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Digitized by tine Internet Archive
in 2010 with funding from
NCSU Libraries
http://www.archive.org/details/cottonspinningcaOOwint
COTTON SPINNING CALCULATIONS
AND YARN COSTS
COTTON WEAVING AND DESIGNING. By
John T. Taylor, late Lecturer on Cotton Weaving and
Designing in the Preston and other Technical Schools.
Revised under the direction of F. Wilkinson, Director of
the Textile and Engineering School, Bolton. With 402
Diagrams, Crown Svo, "js. 6d, net.
THE ELEMENTS OF COTTON SPINNING.
By John Morris and F. Wilkinson. With a Preface
by Sir B. A. Dodson, C.E., M.I.M.E. With 169 Diagrams
and Illustrations. Crown 8vo, "js. 6d.
PRINCIPLES OF WORSTED SPINNING. By
Howard Priestman. With 118 Illustrations. Svo,
7^. 6d. net.
WILD AND CULTIVATED COTTON = PLANTS
OF THE WORLD : a Revision of the Genus Gossypium,
framed primarily with the object of aiding Planters and
Investigators \\ ho may contemplate the Systematic Improve
ment of the Cotton Staple. By Sir George Watt,
C.I.E., M.B„ CM., LL.D. (Abd. and Glasg.), F.L.S.,
formerly Professor of Botany, Calcutta University, and
Reporter on Economic Products to the Government of
India. With 53 Plates, 9 of which are Coloured. Royal
Svo, 30i". net.
JACQUARD WEAVING AND DESIGNING.
By F. T. Belt., Medallist in Honours and Certificated
Teacher in " Linen Manufacturing" and in "Weaving and
Pattern Designing," City and Guilds of London Institute.
^^'ith 199 Diagrams. Svo, 12^. net.
LONGMANS, GREEN, AND CO.
LONDON, NEW YORK, BOMKAY, AND CALCUTTA
COTTON SPINNING CALCULATIONS
AND YARN COSTS
A PRACTICAL AND COMPREHENSIVE MANUAL OF
CALCULATIONS, YARN COSTS, AND OTHER
DATA IN\'OLVED IN ADAPTING THE
MACHINERY IN ALL SECTIONS, AND FOR ALL GRADES,
OF SPINNING AND DOUBLING
JAMES WINTERBOTTOM
LECTURER IN COTTON SPINNING, MUNICIPAL SCHOOL OF TECHNOLOGY, MANCHESTER
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
1907
All rights reserved
PREFACE
The aim of the author of this work has been to provide the
student with particulars of the gearing in all the machines
involved in Cotton Spinning, together with a method of calcu
lating the trains of gearing. These are accompanied by suitable
examples and exercises.
Existing works containing Spinning Calculations appear to
deal with this subject in a manner too abstract for the average
student. In this book the details connected with the calcu
lations and essential in changing the conditions of working, are
fully given.
The effects of twist in yarn are introduced in consideration
of its importance and in the hope of stimulating further investi
gation of its working.
The yarn costs are dealt with particularly to assist students
preparing for the City and Guilds of London Institute examina
tions in Cotton Spinning.
MANCHESTER, ^^,^ ^ \ ) '
Aurjust, 1907. \ J \
^^
UBRABY 01?
K. Ci STATE COIiliB^MB
S5I5
CONTENTS
TRANSMISSION OF MOTION
PAGE
Ascertaining the rate— Direction — Sizes — Effects of changes — Examples
and exercises 1 — 15
COTTON MIXING
Balebreakers or cotton pullers and distributors — Their object — Types —
Actions — Capacities — S^ieeds — Drafts — Merits and demerits — Examples
and exercises — Notes on the stack and direct niethods .... 15 — 25
OPENING AND SCUTCHING
Openers — Gearing — Speeds— Methods of feeding — Drafts — Lap weight — Ex
amples and exercises — Scutchers — The gearing — Speeds — Drafts — Lap
weight— Production — Lap length motions — Changes in speed, weight,
and cotton — Examples and exercises — Positive, semi, and nonpositive
draft connections — Nonstop working — Controlling factors— Speed of
beaters and fans — Sizes of feed rollers — Overscutching and other defec
tive treatment 25 — 56
CAEDING
Cards— The gearing— Speeds— Drafts— Alterations— Functions of parts
Conditions controlling efficiency — Rate of movement of flats — Wrapping
— Names applied to cotton in the processes — Counting cotton — Card
clothing, counting, preparation for mounting, character of its points —
Examples and exercises 56 — 76
PREPARATION FOR, AND COMBING
Sliver lap machine — Object — Names and functions of parts — Gearing —
Speeds — Drafts — Production — Examples and exercises .... 76 — 80
Ribbon lap machine — Object — Names and functions of parts — Gearing —
Speeds — Drafts — Production — Examples and exercises .... 80 — 84
VUl CONTENTS
PAGE
Combing — Alternative preparation of laps — Objects of combing — The
Nasmith comber — Speeds — Drafts, and the limitations in range —
Weights of sliver and waste — Examples and exercises 84 — 95
The Heilmann comber — Differences of the duplex and Nasmith^ — Speeds —
Drafts — Attaching, how adjusted — Draft restrictions — Items controlling
the efficiency — Examples and exercises 95 — 102
ATTENUATING AND EQUALIZING (THE
DRAWING PROCESS)
The drawframe — Objects — Number of heads useful — Object and mode of
testing slivers — System of " putting up " — Allocating the drafts —
Spacing the sliver — Speeds, drafts, counts and production — Suitable
sizes of rollers — Analysis of systems of roller gearing — The arrangement
of heads — A mode of ascertaining the total draft — Examples and
exercises 102 — 110
ATTENUATING (THE FLYFRAME PROCESSES)
The objects of the fly frames : slubber, intermediate, rover and jack — The
necessity for repetition— The object of twisting — The direction of twist
ing, its influence — Twist constants — The gearing in these frames —
The names and functions of parts — Effects of altering the cone train —
Changes in speed, draft, count, twist and spacing — Examples and
exercises — Cone drums and differentials — Reasons for a differential train
of fixed value 110—141
Analysis of the action of drawing rollers with deductions .... 152 — 154
SPECIFICATION OF CONDITIONS IN CARDING
DEPARTMENT
Suitable counts and spindle speeds — "Preparation" defined — Counts practi
cable with the available machinery — Factors controlling the allocation
of the total draft — Examples and exercises — Hank indicators
141—152, 154—156
Full bobbin measuring motions 156
SPINNING
The mule — Description and functions of parts — Twist constants — Factors
controlling the value of all trains — Examples of speeds, twist, draft,
count, builder, gain and production— Gearing in mules by Dobson and
Barlow, Hetherington, Piatt, Trelfall — Jacking, slow roller, double
speed, twisting, hastening, backingoff and takingup and other motions
— Comparison of actual speeds and productions with calculated — Losses
in driving — Use of the tachometer and tachoscope — Hank and other
indicators — Tables of productions 156 — 204
CONTENTS IX
PAGE
The ring frame — Geariug — Speeds— Draft— Twist and other changes—
Examples and exercises — Comparison of calculated with actual speeds
and productions— Losses in driving — Table of productions— Conditions
favourable to ring spinning— The influence of twist on the output 204—213
YARNS
Twist standards for single— Effects of twist in single— Relative breaking
resistance in single 214 216
Twist standards for various kinds of folded yarns— The influence of the
direction and extent of twist in the singles upon the strength and other
features of the folded yarn— The aims of doubling— Equilibrium in
folded yarns— Features developed in folding— To ascertain the suitable
twist 216—224
DOUBLING
The ring doubling frame— Gearing— Speeds— Twistproduction— Examples
and exercises— The twiner mule— Gearing — Speeds— Twistproduction
— Examples and exercises 224 — 230
Winding— Keeling 247—249
COSTS OF YARN
Total and details of expenses— Examples of costing— Comparison of cost
Yarn from single and double roving — Combed qualities — Ring yarn —
Cotton and yarn price lists — Cost of power space— Power required
Extra cost of combing — Departmental costs 231 — 247
INDEX 251
COTTON SPINNING CALCULATIONS AND
COSTS OF YARN
Tkansmissiox of Motion
The Method of calculating the Rate of Motion, when Tooth Gear is
employed. — When wheels are employed in a simple or direct
train, as in Fig. 1, their move
ment, in teeth or circumferen
tially, is alike. Their axial
movement differs only when
the wheels are not alike in
size. This difference is, rela
tively, inverse to their teeth pj^ j
contents. This is proved by
assuming that the wheels A, B, C, and D in Fig. 1 contain
100, 75, 50, and 25 teeth, respectively, and that the first
mentioned moves one revolution. Thus, the wheel A moves
to the extent of 100 teeth, and since its teeth gear with those
of B, and the latter with C, and these also with D, then each of
them will move tooth per tooth of A, and therefore each will
move 100 teeth. Hence, their respective axial movements will
be—
A = lor};}l B = WorU
C = JgOf or 2 D = ^Si or 4
The preceding results show that the axial movement or revo
lutions of wheels, under such conditions, are inversely pro
portional to their relative teeth contents, and therefore as
follows : —
B
fiSOmCTY UBRARY
mr r Qf^ffi C
COTTON SPINNING CALCULATIONS
Tooth contents.
Ratios of their revolutions.
A
B
100
75
1
n
or
75
100
A
C
100
50
1
2
or
50
100
A
D
100
25
1
4
or
25
100
B
C
75
50
1
n
or
50
75
B
D
75
25
1
3
or
25
75
C
D
50
25
1
2
or
25
50
The Direction of the Movement of Tooth Wheels. — In simple
direct trains of wheels this is always respectively alternate.
This is seen on reference to Fig. 1. By numbering the wheels
in their respective numerical order, it is seen that those having
odd numbers will all rotate in the same direction, and reverse
to those having even numbers.
The following are examples in the application of the afore
mentioned points in respect of Fig. 1 : —
Example I. — Assuming A revolves 100 times per minute, at what rates
would B, C, and D rotate in that time ?
Example II. — Assuming B revolves at the rate of 100 per minute, give the
rates of A, C, and D in that time.
■ Example III.— Assuming C makes 100 revolutions, how many would A, B,
and D make ?
Example IV. — If D made 100 revolutions, how many would A, B, and C
make?
Answers —
Example I. — The movement of A expressed in teeth per minute would be
Eevolutions of wheel x number of teeth it contains, this = 100 x 100, which
AND COSTS OF YARN 3
number of teeth B, C, and D must likewise move, and therefore the number of
teeth moved, per minute, by B divided by the number of teeth which it contains,
will give its revolutions in that time.
.*. =v = 133^ revolutions per minute of B
Similarly —
The revolutions per minute of C = ^^ = 200
_ 100 X 100 ._
» » D = 25 ^
Example II. — The number of teeth which B moves per minute = 100
revolutions x 75 teeth, and this number A, C, and D must consequently move,
and therefore —
The revolutions per minute of A = — ^tctt — = 75
Example III. — The number of teeth which C moves are 100 x 50, which
number A, B, and D must also move, and therefore —
rvu ^ r f ^ 1^0 X 50 _
The revolutions or A = — r^^^ — = oO
„ „ D = 15^° = 200
Example IV. — The number of teeth moved by D are 100 x 25, and
therefore A, B, and C will move a like number ; therefore—
The revolutions of A = — , ... " = 25
100 X 25 _ 1
100 X 25 _ .
^  ~50
Tlie Relative Rates of Rotation of the Wheels comprised in any
Direct Train are respectively inverse to their Teeth Contents. — This
is seen to be the case in all the preceding examples. Thus in —
COTTON SPINNING CALCULATIONS
Answer to Example I. —
A:B:
: 100:
; 1331,
or
as 1
n
A:C:
: 100:
;200
!>
1
:2
A:D:
: 100:
:400
))
1
:4
Answer to Example II. —
B : A:
:100;
: 75
»
n
: 1
B:C :
:100:
;150
>)
1 ;
:li
B:D:
: 100:
300
»
1 :
;3
Ansiver to Example III. —
C :A:
:100:
: 50
>J
2:
: 1
C: B:
:100:
: 66
J>
U:
1
C:D:
:100;
;200
V
i :
2
Answer to Example IV. —
D: A:
: 100:
:25
))
4 :
: 1
D:B:
: 100:
;33i
}1
3:
1
D:C:
: 100:
50
)1
2:
1
Examples in Respect of the Direction of Rotation. — In Example I. commence
by numbering A, 1 ; B, 2 ; C, 3 ; D, 4 ; thus A and C move in the opposite
direction to B and D.
In Example II. commence by numbering B, 1 ; A, 2 ; C, 2 ; D, 3 ; thus A
and C move reverse to B and D,
NoTK. — The reason for numbering A and C the same is because that is their
relative order.
In Example III. commence by numbering C, 1 ; D, 2 ; B, 2 ; A, 3 ; thus C
and A move in the opposite direction to D and B,
In Example IV. the numbering is D, 1 ; C, 2 ; B, 3 ; A, 4 ; thus D and B
move in the opposite direction to C. and A.
Direct and Indirect Trains. — When wheels are arranged in an
indirect train! (composed of two or more simple trains), as con
tained in Fig. 2, the conditions of
transmission differ from those obtaining
in direct trains as contained in Fig. 1.
The difference in Fig. 2 consists in
the wheels B and C being united and
have a common axis. These must
therefore revolve together. Motion
from A to D is imparted to the rim
of B by that of A, thence from the
rim of B to its hub, and thence to
the rim of C, and from this part to the rim of D.
The effects of B and C being so coupled are that their
Fig. 2.
AND COSTS OF YARN 5
movement iu teeth is only alike when they contain the same
number of teeth. Their relative movement in teeth differs in
the direct ratio of their teeth contents. Thus, if in Fig. 2,
A, B, C, D contain 40, 20, 60, and 20 teeth respectively —
The revolutions of A will be to those of B
j» jj ^ j> 5> L^
20 : 40, or as 1 : 2
1 : 1
20 : 60, or as 1 : 3
This shows, in two only of the three instances that the
relative rotation is the inverse of their dimensions, and hence
the rule, " revolutions of wheels are relatively inverse to their
teeth contents," is only applicable in respect of direct trains of
wheels.
Fig. 2 is an indirect train, and comprises two direct trains
of wheels, namely, AB and CD. The effects of their combination
may be ascertained by multiplying their separate values,
together, thus —
2x3 = 6
or the movement of A : D : : 1 : 6
If A, therefore, made 20 revolutions, the movement of D
in revolutions would be 20 X 6 = 120, because A and B would
move 20 X 40 teeth, and therefore B and C would make
20 X 40 1 , . r^ ;i T^ n 20 X 40 X 60 , ,,
— ^ — revolutions, C and D would move ^7) teeth ;
and therefore the revolutions of D would be — ^ ^^ — = 120,
ZO X zu
or the value of the train multiplied by the revolutions of its
first wheel.
The following is a summary of the foregoing deductions in
respect of —
Direct Trains of Wheels. — 1. The circumferential or teeth rate
of the movement is alike in all the wheels comprised in a direct
train of wheels.
2. The rate of rotation is relatively inverse to the circum
ference or teeth contents of the wheels comprised in a direct
train.
6 COTTON SPINNING CALCULATIONS
3. The direction of rotation is alternate at each successive
wheel, and when numbered in progressive order, the direction
of the oddnumbered wheels will be alike and opposite to those
which are even numbered.
Indirect Trains of Wheels. — 4. The circumferential or tooth
rate of the movement is alike only in those wheels comprised
in each of the several direct trains which constitute any indirect
train.
5. The rate of rotation is relatively inverse to the tooth
contents of those wheels comprised in each only of the several
direct trains of which the indirect train is constituted.
6. The direction of rotation is alternate at each successive
wheel in any one only of the several direct trains which con
stitute the indirect train.
7. The direction of rotation is alternate throughout an indirect
train when those wheels which are fastened to each other, by a
shaft or other coupling, are regarded, when numbering, as only
one wheel : thus in Fig. 2 the wheels A, B, C, D would be num
bered 1, 2, 2, 3 respectively, so that the direction of B and C
would be that opposite to A and D.
8. The circumferential rate as well as the relative rotation,
in indirect trains, is ascertained by treating them as so many
simple trains as they may comprise.
Classification of Wheels. — When the function of a wheel is to
convey motion from hub or axle to rim, and therefrom to another
wheel, it is termed a driver.
When the motion is received at the rim, from another wheel,
and passes thence to its hub or a^le, it is designated a driven
wheel.
When the function of a wheel is merely to convey motion
along its rim from wheel to wheel, it is termed a carrier wheel,
but when such a wheel has also to transmit movement to its hub
or axle, for driving some other part, it would also be termed a
driven wheel, but only in respect of the latter connection.
Examples in the Classification of wheels in Figs. 1, 2, 3 —
Fig. 1, assuming the motion flowing from A to D —
A is a driver (motion flowing from the axle to rim).
AND COSTS OF YARN 7
B is a carrier (motion flowing merely^along the rim).
n
^ )> jj )j >>
D is a driven (motion flowing from the rim to the axle).
If the motion was from D to A then —
D would be a driver.
C ,, carrier.
B „ „
A ,, driven.
Fig. 2, assuming the motion passing from A to D —
A would be a driver.
B ,, driven (the motion here passes to the axle)
C ,, driver (the motion here passes from axle to
the rim).
D would be driven.
If the motion passed from D to A the above functions would
be reversed.
Fig. 3, assuming the motion passed from A to E, and G —
A to E : A would be a driver.
B ,, carrier.
C ,, driven.
D ,, driver.
E ,, driven.
A to G : A and F are drivers.
B and G are driven.
Examples in respect of the direction of rotation with the motion
as stated above —
Fig. 1. — A and C, their numbers respectively being 1 and 3 ;
B and D, their numbers even 2 and 4, their direction being
opposite to A and C.
Fig. 2. — A and D the same direction and positive (since their
progressive numbers are, according to the definition, odd numbers
positive and even numbers negative) ; B and C being numbered
2, 2, and therefore negative.
Fig. 3. — The numerical order of A, C, D, G, is 1, 3, 3, 3
8
COTTON SPINNING CALCULATIONS
respectively, and therefore in the positive direction ; B, F, E 2, 2,
and 4 respectively, and therefore negative.
The Method of calculating the Value of Wheel Trains. —
A simple method, applicable in direct or indirect trains,
is deduced from the foregoing procedure in ascertaining the
relative movements of the wheels in Figs. 1 and 2. The value
of the trains, in each of those instances, is found by multiplying
the sizes of the driver wheels, in teeth, together for a numerator,
and those of the driven wheels together for a denominator —
the resultant being the value of the train ; or, the relation of
1
4
2
D E
5
G
F
r
3
Fig. 3.
the final wheel in terms of one of the first wheel. This result,
when further multiplied by the revolutions of the first wheel, in a
given time, obtains the revolutions of the final wheel in that time.
Applying this in finding the revolutions per minute of
shafts 2, 3, 4, and 5 respectively, in Fig. 3, when the sizes of
the wheels in teeth, alphabetically, are : 40, 20, 50, 25, 100, 40,
80 ; and (1) is assumed to make 500 revolutions per minute, the
following are the results : —
(1) A is a driver, B a carrier, G is a driven wheel, and
therefore —
The revolutions per minute of shaft (2) = tJ] X 500 = 400
AND COSTS OF YARN 9
(2) A and D are drivers, B is a carrier, C and E are driven
wheels, and hence —
Revolutions of shaft (3) per miaute = fg X ,%'^o ^ ^0^ = 100
(3) Here A is a driver aad B the driven wheels, therefore—
}} X 500 = 1000 revolutions of shaft (4) per minute
(4) Here A and F are drivers, and B and G are driven
wheels, hence —
40 . 40
The revolutions of shaft (5) per minute = ^^ .^^ X 500 = 1333.^
The Effects of changing Wheels. — The effects of changing the
size of any wheel depends upon its function. If a driver wheel,
the axial rate of all other wheels receiving motion from it will be
altered in the direct ratio of the change, because the movement of
the new wheel, in teeth, per revolution, will be altered in that
ratio ; and this will affect all the others depending upon it for
their motion in like terms. Hence, changing A to 30, and
taking the revolutions of A at 500 per minute, would cause —
The shaft (2) to rotate at —
500 X g^, by gear; or,, by proportion :
400 X f g = 300 per minute
The shaft (3) to rotate at —
500 X § X y^fpQ, by gear ; or, by proportion :
100 X fg = 75 per minute
The shaft (4) to rotate at —
500 X f§, by gear ; or, by proportion :
1000 X g = 750 per minute
The shaft (5) to rotate at —
500 X ?,§ X §, by gear ; or, by proportion :
13331 X g = ioOO per minute
In case of a driven uliecl hcing altered, the axial rate of tliose
wheels, dependent upon it for their motion, woidd be affected in the
10 COTTON SPINNING CALCULATIONS
inverse ratio to that change. — Because the rate of movement of its
teeth would be unaltered, because the wheel receives its motion
from the same wheel as hitherto. Its axial rate would be
increased when the new wheel contains less, and diminished if
containing more, teeth. Hence, altering the wheel C to 40 instead
of the wheel A, assuming the latter to make 500 revolutions i^er
minute, would have the following results : —
Shaft (2) would rotate at —
500 X IJ], or 400 X g = 500 revolutions per minute
Shaft (3) would rotate at —
500 X £ X i%\ = 125 revolutions per minute
Shafts (4) and (5) would not be altered.
If B were altered to 30 instead of C, then the following
would be the result : —
Shaf ts'(2) and (3) would not have their speeds affected, because
C would move at the same tooth rate ; thus —
Shaft (4) would rotate at —
500 X II], or 1000 X g = 666§ revolutions per minute
Shaft (5) would rotate at —
500 X *{] X If], or 1333^ X [] = 888 revolutions per minute
The foregoing show that increasing the size of a driver
wheel increases proportionately the speeds of the subsequent
wheels in the train, and vice versa ; that increasing the size of
a driven wheel proportionately decreases the speeds of the sub
sequent wheels in the train, and vice versa. Therefore, to
determine the teeth contents or size of a wheel when it is required
to alter the speeds, the procedure must be as follows : —
In the case of driver wheels : the size of the wheel it is decided
to alter, multiplied by the speed required, and divided by the
existing speed, will give the wheel required, because the size
of this wheel must be altered in the direct proportion of the
present rate to the required rate.
In case of driven wheels : the size of the wheel it is decided
to alter, multiplied by the existing speed, and divided by required
AND COSTS OF YARN 11
speed, will give the wheel required, because the driven wheel
must be altered in the inverse proportion of the present rate to
the required rate.
To determme the sizes or teeth contents of wheels to employ in
a train in order to obtain a specific speed of the final wheel.
Ascertain the value of the train required ; the distance of the
shafts apart ; the space available for the wheels ; the pitch of
the teeth that affords sufficient strength, with due regard to
lightness ; the direction of motion. This latter will decide whether
the number of wheels to employ should be odd or even.
The number of wheels should be as few as possible. The
space available restricts their size.
The distance apart of the two centres multiplied by
2(3*1416) will give the sum of the circumferences of the wheels
required. This divided by the suitable pitch of the teeth gives
the sum of their teeth contents, whatever the number of wheels,
when they are arranged with their centres in a straight line.
If their centres are arranged otherwise, it would be necessary to
determine the sum of their distances apart. The latter would
control the sum of their teeth contents. The contents of each
wheel would then be decided according to the intermediate axial
speeds required.
Under conditions similar to Fig. 2, where the ratio in the train
is 6 to 1 , and the latter has to rotate in the opposite direction
to the former, an odd number of wheels must be employed.
The following would suffice : A, six times the smallest size of D
practicable, and these connected by a suitable carrier, or odd
number of carriers. If there is a wide difference in the sizes of
the wheels this is impracticable, then A, 2*4 times B ; and C,
2*5 times D should be employed.
Exercises. — Ascertain the wheels convenient to secure the undermentionecl
values in the following trains : —
1. A direct train to consist of six wheels with axial motion in the ratios of
1, 2, 3, 4, 5, and 6 respectively.
2. A direct train to consist of three wheels with axial motion in the ratios of
1, I, and 3 respectively.
3. An indirect train of six wheels, comprising three direct trains, with the
axial ratios 1, 16, 3*2, and 8 respectively.
12
COTTON SPINNING CALCULATIONS
4. An indirect train of six wheels, comprising three direct trains with the
difference in axial ratios equally distributed, the whole amounting to 8.
5. An indirect train of six wheels, the whole containing a ratio of 1 : 9, one
of the direct trains to have the value 2C8.
Rope and Belt Driving. — Eopes and belts are extensively
employed in the transmission of motion. The method of
calculating the speeds and sizes of the driving surfaces — pulleys
and drums — is identical with that in wheel gear, the sizes of
the pulleys and drums taking the place of the teeth contents in
wheels ; the measurements usual being in inches or feet
diameter, these measurements being made from diametrically
opposite points of contact of the transmitting medium.
Fig. 4.
Example 1 (Fig. 4). — At what rates per minute would B, C, D, E, F, and
G rotate if the gi'ooved flywheel of the engine A makes 50 revolutions per
minute, was 25 feet, and the others 5, 9, 8, 12*5, 5, and 6 feet respectively ?
Answers —
Eevolutions of B per minute = ;; = 300
5
60 X 25
= 1601
AND COSTS OF YARN 13
Revolutions of D per minute = ^^= 187'5
_60x25_
" ~ 125 ~
_ 60x25 _
" >.  125 ^"^^
p 60 X 25 X 5 ,„„
^ " = 12^^5^6 = ^^^
The reasons for adopting tliis method of determining the speeds of parts
when motion is transmitted by belt or rope gear are as follows : —
The circumference of a drum or pulley or a circle when divided by the
number 31416, gives its diameter; the diameter being easier to measure, it is
customary to ascertain the circumference by multiplying the diameter by that
number. For practical purposes "/ is considered near enough in this kind of
work.
The rate of the movement of the strap in calculating is generally assumed to
be the same as the contact surface of the drum. This, however, varies con
siderably from that rate, according to the working conditions, such as tension,
cohesiveness, and pHability of the belt; distances of the centres apart ; material,
sizes, and shape of drums; amount of load. These are not usually recognized in
making calculations, but are allowed for in general practice.
The rate of the movement of ropes is about the same as the point of contact
in wellconstructed grooved pulleys. In calculating it is not customary to make
an)^ allowance.
The rate of movement of the ropes engaging with the grooved flywheel A
will therefore be the same as that of the pulley at the centre of the part in con
tact with the rope. If this is 12*5 feet from the centre of the pulley, or equal to
25 feet in diameter, the circumference of such a circle would be 25 feet x 3*1416,
and therefore this would be the rate which the rope would move per revolution
of A. In 60 revolutions it would, therefore, move the rope 60 times that
amount, or —
25' X 31416 X 60
The rope moving at this rate about the pulley B, which is 5 feet diameter, or
5' X 31416 in circumference, then the number of times which the length repre
senting the circumference is contained in the length of rope passing over the
pulley in a given time, will be the rate at which it revolves. Therefore —
25' X 31416 X 60 ,, , . , ,• ^ t, onn
f7 TTzrrm — = the rate ot rotation oi 13 = oOO
5 X 31416
Since, in rope and belt gearing, drums and pulleys always work in pairs — a
driver and driven — and these in calculation are always placed on opposite sides
of the equation — when one is the numerator, the other is always the denominator.
The necessity for using the constant 31416, to convert the diameter into the
circumference, occurs just as often a numerator as a denominator, and it always
14 COTTON SPINNING CALCULATIONS
cancel?. It is, therefore, left out of the calculation ; hence the rule is as
follows : —
diameters of drivers revolutions of 1st driver _ ("the revolutions of the last
diameters of driven ^ 1 " I driven drum or pulley
because—
diameters of drivers x revolutions of 1st driver _ ^
diameters of the driven x revolutions of last driven
Example 2 (Fig. 4). — Required the revolutions per minute of F, D, C, B, A
respectively, when, with the gearing as given in Example 1, G is found to
revolve 110 times per minute.
Note. — It is best in working questions of this kind to assume the one moving
at a known rate the driver. This always simplifies the calculation, whether
dealing with rope, belt, or teeth gear.
(1) G is a driver and F driven —
/, = — = 132 revolutions of F
5
(2) G, E, and A are drivers ; F, A, and D are driven —
no X 6 X 125 X 25 ^ 20625 revolutions of D
5 X 25 X 8
(3) G, E, and A are drivers ; F, A, and C are driven—
110 X 6 X 125 X 25 ,„„ • , ,. ^ ^
• — _ = 1833 revolutions of
5 X 25 X 9
(4) G, E, and A are drivers ; F, A, and B are driven—
110 X 6 X 125 X 25 ooA ^ I' eD
xxv/_^ /s^ = 330 revolutions of B
5 X 25 X 5
(5) G and E are drivers ; F and A are driven—
110 X 6 X 125
5x 25
= G6 revolutions of A
Example 3 (Fig. 4).— What sizes of B, C, D, E, and F would be required in
order that their revolutions per minute maybe B, 250; C, 214; D, 187 ; E, 150 ;
G, 100 respectively, assuming A to make GO revolutions in that time, and to
be 25' in diameter ?
Here A is the driver, and the rate of the movement of the ropes will be
GO X 25' X 31416 per minute.
Since B is required to revolve 250 times per minute—
60x25x31416
Circumference of B must be = 059
AND COSTS OF YARN 15
A , FR 9in,' GO X 25 X 31416
or diameter of B x 3lil(j = — ^.^
250
. ,. , .„ GO X 25 X 31410 GO x 25 .,
/. diameter of B = r^ q^ttt^— = oa = ^
250 X 31410 2o0
Diameter of C will be —
60 X 25 _ „,
214
60 X 25 o,
and diameter of D
187
and diameter of E = — — ^ = 10'
loO
In case of F, wliich is also a driver —
GO X 25 X diameter of F
diameter of E x diameter of G
60 X 25 100
= 100 revolutions of F
diameter of E x diameter of G diameter of F
. 60 X 25 _ 1
•• 10 X 6 X 100 ~ diameter of F
.A ^ ct:^ 10 X 100 X 6 .,
/. diameter of F  — ^^ ^ — = 4
60 X 2o
Or, since F and G revolve 150 and 100 respectively, and G is 6 feet in diameter,
and it is known that their sizes must be inversely proportional to those rates,
then —
6' X 100 ,. , „„ ,,
— ^,_ — = diameter of F = 4
150
Bale Breakers or Cotton Pullers. — Fig. 5 is an elevation of the
gearing in a wellknown make of machine of the Roller type.
This type of machine displaced manual pulling, which was
previously in vogue, in reducing the cotton to a suitable
state of mixing. At present this type of machine is used
extensively in old mills which do not make a point of keeping
uptodate. In modern mills a machine known as the Hopper
bale breaker, or cotton puller, is found in place of the former,
the disadvantages of the roller type of this machine being the
dust and noise accompanied by wear and tear and frequent
breakages. Its forcible action, creating heavy pressures upon
the cotton between edged surfaces, are considered to exercise a
16
COTTON SPINNING CALCULATIONS
detrimental effect upon the cotton. There is a great difference
in the principle of the two types of machines named. The
Hopper has a coarse comhing action, and considerable pressures
upon the cotton are eliminated. The productive capacity of a
Fig. 5.
roller pulling machine ranges up to 100,000 lbs. per 55i hours
when worked at the highest pressure. The best results obtainable
are when it is run at a high speed for American cotton and at
a moderate speed for Egyptian and Indian varieties.
The following are the particulars of the parts in the Eoller
cotton puller. Fig. 5 : —
a, the line shaft making 220 revolutions per minute.
h, a drum, 19" in diameter, on the line shaft and driving the
machine strap.
c, c are swing or *' gallows " pulleys.
d represents the fast and loose pulleys on the machine shaft ;
these are 16" diameter.
e, a grooved rope pulley, 19" diameter, fixed upon the
machine shaft, driving a rope which drives the porcupine
cylinder.
AND COSTS OF YAEN 17
/, a grooved carrier pulley for the abovementioned rope.
g, a grooved pulle}^ lOh" diameter, fixed upon the porcupine
shaft and driven b}' the abovementioned rope.
h, a wheel containing 25 teeth, fixed on the machine
shaft.
i, a wheel on the shaft of the lower second pulling roller,
containing 40 teeth, and driven by h.
j, a wheel containing 14 teeth, and fixed upon the axis of i.
h, a wheel containing 76 teeth, and driven by j.
I, a wheel containing 14 teeth, fixed to the axis of k.
Ill, a wheel on the lower first pulling roller, containing
76 teeth, and driven by /.
n, a wheel fixed on the first pulling roller, containing 17 teeth.
0, a carrier wheel, gearing with ii and j?.
}), a wheel on the lattice roller shaft, containing 20
teeth.
q, a grooved rope pulley, 10" diameter, attached to e and
driving /•.
;•, a grooved pulley, 15" diameter.
s, a wheel fixed upon the axis of r, containing 20 teeth.
t, a wheel with 60 teeth, fixed on the lattice roller axis ti.
h, a wheel with 60 teeth, fixed upon the other vertical lattice
shaft and engaged with t.
ui and ;/3, wheels on lattice roller shafts, each containing
38 teeth.
U2, a carrier wheel, gearing with iii and »3.
u, a wheel, 24 teeth, fixed to the lattice roller shaft.
V, a carrier wheel engaging with u and ?f.
w, X, y, z, wheels containing 24 teeth each, distributing lattice
connections.
Kevolutions per minute of the various parts in the roller
cotton pulling machine (Fig. 5).
The machine pulleys r^ z= 261*25
mi r n ..• n 220x19x25x14x14x17 ,„
The feed lattice roller i6x40^76x7Xx20 = ^ ^
The surface speed in inches per minute = 4*7 X 5*5 x ^^^ = 81"24
c
COTTON SPINNING CALCULATIONS
The first pair of pulling rollers —
■p , ,. . , 220X19X25X14X14 _^
iievolutions per mmute = zrp, — 77;^ — W7> — s^ = ^'^^3
^ 16x40x76x76
c n , 220x19x25x14x14x6x22" ..^„„a
Surface speed = ^ — ttt — wt^—^^ ^ =113 76
^ 16x40x76x76 7
The second pair of pulling rollers —
13 1 r • * 220X19X25 _., .^
devolutions per mmute = ^^ ,^ = 163'3
^ 16 X 40
a f 1 . , 220x19x25x6x22 „
Surface speed per mmute = ^^ — ,7^ „ = 3079
^ ^ lb X 40 7
The porcupine cylinder
220 X
nnt.o r^
16x10
■D w • ♦ 220x19x21 .^„.
Eevolutions per mmute = 1 a^^mT ~ 5225
2
The lower conveyor lattice rollers —
T. , ,. . , 220x19x10x20x60 _ „ _
Eevolutions per minute = ^ —   ^^ — „r. = o8'05
^ 16x15x60x60
Surface rate per minute in inches 58'05 X 55 x  = 1003"'5
The righthand elevator lattice roller —
220 X 19 X 10 X 20
16x15x60
= 5805
Surface rate = 5805 x ~^ = 1003"5
The lefthand elevator lattice roller
220x19x10x20x60
16x15x60x60
= 5805
The first overhead conveyor and distributing roller—
.220x19x10x20x34
16 X 15 X 60 X 24
= 5805
Surface rate = 5805 X ^^_iiff = 1003"'5
AND COSTS OF YARN 19
The second overhead conveyor and distributing lattice
roller —
220 X 19 X 10 X 20 X 24 X 2 4 x 24 _
10 X 15 X 60 X 24 X 24 x 24 ~ ^'^"^
Surface rate = 5805 X 5 '5 X '^f = 1003"5
All the machines used in connection with cotton spinning
contain the power to attenuate the cotton. The term which is
most generally used in place of the word attenuation is " draft."
The extent of the ''draft" governs the relative weight of the
cotton at the different points in the processes. The extent
practicable in each machine, and also between the various points
in each machine, should be well understood, because it is this
which governs the relation in the weight of the cotton in any
part of the machine.
If a machine, or a part of it, contains a draft of four, the
difference in the state of the cotton, as regards its weight, would
be four times. This means that it has become four times lighter
and longer between the parts referred to.
The extent of the draft may be ascertained from the relative
rates of the parts moving the cotton, or, from the relation in the
weight of the cotton as it passes under the influence of the two
points in question.
Applying this, in respect of the machine under notice, it is
found that the draft between the feed lattice and the first pair of
pulling rollers is :
(surface movement of the]
first pair of pulling rollers! 1.4
..^ .„ pel* ^i^^^e 1^ i^clies j
minute in inches J
so that the cotton under the influence of the rollers will be 1*4
times lighter than that upon the lattice, and therefore 1*4 times
longer.
The following are therefore the drafts between the
adjacent parts, in progressive order, in the abovenamed
machine : —
20 COTTON SPINNING CALCULATIONS
First and second pair of pulling rollers —
3079
1633
= 1885
Second pulling rollers and lower conveyor lattices —
10035
"3079 = ^^'^
Lower conveyor and the vertical lattices —
10035
10035
= 1
Feed lattice and overhead conveyor lattice—
10035 _.._
'8124'  ^^ ^^
Exercise 1. — What would be the speeds, in revolutions per minute, of the
undermentioned parts, if the lineshaft driving drum was 16 inches in diameter
instead of 19 inches : (a) the machine pulley ; (&) the feed lattice roller ; (c)
the first pair of pulling rollers ; {d) the second pair of pulling rollers ; (e) the
porcupiue cylinder ; (/) the lower conveyor lattice roller ; (g) the vertical con
veyor lattice rollers ; {h) the overhead conveyor lattice rollers ?
Exercise 2. — What would be the effect upon the speeds of the different
parts if the 25 wheel on the machine shaft was changed to 30 after changing the
lineshaft drum to 16 inches ?
The working of the first of these exercises is as follows : —
220 X 16 ,,,^
(a) — jg— = 220
220 X 25 X 14 X 14 X 17 „ , ,„
^^ 40 X 76 X 76 X 20
, ,. 47 X 16 „„
or, by proportion — ^^ — = 6'Jb
, , 220 X "25 X 14 X 14 , ,^ 553 x 16 „ .
(c) ACS — 7? HR = 4'66 ; or t^ = 46fa
^ ^ 40 X 76 X 7b ly
,,,220x25 ,_. 1633x61
i^) 40 ^ ' ^^' 19 "^
,. 220 X 21 ,,^ 5225 x 16 ,,,
(^) loi = ^^^ ' '' —IT— = ^^^
,^, 220 x 10 x 20 X 38 ,.^ 5805 x 16 ,„ „„
^^ 15 X 60 X 38 = ^^^ ' '' ^r— = ^^^^
AND COSTS OF YARN
21
^,220x10x20 ,_ 5805x10 ,„q„
((j) 1^^^A = ■iS?; ; or ^7,; = 4889
15 X 60
19
.,. 220 X 10 X 20 X 24 ,., 5805 x 16 ,_ ^_
('0 T r ■ ■ ..^ c. = 48i} ; or ^^^ = 4889
15 X 60 X 24
Ansioers to Exercise 2 —
(a) Machine pulleys, 220.
{I) 4759.
(c) 557.
{d) 165.
19
(p) 440.
(/) 4889.
{g) 4889.
Fig. 6 is an elevation of the gearing in a cotton pulling
machine of the Hopper type. This type of machine reduces the
Fig. g.
cotton to a very loose open condition. The advantages of this
machine over the roller type of machine are —
Greater opening and cleaning power.
Less noise and dust when well constructed.
Less personal attention.
Greater production, about 200,000 lbs. per 55^ hours, without
pressure.
22 COTTON SPINNING CALCULATIONS
Less risks of fire in this and subsequent machines by its
eliminating hard substances.
Mixing powers considerable, whereas in the roller type they
are very limited.
Fewer breakages and upkeep less costly.
The machine driving pulleys are on the stripping cylinder
shaft, and in the figure they are shown as 12 inches in diameter.
These are driven by a strap from a drum on the line shaft, 26
inches in diameter, and making 220 revolutions per minute.
(1) Eevolutions per minute of the fast and loose drums of
the machine —
220 X 26
12
476
(2) Eevolutions per minute of the supply lattice roller —
220 X 26 X 7 X 24 X 24 X 24 ^
12 X 20 X 90 X 30 X 30 ~
(3) Eate per minute in feet —
2936 X 55 X 22
T^ ;^ = 42
12 X 7
(4) Eevolutions per minute of the spiked lattice roller —
220 X 26 X 7 J< 24 _
12 X 20 X 90 ~
(5) Surface rate per minute —
4449 X 20 X 22
= 233'
12 X 7
(6) Eevolutions per minute of the regulating cylinder
220 X 26 X 7 X 54
12 X 20 X 90
(7) Surface rate —
1001
lQQ1 X 1 4 X 22 _
12 X T  ^^^
(8) Eevolutions per minute of the stripping cylinder —
220 X 26 ,
12 = ^^^^
AND COSTS OF YARN 23
(9) Surface rate —
= 1747''5
476o< 14 X 22
12 X 7
(10) Revolutions per minute of the lower conveyor lattice
roller —
220 X 26 X 7 X 8
12 X 18 X 8
(11) Surface rate —
18537 X 55 X 2 2
12 X 7
= 18537
= 267'
(12) Revolutions per minute of the elevating lattice rollers
220 X 26 X 7 X 6
12 X 18 X 12
= 927
(13) Surface rate
927 X 55 X 22 _ ,
W^f ~ ^^^ '^
Exercise 3. — At what rates, in revolutions and feet per minute, would each
of the parts in Fig. G rotate if the driving puller's were altered to 15 inches
diameter, instead of 12 inches?
Exercise 4. — Ascertain the drafts between the different lattices when the
conditions are as given in Fig. 6, and also when the machine pulleys are altered
to 15 inches ?
Exercise 5. — State the effects of changing the 24 wheel, driving the 90,
to 20, upon the speed of each part, when the other conditions are as given in
Fig. 6.
Answers to Exercise 3 —
(1) 3813 revolutions. (8) and (9) 3813 and 1398 feet.
(•2) and (3) 235 and 30G feet. (10) „ (11) 1483 „ 21362,,
(4) „ (5) 35G „ 18G4 „ (12) „ (13) 741 „ lOG8 „
(G) „ (7) 800 „ 3008 „
Ansivei's to Exercise 4 —
When the driving pulleys are 12 inches diameter, the draft between feed and
spiked lattice is 555.
When the driving pulleys are 12 inches diameter, the draft between spiked
lattice and the lower conveyor lattice is 1lG.
24 COTTON SPINNING CALCULATIONS
"When the driving pulleys are 12 inches diameter, the draft between lower
conveyor and elevating lattices is O'o.
When the driving pulleys are 15 inches diameter, the speed of all the parts
will be decreased in the same proportion, and the drafts will therefore be
unaltered.
Answers to Exercise 5 —
(1) 476^ revolutions. (8) and (9) Unaltered.
(2) and (3) 2446 „ ; 35 feet. (10) „ (11)
(4) „ (5) 37 ,. 194 feet. (12) „ (13)
(6) „ (7) 834 „ 313 3 feet.
The usefulness of this machine is infinitely greater than the
roller puller. Evidence of this is found in the number of mills
which have modified their mixing arrangements since its
introduction.
The most common practice in using this machine is that of
placing the cotton from the various lots of bales in the machine,
in the desired proportions, at a rate permitting only of the
limited exercise of their opening and mixing functions. When
such replaces stack mixing, variations are visible in all the
subsequent stages.
