notes, Finish, &c.

Wheel

Machine

Mins.

For

Diam.

Length

Grind-

Limit

ing

Ni.S.

•4375

First class— valve stem

36-46 L.

Inches
10 x 20 Plain

C.H.S.

First class — gudgeon pin

36-46 L.

10 x 30 „

O.H.S.
C.H.S.
M.S.

15
25
6-8

Commercial ,, „
First class— tube 4"
hole

24 comb.L.
36-46 K.

10 x 30 „
10 X 30 „
12 X 42 Univ.

M.S.

Commercial — loco, work

36 L.

16 X 32 X 72

Plain

•4 C.S.

1-495

26J

First class

36-46 L.

12 x 42 Plain

M.S.

Commercial — hollow J*

24-36 L.

16 x 72 „

thick

M.S.

Commercial — piston

36-46 L.

16 X 72 „

rod

M.S.

Commercial — pipe roll

24-36 K.

16 X 72 „

H.T.S.

M.S.

8
24

12
36

20
25

40
25

Taper roller — to gauge
First class — thin wall

46 N.
36-46 K.

12 X 32 „
12 X 66 „

M.S.

Commercial — hollow

36-46 L.

12 X 66 Univ.

(3f*) sleeve

Ni.S.

17§f

120

First class— |" thick

36 L.

20 X 150 Plain

metal

O.I.

2TSS

180

—

Taper — to gauge ; gas

24 L.

10 X 20 „

plug

O.I.

3-025

Commercial — piston

34-46 L.

10 X 30

C.I.

3-738

Commercial — piston

36 L.

12 X 42

O.I.

Commercial — piston

36 L.

10 X 30

C.I.

150

Commercial — drum

24-36 L.

12 X 66

C.I.

394

Commercial — Corliss

24-36 L.

20 X 96

valve

C.I.

23J

27f

Commercial — press roll

46 N.

24 X 144

C.I.

Commercial — Corliss

24-36 L.

16 X 72

valve

C.O.I.

120

150

Very fine— sheet metal

46 L.

16 X 72 „

roll

O.H.S.

as fig.

3yS

Fig. 198, No. 1 Com-

24 L.

10 X 20 „

mercial

M.S.

154

Fig. 198, No. 2 First

46 M.

10 X 20 „

C.H.S.

10i|

Fig. 198, No. 3 Gloss

46 L.

10 X 20 Univ.

finish

O.H.S.

16| 35

asfig.

Fig. 198, No. 4 Very

46 L.

16 X 30 Plain

true point

Forging

„

24J ! 25

Fig. 198, No. 5 First

46 L.

16 X 42 „

class. Pin ground

from rough forging

Forging

Fig. 198, No. 6 Com-

46 M.

Crank grinder

mercial. Pin ground

from rough forging

•4 O.S.

52*

Fig. 198, No. 7 First cl.

36-46 L.

12 x 72 Plain

Chilled O.I.

1411

Fig. 198, No. 8 Fine I 24-36 L.

12 X 42 „

M.S. and

6' 0"

Fig. 198, No. 9 Com-

24-36 L. 20 X 96 „

O.I.

mercial. Piston and

rod both ground

M.S.

73*

—

Fig. 198, No. 10 Com-

30 M.

16 X 72 „

mercial

M.S.

1500

•3

0-02

Fig. 198, No. 11 Com-

46 M.

16 X 66 Univ.

Iltlll.

mm.

mercial

M.S.

23' 3*

300

Fig. 198, No. 12 First

—

20 x 144Plain

class

Chilled O.I.

37*

Fig. 198, No. 13 First

46 L.

16 X 72 „

class

Chilled C.I

54'

120

Fig. 198, No. 14 First

36-46-60 L.

16 X 72 „

class

APPENDIX

421

•7* -

< ITS" »!

- — fe — •

<• fc *

13- *

•4

Jl ^

~~^~

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-150C?

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10.

r23-3-

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^F^

!.--'•-'. *~(^r ~IT^'C:~I

i 1

T *£

._ J.

1 13 Sil4,

TWO Si

FIG. 198.

422

APPENDIX

0 O 1C 0 <M 10 C<J O 0 «5 0 O 0

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»OOOOt> »OCOOO»O O O
i— I (N CC CO CO i— I >— I <M -—l

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*? H^-l-i-iMiH^H«> H
<N •— I (M CO CO (N O

•gfggg

oo w w w w

0000

. ®

APPENDIX

423

o
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i— i

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10 C<J 10 r^

co co os os

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rH rH rH

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CO CO O O IO

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co co os os os

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pH GSI CO

r— 1 CO CD CO

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CO CO _- _ •

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t- O <N 10

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1 1 1 1 I

<^5 rH CD rH CO
rH <N C^ C^ C^

III!

i fr

CD •!— I
fl

2 o

424

APPENDIX

O
i

IO O U3
I> O <N

<N <M CO

10 »0 O

t> t> p

<£i cs7 eo

8 ££§!§§££

SSS

CO CO •*

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KMO O

FH CO

O O O

IO 1O CO O

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IO IT** tr^

Csi <N CSJ

?IO 10 O
<N (N IO

CO CO CO CO

t^ p p GS1

CO "^ Tt^ ^

?§§

^00
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0 O O

1 cb 6

§888

PH (N (N <N

O »0
IO I>

CO CO CO Th -h Th »O

888

999

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999

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»0 O 10 ! O O »0
(N 10 t^ , O (N <N

pH rH pH <N (N <N

Iff

O O O O

9999

GO O <N rt<
i— l <N (M (N

O O
IO »O

IO O O
J> O O

I'll

APPENDIX

425

Ud
O

5
1

Shells thicker
than f inch

g $

— T 1

? 1 ?

$ g

Ill

1 8

i— i

? 8 8

•— i <M CO

to o

<N O

8 ? |

10 ?

888

Th CO 05

? ?

? 8 8

(N Th CO

! 1

I??

•.+

? 8

r— 1

888

<N CO Th

To be easily
taken apart

IO O
<N ip

»o o o

t> O >p

O W

»p t> o

I— 1

? 8

8 § 8

(N CO >0

»o o

CM ip

888

i— I CM CO

1^1

? |

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CO rH CO

? 8

88?

(N CO Th

{? ?

? ? 8

(N C^ IO

(N l>

IO *O ^O
pH CSI CO

§ 10

8 8 8

rH i—4 CSJ

O O

000

i i

W ;£

H-

•p ?

^^ ^O ^^

0 0

0 0 0

(S8TPTII) £

<M CO CO

426

APPENDIX

TABLE IV.— TURNING
ALLOWANCES FOR GRINDING

Brown & Sharpe allow O'OOS to 0 '01 2 on the diameter for all sizes.
The Landis Tool Co. recommend allowances as below :

Allowances in thousandths of an inch

Length in «
inches

Diam.

up to £ 10

f ! 10

15 20

20 ! 20

20 20

. 20

20 20

20 \ 20

25 25

25 30

30 30

30 i 30

30 30

GRINDING TIME-TABLE (APPROXIMATE)— LANDIS TOOL CO.

Diam. of

Length of work in inches

work in

! 1

inches

12 18

24 | 30 36 42 48

66 72

Time in minutes

15 20

25 30

13 ! 16 | 21

26 31

14 18

20 24

26 30

8 9

20 1 24

9 10

10 12

24 28

75 j 90

26 31

85 100

I 1

Time has been figured on a basis of grinding -fa" from the diameter, and the work
to be ground to a first-class commercial finish. If •£+" on the diameter is allowed
for grinding, take f of the time given in the table. Time is for grinding only.

For Guest formula for grinding times, see page 236.

APPENDIX

427

G?
PH

£5 £f
W tf

£ s p

•gll

J3 W
^J C

J«t*

,3 I

£ sl

.11 O

£ a b

d -2

S o

W
$

^— —

h*
i

•

•'

•

T-l

"c3

American Emery

British Abrasive

Courtland Corun<

1
§
&

T3
§

Carborundum Co

American Emery

s
i

British Abrasive

Norton Elastic

WJ g UJJ

PH .£ w—

1 i g 1 1

a a g * «

It*!*

Ifi-S'-g

^ P—< W* <U *

*^-!i

^ o _ 3 ^

I a|^ o
•sis!*

* -§ ° ^ ^

« fl

o § ? d

a s -0 a a ce

o o , «s o

"g^ p^ p, £ 'o

™S % s^ &

eg P

6 1 1 H

j-ia l*a >,
5 It i^ u

•2i ifi|^ s

§ o 'G <u o

ti^ilj

I *iel

^1-d E f

o be !» ^ 2 d

^ C JH ^*3 S

H -a S -S o -g

S-i CM Q> O

c£ -d T3 «M

2^^ i §

428

APPENDIX

HH
H
O

* 1

^ E

'• w

tii. ^

s||

T^5^

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^co.2 002

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i-HOO

IOIC
gcici

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2 g4 §

O 0

•^

1 026

•fl

APPENDIX

429

£ h4

M M.

mil

«; ^

>-5 M

CO CD

M W

W d

-S *

i :

3o 6

3-
i

r r

^5 -
o

,3 -3

«s a
2

a ^ 'S

3 £2 *

* a

a5 ^ -g c3 g

^ K. "** 2 1

* 3* fr S -S

* f I 1 ^

t> ^ 8 ^ b

liH1

v M> «?

2 i °. s 5

* o

^ ^ 22 ««

i— H ^ P^

11*11

^ a -a N

* i.s
s a a

I »

H .S .

430

APPENDIX

a--i

" '

-s -s

1 1,

1 1

ca yd

1 <a ca

1 f-i FH

1 1 1 1

II UN

i i

-f||3

*il*s

*<0£ld
I ^1
I|l

-SOD

So
Ni

I I

1 1 I

W • •
o

-ft -a

]'i

I ® HH

'S C ^>

APPENDIX

431

TABLE VIII

GRINDING WHEEL SPEEDS

Diam. of
Wheel
(inches)