Extension in the usefulness of the machine is possible by
adopting one puller per 30,000 or 40,000 lbs. per week, and
adjusting them so that their maximum opening capacities are
utilized in that time, the cotton, from the several pullers,
supplied with bale cotton in the usual way but in perfect
rotation, passing into a common trunk, from which the several
exhaust openers draw their supplies. These latter deliver to
hopper feeders attached to further openers, fitted with the full
width type of beaters. From these the cotton may pass to the
scutcher or to the card direct. The hopper feeder to the final
opener should be fitted with automatic supply control attached
to feed of the opener responsible for its supply. By this system,
in a mill consuming 200,000 lbs. of cotton per week, the supply
would be drawn from six times the usual number of bales, with
the additional advantages that the hard and soft qualities would
be unavoidably mixed in the designed proportions con
tinuously.
To derive the fullest benefits from the use of the hopper
V^^ " ^_ ''^" ^^^ a^^ COLL:
AND COSTS OF YAEN 25
cotton puller — as an opening process — it is necessary to bear in
mind that the opening, and consequently the cleaning effect, is
dependent upon : The rate of movement of the spikes amongst
the cotton and the pressure of the cotton against the spiked
surfaces; the distance of the points of the spikes on the
regulating cylinder from those on the spiked lattice, and
the contrasting rates in the movement of these two latter
parts.
The best speed of the spiked lattice is the highest rate at
which it may be worked without undue strain. The rate varies
considerably in the various makes, and also with cotton treated.
American cotton allows of a higher rate than Indian or
Egyptian. The most beneficial speed can be readily ascertained
by test. This decided, the regulating cylinder should be adjusted
to a point at which the machine produces only the amount of
cotton required in the fall working time. Where these items are
disregarded the opening and cleaning utility of the machine is
only partially realized.
The Openee.
Fig. 7 contains particulars of the principal parts and their
connections in a hopperfed compound combined opener. Par
ticulars of the other parts and their connections are contained
in Figs. 8, 9, 10, and 11. The object of giving the details in
five instead of in one figure is to avoid confusion.
The speeds of the various parts in Fig. 7 are —
Counter shaft 495 revolutions per minute
Beater shaft 1028
Cross shaft 21417
Side shaft 42834
Bottom cone shaft . . . 856'73 ,,
Top cone shaft .... 611*95 ,,
Porcupine cylinder . . . 440 ,,
Fan shaft (1) 10154
Fan shaft (2) 1542
26
COTTON SPINNING CALCULATIONS
'220 Revs, per min
Counter
Shaft 16"
EXAMILES OF WORKING OUT THE SpEEDS OF THE AcOVE PaKTS.
^•^O X 36
The counter shaft = — ^,7^ = 490
lb
The beater ,. =
The cross „ =
The side ,, =
The bottom cone =
. The top „ =
The porcupine cj'hnder =
= 1028
220 X 36 X 27
" 16 X 13
220j^86 ><^27 X 5 _ .
16 X 13 X 24 ~
220
X 36
X 27
X
5
X
30
103
16
X 13
X
24
X
15
220
X 36
X 27
X
5
X
30 X
40
16
X 13
X
24
X
15 X
20
220
x36:
><27x
5
X
3C
1x40
x5
16 X 13 X 24 X 15 X 20 X 7
220 X 36 X 18
= 85673
= 61195, say 612
16 X 16
15
557
Fan shaft (1) = 557 x ,;, = 1285
Fan shaft (2) = 1028 x ]} = 1542
AND COSTS OF YARN 27
Exercises kelatikg to Fig. 7.
(1) At what speeds would the parts contained in this figure revolve if the
line shaft made 250 instead of 220 revolutions per minute ?
(2) If the fanshaft pulley (1) was changed to G inches, at what rate per
minute would it revolve ?
(3) At what rate per minute would the bottom and top cones revolve if the
bottom cone and sideshaft wheels, 20 and 40, were substituted by 24 and 36
respectively ?
(4) What size of driving and driven pulleys would alter the rate of the cross
shaft from 21417 to 257 per minute? What effect would such an alteration
have upon the speeds of the other parts ?
(5) What changes would alter the speed of the beater to 1113 revolutions
per minute if the fan and cross shaft are to remain unaltered?
(6) At what rates would the topcone shaft revolve when the cone strap is
■working on the extreme right and left ends respectively ?
Answers to Exercises (Fig. 7) —
(1) The speed of all the parts would be increased in the same proportion as
the change in speeds, thus: 502, 11G8, 2433, 4867, 9735, 684, 500, 11538,
1752 respectivelj'.
(2) The surface rate of the strap and pulley would be unaltered, and therefore
the revolutions per minute would be altered in same proportion as the size of
pulley, namely, to 1100.
(3) Bottom cone, 4589 ; top cone, 645.
(4) A Ginch driver on the beater shaft, or a 20inch driven on the cross
shaft. The side shaft and bottom and top cones would be altered in the ratio
of from 5 to 6, or to 514, 1028, and 734 respectively.
(5) The beater pulley to 13 inches ; the pulley driving the crossshaft pulley
4^*^^ inches, or the crossshaft pulley 26 inches ; the pulley on fan shaft
6 J inches.
(6) 1562 and 3527 respectively.
Calculations relating to the speeds of the parts in Fig. 8.
Eevolutions per minute of —
m 1 wr n 612 X 4 X 9 X 1 X 12 ^ .^^
The supply lattice roller = 9 x 7 x 7 8^85 — " ^^^
The surface speed in _ 0633 X 55 x 22
inches per minute ) 7 ~~
The bottom lattice rollers) ^ 612 x 4 x 23 X 17 X 20 x 20 _
in the hopper J 9 X 55 x 79 X 48 x 48 ~
The surface speed in\ _ 4*25 X 5*5 x 22 _
inches per minute/ 7 —*^^
28
COTTON SPINNING CALCULATIONS
The spiked lattice rollersl ^ 612 x 4 x 23 x 17 _ ^^,^„
in the hopper / 9 X 55 x 79
The surface speed in )
inches per minute/
2447 X 55 X 22
= 42298
■g!i«
f)uir{iiiiDiu!iiiliiDiia
The regulating cylinder =
440 X 6 X 4 X 24
12 X 12 X 48
= 366
AND COSTS OF YARN
29
The surface speed in _ 330 X 18'^ X 2 2 oQr>.;r Qi.i728ft
inches per minute J 9 7 ~ '
The stripping cylinder = ^^ ~ ^^^
The surface speed inl _ 220 x 16 X 22 _ .. ^ ^^^„ or9210ft
inches per minute J ~ 7 "~ '
Questions relating to Fig. 8.
Name the parts affected by each of the followiag alterations, and calculate
the effects in revolutions and surface speed in feet per minute : —
(7) If the cone strap was successively placed at both extreme pohits on the
cone drums.
(8) If the pulley on the topcone shaft was 5 inches diameter instead of 4.
('J) If the pulley on C was changed to 9 inches diameter.
(10) If the 80 on the supply lattice roller shaft and the 12 driving it were
altered to 84 and 14 respectively.
Answers to questions rdaiiny to Fie/, 8 —
(7) When the strap occupies —
The lefchand
extreme position.
. 14*1 revolutions
. 244 feet
. 2 '45 revolutions
. 423 feet
Spiked lattice roller
>) jj
Hopper lattice roller
)) ))
Supply lattice roller
0'358 revolutions
63 feet
The lighthiind
exLreme position.
G2*5 revolutions
1238 feet
1084 revolutions
1876 feet
1*615 revolutions
279 feet
(8) The parts aifected would in this case be the same as in question 7, each
being increased in rate to the extent of f , or —
Spiked lattice roller 30'58 revolutions
52872 feet
Hopper lattice roller
>> »
Supply lattice roller
5"31 revolutions
918 feet
0791 revolutions
1367 feet
(9) In this case only the supply lattice would be affected, and this to the
extent of Jj ; thus —
Revolutions of supply lattice roller .... 0492
Surface speed . . 85 feet
(10) In this instance only the supply lattice would be affected, and this to
the extent of 2 x l^, and therefore —
Revolutions of supply lattice roller = 0*756
Surface speed = 1367
30
COTTON SPINNING CALCULATIONS
Calculations relating to the speed of the imrts found in
Fig. 9.
Eevolutions per minute of —
m 1 u 11 612 X 1 X 34 X 27 X 17 „ ^^„
The lattice roller = ^r;^ — — — — ^ = 5*835
The surface speed of ) ^ 5 835 X 3^^ X 2 2
the lattice in inches ) 7
62 X 40 X 33 X 20
= 55015
1 St. Feedi^olleP
2nd. Pressure i;o*Ter
2V'y
612 revs. J
per.min R C
—..Right side
Left side
In aide
Bottom Cone '"^i "^20
Fig. 9.
The first presser roller = 612x1x34x27x17x28 ^
^ 62x40x33x20x35 '
The surface speed of the) ^ 4667 X 3 '5" x 22 _
first presser roller in ins. ) 7 ~ 51'337
The lower feed roller = 612^^1 X^x2j
62 X 40 X 33
AND COSTS OF YAEN 31
The surface speed in) 6 865 X 3^' X 22 ^
inches per minute ) 7
The second presser roller = 6 2 x 40 x 33~x~33 ~ '^'^^
The surface speed in) ^ 776 x 2" X 22 ^
inches per minute ) 7 ~
The pedal roller = ^^'^ ^ L ^^ = 8'358
^ 62 X 40
The surface speed in I _ 8'4 x 2f " x 22 _
inches per minute) ~ j — /ZUi
Questions relating to Fig. 9.
(11) What would be the effect of changing —
(a) The 17 on the lower feed roller to 16 ?
(h) The 27 on the pedal roller to 32 ?
(c) The cone strap to the extreme loft on the cones, if their diameters at
those points were — bottom, 3J ; top, 8^ ?
Answers to questions relating to Fig. 9 —
(11) (fl) The rate of the lattice roller would be reduced to —
Eevolutions Surface speed in
per minute. feet per minute.
5592 5295
(h) All the parts dependent upon the 27 wheel for their motion would be
aflected directly as the change, namely —
The lower feed roller to .
,, lattice roller to .
,, first presser roller to .
,, lower feed roller to .
„ ^second presser roller to
(c) Each of the rollers in Fig. 9 would have their speed changed to
31 7
^ X ^ 3 X speed of part when the strap is in central position.
Calculations relatiiuj to the speeds of the parts found in Fig. 10,
the drivinc) of the heater being as given in Fig. 7.
Eevolutions and surface speed per minute of —
Topside ) _ 220x36x27x 5 x 13x13x24 ^4455^
shaft) 16x13x24x65x38x24 304
ievolutions
SuTfice speed
er minute.
per minute.
8136
7668
6916
6527
5531
6084
8136
7668
919
794
32
COTTON SPINNING CALCULATIONS
Bottom
cage
1
220x36x2 7x 5 Xl 3 x 13 X 24 X 24 X 40 X 14 X 44
16x 13 X 24 X 65 X 38 X 24 x 30 X 28 X 44 x 115
498960
= 2039
' = 102"'53
2128.115
Surface ] _ 2039x 16"x 2 2_
speed j 7
_ 220 X 36 X 27 X 5 x 13 x 13 X 24 x 24 x 4 X 14 x 44
Top cage  16x13x24x65x38x24 x 30 x 28 x 44 x 151
498960 , ...^Q
= 3^1328 = ^ ^'^^
Too& Bottom
Feedroller to
the Beater
2j"dia,
Cage A /
Rollers /; '"'/"i "■■
3"dia. // A/ .,i3" •, /
Bottom
Calander
Shaft
rop
Shaft
Fig. 10.
Surface 1 15528 X 21" x 22
speed
Cage
rollers
1 =
= 102"485
220x36 x27x 5 xl 3x 13x24x24x40x14
16x13 X 24 X 65 X 38 X 24 x 30 X 28 X 20
178^50^
'' 1520 '
AND COSTS OF TArvN 33
Surface 1 _ 1172 x 3" x 22 , , ^„ ^
speed) ^ = 110 5
Bottom \ ^ 220x3 6 X 27 X 5 X 13 x 13 x 24 x 24 x 40
feed roller] 16 x 13 x 24 x 65 x 38 x 24 x 30 x 28
_ 35640
^28=^^^^
Surface \ _ 16*75 x2i"x 22 ,^,„_
speed/" 7 =131 b
Exercises in Coxxectiox with Fig. 10.
What would be the effects if —
(a) The 44 wheel driving the bottom cage wheel was changed to 4G ?
(b) The 14 wheel on the bottom feed roller was changed to IG?
(c) The 24 wheel on the side shaft was changed to 22 ?
Ascertain the wheels that would make the surface speeds of cages, cage
rollers, and feed rollers as nearly alike as practicable without altering the rate of
the latter.
Calculations relating to the sjjceds of the parts found in
Fig. 11.
Eevolutions and surface speed per minute of —
220 X 36 X 27 X 5 x 13 x 13 x 27 X 25 x 33
16 X 13 X 24 X 65 X 71 X 21 X 25 X 151
= 2203
Q , , 2203 X 21" X 22 .,^n ,^
Surface speed = = =145 '45
rp, , . , 220 X 36 X 27 X 5 x 13 x 13 x 27 x 25 x 33
The bottom cage = —
The top cage =
16 X 13 X 24 X 65 X 71 X 21 X 25 X 115
= 2893
Surface speed = s = 145"51
^, ,, 220x36x27x 5 x 13x13x27x25
The cage rollers = ^ — — ^ — ^, — ^j — =. — ^ — ^
° 16x13x24x65x71x21x16
= 15756
Surface speed = — = 148"55
First or the top) _ 2 20x36x27x 5 x 13x13x27 ^^.^^
calender [ 16x13x24x65x71x23"
n , . 9207 X 5"5 X 22 , .^^ i 
Surface speed = ^ = lo9 lo
34
The second calender =
Surface speed =
COTTON SPINNING CALCULATIONS
220x36x27x 5 X 13x13x27
16x13x24x65x71x22
9626 X "55 X 22 ^ ^ggr/.g^
= 9626
The third calender = ^ 20x36x27x 5 X 13x 13x27 ^^p.„3^
Surface speed =
16x13x24x65x71x21
10084 X 5^^5 X 22 ^ ^^^..^^
23
The fourth or , 220 x 36 X 27 X 5 x 18 x 13
bottom calender
;■} =
16x13x24x65x71
= 7843
^, „ , 7843 X 7" X 22 ,^r,>, ^^
Surface speed = _ = 17255
mu 1 1, 220x36x27x5x13x21x17 „ ^„^
The lap rollers = ,n . ...^..c ..n^. .r,. .^ 7^ = 7179
Surface speed =
16x13x24x65x71x30
7179 X 8r X 22 ^ ^^^,,.^2
Drafts in Openers.— In the processes embraced in spinning
the cotton is attenuated in a somewhat graduated manner, until
AND COSTS OF YARN 35
it is reduced to a siDScific weight per unit of length ; the extent
of the attenuation applied, in each as well as in the collective
processes, depending upon the ultimate fineness or count of the
yarn required. The attenuation is increased with the fineness
of the yarn, and it is distributed amongst the various machines
in proportions which practice has proved most beneficial. A
knowledge of the extent most expedient in each process, as well
as between the various points in each process, is therefore
indispensable.
" Draft " is the term used to denote the attenuation or
difference taking place in the unit of weight of the cotton in the
various stages. It is used also in expressing the difference in
the rate of movement of the parts of a machine. It denotes the
amount of attenuation occurring between two points, which it is
customary to express in terms of one unit of the preceding of the
two points specified. Thus if the draft in an opener is said to
be three, the rate of the delivery in terms of one unit of the feed
is three, and therefore the cotton is elongated to an extent of
three times its original length, and in consequence becomes at
least onethird of the weight per unit of length fed.
The several ways of proceeding to ascertain the amount of
the draft are —
(a) By timing the rate of movement of the respective
parts.
(h) By comparing the weight of the cotton per unit of length
at the respective parts.
(c) By calculating the relative movement of the respective
parts by means of the connecting gearing.
The methods (a) and (h) are, of course, only practicable when
it is convenient to work the machines. The other method (c)
necessitates particulars of the gearing only, and the draft can
be ascertained at any time. It is the method most generally
adopted, and is accurate. When it is inconvenient to obtain
particulars of the connecting gear, an approximate result may
be quickly arrived at by either of the former methods.
The following calculations illustrate the methods (a) and (c),
the speeds representing the former, however, being those already
ascertained by calculating from the connection with the driving
36 COTTON SPINNING CALCULATIONS
shaft, instead of by timing. Examples illustrating the application
of the method (b) will follow.
Calculations rclatinr/ to the drafts hetivcen the various con
ti(juous parts comprised in the opener, as represented in Figs.
7, 8, 9, 10, ajul 11.
The draft between —
The supply and bottom lattice (Fig. 8) —
By the calculated! lS5" _n.„,c,
surface speeds ) 1094"
or, by the connect _ 85 x 78 X 7 X 23 X 17 X 20 x 20 x 5 .^ =G714
ing gear J 12x1x9x55x79x48x48x5^,
The lower hopper lattice and the spiked lattice —
By the calculated surface speeds = nroTg^ = 5 "76
48 X 48 X 5\
or, by the connecting gear = ^q x"20'x~5^' "^ ^"^^
The spiked lattice and the feed lattice to the porcupine
cylinder (Figs. 8 and 9) —
By the calculated] 55*01 _ n.io
surface speeds ) ~ 422*98 ~
By the connect) 79 X5 5x9x 1 X 34x27x17x3
ing gear ( 17 x23x4x 62x40x33x20x 5>, ~
The feed lattice and first presser roller to porcupine cylinder
(Fig. 9)
By calculated surface speeds = „,. = 0*93
28 X 3^"
By the connecting gear = ^ ^ = 0*93
do X O
The feed lattice and the first lower feed roller to the
porcupine —
64'7
By calculated surface speeds = ,_ ^■, = 1*17
oo'Ol
20 X 3
By the connecting gear = = = 117
AND COSTS OF YARN 37
The first lower feed roller and the pedal roller —
By the calculated surface speed = ^. =111
S3 X 2'^
By the connecting gear direct = 5^^—^ "= 1'12
Z ( X o
The pedal roller and the first bottom cage (Figs. 9 and 10) —
102'53
By the calculated surface speeds = rfKj^ = 1"123
By the connecting gear direct
_40x62x7x20xl5xl3xl3x24x24x40xl4x 44 x 16
34 X 1 X5x40 X 30 X 65x38x24x30x28x44x151x2^
= 1423
The first bottom cage and the first cage rollers (Fig. 10) —
By the calculated surface speeds = .. „, .^ = 1*078
15 iu I' A' i. 115 X 44 X 3 69 ,. ^^
By the connecting gear direct = , , ,, or> v ,a ~ ri = l 08
•^ ° ^ 44 X 20 X 16 64
The first cage rollers, and feed rollers to beater —
By the calculated surface speeds = =1*19
20 X 2'
By the connecting gear direct = ^ . o" = 1"19
The feed rollers to beater and the second bottom cage (Figs.
10 and 11)—
By the calcu 1 ^ 11978 ^
lated speeds) 1316
By the connect 1 _ 28x30x24x38x27x25 X 25 Xl6 ^ ^,^^
ing gear direct I 40 x 24 x 24 x 71 X 21 x 23 X 115 X 2.^
Second bottom cage and the second cage rollers (Fig. 11) —
By the calculated surface speeds = ^ . ■,.. = 1"02
By the connecting gear direct = .)o^T('~x~ig ~ ^^'^
38 COTTON SriNNING CALCULATIONS
Drafts (continued) —
First calender (top) and the second cage rollers —
159'15
By the calculated surface speeds = iTnT^r = 1*07
By the connecting gear direct = g q y oq y o' r~ = 1 07
Second and first calenders —
By the calculated surface speeds = ^tq.ip — I'Ol^
23 X 5"'5
By the connecting gear direct = oo y K".r . ~ I'OIS
Third and second calenders —
174*30
By the calculated surface speeds = r/(p7qq = 1'047
22 X 5"'5
By the connecting gear direct = ^ ^777^ = 1*047
As. X 5 '5
Fourth and third calenders —
172*42
By the calculated surface speeds = frjA^on = 0*99
21 X 7"
By the connecting gear direct = ^ ^777= = 0*99
Z I X 5 '5
Lap rollers and the fourth calender —
197*42
By the calculated surface speeds = ^ _ = 1*14
T> +r. r r . 71 X 21' X 17 X 8f , , ,
By the connecting gear direct = 13 x^rx"30"x 7 ^
The draft between the lap rollers and the feed rollers to the
beater —
By the calculated j. _ 197*42 _
surface speeds ) ~ TSTG ~
By the connecting ) ^ 28 x 30 x 24 x 38 x 21 x 17 X 8 j _
gearing direct i 40 x 24 x 24 x 13 x 71 X 30 X 2J ~
By the intervening I _ J 0*91 X 102 X 1*07 X 1*045 X 1*047
drafts 1 (  j X 0*99 X 1*14 = 1*225
' This dt'ficAency ix due to the drafts between the various parts being incompletely
expressed.
AND COSTS OP YARN 39
The draft between the lap rollers and the pedal roller —
By the calculated I _ 197'42 _ ^.
surface speeds j 72'01 ~
By the connect _ 4 x 62 x 7 X 20 x 15 x 13 x 21 x 17 X 8f _ ^.^.^
ing gearing direct j 34 X 1 X5x40x30x65 x71 X30x2
By the iuterven ) _ f 1423 X 1078 x 119 X 091 X 102 x 107
ing drafts 1 j  x 1045 X 1047 X 0*99 X 114230
The knowledge of the amount of the draft between the various
parts in a machine enables the relative weight of the cotton at
each point of its progress to be ascertained, provided any loss
between the points in question is allowed for.
Thus, if in the opener in question, the laps made weighed
at the rate of 12 ozs. per yard, and the visible and invisible loss
therein amounted to 3 per cent., and the draft between the
various parts is as calculated below, the weight per yard of the
cotton delivered by the spiked hopper lattice would be —
/Weight of 1 yard)^ , rper cent, of waste\ rthe draft between the
\ of opener lap / "^ I extracted / ^ points in question
(a) (b) (c) (d)
and .. (120 ozs. x V¥ ) X 2*72 X 112 x 117 X 013
the last four items being the respective drafts from the lap
rollers to the spiked lattice : (a) that between the lap and pedal
rollers ; (h) that between pedal and the lower feed rollers to the
porcupine ; (c) that between the feed and lattice rollers to the
porcupine ; (d) that between the feed and the spiked lattices.
The answer is 574 ozs.
The weight per yard of the cotton at the pedal roller would
be—
12 ozs. + 3 per cent, lost on the original weight X draft
or, 12 ozs. X Vr X 2'72
because the cotton composing the lap has been subjected to a
loss of as 100 : 97, therefore that must be allowed for as well as
' This deficiency is due to the drafts hetween the various jjarts being incompletely
expressed.
40 COTTON SPINNING CALCULATIONS
the length, contracted to the extent of 2'72 times the length
delivered, thereby increasing the weight to that extent. Thus —
■^c^ inn > ro ( thc Weight of tlic cotton 1 ^., __ ,
12 X V? X 273 = {f^^ by the pedal roller (x) } = ^^'^^ ^^' P^^' ^^^
The weight of the cotton at any other points may be similarly
calculated, the weight being only approximate if the loss is
unknown.
The following answers relate to the weight of the cotton at
the various points, the loss between the pedal roller and first pair
of cages being assumed as 2 per cent., and 1 per cent, between
the first and second pairs of cages. The working of this question
is given so that the student may accustom himself to the
working of such exercises.
The weight of the cotton at —
Feed lattice to porcupine 44"1 ozs.
Pedal roller „ .... Ans. = 33'68 „
(Working.) Let x = weight of the cotton at the pedal
roller —
— ArjT = weight of cotton at delivery .'. x„^ = 12 ozs.
.. ^ ^^y^" = 12 ozs. .. « = 12 X Vr X 272 = 3368 ozs. Ans.
First pair of cages A ns. = 23*1 ozs.
Feed rollers to beaters Ans. = 18*2 ,,
Second pair of cages .4/is. = 19'8 ,,
Between calenders 3 and 4 . . . Ans. = 13*68 ,,
It is customary to alter the draft by means of the wheels on
the side shaft, also slight alterations by adjustments of the cone
strap.
Exercises in Respect of Drafts in the Opener as per Details in Figs.
7, 8, 0, 10, and 11 iNCLUsivF, WITH Answers appended.
Find the drafts between the following parts by gear direct : —
(11) Spiked lattice and pedal roller. Ans. 0171.
(12) Spiked lattice and feed roller to the beater. Ans. 031.
(13) Spiked lattice and lap rollers. Aiis. 0212.
AND COSTS OF YAllN 41
(14) Pedal roller to cylinder and feed rollers to beater. Aiis. 1"81.
(15) Pedal roller to cylinder and second bottom cage. Ans. 2*02.
(IG) Pedal roller to cylinder and bottom calender. Ans. 2"38.
(17) Feed rollers to the beater and the first calender. Ans. 1*1.
(18) Feed rollers to the beater and the lap rollers. Ans. 1"5.
(19) The second bottom cage and the lap rollers. Ans. 1"35.
(20) First calender and the bottom calender. Ans. 1'08.
(21) Assuming that this opener produced laps which weighed at the rate of
135 ozs. per yard, what change in that weight would arise from each of the
following alterations : —
(a) Tiie 30 crossshaft bevel changed to 27 ?
(b) The pinion on the bottom cone to 22, and that driving it on the side
shaft to 38 ?
(c) The 5inch pulley on the beater shaft to 6 inches?
Ans. 1215 ozs. ; ll"G6ozs. ; 135 ozs.
(22) What changes would produce a lap weigliing 10 ozs. per yard, assuming
that with the gearing as in the figures the lap made weighs 12 ozs. per yard?
Scutchers.
The Particulars of Driving. — Speeds of the parts in the
scutcher (Fig. 12).
In this figure B is driven by a belt from a 25 inch pulley on
a counter shaft, and the latter is fitted with fast and loose
pulleys, 15 inches in diameter, and these latter are driven by a
belt from a 32inch diameter drum on the line shaft, which
makes 220 revolutions per minute.
The revolutions per minute of the various parts, together
with the calculations, are as follows : —
Beater shaft (B) = ^^^ "^ 15 x 10 = ^^^^*
^ 220 X 32 X 25 X 5 „^^ .
Fan = ^ = = 8381
15 X 10 X 7
^ , „, 220 X 32 X 25 X 6 „„„ ^
Cross shaft = — —r —  = 586*6
15 X 10 X 12
Driver cone 1 ^ 220 x 32 X 25 X 6 X 6 .]r
drum (D) ( 15 x 10 X 12 x 5 ~
Feed lattice ^ 220 x 32 x 25 x 6 x 65 x 45 X 1 X 39 _ ^ . ^o
roller (F) j 15 X 10 X 12 x 55 x 425 X 88 X 60 ~
Surface rate = = 51"121
42
COTTON SPINNING CALCULATIONS
AND COSTS OF YARN 43
p,, ,, 220x32x25x 6 X65X45 xl „,,„
Pedal roller = — , — ^^^ —  — — — — ^ = 8'342
15 X 10 X 12 X 55 X 425 X 88
Q , , 8342 X 2" X 22 „_„ ._
Surface rate = „ = 52 435
Lap motion ) _ 220^ 32 x 2 5 x 6 x 8 _ oo , p
shaft (L) j  " 15 X 10 X 12 x~20 ~ ^"^^'^
^ ,, .^, 220x32x25x6x8x13x20x32 ^ ^^
Bottom cage (C) = r= — :r^ — r?^ — ^rr: — = — — i — — = 3*87
^ ^ ^ 15x10x12x20x71x74x96
Surface rate =  ^  ^ ^^" ^ '^^ = 145"988
Top cage (C) I 220x32x25x 6x8 xl3x20x 32 _o.,...
(19") ) 15x10x12x20x71x74x154"
c; , , 2413 X 19" X 22 ,,,„..
Surface rate = ^ = 14409
rr, , , ,,,,, 220x32x25x6x8x13x20x19 ,^ ^^^
Topcalender(21) = i5>riOxT2^20x7rx 74 x21 = ^^"^^^
Surface rate = ^^'^^^^^"^^^ = 165"094
Eevolutions and surface speed per minute of —
Bottom calender] ^ 220^x 32 x 25 X 6 X 8 x 13 x 20 , , ., „
(1932) j 15^00^12X20^71X74" '^^^'
Surface rate = ^^^^1'^^^ = 182474"
Lap rollers (9.V') ^ 220x32x25 x 6 x 8 x 13 X 11
diameter) ' ( 15x10x12x20x71x74" ^^^^^^*
Surface rate = 6:38Ix_9:5:^2 ^ ^^^..^^^
Drafts between —
Pedal roller and feed lattice—
(«) By gear direct = ^^ = 1025
"^ ^ 39 X 3
52*435
{b) By the surface rates, already calculated = ^it^tt^ = 1'025
ol'lzl
44 COTTON SPINNING CALCULATIONS
Bottom cage and pedal roller —
I A = 88x4x5^x 8 X l3x20x32x 12 " diameter
^'^ 1 X 4.1 X 6.1 X '20 X 71 X 74 X 96 x 2" diameter ~ ^^
Top cage and bottom cage —
, . 154x12" . _^„
^'^^ = 144^09 = ^^^^
Bottom calender and bottom cage —
/ ^ 96 X 5 ^ ^^^
(^^ = 32^ri2 = 1'^^
^^^ 145988 ^^^
Lap rollers and bottom calender —
"> 2 X 74 X 5 = ^'"^
,,, 190696 ,„,^
(''^ r82^74 = 1 °^^
Lap rollers and bottom cage —
^ . 96 X 74 X 11 X 91 , ^^^
r/A 190696
^''^ 145^988 = ^ ^^^
Lap rollers and pedal roller —
(a) 88 X 4 X 5^ X 8 X 13 X 11 X 9.1 _ _ __
^ ^ ■ 1 X 41 X 61 X 20 X 71 X 71 X 2  "^ ^"^
(h) 190696
Lap rollers and lattice roller —
60 X 88 X 4j X 51 X 8 X 13 X 11 X 9i _ ^ _^
^ ^ 39 X 1 X 41 X 61 X 20 X 71 X U>rd ~ "^'^"^
(jb) 190696 _
^' 51121 "^^^
AND COSTS OF YARN 45
Exercises ix respect of the Parts in Fig. 12.
Exercise 1. — What sizes of —
(a) Beater pulley would be required to give lOGG revolutions of that part per
minute ?
(h) Counter shaft drum (25 inches) would be required to give 12G6 revolu
tions of beater shaft per minute ?
(c) Pulley on the fan shaft would be necessary to give 1173/r revolutions
of fan per minute ?
(d) Pulley on the beater shaft would be necessary to drive the fan 1675
revolutions per minute ?
(e) To what extent would the weight produced by the machine be affected
by the alterations (a) and (b) respectively ?
(/) What changes respectively in the gearing would be expedient after
making the alterations (a) and (&), if it was required that the weight produced
in a given time remain as before the alteration ?
Exercise 2. — What would the draft in the machine (Fig. 12) become, if
the following alterations were made in the gearing : —
(a) The 8inch pulley on the cross shaft changed to 9 inches and 7 inches
successively ?
(b) The 65inch pulley on the cross shaft changed to 6 inches and 7 inches
successively ?
(c) The 65inch and 8inch pulleys, both on the cross shaft, are changed to
7 inches each ?
Exercise 3 —
(a) Ascertain the weight, in pounds, per lap in each of the cases (a), (h),
(c). Exercise 2, and also the number of laps made in 10 hours, assuming they
measured 367 yards, and averaged 22 lbs. 15 ozs. each, with the gearing
otherwise as per Fig. 12. Allow 10 per cent, for lost time.
(b) What change in the sizes of the 6inch or 8inch pulleys on the cross
shaft would be necessary to produce a lap 12 ozs. per yard, if that made with
the gearing, as per Fig. 12, weighed 10 ozs. per yard? Also, state the differ
ence in the length and weight, in both instances, which would be caused by the
change.
(c) What effect, upon the output of this machine, would result from an
alteration in the position of the strap on the cones ? Assuming the sum of the
diameters of the cones at opposite points are 8f inches, and the strap is on a
part of the driven cone 4 inches in diameter, what would be the weight per yard
of the lap made, if that produced with the gearing, as per Fig. 12, was 10 ozs.
per yard ?
(d) If the lap made in a machine, geared as per Fig. 12, averaged 36*7 yards
and weighed 22 lbs. 15 ozs., and the loss in the process was 2 per cent., and the
number of laps used at the feed 4, what should* be the weight per yard of each
of the latter ?
46
COTTON SPINNING CALCULATEONS
AND COSTS OF YARN 47
Exercises in Calculatlno the Speeds and Duafts of the Various Parts
IN THE Scutcher (Fig. 13).
Calculate the revolutions per minute of the following parts. The numerals
signify the teeth contents in wheels and diameters of pulleys and other parts in
inches.
Exercise 4 — ■
(a) Fan (5 inches). Ans. 2880.
lb) Lap motion shaft (1530). Aiis. 400.
(c) Side shaft (3060). Ans. 400.
(d) Driver cone (4^ inches). Ans. 800.
(e) Driven cone (5 inches). Aiis. 720.
(/) Feed roller (3080). Ans. 9.
(</) Feed lattice (5^ inches diameter). Ans. 4JY
(^i) Top cage (240)"". Ans. 4842.
(0 Bottom cage (190). Ans. 6116.
(/) Cage rollers (20). Ans. 454.
(k) First calender (235 inches). Ans. 2315.
(l) Second calender (22485 inches). Ans. 242.
(m) Third calender (215 inches). Ans. 2535.
(70 Fourth calender (29707 inches). Ans. 1836.
(o) Lap rollers (35120 and 35). Ans. 1428.
Exercise 5. — Calculate the drafts between the following parts in the
scutcher (Fig. 13) : —
(a) Feed lattice and feed roller. Ans. 10.
(b) Feed roller and bottom cage. Ans. 43.
(c) Top and bottom cages. Ajis. 10.
(d) Bottom cage and cage rollers. Ans. 0976.
(e) Bottom cage and first calender. Ans. 104.
(/) Cage rollers and first calender. Ans. 1067.
{g) First and second calenders. Ans. 1045.
(h) Second and third calenders. Ans. 1048.
(i) Third and fourth calenders. Ans. 0987.
(/) First and fourth calenders. Ajis. 111.
(k) Fourth calender and lap rollers. A^is. 10.
(J) First calender and lap rollers. Ans. 111.
(to) Feed lattice and lap rollers. Ans. 4763.
Exercise 6 —
(a) Give the drafts, from 4763 to 32, which the following range in sizes of
driver and driven draft change wheels would obtain, limiting the range in the
driver 3045 with 30 driven, and in the driven 2030 with 30 driver.
(b) What single and pairs of draft change wheels, within the following sizes,
driver 2040, driven 2050, will give drafts nearest 45, 41, 38, 3 5, 325, 30,
and 285 respectively ?
48
COTTON SPINNING CALCULATIONS
Answers to Exercise G (a) ■
Driver
31
32
33
34
35
36 37
38
Draft .
4Gl
45G
435
42
408
397 38G
37G
Driver
39
40
41
42
43
44 45
Draft .
3GO
357
348
34
332
324 317
Driven
30
29
28
27
2G
25
Draft . .
476
46
445
428
413
397
Driven
24
23
22
21
20
Draft.
381
367
35
334
317
Ans^cers
to EoL
ercise G (h) —
45 :
driver
driven'
4a 51
4 5) 23
325
= ff
41 =
= u
30
= sf; ft
3
8 =
24 2 7
30? 35
;f§
35
— 3 e . 25
— 48 5 34
285 = §1
The Hunting Cog Measuring or Length Motion used in Openers
and Scutchers. — In Fig. 14, K and A represent the calenders and
C=^
Fig. 14.
also the connecting wheels ; H is the dropshaft wheel ; G the
dropshaft lever, Gi being its pivot, g is a projection of G sup
ported by the lower part of catch lever F, F is pivoted on P and
AND COSTS OF YARN 49
coupled to the lower part of lever D by Di, D having its fulcrum
at E. The spring I presses against D, forcing the wheel C,
which is loose upon a stud attached to D, to gear with wheel B,
the latter being fixed upon the shaft of the calender A. E and
B are projections from the sides of the wheels C and B, which
are in gear. When the projections meet the wheel C is forced
out of gear with B, this action causes the levers D, Di, and F
to release g, and consequently G falls to T, thereby disengaging
H from J, and, since the latter is driven by the former, J ceases
to rotate. The fall of the lever G disengages the feedmotion
clutch by rod connections with G shown at point Z. The lap
continuing to rotate after the calenders have ceased delivering
effects the severance and completion of the lap.
The length of the lap made is governed by the revolutions
which the wheel B makes in causing its projection to have
contact with E, on C.
The revolutions of the wheels B and C, per lap, are the least
whole numhers which express the relation of their tooth contents,
their relative revolutions being inverse to those numhers. Thus,
if B is 21, and C ranged from 71 to 81 teeth respectively,
the revolutions of these wheels, per lap, would be as given in
the first part of the table on p. 50. If B had 72, and C
ranged from 71 to 81 teeth, then their revolutions per lap would
be as given in the second part of that table. If C had 80 and
B 2 teeth, then their respective revolutions would be 1 and 40.
Should C be any number which has no common divisor between
itself and unity, then, if B contains less teeth than C, the
revolutions of B per lap would be the same as the teeth contents
of C.
Assuming the diameter of the calender 5 inches, then the
length of the lap would be —
5" X 3*1416 X revolutions of B per lap ,
33 i '^ = yards
or, revolutions of B per lap X 0'4363 yard
50
COTTON SPINNING CALCULATIONS
Ratio of their teeth
j
Sizes of the wheels
Relative
rate of
contents expressed
'
(in teeth).
their rotation.
in smallest whole
numbers.
Revolutions
of B per lap.
1
71
Length of the lap in
yards as ascettained
by calculation.
B. ! c.
B.
c.
B.
C.
71
21 71
71
21
21
3098
21 72
72
21
7
24
24
1047
21
73
73
21
21
73
73
3185
21
.74
7i
21
21
74
74
3229
21
75
75
21
7
25
25
1091
21
76
76
21
21
76
76
3316
21
77
77
21
3
11
11
48
21 78
78
21
7
26
26
1134
21 , 79
79
21
21
79
79
3947
21 1 80
80
21
21
80
80
3990
21 81
81
21
7
27
.7
1177
72 71
71
72
72
71
71
3098
72 , 72
72
72
1
1
1
04363
72 1 73
73
72
72
73
73
3185
72
74
74
72
36
37
37
1614
72
75
75
72
24
25
25
1091
72
76
76
72
18
19
19
829
72
77
77
72
72
77
77
3859
72 ' 78
78
72
12
13
13
567
72 79
79
72
72
79
79
3947
72 80
80
72
9
10
10
436
72 81
81
72
8
9
9
396
Example. — If C is 78 and B 41, and the diameter of the calender 5 inches,
and the draft between this calender and the lap rollers 1 '045, then the approxi
mate length of the lap ^YOllld be as follows :—
The ratio of the tooth contents of C and B cannot be expressed in less
whole numbers, and hence B will make 78 revolutions per lap,
.*. 78 X 5 X 3141G x 1045 = length of lap in inches (approximate)
= 128036 inches = 1067 feet
It is found that, when the lap is verj thick, the lap exceeds somewhat the
calculated length ; but as this discrepancy^ is the same in respect of each lap of
the same weight, it is generally neglected, and the calculated length taken as the
actual.
The advantages of the huntingcog motion is that it obtains the same length
on each lap, and this cannot be claimed in respect of the other motions. This
arises through the slow and irregular disengagement of the knockingoff catch in
the latter.
Laps of a length representing any number of revolutions of the operating
calender can be made by this motion.
AND COSTS OF YARN
51
EXEKCISE 7 —
(a) How many revolutions would B make, and what length of lap would
result, if B and C were 41 and 81 respectively and calender 5 inches diameter ?
Ans. 106 feet.
(b) What length of lap would be made if B had 42 and 81 teeth when the
calender B is 5 inches in diameter? Ans. 353 feet.
(o) What sizes of B may be used for a lap of 36*2 yards if C had 83 teeth
when the calender B is 5 inches in diameter ? Ans. 182.
Platt's Knockingoff Motion
In Fig. 15, K is the bottom calender and A is a single worm
secured to it ; B is a worm wheel driven by A, and C a pinion
fixed upon the axis of B ; C drives the
"knockingoff" wheel D, the projection
E on D pulls the catch F and the lever
G, to which it is attached, in passing
that point. This movement moves the
lever G to the right on its pivot X until
G ceases to support H. The latter is the
dropshaft lever and in consequence of
the withdrawal of the support G, the drop
shaft wheel is disengaged from driving the
calenders and other parts dependent upon them for their motion,
and hence, delivery ceasing, the lap is completed.
To start a new lap, G is raised at a point on the left to enable
the clearance of the catch F from E, F is supported by a
finger of the right hand, whilst the left lifts the drop lever
H, when the weighted portion of G, to the left of X, causes it to
move into a supporting position for H. This action engages the
dropshaft wheel, and sets the delivery and feed parts in action.
The length of the lap will vary according to the revolutions
which the calender makes in turning the wheel D one revolution.
The gear may be as follows : — Bottom calender, 7 inches
diameter ; A, 1 ; B, 25 ; C, 18 ; D, 48.
The revolutions of A per one of D will therefore be —
Fig. 15.
48 V
18 ^
25
1
12
IS
and the length of the
lap in yards
1 =
1200 .7" X 31416
= 40724
18 36
This type of length motion tends to the production of laps
52 COTTON SPINNING CALCULATIONS
slightly varying in length. This arises from the slow move
ment of part G during its "withdrawal, and the tendency of its
supporting surface to wear smooth and somewhat rounded ; this,
assisted by the vibration, causes the supporting part G to fall
away at slightly varying intervals 'measured in revolutions of
the calender.
Exercise 8. — Calculate the length of the laps —
(a) When C is 16, 17, 19, and 20 respectively.
Ans. 4575, 4315, 386, 3615 yards.
(i) When the following wheels are used together instead of those previously
given: A, 1 ; B, 24; C, 17 ; D, 50. A7is. 4315 yards.
(c) When B is altered to 24? Ans. 391 yards.
{d) When D is altered to 50? Ans. 425 yards.
Exercise 9 —
If a lap 50 yards long is required, what single wheel would give the nearest
result? Ans. Changing D to 59.
Exercise 10 —
If a lap 48f j\irds was required, what size of C should be used ? Aiis. (5).
Exercise 11 —
(a) What length of lap, in yards, would be made if the huntingcog lap
length motion wheel on the top calender contained 82 and the wheel on the
knockiugoff lever 83 teeth ? Ans. 4021.
(6) Find the time taken to make a lap 4021 yards in length,
Ans. 3 845 minutes.
(c) What would be the weight of one lap and also the production in lbs. per
10 hours, if 2 per cent, waste was extracted and the time lost in taking out the
laps and other incidental stoppages equals 8 per cent, and the weight of the four
laps comprising the feed each average 118 ozs. per yard. Assume the length of
the lap 4021 yards. Ans. 39 lbs. ; 6006 lbs.
(d) What changes in the gear would be best to reduce the output to a
normal amount, say to 3000 lbs. per 10 hours, v.ithout changing the count of
the lap ?
Ans. Keduce size of 8 inches, and increase size of 24 inches in conesponding
proportions ; or 8 inches to 6 inches, 24 inches to 30 inches.
Practical Notes.