Rev. per minute for a surface speed, in feet per minute, of

4,000

4,500

5,000

5,500

6,000

6,500

7,000

15,279

17,189

19,099

21,009

22,918

24,829

26,738

7,639

8,594

9,549

10,504

11,459

12,414

13,369

5,093

5,729

6,366

7,001

7,639

8,276

8,913

3,820

4,297

4,775

5,252

5,730

6,207

6,684

3,056

3,438

3,820

4,202

4,584

4,966

5,348

2,546

2,865

3,183

3,501

3,820

4,138

4,456

2,183

2,455

2,728 i 3,001

3,274

3,547

3,820

1,910

2,148

2,387

2,626

2,865

3,103

3,342

1,528

1,719

1,910

2,101

2,292

2,483

2,674

1,273

1,432

1,592

1,750

1,910

2,069

2,228

1,091

1,228

1,364

1,500

1,637

1,773

1,910

955

1,074

1,194 1,313

1,432

1,551

1,611

849

955

1,061 i 1,167

1,273

1,379

1,485

764

859

955

1,050

1,146

1,241

1,337

637

716

796 875

955

1,034

1,114

546

614

683

750

819

886

955

509

573

637

700

764

827

871

424

477

531

583

637

689

743

Suitable for
Wheels of
Grade

H I J K L M N

J. J. Guest.

432

APPENDIX

ONS PER
OF—

REVOLUT
ER MINUTE,

Q 02

1 1

02 g

S 3

•^^ rv.
pq OH

g i

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l-H

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CO I> O5 IO

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00 CM 00 <M

•* Tt< CO CO

CM I-H t- CO
CM I-H O O
CM CO M< CO

-* T£ IO CO

£§££

l-H rH

CO l-H rH -^

CO CD IO •*

CO •* I-H IO
CO CO CO <M

O IO l> I>

r- co 10 co

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05 T* CO CM

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i-H
O5 >O CO O5
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CO CO (N <M

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rH CO Tt< CO
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CO CO CM CM

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05 I> 10 CM

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CO "^ GO CO
IO "^ CO CO

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CO CM CM 05

tr^* O5 T^ C^i

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rH rH rH rH

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SS85

M£?

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G4 O5 IO CO

i-H O O5 t^-

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o o o c-

rH rH T^ 00

CO »O "* CO

— 1^5 ^<j ^H

CO (N CM 05

O CO t> C5

IO IO CO Tt<

l> »O CM O

O5 CO t^ CO

T* CM 00 CO
CM i-H

O5 rH IO O

T^ Tt CO CO

^S^g

CD CM CM t>

CO CM O CO

CO 00 rH rH

t^ CO CO 10

CO (M I-H CD
00 05 CD ^

l-H

I^» O CO CO
CO CO <N (N

CO <N rH ^

(N CM CO »O

t> I-H CO 00

GO IO CO rH

O O5 l> CO

l-H

10 10 -* CO

Work
Diameter
in Inches

SttW

H*iCO ^irfi

H?iiO CO l>

00 O5 O <N

APPENDIX

433

434

APPENDIX

TABLE X

CUTTER GRINDING
SETTINGS FOU CLEARANCE WITH DISC WHEEL

Amount wheel axis is set above or belo,v cutter axis (inches)

Sin 5° = 0-087156.

Sin 7° = 0-12187

"Wheel Diameter
(inches)

5° Clearance

•087

•098

•109

•120

•131

•142

•152

•163

•174

•185

•193

•207

•218

•229

•240

•251

•262

6£

•284

•305

7° Clearance

•122
•137
•152
•168

•183
•198
•213

•228

•244
•259

•274
•289

•304
•320
•335
•350

•365
•395
•426

APPENDIX

435

TABLE XI

CUTTER GRINDING

SETTINGS FOR CLEARANCE WITH CUP WHEEL

The amount the tooth rest is to be set above or below the cutter axis — inches.
The diameter of Angular Cutters is reckoned where the tooth rest touches them.
For intermediate cutters interpolate by adding : thus for a 6f inch diameter

add the amounts for a 6 inch and af inch cutter = -261 + -033 = '294 inch

for a parallel cutter.

J. J. Guest.

Diam. of Cutter
(inches)

Parallel Cutters
For 5° For 7°

Semivertical angle, 30°
For 5° For 7°

Semivertical angle, 45°
For 5° For 7°

•Oil -015

•013 -017

•016 -021

f -016 -022

•018 -025

•023 -032

•022 -030

•025 -035

•031 -043

•028 -038

•032 -044

•040 -054

•033 -046

•038 -053

•047 -065

•038 -053

•044 -061

•054 -075

•044 -061

•051 -070

•062 -086

•054 -076 -062 -088

•076 -107

•065 -091

•075 -1

•092 -129

•076 -106

•089 -122

•108 -150

•087 -122

•101 -141

•123 -172

•109 -152

•126 -175 -154 -215

•131 -183

•151 -211

•185 -259

•152 -213

•175 -246

•215 -302

•174 -244

•201 -282

•246 -345

•218 -304

•252 -351

•309 -430

•261 -365

•302 -422

•370 -517

•305 -426

•352 -497

•432 -603

•348 -487

•402 -562

•492 -690

•392 -548

•453 -635

•555 -775

•436 -609

•504 -703

•617 -860

•478 -670

•552 -774

•676 -948

•522 -731

•602 -845

•738 1-035

For 60° set the amount for a parallel cutter of twice the diameter.