Changes in the Weight and Count of the Laps made by Openers
and Scutchers. — The position of the cone strap is automatically
controlled by the feed regulator. To facilitate adjustments in
the weight of the lap, as circumstances demand, an adjusting
screw connection is provided. This latter, and changing the
AND COSTS OF YARN 53
draft gear, are the means of controlling the draft, and therefore
of the weight and count of the lap made. The range of adjust
ment practicable, in respect of the draft by gearing, is unlimited ;
but that by the adjustment of the cone strap is very limited, and
should only be availed of for temporary adjustments.
The best position for the cone strap, when the feed is of the
mean or normal weight, is at the centre of the cones. This secures
the widest and most useful range of action of the cone strap,
adaptable equally toward light and heavy variations in the feed.
When, by temporary adjustments, so often necessitated by varia
tions in the character of the cotton, and actions of the machine,
common in ordinary working, the cone strap has been gradually
moved and settled in a position otherwise than central, steps
ought to be taken to alter the draft to an extent which will
restore the cone strap to the centre position, or otherwise the
efficacy of this part of the machine is interfered with.
The system of connecting the feed and delivery parts, in
these machines, by belt, is being superseded by rope or tooth
gear. The method shown in Fig. 12 is not always satisfactory.
Variations in the slippage of the abovenamed straps affect the
draft, and add to that arising from the cone strap. Positive
driving reduces the possibilities of such defects without intro
ducing any disadvantages.
Fluctuations in the draft are also often occasioned by variation
in the slippage of the feed lattice ; too highly tensioned or slack
lattices, lattice roller bearings out of alignment, and obstructions
about these parts, binding of the lattice against the sides, these
are amongst the chief causes of variations in the weight and
count of the lap. The system of connecting the feed lattice
rollers by tooth gear should receive consideration whenever the
variations in the weight of the laps is unsatisfactory and
cannot be eliminated.
Productions, Speeds, and their Controlling Factors. — In the
spinning of coarse and medium counts of yarn from American
and similar and lower types of cotton, exhaust openers are
extensively used. In these machines the practice of dispensing
the lap measuring and " knockingoff" motion is extensive.
The advantages of such practice are, the elimination of the
54 COTTON SPINNING CALCULATIONS
thick and thin place, usually following the stoppage, and in
creased production ; it is also a deterrent towards dilatoriness
on the part of the attendant. Productions ranging as high as
40,000 lbs. per week of 55?, hours are not uncommon under such
conditions.
The rate of delivery ranges up to 30 feet per minute, and the
rate of the feed about onethird of that amount. The weight of
the cotton delivered ranges to 0*75 oz. per yard per inch of
width, and that of the feed 25 ozs. per yard per inch of width.
The sizes of ^feed rollers are from 2j inches to 3 inches in
diameter.
The highest surface rates of beating instruments range up to
10,000 feet per minute. Creighton porcupines up to 1000,
small porcupine cylinders up to 1100, porcupines (discs) 900,
large porcupines (36 inches and upwards) to 600, threebladed
beaters to 1250, twobladed beaters up to 1500 revolutions per
minute.
Fans range up to 2500 revolutions per minute.
The Controlling Factors in respect of the Parts and Speeds Named.
— Small feed rollers are only adapted for light feeds at low rates
and pressures. Feed rollers which have insufficient holding
power depreciate the opening action by allowing "plucking."
Overweighting in order to secure increased pressure — better
holding power — has the same tendency. High rates of feed and
beating, as well as heavy feeds, require larger feed rollers
irrespective of the length of the staple. Too quick and over
feeding produces an excess of good cotton with the droppings,
and interferes with the opening and cleaning actions. The sizes
of feed rollers are from 2 inches to 3 inches diameter ; 21 inches
are only suitable when the feed is light, slow, and the pressure
moderate. High speeds, accompanied by a heavy feed and
pressure, necessitate rollers 2 inches to 3 inches diameter ; 21
inches are only adapted for moderate conditions. Too close
setting of these tends to weakening the fibres, whilst the opposite
causes a stringy tendency in the appearance of the cotton.
When large rollers are used {^■ inch would be satisfactory for
the heaviest feed. With small feed rollers distances less than
^ inch are doubtful,
AND COSTS OF YARN 55
High rates of beating cause good cotton to be forced through
the beater bars, imparts a curly appearance, and also weakens
the fibre.
Overscutching is distinguished by the development of the
curling tendency.
There is a great variation in the rates at which fans are
worked. This arises from constructional differences in respect
of the exhaust trunks, passages, flues, etc., and dimensions of
the fans. Deficient fan rates are signalized by the cotton being
overscutched, desultory movement of the cotton from the beaters
to the cages, presence of good cotton amongst the droppings.
Too high rate of this part is distinguished by the rapid flight of
the impurities along the passages, compact state of the cotton
collected on the cages, absence of fine light impurities in the
clearing casements and its presence in the cotton, low percentage
of impurities extracted.
Miscellaneous Questions appertaining to Opening and Scutching.
(12) What number and weight of laps would be made in 10 hours imder the
following conditions ? — 4 laps comprise the feed in the scutcher, and these average
10 ozs. per yard each ; the draft in the machine is 3, and the loss H per cent.
Tlie laps made are 42 yards long. The lap rollers are 9 inches in diameter, and
make exactly 9 revolutions per minute, 30 seconds being lost at the completion
of each lap. Ans. 108 ; 3720 lbs.
(13) How many scutchers, woiking under the conditions given in the last
question, would be necessary to supply the laps for 108 cards, assuming each
card produced 120 lbs. of 02 hank sliver and made 5 per cent, waste. Ans. 4.
(14) What should be the length in yards, the weight in pounds, and the
number of laps made per 10 hours, if 4 laps, each weighing 10 ozs. per yard,
form the feed in the scutcher geared as in Fig. 12, and the time lost altogether
equals 10 per cent. ? Ans. 10456 ozs. ; 2860 yds. ; 1896 lbs.
Exercise 15 (Speeds). — Calculate the revolutions per minute of the principal
parts in Fig. 13.
Answers —
Cross shaft, 400. Top cage, 484.
Fan shaft, 2880. Cage rollers, 454.
Side shaft, 400. First calender, 23*15.
Driver cone, 800. Second calender, 24'2.
Driven cone, 720. Third calender, 2535.
Feed roller, 9. Fourth calender, 1836.
Lattice roller, 49, Lap rollers, 1428.
Bottom cage, 611.
56 COTTON SPINNING CALCULATIONS
Exercise 16 (Drafts).— Calculate the drafts between the following parts
in Fig. 13 : —
Lattice and pedal rollers. {Ans. 1.)
Pedal roller and bottom cage. {Ans. 43.)
Bottom cage and cage rollers. {Ana. 0"97G.)
„ „ top calender. {Ans. 104.)
First and second calender. {Ans. 1"045.)
Second and third calender. {Ans. 1048.)
Third and fourth calender. {Ans. 0987.)
Fourth calender and lap rollers. {Ans. I'O.)
Production in pounds in 10 hours' uninterrupted working, assuming the lap
weighs 5250 grains per yard. {Ans. 5050.)
Also, the draft between the feed lattice and lap rollers. {Ans. 476.)
Also, tlie weight, per yard, of the cotton fed, assuming the lap produced to
weigh at the rate of 5250 grains per yard, allowing 2 per cent, for loss in waste.
{Ans. 25,500 grains.)
Card Calculations.
Fig. 16 represents the gearing common in cards of the
revolving flat type. In the different makes of these machines
wheels and other parts of varying dimensions are adopted, to
adapt them for the conditions under which they work. The
subtended calculations relate to the speeds of all the parts which
they contain ; they are arranged in the following instances,
as far as convenient, in progressive order. Slippage and thick
nesses of belts and ropes have not been taken into consideration
in these calculations, but it is advisable to do so in practice. In
belt drives, under bad conditions, this is sometimes considerable,
but under fair conditions should not amount to more than two
or three per cent, at each point in transmission. The actual
speeds will be, therefore, somewhat less than the calculated.
The speeds given are those in common use in treating ordinary
Egyptian and the better classes of American cotton.
The line shaft from which the strap driving the card, in the
figure, is driven is assumed to make 220 revolutions per minute,
and the drum upon it to be 12 inches in diameter.
The dimensions given refer to the diameters in inches in
respect of pulleys, or teeth in cases of wheels.
AND COSTS OF YARN
57
58
COTTON SPINNING CALCULATIONS
Details of calculation.
Lap roller —
220xl2xl8x 5 X 28 X 40 x40x 14 Xl7
15x 7 Xl0xl00x216x40xl20x48
04848 X 6 X 22
7
The feed roller (120 x 17 X 21")—
2 20xl2xl8 x 5 X 2 8 X 40 x4 0x 14
15 X 7iri0 X 100 X 216 X 40 xT2d
1369X 2i"x22
The lickerin (7" X 5")—
220 X 12 X 18
15 X 7
45257 X 9" X 22
The cylinder (15" x IS" X 50" x GJ")—
220 X 12 .
15 "
176 X 50" X 22
The flats (40 X 12): hero, in estimating
the surface movement, it is assumed that the
distance from centre to centre of the flats
measures IJ inches, and are driven by a wheel
containing 12 teeth, eacli of which engages a
" flat." The worm, driving the worm wheel
(40), has a double tliread.
220 X 12 X 6^ X 1 X 2 _
15 X 12 X 24 X 40
143 X 12 Xj£' ^
720 X i X 1
Brushes : not shown. The driving gear for
the brushes that clean the flats is not con
tained in the figure. The speed of that part
varies ; under exceptional circumstances it is
worked as high as 300 revolutions per minute.
The normal rate of the ordinary brush is about
40 revolutions per minute. A patent com
bination brush — which gives encouraging
results — is worked as low as 5 revolutions per
minute. The stripping brush used in cleaning
the cylinder and doffer is driven, during that
Revolutions
per
minute.
04848
13G9
45257
176
Surface speed per minute.
In inches.
91413
In feet.
07GI7
9G8
1278698
27657
143
720
0806
106558
230475
3574
AND COSTS OF YAEN
59
Details of calculation.
operation, from a groove in the loose pulley
on the cylinder shaft, the diameter being
15 or 10 inches, whilst that on the brush
varies from 5 to 10 inches, thus giving —
From
To
220 X 12 X 15
15 X 10
220 X 12 X 15 _
15x5
The doffer (21G x 9" x 40)—
220 X 12 X 18 X 5 X 28 X 40 _
15 X 7 X 10 X 100 X 21G
176 X 26 X 22 ^
15 7
The bottom calender (30 X ol)—
220J<J2J< 18 x5 J<^8_xj0 ^
15 X 7 X 10 X 100 X 30
[Note. — The dofier wheel is here a carrier]
8448 X 4 X 22 _
7
The coiler delivery rollers (10) —
220x l2xl 8x 5 X 28 X40x31x20xl6 _
15 X 7 XlOxlOO X 30 X 15 X 20 x 10
17457 X 2" X 22 ^
7
The coiler (106)—
220xl2xl8x 5 X 28 x40x31x20x 38 _
15X 7 X10X100X30X15X20X10G
The radius of the centre of the coiler tube
at the point of exit is 3 inches —
The distances traversed by this point =
The can table wheel (82)—
220xl2x 18 X 5 X 28x ^OxS 1 x 20 X 16
15 X 7'x 10 X 100 X 30 X 15 X 20 X 48
^ 16xl4 _
48x8:i~"
{ Revolutions
per
minute.
264
528
1173
8448
17457
625
Surface speed per minute.
In inches.
In f( et.
0;)878
r9898
106203
885
1097 423
91452
1178 9816
531
60
COTTON SPINNING CALCULATIONS
Details of calculation.
The number of coils laid per revolution of
the cati —
625
331
Occasionally an alteration in the rate of
the can is necessary through considerable
chantre in thickness of the "sliver. If the
8])eed of the can is insufficient, the adjacent
coils adhere instead of freely uncoiling. If
the rate of tlie delivery is greater than the
coiling rate, the sliver sticks to the sides of
the can. and vice vend.
The doflfer comb (4")—
220 X 12 X 18 X 1 2
15 X 6 X I ~
It is now usual to furnish this part with a
stepped pulley, also the driver of this is like
wise stepped, so that the speed of the comb
may be adapted to the rate of the doffer.
The grinding disc, or roller, on the '
cylinder (5" x 7") —
220 X 12 X 18
6336 X 7 X 22
7 ~
The grinding disc, or roller, on the doflfer •
the doflfer during grinding is driven from the
ISinch pulley on the cylinder during this
action, the other gear being disconnected,
the speed teing —
220 X 12 X 18
15 X 9 ="
352 X 26 X 2 2
7 ~
The direction of the cylinder when grind
ing is opposite to the normal working direction.
The doflfer rotates in the same direction. This
direction is opposite to that indicated by the
bend of the card wire in both instances. ' The
direction of the emery discs, or rollers, is
opposing the movement of the parts to be
ground.
Revolutions '
per
minute.
Surface speed per minute.
188
In incbes.
In feet.
1581
15 X 5 ~ I ^336
13,944
1162
352
28,704
2392
An increased or diminished rate of any of these parts may
be obtained by altering the size of any of the wheels or pulleys,
AND COSTS OF YARN 61
not a carrier, in the intercepting train, the effect being in direct
ratio in case of drivers, and inverse when driven wheels or
pulleys.
The grinding of the flats is done at a similar speed to that
of the cylinder, rollers being preferred to discs for this work.
To alter the Speeds of the Various Parts. — The speed of the lap
rollers may be altered by changing the 48, driven wheel, on the
laproller shaft, and also by the 17, driver wheel, on the feed
roller shaft.
The speeds of the lap and feed rollers may be altered by
changing the 120, driven wheel, on the feed roller ; the 14,
driver wheel, on the side shaft ; the 40, driven, on the side shaft ;
and the 40, driver, on the doffer shaft.
The speeds of the calender, coiler delivery rollers, coiler and
can wheels may be changed by altering the doffer, 216, or the
30, calender shaft wheel.
The speeds of the doffer, feed and lap rollers, calender and
coiler delivery rollers, and also the coiler and can wheels, may be
changed by altering the 5inch driver pulley on the lickerin
shaft, the 10inch barrow pulley (driven), the 28 driver wheel on
the hub of the latter, the 100 and the 40 driven and driver
respectively. All these are connections in the train driving the
doffer from the lickerin.
The speeds of all the above parts may be changed by any
alteration which increases the speed of the lickerin.
In the event of a change in the speed of the lickerin being
required without change in the speeds of the parts driven from
it, it would be necessary to alter the connecting train at some
point between the lickerin and the doffer wheel, inversely to the
former change.
Alteration in the movement of the flats may be effected by
changing the 6^ inch driver on the cylinder shaft, or the 12
inch driver pulley on the flatmotion shaft, or the double, for a
treble, worm.
62 COTTON SPINNING CALCULATIONS
Exercises ke Alteration of Speeds of Various Parts.
Exercise 1. — If the card cylinder makes 178 revolutions per minute when
its fast and loose pulleys are 16 inches in diameter, at what rate would each of
its parts work after changing the fast and loose pulleys to 18 inches diameter ?
Answers —
Cylinder, 158'2. Coiler, 506.
Lickerin, 4022. Can wheel, 294.
Doffer, 1043. Doffer comb, 1408.
Feed roller, 1217. Stripping brush, 235470.
Lap roller, 0*431. Grinding discs, 563.
Calender, 751. Doffer (when grinding), 313.
Coiler delivery rollers, 15518. Flats (inches per minute), 1589.
Exercise 2. — What alterations would be necessary to restore the speeds of
all the parts implied in the last question, excepting the cylinder, to the original
rates ?
Answer's —
18inch pulley driving lickerin to 2025 inches.
7«inch pulley driving barrow pulley to Gfi inches.
18inch pulley on cylinder driving the doffer comb to 20.j; inches, or 6inch
pulley to 5 j inches.
65inch pulley on the cylinder driving the flats to 731 inches.
5inch pulley on the grinding disc to 4r^ inches.
Exercise 3. — A card having a doffer 2475 inches diameter, making 18
revolutions per minute, produces 550 lbs. of sliver per week. The driving
pulleys are 16 inches diameter, and the cylinder makes 180 revolutions per
minute. What size of pulleys would be needed to reduce the speed to 160
revolutions per minute ? What effect would this change have upon the revo
lutions per minute of the doffer as well as upon the length and weight produced
per week ?
A71S. 18 inches ; ^J less length ; 488'^ lbs. per week.
The Drafts between the Various Parts, how ascertained. — The
draft may be ascertained by coraparing the weight per unit of
length of the cotton at the different points in the machine ;
also, by timing the speeds of the respective parts and ascer
taining from this their ratio; and again, by calculating the
mechanical value of the connecting train of gear and dimensions
of surface.
It is preferable wherever possible to do this by the latter
system, as it furnishes the most reliable data. The two other
ways serve very well in ascertaining approximate results, and
also in checking the calculated draft.
AND COSTS OF YAllN 63
The results given below are arrived at, from, (a) the
calculated speeds, as ascertained in the previous calculations ;
(b) the connectional gear and sizes of the surface.
The drafts between —
Lap and feed roller—
/ N 968" , ..
Feed roller and lickerin—
(a) i?^^^^ = 1321
968
,. 120^x4^x216x100x10x9 _ ,o„,
^ ^ 14 X 40 X 40 X 28 X 5 X 2 j ~ "^"^^'^
Lickerin and cylinder —
Flats and cylinder —
27657
() ^;;l = 15476
.J 40 X 24 X 12 X 50 X 22'^
^ ^ irxT~>r6i X llx 12 X 7 "" ^^^
95878
Cylinder and doffer—
(«) ^'^^ = 00346
V y 26757 " ^^^^
,j 18X 5 X 28 X 40 X26 _
^ ^ 7 X 10 X 100 X 216 X 50" ~ " ^"^"^^
Doffer and calender —
, ^ 106203 , ,^„
^"^ 95878 = IIO^
46 COTTON SPINNING CALCULATIONS
Calenders and coiler delivery rollers —
, , 1097423 , _^.3
("> 1062^)3 = 1 ^^^
31 X 20 X 16 X 2" _
^^^ IS'x 20 X 16 X 4"  ^'^^
The Drafts between the Various Parts, how altered. — It will be
seen from the foregoing that the drafts between any of these
parts may be altered by changing the size of any driver, or
driven wheel, comprised in their connectional gear. Increasing
the size of a driver increases the rate of the part nearest the
feed, of the two parts concerned, and therefore reduces the draft,
and vice versa. Altering the driven wheels has the inverse of
the aforementioned effects.
To ascertain the draft between other points than those given
— which are those contained in the adjacent parts progressing
through the machine — all that is necessary is to multiply
together the intervening drafts between the parts involved.
Thus—
The total draft, i.e. between the lap and coiler delivery
rollers —
(a) = 104 X 1332 X 216 X 00346 X 1107 X 1033 = 1184
By comparison of the surface speeds of these two parts —
_ 1097423 _
^^^ ^1413^^^^
By the connectional gear and sizes of parts —
_ 48 X 12 X 40 X 216 X 31 X 20 X 16 X 2" ^
^"^^ ~ 17 X 14 X 40 X 30 X 15 X 20 X 16 X 6" ~
The draft between the feed roller and the doffer —
(a) = 1298 X 216 X 00346 = 97
(h) =^11^^ = 9904
_ 1 20 X 40 X 26 _
^'^  14 X 40 X 2} " ^^ "^
AND COSTS OF YARN 65
Points to be considered when altering the Drafts. — The following
should always be borne in mind when deciding the drafts between
the various points : —
The draft between the lap and the feed rollers should not be
more than sufficient to keep the lap straight. If this is exceeded
irregularity in the cotton fed will result. Smooth lap rollers are
liable to cause slipping of the lap, causing fluctuations, and
a greater draft than that estimated. The corrugated and ribbed
forms of lap roller eliminate this tendency.
The draft between the feed roller and lickerin varies con
siderably. It is customary to alter the speed of the former part
whenever a change in the draft is necessitated. That of the
latter part is rarely interfered with, being generally about one
half the rate of the cylinder. Altering the draft at this point,
therefore, changes the rate at which the fibres are presented to
the action of the lickerin, and therefore controls the duration of
its combing action upon any given fibre.
The draft between the flats and the cylinder is regarded
generally as fixed for different classes of cotton. Alterations
in this are made by varying the speed of the flats. The rate of
movement of the flats in the main governs the duration of the
cylinder's action upon a given body of fibres, and also the
amount of clean carding surfaces introduced, and hence it is
proper to vary their speed according to the exigencies of card
ing. With neppy, dirty, and matted cottons a higher rate of
this part is expedient. For low American, Indian, and like
qualities of cotton, they are worked at about double the rate in
vogue for the clean qualities of American and Egyptian.
The draft between the cylinder and doffer is also varied,
probably more than is expedient. In this the speed of the doffer
is often regarded as subordinate to the count of sliver. The
propriety of this is discussed elsewhere. The draft between the
dofler and the calender is only varied slightly. It should always
be such that the sliver, or " web," does not sag to an extent
which is detrimental. On the other hand, if the draft is too
much, irregularity through overstretching will result. The
draft between the calender and the coiler delivery rollers should
be sufiicient to maintain a slight tension at all times.
F
66 COTTOJ^ SriNNING CALCULATIONS
Conditions controlling the Output of a Card. — General con
ditions. — When circumstances demand an alteration in the
quantity of the output, a know'ledge of the limitations of each
action are essential in deciding the best manner of procuring
the same. This knowledge cannot be gained without intimate
association with the work. Assistance of a general character
may be afforded, and this is attempted in the following state
ments.
Greater the contrasting speeds of the carding parts, longer
the fibres are desired to remain in the carding action ; greater
the length of the fibres treated, closer the carding surfaces;
more numerous the fibres treated the greater the tendency to
strain the fibres.
The greater the length of the fibres treated the longer the
duration of the action of carding by reason of increased difficulty
involved in their separation.
The more numerous the body of fibres present in the carding
influences, beyond a certain limit : the greater the tendency of
damage to them by rolling and excessive straining. This occurs
whenever the quantity of fibres are in excess of the capacities of
the available carding surfaces, and results in some portion of
the weight of the flats being borne by the body of fibres instead
of by the bend. This tendency increases as the crowding becomes
more intense. This becomes apparent through the increased
power required to drive the card. Such conditions are more
likely to arise in treating long than with short, fibred cotton.
Inconsistent increases in the power consumed by these
machines, after alterations of this nature, may be regarded as
signs of overcrowded carding surfaces and straining of the
fibres.
Distinct conditions in respect of the actions of the carding imrts.
— The functions of the lickerin are to straighten the fibres
composing the fringe of the lap, eliminate foreign matter,
carry forward the treated fibres to the range of the cylinder's
action.
The functions of the cylinder are to take the fibres from the
lickerin, to carry them into the range of action of the card flats,
whereupon the latter arrest those fibres otherwise than straight.
AND COSTS OF YARN 67
The action of the cylinder, about this latter portion of the
machine, is directly upon those fibres held by the flats, and
partially projecting in the carding action. The gradual straight
ening and withdrawal of these, introduces others more or less
contiguous to the carding action. In this way the super
abundance of fibres which the flats receive during the earlier
period of their action are held in reserve, and gradually
brought into the action. As the fibres are gradually separated
and straightened, they are carried off by the cylinder.
The functions of the flats are to receive foreign bodies, fibres
that are entangled as well as those that are not straight —
not in line with the direction of the carding movement ; to
present such fibres to the range of action of the cylinder for a
definite period. The facility of the flats to arrest and detain
foreign bodies and to retain and present the fibres requiring
carding, depends upon the efficacy of the points, composing those
surfaces, and the quantity of these available.
Numerous sharp carding points accompanied with reasonable
spacing are the active agents in arresting and presenting fibres
for disentanglement and the retention of foreign matter and short
fibres. A sufficient supply of clean wire points should be con
tinually passing into action. Should this latter be insufficient
the imperfectly carded cotton from the lickerin would be carried
forward by the action of the cylinder, and in passing the
crowded surface of points of the flats, would tend to embed those
fibres already engaging the wire. Those fibres, brought forward,
which cannot be accommodated byreason of the crowded character
of the surfaces, are subjected to the pressure previously referred
to, and are thus strained, ruptured, and nepped according to the
degree of overcrowding.
To guard against the fibres becoming embedded care should
be observed to ensure that the proper inclination of the bend in
wire is preserved. This is often depressed through the stripping
brush being used in an unclean condition, also by its being
set too deep. The wire on all surfaces should have a fine
keen point, and this should be maintained in as uniform a
condition as possible.
The Rate of Movement of the Flats.— It would seem that if the
G8 COTTON SPINNING CALCULATIONS
wire surfaces act as heretofore described, a period very much
less than forty minutes would raore than suffice for the selection
of all the desirable fibres from those received by the fiat whilst
occupying the first position on the bend. Such may be the
case, but since the flats when even in their last position arrest
fibres— proved by passing a little coloured cotton in with the
lap, this making its appearance on the next flat exposed — the
best way in deciding the proper speed of flats is to recognize the
strips from them as the index. The speed should be adjusted
to give the lightest "strip" that will strip satisfactorily. To
adjust the percentage of strip by manipulating the front stripping
plate is wrong in principle. There is only one correct position
for that part, and that is as near the flats and cylinder as
practicable. Increasing its distance from the flats causes the
detachment of portions of the entangled fibre and impurities
selected in the carding action from the flats as they move out
of action, and thus polluting the work otherwise accom
plished.
In considering the rate of movement of the doffer, its
functions as well as the length or the weight must be kept
in mind.
The function of the doffer is to take the fibres from the
cylinder. The more completely this is accomplished the better.
Should the cylinder be only partially cleared of the fibres
borne upon it, its influence in carding will be interfered with
to that extent ; because it reduces the extent of the surface of
carding points at liberty to act upon those fibres presented by
the lickerin and " flat " surfaces. The aim, therefore, in working
the doffer should be to clear the cjdinder as completely as
possible, and to ensure this its surface rate should be as high as
practicable. This rate cannot be specified only in general terms
on account of the wide variations in the working conditions.
Light slivers, poor staple, bad laps, poor selvedges, unsatis
factory doffing combs, badly constructed sliver casements,
draughty rooms, all tend to restrict the speed at which the doffer
can be run. Under favourable conditions 16 revolutions per
minute can be attained.
The rate of the flats is as high as 3 per minute.
AND COSTS OP YARN 09
The rate of cylinders is 170180 revolutions per minute for
low American and like cottons.
The rate of cylinders is 160175 revolutions per minute for
Egyptian and American better qualities.
The rate of cylinders is 120160 revolutions per minute for
the longer stapled cotton than those enumerated above.
Changes in the Total Draft. — These are accomplished by altering
any of the following four wheels : Bevel wheels on the dofifer
and side shaft and feed roller. Since the side shaft transmits
the motion to the feed parts, a driver wheel will influence the
rate of the feed in the direct ratio and the draft inversely, whilst
a driven wheel will have the inverse effect. It is customary to
alter the draft by means of the side shaft wheel, driving that
on the feed roller, and hence it is called the draft change wheel.
Whenever this is impracticable, on account of the limits in size
of wheel applicable, it is customary to alter that on the feed
roller to an extent providing a more convenient range of drafts
with the wheels available. Occasionally the side shaft and doffer
bevels are altered, but usually these are inconveniently fixed for
this purpose.
ExKuciSE 4. — What changes in eaoh of the wheels formhig the draft gear
in Fig. IG would give IGO of a draft, assuming the present draft 120?
Workhifj and Ansivers^
Bevel wheel on doffer shaft = ^^ ^^}~^ = 30
Bevel on side shaft = —f^f— = b^
Sideshaft change wheel = li><J^ ^ jqi J (inconvenient ;
IbO  \ too small)
Bevel wheel on the feed roller = ^^^ ^^^''^ = IGO i
Exercise 5.— What drafts would the following sideshaft change wheel give,
respectivel}', assuming the card contains 120 of a draft when that wheel contains
18 teeth : 14, 15, 16, 17, 19, 20, 21, and 22 ?
Ans. 1543, 144, 135, 127, 1136, 108, 1028, 083, respectively.
Exercise 6. — What sizes of sideshaft change wheels would be required to
» Usually changed to secure fresh range of drafts for the available iideshaft
chansre wheel
70 COTTON SPINNING CALCULATIONS
obtain the following drafts, assuming 14 gave a draft of 120: 112, 105, 99
935, 885?
Ans. 15, 16, 17, 18, 19.
Exercise 7. — What size of feed roller wheel would be necessary, assuming
that card drafts ranging from 112 to 160 are required with the sideshaft change
wheels 14 to 20 inclusive, and a 14 sideshaft change wheel driving a 120 on the
feed roller give 120 of a draft?
Ans. 160.
What drafts would the various sizes of sideshaft change wheels give after
making the alteration referred to in the last question ?
Anstvers —
With the sideshaft change wheel 14 15 16 17 18 19 20
The draft would be . . . 160 1493 140 1318 1244 118 112
Weapping.
For measuring sliver and roves a special machine is used,
called a ■v\'rapping machine. This is arranged to measure one
yard per revolution. In using this instrument care must always
he taken to secure the movement of the cotton in a straight
line and also at a uniform tension, and at the same time pre
cautions taken against slippage. Five or six yards will be
sufficient length, and the sliver tested should be obtained from
different parts of the can, and from several of the cards in the
"preparation," in order to get precisely the conditions pre
vailing. The cotton, after being measured, should be compactly
wound in the form of a ball to obtain accurate weighing.
Exercise 8. — What should be the weight in grains per yard of the sliver
produced in cards containing the following total drafts respectively: 160, 149*3,
140, 181*8, 124*4, 118, 112, if the loss in the process m each case amounted to
5^ per cent., and the lap fed weighed 4375 grains per yard ?
" Ans. 258, 27*6, 295, 31*4, 33*2, 35, 36*8 respectively.
Exercise 9. — AVhat should the sliver weigh, per 5 yards, respectively, with
draft change wheels ranging from 15 to 22 inclusive, if 5 yards of the sliver
weigh 134 grains with a 14 wheel?
Ans. 5 dwts. 23^ grs., 6 dwts. 9 grs., 6 dwts. 19 grs., 8 dwts. 4 grs., 8 dwts.
14 grs., 8 dwts. 23 grs., 9 dwts. 9 grs., 9 dwts. 18 grs.
Exercise 10. — What draft change wheel would give slivers weighing
9 dwts. 6 grs., 9 dwts. 20 grs., 10 dwts. 11 grs., 11 dwts. 2 grs., 11 dwts. 17 grs.
respectively, per 6 yards, if with a 14 draft change 6 yards of the sliver weighs
203giains?
Ans. 15, 16, 17, 18, 19.
AND COSTS OF YARN 71
The Names applied to Cotton in its Preparation.
The following are terms used to designate the cotton in its
different stages of preparation : —
Yarn is the completely twisted thread of fihres.
Eove, or roving, the band of fibres twisted to bind them
sufficiently to resist handling. It is thus described after treat
ment in the slubbing, intermediate, roving, and "Jack" machines.
Sliver, is the band of fibres devoid of twist ; at least, it is
regarded as such. This term is used when the cotton is in a
round state, in the processes, between the carding and slubbing
stages.
Lap, denotes that the fibres are in a sheet or ribbon, formed
in a roll. This is the state at the opener, scutcher, card sliver
lap, ribbon lap, and combing machines.
The System of "Counting" Cotton in its Various Stages of Pre
paration. — This is adopted to express the length per unit of
weight in a concrete and simple form. The basis of the system,
used, is that of numerating the units of length contained in one
pound, avoirdupois ; the unit of length, used, being one hank.
A special length table is used for subdivision of the hank. It is
as follows : —
54 inches (1^ yds.) = 1 thread
80 threads (120 yds.) = 1 lea
7 leas (840 yds.) = 1 hank
The table of weights are—
24 grs. = 1 dwt.
18j1t dwts. (4371, grs.) = 1 oz.
16 ozs. (7000 grs.) = 1 lb.
Note. — The work is very much siraplitied by the adoption of grain weights
and pounds. Much vahiable time is lost in calculation when penny
weights and ounces are used.
Thus, the count signifies the number of hanks, in length, of
the cotton which are required to weigh 1 lb., and therefore —
1 hank (840 yds.) of No. 1 =1 lb. = 7000 grs.
1 lea (1 hank, or ^f^ yds. = 120 yds.) of No. 1 = ^" = 1000 „
72 COTTON SPINNING CALCULATIONS
I lea(T\bank,or^V4''y<^s.= 60yds.)of No. 1 = ^^'= 500 grs.
1 <'! 540L = BO ") =rJ^"= 250 ..
i / L 84^ = 12 ^ =L'^=. 100
10 " \ 70 " 70 " ^"^ " / " rjQ ^^^ >i
J <'J^ ^4ft = fi \ =t}^ — 50
20 " V140 >' 140 >' "J >) 7 5> 240 "
1_ / 1 8 40 — 1 "I — " •— 25.
120 '> \840 " 840 >' ~ ^ 5J ; )) ~ 840 ~ ''^ "
The above are the fractions of a hank usually measured
when testing the count of the cotton in the various stages of its
preparation.
In connection with the weight table a difficulty is experienced
in remembering that IS^^ dwts. make 1 oz. To remember that
7000 grs. make 1 lb., and that 24 grs. make 1 dwt., also that
16 ozs. make 1 lb., reduces the difficulty experienced in recalling
the number of pennyweights per ounce, because the penny
weights may then be reduced to grains and the grains to pounds.
If a similar difficulty occurs with the number of grains in an
ounce, by noting that 7000 grs. are contained in 1 lb. of 16 ozs.,
then ^f{]o = 437^, the grains in an ounce. In this way the
difficulties so often experienced by beginners are overcome.
In order to ascertain the count when the weight of a given
length is known, the procedure is to divide the weight into that
of a similar length of count No. 1, each expression being reduced
to common weight terms. Thus —
Examples —
For reasons, see page 73.
(rt) Required the count when 1 lea = 50 grains — ^t = 20
v'J }) » >> ^ " 1 X 24
(c)  4375  i^^^~ = 2285
(d) „ „ „ =i]b. =nr7ooo = ^'i^
(e) „ ,, 1 hank = 4375 grains = y = 1^
7000
~ 24
= 292
7000
100
= 70
1
~ 840 X
n "^
000119
1 X ]
16
001 905
840 X
: 1 ~
\J \J X U\J\J
1 X 7'
000
0H47
"840 X
24"
• \J iJt: 1
1
 840 ^
7000
1
= 83
AND COSTS OF YAllN
(/) Kequired the count when 1 hank = 24 grains
(9) „ „ „ =100 n
(/*) „ „ 1 yard = 1 lb.
(0 „ „ „ = 4375 grains
(^) „ „ „ =1
Notes on the worhing of the preceding Examples.
(a) The weiglit of 1 lea of No. 1 = 7 lb., ov^p^ grs. ; thus, the numerator
is 1000 and the denominator 50.
(h) The numerator is ] of the pennyweights in 1 lb., because it is the weight
of 1 lea of No. 1 in pennyweights, the weight expression of the denominator
used in this case.
mi • 1 i. • 1 i 1 11 1 X 7000
The pennyweights ui 1 of 1 lb.   — ^^
These converted to grains = M^iu  iqoo
and 1 dwt. in grains = 24
• iQoa — 4.17
(r) The numerator here is I of 1 lb. in ounces = ^£', and the denominator 1 ;
. 16 ooQf; 7000 1
..^^ =2285...; or, X 437:5
{(I) The numerator in this case is again } of 1 lb. and the denominator 1 ;
.. } X I = } = 0142...
(e) In this instance the numerator is 1 lb., or IG ozs., and the denominator
^■^r lb. or 1 oz. respectively, and hence the count = —  or ^' respectively.
ic
(/) The weight of pounds and ounces can always be more conveniently
expressed in grains than in pennyweights, and hence the numerator is reduced
to 7000 grs., and the denominator to 24 grs. ;
• 2.00(1
(//) One over 840 is the numerator, because it is the weight of yard of
No. 1 expressed in pounds, and 1 the denominator.
Exercise 11. — What are the counts of—
(a) 1 lea = 4 dwts. 4 grs. ?
(&) 60 yards = 2 dwts. 2 grs. ?
74 COTTON SPINNING CALCULATIONS
(c) 95 yards = 50 grs. ?
(d) 21 leas = 125 grs.?
(e) 4 leas = 1 dwt. 16 grs.?
(/) 1 yard = 1 dwt. 1 gr. ?
(g) 5 yards = 7 dwts. 12 grs. ?
(h) 1 yard = 12 dwts. ?
What should be the weight in grains of —
(i) 1 yard of No. 1 ?
(j) 1 lea of 40', 3G\ 84^ 79' ?
(k) 30 yards of 4' ?
(0 60 yards of 10'?
(m) 6 yards of 02' ?
(n) 15 yards of 025'?
(o) 1 yard, 00340, in ounces?
Exercise 12. — What would be the count and weight in ounces per yard of
the laps fed in cards containing each 120 of a draft if the amount lost in waste
is 5 per cent., and the count and weight of the sliver are —
Kespective count
Kespective weight in grains per yard
Ans. Count = 0002225
Ounces per yard = 9
Exercise 13. — What would be the count of the sliver and its weight in grains
per yard if the draft in the card was 152 and the lap weighed 80 ozs. per yard,
the loss in waste being 5 per cent. ?
Ans. Count =: 032
Weight = 2735 grs.
Exercise 14. — What weight of sliver, in grains per yard respectively, would
be necessary to enable a card to produce 800 lbs. of sliver per week of 55
working hours with a doffer 126£ inches diameter when run at 16, 15, 14, 13,
and 12 revolutions per minute respectively?
Ans. 455, 485, 52, 56, 617.
Exercise 15. — What would be the count and weight of the sliver, in grains
per yard, in cards containing 120 of a draft, if the lap fed averaged 10, 11, 12
13, and 14 ozs. per yard respectively, and the waste in carding was 5^ per cent. ?
Ans. 0242 022 0202 086 count.
344 3785 413 4475 weight in grains per yard.
Exercise 16. — What should be the weight of the sliver, in grains per yard,
produced by a card containing 120 of a draft, if the lap weighs 10 ozs. per yard
and the waste extracted is 5 per cent. ?
Ans. 346 grs.
0267
0241
0192 0.16
d 312
346
433 52
0002083
00016
000133
10
12,^
15
AND COSTS OF YARN 75
Exercise 17. — What should be the weight of the lap suitable for a card it
the loss in waste is 5 per cent., the draft being 120 and the sliver is required
to weigh 36 grs. per yard ?
Ans. 4547 grs., or 1038 ozs.
Exercise 18. — At what rate, in revolutions per minute, should the doffer in
a card be worked in order to produce 400 lbs. of sliver of 34*G grs. per yard
in 54 liours' continuous working, if the doiler is 24*75 inches in diameter and the
draft between this part and the coiler delivery roller is 1*10 ?
Ans. 10"5 revolutions.
The Length of Fillit required to Cloth the Cylindrical Surfaces. —
In calculating the length of the fillit required, it is necessary
to allow one coil extra in addition to that sufficient for holding.
Thus, a cylinder 50 inches diameter, 38 inches wide, to be
covered with fillit 2 inches in width, would require 4f coils + 1,
and the length for holding, say, about 6 feet —
/. f ^ X 2^ X ^ feet + 6 feet = 268 feet
Doffers 24 inches diameter, 38 inches wide, clothed with 1^ inches
fillit, require about 4 feet for holding, and —
fl X ^^ X ^^ feet + 4 feet = 130 feet
The following is the procedure in forming the spirals, termed
" halflap " and tapered tail ends, respectively. The latter is
commenced the width of one staple and increased gradually to
the full width in a length equal to the first coil. The former is
commenced onethird or onehalf the width, and the spiral
obtained in one and a half or two coils, the finishing ends
terminating in the inverse manner.
Example of preparing "Halflap." — Assuming the fillifc contains
six columns in the width, half the width will be convenient for
the commencement; maintain this width for half a coil, and
then proceed to add a column, on the righthand side, at points
equidistant in the next half coil. In doing this it is necessary
to have the commencement of the last row of each column a
distance from the first row of the next column of ^ of A of l the
circumference of the cylinder. Thus three columns would be
added in the latter half of the first coil. Afterwards, com
mencement is on the right hand, the left half of the end of the
first coil must be secured to the "jumpend" of the beginning
76 COTTON SriNNTNG CALCULATIONS
of the first coil, and the second coil is commenced with the
righthand half. The lefthand portion is prepared for the cut
away portion as follows : Proceed to widen the right half of the
second coil by the addition of rows and columns on the lefthand
side in the same manner and at the same rate as with the
tapered portion of the first coil, but from the commencement of
the second coil, thereby obtaining the full width at a point
opposite the commencement of the taper in the first coil. This
completes the preparation for cutting.
When the columns are odd in number, for instance, seven,
commence with the width of three columns to extend over 2 of
the circumference, and then proceed to make the tapered portion
over the remaining i of the first coil, and put in the remaining
three columns required to complete the spiral, in the first 2 of
the second coil. In the former instance the spiral extends over
1^, coils at each end, and in the latter over If.
The tapered tail end — completed in one coil — is defective in
that the terminals cannot be sufiiciently tensioned for satis
factory grinding and working. The tapering should always be
on the inside and not on the outside, this being the most com
mon method. Extending the taper in halflap over the whole of
the first coil, necessarily extends the taper over the second coil.
This would largely reduce the number of wire points over these
portions, making wide gaps of absent points. The finishingoft"
preparation is exactly the inverse of the commencement.
licmemher that uniformity in the character of the point
is dependent upon uniform resilence of the wire, and this
support it obtains through the medium of the tension at the
foundation.
The Slivee Lap ^Machine.
Fig. 17 represents some of the principal parts and the
gearing in the sliver lap machine.
The object of this machine is to prepare a ribbon of fibres of
uniform width, weight, and, as far as practicable, with the
fibres laid parallel and distributed uniformly. This latter is
only partially obtained, and hence the succeeding process.
AND COSTS OF YARN
11
The machine consists of parts having the following
functions : —
29
72
50
26
33
6*1
64
12"Dia.
12'Dia.
5 Dia.
5 Dia.
l2Dia.
1^Dia.
30
30
73
21
21
16 Dia.
I^Dia. 
22,
26
Fig. 17.
(a) The feed parts, not shown, for presenting a fixed number
of the carded sHvers in uniform tension, alignment, and placed as
78 COTTON SPINNING CALCULATIONS
close as practicable. Also means for the detection of missing
slivers and stopping the machine.
(&) The rollers (1[, X li X ll) for attenuating the above
named slivers to the most beneficial extent, this is generally up
to about 2.
(c) The calenders (5" X 5") for smoothing and pressing the
attenuated ribbon of fibres.
(cl) The lap rollers (12" x 12") for winding the continuous
ribbon of fibres tightly upon a wood roller.
Calculations relating to the Sliver Lap Machine (Pig. 17). — This
machine is driven by a strap from a 9inch drum on a line shaft
making 220 revolutions per minute.