2F2

ENGLISH AND METRIC ^CONVERSION

TABLE XII TABLE XIII-

1 in. = 25-39998 mm. 1 metre = 39-.37079 in. = 3 ft. 3| in. (nearly)

Inches Millimetres
1 = 25-400
2 = 50-800
3= 76-200
4 = 101-600
5 = 127-000
6 = 152-400

Milli-
metres Inches
1 = -0394
2 = -0787
3= -1181
4 = -1575
5 = -1968

Milli-
metres Inches
51 = 2-0079
52 = 2-0473
53 = 2-0866
54 = 2-1260
55 - 2-1654

7 = 177-800

6 = -2362

56 = 2-2047

8 = 203-200

7 = -2756

57 = 2-2441

9 = 228-600

8 = -3150

58 = 2-2835

10 = 254-000

9 = -3543

59 = 2-3228

10 = -3937

60 = 2-3622

11 = -4331

61 = 2-4016

8ths Inch Millimetres

12 = -4724

62 = 2-4410

j. = -125 = 3-175

13 = -5118

63 = 2-4803

£ = -250 = 6-350

14 = -5512

64 = 2-5197

|= -375 = 9-525

15 = -5906

65 = 2-5591

| = -500 = 12-700

| = -625 = 15 875

16 = -6299

66 = 2-5984

1 = -750 = 19-050

17 = -6693

67 = 2-6378

| = -875 = 22-225

18 = -7087

68 = 2-6772

1 = 1-000 = 25-400

19- -7480

69 = 2-7166

20 = -7874

70 = 2-7559

21 - -8268

71 = 2-7953

16ths Inch Millimetres

22 = -8661

72 = 2-8347

1 = -0625 = 1-587

23 = -9055

73 = 2-8740

3 = -1875 = 4-762

24 = -9449

74 = 2-9134

5 = -3125 = 7-937

25 = -9843

75 = 2-9528

7 = -4375 = 11-113

26 = 1-0236

76 = 2-9922

9 = -5625 = 14-287
11 = -6875 = 17-462

27 = 1-0630
28 = 1-1024
29 = 1-1417

77 = 3-0315
78 = 3-0709
79 = 3-1103

13 = -8125 = 20-632

30 = 1-1811

80 = 3-1496

15 = -9375 = 23-812

31 = -2205

81 = 3-1890

32 -2598

82 = 3-2284

33 = -2992

83 = 3-2677

32nds Inch Millimetres

34 = -3386

84 = 3-3071

1 = -03125 = 0-794

35 - -3780

85 = 3-3465

3 = -09375 = 2-381

5 = -15625 = 3-969

36= -4173

86 = 3-3859

7 = -21875 = 5-556

37 == -4567

87 = 3-4252

38 = -4961

88 = 3-4646

9 = -28125 = 7-144

39 = -5354

89 = 3-5040

11 = -34375 = 8-731

40 = -5748

90 = 3-5433

13 = -40625 = 10-319
15 = -46875 = 11-906

41 = -6142
42 = -6536

91 =, 3-5827
92 = 3-6221

17 = -53125 = 13-494
19 = -59375 = 15-081
21 = -65625 = 16-669

43 = -6929
44 = -7323
45 = -7717

[

93 = 3-6614
94 = 3-7008
95 = 3-7402

23 = -71875 = 18-256

46 = -8110

96 = 3-7796

47 = -8504

97 = 3-8189

25 = -78125 = 19-844

48 = 1-8898

98 = 3-8583

27 = -84375 = 21-431

49 = 1-9291

99 = 3-8977

29 = -90625 = 23-019

50 = 1-9685

100 = 3-9370

31 = -96875 = 24-606

(100 mm. =

1 decimetre.)

APPENDIX

437

TABLE XIV

TAPERS

Taper per
Foot

Included
Angle

; Taper per Included
cent. Angle

Taper per
Foot

Taper per
cent.

Inches

Deg. Min.

Deg. Min. Deg. Min.

Inches

0 18

0 341 0

0-069

•58

0 36

1 8f 0

0-138

1-15

3
To"

0 54

1 43 1

0-209

1-74

1 12

2 17£

_5_

1 30

0-313

2-61

1 47

2 51| 2

0-418

3-48

To"

2 5

3 26

0-629

5-24

2 23

4 0^

2 40

4 35

0-838

6-98

f 10

2 58

1-049

8-74

3 16

5 9

1-258

10-05

3 34

5 45£

3 52

6 18 7

1-469

12-25

4 10

6 52 8

1-678

13-98

4 28

1-889

15-75

4 46

7 26

5 22

8 0£ 10

2-100

17-5

5 58

8 35

*»

6 34

9 9

7 9

* if

7 44

9 43

8 20

10 17

8 56

10 51

9 31

11 25

Morse Tapers.

•

No. 1 2

5 6

Diam. of small end — inches

. -374 -574

783

1-027 1

484 2-117

Taper per foot — inches

. -605 -600 •

605

•615 •

625 -634

Brown & Sharpe Tapers. No. 1 2 3 4 5 6 7 8 9 10

Diam. of small end— inches -20 -25 -313 -35 -45 -50 -60 -75 -90 1-05

Taper per foot — inches . -5 -5 -5 -5 -5 -5 -5 -5 -5 -5161

No. 11 12 13 14 15 16 17 18

Diam. of small end— inches . 1-25 1-50 1-75 2 2-25 2-50 2-75 3

Taper per foot — inches . -5 -5 -5 -5 -5 -5 -5 -5

Jarno Taper. Diam. small end =

No. of Taper
lu

No. of Taper
Diam. large end — — — - —

No. of Taper
Length = — — „ —

All Tapers 0-6 inch per foot, or 1 in 20, or 2° 51' 40" included angle.

2 F 3

488 APPENDIX

MISCELLANEOUS NOTES

Grinding Solutions. —

For hardened steel and cast iron — 1£ to 2 oz. of soda (washing) to 1 gallon

of water.
For unhardened steel, bronze, &c. — either the above, or soluble oil 1 part.

water 20 parts.
Density of Wheels. —

Vitrified— 0 '09 to O'l Ib. per cubic inch. Silicate— 0' 105 to 0'12.

Mokr's Scale of Hardness^- The hardness of any substance

1. Talc. 6. Orthoclone. which win scratch any one of these

2. Gypsum. 7. Quartz. minerals, and can be scratched by the

3. Calcite. 8. lopaz. Qne next higher in the scale> is said to

4. Fluorspar. 9. Corundum. haye ft yalue between the numbers of

5. Apatite. 10. Diamond. the minerals.

Steel.—

The ultimate tensile strength varies from 50,000 Ib. per square inch for

soft steel up to 250,000 Ib. per square inch for the high tension steels

(nickel, chrome, vanadium).
The elongation at fracture varies from 33 per cent, in a length of 8 inches,

downwards to 3 per cent, or 4 per cent., according to the quality and

heat and mechanical treatment.
The elastic strength (yield-point stress) varies from 40,000 to 160,000 Ib.

per square inch, being from 0'6 to 0'85 of the ultimate stress.
The elastic extension is proportional to the stress producing it (Hooke's

Law).
Ductile materials fail elastically when a certain shearing stress is reached

(Guest's Law).
A material will break after a large number of repetitions of a lower (about

half) stress than the yield point (Wohler's Law).
Young's Modulus, E, average 29,500,000 Ib. per square inch.
The Modulus of Rigidity (or Torsion), C, average 11,000,000 Ib. per sq. in.
Poisson's Ratio — the proportion of side contraction to elongation —

averages 0'35.

Weight = 490 Ib. per cubic foot = 0'28 Ib. per cubic inch.
Sp. gr. = 7-84.

The expansion per 1° F. = 0'0000067 of the length.
The expansion per 1° C. = 0'000012 of the length.
The sp. heat is 010983.

Temperature for carbonising is 800° -900° C. or 1470° - 1550° F.
Temperature for hardening must be above the A point (at which recales-

cence occurs) = 700° or more.
Temperature for tempering hardened steel tools —

Temper Colours — Straw Yellow Brown Light Purple Purple Dark Blue Pale Blue

Temperature in 44Q 4go 510 530 550 570 60o

degrees F.
Slightly overstrained steel can be restored by annealing at the boiling

point of water.
Units, &c. —

Circumference of Circle = ^ = 3.141592654 _ or 3.1416 or ^ (nearly).

Diameter

1 inch = 2-539998 cm. I 1 cubic inch = 16'38702 cubic cm.

1 square inch = 6*451589 square cm. j 1 Ib. - '45359 kilogramme.
1 electrical unit (Board of Trade unit of electrical energy) = 1 kilowatt

hour = 100° or 1'34 of 1 h.p. hour.

746

1 h.p. = 550 ft.-lb. per second = 33,000 ft.-lb. per minute.
1 British thermal unit (heat required to raise 1 Ib. of water at 39° F.

1° F.) = 778 ft.-lb. (Joule's equivalent).

INDEX

ABRASIVES, 17-24, 42, 430

artificial : alundum, 22, 42, 430

carborundum, 21, 42, 430
grading fine, 387
natural corundum, 21, 42, 430
emery, 20
gritstones, 18
Accuracy, basis of, in grinding, 13, 15,

16
in grinding, 4-8, 226, 255-258,

420-425

in lapping, 390-391, 395
is naturally enforced, 4-5
of machines, 11, 226-227, 255-

258

of reversing, 116-117
Allowances, castings, 308
drop forgings, 214, 308
for finishing, 218, 235
for lapping, 390

in manufacturing, 5-10, 215, 216
in turning for grinding, 215, 217,

426

Aloxite. See Alundum
Alundum, 21, 42, 430
Annealing, 93, 438
Arc and area of contact, 61-64, 69,

73-74, 261

Automatic cross-feed, 119, 162-172
cross-feed throw-out, 119, 163-

164

reversing mechanism, 155-162
steady, 176-177

BALANCING, 35, 36, 105-110, 226

wheels, 35, 36
Ball bearings for spindles, 142, 143, 355

slip occurrence, 143-145
Balls, grinding, 382
Bearings, 124-130, 138-140, 142-145,

384-386
Belts, centrifugal effect in, 148, 149

for internal grinding spindles, 260

laces, 227

polishing, 313, 386
Bonds, elastic, silicate, and vitrified,
25-28

selection of, 45-48, 429-430

wheel speed dependent on, 28-31
Brass, 42, 428-430

Bright drawn steel, 92, 382
Broaches, 239, 344
Bronze, 42, 428-430
Brown & Sharpe tapers, 437
Brownian Movement, 388
Burnishing, 387

CALIPERS, micrometer, 407-411

Cam grinding, 372-374

Capstan work, allowances in, 215,

216, 426

Carbonising steel, 216-218, 438
Carbons, diamonds, 39
Carborundum (carbide of silicon), 21,