The calculated revolutions per minute of the various parts
are as follows : —
Machine shaft ,_ ^^^^ ^ 220x9
(16"1329) /  ^"^"^ ^^> °^'' ~~16~
First drawing roller \ _ o , o 220 X 9 X 29 X 21 x 50 X 41 X 33
(6426U") I  «^ , or, 16 x 72 X 21 X 26 X 24 x"64
Second drawing \ _ qq f; 220 X 9 X 21 x_50 X 41 x 33 X 26
roller (221^" / " '^'^'^> ^^'' 16 x 21 x 26 X 24 x 64 X 22
842x26
or, — 22—
Third drawing roller^ _.noo 220 x 9 X 29x21x50 X 41
(2433U") /  ^^^ ^' 0^' 16 X 72 X 21 X 26 X 24
First and second] 220x9x29
calenders > = 49'8, or, . — z^
(505"), (725") J 1^ ^ 7^
, 220 X 9 X 29 X 21
^""^ 16^02^^
Lap rollers . „^ ^ , 220 x 9 x 13
(12"7330) } = 22 04, or, ^^^^
220 X 9 X 13x30
16x73x30
Drafts —
Between second and \ , ., o . 26 x 11"
first rollers /  1 1°, or, 22x1.^"
Between third and \ _ ^ 22 x 64 X 1^ "
second rollers / — 1 "4, or, 26x33x1}"
and
AND COSTS OF YAEN 79
Between third and^ _ , q < 64x1?/
first rollers /  l'^^, or, ^^ ^ ^y,
Between calender \ _ , ^, . 24 X 26 x 5"
and third roller / " ^'^^^^ °^'' 41 X 50 x V/
Between calender  _,.n7 . 64 X 24 x 26 X 5''
and first roller /  ^"^ ' ' ^^'' 33x 41 x 50 X IV'
Between lap roller! 72x13x12^^
and calender •' ~ ' °^'' 29 X 73 x 5"
Between lap roller ^ _ 64 x 24 x 26 X 21 X 72 x 13 X 12"
and first roller } " '^'^^' °^' 33 x 41 x 50 x 21 x 29 X 73 X 1 y'
Production. — What should the lap weigh in grains per yard
if the number of slivers fed are 14, and each weigh 30 grains
per yard ?
, ,_^ 14 X 30
Ans. 202, or, ^^^^ .
What should be the weight of lap produced in pounds per
week of 55 hours, no allowances ?
^,^^ 2204 X 55 X 60 X 12 X 22 x 202
Ans. 2182, or, ^^^ 7 X 700~0
What length in hanks per week should be delivered under the
conditions given ?
2204 X 55 X 60 X 12 X 22
Ans. 90, or.
840 X 36 X 7
To alter the Production. — To alter the length delivered :
Change the speed of the whole by altering the machine pulleys.
To alter the weight delivered : This may be done by allow
ing the length to remain unaltered or otherwise ; in the latter
case the weightunit of the lap need not be altered, but in the
former it would be necessary. The weightunit of the lap and
of the production may be altered by changing the draft or the
weight of the feed. Draft affects the weight in the inverse pro
portion, whilst change in the weight of the feed would act in
the direct proportion.
Changes in the draft of this machine are not frequent.
When necessary they are confined to the alteration in the draft
between the first and third drawing rollers.
80 COTTON SPINNING CALCULATIONS
Exercises in Changing the Sliveu Lap Machine.
Exercise 1.— With the speeds as in the figure (17), what effect would changing
the weight of the sliver, from 30 to 36 grains per yard, have upon the laps
produced : (a) The weiglit per yard ? (b) The weight produced per unit of time ?
(c) The length produced in hanks? Jns. 252 grs. ; 2620 lbs. ; 90 hanks.
Exercise 2.— What changes would be necessary if the sliver used was altered
from 30 grains to 36 grains per yard, in order that the weight and length units,
delivered, be unaffected?
Ans. Alter the draft change wheel to increase the draft : : 30 : 36.
Exercise 3. — What changes would secure the same weight per unit of time,
and at the same time alter the weiglit of the lap ^ ? Ans. Altering the draft ^.
Exercise 4. — What would be the weight per yard, and of laps per 10 hours,
if each lap measured 280 yards and one minute is lost at the completion of each ?
The lap rollers being of the size given in the figure, and make 20 revolutions
per minute ; each of the fourteen slivers fed weigh 28 grains per yard, and the
draft in the machine is 208.
The Ribbon Lap Machine.
Fig. 18 represents some of the principal parts and the
gearing in a ribbon lap machine.
The object of the machine is : to prepare from the sliver laps
one which has the fibres arranged in the most suitable manner
for combing ; to make the ribbon of fibres uniform in thickness,
width, and weight throughout, and with all the fibres parallel.
This machine consists of parts having the following functions :
(a) The feed parts : Lap rollers 3 ins. diameter, and the
detector of missing and light laps ; the latter is not shown.
(h) The rollers (1] x 11 X li xlJ,) for attenuating the
ribbon of fibres to the extent necessary, to lay the fibres parallel,
and to make the ribbon the desired weight.
(c) The curved folding plate C guides the ribbon, passing
from the rollers, on to the folding table D, placing it upon the
latter at right angles to the rollers. In the figure only one
head is shown. The machine is usually made with six heads,
to treat six sliver laps, and hence the rollers are constructed to
deal with that number. There are, therefore, six curved folding
plates, and the folding table is continued to the left accordingly.
(d) The carrier and compressing rollers, 3 ins. diameter, are
placed at intervals along the folding plate to move forward the
folded ribbons.
AND COSTS OF YARN
81
rrt
c^
o
in
ol
b
^1
1
in
1
ci
cj
82 COTTON SPINNING CALCULATIONS
(e) The calender rollers (5" X 5") for smoothing and
pressing the ribbons and completely uniting them.
(/) The lap rollers (12" X 12") for winding the continuous
ribbon of fibres, or lap, tightly upon a wood roller.
The machine is driven by a strap from a 9inch drum on the
line shaft which makes 220 revolutions per minute and drives
the 16inch pulleys on the machine shaft.
The revolutions per minute of its various parts are as
follows : —
T. n 1 n /o'/N iQ.r 220x9x72x25x54x30
Feed lap rollers (3 ) = 13*5, or, — :r^ — wt^ — ^r^r — —  — —
^ ^ ^ ' ' 16x68x100x70x56
The first draw roller \ _ o^ o 220 x 9 X 72 x 2 5 x 54
(374070) I  ^5 d, or, 16 x 68 X 100 x 70
The fourth draw roller. _ ,^, 220 x 9 X 72
(6825li") }  ^'^^' ^^''
The carrier and com \ _ „,
pressing roller (223") / ~ '^' ^^'
The calenders (215") = 4425, or.
The lap rollers (12"12") = 1855, or,
)
16 X 68
220 X
9
X
31 X
22
16
X
54 X
22
220
X
9
X 20
X
15
31,
16
X 40
X
21
220
nv
X
9
X 20
X
15
X
21
16 X 40 X 21 X 50
Drafts —
Between first roller and^ _ ^ ^o "^^ ^ ^
the feed lap roller / " ^'^^' °^*' 37 x~3
Between second roller \ _ ^^ 37 x 1^
and the first roller / " ^''^'^' °^' 30 X 1
Between third roller and \ _ ...q 30 X 40 x li
the second roller /  ^''^^' ^^' 37 x 22 X li
Between third roller and ) _ ^ qo 40 X li
the first roller /  ^'^^' °^'' 22 x l
Between fourth roller and I ^ op 22 x 70 x 100 x Jj
the third roller / " ^'^^' ^^> 40 X 54 x 25 xTi
Between fourth roller and I _ ^ in "^^ ^ ^^^ ^ ^l
the first roller /  '^'^^> ^^> 54 x 25 X ll
Between carrier and the ^ _ . ^ ^ 68 x 31 X 22 x 3
fourth roller   1"18, or, 72 x 54 x 22 x 1
Between calender and \ ^ ^.o 22 x 54 X 20 X 15 X 5
carrier roller )  ^'^^' ^r, 22 x 31 x 40 x 21 X 3
AND COSTS OF YARN 83
Between lap rollers and ■» _ , ./^, . 21 x 12
the calenders  ~ ^'^^' °^*' 50 X 5
Between delivery lap rollers and the feed lap rollers = 6*05,
. 76 X 70 X 100 X 68 X 20 X 15 X 21 X 12
°^'' 37 X 54 X 25 X 72 X 40 X 21 X 50 X 3
Production. — The weight, per unit of length of the lap made,
is controlled by the weight of the laps fed, and by the total
draft. Any alteration in the latter items affect the former in
the direct and inverse proportions respectively, namely —
The heavier the feed, the heavier the lap, and vice versa.
The greater the draft, the lighter the lap, and vice versa.
The length delivered is only affected by the alteration of
speed of the machine shaft.
It is customary to regulate the weight of the lap by altering
the draft ; but sometimes by altering the weight of the lap fed.
The draft can be altered to a very considerable extent with
out influencing the quality of the work.
The customary changes are made through : The pinion (54)
or the backroller wheel (70) for the draft ; the machine pulleys
(16 inches) for speed.
The restrictions in altering the draft and weight of the feed
arise from the gross weight of the laps J;hat are required for the
combing machines.
Example 1. — If this machine has six heads, and the laps fed each weigh at
the rate of 202 grains per yard ; what weight of laps in pounds would be produced
in 10 hours' uninterrupted working, and what would be the weight of these
in grains per yard ?
. 202 X 6 f.^^ . 1
4«s, — —  — = 200 grains per yard
605 ^ ^ •'
^^.. 12 22 10x60x200 „„„ „
1855 X 3^ X y X .QQQ = 333 lbs.
EX.UIPLE 2. — What would be the weight of the laps per yard if the draft
change pinion 54 was changed to 3G ? How would this change influence the
weight and length produced in ten hours ?
Ans. The draft would be altered in the inverse proportion to the change
wheels, and hence —
605 X 54 _ q.()7
36
84 COTTON SPINNING CALCULATIONS
and the weight per yard of the lap produced would become lighter in direct
proportion to the change in this wheel, and therefore —
200 X 36 , „„ . ,
^2 = 133 grains per j^ard
And the weight produced in 10 hours would be affected in the same terms,
54 : 36, the length remaining unaffected.
Exercises.
1. The feed consists of six heads, and the weight per yard of the laps is 240
giains, the draft required being 5. What weight of lap, per yard and per 10
hours, should be produced, allowing 2^ per cent, for stoppages ? Also, what
draft pinion wheel would be necessary to adapt the machine, other particulars
being as per Fig. 18?
2. If the machine was producing laps weighing 240 grains per yard, geared
as in Fig. 18, what would be the average weight per yard of the laps fed ?
3. Upon testing the weight of the laps produced, they are found 224 giains
per yard instead of 240 grains : what sizes of draft pinion or backroller wheel
would restore the laps produced to their proper weight ? Also, give the pro
portional alteration that this change would make in the weight of laps produced
per unit of time.
4. If the draft pinion 54 was changed to 60, what effect would it have upon
the drafts between : (a) the first and second ; (6) the second and third ; (c) the
third and fourth rollers respectively ?
5. If the weight per yard of the laps produced became 240 grains instead
of 200, what would you suspect, and what would you do ?
Combing Machines.
Fig. 19 represents the gearing in the Nasmith combing
machine.
The object of this machine is to comb the fibres and reject
those that are defective and below a specified length.
The cotton for treatment in this machine is prepared from
the card sliver, by the sliver and ribbon lap machines, an
alternative to these processes being one head of drawing followed
by the Derby Doubler. The former is the modern system, and
has many advantages over the latter, the chief of these
advantages being a reduction in the good fibres wasted.
The names of the parts in the figure are as follows : —
E, the lap rollers,
F, the pawl actuating the lap roller gear.
AND COSTS OP YARN
85
CM//"
Nr.iK
o
<N"H —
CM CO
g "Si
^■^J»
86 COTTON SPINNING CALCULATIONS
G, a crank on the oscillating shaft H.
HI, the oscillating shaft for operating the feed and the
advancing and receding movements of the nippers.
J, a lever coupled to the shaft HI at I.
K, a crank ; its stud and slide operate the lever J.
L, the machine driving shaft.
U, a cam on the comh cylinder shaft.
T, a quadrant rack lever centred on HI, and actuated by a
stud and bowl, the latter projecting into the cam U.
E and 30 is the quadrant rack pinion and spindle.
47 is an escapement clutch, the left toothed portion being
secured to the spindle E, the right portion being loose upon
E, and engaged and disengaged with the left portion to obtain
movement of the wheel containing 47 teeth.
P, a cam for controlling the clutch Q.
V are the detaching rollers connected by a train of wheels,
47, 20, 18, 17, with the clutch.
M, the comb cylinder.
N, the brush cylinder.
0, the card cylinder.
W, the head calender ; there is one for each head.
30, 25, 17, 20, are the " drawbox." The drawrollers are
four in number, to attenuate the combed slivers.
Y, the drawbox calender.
Z, the coiler delivery rollers, and the coiler and can wheels
are shown beneath.
The speed of the comb cylinder in this machine ranges from
90 to 100, according to the quality of staple treated. This
machine is especially adapted for combing the shorter staples
from the equivalent of G. Middlings American and upwards.
Another feature of the machine is the wider range of selection in
respect of the length of the fibres rejected. With good staples
this can be reduced to as low as 12 per cent, without interfering
with the thoroughness of the combing. The piecing is accom
plished on a much better principle, and the adjustments are all
much simpler than in the machines constructed on the Heilmann
system. The production is also considerably greater.
The following are the speeds of the various parts and manner
23 X 90
100 X 90 X 24
23 X 20
. 100 X 25 X 1
25 X 32
100 X 4 X
42
X
35
75 X
80
X
47
lOOx 5 X
42
X
35
^^' 75 X
80
X
47
AND COSTS OF YARN 87
of ascertaining them by calculation when the comb cylinder makes
100 revolutions per minute : —
Machine pulley = 391/. : ^^^^^
Cam shaft = 100 :i^^^^^AB
Brush cylinder = 470 :
Card cylinder = 3125
Lap Rollers.
Assuming the pawls to move \
four teeth per revolution ( = 2*085
of the comb cylinder )
Ditto five teeth ditto = 2606
Note.— The number of teeth moved bj^ the pawls may be adjusted to give
the desired length of feed. This is the medium of altering the draft. There
are two pawl levers, one actuating the feed and the other the lap rollers, in a
similar manner, but separately driven.
Detaching Rollers.— These are actuated through the medium
of the quadrant rack and escapement clutch, the movement of
the former being communicated to the rollers only when the
latter is closed. The quadrant moves up and down seventeen
teeth each revolution of the comb cylinder. The clutch escape
ment is open during a period amounting to eight teeth of the
upward movement of the quadrant rack. At this point, in
the upward movement, the latter makes a pause to enable
the escapement clutch to be closed, and then it resumes the
upward movement. This has the effect of turning the detaching
rollers backward to the extent of nine teeth of the movement of
the quadrant rack. The clutch remains closed during the whole
of the downward movement, and hence the detaching rollers are
moved backward nine teeth and forward seventeen teeth of the
quadrant's action. The pinion engaging the quadrant rack con
tains thirty teeth, and therefore makes ^ of a complete oscillation
each revolution of the comb cylinder ; s% and Ifj of this move
ment are therefore utilized in turning the rollers backward and
88 COTTON SPINNING CALCULATIONS
forward, respectively. Hence, these movements result in the first
9 X 47 17 X 47
detaching roller moving ^ — ^. backward, and ^ — ^ forward,
respectively, per revolution of the comb cylinder. This amounts
to the following rates per minute : —
Backward, ;^ ^ = 70 "5 revolutions
„ ^ 100 X 17 X 47 ,„.,, , ,.
Forward, — ^rr ^ = 133^ revolutions
oU X Ay)
the forward progress per minute amounting to (133^ — 70"5)j"o
X 52 = 177"2.
The second detaching roller exceeds the movement of the
first as 18 : 17 on account of the gear.
These amounts must be regarded as fixed, as adjustments of
this gearing are not arranged for.
The combing head calenders are 2f inches in diameter, and
make 19*947 revolutions per minute —
100 X 48 X 43 X 40 X 16 X 17 X 33 X 20
24 X 40 X 50 X 25 X 43 X 72 X 20
The revolutions per minute of the first draw roller = 58'645—
100 X 48 X 43 X 4 X 1 6 X 17
24 X 40 X 50 X 25 X 30
The revolutions per minute of the second draw roller
= 70374—
100 X 48 X 43 X 40 X 16 X 17
24 X 40 X 50 X 25 X 25
The revolutions per minute of the third draw roller = 110 —
100 X 48 X 43 X 40 X 1 6
24 X 40 X 50 X 25
The revolutions per minute of the fourth draw roller
= 27742—
100 X^ 48 X 43 XjlO
24 X 4'0~xl^l
AND COSTS OF YARN 89
The revolutions per minute of the drawbox calender = 126 —
100 X 48 X 43 X 40 X 2
24 X 40 X 31 X 44
The revolutions per minute of the coiler delivery rollers
= 17943—
100 X 48 X 43 X 40 X 70 X 20 X 20
24 X 40 X 55 X 61 X 20 X 20
The revolutions per minute of the coiler = 5216 ;
„ ,, can = 694 —
100 X 48 X 43 X 40 X 70 X 20 x 13 X 18 X 18
24 xlOlTSS^X 61 X 20 X 3^"x¥6 X 84
The drafts between the parts in progressive order work out
as follows : —
(a) Lap and first detaching roller by gear direct. The
progressive movement in respect of the detaching roller amounts
to 17  9 = 8 teeth of the quadrant wheel, or o^^ of the 47
clutch wheel which drives that roller, per revolution of the
comb cylinder, and therefore —
 „ — 90 = ^^® progressive movement or the amount gained in
revolutions of the detaching roller per revolution
of the comb cylinder or per nip.
The movement of the lap rollers train of wheels is derived
from a pawl moving the ratchet wheel, 75, a certain number
of teeth each nip ; the extent of this movement can be varied,
and is one medium of tensioning the lap. The feed roller is
not shown, but it is also worked by a pawl and ratchet, the
pawl being operated each nip, and the ratchet wheel is
secured upon the feed roller. The movement of the feed roller
is adjusted in altering the draft. If the pawl is moved four
teeth per nip or revolution of the comb cylinder, the movement
of the lap rollers per nip will be the denominator in the
succeeding calculations. Hence the draft —
90 COTTON SPINNING CALCULATIONS
(a) By gear direct —
8 X 47 X 9 '^
^ 30x20x10 ^ 8 X 47 X 9 X 75 X 80 X 47 X 4 _
4 X42X35 ,,, 30X20X10X 4 X42X35~X 11 ~^'^^
75 X 80 X 47 ^
(b) By calculated surface speeds per minute—
The draft between the first and second detaching rollers —
('') = }f[: = 1058
The draft between the second detaching rollers and the
combing head calenders —
48x43x40x16x17x83x20
^ 24 X 40 X 50 X 25 X 43 X 72 X 20 ^ ^
8 X 47x18 X 9
30x20x17 xlO
= 48x43x40 xl6x ITx 33 X 20 X 11x30x20 x 17 x 10
24 X 40 X 50 X 25 X 43 X 72 X 20 X 4 X 8 X 47 X 18 x"9
= 0916
1 72"4
<'') =187^8= O^lS
The draft between the combing head calenders and the first
drawhead roller —
(a) = 20X72X43X li _
"^ ^ 20x33x30x21 ~ ^"^^
W ^ 207:35 ^
^ ^ 1724 ^ ^
The draft between the first and second drawhead rollers —
, , 30X9X8 , ^
(^^ =28^8X9 = ^"'^
n\ 24882 ^^
^'^ = 207^5 = ^'^
(«)
AND COSTS OF YARN 91
The draft between the second and third drawhead rollers —
/ N 30 X 9 X 8 . _ _ .
^«> = I7x¥x9 = ^'^^'
^^ ~ 24882
The draft between the thhd and fourth drawhead rollers —
(b) = i^^ = 279
^^^ 38921 ^ ^^
The draft between the fourth drawhead roller and the
subsequent calender —
/ N 20 X 2 ,
1089 .
^^> = 1089 = ^
The draft between the drawhead calender and the coiler
delivery rollers —
. . _ 44 X 31 X 70 X 20 X 20 x 2 _
^""^ ~20x55x61x20x20x2i~^^'^^
(^> = w = '■'''
The draft between the lap rollers and the coiler delivery
rollers, when the pawl moves 4 teeth per nip —
48 X 43 X 40 X 70 X 20 X 20
. , 24 X 40 X 55 X 61 X 20 X 20
(a) =
X2
4 X 42x35 ^„
X2J
75X80X47
^ 48x43x 40 x70x20x20x 2 X 47x 80x75
24 X 40 X 55 X 61 X 20 X 20 X 2j X 35 X 42 X 4
= 6258
Draft between the lap and coiler delivery rollers when the
pawl moves the feedratchet wheel 5 teeth and 8 teeth
respectively —
(«) = "^ = 5008
92 COTTON SPINNING CALCULATIONS
(i) = ^iS? = 3129
By proportion —
By proportion —
3604
6258 X 4
5
6258 X 4
= 5007
= 3129
The percentage of waste at this machine is rarely lower than
14 per cent. If 15 per cent, be allowed, and the weight of the
laps per yard be each taken as 28 dwts., a machine with 4 heads
... 28 dwts. X 24 grs. X 4 heads ^ 85
would produce a sliver weighmg fi2^^8 lOO
when the feed pawl moves 4 teeth per nip = 3651 grs. per yard.
28 X 24 X 4
And when the feed is actuated 5 teeth per nip, kTvau"
^ 100 ^ 4562 grs. per yard.
Note. — The length fed of lap per nip when the pawl moves 8 teeth would be
The latter length would prove in most cases an impracticable
amount in this machine. It would make the combing action
very severe, throwing a great deal more work on the top comb
than it is capable of accomplishing. Another way of adjusting
the draft in this machine is by changing the wheel compounded
with the feed ratchet wheel ; this may be called the draft
change wheel. Altering this wheel will alter the draft in the
inverse ratio, because it will reduce the length feed when it is
reduced in size. Changes in the weight of the sliver and the
output of the machine may be accomplished by —
(a) The draft is altered by the wheel coupled with the ratchet
wheel, or by increasing the radius of the pawl lever.
Note. — This wheel can only be altered to a limited extent, owing to its alter
ing the ratio between the lap and the feed rollers ; unless the pawl lever, operating
the latter, is altered at the same time. The lap is liable to be unduly stretched
or puckered if this is not done.
AND COSTS OF YAEN 93
(b) Altering the weight of the lap.
(c) Altering the length delivered by changing the speed
of the machine.
The production in hanks and pounds per week of a Nasmith
machine geared as in the figure and having four heads, the
comb cylinder making 100 nips per minute, using laps 28 dwts.
per yard, the draft 62*58, 15 per cent, being lost in strips,
time lost 10 per cent., engine time 55 hours per week, would
be computed as follows : —
55 X 90 X 60 _ (minutes worked per week
100 ~ i less allowances
55 X 90 X 60 X 17943 X 2" x 22 ^ i inches delivered per week by
^110 7 ~ ^ the coiler delivery rollers
55 X 90 X 60 X 17943 x 2" x 22 ^ j hanks delivered per week by
100 X 840 X 36 7 1 the coiler delivery rollers
= 11082
Percent. Revs. P.M. Dia. HrB. Mins. [yards delivered by the
90 X 1794 3 X 2^^ X 22 X 55 X 60 ^ coiler delivery rollers
100 X 36" 7 ( per week, less stoppages
Grs. D«t8. Laps. Percent.
24 X 28 X 4 X 85 _ j weight of the sHver in
6258 X 100 ~ I grains per yard
Draft.
Weight in pounds of the sliver delivered by the machine per
week of 55 hours, no allowance
24 X 28 X 4 X 85 X 17943 X 2 X 22 X 55 X 90 X 60
6258 X 100 X 36 x 7 X 100x7000
= 4853
The production, in case the feed pawl moved 5 teeth per nip
instead of 4, would be —
Weight of the sliver per yard when pawl moved 4 teeth —
4 X 28 X 24 85 ^^ „
6258 ^ 100 = ^^"^ ^^^^^^
Weight of the sliver per yard when the pawl moves 5 teeth —
_ 365 X 5 _ ^^.^
94 COTTON SPINNING CALCULATIONS
Production in pounds per week of 55 hours —
4853 X 5 ^^^ . ,,
= 606*5 lbs.
4
The length delivered after the alteration would be the same,
but the length fed would be one quarter more, and therefore the
weight delivered would be proportionately increased.
The production per week, if the feed pawl moved the lap
rollers 8 teeth, would be —
4853 X 8
lbs. = 9706
Exercise 1. — Assuming the speed of the comb cylinder 100 revolutions per
minute, and the machine puUej's 14 inches in diameter are changed to 12i inches,
what would be the speeds of each of the parts of the machine ?
Ansiver —
Lap rollers with the pawl moving 4 teeth 2335
,, ,, „ ,, o'oob
First detaching roller, backward . . . 78'96
„ „ „ forward . . . 149146
Second „ ,, backward. . . 830
„ ,, „ forward . . . 15792
Cam shaft 112
Comb cylinder 112
Machine shaft 4382%
Brush cylinder 404*5
Card „ 35
Combing head calenders 23936
First drawing roller 65082
Second „ 78818
Third „ 12329
Fourth „ 31071
Drawbox calender 14112
Coiler delivery roller 20096
Coiler 5842
Can 777
Exercise 2. — What would be the consumption of laps and production of sliver,
in hanks and pounds, per 50 hours' uninterrupted working of a Nasmith comber,
and the weight of the lap per yard ; also the percentage of the waste extracted,
under the folloAving conditions ? —
Sliver produced in 1 minute, 1117 grains.
Strips ,, ,, 292 grains.
AND COSTS OF YARX 95
Weight of the sliver, 40 grains per yard.
Number of combing heads, 4.
Draft in the machine, 50.
Ansiver —
Length of lap in hanks = 8*328
Weight of laps in pounds = G24'8
Length of sliver in hanks = 104"1
Weight of sliver in pounds = 499'7
Percentage of waste = 20
Weight of the lap per yard = 649 grains.
Exercise 3, — Calculate the amounts of the laps consumed and the sliver
produced, in hanks and pounds, if the pawl moved 5 teeth instead of 4,
assuming the latter gives 625 lbs. weight of sliver, and the other conditions as
given in the answer to the previous question.
625_^x^5^3^^^3^.2^jj^^_,^^^^
^'^^^ ^ ^ = 1041 hank of lap
4
The length of the sliver would be unaltered.
The weight of the sliver would be • ^ = 6246 lbs.
Exercise 4. — What would be the consumption of laps and the sliver produced,
in hanks and pounds, per 50 hours' uninterrupted working in a Nasmith comber ;
also, the percentage of the waste made when the conditions are as follows ? —
Production in one minute, 1120 grains of sliver ; strips, 280 grains ; weight of
one yard of sliver, 40 grains ; number of combing heads, 4 ; draft, 50.
Answer — Sliver Laps
Hanks per week .... 100 8
Pounds „ .... 480 600
Percentage of the waste, 20
Fig 20 represents the gearing in a single acting combing
machine on the Heilmann system.
The object of this machine is to comb the fibres and reject
those that are defective and below a specified length.
The cotton is prepared for this process in the same manner
as that for the Nasmith combing machine, the range in the
weight of the laps for the Heilmann being from 200 to 400
grains per yard, and for the Nasmith about double that
weight.
The actions in these two types of combing machines differ,
fundamentally, in that the fibres in the Nasmith machine are
96
COTTON SPINNING CALCULATIONS
only submitted to once combing, whereas in the Heilmann they
are submitted a number of times, their introduction to that
action being graduated. The effect of this is that the Heihnann
AND COSTS OF YAllN 97
wields greater powers of discrimination in respect of the length
and other features of the fibres selected by it.
The respective parts are named as given in the figure. The
revolutions of the comb cylinder range from 60 to 90 per minute.
This is often spoken of in terms of nips instead of revolutions,
there being one nip or complete cycle of actions per revolution
of the comb cylinder in the single acting type. In the Duplex
type the cycle of actions are accomplished in each half revolution
of the comb cylinder.
The following is the mode of calculating the speeds of the
various parts, for this purpose the comb cylinder being assumed
to make 80 revolutions per minute : —
Eevolutions of machine \ _ on^i o , 80x80
pulley per minute ' ~  1 ' °^ ' ^21
Eevolutions of lap rollers! . , 80 x 1 X 18 X 21 X 20 x 30
per minute /  1 7 /, or, ^ x 38 X 20 X 55 X 49
Eevolutions of feed roller ^ _ 80 x 1 x 18
per minute J ~ *'^^> °^' 5 X 38
Eevolutions of comb head ^ _ . . .  <. . 80x80x 2 x20
calenders per minute } ~ ^^^^^ or, 80 X 14 x 20
Eevolutions of first roller] 80 X 25 X 14
in the drawbox perl = 23*33, or, ^ .„
minute J ^5X4H
Eevolutions of third roller 80 x 25 X 50 x 40
m the drawbox per > = 1045, or, ^ — tz — ^
minute ) Z5 X 45 X d4
Eevolutions of drawbox  _ ^ 80 x 25 x 50 x 40 X 22
calender per minute i  ^i ^> or, ^^ x 45 X 34 x 40
Eevolutions of coiler de i _ oi . « 80 x GO X 22 X 18
livery rollers per minute f ~ ^^ ^> o^"' 59 x 22 X 18
Eevolutions of brush \ 80x34x80
cylinder per minute •' "~ ' °^'' 25^^1
Eevolutions of card cylinj _ 80 x 1
der per minute / — z 5, or, ^
Drafts —
Between lap and feed rollers = 1166,
49 X 55 X 20 X 1
or,
30 X 20 X 21 X 25
H
98 COTTON SPINNING CALCULATIONS
Between lap and comb head calenders = 6'45,
49 X 55 X 20 X 38 X 5 X 80 X 2 X 20 X 2f
or — — 
' 30 X 20 X 21 X 18 X 1 X 80 X 14 X 20 X 2^
Between lap and first draw roller = 6*58,
49 X 55 X 20 X 38 X 5 X 25 X 14 X If
or 5.
' 30 X 20 X 21 X 18 X 1 X 25 X 48 X 2
Between lap and third draw roller = 29*51,
49 X 55 X 20 X 38 X 5 X 25 X 50 X 40 X 12
or 
' 30 X 20 X 21 X 18 X 1 X 25 X 45 X 34 X 2f
Between lap roller and drawbox calender = 32*5,
49 X 55 X 20 X 38 X 5 X 25 X 50 X 40 X 22 X 2
' 30 X 20 X 21 X 18 X 1 X 26 X 45 X 34 X 40 X 2
Between lap and coiler delivery rollers = 33*4,
_ 49 X 55 X 20 X 38 X 5 X 60 X 2 X 22
or,
' 30 X 20 X 21 X 18 X 1 X 59 X 22 X 2f
Between first and second draw rollers —
Miiil = 124
25 X If
Between first and third draw rollers —
48x50x40xlf , ,^
— = 4*48
14x45x34xlf
Between second and third draw rollers —
25 X 48 X 50 X 40 X If _ q p
31xl4x45x34xlf ~
Between third draw roller and drawbox calender —
= 11
22x2f
40xlf
Between drawbox calender and the coiler delivery rollers
40 X 34 X 45 X 25 X 60 X 22 X 18 X 2
22 X 40 X 50 X 25'x 59 X 22 X 18 X 2
= 1025
The movement of the detaching rollers is derived as follows :
The quadrant rack is a part of a lever actuated by a bowl pro
jecting from it into a cam. The rising and falling movement
AND COSTS OF YAKN 99
of the quadrant rack is about 12 teeth, so that the 14 wheel
receives movement equal to f of a revolution per (nip) revolu
tion of the cam shaft. The cam on the left hand engages and
disengages the escapement clutch, and by this means the
difference in the extent of the backward and forward rotation
of the detaching rollers is obtained. The clutch is open during
the first five teeth of the upward movement of the quadrant
rack ; after that movement the quadrant rack pauses to allow
the clutch to be engaged, and upon the resumption the detaching
rollers commence their backward movement — this is a constant
amount, and is equal to seven teeth of the rack pinion. The
clutch remains engaged during the whole of the downward move
ment of the rack, and therefore the backward and forward move
ments of the detaching roller amount to ^ and 1 1 of a revolution
respectively. This difference in the movements is insufficient to
provide the necessary overlay for piecing. Further variations
are obtained, to any extent within these limits, by deferring the
placing of the leather detaching roller upon the fluted segment
until the length of those fibres, already within the nip of the
detaching roller, project only sufficent for the necessary overlap.
It must be noticed that variations in the overlap cannot be
obtained by altering the timing of the closure of the clutch cam.
The clutch cam can only be satisfactorily closed at the
moment that the pause occurs in the upward movement of the
quadrant rack. Closure at any other period will result in
damage to the clutch.
Notes respecting the Permissible Adjustment in the Drafts. —
The drafts between the lap and feed rollers, detaching rollers
and head calenders, head calenders and first draw rollers, third
draw roller and drawbox calender, drawbox calender and the
coiler delivery rollers, must always be such that the cotton is
in slight tension without straining.
The point admitting of variations in the draft is therefore
between the feed and detaching rollers. Alterations in this
alter the character of the combing, because it is accomplished
by introducing the fibres more or less gradually, and hence
the number of combing actions which they are subjected to is
altered thereby.
100 COTTON SPINNING CALCULATIONS
Feeding a considerable length of lap generally results in
greater waste ; hence, light laps and low drafts together are
not beneficial.
Moderately high drafts — provided the fringe of the lap is well
held by the nippers and the more numerous combings are not
injurious — are conducive to better selection of the fibres.
The weight a machine is required to comb always decides
the count of the combed sliver.
The length of the staple decides the suitable speed.
Eesults must always decide the weight of the lap as its state
as well as that of the machine differ so much.
The waste made ranges from 15 per cent, upwards, according
to the state of preparation of the laps, the amount of short fibre
which it contains, and the settings.
With laps each weighing 240 grains per yard, a machine,
containing six combing heads and a total draft of 33"4, the loss
in waste being 18 per cent., would make sliver weighing —
240 X 6 82 „„ „ . ,
 33.^ ^ 100 "^ ^^^^^ ^^^ ^
The percentage of the waste is always based upon the weight
of the feed.
The weight of the waste and of the sliver, delivered per
unit of time, together, equal the weight of the cotton fed in that
time.
These machines usually contain six or eight combing heads,
and therefore the amount fed is always that number multiplied
by the average weight per unit of length of the lap fed, whilst
the length delivered exceeds that fed, in one head, in the terms
of the total draft.
Exercise 1. — The sliver and the waste produced in a given time weigh
respective!}' 520 and 130 grains, the waste discharged by the six combing
heads weighing 20, 20, 21, 22, 23, and 24 grains. Give the individual and total
percentage of the loss at each head.
Exercise 2. — The sliver produced by a combing machine having six heads
is at the rate of 8 lbs. per head per 10 hours. The total draft is 32, and the waste
made in that period weighs 10'2 lbs. What is the percentage of the waste made,
the weight in pounds, and the length in yards of the laps consumed ?
AND COSTS OF YARN
101
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T— 1
102 COTTON SPINNING CALCULATIONS
Exercise 12. — If the machine pulleys in the last question, 15 inches in
diameter, are changed to 16 inches in diameter, what difference in the weight of
combed sliver, waste, and laps would result ?
The Drawing Fkame.
The object of this process is the elimination of the irregu
larities, found in the weight of the sliver, at this stage. This is
accomplished by repeating the process of aggregation and
attenuation. In this process there are usually three repetitions,
but sometimes two or four are adopted, the former in coarse, and
the latter in fine, work. Eepetition of the process should be
discontinued when the desired standard of uniformity is attained.
The heads are numbered corresponding with the repetitions
respectively. Thus a draw frame of three heads means that the
cotton is treated to aggregation and attenuation three times,
namely: in the first, second, and third heads. It is necessary
to test the sliver, preferably at the last head, at frequent and
fixed intervals, four times per day at least, so that any deviation
from the standard weight may be detected and dealt with. The
tests should be recorded along with the precautionary or correc
tive measures taken in instances of variation. In these tests,
5, 6, or 15 yards will be found convenient lengths to wrap. The
sliver tested should be taken in a manner ensuring correct
representation of the prevailing condition, the best way being
to take a little from each delivery, but not off full cans. The
weight is liable to frequent variation at this stage ; the cause of
this is not always apparent. The variations foreshadow the
working qualities of the cotton and irregularities in the treat
ment prior to this stage.
When variations are disregarded, more than corresponding
differences may be expected in the subsequent processes, and
often complications of an involved character arise through
these faults being unchecked.
During very dry weather the wrappings tend to the heavy
side. A sudden change in the atmosphere will sometimes
necessitate an alteration of quite a few teeth in the change wheel.
Changes in the mixing which result in the cotton differing are
similarly liable. Cottons which are softer than usual should
AND COSTS OP YARN
103
be kept on the heavy side, and vice versa. It is also advisable
to keep the change wheel as large as convenient. By noting
at the commencement of new mixings the quantities and
character of the new lots of cotton contained in them, the
space occupied by the scutcher laps, and the waste made in
carding, it is possible to discern features that are likely to
develop in the subsequent stages. These, together with the tests
of the sliver at the third head of the drawingframe provide
a good index of the subsequent working capacities of the cotton.
The cans should be " put up " systematically at the feed of
each head, the aim being to obtain like conditions at each
delivery. ** Putting up " more than one full can per delivery is
detrimental.
Fig. 21.
Calculations relating to Draw Frames (Fig. 21). — Drafts between
the Various Parts. — Lifting roller A and No. 1 draw roller —
^Qxlt _ 1.047
21 X Ij  ^ ^^^
104 COTTON SPINKING CALCULATIONS
Nos. 1 and 2 draw rollers —
18 X If ^ '^'^
Nos. 2 and 3 draw rollers —
MA^J^.ii  1925
25 X 16 X If ~ ^ ^^^
Nos. 1 and 3 draw rollers —
^^ ^^ = 267
16 X !■• ^'
Nop. 3 and 4 draw rollers —
16 X 100 X 100 X 1
47 X 60 X 20 X 11
= 312
Nos. 1 and 4 draw rollers
100 X 100 X 1  _
60 X 20 X 1~ "*
No. 4 draw roller and coiler delivery roller E
22 X 3
48 X If
= 1
Lifting roller and coiler delivery rollers, A and E, the total
draft —
20 X 100 X 100 X 22 X 3^^ _ o 7^^
21 X 60 X 20 X 48 X 1 1" ~ "^
There is much difference of opinion in regard to the system
of allocating the draft in the draw rollers of drawing frames
which gives the best results. The following has proved a good
rule, and is in accordance with the working conditions : —
Draft between first and second draw rollers : not more than 1*2
,, second and third
V
draft between first and fourth
12
„ third and fourth draw rollers : (draft between
the second and third rollers)^.
Example. — TIuir, if the total draft in the draw rollers = x, and that between
AND COSTS OF YAKN 105
the first and second .Xj, that between the second and third x^, and that between
third and fourth x^ {x in the figure = 8'33) —
then, cc = ajj X ir2 X x^
since Xj = 1'2
a; 833
,'. «2 X X3 = p^ =: j.^ = 695
The draft a'a is, in most makes of these machines, incou
venieut for changing. Changes in this are only necessary when
the total draft referred to becomes abnormal. With this draft
a?2 regarded as fixed, the defects arising are through the draft Xo,
approaching in amount that of x^ ; when the total roller draft is
reduced to 4"38, then x^ and x^ are alike.
It must not be inferred from the latter statement that a
change of the draft between the first and third rollers is
advocated whenever the total roller draft is altered. It is only
desired to point out the error arising when considerable change
is made in the total draft, and the expediency of affording relief
by a slight alteration in the draft between the first and third, in
order to redistribute the drafts in reasonable proportions.
It is necessary also to draw attention to the desirability of
using change wheels of moderate size, avoiding small ones.
The revolutions of 1 _ 22 X 18 X 42 _
the coiler per minute] " ^^" ^ l6~x"Wx 69 ~
The revolutions ofl _ 22 x 18 x 18 X 10 x 20
the can per minute J "" ^'"^ ^ 46 X 20 X 34 X 36 X 104 ~
Whenever draw frames are changed from heavy slivers,
to the other extreme, the coils are frequently illspaced in the
can, and vice versa. This may be remedied by remembering
that heavy sliver requires more space, and hence higher speeds
of the can than light fine slivers.
When the sliver is coiled too widespread it is liable to be
troublesome through too much tension caused by binding in the
can. This may be overcome by slightly increasing the rate
106
COTTON SPINNING CALCULATIONS
of the coiler. On the other hand, when the sliver is not fully
distributed — indicated by a wide space between it and the can
side — the cans cannot contain as much as desirable. This may
be overcome by slightly reducing the rate of the coiler. When
the unoccupied space in the centre of the can is greater than
desired, it is due to the can being "too eccentric" with the
coiler. By reducing this, and at the same time the rate of the
coiler, this objection may be removed.
The quantity of the production in draw frames varies accord
ing to the speed, the system, and the efficiency of the workers.
In some mills, as high as 90 per cent, of the production, calcu
lated from the actual speeds, are obtained with slivers as high
as 70 grains per yard.
The above may be considered practicable under the best con
ditions. This would give the following, per delivery, in a week
of 55^ hours : —
Revolutions of front
roller.
Weight of sliver in
grains per yard.
Hanks per delivery.
Pounds per delivery.
320
55
50
55
60
65
70
13719
55
55
823
905
987
1070
1152
Productions for Speeds ranging from 320 vv to 380 Eevolutions pee Minute
OF 13iNCQ Front Roller.
Revolutions of front
Weight of sliver in
Production in pounds per
roller per minute.
grains per yard.
week.
320
70
1152
330
1198
310
1234
350
1270
360
1306
370
1337
380
»
1366
In medium fine (50''80*) counts, the former of the above
speeds and productions would be considered ample, and the sliver
would range from 50 grains per yard downwards, according to
AND COSTS OF YARN
107
quality of the yarn and the quantity of preparation machinery
available.
Revolutions of front
Weight of sliver in
Production in pounds per
roller per minute.
grains per yard.
week per delivery.
320
500
823
»
475
783
»
450
744
425
704
400
765
375
726
»>
360
687
In fine counts, 80^ upwards, the speeds would range from
280 downwards, and the rollers would be 1^ inches in diameter
in three positions instead of If inches, and the slivers down to
24 grains per yard. The productions are —
Revolutions of front
roller per minute.
AVeight of sliver In Production in pounds per
grains per yard. week per delivery.
280 X 1^ F.E.
360
330
300
270
240
658
603
548
493
438
Calculations relating to the Drafts in the Rollers (Fig. 21, Y).
Between —
First and second = 7^ ^. =12
Second and third =
30 X 24
24 X 30 X 80 X 100 x 20 x 30 x 9
36 X 24 X 60 X 20 X 47 X 38 X 10
= 168
Third and fourth = !^ ^ !! ^ ^? = 3*30
30 X 20 X 9
„. , , . ,, 80 X 100
First and fourth = ,^ _ — ^^
60 X 20
66
First and third = 77
80 X 100 X 20 X 30 X 9
60 X 20 X 47 X 38 X 10
= 201
108 COTTON SPINXIXG CALCULATIONS
Xotcs in respect of this System of Gearing Rollers.
(a) That, since P is the customary change wheel for varying
the total extent of the attenuation and the weight unit of the
sliver produced, any alteration of P or of the back roller wheel
disturbs the draft between rollers 2 and 3 only, and if the total
draft be altered by this means gradually to 3'968, that between
2 and 3 would be gradually diminished, no attenuation would
then take place between those rollers, and if altered to less
than that amount contraction instead of attenuation of the
sliver must result between those points.
(h) The draft between the rollers 3 and 4 would, under the
circumstances mentioned in paragraph (a), always be constant,
and hence should the wheels be altered to exercise a greater
draft than 6'6, the draft between the second and third rollers
only would be increased. Thus, in case the total draft was
raised to 11'9, the draft between the second and third rollers
would then become as much as that between the third and
fourth.
By this system of gearing the variable draft is placed at a
point which is not the best. This also may be said of system X
(Fig. 21), with this addition, that there is room for error in calcu
lation by overlooking that the two trains — eight wheels — are
involved in the calculation of the total draft. Another feature
in these systems of gearing (Y and X) is the backlash due to
the increased number of wheels and indirectness of the gear.
This is best understood when the effects upon the sliver are
considered with the wheels loosely geared or worn. On refer
ence to the gearing it will be seen that 3 will start after 4, and
2 considerably after this, because in the former there are only
three or four wheels against eight in the latter.
The system of driving the (2) and (3) rollers direct from the
back roller as shown in the other figure has many advantages
over X and Y. It ensures the variable draft between those
rollers having the lightest work to perform, greater facilities for
changes and calculations ; occupies less space, simplifies the
parts, fewer wheels are required, and permits the use of larger
wheels.
AND COSTS OF YARN 109
Exercises. — Calculate the drafts in Fig. 21 between —
(a) 1 and 2, 2 and 3, 3 and 4, 1 and 3, 1 and 4, 2 and 4, when tlie compound
wheel between 1 and 2 is 20 and 30.
(b) 1 and 2 when the wheel marked 20 is 21, 22, 23, and 24 respectively.
(c) 1 and 4 when the wheel marked 20 is 21, 22, 23, and 24 respectively.
(d) 1 and 4 when P is the inclusive sizes from 40 to 60.
(e) 2 and 3 when P is the inclusive sizes from 40 to 60.
(/) 1 and 4 when the 60 on the roller 2 is 40, 50, 70, 80.
(g) What should be the weight, in grains per yard, and count of the sliver
delivered, in each of the three types of gearing given, if the number of slivers
fed per delivery were in each case six, and each of these weighed at the rate of
48 grains per yard ?
(Ji) If the sliver delivered by a machine, geared as in Fig. 21, weighed 54
grains per yard, what should it weigh if the wheel P was successively 40, 45,
50, and 55 respectively ?
(i) What would be the production in pounds per delivery per week with P
40, 45, 50, and 55 respectively, if with a 60, P, 1152 lbs. were produced?
The Arrangement of the Drafts in the Several Heads consti
tuting the Draw Frame. — The condition which should govern the
extent of the total drafts allotted to each head is that each
should be so rated as to be continuously working without pro
ducing more or less than is required by the succeeding machine.
It is the most common practice to have the same number
of deliveries in each head, and also for the front rollers in these
to revolve at the same rate. Practice has proved this most
expedient. To get the best results under such conditions,
arrange the drafts so that the condition contained in the last
paragraph may be realized.
The variations in the contents of the cans from the cards
occasion considerably more loss of time in the first head, through
stoppages, taking this at 10, 7, and 7 per cent, respectively in
the three heads, and the revolutions of the front roller at 320
per minute and If inches in diameter, the card sliver at 36
grains per yard, and that at the last head at, say, 60 grains
per yard. Then the productive capacity of the third head would
amount to —
55 hrs. X 60 X 320 X If" 22 60 93 ..^^^ „ ,,.
36^<7000 ^ y ^ T "^ 100 = ^^^^ ^^'' ^''' ^'^'''''^
Hence, the front roller in the second head would require to
produce sliver at the same rate per yard, whilst that delivered
110 COTTON SPINNING CALCULATIONS
by the first head would require to be heavier to the extent of the
difference in the loss of time, and therefore —
60 X 93 ^^ . T
— ^r — = 62 grams per yard
The draft in the respective heads on the assumption that
the doublings are 6, in each case must therefore be
In the first head —
36 X 6
draft
= 63
91 fi
draft = ~ = 343
And in the second head —
62 X 6
draft
= 60
•. draft = ?^ = 62
dO
And in the third head —
60 X 6
draft
= 60
/. draft = TTTT = 6
oU
Fly Frames.
The primary object in fly frames— slubber, intermediate,
rover, and jack — is to attenuate the sliver obtained from the
drawing frame to the extent necessary to prepare it for the
spinning machine.
It would be possible to dispense with fly frames if drawing
rollers were perfectly adapted for attenuating cotton. Drawing
rollers, as at present constructed, cannot attenuate perfectly
bodies of fibres varying in length. Cotton cannot be obtained
which does not vary in the length of its fibres. In consequence,
the relative sequence of the fibres is altered during attenuation
in a degree proportionate to those variations and the extent of
the attenuation attempted. This means, that a sliver or rove
with its fibres uniformly distributed would have its fibres
AXD COSTS OF YAKN 111
otherwise arranged. The less the variation in the length of the
fibres the greater the draft practicable.
Eepetition of these processes is necessitated to admit of
doubling and thereby absorption of the irregularities referred
to. There is no doubt that doubling of more than two ends
would be advantageous. The difficulties connected with pre
senting more than that number are the most likely reason of its
not being adopted.
The Object of Twisting. — Twisting assists cohesion, and is
employed to the extent sufficient to protect the bodies of fibres
at these stages.
The Direction of Twist and the Range of Usefulness of Twist, —
The rule in respect of the direction of the twist, in rove, is
< twist : although there are instances of > weft twisting.
I I
The direction of the twist has a slight influence on the spin
ning : a twist rove makes better and stronger yarn when it is
twisted finally in the same direction than when this is done
reversely. It is undoubtedly the case that roving twisted in
the same direction as the ultimate yarn, would secure better
results in spinning. The only reason which can be given
for this not being practised, in respect of weft and " reverse "
yarns, is that it may not be so convenient to produce on account
of necessitating the use of the left hand in piecing. It is advan
tageous, in preparing roving for twist yarn in ring frames, to
use the maximum, and for weft or reverse yarn the minimum
twist, constants. Twist has a beneficial influence, when it is in
the same direction as that required in the yarn, and when not
used to excess. The reason for many carders preferring the
minimum twist is because it enables a greater production, from
their point of view, but this is not the case with the spinner.
Eoving may contain too little twist without breaking in the
creel. Care should always be exercised to avoid twisting to the
extent which may bind the fibres in excess, causing them to
withstand the subsequent attenuating powers.
Twist Constants. — The efficacy of twist varies in the various
grades and kinds of cotton ; it is also influenced by the degree
112 COTTON SPINNING CALCULATIONS
of uniformity of the length of the fibres and touch of the cotton.
The amount of the twist per inch necessary to bind the fibres
to the proper extent varies from \/count X 0*8 to \/count X 1'5.
Cottons which are long and harsh and lie compactly require
least, whilst those which are short and do not lie compactly
require most, twist.
The following is a table of the normal twist constants.
These, when multiplied by the \/counts of the actual rove, will
give the twist per inch suitable under most conditions.
Slubber.
from : 08
to : 10
from: I'O
to: 12
from: 1*1
Inter.
Rover.
09
09
M
12
11
12
125
13
12
14
14
15
Sea Island and Egyptian cottons . . <
Brazilian, American, and similar cottons <
Indian and similar cot'. ons . . . . j , . ...^
The Gearing in Fly Frames (Fig. 22). — The gearing in fly
frames is identical in all the principal makes. It consists of
a principal shaft called the frame shaft, and from this all the
parts receive their motion.
(a) The Rollers. — The front roller is connected with the frame
shaft referred to by means of a train consisting of four or five
wheels, F, E, D, C, B, named, respectively : the twist, the twist
carrier or compound, the top cone, the end of top cone, and the
end of the front roller w^heels ; a compound wheel instead of E
being necessary when considerable range of twist are necessary.
The back and middle rollers are connected with the front in the
following manner : a train of four wheels, 28, 90, 40, 56, and
named respectively the front roller (F.E.W.), the crown (C.W.),
the pinion (P.W.), and the back roller wheels (B.R.W.) ; these
comprise the connection to the latter roller, the crown and
pinion being compounded. The middle roller is connected with
the back through the medium of three wheels, 25, C, 18 ; they are
named the back roller (driver), carrier, and middle roller wheels.
(h) The Spindles. — The shafts driving these, one only is shown,
are connected by a train of three wheels, 33, H, 33, in case of
the back line of spindles ; and a fourth wheel on the front shaft
gears with that on the shaft driving the back line of spindles.
AND COSTS OF YARN
113
These spindle shafts are furnished with skew bevels, 60, and
these drive the bevels, 21, on the spindles. The value of this
train is fixed.
(c) Winding. — The Bobbins are driven from two points upon
the frame shaft, T.W. and M, the motion from these two points
being brought together at the terminal wheel, 14, in the differ
ential. The bobbin driving shaft (O) is connected with the
sleeve wheel of the differential N, by means of four or five wheels
V'dia.
/ I
1 Top Con
nl
one t
f pitch 60^^
Ratchet Wheel
Bottom C
Fig. 22.
in case of the front, and three or four, 45, C, 40, in case of the
back bobbin shaft. These wheels are known as the swing
train. The sleeve N acquires its motion from the two points,
receiving a fixed contribution from one, M ; and a variable con
.tribution from A, the other of these two points ; the fixed portion
here referred to being contributed by that part of the differential
which is fixed to the jack shaft. In some cases that part is a
wheel. The variable contribution is received by the differential
from the twist wheel, T.W., on the frame shaft, the motion
passing through the top and bottom cones, and thence through a
114 COTTON SPINNING CALCULATIONS
train consisting of a varying number of wheels, numbered on the
figure 36, 36, 46, 50, 46, 106. The fixed contributor is arranged
to supply the movement necessary to rotate the bobbins at the
same rate as the spindle ; the variable contributor communi
cating only that necessary to obtain winding at the desired
tension. By this arrangement, the cones completely control
the winding. When they cease to contribute, winding ceases,
through the bobbins then assuming the rate of the spindles. The
wheels in this latter connection are known by the following
names : the bottom cone, change shaft, winding shaft, differ
ential, differential sleeve, swing, bobbin shaft, skew bevels, and
bobbin wheels.
The Consequences of altering the Value of the Cone Train. — The
value of the wheel train, connecting the fixed contributor with
the bobbins, should be a constant, and therefore any departure
from the abovenamed conditions will result in imperfect wind
ing. The value of the wheel train connecting the twist wheel
with the differential should likewise be constant. The value
of the belt connection on the two cones is the medium for pro
viding the acceleration or retardation of the bobbin necessary
to obtain the proper winding tension ; this being a plus or minus
contributor according to the conditions of winding adopted. The
two conditions in respect of winding, referred to, are bobbin lead
and flyer lead. In the former of these the winding is occasioned
by the excess in the rotation of the bobbin over that of the flyer ;
and vice versa in flyer lead. In flyer lead the bobbin must
be accelerated to the extent coincident with the proportional
change in the size of the bobbin at the commencement of each
new layer of coils, but only in respect of that portion of their
motion supplied through the medium of the cones. In bobbin
lead retardation takes the place of acceleration. The connection
of the front roller with the bobbins is, therefore, such that the
latter creates a winding rate coinciding with the rate of delivery
by former. Any change in the rate of rotation of the front
roller obtains a corresponding change in the winding rate.
The cone drums are constructed to comply with the require
ments of certain sizes of bobbins, each portion being adapted
for a certain size, and that only. Altering the value of this
AND COSTS OF YARN
115
train of wheels is most likely to place the cone strap on a wrong
part of the cones. There is only one part that will give the
fractional change of speed corresponding with the fractional
increase that each added layer bears to the size of the surface
it is laid upon. If the strap is not on that portion of the cones,
then the tension of winding will be inaccurate.
((?) The Spacing of the Coils. — This is obtained by the move
ment of the bobbin, vertically, past the guiding point of the
flyer. This raising and lowering movement of the bobbin is
derived also from the twist wheel, through the cones, by a con
necting train intercepting the train between the bottom cone and
the differential connections, namely, 13, 60, (W), 10, 100, (V),
14, 56, (U), 36, 50, (T), 14, 90, (S), 22. The necessity for this
vertical movement being derived from the cones arises through
the number of coils wound retarding at a rate inverse to the
increasing size of the bobbin. The number of wheels employed
in this connection vary somewhat. The reversion in the direc
tion of the vertical movement is obtained by means of E.B., the
reversing bevels ; these alternately engage their driving bevel.
The wheels in this connection are known by the following
names : Top change, top of upright, strike bevel, reversing
bevels, reversing bevels shaft, cannon shaft, bottom change
shaft, lifting shaft wheels, and lifting racks.
Speeds of the Parts in Fly Frames.
Subject.
Details of calculation (Fig. 22).
Revolu
tions per
minute.
Surface rate in
inches per
minute.
Front roller, B
Spindles, P . .
Twist per inch
Twist constant
350 X 39 X 35
35 X 130 ~
105 X 1" X 22
7 ~
350 X 33 X 60 _
33 X 21
revolutions of spindle per minute
inches del. by the F.R. per minute
 330"  ^ "^
twist per inch
V count
Note. — Count suitable deiJends upon the
twist constant used.
105
1000
330"
116
COTTON SPINNING CALCULATIONS
Subject.
Top coue (0, D)
Bottom cone, Y
Details of calculation (Fig. 22).
Draft between"!
the back and I
front rollers [
(1st and 3rd) j
Bobbin lifting\
shaft, S /
Bobbin . . .
350 X 39 _
35 ~
Assuming the strap on the parts G" top
cone and o\" bottom cone —
350 X 3) X 6 _
35 X 3i ~
Assuming the strap on the parts 3J"
diameter top cone and G" diameter
bottom cone —
350 X 39 X 3 1 _
35 X G ~
56x90 X r_ ,.g
40 X 28 X 1"~
3 50 X 39 X 6 X 36 X 13 X 10 X 1 4
35 X 3i X 36 X 60 X lOOx 56
36 X 14 _
^ 50 X 90 ~
Note. — The above is when cone strap is
assumed in positions 6" in diameter
driver cone and 3J" in diameter driven
cone.
And when cone strap is in positions,
rcspectivclv, SJ", 6" —
350 X 39 X 3J X 36_X 13 x 10 x 14
35x 6 X 36 X GO X 100 x 56
36 X 14 _
^ 50 X 90 ~
To wind without stretching, assuming
the winding circle
and bobbin lead —
1" in diameter
330
If flyer lead —
li X
+ 1000 =
1000  ,
330
n X f 
Maximum size of bobbin that the cones
are adapted for —
Its, ^X6 _ 425"
When the bobbin is the maximum bize,
4J", and bobbin lead —
If flyer lead —
For calculations of the speeds of the
bobbins as per gearing, see p. 127.
Revolu
tions per
minute.
390
720
2112
Kaiio
1 :45
0437
Surface rate in
incliea per
minute.
0128
1084
916
10247
9753
088
330" in excess
of flyer pres
ser
330" slower
than flyer
pressure
AND COSTS OF YARN 117
The Change Wheels in the aforementioned Trains respectively.—
The following are the customary change wheels :—
(a) For altering the rate of the rollers relative to the spindles
and thereby the twist— twist, compound, and top cone shaft
wheels, in the order named.
For altering the total draft or the attenuating powers of the
rollers— pinion, back roller, crown, and front roller wheels.
For altering the drafts between the individual rollers, the
small wheels on the back or middle roller.
(b) None of the wheels in this train are altered.
(c) For altering the tension of winding. This should be
done by the ratchet wheel or adjusting the position of the cone
strap forks. The practice of changing one of the wheels in this
train, connecting the differential, which is generally recognized,
is open to serious objections, which are stated in the section
dealing with winding, p. 127.
00 For controlling the spacing of the rove upon the bobbin.
The lifter change shaft wheel and strike bevel are the usual
change points.
Alterations in the Draft.— Alterations in the draft are neces
sary when the count, or the weight per unit of length, are not
as desired. Also, when a change is made in the feed, and a
corresponding change in the delivery is not required.
The formula when changing the draft or the counts, is—
Present draft X count desired ,^ count of present feed _i draft
present count count of distended feed~iequired
When the weight takes the place of the count, it is necessary
to bear in mind that the weight is inverse to the count, and that
this necessitates the inversion of the two terms, desired and
present, in the above equation.
The total roller draft may be altered by changing the size of
any of the four wheels in the train connecting the back with the
front roller. The pinion wheel is the recognized change wheel,
and the back roller wheel is changed when the limits in respect
of the former have been reached. When the limits of the two
former are exhausted the crown wheel is changed, but this is
not often necessary.
118 COTTON SPINNING CALCULATIONS
Changes in the count delivered may be made by varying
the count of the feed or the draft in the direct proportion.
Changes in the count fed may be checked by inverse changes
in the draft.
Changes in the sizes of the drivers, in the draft train of
wheels, obtain inverse changes in the draft and count, and
direct changes in the weight per unit of length.
Changes in the sizes of driven wheels in the draft train have
the inverse effect to the drivers.
Alterations in the Draft, how made. — Changes in the draft, or
in the count produced, do not affect the extent of the length
delivered by the front roller. Such changes always affect the
weight of the delivery, per unit of length, in inverse terms.
The draft, as contained in the present roller gearing (Fig. 22),
is as follows : —
25 X —
Between the first and second rollers = =^ A = 1*21 6
18 X 1"
, ,,,. , 18 X 56 X 90 X I ^„.
second and thnd „ = 25 x 40 x 28 X r = ^ ^^
„ , , ,, . , 56x90 X 1" ...
„ first and third „ = 40^28 "xl.^' ""
Any change in those wheels would have effects correspond
ing with those noted in respect of the rollers in drawing
frames.
The count obtained by the above attenuation in the rollers
would be 4*5 times finer than the feed.
The feed in the slubber generally consists of one end per
rove delivered, whilst in the intermediate, rover, and jack it
always comprises two ends. Thus, in the case where 0*2 is the
count of the feed in a slubber having 4*5 of a draft, 0*2 x 45
= 0"9 would be the count delivered. An intermediate with
0*9
4'5 draft, treating slubbing of 0*9 count, would produce „ ^ ^'5
= 2025 count. A roving frame, with a like draft, using that
2*025
count of intermediate rove, would produce — ^ — X 4*5 = 4*556
count.
AND COSTS OF YARN
119
A change in any of the wheels connecting the first or back
with the front roller would have the following effect : —
If a driver, the count and the draft would be altered in the
inverse, and the weight in the direct proportion.
If a driven, the count and the draft would be altered in the
direct, and the weight in the inverse proportion.
Altering the Draft. — The following would be the draft and
count with the draft wheels, as stated below, when the other
roller gear is as given in Fig. 22 ; the count of the rove fed
beinor 2025.
If the pinion was altered to 60
50
45
36
30
Tlie draft would become 30
36
40
50
60
The count would become 303
364
405
505
606
If the backroller wheel was altered to
51 48
42
60 65
70
The draft would become
41 386
337
482 522
562
If the front roller wheel was altered to
26
24
22
20
The draft would become
485
525
573
63
If the crown wheel was altered to 130
120
110
100 80
70
The draft would become 65
60
55
5 4
35
Note. — The front roller and pinion wheels (28 and 56) are drivers.
The crown and back roller wheels (90 and 56) are driven.
The ratio of the crown to the front roller wheel.
The ratio of the pinion to the back roller wheel.
That any pairs of these wheels possessing these ratios will produce the same
results.
Examples and Exercises in Changikg the Draft.
1 2
2 ?
3 2
"Boi:
Draft.
?
6
55
Draft gear. Diameters of F.R.
and Back R. alike.
F.R.W.
C.W.
P.W.
B.R.W.
25
25
25
100
100
100
?
40
?
50
60
.T. 1. , T^ rx 5x2 ^ 50 100 _
A^ orking 1.— Draft  —^ = ^ ." p^ X ,^^ = 5
Working 2. — Count fed =
50^
W
5X2
5 2j
,„ B.R.W. 100 „
...B.R.W. = i^^^^^ = 60
120
COTTON SPINNING CALCULATIONS
^v T o n .IV 1 2 . .   CO X 100 . _
>\ orkinsr 3. — Count aelivered =  x oo = 5o; — r ^ = o'5
° 2 ? X 2o
.p.W. = ^^^? = 436
55 X 2o
9
10
11
12
5J c rti "^^
.Q S
0}
" c *
'tc = > Draft.
2775
30 yds. =
125 prrs.
30 yds. =
125 grs.
30 yds. =
135 grs.
30 yds. =
125 grs.
30 yds. =
135 grs.
018
017
?
02
to = >
I ?
60 I
Ditto I
G0 1
30 yds. =
50 grs.
52 I
50 !
^^
6
"
5
u
G
»1
G
1
?
1
?
1
07G5
1
096
Draft gear. Diameters of F.R.
and Back R a ike.
F.E.W. C.W. P.AV. B.R.W
28
28
28
28
25
25
25
25
90
90
28
90
28
90
„
5»
»
»
90
90
100
?
100
100
40
50
40 i 56
40 I T
Eatio ?
40 [ 56
Eatio ?
56
56
60
CO
? ?
50 I 60
56 '. 63
50 1 ?
j Change to the latter
' of these conrU
! tions.
From these condi
tions change to
the latter.
From these condi
tions change to
the latter.
The following must always be known to enable the gearing
to be adapted for the production of any specific count : —
(1) The count required.
(2) The count of the feed.
(3) The characteristics of the cotton.
(1) and (2) determine the draft.
(1) and (3) determine the twist.
The Eate of the Winding and Spacing of the Coils cannot be
accurately ascertained by calculation on account of the dissimi
larity in the size of rovings. The winding must be regulated
by adjusting the position of the strap on the cones. The rate
of the vertical movement of the bobbin rail must be adjusted
to space the coils without tendency to override or apertures
Generally about six coils of count one can be laid per inch
This is useful as a basis in the absence of other data.
AND COSTS OF YAEX 121
The twist per inch obtained by the gearing as per Fig. 22
= 303 inches. According to data on p. 112, the twisting
would be adapted for —
(a) If Sea Islands cotton (?^J = O'l
(h) If Egyptian cotton (^~f = 91 to G4
(c) If Brazilian cotton f^Y = (3.4
(d) If American cotton (^^^2^)' = 64 to 54
(e) If Indian cotton (^~~^f = 47 to 41
Thus five frames employed as above stated with the draft
45 : the count of the feed and that in the creel would be
respectively —
9'1
(«) 475 = 202 /. 202 X 2 = 404
C 'A
^^^ ¥5 " ^'^'^ •*• 1"^2 X 2 = 284
p • i
^""^ 4^ " ^'^^ •'• 1^2 X 2 = 284
5*4
(d)  = 12 .. 12x2 = 24
4*7
(0 4:5 = 104 /. 104 X 2 = 208
41
°^' 4:5 = 091 .. 091 X 2 = 182
A change in the pinion wheel would have the inverse effect
upon the counts produced, and would influence the weight per
unit of length in the direct proportion. Therefore a 30draft
pinion instead of 40 would produce the following counts, assum
ing the feed as in the above instances :—
30
64 X
40
30
64 X
40
30
54 X
40
30
47 X
40
122 COTTOX SPINNING CALCULATIONS
(«) — on— = 12 1
(c) "^3^ = 85
id) ^^^^ = 72
(.) ^ = 627
A change in the back roller wheel would have the inverse
effect to that of the pinion.
Whenever the count is changed, it would become necessary
to readjust the twist per inch to \/ count X twist constant.
The rate of the front roller would need altering in the pro
portion inverse to the twists. Thus, assuming the twist wheel
in each of the frames, referred to in the lastmentioned examples,
39, the changes in count would necessitate the following altera
tions in the twist wheel : —
T. , s 39 X \/9l
For (a) ^
Note. — The twists are in the direct proportion of the square root of the
counts, and hence the latter may substitute the former.
For (h)
39 X \/64
\/8"5
For (c)
39 X \/¥l
\/¥5
For (d)
39 X\/r2
\/5^
For (e)
39 X \/47
Assuming x the size of the ratchet wheel and y that of the
lifter change wheel, the following procedure would obtain x and
AND COSTS OF YARX 123
y adapted for the abovenamed changes : because the size of
the rove and yarns of a given class are found to vary inversely
as the square root of their counts when other conditions are
equal.
For (a) \ and ^ ~
^ ^ v/91 \/l21
.,. aj\/85 , 2/\/85
Note.— ic must contain more teeth, because these wheels are
made a standard size by each maker ; they differ in the pitch
of their teeth only.
«, controls the movement of the cone strap at the completion
of each layer on the bobbin. It is this movement that obtains
the retardation in the speed, of the bottom cone, necessary to
secure perfect tension in winding. The extent of the movement
of the cone strap must be in accordance with the proportional
increase resulting from each layer laid upon the bobbin. Hence,
the number of teeth contained in these wheels must be altered
relatively, inverse to the square root of the counts, which sum
represents the thickness of the roves wound.
y must contain fewer teeth for smaller roves in the direct
proportion of their diameter, these are, for the same kind of
cotton, relatively inverse to the square root of their counts ;
because a smaller rove requires less space, and hence slower
speed of the bobbin rail, of which train 2/ is a driver. If it was
preferable to alter a driven wheel in that train, then a wheel
containing more, instead of less, teeth would be necessary.
Exercises ik Miscellaneous Fly Frame Calculations.
1. In a roving frame the twist wheel has 30 teeth, and drives hy a carrier
the wheel in the middle of the top cone shaft, containing 40 teeth. On the end
of the latter shaft a 48 gears with one on the front roller containing 130 teeth.
The front roller is 1^ inches in diameter. The spindle bevel wheel has 30 teeth,
and that driving it has 55 ; a wheel of 40 teeth on this latter shaft is driven from
the frame shaft by one of the same size. Find the twist per inch.
2. Ascertain the twist per inch, the twist constant, the production in hanks
124 COTTOX SPINNING CALCULATIONS
and ounces per spindle per 10 hours, under the following conditions in a roving
frame. Revolutions per minute: spindle, 1150; F.R. 120: diameter, IJ inch;
draft, 5, count fed : two ends of 35 hank intermediate rove ; loss of time,
8 per cent.
3. A roving frame is required to produce 9hank rove containing twist equal
to vcount X 1'4, and the spindles making 1200 revolutions per minute; the
diameter of the front roller is 1} inch. At what rate must the roller be driven?
4. At what rate must the bobbins rotate to obtain good winding during the
first layer under the following conditions : Gear from the front roller to the frame
shaft, JjSii^ 11^ that from the frame shaft to the spindles, ^, f]g ; diameters, of
front roller, IJ inch, of the bobbin, 1 inch ; revolutions per minute of the frame
shaft, 300?
5. A fly frame making a 6hank rove has the following change wheels :
Draft pinion, 42 ; twist, 36 ; ratchet, 40 ; lifter (driver), 26. What sizes of
these wheels respectively would be required for a 5hank ?
Ans. 50, 39, 37, 29.
6. The spindles in a slubber making a 075hank rove are observed to rotate
4"5 times per 1 of the front roller, which is 1] inch in diameter : the change
wheels are — twist, 40 ; ratchet, 19 ; lifter, 26 ; draft pinion, 42 : and the spindles
are known to make 550 revolutions per minule. Ascertain: («) the present
twist per inch ; (i) the twist per inch suitable for 0'58hank, and also the change
wheels required ; (c) the rate of production in both cases in hanks and ounces
per spindle per 10 hours, assuming 15 per cent, represents the loss of time.
Ans. 115 ; 101, 49, or f , 32, 63 ; 81, 173 ; 993, 358.
7. What lifter wheels would be most suitable in using the same cotton for
I'O and for 0'5 hank, if it was known that 6 coils per inch was the most satis
factory spacing for 1 hank and a 28 lifter wheel (driver) gave 7 coils per
inch? Ans. 24; 17.
8. What sizes of ratchet wheels would be most suitable in using the same
cotton for 1*0 and for 0'5 hank, if it was known that a 14 was most suitable for
068 hank? Ans. 17; 12.
9. The spindles in a roving frame producing 7hank roving make 1120, and
the front roller 100, revolutions per minute ; the latter is 1^ inch in diameter.
What twist per inch should the rove contain ? Give the twist constant and the
hanks produced in 10 hours' uninterrupted working. Ans. 3*17 ; 1*2 ; 7'02.
10. The draft in the rollers of a roving frame is 6 and the intermediate
roving is 2*6 hanks, and two of these are doubled : what count of rove will be
made ? If the count, ascertained, has to be changed to 6', and the draft wheels
and rollers are F.E.W. 20, C.W. 80, P.W. 40, B.E.W. 60; diameters, F.R. IJ
inch, B.R. 1^ inch, which of these wheels would you alter, and to what extent ?
Ans. 78— P.W. to 52.
11. A roving frame is making 78 hankroving with the following wheels:
Draft pinion, 40 ; twist wheel, 38 ; ratchet, 46 ; lifter, 28, What wheels would
be needed for 6 ? What eftect would these changes have upon the length and
weight produced ?
Ans. 52, 43, 40, 32 increase in lengtli, 38 to 43 ; increase in weight,
6 to 89.
AND COSTS OF YARN
125
Exer
'
Cottiin and
count.
Twist.
Roller gear.
AVind
iiig.
Spacing
lifter
wheel.
Count
fed.
Twist
cise
No.
b.
S
OS
.o
'a
J3
Pi
1
13
a 03
O I*
& P.
stant.
Present
Required
Present
Required
Present
Required
Present
Required
Present
Required
Present
Required
American 4
8
Egyptian 10
12
American 42
3
Indian 2§
„ 2J
Egyptian 16
20
Indian 3
303
?
?
45
?
?
?
?
48
p
?
?
39
■?
?
?
?
?
?
?
36
?
50
?
45
?
5
?
?
?
?
?
5
?
?
5
45
?
9
?
?
?
?
?
60
?
50
?
56
?
?
?
?
9
56
56
60
60
54
54
40
?
52
?
33
?
20
?
56
9
24
9
14
?
14
17
?
?
?
18
?
56
?
42
?
56
56
48
?
42
?
284
55
?
5
14
5»
10
?
14
»>
128
I'l
?
13
r4
55
?
?
14
15
Winding in Fly Frames is obtained by the Bobbin. — Winding
in these frames is clue to the bobbin rotating at a slower
or quicker rate than the spindles. In the former case the
" flyer leads " and in the latter the " bobbin leads." The rates
of rotation of the spindles and rollers being constant, winding is
obtained by that of the bobbin differing from the former of
these to an extent sufficient to wind the amount delivered by
the rollers. Generally, the range in the size of the bobbins is
from 1^ inch upward, empty, to below 6 inches when full. It
is not often that full bobbins exceed more than four times
their size when empty.
Winding is arrested, in these machines, when the bobbins
assume the same rate of rotation as the spindle or flyer. Thus
if the latter exceeds the former, or vice versa, the difference
represents the coils wound. However large the bobbin becomes
— when winding is required — the rate of rotation must, as its
size develops, approach that of the spindle, but never attain
the same speed equal to it. Therefore, if the bobbin leads and
the spindle makes 1000 revolutions per minute, however large the
bobbin may become, its rate must be something more than 1000.
In the case of the bobbin being 1^ inches in diameter, empty,
and 6 inches diameter when full, and the length wound equal to
120 times the circumference of the former size, then the bobbin
126
COTTON SPINNING CALCULATIONS
must revolve at the rate of 1000 +
120 j< 1.^
6
= 1030 revolutions
when full, as against 1000 + 120 empty.
The Use of Cone Drums. — Cone drums are used to give the
necessary variations in the speed of the bobbins. Their work
consists of contributing toward the driving of the bobbin an
amount sujBicient only to ensure winding at the desired
tension, the remainder an amount which is always equal to the
rate of the spindle being obtained from a fixed contributor.
The Use of Differentials. — Differentials admit of the trans
mission of the motion from the two abovenamed sources with
the most satisfactory results. A simple way of calculating the
motion transmitted through the differential gear is as follows : —
Let n denote the motion issuing from it ; m, that portion
of n derived from the fixed contributor ; a, that portion of
n derived from the variable contributor; M and A, the rates
of those parts of the differential responsible for m and a
Fig. 23.
respectively ; t, the values of the respective connecting trains
connecting M and A with n —
then n consists of ??i ± a
Applying this to the Holdsworth differential gear (Fig. 23) : —
When M is at rest and motion is imparted to A,
revolutions oi n = k ± Kt (in the same direction).
AND COSTS OF YARN 127
When A is at rest and M is moved, then —
revolutions of w = Mt
in the opposite direction to M. Therefore when A and M rotate
in the same direction,
revohitions of n = K ± A.t ~ Mt
and when A and M revolve in opposite directions,
revolutions oi 71 = A ± At + Mt
Thus, if M makes 300 and A 60 revolutions, both in the same
direction, and the value of i is 1, then, by using n = a — m, or
its equivalent, n = A + kt — M —
M = 60 + 60 X 1  300 X 1 = 120  300 =  180 revolutions
.'. )i = 180 revolutions in the direction opposite to A
Should A and M move in opposite directions at the rates of 60
and 300 revolutions respectively, then —
)i = a + m
or, n = A + At\ M?
.. 7t = 60 + 60 X 1 + 300 X 1 = 420 in the same direction as A
Thus, the fractional movement of n, due to a, is, in the latter
instance, 120, and that due to m is 300, so that the plus 60 has
become plus 120, and the minus 300 has changed to plus that sum.
Examples in Calculating the Length Wound upon the
Bobbin with the Principal Types of Differentials.
The particulars contained in Fig. 23 are those existing in a
roving frame in working condition. The particulars not given
in the figure are — The diameter of top cone, in the part on
which the centre of the cone strap rests, is b\\ inches, and the
diameter of the bottom cone, also opposite the centre of the
strap, 3/g inches; the diameters of the empty bobbin 1^^"^,; inch,
and that of the front roller 1] inch. Under these conditions the
revolutions of the spindle per mhiute = r = 11425
^ ^ 33 X 21 ^
128 COTTON SPINNING CALCULATIONS
and the revolutions of the bobbin per minute, when the bottom
C3ne is stopped, or when the twist wheel is —
40 X 21
Since the two wheels in the sun wheel are carriers, and the wheel
on the frame shaft driving them is 36 and that driven by this
train is also a 36, t therefore equals H}; = 1. Hence the revolu
40 X 60
tions of the bobbin per minute = 400 X 1 X = 1142f
or the same speed and in the same direction as the spindle.
The revolutions of the bobbin per minute, when the bottom
cone is working and the twist wheel is 50, are
., , A. 4 Tir.N^O X 60
or —
r/ 400 X 50 X 91 X 2 3 X 19 400x50x91x 23 X 19 V .^ 1
LV 1 X35x55xr20xl30"^ 1 X35 x55 X 120x 130 /" J
40 X 60
^ 40 X 21
Here ^ = 1, and the sun wheel moves in the opposite direction
to M, and, therefore, the sign is +, hence
/o w 400 X 50 X 91 X 23 X 19 , ,^^\ 40 x_60
V 1 X 35 X 55 X 120 X 120 / 40 X 21
= revolutions of bobbin per minute
= (57 X ^ + 400) X ^^ = 13068
Therefore, the revolutions of the bobbins in excess of the
spindles
= 13068  11428 = 164
The length of rove wound upon the bobbin per minute,
neglecting the facts that the rove is wound spirally, and also
that the actual winding radius is greater than the radius of
the bare bobbin, is
= 164 X r = 612 inches per minute
lb X 7
AND COSTS OF YARN
129
the revolutions per minute of the front roller being — ^^ — ^t^ — >
^ *= 35x130
and the length delivered by it in that time —
400 X 50 X 35 X 5" X 22 ^^^ . ,
= 1 X 35 X 130 X 4 X 7 = ^^^ ^^'^"'
Upon this basis the bobbin is shown to wind 7 inches more
than the actual length delivered by the front roller. When the
amount due to contraction in the roving, by reason of the twist
inserted in it, is added to the difference due to the spiral dis
posal of the coils, and also to the difference between the actual
radius of these coils and that of the bobbin, the tension of
winding must be considerably more than is represented in the
calculation.
The particulars contained in Fig. 24 are of a roving frame.
30 9,0 14 308 revs.
25 >,ni^^1R pei^^min.
Fig. 24.
the differential in this instance being of the Curtis and Ehodes
type.
Proceeding to deal as with Fig. 23 —
n = m ± a
When M is at rest it will be seen, upon examination of this
differential, that, if the bottom cone is rotated,
n = a, or Kt
and in the same direction.
130 COTTON SPINNING CALCULATIONS
When A is at rest and M is rotated,
n = 111, or M — M^
and when M and A revolve in the same direction,
11 = m + a, or M  Mi + At
Therefore when M and A revolve in opposite directions,
n = m  a, or M  lit — kt
The value of t in each of the above instances is the same,
being —
30 X 18 X 14
25 X 30 X 90
According to the particulars contained in the figure, it mil
be seen that when A is at rest,
n = 308  S08t
308 X 30 X 18 X 14
n = 308 
25 X 30 X 90
The portion of n denoted by a, when the diameters of the
cones at the points opposite the centre of the strap are — top, 5,
bottom 3^ inches ; equals
308 X 39 X 5f X 36 X 46 X 46 x 30 X 18 X 14
35 X 3i X 36 X 50 X 106 X 25 X 30 X 90
M and A are indicated in the figure as working in the same
direction, the flyer and the bobbin are also revolving in the same
direction, the latter leading ; the connecting sign between m and
a must therefore be plus —
.. It = (3O8 
308 X 30 X 18 X 14^
25 X 30 X 90/
/ 308 X 39 X 5 X 36 X 46 X 46 x 35 x 18 x 14\
\ 35 X 31 X 36 x 50 X 106 X 25 X 30 X 90/
Under these conditions the revolutions of the bobbin per
minute will equal —
4 5 X 60
" ^ 40 X 21
AND COSTS OF YARX 131
or —
F/^QAQ 308 X 30 X 18 X U\
Li^aOS 25 X 30 x~90/
4
25 X 30 X 90^
/3 08 X 39 X 5 X 36 X 46 X 40 x 35 x 18 X 14
\ 35 X 3i X 36 X 50 X 106 X 25 x"W X 90
)]
45 X 60
^40X21 = ^^^^^
Of this sum the exact amount due to the cones, signified by
a, is —
/308 X 39 X 5 X 36 X 4 6 X 46 X 35 X 18 X 14 \ 45 X 60
V 35 X 34 X 36 X 50 x 106 x 25 x 30 x 90/ ^ 40 x 21
= 87'27 revolutions per minute
The amount contributed directly from the shaft through the
differential, and signified by m, is —
/ 308 308 X 30 X 18 X 14\ . . 45 X 60
= 8791
\ 1 25 X 30 X 90/ 40 X 21
The revolutions which the spindles would make per minute
are
= 308 X ^^ = 880
in the same direction as the bobbin. Thus, the bobbin leads the
flyer to the extent of
96637  880 = 8637 revs.
This represents the amount of rove wound, which should of
course be approximately equal to that delivered by the rollers.
The revolutions of the front roller in the same time are
Therefore the length delivered per minute is
= 924 x22 = 2904
The amount which the bobbin would wind, assuming the
material wound was  inch radius from the centre of the bobbin,
equals
8637 X li X V = 33971 inches
132
COTTON SPIXXIXG CALCULATIONS
Under these conditions the 290*4 inches of rove delivered by the
front roller per minute would be stretched to 339'71, or to the
extent of
83971  2904 = 49 31
this being 17 per cent.
A noticeable feature in respect of the gearing in this figure
is that the bobbin is not driven at the same rate as the spindle
"uhen the cone drum ceases to bo a contributor. This makes
the correct adjustment of winding impossible. Thus, when the
cone is stopped, the revolution of the bobbin per one of the
spindle is —
21 X 33" / 21 X 33 X 30 X 18 X 14
60 X 33 X 25 X 30 X 90
r 21 X 3^ _ /
Uo X "33 \
)]
45 X 60
40 X 21
= r^i  "^^ 1 45 X 60 26250  2940 . 45 X 60
Uo 1250 J ^
60 1250J '^ 40 X 21
23310 X 45 X 60 999
75000 ^ 40 X 21
= 0999
75000 X 40 X 21 1000
The bobbin moving slower to the extent of O'OOl per revolution of
the spindle, and thus, whilst the cone is stopped, if the spindle
makes 880 revolutions, the bobbin would make
880 X 0999 = 87912 revolutions
T.W.46
256 revs,
p er, min.
'" ^'^,414850 40
Ftg. 25.
The particulars given in Fig. 25 are taken from an
AND COSTS OF YARN 133
intermediate frame. The differential in this case is of the
Tweedale type. Dealing with this as with the previous ex
amples —
n = m ± a
When M is at rest and the bottom cone is actuated,
n = a, or At
and in the same direction. When A is at rest,
71 = OT, or M — M^
When M and A revolve in the same direction,
n = m + a, or M Mt + At
When M and A revolve in opposite directions,
n = ??t — a, or M.  Mt  At
The value of t in this case is —
18 X 16
80 X 48
Taking the speed of the frame shaft at 256 revolutions per
minute with the bottom cone at rest —
n  2562 _ 256_x 18 x^e
''  "^""^^ 30 X 48
This being the portion contributed to n, from source m, when M
and A are both in action together.
That portion of n contributed from source a, when the dia
meters of the top and bottom cones — at the points opposite the
centre of the strap during the winding of the first layer — are
5^ inches and 3 inches respectively, will be —
2562 46 X 57 X 18 X 44 X 18 X 16
'^ ^ 48 X 3 X 68 X 84 X 30 X 48
therefore when the M and A are working together —
/ 256 X 18 X 16\ / , 46 x Sj X 18 X 44 x 18 x 1 6\
n[Zob,, 30^^/ + V^^' ^ 48x3^x68x34x30x48^
the revolutions of the bobbins being —
50^^
'' ^ 42 X 30
134 COTTON SPINNING CALCULATIONS
The revolutions of the bobbin per minute are therefore—
r(o^a2 256§ X 18 X 16 \ f ^ 46 X 5 X 18 X 44 X 18 X 1 6^
50 X 55 P/o/rfl.A ^1 o\ 1 OT ol 50 X 55
= (2053 + 273) X f^^^ = 508
The revolutions per minute which the bobbins would make
if the bottom cone was stopped would be —
(2566  513) X ^2^0 = ^^^'^^^
The revolutions of the spindles per minute would be —
The revolution of the bobbin per 1 revolution of the spindle,
according to the above working, is therefore —
448148 ^ ^
448148 ~
Working directly from the spindle to the bobbin, this last
result is proved as follows : —
[ 30 X 42 _ / 30 X 42 X 18 X 16 \i 50 x 55
L55 X 40 V55 X 40 X 30 X 48/J ^ 42 X 30
= revolutions of bobbin per 1 of spindle
_ r315^ 63 1 50 X 55 _ 252 x 50 X 55
~ L55O  550J ^ 42 X 30 ~ 550 X 42 X 36
= } = 1 revolution of bobbin per 1 of spindle
The revolutions per minute of the front roller are —
2562 ^ 46 X 48
^'^ ^ 48 X 130
The length of rove delivered by the front roller per minute —
orA2 ^ 46 X 48 X 1" X 22 __^ . .
2564 X J7Z zr^rx z = = 285 inches
^ 48 X 130 X 1 X 7
AND COSTS OF YARN
135
The number of coils of rove wound per minute, being the
difference in the revolutions as compared with the spindle —
= 508  448i48 = 5985 nearly
The length actually wound on the bobbin, assuming the radius
of the coils ~, 1^ inches being the diameter of the bare
bobbin, would be —
= 5985 X i— ^^^ = 3056 inches
8x7
Thus the length of the rove wound on the bobbin exceeds that
delivered by the roller to the extent of 3056285, or 206
inches, equal to 7*2 per cent.
Fig. 2G.
In Fig. 26 the differential is that known as the Fallows
motion. The particulars herewith given are of a slubbing
frame. This differential differs considerably from the usual
types, and an explanation of its action is deemed advisable.