42, 430

Carriers, 218-219, 226
Case-hardened work, 72, 73, 216-218

438
Cast iron, 45, 428, 430

and embedded grit, 44
Castellated shafts, 361
Centre grinding heads, 189

holes, 213, 214, 221
Centres, 218, 226

square, 219

Chains, driving by, 291, 380-382
Change of work shape, 88, 90-93, 307
Chatter, 98-105, 227-228
Chilled iron, 420, 428-430
Chips in grinding, 14, 55-65, 70-72
Chucks, distortion caused by, 258

magnetic, 297-302

split, 258, 259
Clearance, grinding with cup wheels,

338-342, 435

disc wheels, 325, 326, 331-
333, 334-338, 434

of cutters, 316, 317, 319

secondary, 319, 320, 335

simplified setting, 333, 343
CoUars, grinding, 277, 278, 358, 359
Collet, for wheels, 145-148

mechanism in Universal grinders,

280

Combination grits, 24, 428, 430
Concave surfaces, grinding, 303, 304
Connecting-rod pins, grinding, 247
Controlling factor in disc wheel
grinding, 67-68

440

INDEX

Corners, nicking in, 221, 277
Corundum, 21, 42, 430
Costs, 10, 237

Crankshafts, grinding, 215, 231-233
Cross-feed, 52, 65-69, 74-78, 263-269
automatic, 119, 120, 162-172,

211, 225, 226
elimination of backlash, 170-172,

380, 382

Crystolon. See Carborundum
Cup and cone grinding, 356-360
Cup wheels, action of, 81-83
bevelling, 83, 315
chips from, 55-57, 83
chucks, 129-131, 147-148
grade, 47, 48, 82, 83
machines using, 292-297, 313
Cut, depth of, 52, 65-69, 74-78, 119,

263-269
Cutters, angular, 332, 337, 338, 341,

342
clearance, 315-317, 319, 325-326,

331-333, 338-339
parallel, 320, 321
sharpening, 314-350, 372
tables for setting, 434, 435
types of, 315, 316
Cylinder grinders, 239, 245-257
feed of wheel, 245-255
grinding, 252, 253

times, 269
Cylindrical work, grinding allowances,

215-217, 426
lapping, 394, 395

DEAD centres, advantages of, 89, 110,

189

gears, 197, 228
pulleys, 189, 280
Decimal equivalents of fractions, 436

metric, 436
Defective work, causes, 89-93, 226-

229, 255-257

Diameter of wheel, influence on
work speed, 69, 263-267, 433
of work, influence on work speed,

69, 76-79, 433
influence on grade, 77-79
Diamonds, 38-41

effect of blunt, 40

laps, 40-41

setting, 39^0

tools, supporting, 150, 151, 268,

361, 367
Difficulties, due to wheel wear in

internal work, 263-268, 433
glazing, 52, 74, 75, 224
untrue work, 89-93, 226-229
wasting of wheel, 52, 74, 75, 223

Disc grinders, 306-313

with rotation work head, 311

with two wheel heads, 313
Disc wheel, chips from, 56, 59, 65-67

theory of action of, 52-81
Disintegration of wheel face, 14, 15,

25, 26, 237

Distortion of work — heat effects, 87,
90, 243-245, 307, 312

in internal work, 243-245, 258

strain effects, 90-94
Double head grinder, 313
Dressers for wheels, 37, 38
DriU grinding, 218, 302, 303, 350, 351
Driving of machines, 120-122, 190-

211, 241, 242
Drop forgings, 215, 308
Dry grinding, 84, 87, 243, 307, 315
Dust, 85, 286, 287

ECONOMY, 235, 237
Elastic bond, 27, 28, 45, 383, 428-430
Electricity, use of, in cross -feed throw-
out, 164

in driving machines, 204-208
in magnetic chucks, 297-306
in measurement, 403
Emery, 20
End and line measurement, 400, 401,

404, 405

End mills, sharpening, 334, 335
End thrust bearings, 128-130
Errors, due to change of work axis,

88-89
due to machine, 226-227, 255,

256

due to release of stress, 90-93
of roundness, 89, 231
Expansion, of work, 88, 244, 245

of steel, 87, 438
External (plain) grinding, times for,

236, 237, 418-420, 426
wheels for, 42-48, 428, 430

FACE cutters, sharpening, 334, 335
Face grinding, 60, 61, 81, 83
Finish, as affected by grit, 43
Finishing speeds, 50, 51, 79, 225
Fits, allowances for various, 423-425
Flat surfaces, grinding, 280-283,
285-297

lapping, 391-394
Follow rest, 178
Forced fits, 5, 6, 423-425

vibration, 103-105, 227
Forces involved in grinding, 70, 71

INDEX

441

Form grinding, 165-166, 225, 232,

356-372

Formed cutters, sharpening, 344-347
Fractions and decimal equivalents,

436

GAUGES, flat, 395, 406
limit, 5-10, 411-415
making, 119, 396, 413, 414
standard, 406

Gear cutters, sharpening, 344-345 '"
grinding teeth of, 361-368
setting for grinding holes, 259

Glazing of wheels, 52, 74, 75, 224, 263,
267

Grade of wheels, 14, 18, 25-31, 45-48,

427-430

and strength, 30, 31
effect of changed, 78, 79
machine's influence on, 48
selection of, 47, 48, 427-430
table of comparative, 427

Graduation of machine tables, 181

Grinding, allowances for, 5-10, 215,

216, 426
arc of contact in, 61-65, 69,

73-74, 261

black work, 214, 308
characteristics of, 1, 3, 10, 11
controlling factor in, 52, 67, 68
dry, 84, 87, 243, 307, 315
finishing, 235, 236
flat work, 280-283, 285-297
form, 165-166, 225, 232, 356-