The right extreme of the portion marked A consists of a cam,
the face of this bears against the side of a disc formed upon the
rim of a double wheel. Wi and W2 denote the left and right
hand sides of this disc wheel. The teeth are of special design,
and the wheel is mounted, loose, on a spherical bearing. This
spherical bearing is secured to the driving shaft. This form of
bearing admits of a portion of Wi being in gear at a point with
M, and a portion of W2 also in gear at a point with N, but on
the opposite side of the axis. Thus, the double wheel gears and
136 COTTON SPINNING CALCULATIONS
worbs in an oblique position, and this is maintained by the
pressure of the cam against the sides of the disc. Under these
conditions Wi and W2 act as a compound wheel toward motion
passing from M to N. Under these conditions the value of the
train would be —
= K ^
Wi ^ N
The effect of the movement of A, when M is at rest, is that
the cam would compel the gearing points of Wi and W2 to circu
late, the teeth of the former entering and emerging from the
teeth contained in M as A revolves ; therefore if Wi contains
the same number of teeth as M, no circumferential motion
of Wi or W2 could accrue. This reasoning applies in a similar
manner to W2 and N. Should M and Wi contain different
numbers of teeth, then circumferential motion will be imparted
to Wi and W2 in the direction opposite to that of A, when Wi
contains less, and in the same direction when Wi has more,
teeth than Wg. Thus, the movement of Wi would be Wi — M,
in teeth per revolution of A, and its rotary movement would be —
Wi  II
Wi
The movement in teeth made by W2, in the same time, would
be—
W i  M W2
Wi ^ 1
and, therefore, if N contained the same number of teeth as W2,
the movement of N would be the same as W2.
If the number of teeth in W2 and N were not alike, the
movement would be further affected by reason of the cam A
causing all the teeth in W2 to enter, and emerge from, as many
of those in N as are contained in W2. Thus, the action in this
case must be, when M is at rest and A makes one revolution —
= ^Vi M W2 N  W2
Wi" ^ N "^ N
In this differential t has two values. In respect of the motion
from M its value is —
M W2
W ^ N
AND COSTS OF YARN 137
Let this be termed ti. "When the motion is from A its value is —
Wi  M W2 , N  W2
Wi N ^ N
Let this latter be denoted by fa
it will now be possible to proceed to deal with this in the
same manner as with previous examples —
n = 111 ± a
under all conditions.
Therefore when A is at rest —
n = M^i
in the same direction.
When M is at rest —
n = Af2
the resultant direction depending on the differences in the
number of teeth contained in the wheels M, Wi, W2, and N.
This will be indicated by the sign being either plus or minus.
When M and A revolve in the same direction together—
n = Mti + A?2
Taking the particulars of the gear as contained in Fig. 26, and
the diameters of the cones at the j)oints opposite the middle of
the cone strap, when the first layer is being wound, as follows : —
top 11 inches, bottom 3; inches, and that of the bare bobbin
li inch; then: the revolutions of the bobbin per minute when
the twist wheel is 0, or when the bottom cone is not engaged,
would be, according to the formula —
165 X 32 X 36 X 63 X 50 ^r^n onn
1 X 3b X 36 X 58 X 2b
The revolution of the bobbin per minute with a 50 twist
wheel, assuming M to be at rest whilst A is in motion —
_ rl 65x46x7^x26x80 . 363 2 36 3636 H 63^50
~ L 1 x24x3jx75x50V 36^^36"^ 36 Jj ^ 58 x'26
_ 165 X 46 X 57 X 26 X 8 X 4 x 63 x 50 _
~ 1 X 24 X 27 X 75 X 5 X 36 X 58 X 26 ~
Therefore the revolutions per minute of the bobbin during
the winding of the first layer would be —
= 306366 + 8595 = 392316
138 COTTOX SPINNIXG CALCULATIONS
or —
1 165 X 32 X 36 /165 x 46 x 7^ X 26 x SO V 36  32 36 3636 \i
L 1 x36x36'^V 1 x24x3tx75x50A 36 ^36^ 36 /J
x^^^? = 392316
58 X 2o
The revolutions of the spindle per minute are —
^f '"'.I'^f. = 306306
1 X 58 X 2o
The number of coils of rove \Y0und upon the bobbin per
minute are therefore —
= 392316  306366 = 85*95
The following will therefore represent the length of rove wound : —
1 X 22
8595 X ^= — = 405193 inches per minute
The front roller, in that time, makes —
165 X 46 X 40 , ,.
fr. T, r revolutions
24 X 115
or delivers —
165 X 46 X 40 X It X 22 ^^_ noo • i,
^, ^^^ ^ = 388928 mches of rove
24 X Ho X 7
Therefore that length is stretched, if the rove is assumed to
have no thickness, to 405193 inches, or to the extent of
13265 inches more than the rollers deliver; this is equal to
nearly 4 per cent.
The particulars contained in Fig. 27 are those of a slubber
frame, the differential being that known as Brooks and Shaw's.
The action of this differential is readily understood. Applying
the formula as in the previous examples —
n = m ± a
for all conditions of working, the revolutions which the bobbin
would make per minute, if the bottom cone was stopped, or if
the twist wheel was 0, are —
, ^ , 74 X 50
= ^" ± '^ ^ 5^^4
AND COSTS OF YAEN
139
Here —
[0±(
(
m = Mt
a = k — At
_ 30 X 18
^ ~ 18 X 37
M = 200, and
A =
200 X 46 X 6il X 30 X 20 X 56n
X 32 X 3^ X 41 X 40 X 64.
200 X 46 X 6f ji X 30 X 20 X 56 X 30 X 18
X 41 X 40x64x18x37
32x3i
)]
74x50 ,^^^
X =7, — ^, = 1005
52 X 24
The sign ± in the last instance is determined by the directions
of M and A ; when they move in the same direction it is + ,
and when opposite it is — .
Fig. 27.
The revolutions of the bobbin per minute, when the cone
strap is in the initial position and M and A are in motion, as per
conditions in the figure, may be ascertained by adding the speed
under the two sets of conditions together, i.e. —
48077 4 1005 = 58127
obtained as follows : —
r200 X 30 X 18 ^ /200j< 46 x 611 x 30 x 20 x^6^
18 X 37
32 X 3i X 41 X 40 X 64.
_ 1^2 00 X 46 X 6i^ X 30 X 20 X 56 x 30 x 18 \i . 74 x 50
32 X U X 41 X 40 X 64 X 18 X 37/
52 X 24
140 COTTOX SPIXXIXG CALCULATIONS
therefore, of these the bobbin ^ould make —
/200 X 30 X 18\. ^\ 74x50 ,^^,f, , , . ' . ,
( ^i T7^ — 7^ ± ) X ^c — 277 = 480] y revolutions per minute
V 1 X 18 X 37 ^ £)2 X 24 ^ " ^
Calculating directly from the spindle to the bobbin, the revolu
tions of the latter per one of the former would be —
/24 X 52 X 30 X 18 ^ ^\ 74 X 50 ,
± X ^ ^ = 1
\50 X 60 X 18 X 37 ~ / 52 x 24
The revolutions of the bobbin, assuming the bottom cone to
rotate whilst M is at rest and the diameters of the top and
bottom cones, at points opposite the centre of the cone strap
whilst in the initial positioji, being G\\\ inches and 3i inches
respectively, would be —
= [162162 + (179177  145278)] x 14^^
= (162162 + 33899) x L^ T: = 58127
The rate at which the coils are wound during the first layer
laid upon the bobbin is therefore —
58127  48077 = 1005 per minute
The rate at which the rove is wound —
1005 X 1^ X ' = 47378 inches per minute
The rate at which the front roller revolves —
46 X 65
200 X q5 :r^ revolutions per minute = 1431
oA X LoU
The length delivered per minute by the front roller is —
„„„ 46 X 65 lyV X 22 ,„^^. ,
200 X ^ ^ X ^^ = 4800 inches
oZ X ioU /
The amount of rove which the bobbin winds in excess of
that delivered by the front roller, assuming the radius of the
winding circle of the rove f inch —
= 480  47378 = 6*22 inches
or 13 per cent, less than that delivered.
The Speed in Fly Frames. — The speed at which the most
satisfactory results are obtained var} with the working
AND COSTS OF YAllN 141
conditions : the kind of work, the efficiency of the machines,
skill and organization of the operatives.
Data on this suhject should not be regarded as inflexible,
but should be subjected to modification such as experience and
developments, in the application, suggest.
The rates of spindle speeds attainable in modern makes
of these frames, fitted with long collars, are —
Kind of cotton.
Slubber.
Intermediate.
Rover.
Jack.
Egyi)tiau
45050U
G50800
9501050
1 00011. jQ
American
550700
700850
10501200
Indian
tJOO700
750850
10.501200
Adopt the highest beneficial speed and fix other conditions so
that the whole of the machinery is continuously occupied in
producing the required amount.
Proportions of Machinery in the Carding Department. — The fly
frame processes usually consist of three stages, but sometimes
two and four are adopted. They are named respectively : slubber,
intermediate, rover ; slubber, rover ; slubber, intermediate,
rover, jack.
The number of these processes expedient depends upon the
extent of the attenuation desired prior to spinning, and also, to
some extent, upon the character of the cotton. Uniform stapled
cottons are influenced less detrimentally^ by high drafts. Bej^ond
a certain count the roving can be more economically prepared by
an additional process. That limit cannot be fixed. It ranges
upwards from between 15 and 20. The draft necessary to
attenuate the drawing sliver to the desired extent for sj^inning
is distributed amongst these two, three, or four processes in
certain proportion (see p. 142).
In the machinery from the card onward to spinning it is
customary to arrange the machinery in what are termed " pre
parations." A "preparation" consists of one slubber and all
the other machinery necessary to prepare as well as to deal
with its product. Such may be literally expressed as a slubber
142
COTTON SPINNIXG CALCULATIONS
and its complement. The following are the proportions of the
machinery forming one preparation in —
Cards.
Combers.
1
Draw frames. Slubbers.  Intermediates. Rovers.
Mule spin
9 to 1.3
6 to 10
One frame of One frame of Two frames
Four frames
ning
18 to 24
80 to 100 of 120 to
of 1G8 to 200
dels, divi
spindles 140 spdlea.
spindles ,
ded into
each
each.
three heads
Bing frames
Ditto Ditto
Ditto
Ditto Ditto
Five frames
of 168 to 200
1
spindles.
The following are therefore the proportions of the above
named machines per slubbing spindle, respectively : —
(deliveries) (spindle) (spindles) (spindles)
01125015 007501 0075001 VO 27230 SOIO'O
These proportions are those ruling in the bulk of spinning
mills, and it is therefore reasonable to assume that they repre
sent what is found most useful.
Drafts in Fly Frames. — The following are the factors control
ling the division of the combined attenuation required in the
respective fly frame processes : —
(1) Number of spindles of each type available ;
(2) Speeds practicable ;
(3) Extent of the combined attenuation required ;
(4) Efficacious twist constant at each stage ;
(5) Time lost at each stage.
These decided, for example, as given below, the respective
drafts are arrived at as follows : —
Speed of spindles (per minute).
Slubber, 550.
Intermediate, 800.
Rover, 1200.
Per cent, time lost (approx.)
Twist constant ....
Proportions of spindles
Count at each stage . .
Draft at each stage . . .
1.5
1
1
c,
10
1
3
c.
7
1
8
Ca
^3
Total draft in these fly 1
frames j
This is always fixed by the count of roving
decided upon for spinning and by the weight of
sliver, most suitable, at the drawing frame.
AND COSTS OF YAKN 143
]rHJi fixed quantities of fiy frames and S2)in)iin(j niacltincrij
available, tJie adoption of the most suitable spindle speeds decide
the drafts by fixing their capacity in respect of their twisting
rates. The demands of the spinning machines having been
ascertained, the highest rate at which the roving spindles
can be satisfactorily run will decide the most suitable count
of roving to prepare and also the draft in the spinning machine.
Let the count of roving be denoted as x lbs. per spindle, and
C3, C2, Ci, the counts of the roving, intermediate, and slubbing,
respectively ; then the amounts required from the intermediates
and slubber will be —
8c
Intermediate, 3 per 8 roving, spindles, ^
o
8a;
Slubber, 1 per 8 roving, spindles, —
Hence the following equations : —
Roving —
1200 X ^^
— = ^^^ = X lbs. per minute per spindle
VCg X C3 X 36 X 840 ^ ^ ^
Intermediate —
800 X tKir 8.^3 „ . . . ,,
Slubber—
550 X — 
— — — LOO _ g,^ Y\)B. per minute per spindle
x/Ci X Ci X 36 X 840 ^ ^ '
From the above equations the separate values of Ci, C2, and
C3 may be found, when the sum of the draft involved in this
production is known. The sum of the drafts in the rover,
intermediate, and slubbing frames is found by ascertaining
the weight per yard, or count, of the sliver at the finishing head
of the draw frame that will produce the required weight when
running at the most desirable speed, and comparing this with
the count of roving required.
An example is provided by assuming the conditions, in
respect of the counts, deUvered, at the drawing and roving
144 COTTON SPJNNING CALCULATIONS
frames : 0"2 and &0 respectively. Under these conditions the
total draft or the attenuation in the slubber, intermediate,
and roving frames would be = ^ x (2 X 2), the latter allow
for the two doublings in each of the latter stages ; = 120.
Therefore the weight produced per roving spindle per
55 hours
55 60 X 1200 X 93 ^ .^ „
= y ~^ = 8'3 lbs.
36 ins. X 840 yds. x/6 6 100
(C3) (C3)
The weight produced per intermediate  _ ^ qq 11
= ^ X 83 lbs.
spindle per 55 hours j 3
55 X 60 X 800 X 90
36^X 840 X V/C2 X C2 X 100 3
.^ _ 55 X 60 X 800 X 90 X 3 _ 
•'• ^'^^'  36 X 840 X 100 X 8 X 83 ~ "^
.•. Co = 233, the count of the intermediate rove
The weight produced per slubbing) _ 0.0 w 8
spindle per 55 hours j ~ 1
55 X 60 X 550 X 85
36 X 840 X v/CT X Ci X 100
yyr n 55 X 60 X 550 X 85 _ „.,.^_
•' V ^1 X Oi  3(3 X 840 X 83 X 8 x 100 " " ^^^
.. Ci = 0*725, count of the slubbing sliver
The drafts in the respective fly frames may be now ascer
tained from the above counts, and they are as follows : —
Draft in the rover —
count of roving X2 _6x2 ^.„
= 83x8 lbs.
count of intermediate 2'33
Draft in the intermediate —
count of inter, rove x 2 _ 2*33 x 2
count of slubbing ~ 0"725
= 643
AND COSTS OF YARN
145
Draft in the slubber —
count of slnbbing _ 0*725
count of sliver 0'2
= 3G25
It is seen, from this procedure, that the drafts in these
machines depend not only upon the proportions of spindles, but
also on the other productive factors mentioned on p. 142, and
numbered 2, 3, 4, 5.
Particulars of Fly Fbames,
Machine.
Eover . . .
Intermediate
Slubber . .
Loss of time
due to oiling,
cleaning, and Usual sizes
incidental of full
stoppages bobbins,
apart from
dofiSng.
Usual
gauge?.
Usual lift=
Contents in
ounces per
bobbin.
SP/o
4i" to 4J"
5f"
Time lost
per doff.
]i" to 3f " ! 5" to 51" 7" and 8" 8 to 11 oz.s. 12 mins.
6"to6J" 9" and 10"; 18to24ozs.
9" j 10" to 12" 24to30ozs.
The Production in Fly Frames. — To estimate the production of
the abovenamed machines. Eover, spindles making 1150
revolutions per minute ; hours worked, 55. Allow 5^ per cent,
for loss occasioned through breakages, and proceed as follows : —
Weight of contents] .qq [the weight that would be delivered
of full bobbin ii^f ^(n.^~l ^^ *^® period required to make a
) " "^ ^ ( doff, if no stoppages = {x)
the weight in ounces
_ I delivered by the roller
in one minute, uninter
rupted vi^orking = (.?/)
ounces
1150 X 16
twist per inch x 36 x 840 X count
55 X 60
= minutes required to fill a set of bobbins
y
■X . ,. 1 . • 1 ft r minutes taken to fill and
 + time lost m doflmg = { ^^g ^ ^^^ ^^ ^^^^^^ ^ ^^^
/weight of contents oh _ ^production per spindle in
^ a bobbin in ounces / ~ t ounces per week
146 COTTON SPINNING CALCULATIONS
Therefore, with the count produced by the roving 6, the twist
constant 1*2, and the contents of a full bobbin 10 ozs., the
production per spindle in ounces and hanks per 55 hours,
respectively, would be —
55 X 60
100
10 X ^rT:v
1150 X 16
\/6 X 12 X 36 X 840 X 6
X 10 = 10352 ozs.
Hanks = l°«:f^« = 388125
lb
With the count produced by the intermediate 233, the twist
constant 1*2, and the contents of a full bobbin 22 ozs., the
production per spindle in ounces and hanks per 55 hours
respectively, would be —
55 X 60 ^
100 /
"" 945 + 12 X 22 = ^11^^22 = 294 ozs.
800 X 16 Zd5 + iZ
^233 X 12 X 36 X 840 x 233
^ , 294 X 233 .o Q
Hanks = ^ — = 428
lb
With the count produced by the slubber 0"715, the twist
constant 1*2, and the contents of a full bobbin 28 ozs., the
production per week in ounces and hanks per 55 hours
respectively, would be —
55 X 60 ^
28 X^
^^ ^ 945 + 12 r^ ^^ " ^^^^ ^^^•
550 X 16
V^O725 X 12 X 36 X 840 X 0725 J
„ , 1055 X 0725 ,„
Hanks = z.^ = 47
lb
AND COSTS OF YARN
147
Examples of arranging the speeds, drafts, and counts to suit
the mill specification. The following being the quantities of
each kind of machinery, ascertain the suitable speeds, drafts,
and counts.
Spinning spindles, mule — .
32 pairs weft IJ" gauge, 64" + 4" draw
IG
twist If
Total spindles
Spindlea.
83,688
34,488
118,176
The weft are engaged upon, average counts, 46^
„ twist ,, ,, „ 36'
The production of these per 55. j hours would be about
27i hanks of 46^ W. ; 29i hanks of 36' T.
The other machines —
Roving.
Intermediate.
Slubber.
Dr. F.R.
Cards.
Scutchers.
Number of frames
Spindlea or beads
Gauge ....
Lift
60
176
8 in 20f'
7"
24
140
8 in 26"
10"
12
96
4 in 19"
10"
12
(3 beads 2 x 4
\of 8 dels, each/
18
120
45"
8
4 laps up
45"
Reasonable allowances in such a mill — ■
Doffing,
mins.
Cleaning.
Stoppages.
Other loss.
Weight on bobbin.
hrs.
mins. per doff
per cent.
07.S.
Mule ....
8
'^
—
^
—
liovers ....
Intermediates .
12
12
•>
U
22
Slubbers . . .
14
ft
14
"
28
Suitable roving for the above counts of yarn : 5^ for weft and
4i hank for the twist.
The relative productive rates in the roving frames —
Count 5^ X y/5^ = time per lb. 5^
„ 4^ X ^U = „ U
148 COTTON SPINNING CALCULATIONS
If all 5^liank rovings were produced, the total weight
would be —
28160_Xv/:4L >^ =20,777 lbs. + 50,280 lbs. = 71,057 lbs.
The amount of 4^hank roving required per week is
28,160 lbs.
The number of roving spindles required to prepare 50,280 lbs.
of 5ihank must be —
50280
10,560 total roving spindles x rfjonrj = 7472, say 42 frames
Leaving 18 frames for the 4^ hank.
Another way of arriving at the number of roving spindles to
engage on each count is —
50,280 lbs. of 5i hank = 276,540 hanks
28,160 lbs. of 41 „ =126,720 „
403,260 „
Therefore, if 60 frames of 176 spindles produce the above,
and the respective productive ratios are —
For 4^^ 4:}j X v^5i in hanks or length
then the number of frames required for 126,720 hanks of 4J* —
 60 x^^^^™x^^ 18 frames
^^"^ 403260 ^ ^51 "
and for 276,540 hanks of 5^^—
= 60 X ?L640 ^ VSi ^ ,2 ,^^^^^
403260 ^4^
The production of the fly frames, drawing frames, and cards,
in pounds, must be as follows, allowing i per cent, for waste at
each stage : —
5^ hank : Production, in pounds, per roving spindle —
50280 X 1 00 _
42 X 176 X 99h~
v^^^^i^
AND COSTS OF YARN 149
U hank : Production, in pounds, per roving spindle—
21860 j<JOO_ ;
18 X 176 X 991 ~ 893
Production, in pounds, per intermediate spindle. All these
frames making the same count—
78440 X 100
3360 X 99 ~
Production, in pounds, per slubbing spindle—
78440 X 100 _
ll52"x 98i~ ^^'^^
Production, in pounds, per draw frame delivery—
78440 X 100
~96~>r98~ = S^4 lbs.
Weight per card (see later).
The Speeds of the Spindles in the Roving Frames.— Takin^r the
twist constants at 12 in each of the fly frames, and" the
stoppages and allowances as indicated, proceed to ascertain
the rate of rotation of the spindles.
Eoving, 51 hank : The doffs per week—
The time to complete a set of bobbins and doff—
97
^ (551  21) ~  11928 (mins. per doffing)
9^94 = 5 hours
Speed of spindles ; revolutions per minute—
. 11 X 51 X 840 X 36 X ^51 X 12
" 16 5~>r60 " = ^^^^
Koving, 41 hank : The doffs per week—
893 X 16 _
 JJ = 12993
150 COTTON SPINNING CALCULATIONS
The time to complete a set of bobbius and doff
Q7J
(55L  2i)^  12993 X 12 mins. ^^.^
^^^ = T^^. = 378 hours
12993 12993
The Count of the Intermediate Roving. — The weight on an
intermediate bobbin = 22 ozs.
Eevolutions of spindle per minute, 800 ; allowances : 12
minutes each doff, and 2 per cent, after 2i hours for cleaning.
rr,. 1 , . . rv> 236 Ibs. X 16 .^ ^^.. .
Time lost m doffing = ^ X 12 = 206 mms.
97I
Nett time working = 53 hrs.  206 mins. x ^r^ = 2887 mins.
•'• ^^' ^^^^^* = 243 X 700
2887 X 800
l2\/Cx 36 )
25 X 2887 X 800
3 X 243 X 7000 X v/C X 12 x 36
263
The count =
:. count X \/count = 2'63
.'. count = 190
The Count of the Slubbing Rove. — The weight of the slubbing
bobbin = 28 ozs.
Eevolutions of spindles, 600 ; allowances : 14 minutes per
doff, and 2i per cent, after 2^ hours for cleaning.
The production required per spindle per week = 69" 12 lbs.
Time lost in doffing = ^^^ x 14 = 553 mins.
971
Nett time working = 53 hrs.  553 mins. x —^ = 2547 mins.
AND COSTS OF YARN 151
The count = gcjic/x 7 000
f '2547 X 600
I l2v/Cx 36 )
25 X 2547 X 600
The count
3 X 6912 X 7000 X 12 X V'C X 36
0663
Count X v/count = 0737
The Count of the Sliver at the Drawing Frame.— Third head ;
weight per dehvery, 834 lbs.; speed of F.Pw, 320; 1^ inch
diameter ; allowances : 2^ hours for cleaning and 2^ hours for
breakages.
Length delivery per week in yards
= 320 X ^ X ^ X 60 X 53 X ^^^
Weight of the sliver delivery in grains per yard
_ 834j^7_000^^^^6j<^2O00 ^ ^^ .^^^
~ 320 X It X 22 X 60 X 53 X 97i
Drafts.
The Drafts up to this stage.
Slubber = ^ ^^ ^^ = 433
Intermediate = ^ rron =516
u tot
Piover for 5h = ^^rrr  5
^ 19
Rover for 4^ = ^. .^ = 473
19
152
COTTON SPINNING CALCULATIONS
Weight of Card the Sliver. — Number of cards, 120 ; allow 4 for
grinding. Hours worked, actual, 55, less 2h per cent. —
78440 ^ 100 ^^„ „
j^ X ^Y = ^97 lbs., say 700
Revolutions of doffer 15 per minute 26 inches diameter.
Weight of sliver per yard —
7000 X 700 . . „ ■
ofi — oo cvfi = ^^'7 grams
Analysis of the Action of Deawing Rollers.
Provided it is reasonable to assume that top rollers move
at the rate of the cotton with which they are in contact, then
Figs. 28 and 29 are records of the action of the drawing rollers
in the various frames, under ordinary working conditions.
Fig. 29 gives the particulars of the observed relative move
ment in slubber, intermediate, roving, and spinning machines.
Draft: ^1045^<57 ^
Revs: 37 33 63
Cir; f71 mm] p4 mmA p2 mm.,
fv y tv yv y^
Dpaft;096>^<115>— < >— CIO
Revs: 10 85 41f
Draft: .^ i 24 ^<52^
Fig. 28a.
Cir: > (80 ni m V 70 m m) (80 m m .
Revs: 31 40^ ^if^
Draft: _j_i.255^^502^
Fig. 28b.
Those, subsequently given, marked S.W. being of the self
weighted type, i.e. only the front top roller being weighte.i.
The rest are of the ordinary weighted type.
Figs. 28a, 28b, show the manner of obtaining the data.
The revolutions given are exclusively in respect of each pair
of rollers (bottom and top). The relative rotation of the
different lines are contained in the draft.
In these figures the rollers are arranged in the order of their
AND COSTS OF YARN 153
sequence, from left to rigbt, back to front. Their circumference,
revolutions, and draft are placed opposite the parts to which
they refer.
The top line of numerals, in figs., are the observed ratio in
the movement, or draft, in the top rollers, in each instance in
terms of one of the precedent roller. Thus, 1'003 is that of the
second in terms of 1 unit of movement of the first top roller.
The middle line of numerals relate to the difference in the
movement of the top and the bottom rollers in terms of one of
the latter.
The bottom line of numerals gives the ratio between the bottom
SLUBBER INTERMEDIATE ROVER
^115 ^432^ ^1.045^57^ ^V013^3.98^
1015 107 0982 0962 Vie 1008 10 1205 10
Vl218J<~397j VT 255^:^5 02 J' V121 5 J«_3315y
ROVER (S.W.) RING FRAMECS.W.)
1'003^P$— 64 ^ fg 108  > T < 705>»
^V003^64^ ^108^
1(l 1287 1005 1Q2 1125 10
lUl 24 i 5 2 i >L 1 21 JU^6 36 J
Fig. 29.
lines of rollers, in each instance, in terms of one of the precedent
roller.
The features most noticeable, fig. 29, are the variations in the
slip of the cotton, indicated by the movement of the respective
top rollers. Except in the slubbing frame, this slip is consider
able. With that exception the effect of the action of the first and
second pairs of rollers appears to be only that attributable to the
elasticity of the rove, being : 4"5 per cent, in the intermediate,
1'3 per cent, in one rover and 03 per cent, in the other rover,
whilst it is almost 8 per cent, in the ring frame.
The Functioiis of the Respective Lines of Draw Rollers. — There
are no reasons for suspecting that the ratios given in the last
paragraph differ from those generally obtaining. Those results
imply that the functions of the middle and back top rollers
are, first, that of obtaining a uniform tension in that portion
154
COTTON SPINNING CALCULATIONS
of the rove between them ; second, that of controlhng the body
of fibres not within the nip of the front pair of rollers. If
these inferences are true, it cannot be an advantage to place
the middle and back rollers widely apart, also in having a
draft greater than that which covers the possible variations in
tension and natural elasticity of the rove. For these reasons
the draft between the first and second lines of rollers should
always be low and in accordance with the lastnamed
conditions. The difference in the condition in which the
cotton is presented in the slubber, accounts for the almost
complete realization of the draft between the first and second
lines of rollers in that machine.
Front rollep
Hank Indicators.
Figs. 30 and 31 contain the gear common in the old and new
types of hank indicators used in drawing, fly, and ring frames.
In Fig. 30 the dial is numbered from to 100, and this part
is connected with the front roller by the following train of
wheels : A single worm
on the front roller drives
a worm wheel of 51 teeth,
the subsequent gear being
„ . ^  drivers ,,
.6_ _5 _5 . •!_ thp
6o» 60» 60» 60' (Jriven'
latter denominator being
the dial wheel.
This form of indicator
does not admit of reliable
fractional readings, and
for this reason is being
discarded.
The above gear is
only applicable to frames containing a front roller 1^ inch in
diameter.
An allowance of 2 per cent, is always made for breakages,
so that the indicator registers 2^ per cent, less than the actual
length delivered.
Fig. 30.
AND COSTS OF YARN
155
111 the present instance the actual length delivered per
100 hanks registered would be —
GO X GO X 60 X GO x 51 x Ij, x 22 X 1
5X5 x5xGxlx36x7x840
= 10304
This is equal to an allowance of 2"95 per cent.
The particulars of the size of roller and of the gear are now
stamped upon each indicator.
ExiCRCiSE 1. — Assuming the other gear as above, what size of worm wheel
would be suitable for 1 J, If, and 1^ inch in diameters of rollers ? Ans. 46, 41, 38.
Exercise 2. — What lengths, in hanks, would be delivered per 100 indicated,
if the indicators used in frames, containing front rollers f, 1, 1}, If, and 1.^ inch
in diameter, were geared as in Fig. 30, with the exception of the worm wheels,
these latter being 65, 57, 46, 41, 38, respectivety ?
Ans. 102, 1025, 103, 1009, 1023.
ExERCisK 3. — What weight would be produced in 10 hours per frame of 186
spindles if 94 hanks are recorded and the count of the rove is 35 ? Ans. 500 lbs.
Exercise 4. — At what rate would it be necessary to run the spindles per
minute, if the loss of time, including doffing, was 5 per cent., tlie twist per
inch 22, and the count 3i, in order to register on the indicator 94 hanks in
10 hours? " ^«s. 1125.
In Fig. 31 there are three index discs, that on the left hand
recording tens, that in the centre the units, and that on the
right hand the decimals, each
disc being numbered from 1 to
10 and each free upon the
central spindle. The driving
from the front roller is by a
worm driving the 36, and thence
to the decimal dial wheel : the
gear is
•2 4
_^8
2 0'
The units
dial is driven from the decimal
dial by a train ^ X .f^y, and the
tens dial is driven from the latter by
Fig
2 0"
Thus the calculated length delivered per 100 recorded
20x4x20x4 X 20x4x24 X36x9x22x 1 X 1
~ 8x1x8x1x8x1x1 Xl X8X7X36X840
= 101 hanks
156 COTTON SPINNING CALCULATIONS
Exercise 5. — What length iu hanks would be delivered per 100 recorded if
the 36 worm wheel is changed to 37 ? Ans. 1038.
Exercise 6. — What length in hanks would be delivered per 100 recorded if
the 36 and 34 worm wheels are changed to 35 and 25? Ans. 102*3.
Exercise 7. — What w^eight of 4' roving will be produced in a frame
containing 200 spindles per 52 hanks recorded by an indicator, as in Fig. 31,
assuming the loss is actually 2i per cent. ? Ans. 2560 lbs.
Length or Full Bobbin Stop Motions.
Fig. 32 represents a length stop motion applicable in fine
work when a number of sets of bobbins are required containing
exactly the same length. This motion is very
^"i^^ c 1 °^^° convenient in the preparation of special rove
I— H ni for spinning samples and small quantities, and
O P"i I n "when not more than the roving necessary to
make the yarn is required.
A is a worm on the front roller, B a worm
Fig. 32. wheel, C a worm on the latter, driving D, D is
compounded with the worm E ; E drives F,
and this is attached to a peg disc G ; a suspended catch H
operates the strap control release bar I at each revolution of G.
B is the change wheel.
The length of roving delivered per action of this motion with
the front roller 1' inch in diameter = ^ X ^^ X ^ X ^^4^
1 1 1 do
= 4295 yards.
Exercise 1. — What size of change wheel (35) would be required to make
bobbins containing 21 leas, 73 yards? Ans. 27.
Exercise 2. — A roving frame containing 200 spindles is required to prepare
500 lbs. of 20' roving for a mule using double roving and containing 1000 spindles.
What change wheel will give the nearest approach to the necessary length on
each bobbin ? Ans. 34.
Exercise 3. — What lengths of roving will be delivered by the front roller
per action of this part with change wheels ranging from 25 to 45 respectively ?
Mule Calculations.
The Gearing in Mules. — The parts engaged during spinning
receive their motion from the rim shaft.
Those parts that are engaged whilst spinning is in abeyance
AND COSTS OF YARN 157
receive their motion through the shaft designated the backing
oflf and takingup motions shaft.
The rim and the backingoff and takingup motions shaft
receive their movement from the line shaft, usually through the
medium of a counter shaft. This system of driving obtains
better control than when driven direct from the line shaft.
The draft gear in these machines is identical with that in
the fly, and ring frames. Eeference to those will make clear all
that can be said respecting drafts and changes in the counts in
mules. Examples are given later in this section.
(a) The spindles are connected with the rim shaft by an
indirect train, comprising two direct trains of pulleys and bands,
the rope from the pulley on the rim shaft being guided to one
on the tin roller shaft by suitable carriers. The lastnamed
shaft is coupled to a series of long drums known as tin rollers,
these drive bands conveying the motion to grooved pulleys or
wharves on the spindles. The rim pulley is the usual change
part in this train. In some makes slight changes are also
arranged for, in the size of the tin roller pulley ; it is then made
in two detachable portions. When a change in the speed of the
spindle is expedient, this change is used for altering the rate of
rotation of the spindle and its relation with other parts.
(b) The connecting gear from the rim shaft to the front roller,
in most makes of mules, consists of an indirect train of six wheels,
arranged in three direct or simple trains. These are conveniently
mounted to enable at least one driver and one driven wheel to
be changed. A change in the value of this train is necessary
when an alteration in the relation of the rollers with the rim
shaft is required. Also, when a change in the speed of the
spindle is desired, but without any alteration in the relation
between this part and the rollers.
(e) The front roller is connected with the back roller by an
indirect train of four wheels comprising two direct trains. These
wheels are named the draft wheels and, respectively, the front
roller, crown, pinion, and back roller wheels. The two latter
are conveniently mounted for changing, being the medium of
alterations in the draft.
The middle back rollers are connected by a direct train.
158 COTTON SPINXIXG CALCULATIONS
comprising three wheels, in the same manner as in fly
frames.
((/) The carriage, of spindles, is drawn outward by two sets
of ropes attached to drums secured upon the back shaft. The
latter being connected with the front rollers by an indirect train
of five wheels, these comprise two direct trains. Those wheels
are conveniently arranged to enable a driven and a driver to be
changed. They are known as the gain and gain boss wheels
respectively, the last named driving the wheel on the back
shaft. These wheels are the medium of alterations in the rate
of movement of the carriage, relative to that of the front roller ;
and therefore they control the tension in the yarn during
spinning. In spinning the poorer classes of yarn gain is often
a minus quantity. The "jacking," " ratching," or stretching
motion is the means by which yarns may be improved, during
spinning, by the elimination of soft thick portions. The motion
is not usually adopted for other than fine work, because it
reduces the production considerably, thereby increasing the cost
of spinning. It is the medium for actuating the backshaft train
at } to I the normal rate, and during this action the rollers are
either at rest or moving at an almost imperceptible rate. This
action has the effect of moving the carriage at from ^ to I of the
normal speed, and hence the yarn is stretched and made more
uniform by the thicker portions being attenuated. In accom
plishing this successfully it is necessary that the 3'arn should
only receive a portion of its twist prior to this action. The
exact amount cannot be stated, because it varies in extent, with
the circumstances, from ^ to  of that required, being lowest in
the bestprepared and longstapled cottons. When the com
pleted yarn contains above the standard twist, much twisting is
necessary "at the head." This, if completed at the ordinary
speed of the spindle, results in a considerable loss of time.
The gearing, comprised in this motion, varies in the different
makes. Three types are contained in Figs. 34, 36, 37, and 38.
(e) The slow roller turning, or " receding," motion, contained
in Figs. 34 and 36, consists of a train of wheels in uninterrupted
connection with the rim shaft. This prevents the front roller
from being at rest whilst the rim shaft is rotating in the
AND COSTS OF YARN 159
"twisting" direction. Tiiis action eliminates the tendency of
** twisting down " of the ends during jacking. It is constructed
with an escapement allowing the front roller to be driven by
the major movement active.
The twisting motion, shown in Figs. 34 and 36, controls the
twist. It is only used in those mules wherein the twist cannot
be, advantageously, completely inserted whilst the carriage is
moving, necessitating the completion of twisting with the
carriage at rest at the "head." This motion controls the rim
shaft driving strap. The mechanism consists of a detent catch
for holding the strap fork lever, this is released by a " tumbler"
operated by a train of wheels that are in connection with the rim
shaft. One or two of these wheels are mounted conveniently for
changing. These change wheels are termed the twist wheels
because they control the revolutions which the rim and the tin
roller shaft and the spindles make per draw, and thus the twist
inserted in the yarn.
The double speed motion, for rotating the spindles at two
different rates, aims at the reduction of the time occupied in
spinning, when "jacking " is in vogue, by actuating the spindles
at the maximum rate throughout. Prior to jacking, the speed
of the spindles must be in accordance with the resistance of the
yarn. As the degree of twist increases and improves the strength
of the yarn, the spindles are rotated at a higher speed, some
times almost double the former rate. For this work two drums
of different sizes may be employed, to drive the counter shaft
alternately, as shown in Fig. 35.
Two different sizes of rims separately driven are also used
for the same purpose.
The building motion consists of a mechanism for raising the
range of movement of the directing faller wire so that the yarn
is laid in layers, progressively ascending, upon the spindle. The
rate of this movement determines the thickness of the body of
yarn so formed, and therefore that of the cop. The parts
actuating this movement are : a screw, which operates the with
drawal of the inclined plates supporting the copping rail,
having a ratchet wheel secured to it — the latter being actuated,
by the passage of a curved or inclined bracket secured to the
160 COTTON SPINNING CALCULATIONS
carriage front ; an adjustable number of teeth per draw, through
the medium of a pawl and pawl lever. The pawl lever, at
each passage, is pushed prior to the termination of each outward
movement of the carriage. The extent of this movement is
adjusted by varying the inclination of the curved bracket, and
also, by the use of screws of difterent pitch. Eatchet wheels are
made a standard diameter by each maker, but with varying
numbers of teeth. Whenever convenient the wheel is moved
one tooth per draw only.
The Roller Delivery Motion, during Winding. — This motion
usually consists of a direct train, composed of three wheels, for
driving the front rollers during the inward run of the carriage.
This is effected from the back shaft. The wheel on the latter,
or that on the front roller, is furnished with an escapement that
allows of the front roller being driven by the major movement
active.
The winding motion is similar in construction in all the
types of mules in general use. It consists of an actuating
chain and chain barrel, with a direct train connection to a wheel
on the tin roller shaft. This generally consists of two wheels,
one of these communicating the movement to the shaft through
an escaj^ement that allows the tin roller to be always under the
influence of the major movement. The rate at which the chain
is unwound from the barrel controls the spindle. The rate of
the unwinding of the chain is determined by the radius described
by the other end of the chain. This is secured to a nut on a
screw within the quadrant arm, the screw being actuated in one
direction only, and this increases the radius described by the nut.
This is the function of the automatic winder governing motion.
The backingoff and takingin motion is shown in each of the
Figs. 33 and 34. This is the same in all types of mules except
that the value of the train and rate of movement are varied.
During recent years considerable improvement has been
made in this motion. The change enables the tension, to
which the yarn is subjected, to be adjusted in the most desirable
degree. This is obtained by the introduction of parts which
control the engagement of the backingoff friction, and allow this
to be deferred until the momentum of the rim shaft is reduced to
AND COSTS OF YAKN 161
the desired degree. The effects are that backingoff frictions
may be run at slower rates and are more reliable. They can be
adjusted more definitely to the requirements.
The Hastening Motion. — The usefulness of selfacting mules
for the finest counts has been improved by the introduction
of figure 35 type of this motion. Its aims are to secure the
desired adjustment in the number and spacing of the coils
wound upon the spindle at the termination of winding. Also,
to relieve thereby the strain upon the yarn during the action
of bacldngoff.
Twist. — The following are the common twist constants'
standards in connection with the ordinary qualities of single
yarns : —
Descriptiou of the V count x constant
cotton and yarn. = twist per inch.
Egyptian weft 318
American „ 3'25
Doubling „ 349
American twist 3*75
Egyptian „ 3606
Ring „ 40
The Conditions governing the Various Changes in the Wheel
Train Values in Mules. — (1) The speed of the spindle should be
the highest consistent with the quality of yarn required, and with
due regard to the wear and tear of the machine. The rim pulley
is the medium of alteration.
(2) The twist required in the yarn must conform with the
standards given above. This controls the sizes of the rims,
twist and speed wheels. «
(3) The most beneficial rate at which the carriage may be
moved outward often restricts the speed at which the spindles
run, and determines the size of the speed wheel. Five draws
in 60 seconds is considered the maximum rate at which the
carriage may be worked.
(4) The count of the roving available and that of the yarn
desired.
(5) The "gain" or ''drag" must be governed by circum
stances ; generally it is beneficial in attenuating the thick soft
and breaking the weak parts of the yarn. At the same time it
M
162 COTTON SPINNING CALCULATIONS
eliminates snarls, and is usually applied to the greatest extent
practicable. This governs the relation between the movement
of the carriage and rollers.
(6) "Jacking" or "ratch" can only be adopted when time
and other circumstances permit. Generally it is only adopted
to a very limited extent in other sections than the production of
fine yarns. It is essential in the production of yarns of a
superior quality ; sometimes it is applied to the extent of as
much as 4^ inches in a draw of 60 inches.
(7) The " shaper" wheel governs the thickness of the cop.
In changing, the following precautions should be noted : —
(1) Avoid changing the twist by means of either the speed wheel
or rim pulley before ascertaining whether a change in the
spindle or carriage speed will be most beneficial, and to what
extent each of these may be altered to advantage.
(2) Before changing the twist wheel, consider whether the
proposed alteration can be accomplished to greater advantage by
means of the rim or speed wheel.
(3) Always notice and collect data of the difference between
the calculated and actual results. These vary very considerably
in the nonpositive gear, and can only be satisfactorily deter
mined in this way.
(4) Check the accuracy of the effects of the draft. This is
readily done at the spindle point by taking a sufficient number of
ends, of a standard length, to enable the counts to be ascertained.
(5) The differences in the rate of spindles vary very much,
and in ascertaining the actual twist, several tests should be made.
Calculations and other Particulars of the Various
Trains of Gearing.
Fig. 33 is a plan of the gearing as found in the Hetherington
mule for coarse and medium counts The particulars relating to
the driving of the rim shaft in this figure are —
Line shaft, 235 revolutions per minute ; diameter of drum,
32 inches.
Counter shaft : fast and loose pulleys, 16 inches ; driving
drum, 28 inches diameters.
AND COSTS OF YARN
163
Revolutions of tlic rim shaft jX'V minute —
235 X 32 X 28
16 X 14
= 940
(a) Revolutions of the spindles per minute, when the rim pulley
is 12 inches and the tin roller pulley 12 inches —
940 X 12 X 6
12 X 5
= 7520
50
Taking in
^?7 ^sha ft 2f revs.
per draw
75
Back Shaft
3rrevs.= 64'
10/
Fig. 33.
Therefore, the different speeds of the spindles obtainable
by the range in the sizes of rims (12 to 22 inches) are =
13" 14" 15" 16" 17"
Size of rim 12"
SizeofT.KP 12"
Revs, of spindle per miu. 7520
8150 8780 9420 10,050 10,080
164 COTTON SPINNING CALCULATIONS
Size of rim 18" 19" 20" 21" 22"
Size of T.E.P 12"
Kevs. of spindle per min. 11,300 11,730 12,530 12,970 13,600
2sfoTE. The actual will differ considerably from the calculated speed. The
loss between the rim shaft and the spindle will be from 5 per cent, upwards,
when the diameters of the surfaces in the train are measured in the customary
way.