372

hardened steel, 72
internal, 239-269
magnitude of quantities in, 69, 70
plain (external), 213-238
quality of surface, 43, 232, 245
reasons for its adoption, 416, 417
shoulders, 97, 221, 277, 278
slender work, 229-231
solutions, 86, 87, 218, 438
surface, 285-297
temperature rise in, 71, 72
theory of, 52-83
times, 236, 237, 268, 269, 426
wet, 85-87, 243, 244

Grindstones, 17-20

Grit, 14, 24, 25, 43, 44

Bilston and Derbyshire, 18, 19
embedded in work, 44
finish corresponding to, 43, 44
protection against, 85, 134
size of various, 24, 25

Guards, table, 120, 181-188
wheel, 152

HARDENED work, grinding, 72
Hardness, 17, 20

Mohr's scale of, 438
Headstocks, plain, 188-197

secondary, 219
Heat, effects of, 71, 226

thermal unit, 438
Hobs, sharpening spiral, 345, 346,

372

Hole, basis of limits, 6-10
Holes, gauging, 410-414

lapping, 395

production of, 239

test for parallelism, 257, 258
Hollow work, 220, 281

INCH, fractions and decimals table,
436

and metric conversion table, 436
Internal grinders, 239-255
Internal grinding, measuring tools
for, 410-414

narrow wheels, 267

regimen variable, 263-267

spindles for, 134-143

times for, 268, 422

wet, 243, 245

wheels for, 262, 268, 428, 430

work speeds, 263-267, 433
Internal work, lapping, 395
Iron, cast, 42, 428-430

chilled, 428-430

JIGS, 259, 309, 311, 383, 413
KEYWAYS, 214

LAPS, 40, 392-395

Lapping, 1, 2, 4, 231, 387-397

accuracy of, 395, 396

allowances for, 390

cylindrical work, 394-395

flat work, 391-393

internal, 395

machines for, 389

principles of, 389-391

spherical work, 391
Lathe finish, 235

work, 215, 216, 426

tool sharpening, 353-355
Limits, 5-11

gauges, 6, 7, 411-413

on hole or shaft basis, 6-10

tables for various fits, 422-424
Link grinding, 374-376
Loading of wheels, 223
Lubrication of spindles, 131-134, 385

442

INDEX

MACHINE bodies, 178-179
Magnetic chucks, 297-301

action of, 297-300

secondary pieces, 305
Mandrils, 220
Manufacturing grinders, special, 376-

380
Marks on work, chatter, 98, 227-231

from gears, 219J

travel, 95, 96

Maximum output, 68, 69, 78, 79,
225, 234

wheels for cutter sharpening,

336-338, 429
Measurement and its basis, 398-416

English and metric conversion,
436

of holes, 412-414

Measuring rods (spherical ends), 413
Metal slitting saws, grinding, 301-305
Micrometers, external, 407-409

internal, 410-411

truing anvils, 393-394

use of, 409

Microphotographs, 19, 23, 27, 54, 56
Milling cutters, sharpening, 313-346
Mirror, used on large grinders, 208
Mohr's scale of hardness, 438
Morse tapers, table, 437

NORMAL material velocity, 57, 58,

65-69, 75
Nozzles, 153-155

OIL, on wheel, 245

Oilstones, 17, 18

Ordering wheels, data for, 36, 430

Output, 68, 69, 78, 79, 225, 234

PARALLEL work, 222, 230, 257
Pause at reverse, 96, 97, 161
Plain grinders, 180-213

development, 180

characteristics, 180-181

driving, 190-211

use of, 218-236

Planer tools, grinding, 353-355
Polishing, 384-387

belts, 386

lathes and spindles, 384-385
Power, 12, 237
Preparation of work, 213-218
Protection against grit, 85, 134
Pumps, suitable for grinders, 153,

154
Push fits, allowances for, 423-425

QUALITY of surface, 43, 51

RADIUS truers, 232-234

Reamers, land in, 316

Repetition work, 165, 229, 235,

418-421
Rests for cutter teeth, 322, 323

for steady, 120, 172-178
Reverse, accuracy of, 116, 117

cushioned, 162

mechanism of, 155-162

stops (or dogs), 161
Rods, grinding, 178, 380-382
Roll grinder, 208
Running fits, limits for, 423-425

SAWS, grinding, 301
Screws, lapping, 396
Selection of wheels, 42-48, 428-430

of machines, 417
Self-contained grinders, 201-212
Setting cutters for clearance, 325, 326,

331-333, 338-344
tables for, 434-435
work parallel, external, 221. 222

internal, 257
Shaft basis of limits, 8
Shafts, grinding, 380-382
Sharpening cutters, 314-350

clearance with cup wheels, 338-

344

with disc wheels, 325, 326
direction of wheel rotation, 336
end miUs and face, 331-335
gear and formed, 344-346
hobs, 345, 372
incorrect methods, 317, 318
Sharpening lathe and planer tcols,

353-355
reamers, 316
taps, 347

twist drills, 350-352
Shoulders, facing, 97, 221, 277, 278
Silicate bond for wheels, 28, 45
Silicon, carbide of, = carborundum, 21,