(h) The rate of rotation of the front roller relative to the
spindles is varied in order to obtain the desired twist. The train
connecting the front roller with the rim shaft is provided with
suitable change gear for that purpose. The length delivered by
the front roller during the outward run of the carriage, varies
with the amount that the latter is desired to *'gain." The
movement by the carriage is from 68 inches to 58 inches, the
former in mules for coarse, and the latter in those for fine, work.
Assuming no " gain," the surface rates of the movement of the
rollers and carriage correspond. Thus, with the front roller
1 inch in diameter and the draw 64 inches, the front roller
makes —
jj — 22" = 2^A revolutions per draw
With the gearing from the rim shaft to the rollers arranged
to give the quickest movement practicable within the range of
change wheels stated : the largest driver and the smallest driven
change wheels must be adopted ; whilst in the train from the
rim shaft to the spindles, the smallest drivers and the largest
driven change wheels are necessary. Thus, neglecting the
slippage arising in respect of the connection to the spindles, the
revolutions of the spindle per 20 1\ revolutions of the front
roller would be —
20 4 X 38 X 35 X 40 X 12 X 6 ^
"^^11 ^ 20 X 35 X 30 X 12 X I
This represents the least twist per draw under the
conditions named,
412*5
The twist per inch of yarn is therefore ^^^ = 6*44.
Thus, driver wheels and driven pulleys in this connection
29
28
27
26
25
24
426
441
457
475
494
515
666
088
714
743
782
805
22
21
20
19
18
17
562
588
618
650
687
728
AND COSTS OF YARN 165
reduce the twist inversely to changes in their size, whilst driven
wheels and driver pullej's have the inverse effect. Therefore,
the revolutions of the spindles per draw and the twist inserted
per inch of yarn spun, with other change wheels than those
given in the previous calculations, are as follows : —
(pi) Size of wheel on the rim shaft . 30
Eevs. of spindle per draw . . 412
Twist per inch 644
Size of wheel on the rim shaft . 23
Revs, of spindle per draw . . 537
Twist per inch 84 878 92 966 1015 107 1137
The revolutions of the spindles per draw possible with the
range in speedwheels (4060), as specified, and the rest of the
speed gear, excepting that a wheel of 17 teeth replaces the 30
on the rim shaft, as given in the previous calculation, are as
follows : — The train from the rollers to the rim shaft when
Of. y. Q" Tw obtains 728 revolutions of the spindle per draw
of 20/^ revolutions of the front roller. The 40 in this train
is the speed wheel and therefore increasing the size of this
will cause a reduced rate of movement, by the rollers and
carriage, inversely to the change in these wheels, and hence
proportionately more twist in the following amounts : —
(6,) Size of speed wheel . . 40 41 42 43 ... 50 ... 55 ... 60
Revs, of spindle per draw 728 746 764 782 .. . 910 .. . 1002 . . . 1092
Twist per inch .... 1137 116 119 122 . . . 142 . . . 156 ... 17
FurLher increases in the twist may be obtained by increasing
the value of this train. This may be accomplished by reducing
the number of the teeth contained in the wheel on the same
axis as the speed wheel (35), and also the bevel wheel (20),
driving that on the front roller shaft. The latter is named the
front roller clutch bevel. By replacing these with 27 and 17
respectively, the range of twist obtainable when a 60speed
wheel is also employed, becomes —
4 38 X 35 X 60 X 12 X 6 ^ ( 1670 revolutions of twist per
^^ 1 17 X 27 X 17 X 12 X ^ ( draw
45 . .
. 50 . ,
, . 55 . .
, . 60
1250 . .
. . 1390 . .
, . 1530 . .
. 1670
195 . .
. 216 . .
. 238 . .
. 261
166 COTTON SPINNING CALCULATIONS
Thus : when the speed wheel is altered to 40 the twist per
draw becomes —
„„ 4 ^ 38 X 35 X 40 X 12 X 6 ...^
^' 17 X 27 X 17 X 12 X ^
Hence, the revolutions of the spindles per draw and the
twist per inch obtainable by using the various sizes of speed
wheels comprised in the range will be —
(Jg) Size of speed wheel . . 40
Revs, of spindle per draw 1112
Twist per inch .... 173
Assuming that, after the abovestated changes, the range in
the sizes of the speed change wheels exhausted, further altera
tion in the twist would only be practicable by changes in the
train of rope and band driving gear, from the rim shaft to
the spindles. Such would, at the same time, alter the speed
of the spindles as per paragraph (a). The changes in twist
obtainable with the range in sizes of rim pulleys available, as
specified, are —
Size of rim in inches
Twist per inch with the \ 40
appended speed wheels ) 60
Size of rim in inches
Twist per inch with the? 40 = 245
appended speed wheels i 60
Basis 64 inches = draw.
It is customary, also, to make the tin roller pulley in halves
in order to admit of its being changed : the range is from
10 inches to 12 inches. In the present instance the latter is in
use. Altering this would affect the twist and at the same time
the speed of the spindles in the inverse proportion.
(c) " Gain" Changes. — The back shaft, in pulling out the car
riage, is assumed to make a fixed movement. This is not exactly
the case, because this movement must be subject to variations
arising through differences in the tension of the ropes and
matters influencing the resistance to the movement of the
carriage. For the purpose of calculation it is convenient to
12
13
14
15
16
173
187
202
216
230
261
283
305
326
348
17
18
19
20
245
259
274
288
37
392
4L4
435
AND COSTS OF YAKN 167
make the assumption named. In the present instance, the
movement of the back shaft is taken at 3g revolutions per draw,
so that with the smallest gain boss (2527) and gain wheels
(97112), and with the rest of the connecting gear from the front
roller to the back shaft as specified, the length delivered by
the front roller during this movement would be —
S^ X '^^ = I "'•''' '^^ ^revolutions of the
^ 25 X 60 front roller per draw
and therefore 17'46 x 1 x ^ = 5487 inches delivered
With the following **gain" change wheels, the length
delivered by the front roller and the *' gain " would be : —
Gain wheel 97 98 99 100 101 102
Gain boss wheel 25 25 25 25 25 25
Inches delivered by rollers per draw 5i87 555 560 566 572 577
Gain in inches 913 85 80 7*4 68 63
Gain wheel 103 104 105 106 107 108 109
Gain boss wheel 25 25 25 25 25 25 25
Inches delivered by rollers per draw 583 588 594 600 60G GM 617
Gain in inches 57 52 4*6 40 34 29 23
Gain wheel 110 111 112 112 111 110
Gain boss wheel 25 25 25 26 26 26
Inches delivered by rollers per draw 623 628 634 609 603 598
Gain in inches 17 12 06 3*1 37 42
Gain wheel 109 ... 112 111 110 109 .. .
Gain boss wheel 26 ... 27 27 27 27 . . .
Inches deHvered by rollers per draw 593 . . . 587 582 577 571 . . .
Gain in inches 47 ... 53 58 63 69 ...
The changes in the length delivered by the front roller per
draw during the outward run of the carriage, is directly pro
portionate to the changes in the size of gain, and inversely in
respect of the gain boss, wheels.
Yarns highly twisted and of poor quality do not admit of the
carriage gaining on the rollers. In such, the rollers more fre
quently deliver at a rate in excess of that moved by the carriage.
This is sometimes as much as 10 per cent. In the production
of the best qualities of yarn, when fully twisted as the carriage
moves out, only a slight " gain " is practicable. *' Gain " is
168 COTTOK SPINNING CALCULATIONS
most applicable with low spindle speeds and when the yarns are
not fully twisted during the movement of the carriage.
Changes in the Builder Wheel. — The approximate size of suit
able builder wheel, may be ascertained as follows, when the size
of cop required is known : —
J = suitable builder wheel
dc
b = the length in inches of the yarn contained in the cop.
d = tJie length wound in inches per draw.
c = the revolutions of the copping screw necessary in
completing the cop.
h, is ascertained from the weight of the cop in grains,
divided by the weight of one hank in grains, and multiplied by
the inches per hank. Thus —
nettTveishtrf^cop in grains ^ g^^ ^ gg ^^
count
c, is ascertained by marking upon the spindle the length
which the cop measures, from the cop bottom to the bottom of
the chase; and then proceeding to turn the copping screw
sufficient to pass the winding faller wire through the movement
marked on the spindle, opposite. This must be done whilst the
carriage is at rest, with the trail lever bowl on the ridge of the
copping rail, and the revolutions of the screw counted.
Ascertaining the Suitable Builder Wheel in changing Counts. —
Changing the counts affect the weight of the cops in the inverse
proportions, and, assuming the tension of the yarn during
winding proportional to the area of the yarn, the diameter of
the cop would be affected in the inverse proportion to the
^/counts. Thus, the mode of calculating this wheel, in order to
obtain a cop of constant size, should be as follows : —
Present wheel X ^required count ^ ^^^^.^,^^ ^^^^^
^/present count
Note. — A difference in the size of the cop must alwaj's result when the yarn
is wound at other tension than inversely proportional to the difference in the area
AND COSTS OF YARN 169
of the yarn. Also, when (lie change alters the quality of the yarn in any way,
the difficulty of adjusting the tension in the correct order is such that the above
rule cannot be relied upon. The following rule will be found more reliable but
must not be regarded as accurate in all cases : — '
Required wheel = Pi'esent wh^Vrequire d^ount _^ present wheel x required count
2v'present count 2 x present count
Ascertaining the suitable builder wheel in changing the size of the cops
only — ^ '
Present wheel (diameter of requi red cop)2
(diameter of present cop)^
The following are exercises in calculating the alterations
necessary to adapt the gearing in Fig. 33 for the work given.
They are given in tabulated form because it is more convenient
Allow 10 per cent, for slippage in the driving of the spindles
from the rim shaft, and use the customary twist constants where
the twist is not given.
Explanation of the tahulated exerdscs.—llho^Q columns
numbered 1 to 16 are separate exercises. The data required
is signified by (?). Base the calculations for the builder wheel
on that given in Exercise 1. The items referred to in each
column are contained opposite in the first two columns on the
left hand.
170
COTTON SPINNING CALCULATIONS
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AND COSTS OF YARN
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172 COTTON SPINNING CALCULATIONS
Examples in Calculatixg the Exercises on Page 1701.
The following changes would be necessary to adapt the gear in Fig. 33 for
the conditions stated : —
ExEKCiSE 1. — To drive the spindles at 6000 revolutions per minute, actual,
with a 12inch rim:
The calculated rate of the spindles will = ^^^^on ^^^ = ^^^^ ^^^ •'' *^^^
Revolutions of Rim Shaft. — With the minimum and maximum sizes of driver
and driven change pulleys respectively (see par. (a), p. 163) —
Revolutions of the rim shaft per minute = ^^^^ ^ i^]l = 834
6 X 12
Speed and Twist Changes. — The front roller, if 1 inch in diameter, and there is
64" X 7
no gam, will be required to make — ^ — = 20i\ revolutions per draw. During
this movement the spindles are required to insert twist to the extent of
375 v'S = 106 per inch, or 375^8 x 64 (inches per draw) = 753, actual; and
therefore the calculated revolutions of the spindle per draw are ^^ = 837,
or S^j^ = 131 calculated twist per inch.
The train of gear connecting the spindle and the front roller (see pars, (a), (b),
pp. 1634) must therefore have the following value : ^ = ^^\^/^ = 411.
According to the range in the change wheels given in Fig. 33 the lowest
, .,,.,.. 60 x 12 X 40 X 35 X 38 ^^ „
value of this tram is ,r^r^ ^ ^r — ~ — = 202.
075 X 12 X 30 X 35 X 20
Hence, altering the value of any of the wheels contained in this train, to
increase their ratio 20*2 to 411, will have the effect desired. Namely, changing
the twist to 13*1 calculated.
(driven)
40 . 40 411
Therefore the wheels 7.^ = 13 must be altered in value to oq x oKTo
(driver)
 "= '  20
Therefore the required wheel on rim shaft = 20, and the speed wheel = 54.
For "Gain" Wheel, see pp. 1667.
The Draft required in the rollers is that necessary to attenuate 11' to
8 16
8' count, or y^ = o = 5. By assuming the draft change pinion necessary,
Ig o
X, the following equation is obtained : —
54 130 1 Ki 54 130
^ X 16 X I = ^ ••• ^ = 51 >< T6
The range of sizes of draft pinion wheels that can be accommodated is,
approximately, from 30 to 60, and on the back roller from 40 to 60. The wheel
AND COSTS OF YARN 173
82 is, therefore, too large, and hence it is necessarj' to reduce the size to within
driver 82
the ransre of accommodation. The ratio of these two wheels is r— = i^,
° driven 54
or 152.
Hence, any of the following pairs of wheels would be suitable for the
47 56 59
position: 31, 3. 3C,
Exercise 6. — In this instance the length of yarn to be wound each draw
is 64 + 4 inches, and hence the twist inserted must be in accordance therewith.
Twist per inch required in the yarn wound = ^^24 x 375 = 184
/. Twist per draw = 68 inches x 18'4 = 1250
According to par. (^3), p. 163, the gear should be — tracing the train from the rim
shaft to the F.R. : 17 driving 45, 27 driving 35, 17 driving 38 = 1250 revolutions
of rim per draw; and therefore ^p = 18*4 twist per inch, this being with a
12inch rim pulley and at the rate of 7520 revolutions of the spindle per minute.
The Size of Eim. — The rate of the spindle required is 9500 revolutions per
minute, actual; hence, with the rim shaft making 940 revolutions per minute,
and the size of the rim x, and 10 per cent, allowed for slippage, the following
equation is obtained : —
940 X a; X 6 9500 x 100 .^...
= 10555
12 X I ~ 90
10555 X 12 X I i^o, .„ . ,
.'. X = pTfT. 75 — ~ = 16*85, say 17 inches
940 X 6 ' ^
The revolutions of the spindles per draw, actual = 1250
Allowing for slippage, the calculated revolutions of spindle per draw = 1390
Proof that the above is satisfactory : —
The Speed Train of Wheels. — The train connecting the rollers with the spindles
1390
must therefore have a value of ^tt^ = 683.
This means that the spindle must be calculated to move 68*3 revolutions
per 1 of the F.E., and hence the following equation, when the speed wheel has
the value x : —
683 X f X 12 X 17 X 27 X 17 _ . _ „.
6 X 17 X a; X 35 X 38 ~ . . x  60 i
Alternative sizes of suitable wheels : —
The smallest speed wheel practicable being 40 (4060), and the ratio required
17
between this and the wheel on the speed shaft being ^^, the follo'W'ing other
wheels, within the range of accommodation, will give, approximately, the desired
, 23 24 25 26 wheel on rim shaft
results: ^g, ^, ^, g^, gpeed wheel "
The draft required in the rollers is that necessary to attenuate 3' roving
174 COTTON SPINNING CALCULATIONS
into 24' = g^ = 8. B} assuming x tlie draft claange pinion, the following
equation is obtained : —
54 X 130 X 1 Q . 54 X 130 ^. ^. ., _. , ^
^ . =8 :.x ^ ^ = 55, Draft pinion
a;xl6xl 8x16
12 X a/24 12 X 24
Builder Avlieel = ^ y + . t = 104 + 18 = say 28
2 »/ 8 / X o
Exercise 7. — The draft for 28' W, from 3' single roving = ^^ = 9J.
Assuming x the draft change pinion, and 54 the B.E.W., the following equation
is obtained : —
54 X 130 X 1 oi . 54 3 X 130 .^ t^ .. • •
. X 16 X 1 =^^ • • ^ = 28 >^ 16 = ^^' ^''^' P^"^°^
The size of rim necessary to obtain the rate of rotation of the spindles,
10,500 + 10 per cent, for loss, may be obtained from the following equation, when
X = the size of the rim in inches : —
„., X 6 10500x100 ...Q^
940 X Y^ X ^ = OQ = 11680
940 X 6 1
11680 X 12 X f ~ a;
11680 X 12 X ? X io ^K in • 1 T> ,
.". TTTK T. — ~ = T = 1865, say 19 inches, Eim
940 X 6 1 ' •'
The twist per inch = ^Wx 325 = 172
Therefore the twist per draw (68 inches) = 17*2 x 68 inches = 1170
Assuming the front roller makes 20y*j revolutions per draw, and the speed
wheel contains x teeth, the following equation contains the value of x, allowing
10 per cent, for slippage : —
4 38 X 35 X x X 19 X 6 _ 1170 x 100 _
^^11 ^ 20 X 35 X 30 X 12 x § ~ 90
1300 X 20 X 35 X 30 X 12 X f x „nr, ^ i i. i
•*• — oTs^i q5 OK iQ ?^ = T = 79*7, Speed wheel
20y\ X 38 X 35 X 19 X 6 1 ^
This wheel being too large, a pair of wheels of suitable size may be obtained
from the ratio provided by these change wheels, therefore —
driver 30 20
or 7077' say xq
driven' " 797' '' 53
The gain wheels necessary to give 3 inches " gain " are —
75 64 — 3
3 X TTp; X X = — —, — revolutions of the front roller = 19 4
"^ bO ^
here x = the value of the ^^ , change wheels
driver
• ^^ 75 ,Q, . 60 X 194 . „,
• • 3 X ^,. X a; = 194 .•. x = ^^ ^r^ = 431
60 3*6 X 75
AND COSTS OF YARN 175
Any pair of wlieels witliin the range of size applicable and having this ratio
would suffice.
.. 4:31 = say 26
These would give the nearest to that required.
The builder wheel = ^^ ^ ^^^ + ^^^^ x ^' "" ^" = 208, say 21.
Note. — The differences in the size of the cop required \vill affect the wheel
directly proportional to their areas, and therefore as their diameters^ (squared).
Exercise 13. — The draft required to attenuate the 13hank roving, double,
to 80 = ^^^ = 123.
The ratio of the draft change wheels, x, is found as follows : —
10 Q 130 . 123 X IG . ...
123 = j^xx .. — ^3Q = X = 15U
„ ,. driven B.R.W. 59 56 53
Katio = J. — or — r^ — = ^^, or ^^, or ^7^
driver pinion 39' 37' 35
The revolutions of the rim shaft per draw —
Twist per inch = 3*6^80 = 32*2
„ draw = 322 x 68 = 2189
The size of rim, a;, allowing for 10 per cent, for slippage —
.„ X ^6 9000 x 100 10000 x 12 x  ^,^„
= ^^0Xj2X=— yo— ^ 750 X 6 ^Q
The speed change wheels ratio, x, assuming no pause twisting at the head,
and the gain 4 inches ; is found as follows : —
2189x100^1x12 27x17 604 .„ ^ , , , „ ,
X I ^ XXX o^ — 5^ = — i7^r— = 178 revs, of h .R, per draw
90 6 X 20 35 X 38 ^f
_ 178 X 90 X 6 X 20 X 35 X 38
* ~ 2189 X 100 X 075 x 12 x 27 x 17
= 0283
Therefore the only possible wheels within the ranges specified in Fig. 33
60
arej^.
Gain. — The revolutions of the back shaft and front roller required per draw
respectively, being 3*38 and 178, the following equation gives the value of x,
the gain change wheel ratio : —
9QQ 75 ,_ . 178x60 .„,
338 X g^ X a: = 178 •*•«= = 338 x 75 = ^^1
176 COTTON SPINNING CALCULATIONS
The pair of wheels within the range specified having the nearest to this
105 gain
ratio are tf, — . — ^^ r — 1«
15 gain boss wheel
The builder wheel = 1^^ + "^^ x ^^^ 57
2V8 2x8 my
100 X 2
Exercise 16. — The draft required in the rollers = — ^n — = ^^•
The draft change wheels ratio, x, must be —
V^," X :c = 10
_ 10 X 16 _ 160
•'• ^ ~ 130 130
= V2[
Therefore the suitable draft wheels are —
B.B.W . ^ 48 53 54
P.W. ~ 39' 43' 44
The twist per inch required = 3*18^100
draw „ = 64 X 318^100 = 2035
Allowing for 10 per cent, loss, the calculated revolutions of the spindles per
. . 2035 X 10 ,„oo
draw required = „ = ^zdS.
The actual revolutions per minute of the spindles required = 8000
^ , 8000 X 10
.*. „ calculated „ „ „ — g
With the size of rim required 570 x ;r7, x g
X 10 X I in.r
••"= 570x6 " = 195 say
The revolutions of the front roller per draw required = — ^ — = 17*8
^ r ca ■ X. a 1 ^888 X 10 X  ,,„
The revolutions of the rim shaft per draw = ^^ — ^— ^ = 143
The speed change wheels ratio, x, is therefore —
178 X ^"^ X 3^ X a;  143 x ^^^ ^il^^^  1755
17 8 X ^^ X g^ X a;  14d x ^^.^ x 60 x 35 " ^ '^^
Therefore any of the following pairs of wheels would be suitable : —
speed wheel _ 42 44 49 51
rimlhaft wheel ~ 24' 25' 28' 29
AND COSTS OF YARN
177
Gain.— The revolutions of the back sliaft and front roller reiiuired per draw,
respectively, being 338 and 178, the following equation gives the value of x
the gain change wheels ratio : —
338 X /.iJ X cc = 178
X = 421
And hence the following pair of these wheels are most suitable —
105 _ gain wheel
15 gain boss wheel
+
rr, 1 n 11 12V100 , 12x100
The builder wheel —
2V8
X ^'^^"l  47
2x8 (\if ~
Particulars of Gearing in *' Dobson's Ord." Mule.— Fig. 34 shows
Fig. 34.
the arrangement of the gearing in mules for medium and
medium fine counts as made by Dobson and Barlow.
The following are particulars of the various trains and the
range in the size of the wheels shown : —
N
178 COTTON SPINNING CALCULATIONS
(rt) Train to Sjnndles. — Revolutions of the rim shaft (H G)
per minute from 400 to 850 per minute. Eim pulley, D, 12
22 inches ; tin roller pulley, D3, 1012 inches ; tin roller, U,
6 inches ; spindle wharves, vi, 34 inches.
(h) Train to the Rollers.— J, 19 ; K, 58 ; L, 3056 ; C, 60
100 ; R, 32 ; S, 25.
(c) Roller draft gear : 7c, 20 ; Z, 180 ; A, 3060 ; m, 3070.
Diameters of rollers : front, 1 inch ; middle,  inch ; back,
1 inch,
{(1) Train to the Bach Shaft from the Front Boiler Shaft. — T,
5155; 0, 55; E, 7078; P, 1620; Q, 68; M, 15: N, 55.
Revolutions of the back shaft per draw : 3*5 for 64inch
draw ; 3*28 for 60inch draw ; 3*06 for 56inch draw.
(e) Train for Slow Boiler Turning, sometimes called the
Eeceding Motion.— JJ, 20; V, 40; W, 1 ; X, 30; Y, 24; Z, 24.
Train for Holler Delivery during the Inward Run. — i,
1417 ;i, 40.
Takingin and Bachingoff Motion Gear. — a, 14 inches ; c, 17 ;
/, 24 ; (7, 14 ; h, 40 ; c, 10 ; d, 73.
Takingin motion shaft, a : 170350 per minute.
Revolutions of takingin motion shaft (/ per 64inch draw, 3.
Building or Shaper Motion. — Wheel, 1270, and various
pitch of screws.
Twist Wheel— ^0120.
ExEKciSES. — Ascertain the following, from the particulars contained in
Fig. 34 :—
1. The range in the rates per minute at which the spinrlles may be driven.
2. The range in the twist that may be inserted in the yarn.
3. The range in the draft.
4. The range in the counts, twist and weft, which the machine is adapted for
in the respect of twisting with the normal twist constants.
5. The ratio in the movement of the carriage before and under the influence
of the jacking motion, assuming that during the former movement the drawing
out band is on the fullsized portion of the scroll ; and at the termination of the
latter movement, on the halfsized portion of that part.
6. The ratio of the roller and carriage movements during twisting at the
head and when in ordinary action.
7. The ratio in the rates of the spindles during spinning and Avhen backingoff.
8. The time, in seconds, taken to move the carriagein, at the slowest and
quickest rates.
9. The length, in inches, delivered by the rollers during the inward run.
AND COSTS OF YAEN 179
Answers —
1. 320014,960.
2. 7'28445.
3. 4521.
4. 40^ twist, 5''25 weft to 210' weft, 152" twist.
In the above calculation, the calculated twist is as obtained without the use
of twist wheels. By using twist wheels, the twist may be extended to suffice for
all practical rctiuirements, taking the above as representing f of the possible
twist then the range could be extended to 78'4 turns per inch.
Example in respect of Exercise 5. — The difference in the train pulling out
the carnage during jacking : R, S, being in abeyance, and the motion is obtained
through M. N.
The train prior to jacking, from the side shaft, is E, S, T, 0, E, P, Q ; and
during jacking M, N, 0, E, P, Q.
mu Acv • ., 1 32 55 16 , 15 55 16 32 ,
The difference m these values are ' i^i n7\< fs ^^^^^ rE> ^n^ po> or, ^ > and
15
^ respectively, or 3'5 : 1.
This is the ratio, when jacking is proceeding, with the drawingout band
wound upon the fullsized portion of the scroll. As the scroll portion is gradu
ally brought into action this ratio increases. When the halfsize portion is acting,
the reduction in the rate of the movement has attained 3*5 x 2 = 1, of the
normal rate.
Exam2)le in respect of Exercise 6. — The difference in the trains driving the
rollers whilst the carriage is at rest, and twisting " at the head," is as follows : —
The wheel train RS is in abeyance, and motion is obtained through train
U, V, W, X, Y, Z, and therefore—
32 20 1 24
The values of these trains are respectively .^Z and jr., ^, ^, or as 77 : 1.
Example in respect of Exercise 7. — The difference in driving the spindles
during spinning and " backingoff " are respectively —
Lowest rate of the rim shaft during spinning, 400
.„ 170 X 10
" backingoff,'
73
and therefore the rate of the spindle during the latter period is z.rf7. ^j^ times
less than during the former period = slightly more than ■^.
Example in respect of Exercise 8. — Assuming the takingin scroll shaft makes
3 revolutions per draw of 62 inches, the time in seconds taken to draw the
carriage in, is —
3
lowest rate .„^ ,^^ ^ x 60 = 4'27 seconds
170 X \'i xji
or, average rate, 14^ inches per second.
180 COTTON SPINNING CALCULATIONS
Example in respect of Exercise 9. — Assuming the back shaft makes 3*39
revolutions during the drawing in of the carriage and the 17 wheel is in use on
the back shaft, the length delivered, equals —
17 1" X 22
339 X 77. X = — = 452 inches
Exercises. — Ascertain the production in hanks per 55 hours, without
allowances for stoppages ; and the various change wheels necessary to adapt the
gearing, as contained in Fig. 34, for the undermentioned counts and conditions
of production.
Allowances : For slippage, in driving the spindles from the rim shaft, 10 per
cent. ; draw, 60 + 4^ inches, the latter delivered during the inward run ; backing
ofif and runin to occupy 5 seconds ; loss of speed due to changes, 10 per cent.
1. GO W. from 10hank double roving, Egvptian : actual speeds of rim and
spindles, 850 and 10,000 revolutions per minute ; gain, 1 inch ; jacking, 1 inch ;
5 per cent, of twist being inserted after jacking.
2. 60 T. from 12hank double roving, Egyptian : rim and spindle speeds, 840
and 10,000 revolutions per minute actual ; gain, U inch ; jacking, 1 inch ; 12 per
cent, of twisting after jacking.
3. 80 W. from 14hank double roving, Egyptian : rim and spindle speeds,
840 and 9000 revolutions per minute actual ; gain, 2 inches ; jacking, 1 } inch ;
8 per cent, of twisting after jacking.
4. 80 T. from 16hank double roving, Egyptian : rim and spindle speeds,
840 and 9500 revolutions per minute actual ; gain, 2 inches ; jacking, 2 inclies ;
12 per cent, of twisting after jacking.
5. 94 W. from 16hank double roving, Egyptian : rim and spindle speeds,
840 and 8700 revolutions per minute actual ; gain, 2 inches ; jacking, 2 inches ;
10 per cent, of twisting after jacking.
6. 90 T. from 16hank double roving, Egyptian: rim and spindle speeds,
840 and 8700 revolutions per minute actual ; gain, 1 inch ; jacking, 2^ inches ;
12^ per cent, of twistmg after jacking.
Example of working Exercise 1. — The spindle speed will be attained by
using a rim and tin roller pulleys of the following diameter : —
Let X = the spindle speed change ratio ;
then 860 X . X « = ^^^ .: . = ^m = 1634
.'. 18 inches R.P. and 11 inches T.E.P. or, others giving this ratio.
The revolutions of the rim shaft per draw must be —
GO h 4i X 318 /6U _ . ,
18 "6 Tiu ^^^
II ^ V ^ 100
AND COSTS OF YARN 181
The speed change gear must be arranged to obtain the delivery of 60  2 inches
3*28 X 59
whilst the back shaft is moving the carriage out 59 inches, and therefore the — gQ —
revolutions of the back shaft are required in the same period. During this move
ment the spindles are required to insert twist in accordance with the state
specified, i.e. 100 per cent. — 5 per cent. — x per cent, twisting during jacking.
During "jacking " the carriage is assumed to move at f the normal rate, and there
fore requires a period equal to that required to move the carriage 3^ inches at the
latter rate. Hence, 95 per cent, of the twisting equals the period required for
59 + 31 inches of movement at the normal rate, and therefore the revolutions of
the rim, during the above 59 inches, must be —
roi = 8^1 P^^ cent, of 135 = 120 revolutions of rim
During the run out of the carriage, the front roller is required to deliver
58 inches, and therefore it must make —
58
1 X T
= 18'43 revolutions
The speed change gear ratio {x) is therefore —
120 X \% XXX ^ = 1843 .. X = ^fon^f \^^ = 0366
^*' ■> 120 X 19 X d2
The speed change wheels, within the range having this value, are —
driver 34 _35 36 37 38 39 40
driven lOr 104' 107' 110' 113' 116' 119
328 X 59
TJie "gain" change gear must be arranged to impart „^ — revolutions
to the back shaft per 1843 revolutions of the front roller, before jacking
commences. Therefore the gain change wheel ratio (x) must be —
,„ ,„ 55 328x59 328x59x68 .....
1843 X .T5 x a; = ^,7:^ /. x = ^~r^ ^^ — ^  0216
68 60 1243 X 60 X 55
The change wheels nearest to this value are —
driver 16 ^
driven 74
TJie draft and draft change wheels, — A 10hank double rove would necessitate
a draft of ^^ = 12, if the draft due to gain and jacking is neglected.
Taking the latter into account, it would l)e —
12x621 ^..
182 COTTON SPINNING CALCULATIONS
The draft change wheel ratio (x) to give tlie latter draft must be —
L8^ xx= 116 .. X = ^^^^^ = 129
The draft change wheels, within the range specified, containing this value
driven _ 62 58 53 49
driver " 48' 45' 41' 38
Twist wlieeJs are necessary when the rim shaft is required to rotate a
definite amount after the carriage has reached the " head." Usually it is
most convenient to arrange them to make one or two revolutions per draw,
and therefore, in this instance, since 135 is not available, ip, say G8.
rr 1 135 60 X 100 ^ ,^,, , ,,,,
Time per draw = gjQ x — ^^ — + 5 = 1015+5 = 1515 sees.
TT 1 • ;ii 1 60 X 60 X 55 X 64^ „„ „
Hanks per spmdle per week = — tttk o^ ottt^ = 27*8
il515 X 36 X 840
Examj)Ie of working Exercise 6. — The required speed of spindle will be
obtained when the change pulleys in the gear from the rim to the spindles have
the ratio x in the following equation : —
.*. a = 144
.'. ratio = rp p p = 11 nearest
Tlierefore the revolutions of the rim per draw, if the latter are adopted—
 CO + 4^ X 36 X V90 X 100 _ ^.„
16 w~: — "^^^
zy X ij X 90
Note. — The ^^ is the slippage.
The speed change gear must be arranged to obtain the delivery of 60 — 3^ inches
whilst the carriage moves 57^ inches outward, and therefore the back shaft makes
328 X 57V' '.
pjTT — ^ = 314 reA'olutions during this roller movement. The spindles
are required to insert twist amounting to the following, in the same period,
210 X 87i X 57
and hence zrj~ ~ revolutions of rim per draw = 159.
100 X 6b ^
573 .
^pf is the fraction of 87J per cent, of 210 revolutions, during which time the
carriage and rollers are moving at the normal rate. This is ascertained from the
rate of jacking proceeding at ^ slower than the normal rate, the jacking rate
being from 05; to i the normal depending upon the extent of the scrolled portion
of the drawingout barrels, on the back shaft, in action,
AND COSTS OF YARN 183
The front roller is therefore required to make ~, —   revolutions prior to
1 X f ^
jacking, and whilst the rim shaft makes 159 revolutions, and hence the speed
change wheels ratio, x, is contained in the following equation :—
159 X >^ X a; X „^ =  — i., = 18
58 2o 1 X J^
. _ 18 X 58 X 25 _ .
" ^ 159 X 19 X 32 " '"
The speed change wheels nearest to this value are ,??r '^^^.
111 driven
The 111 wheel is beyond the range stated on the figure, but in this case 110
would probably suffice ; if not, it would then be necessary to make an alteration
in some other wheel of this train. For values lower than 027, the most con
venient alteration is R.
The " Gain " Chainje Wheels must be arranged to give 314 revolutions to the
back shaft whilst the rollers make 18 ; therefore the gain change wheels ratio,
X, must be —
18 X tg X cc = 314 /. X = ^^^ = 0216
The " gain " change wheels having this ratio and within the ranges specified
10
are:^^.
The Draft and Draft Change Wheels.— A IGhank double rove will necessi
90
a draft of ^^ = 11], if allowance
Allowing for the latter, it would be —
90
tate a draft of ^ = 11], if allowance is not made for "gaining" and jacking
Hi X g^^j = 10G^
*2
The draft change wheel ratio, x, is contained in the equation —
^A xx = 1063 .. X = 118
Therefore the draft change wheels suitable are —
driven _ 53 59 65 66
driver ~ 45' 50' 55' 56
The time per draw in seconds =  !^ ^ ? ^ l^i^ + 5 = 217
840 X 1 X 90
The hanks per spindle per week = ^A^^^'^P^ = 195
217 X 36 X 840
Mule Calculations. — Figs. 36 and 37 show the gearing as in Piatt's mules.
The following examples are taken from those figures.
Motor drum, 800 revolutions and 11 inches diameter. Line shaft drum driven
from the motor, 38 inches diameter ; for driving the mule, 28 inches. Counter
shaft drums : driven, 18 ; driver, 24 ; grooved pulley for Tup motion, 12 inches.
184 COTTON SPINNING CALCULATIONS
The revolutions of back shaft for G2iinch draw = 3i
„ „ „ 60 „ = 365
„ „ „ 58^ „ = 356
Alterations for counts 100' from double 18 hank Sea Islands JRove, assuming
the present speed of spindle suitable.
The present speed of spindle
o^„ 11 X 28 X 24 X 16 X 6 p.,Q„ _ , ,. . ,
= 800 X jTTs Tn tt; T^ Q = 6287 "7 revolutions per mmute
38 X 18 X 16 X 11 X f ^
Twist constant = 36
,, per inch = 36
Twist per draw of 62" put up, i.e. 58V' + 3i" = 62" x ^m x 36 = 2232
The revolutions of the rim must be such as will give 2232 revolutions of spindle
per draw.
Assuming a loss of 5 per cent, in transmitting the motion to the spindle
from the rim shaft, then the revolutions of the rim shaft per draw should
be—
2232 X 100 X 11 X 075 ^.^
TT^ — . ^^ = say 202
95 X 10 X b ''
The duty of the twist wheel is to control the revolutions per draw of the rim
shaft. In this case the twist wheel divided by 2 equals the revolutions of the rim
shaft.
.. 2A2 = twist wheel = 101
If there were no gain between the movement of the caftiage as compared
with the length delivered by the front roller, then the rollers must deliver, during
the outward run of the carriage, 58^ inches, and therefore the front roller must
make —
^„ ^,, = 17518 revolutions, say 1752
The present gear would deliver —
202 X ,^ 7^ oTs = 303 revolutions of front roller instead of 1752
70 X 60 X 30
Therefore if the change be made at the speed wheel, a — TnTKr, — = 10^ wheel
would be necessary.
Such a large wheel would probably be impracticable. Usually the driver of
the speed wheel is constituted a change wheel, in which case the extent of the
dilTerence in the change practicable, in the speed wheel, and that required, would
be possible at the driver Avheel.
Assuming that up to 90 are the available sizes of speed wheels, then the
speed wheel driver would need to contain—
^^ = 62 teeth
104
AND COSTS OF YAEN 185
N.B, — III such a case it would be unnecessary to use the twist wheel, as the
fact of the carriage getting out to the head would control the revolutions of the
rim, but less accurately.
No Gain. — The gain wheel and its train controls the ratio in the movement
of the carriage relative to the spindle. The rollers must necessarily deliver 58}
inches, and the carriage must move that amount.
The movement of the back shaft in drawing the carriage out G2?,inch draw
is given at 3* revolutions. Therefore, for 58^inch, proportional movement
34 ^ 531
\vill be required, or — t.^, —  = 356, instead of 38.
0<iTy
Should this be the case, then the front roller must make ^^ — ^— ; revolu
IB ^ 7
tions, whilst the back shaft makes 356 revolutions ; therefore the revolutions of
the front roller = 1752.
Note.— Variations in the tension and size of drawingout bands will cause
variations in the revolutions of the back shaft per draw.
With the present gear the revolutions of the front roller per 3*56 revolutions
of the back shaft, are (see p. 192) —
35G =
/ revolutions of F.R. x 20 \ / revolutions of F.R. x 40 ^
V 2 X 60 j "^ I 2 X 40 y
(revolutions of F.R. . revolutions of F.R.\ „/. .k
__ + 3G X 45
.. ^u^  ^ 2 /
60 X 90
/revolutions of F.R. 3 revolutions of F.R.\ G
•■• 3^« = \ 6 + 6 J20
• a KR _ '^^ 6 _ 4a3 _ a;
..dob_g X2Q205
.. 356 X 5 = a;
.. X = 1780 revolutions of F.R.
The gain wheel must therefore be altered to give 17*52 revolutions, and
therefore —
356 =
/ 1752 X 2^\ /1752 x 40\
V 2 x 60 / V 2 X 40 }
60 G.W.
36 ^ 45
/1752 , 1752\_ ,,
(^g + 2J36x45
356
60 X G.W.
186
COTTON SPINNING CALCULATIONS
/17;52
Sx 1752^
6 \
36 X 45
GU X (i.W
. „ _ 7008 3G 45
..6bb ^ Xg^x^^^,^
1
356 X 6 X G O
7008 X 3G X 45 ~ G.W.
7008 X 3G X 45 G.W.
356 X G X GO
1
700 8 X 9
^56^>r2
.. G.W. = :^v~ = 885, say 80 or 88
" " Gain " CImnges. — The 36 gain boss wheel combined with an 88*5, gives,
according to previous calculations, a delivery by front roller of 585 inches,
Taking this as a basis, the amount, in inches, delivered by the front roller per
356 revolutions of the back shaft, with various other sizes of gain wheels, is as
follows : —
Gain boss
wheel.
36
36
36
36
36
36
36
36
36
35
34
37
36
Gain wheel.
88
87
86
85
89
90
91
92
90
90
90
90
91
58J X
885
88
585 X
885
87
585 X
885
86
585 X
88 5
85
585 X
885
89
585 X
885
90
585 X
885
91
585 X
885
92
585 X
885
90
5752 X 36
85
57*52 X 36
34
.5752 X 36
37
5689
58 83
595
602
609
5817
5752
5689
5626
5752
5916
G09
559
Variations in count
resulting.
995
984
972
960
1005
1016
102S
1040
101G
990
960
1046
1028
AND COSTS OF YARN
187
Gain boss
wheel.
Gain wheel.
Variations in count
resulting.
35
91
"'=■«!.>'''= 58 31
1005
34
91
''■'I'' "" = 6002
972
37
01
5689 X 36 „ „.
_ oo3o
10.. 8
36
89
5817  02S ("gain)
1006
35
89
5983 + 133 „
978
34
89
6132 + 282 „
954
37
89
566  19
1033
36
88
5883 + 033 „
994
35
88
0051 + 101 „
907
37
88
5724  126 „
1020
The effect of gain on the counts of the yarn spun (see righthand cohimn).
The EoUer Draft Wheel. — The draft necessary to attenuate two ends of 18'
rove, so that it is delivered by the F.R. 100' count, must be —
l^'lUorXon
jLa ~" '•" 'J
The ratio in the surface movements of the front and back rollers respectively,
must therefore be 100 : 9. With the diameters of those two parts alike, and the
draft wheels as given, then the pinion wheel (x) would need to be —
lOOo;
9
54^ 140
X 16
100 54 X 140
54 X 140 X 9 ,.T .
•• 100x16 =«' = ^25
Hence, the wheel used must either be 42 or 43 ; the count in these instances
would be 101"1 or 988. If the exact count was required, it would be necessary
to employ a pair of wheels having a ratio of 7875 : 10,000,
Draft Wheels. — Other pairs of wheels, giving a close approximate to ^p^J*^,
are —
B.R.W. = 80
75
70
GG
61
56
52
47
Pinion = 63
59
55
52
48
44
41
37
■Count = 1000
1001
1002
9995
1000
1002
99 88
1000
Exercise 1. — Assuming the spindle speed 6287 revolutions per minute is too
slow, and that it is required to be 7073, what changes would be necessary ? —
(1) To obtain the desired spindle speed.
The readiest way is by increasing the size of the rim —
16 X 7073 ,Q . , .
~ 6287 — ~ lomch rira
188 COTTON SPINNING CALCULATIONS
(2) To obtain the riglit speed of the carriage and rollers relative to the
spindles, it will be necessary to change the speed wheel.
Speed Wheel. — If 90 x 52 constitute the driven and driver, change wheels,
the speeding of the spindles means that twisting takes place quicker, and there
fore the rollers must be made to deliver quicker in like proportion.
. 90 X 16 _ 720 .. , , ,
. . — .r. — = q = oO speed wheel
The rate of the production would be the time taken to twist G2 inches of
yarn, after allowing 5 per cent, for loss in transmission, with the spindle making
6287 revolutions per minute.
rp, ,. . , , 1 , , ., 22x32x100x60 „„ ,,o
Ihe time in seconds taken to twist = ^ ^ ^= — =22418
95 X 6 X 287
The time in seconds taken to backingoif and run in = 45
Time per draw = 26918
The production after changing, i.e. revolutions of spindles to 7074 instead
of 6287—
rr + • ,• 22418 X 16 ,„„^»
Time twisting = ^^ = 19 927 sees.
Time twisting backingoff and run in = 4*5
Total time = 24427
Production in hanks per week of 55 hours, in case of 18inch rim —
60 X 60 X 55 X 62" ....,, . n
24427 X 36 X 840 = ^^'^^ ^^''^"^^ P'^' ^P"^*^^'
Production in case of 16inch rim : when the rate of spindle in revolutions
per minute with 18inch rim is —
800 . "JlfS? 24 X 18 X 6 ^,„„
38 X 18 X 16 X 11 X I
and —
60 X 60 X 55 X 62" _ ( production in hanks with 16inch rim on
26918 X 36~>r840 \ and spindle revolving 6287
= 1508
Exercise 2. — A mule making 50' T. has the following change wheels :
Draft pinion, 40; rim, 18 inches; speed, 80; builder, 50. What changes in
these would alter the counts to 36' with —
(a) The speed of spindles unaltered ?