42, 430

Slender work, grinding, 229-231
Solutions for use in grinding, 86, 87,

218, 438

Speeds for wheels, 28-32, 48, 49, 431
for work, 49-51, 74-79, 223-225,

260-268, 291-292, 432^33
Spherical surfaces, lapping, 391
Spindles, wheel, 123-143

driving by chain, 149, 291, 380
Split chucks, 258, 259
Springing of work for grinding, 229-
231

INDEX

443

Square centres, 219

shafts, grinding, 283
Standards of measurement, 398
Steadies, 120, 172-178, 380, 382
""automatic, 176, 177
"object of, 228, 229

screw type, 175, 176

slender work, springing by, 229,
230

spring type, 173-175
Steel, expansion of, 87, 438

grinding hardened, 72

miscellaneous data, 438

wheels for grinding, 42, 428-430
Stops, reversing, 160, 161

setting reversing, 221
Straightening, effect of cold, 90-92
Strains, initial, 90-93
Strength 'and speed of wheels, 28-31

effect of sharp corners, 221

of wheel material, 30, 31
Stress, effects of, 90-93, 226
Surface grinders, 285-297 I

grinding, work speeds, 291, 292
Surface, quality of burnished, 387

ground, 1, 43, 51

lapped, 2, 387

polished, 2, 386, 387

TABLES, guards for, 120, 181-188

sections of, 181-186, 233
Tables I-XIV, 423-437
Tailstocks, use of spring adjustment,

88, 221
Tapers, by swivel-ing wheel slide, 117-

119

work table, 113-115
grinding double, 275-277
in cylinders, 252
tables of, 437

Tarry at the reverse, 96, 97, 161
Teeth of cutters, sharpening, 314-350
Temper, drawn in grinding, 315

colours, 438

Temperature effects, 71, 87-90,226, 307
Tension idler pulleys to wheel belt,

190, 201

Theory of grinding, 52-83
Times for external (plain) work, 236,

237, 418-421

internal work, 268, 269, 422
Tolerances, 5-7
Tool grinders, 153, 353-355
Tool steel work, 214
Tooth rests for cutters, 322-324
Travel marks, 95, 96
Travelling the wheel or the work,
112-113

Traverse, action of, 80

marks on work, 95, 96

motion, driving, 190-192

rate of, 94-96
Truing wheels, 37, 38, 150-152

for formed grinding, 232, 233,

358, 363

Turning, allowances for grinding,
215, 216, 426

for case hardening, 216-218
Twist drills, grinding, 218, 302, 303

sharpening, 350, 351

UNIVERSAL cutter holders, 349, 350
grinders, 3, 110-122, 270-275
swivelling crossways, 117-
119, 275

VIBRATION, 52, 76, 98-105, 227-231

causes of, 104, 105, 227

checking, 179, 227-231

damping, 102

forced, 103-105

free, 98-103

Vitrified bond for wheels, 26, 27, 45,
429, 430

WATER in external (plain) work,

85-87, 90, 120

in internal work, 243-245, 260
solutions used, 86, 87, 218, 438
supply, 226
Wave-length of light in measurement,

399

Ways, types of, 115
Wheels, abrasives, 17-24, 42, 430
action of, 12-14
and the work, 42-83
area of contact of, 61-64, 69,

73, 74, 261
balancing of, 35, 36
bonds for, 25-28, 429, 430
chips from, 14, 55-65, 70-72
collets for, 32, 33, 145-148
cutting points on, 53-55
density of, 438
direction of rotation, 49, 336
dressers for, 37
effect of diameter on work speeds,

265

elastic, 27, 28, 45, 383, 428-430
examination of, 32, 48
face of, 27, 54, 77
glazing of, 52, 74, 75, 224, 263,

267
grades of, 14, 18, 25-31, 45-48,

427-430
tables of comparative, 427

444

INDEX

Wheels, grit of, 14, 24, 25, 43, 44
guards for, 152
gyroscopic effect of, 262
hardness of = grade
holes, standard, 37]
inserted segment, 34
for internal work, 262, 268
limiting diameter for cutter

sharpening, 333, 336-338
mounting of, 32-35, 222
ordering, 36, 430
selection of, 42-48, 428-430
shaped, 36 <
silicate, 28, 45
soft, advantages of, 238
speed of, 28-32, 48, 49, 431
effect of, 80
limitation of, 28, 29
peripheral should be constant,

spindles, 123-143
strength of, 28-31
truing, 37, 150-152, 222, 232,

233, 358

vitrified, 26, 27, 45, 429, 430
wear of, checking, 52, 74, 75,

223, 263-267
why truth is so necessary in, 13,

94-97

wide, advantage of, 13
width of, for internal work, 260-

262, 267, 428, 430

Work and the machine, 84-122

case hardened or carbonised,

216-218, 438

driving the, 199, 204, 218-220
handled more than once, 223
hardened, 72, 73, 218
holding for internal grinding,

258-260
hollow, 220
parallel, external (plain), 219-222

internal, 257
preparation of, 213-218
repetition, 165, 229, 235, 418-

421

spindle, live, 278-280
slender, 229-231
speeds, 49-51, 74-79, 260-268,

432, 433
effect of wheel diameter,

265-267

of work diameter, 74-79
finishing, 50, 79, 225
illusion of standard, 79
in internal grinding, 263-

267, 433
methods of changing, 190,

212

modern and former, 49, 50
selection of, 49-80, 224,

260-267,432,433
taper, 113-119, 275-277
Worm grinding, 369-372

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