(6) „ „ increased \ ?
Answers —
(a) (b)
Draft pinion 56 56
Speed 68 58
Eim — 21
Builder 1 47 47
' Rule given on p. 1G8 is here used.
AND COSTS OF YARN 189
ExiiRCisE 3. — x\. imile containing 1000 spindles and spinning 48', the draw
being 62 + 4 inches, and 1100 draws are made in forming a set of cops. Find
the weight of the set of cops, allowing 2 per cent, for breakages. A)is. 48 8 lbs.
Exercise 4. — The carriage in a mule, producing 46' W., is known to move
G per cent, slower than the front roller, single 6hank rove being used. Find
the draft required in the rollers. Ans. 8'17.
Exercise 5. — A mule completes 5 draws of 64 + 4 inches each in 68 seconds
when spinning 40' T. The time occupied in backingoff and winding is 4 seconds.
Wliat will be the calculated and maximum actual rate of revolutions of the
spindles, assuming the slippage and loss of time, due to reversing, is known
to be 25 per cent. ? Take the twist standard for American cotton.
Answer,
TV 1 68  (5 X 4i) 46?
Time per draw — ^ ^ = ■*
o
= 9"35 seconds
Twist and actual revolutions of spindle per draw = 375,v/40x68 = 1612
Calculated revolutions of the spindle per draw = 3*75v'40 x 68 x ^fP = 2150
Actual maximum rate of revolutions of spindle "» _ 375^40 x 68 x 60
per minute / 9^35 ~ 10620
Calculated rate of revolutions of spindle perj _ 10620 x 100 _ .,070^
minute / 75 ~ lo70
Exercise 6. — What would be the production in hanks and pounds, per week
of 55^ hours, per spindle, and per mule of 1200 spindles, when the following
allowances are made: 8 minutes per doff; 9^ hours for cleaning; 2h per
cent, for other stoppages, the cops weighing at the rate of 10 per pound ?
Eequired : the twist per inch minus time per draw, and the production in
hanks and ounces per spindle, per 55^ hours, in a mule making cops that weigh
10 per pound, and working under the following conditions : Nett time worked,
53 hours ; allow 2h per cent, for breakages ; for doffing, 8 minutes per dofif ;
counts, 120' W. from combed special Egyptian cotton, (twist constant, 318).
Spindles working at two rates of speed — first, 5880, and second, 9000 revolutions
per minute. Fiveeighths of the twist only is put in at first speed. The backingoff
and run in occupies 5 secoads, and the length of the draw is 58i + 3 inches.
Answer —
Twist per inch = 318^120
Twist per draw = 318^120 x 62 = 2160
,,,. , . T 2160 X 5 X 60 2160 x 3 x 60 . ^,
Imie per draw m seconds ^ ^^^^^^^ sees, f ^^^^^ ^ ^^ ^ + 5h
= 138 + 54 + bh = 247
1 ^ 120 X 840 X 36
10 ^ 62 —
190
COTTOX SPIXXIXG CALCULATIONS
Time per doff, including dufBng, \ _ 1 120 x 840 x 36 247
/ " ro ^ 62 ~
m minutes
60 X 60 "^ 60 ^""^'
= 402 + 0133
53 X 60 X
Doff per week =
971
100
10 120 X 840 X 36 x 24 7
16 62 x'60 X 60
= 122
Weight per week in ounces = 122 x \% = 195
Hanks per week = ittt x   = 1462
lb 1
Dobson Double Speed and Hastening Motion. — Fig. 35 shows the
arrangement in Dobson and Barlow's fine mules for driving the
spindles at two speeds.
A and B are drums of different size on the line shaft ; these
are connected to the counter shaft by belts under control of
Line Shaft
Counte
Taking in
Motion Shaft
Fig. 35.
forks attached to the same bar. The stop rod, operating the
straps, is notched to occupy the three positions as follows —
(1) Machine stopped; (2) first speed, B strap driving;
(3) second speed, A strap driving.
This rod is operated in its second and third movements by
the movement outward and inward of the carriage. The speed
may be changed from the second to the third at any point in the
outward run of the carriage, by adjustments.
AND COSTS OP YARN
191
The special counter shaft has provision for driving the
talangin motion shaft and also for driving the rim ""shaft.
The former has been introduced to displace the friction clutch,
driving the takingin movement, with the view to obtaining
smoother action. The latter is for driving the rim shaft at the
closing stages of each draw, and to secure more reliable move
Back Shaft
Peg release" '
wheel for
strap dis
engagement
Front
Roller
Click
escapement
Clutches
Speed
change wheels
20 iTwist
I— flpwheel
^"•ix,
I25 nrrH
Back Shaft
Scroll
36
Change wheels
''^Tor'gain
B.R.W.
1401 20
90 i ,
60 1401 
[4^
30
F.R. Clutch
40
16/
^20
^^2
Tin roller
shaft
Fig. 36.
^
ment of the spindles during that period and extending durin.^
the unlocking of the fallers, thereby controlling the coils wound
upon the bare spindle. This latter action is that commonly
attributed to motions described as " hastening motions."
Piatt Bros. Jacking Motion.— Figs. 36 and °37 show a plan of
192
COTTON SPINNING CALCULATIONS
60
Gain Wheel 
•Back Shaft
that motion. m{60  40) and a (40  34) are compound wheels
loose on the s^Dindle NX, and they are driven from M and A on
the front roller. M is loose
on the front roller spindle,
whilst A is fastened to it.
Movement of NX is therefore
obtained from A and M, one
half being expended in turning
the wheels with 27 teeth, upon
their axes, and causing them
to roll upon the two 34. Thus
onehalf of any motion con
tributed to a or m passes to
the T arms of NX. In calcu
lating, the formula is —
Gain Bosswheel
M36
60,34^
34
Fig. 37.
2 2
40 X 34
U =
to =
40 X 34
20 X 34
60 X 34
Thus, with the front roller clutch closed and making 100
revolutions per minute, the rate of the back shaft would be —
lOOt.2 ( 45 X 36 \^( 100 X 1 , 100 X ^ A 1
2V90X60/ V 2 2 ^2
3
2^5
2 ■ 2
= (66)fo = 20 revs, per minute
If the front roller clutch was opened, then the rate would
be
100f.2/'4o X 36\ 100 X + 3 ^ , .. • „,
^(90^r6()) = ^^ ^ To = ^ revolutions per mmute
The rate of the carriage during the jacking is thus onefourth
the normal, and in addition that due to the size of the portion
of the back shaft scroll in action.
AND COSTS OF YARN
193
To find the revolutions of the front roller when the revolu
tions of the back shaft are 3i per draw of 62iinch draw :
Let X = revolutions of front roller. Then —
X X 40 X S4: X X 20 \45 X
* V2 6ao ■'' 6
36
2 X 40 X 34 ' 2 X 60^90 X 60 ~ "^^
19 X 10
190 X 6
eao "•''6 5X3' ■ ~ 15 X 4
.. a.' = ^:;^ = 19 revolutions of front roller
In mules not arranged with this motion, the gain wheel is
driven by a wheel on the front roller.
In Trelfall's Jacking Motion (Fig. 38), the right and left clutch
wheels, 130 teeth, are loose upon the shaft ; the central portion
36
Back Shaft
13
T
li5Up— I 1.
't i o 11 '"^^''''^''^^'^''^^'^'^^^
40
130
Jac
mot
Clutch > I A in
130
SN\yV\f7V\NV^N'.
70
50
/
Gain'Wheel
Rim Shaft
148
50
I—
70 \
(„ Speed change
^^ wheel
Rollec motion
48
plw^^wwjwlvl •": Clutch
Front roller I
Fig. 38.
is connected to the shaft upon a feathered key or the equivalent.
The clutch is now shown with the carriage driven at the normal
rate. The movement of the clutch towards the back shaft to
engage the other 130 part of this clutch, would set the back shaft
moving at the slowest rate, namely —
53 X 70
50 X 130
= normal rate
40 X 20 . ,.
7Q ^ ]^3 Q = jacking rate
= f;: the normal = 65
194 COTTON SPINNING CALCULATIONS
The Losses in Driving in Mules. — The following is an instance
of the difference between the calculated and actual speeds of the
parts in a mule when the former were made without allowances
for losses arising from slippage in the nonpositive gearing.
The revolutions per minute of the line shaft was 235, and the
connection to the rim shaft and spindles, respectively, fa ^ i It'
17'^ X 6
~i4 VT. The time taken to draw the carriage out to a head
111 X f
was 12j sees.
The calculated The actual
revolutions in revolutions in Loss
drawing the drawing out per cent,
carriage out. the carriage.
Kim shaft 1725 138 = 188
Tin roller 263 211 = 240
Spindle 1537 2100 = 268
Percentage of slippage in driving from :
The rim to spindles 8*9
The rim to tin roller 5*2
The tin roller to the spindles . . . 3*93
The loss shown in the third column is inclusive, and repre
sents the extent which the actual differs from the calculated.
Deductions. — The allowance in calculating the time taken, and
the speed, during twisting, should be about 25 per cent, when
the conditions are normal.
In arranging the driving gear, from 3 to 5 per cent, should
be allowed for each band drive. The losses noticed in belt
drives when the conditions are good — i.e. rational sizes of drums
and widths of pulleys, and when not reversing — are only very
slight, and need scarcely be taken into account.
In cases of very high speeds the losses will be greater. Con
siderable variation existed in the loss recorded at different
spindles, most probably due to differences in their resistance
and in the tension of their bands.
The slippage in the gear between the rim and line shaft is
only slight when the best systems are adopted. The chief loss
is that due to reversing.
Further examples of loss in driving mules follow.
Particulars relating to the Driving of the Parts in Fig. 35,
Dobson and Barlow's Mule for Fine Numbers.
AND COSTS OF YARN I95
Revolutions of the line shaft, 235 per minute, actual,
Drums on the line shaft, A, 32 inches ; B, 18 inches.
Counter Shafts.— The principal counter shaft : C, 20 inches ;
D, 20 inches ; G, 12 inches ; E, 24 inches diameter.
The auxiliary counter shaft: H, 20 inches; I, 9 inches;
K, 15 inches diameter.
lUiii Shaft.— Fast and loose pulley, F, 16 inches ; hasten
motion pulleys, J, 15 inches; rim pulley, 16 inches (1222 inches),
diameters.
rahimjin and Bachingoff Motion Shaft PuUrys.—L, U inches
diameter.
Sjnndles.— mm, 16 inches; tin roller pulley, 10 inches; tin
rollers, 6 inches ; spindle wharves,  inch diameters.
Eate of revolutions per minute of : —
The principal counter shaft —
. , , 235 X 18
first speed, ^ = 2115
second speed, ~~~ = 376
^0
The auxiliary counter shaft —
first speed, ?5^2ii§^12^ 1269
^ ' 20 X 20 ^ ^
second speed, ?35_x_32j<jL2
20 X 20 "^"^^ ^
The rim shaft—
n . , 235 X 18 X 24
first speed, g^ = 31725
second speed, ?35j^ll2ili = g..
Under the hastening motion
High speed, ^MA2J<J^XJ^ ^
^ 20 X 20 X 15 ^"^^
Low speed, 235j<J^8j^l2 x 9 _
^ ' 20 X 20 X 15 ~ ^^ "^
NoTE.The latter are successively in action at the close of winding.
196 COTTON SPINNING CALCULATIONS
The rates of rotation per minute of spindles —
,,, 235 X 18 X 24 X 16 X 6 ,_„ „ , ,
^1) 20 X 16 X 10 X l = ^^^^ ^''^ '^''''^
.„. 235 X 82 X 24 X 16 X 6 _„,„ , ,
(2) 20 X 16 X 10 X ^ = ^^^^ ^^^^^^ '^''^
.o, 235 X 82 X 12 X 9 X 16 X 6 i„oo n t i, i ;i •
^^> 20 X 20 X 15 X 10 X r ^T^ "^^ speed during
the action ol the hasten
ing motion
,, 285 X 18 X 12 X 9 X 16 X 6 ^„ ^ a ■, ^ ;■.*
^^> ' l X20X ^ X15X10X^ = ^^^'^ ^"^ 'P^'^ ^^**°
The Losses in Driving. — Under the above conditions in respect
of the gear the actual rates of the spindles were observed to be
less to the extent of : (1) 225 per cent. ; (2) 235 per cent. ;
(3) 18*75 per cent. ; (4) 11*15 per cent.
Further, the twist wheel contained 72 teeth, and moved 2
revolutions per draw; during twisting the movement was
140 teeth, and the revolutions of the spindle, in the correspond
ing period, 1454. This shows a loss of 18*8 per cent., the
calculated speed being as follows : —
1^0 X 16 X 6 _
icr>u ~
or 388 revolutions of the spindles more than the actual.
The time occupied in making this movement was 12i seconds
at first speed, and 8^ seconds at second speed, in these periods
the actual revolutions of the spindles being, respectively, 672
and 782.
These speeds represent, resjDectively, the following average
rates per minute : —
672x60 „,_ ,782x60_.„^„
— TTri — = 3150, and — ^^^ — = 5520
Iz* o'5
The loss of time by the rim shaft, as indicated by the above
speeds, is therefore as follows —
AND COSTS OF YARN 197
Calculated revs, of rim shaft in 8i sees, at second speed = 800
" >' » 121 „ first „ = 675
1475
Thus, 140 revolutions require the time of 1475, or time lost
by the rim shaft = S'OS per cent.
_ From this it is seen that 508 per cent, of the 188 per cent.
IS between the rim and the driving shafts, the major portion,
Id per cent., being between the spindles and rim shaft.
Twist per Iiich._The length wound per draw was as
lollows : —
Distance moved by the carriage each draw = 595"
Length del. by F.R. during the runin of the carriage = 45"
The approximate length wound = 640"
Actual twist per inch = ^^ = 227
Calculated twist per inch = ^H^ = 28
The actual count spun was 60^ so that the actual twist
227
coefficient = ^ = 293, as against 362 calculated.
The front roller made the following movements each draw :
(1) During the engagement of the F.R. clutch, ] , , ,„
164 revolutions = o46
(2) During the jacking and twisting at the head )
actions, 1^ revolution = 1
(3) During the inward run of the carriage )
1 revolution ( '^'^"
Total length delivered per complete draw = 600"
Length wound per draw = 64"
The total stretching of the yarn per draw is, therefore,
64  60 = 4 inches. Of this, the amounts obtained during the
abovenamed periods are —
198 COTTOX SPINNING CALCULATIONS
(1) the movement of the carriage being 56" = 56" — 54*6, =1'4
(2) „ „ „ 3i" = 3rl, =2^
39
Length not accounted for =0*1
40
The actual revolutions of the rim shaft after the disengage
ment of the F.E. clutch, i.e. during jacking and twisting at the
head, were 73. Therefore the length which should be dehvered
by the F.E. during this period, by reason of the action of the
slow roller turning motion, is :
^ 73 X 19J< 20 X 1 X 24 X 1,V X 22 ^ .^^^^^
58 X 40 X 30 X 24 X 7
The actual length observed was 1 inch. The difference was
undoubtedly due to the backlash in the motion.
Note. — The difference noted in the actual and calculated rates of the spindle
emphasize the importance of not relying on the calculated revolutions of tlie
spindle unless due allowances have been made for slippage in the belt and band
driving gears. The use of a tachometer is very helpful when arranging the
gearing. The particulars given were ascertained, accurately and expeditiously,
by the aid of that instrument.
Speed Indicators.
Losses in the Transmission of Motion, and how Ascertained. —
The most convenient mode of ascertaining the extent of losses
arising in the transmission of motion is by the aid of a self
time registering tachometer. The ordinary tachometer is defective
in that the attachments for connections are imperfect, and in
addition the timing has to be done either by a second person
or the attentions of the operator divided between the timepiece
and the tachometer^ In either case the work is not altogether
satisfactory.
The illustration (Fig. 39) is of a tachometer, and suitable
attachments for spinning machinery. It consists of a recording
AND COSTS OF YARN 199
timepiece, D, with minutes and seconds dials combined on the
II
4 *
m
D
Fig. 39.
left hand. This is fitted ^Yith a flyback action. The timincr
200 COTTON SPINNING CALCULATIONS
commences upon pressure being applied to the recording
spindle 2, the centre finger recording from I to 60 seconds,
and the lower finger the minutes. The lower projecting milled
head is for setting back the minutes finger, and the slight
projection on the left hand is the flyback release for the
seconds. The large righthand deal finger indicates the
revolutions up to 100, and the small one on the inner left
the hundreds, whilst that on the inner right records the
thousands. The projection on the underside of the right dial
is the flyback release for the unittens finger, the hundreds
and thousands fingers being reset by means of milled heads at
the back.
F, H, are rubber cupped detachable ends for the spindle of
the tachometer.
E, and that on the left of centre are rubber pivoted detach
able ends for the spindle of the tachometer.
That on the right of centre is a pyramidal recessed end for
the spindle of the tachometer.
J, K are pyramidal ends for fitting to mule and ring spindles
for use in connection with those found on the left and right of
centre.
This instrument is held by the detachable handle D. In
use its great feature is that it can be held in one hand, and
with this exception the whole of the attentions of the operator
are available for other work throughout the observations. The
dials record the results, the range of speed being up to 10,000
revolutions per minute.
Length and Hank iNDicATOPtS.
Fig. 40 shows the gearing in an indicator for registering the
number of draws in mules. The segmental wheel is driven by
a worm placed upon the back shaft of the mule (drawingout
shaft). The sector lever, b — hi, secured to a, operates the star
wheel c ; to the latter a 3treaded worm is secured, and this
drives the worm wheel d on the spindle ch — f/2. Five dial discs are
mounted on this spindle, and these record units, tens, hundreds,
thousands, and tens of thousands respectively. Each of these
AND COSTS OF YAEN
201
are connected, in sequence, by a train 1 driving a 4, the latter
being compounded with an 8, which drives the 20 secured to the
next dial. The first dial is secured to di — d2, and the rest are
free upon it. Thus this instrument records from to 99999
20, 20, 20, 20.
8, 8, 8, 8,
,4, 4. 4, 4.
Fig. 40.
draws, the object being to record the work done in a given time
for estimating the earnings and for other purposes.
The record is exact, as shown by calculation. Thus —
20 X 4 X 20 X 4 X 20 X 4 X 20 X 4 X 10 X 3
8x1x8x1x8x1x8x1x3x1
= 100,000 hanks
recorded on the dials by its moving from 00000 to 99999, and
then 00000, or one complete revolution of the lefthand dial.
Fig. 41 shows the gearing in a hank indicator as used in
mules. These instruments are arranged to record the production
of the whole of the spindles in the machine, and hence the gear
is varied to adapt them for the different numbers of spindles
which the mules contain and the length of the draw. In the
figure the particulars are of one designed for a mule containing
202
COTTON SPINNING CALCULATIONS
184 spindles only, and making a draw of 58^ inches. It records
from up to 20,000 banks, the customary allowance for loss
through breakages being 2^ per cent. The action in this case
is as follows : —
a, rti, aj, 03, cii are attached, this part is actuated by a worm,
X, placed upon the back shaft. By that means a, ai, a^,
oscillate, each draw, and the sector lever a^a^^ moves the star
wheel h one tooth, h is compounded with c, 30; this latter
Fig. 4L
drives cl, the 15. d is compounded with the worm c (1), which
drives j (20). f is compounded with the single worm g, and the
latter drives h. The lever i, i, is fastened upon the axle of h,
and this is loose on the central spindle. At the extremity of
this lever is the wheel 21, mounted free on a stud, and its teeth
engage two wheels, JcS9 and /40 respectively, k being secured
and cannot rotate. /, being free, is moved one tooth per revolu
tion of the lever /, /, upon its centre. The index finger ki is
AND COSTS OF YARN 203
attached to I, and this moves in front of the dial indicating from
to 20,000 hanks.
The length of yarn made, per 184 spindles winding
58^ inches per draw and assuming no loss, per 20,000 hanks
registered,
_ 40 X 48 X 2 X 15 X 8 X 18 4 X 58V'
 1 X 1 X 1 X 30 X 1 X 840 X 36
NoTK. — 512 hanks = 2^ per cent.
= 20,503 hanks
Exercise 1. — A mule containing 796 spindles and winding G7 inches per
draw has the following wheels stamped upon it, IG x 6 x 3 x 41, and it indicates
20,000 hanks per draw. What percentage does it allow for breakage ?
Ans. 3'9G, or 1'4G in excess.
Exercise 2.— For what number of spindles per mule would the following
20 20 21 15 3
hank indicators be adopted ? Particulars of their gear, y' ^' y' on' ^' assum
ing the length wound per draw 68 inches, and the indicator to record up to 20,000
hanks. Ans. G8G.
Exercise 3. — What number of hanks must be recorded per draw by the
hank indicator in a mule containing 1200 spindles and winding 64 + 4 inches
per draw, if 2i per cent, is allowed for breaknge ? Ans. 2*63.
Exercise 4. — What alteration in the value of the following underhned
portions of the gear in an indicator would adapt it for a mule of 1200 spindles,
making a 64inch draw and 4 inches inward roller delivery, allowing 2^ for loss?
,, , ^^, 20 20 21 15 3
Value of the gear, y, ^ , j, ^, ^■
A71S. Present value of the train = 12.600, or number of draws to move the
dial one revolution.
Piequired value of the train = 7601, or number of draws to move the
dial one revolution.
Value of the gear required = ;5 — ^ = 5067
oX^
204
COTTON SPINNING CALCULATIONS
Productions ix Mules.
Production iu
Production in
Production in
Production in
hanks per spindle
hanks per spindle
hanks per spindle
hanks per spindle
Count.
per 55i hours
per 55 hours
Count
per 55 f hours
per 55 hours
inclusive.
inclusive.
iLclusive.
inclusive.
Twist.
Weft.
Twist.
Weft.
16^28
3235
3034
61 '80
16751975
17205
30
3133
3133
82
165195
—
32
2932
3032
84
15751925
—
34
2831
2931 2
86
15519
16520
36
275308
28531
88
1525188
.
38
2730
283075
90
151186
16197
40
265295
27295
92
149184
—
42
2629
26529
94
14818 1
—
44
2552S5
26285
96
1461775
155193
46
2528
2528
98
144175
48
245275
245275
100
1421725
1519
50
2427
2427
110
1417
15185
52
235265
235265
120
137165
141725
54
2326
2326
130
133155
13516
56
225255
225255
140
131425
58
2225
2225
150
122614
—
60
21 •5245
225265
160
1213
— .
62
21235
2226
170
1112
64
20225
21 5256
180
1011
66
19522
21248
190
95105
68
19215
2024
200
910
70
1852125
195232
240
7282
72
1821
19228
260
6474
74
175205
—
280
5666
76
17252025
18219
300
4959
78
1720
—
The Ring Frame.— Figs. 42 and 43 represent the gearing
common iu ring frames.
A = The back roller and its wheel for driving that on the
middle roller.
B = The carrier wheel connecting the back and the middle
rollers.
C = The wheel upon the middle roller.
D = The draft change wheel on the back roller.
E = The draft change pinion driving the back roller wheel.
F = The crown wheel compounded with the draft change
pinion and gearing with the front roller wheel.
G = The wheel on the front roller for driving the above gear.
H = The wheel on the front roller gearing with the train
I, J, and K.
AND COSTS OF YARN
205
K = The twist change wheel.
L = The twist stud wheel, and MN the connecting train
from the tin roller shaft.
N = The tin roller shaft wheel, this is changed when an
extension in the range of the twist is desired beyond that
procurable by altering the twist wheel.
P, Pi = The tin rollers driving the spindle bands.
Q = The spindle wharve. The spindles are arranged in
rows on either side. The band indicated by the dotted lines
shows the driving when double tin rollers are used for one
side only.
Fig. 43 shows the driving of the cam W for reciprocating
Fig. 42.
m
V
Fig. 43.
W
the ring rail, the rate at which this is driven controls the pitch
of the coils contained by the bobbin.
S, T, U, V, are the train of wheels connecting W with I. W
produces the reciprocation of the ring rail through the medium
of a series of levers, rods and chain connections. The relative
positions of their movement is advanced through the agency
of a ratchet wheel and a pawl, the ratchet wheel being termed
the builder wheel.
The number of teeth in the builder wheel and the value of
its driving train, S, T, U, V, control the length, and therefore
206 COTTON SPINXIXG CALCULATIONS
the weight of yarn placed upon the bobbins. When the rate
of reciprocation is insufficient, and other means have been
exhausted, the speed of this part is changed by introducing a
single, double, or a treble worm at T. The movement of the
pawl operating the ratchet is adjustable to the extent of the
var3ang sizes of the teeth in the builder wheels applicable.
D, E, F, G, are the gear for driving the rollers on the right
hand side, and these are a duplicate of those on the left side.
Pi, is the driving pulley connected by belt or rope with the
line shaft.
The speeds of the spindles in these machines usually range
from 6000 to 11,000 per minute, actual. The usual sizes of
rollers are from I to 1,^ inch for the front and back positions,
and I less for the middle roller ; ^ inch is used for short and
1^ inch for longstapled cottons.
The recognized twist for ring yarns is 4\/count per inch.
This is not rigidly adhered to, exceptions being made when
it secures better spinning and the amount of the twist has not
been stipulated.
The Speeds of Spindles. — The circumstances that govern the
best speeds of the spindles are : quality and count of the roving
and yarn ; condition of the machine ; expertness of the workers.
Under the most favourable conditions, a speed of 10,500 revo
lutions actual may be attained with counts 30'36'. For other
counts, under the best conditions, the following revolutions per
minute of spindle are given as a guide : —
For counts below 30^ —
10000\/intended count
VBO
For counts above 36* —
lOOOOv/36
^/intended count
When the conditions are identical but not satisfactory for the
above :
For counts below 36* —
known satisfactory speed X i/'intended count
\/count
875
AND COSTS OF YAl^N 207
For counts above 36^ —
known satisfactory speed X v^count
^/intended count
With the largest and smallest sizes of the twist change wheels
given in Fig. 42, and the spindles making 10,000 revolutions
per minute, the speed of the parts would be as follows : —
Parts. AVith the smallest change wheels. ^^5'^ "^® largest
" change wheels.
Tin roller shaft and ) 10000 x ^ _ .
machine pulley f 10 ~
,. , 1, 10000 X I X 25 X 25 ._ .,.,0
1 rent rollers .... l(rxT2T^80 = ^^ ^"^
"With rollers of the following diameters, the lengths delivered
per minute respectively are —
Parts. With the smallest change wheels. Yhfnge wS"
T3 X' . „ 7» J . 57 X ^ x 22 , _„ 228 x Z x 22 ^.^„
by iront roller, ^ diameter . ^ ^ = lo< ^ = 628
By front roller, 1^" diameter . 203" 812"
The twist per inch under the above conditions would there
fore be —
Parts. With the smallest change wheels. ^h'ange wS.'
By front roller, " diameter . . . ia§ao ^ (53.7 iaa<i = 159
By front roller, l^" diameter . . . Hggfi = 492 itt'l^Q = 123
Thus the twist, with the sizes of change wheel applicable
and the front roller ^ inch in diameter, ranges from 15"9 to 63'7
turns per inch of yarn delivered by the front roller.
This calculation is based on the twist being equal to the
revolutions of the bobbin. This is inaccurate when the yarn is
unwound from the side of the bobbin, but correct when the yarn
is unwound from the ends of the bobbins. To arrive at the
actual twist inserted during spinning, it is necessary to deduct
from the revolutions of the bobbin, the revolutions about the
bobbin made by the yarn in obtaining winding.
The different sizes of the twist wheels applicable w'ould
therefore obtain the following amounts of twist when the tin
208 COTTON SPINNING CALCULATIONS
roller wheel is 25 and the front roller is
I inch in
diameter : —
Size of twist wheel 25 26 27 28 29 30 ... 35 . ,
,. 40 ... 45
Twist per inch . .637 612 590 568 549 530 ... 455 . .
. 398 . . . 353
Size of twist wheel 46 47 48 49 50
Twist per inch . .346 339 332 325 318
The above are ascertained in the following manner : —
Eevolutions of spindle per inch delivered by the front roller
80 ., 120 ^ 10" ^ 1
T.W. T.R.W. I"
and hence with a 25 tin roller wheel, and a 50 twist wheel, the
revolutions of the spindle per inch delivered by the front roller
_80 120 10 1 _
25^ 59 ^I^r^^^^^
These results may also be ascertained as follows : — Assuming
that the tin roller wheel was 25, and the twist wheel contained
only one tooth, the twist per inch would be 63'7 X 25. (This
is called the twist change wheel constant number for a 25 tin
roller wheel, and the front roller I inch in diameter.)
63'7 X 25
.*. — ^7, = the twist per inch when a 26 wheel is used
T.W. constant ,, , . , . ,
oi'j ^~. — jT — i — 1 = the twist per mch
mtended wheel ^
T.W. constant • i , i
.'. ■ ■ , . — r = required wheel
twist per inch ^
When the limit in the range of sizes of twist wheels is reached,
they may be rendered again available by altering the size of
the tin roller wheel, in the proportion which the range of
wheels represent. The limit in the present instance is reached,
with a 25 tin roller wheel, when the twist wheel is 50, the twist
in the yarn is 318 per inch. By adopting the size of tin
roller wheel that, together with a 25 twist wheel, will produce
31 '8 twists per inch, the range of twist wheels are again avail
able. Thus —
AND COSTS OF YARN 209
63*7 X 25 = the tin roller change wheel constant number for
a twist change wheel of 25 teeth
.. — ^^ „ — = the required tin roller wheel = 50
and, therefore, with a 50 tin roller wheel, and with the
stated range of t\Yist wheels, the following twists will be
obtained ; —
Size of twist wheel 25 26 27 . . . 30 . . . 34 35 . . . 40 ... 45
Twist per inch . . 318 306 294. . .265. . .234 229. . .198. . .176
Size of twist wheel 46 47 48 49 50
Twist per inch . . 173 169 165 162 159
Twist change wheels are usually drivers in the train to the
front rollers, and therefore increasing their size increases the
length of yarn submitted for twist in direct proportion, and
hence the twist is reduced inversely.
To change the Counts. — This is done in the same way as in
the previous machines —
(a) By altering that of the feed.
(b) By altering the extent of the attenuation or draft.
The results are directly proportional to alterations in either
case. Thus :
the weight unit of the feed ,, .,. .. f,, ,,.
, , ... = the weight unit oi the delivery,
and vice versa
the count of the feed x the draft = that of the delivery, and vice
versa
The draft is also determined in the same manner. Assuming,
the smallest driver, and the largest driven, of the draft change
wheels are used, and the back and front rollers alike in size,
then —
the draft = §] X \Pf = 10
Hence, with the back roller wheel 60, the range of pinions,
applicable, would produce the following drafts : —
Draft pinion 30 31
Draft. . . 100 965
Draft pinion 56 57 58
Draft. . . 535 526 517
32
33
34
35 . .
, . 40 .
. . 50 .
. . 55
937
91
882
857 . .
. 75 . .
. . 60 .
. . 545
58
59
60
517
508
50
210 COTTON SPINNING CALCULATIONS
It is thus seen that the fractional change in the draft
corresponds with the fractional change in the wheel, and hence
large wheels command a finer adjustment of the count,
and for this reason the use of small change wheels should be
avoided as far as practicable.
Whenever the size of pinion required is not available, alter
the back roller wheel in the inverse proportion, or change
the back roller wheel, altering its size to the extent that will
enable the use of the available wheels, as pinions. The following
is then the procedure : —
Ratio of pinion and back roller wheels, ^. ^' — ' ; and any
^ pmion
two wheels which give a near enough ratio will be satisfactory.
Always remember that the back roller wheel has the inverse
effect to the pinion, the former affecting the draft in the direct
ratio and the latter inversely.
The Builder Wheel (Ratchet). — In changing the count, the
weight of the yarn is affected in the inverse proportion, so that if
the bobbins are required to contain the same weight, then the
ratchet wheel must be changed in direct proportion to the count.
This is not always admissible in practice on account of the
bobbins being filled too full for the rings, through the yarn not
being wound sufficiently compact. The rule in calculating the
builder wheel is —
Builder wheel X count required , , ., , ,
, = wheel suitable
count spun
When the size of the empty bobbins are changed or a
different size of full bobbin is required, the wheel should be
altered in direct proportion to the area of the crosssection
of the yarn contained on the full bobbin.
The relative area of a crosssection of the yarn = (diameter
of full bobbin — diameter of empty bobbin)^.
the wheel X area of section of yarn on bobbin required
area of section of yarn on present bobbin
When the bobbins are insufficiently hard, and the traveller
is the heaviest practicable, speeding up the traverse of the ring
rail by the most convenient of the wheels S, T, U, Y, will have
a beneficial effect.
AND COSTS OF YARN
211
Exercises is chaxging the Counts .vnd otukii Coxditioxs of Spixxixg in
THE RiXG Frame (Fig. 42). The Froxt axd Back Rollers are
takex at I Ixcn in Diameter.
EzerciEe numbers.
(1) Count of tlie^
yarn 
(2) Count of thel
rove /
(3) Rove, whether
single or
double
(4) Draft . . .
(.")j Draft wlieels —
F.R.W. . .
C.W. . . ,
P.W. . . .
B.R.W. . ,
(G) Twist per inch .
(7) Twist wheels —
T.R.W. . .
T.W. . . .
(8) Twist change!
wheels con 1
staut number )
(;») Revolutions otj
spindles per j
minute )
(10) Size of empty)
and full bob
bins j
(11) Builder wheel ,
(12) Hanks pro^
duced per 10
hours (no
allowances) J
375
21
105
40
60
50
?
79.)
10,000
f " and
13"
la
40
10
21
105
?
60
253
50
?
795
50
2
10
21
105
?
60
?
25
60
15
21
105
?
60
31
25
80
20
21
105
•?
57
?
25
9
9500 9000 8500 8000
30
?
21
105
ratio
9
50
?
20
3^
21
105
40
179
50
9
10,500 9000
f " and
U"
—
1" and
k"
f " and
•?
?
?
?
?
?
?
16
?
1
53
21
105
ratio
?
50
9
8000
f'and
If
?
9
Axswers to Exercises.
Number of Exercise.
Particulars.
1
2
3
4 , S
6
7
8
No. 1 . .
_ 1 _
_ 1 _
_
_
•}
10
—
10
— —
5
—
;{
„ 4 . .
75
8
8
8
—
572
„ 5 . .
. —
35
30
35
35
P. 5
B.R.W. 6
46
P. 50
B.R.W. 53
„ 6 . .
. 245
283
358
219
—
16
„ 7 . .
. 324
314
562
51
445
36
44
50
„ 8 . .
1590
1590
1590
795
795
795
„ 11 . .
—
38
48
58
49
415
276
30
., 12 . .
. 81
746
633
545
445
95
103
166
212 COTTON SPINNING CALCULATIONS
EXASIPLES IX THE WoKKIXG OF TUE ExERCISES OX PagE 211.
37.5 v^ 2
Exercise 1. — The draft = fg ^ W"! ^^^^ count of the rove = j r. ^
795
the twist per inch = 4 V count ; twist wheel = ; the hanks pro
, , revolutions of F.R. per 10 hours x circle of F.R.
duced = . — r T — 1
inches per hank
40
Exercise 2. — The draft = jj~ = 8 ; the pinion wheel (a) is contained in this
,. 60 105 o .1 /• ^ 11 795 . ,, . ,, .
equation — x ^ = 8 ; the twist wheel = ^^.^, or, as x in the following
,. 80 120 10 1 or: a .1 1 n i i 36 X 40 „„ ,
equation, ^ x ^ x ^ x j ^ = 25*3 ; the builder wheel = — =384.
Losses in driving the Spindles in Ring Frames. — The following
are instances of the observed and calculated speeds of the
spindles, together with the losses arising from slippage : —
King frame with two tin rollers, one of these being fixed to
the machine shaft, and the other driven by the spindle bands.
Driver T.R. side. Driven T.R. side.
Actual revolutions of T.R 565 555
Actual revolutions of spindle .... 6250 6824
Calculated revolutions of spindle . . . 6460 6342
Percentage of loss 3*25 8*1
The following were recorded after rebanding the spindles on
the driven tin roller side, these bands being driven by the driver
tin roller : —
Driver T.R. side. Driven T.R. side.
Actual revolutions of T.R 570 5G2
Actual revolutions of spindle .... 6026 6020
Calculated revolutions of spindle . . . 6541 6422
Percentage of loss 6"67 7*5
The following were recorded in a frame having" the tin
rollers connected by an endless rope drive : —
Driver side. Driven side.
Actual revolutions of T.R 658 650
Actual revolutions of spindle .... 7184 7065
Calculated revolutions of spindle . . . 7500 7430
Percentage of loss 4*2 4*7
The productions in ring frames vary considerably, depending
AND COSTS OF YAllN
213
upon the speed of spindles, twist per iiicli,^ strength of tlie yarn,
skill of the operatives and their management.
The spindles are run at rates as high as 11,000 revolutions
per minute, this being exceptionally high, and only practicable
under the most favourable conditions. The production ranges
as high as 96 per cent, of the calculated when based upon the
actual spindle speed.
The highest speeds are only practicable with about 36^
to 40^ counts under normal conditions.
Productions in Ring Spinning.
Actual speeds of
Produotiou in
Actual speeds of
Production in
Count.
spindles per
hanks per spindle
Count.
spindles per
hanks per spindle
minute.
per 55J hours.
minute.
per 55i hours.
16
70008000
4351
40
950011,000
3945
20
75008500
4348
50
850010,000
3137
24
80009000
4247
60
850010.000
2834
28
8.5009500
4146
70
80009000
25530
36
900010,500
3945
80
80008500
24255
Productions in Ring Spinning. — In spinning yarns from single
roving, with a high draft, or from an inferior or irregular stapled
or soft cotton, or in exposed buildings, lower speeds are
necessary.
The ring spinning machine cannot be as profitably em
ployed in the production of yarns other than the best descrip
tions, when in competition with those produced in the mule
spinning machine.
Ring frames require better cotton and finer roving for the
ordinary classes of yarn. They are principally employed, in
this country, in the production of the following yarns : —
(1) Yarns containing above the average twist.
(2) Yarns made from above the average quality of cotton for
the count.
(3) Yarns of above the average quality.
(4) Yarns which are required in bundle or warp form for the
subsequent requirements.
In all these, this machine can produce to greater advantage
when the counts are within a certain range.
' Sec effects of twists in single yarns, p. 215.
2U COTTON SPINNING CALCULATIONS
Twist Standards for Single Yarns.
The object in applying twist in spinning yarn is to secure a
common bond amongst the fibres, and thereby create a certain
tensile resistance to tension. The purposes for which the yarn
is required will therefore control the extent of the twist applied.
The ordinary standards in use are as follows : —
Mule Yarns. —
Turns per inch in —
V^count X 3*18 = Egyptian weft
Y^coun^ X 3'25 = American weft
y/count X 3'39 = Egyptian medium
\/count X 3*5 = American medium
^count X 3*606 = Egyptian twist
^count X 3"75 = American twist
Ring Yarns. —
" Soft weft " = Vcount X 325
/ " Medium weft " = A/count X 35
/ " Soft twist " = v'^ount x 3*75
\/count X 4*0 = Ordinary twist
^count X 4'2o = Water twist
^/count X 4"5 = Hard twist
\ ^couut X 4*75 = Extra hard twist
\ v^count X 559"0 = Crepe
The above twists are not rigidly adhered to. Slight modi
fications are made in them by the spinner, such as circumstances
connected with the operation of spinning render expedient.
A knowledge of the effects of twist, apart from the ordinary
standards, is most essential in spinning.
The influence wielded by twist varies with the character of
the cotton. It is greater in those fibres which are long, uniform
in their length, and silky in texture, and well prepared. The
shade of the yarn is always darkened with increased application,
and the touch is also hardened. A decided curl, or shrink, is
also thereby developed. This latter tendency is greatest in yarn
which is irregular in diameter or made from harsh cotton.
AND COSTS OF YARN
215
Yarns that are highly twisted are less absorbent and colder
to the touch, more difficult to dye satisfactorily. Such often
become weaker in sizing, bleaching, and dyeing, whereas those
less twisted are not unusually strengthened thereby.
The Effects of Twist in Single Yarn.— The effect of twist
upon the strength of yarn is graphically illustrated in
Fig. 44. This diagram was prepared from the breaking
resistance of 20' yarn made from Gd. Brown Egyptian cotton.
This, in its preparation, had been combed and otherwise most
1  2
4 5 6
TWIST CONSTANTS
Fig. 44.
10
carefully prepared. In spinning, double roving was used. These
abnormal conditions being considered essential for the end in
view, as it must be recognized that to obtain the most satisfactory
results, such work could only be useful by attaining the best
conditions. Yarns were prepared containing twist ranging from
13 to 415 turns per inch. In testing their strength the greatest
care was exercised to ensure reliable results. Altogether the
number of tests made exceeded 12,000.
In testing the yarns, considerable difficulty was experienced,
216 COTTON SPINNING CALCULATIONS
ill using the ordinary strength testers, with those hardest
twisted, and the results obtained were unreliable.
Ultimately, the tests were accomplished, satisfactorily, by
using the Moscrop patent single thread tester made by Messrs.
Cook of Manchester. The whole of the tests, made use of in
plotting this diagram, were executed on the same machine.
The diagram gives the strength developed in terms of
an increasing twist constant, and also in strength per turn of
twist. The upper curve shows the former, and indicates the
point at which twist ceases to add to the strength, and the
lower curve shows that obtaining the greatest value in strength
per turn of twist inserted.
The inferences drawn from these tests, and from inspection
/of the yarn, are —
(a) That in the best yarns the strength contributed per turn
of twist becomes gradually less at \/count X 3.
(b) That in the best yarns the strength ceases to increase
with the added twist at \/count x 5.
(c) That the shade and touch and tendency to shrink becomes
appreciably affected after \/count X 3*5.
(d) That the shade is only very slightly affected up to
3'0\/count, and after 5Y/count it becomes very appreciably
darkened.
(e) A coincidence was that the twist constant realizing the
greatest strength per turn of twist was 3'17\/ count. That
adopted by the trade generally in spinning weft from Egyptian
cotton is 3'18\/count.
Twist Standards for Folded Yarn. — The following are the twist
constants used in doubling : —
Twofolds—
XXXX Soft 134
XXX „ 152
XX ,, 18
X ,, 22
O.Q
}J ^ O
Medium 3*39
Common 4'0
AND COSTS OF YARN
217
Lisle ....
Double spun .
Hard . . .
X
XX
45
5*0 (singles)
50
54
56
Single yarn.
Sewings Constant or Coefpicient.
Twofold.
Sixcord.
As low as possible M^S^^^^^^ ^ constaut ^
45
single constant
6
X constant
65
Single yarn.
Weft to twist turns
Crochet.
Twofold.
65
Yarns for Fish Xettixg.
•Single yarn.
Twofold.
Common ....
/ single count
\/ number of singles
X 4o
Sixcord.
single count
number of singles
X 65
Kkitting Yarns and Embroidery and for Mercerizing.
Singles.
Fold.
As low as practicable . .
/ singles
\/ number of singles
X 30 to 325
218
COTTON SPINNING CALCULATIONS
The Influence of Direction of Twist in Folded Yarn.
The diagram (Fig. 45) shows the influence of the direction
of twist upon the strength in the twofold yarn. This figure
was plotted from the breaking strains of two series of twofold
yarns, one set being twisted reversely and the other twisted
in the same direction as that contained in the singles. The
3 4 5 6
TWOFCLD TWIST CONSTANTS
Fig. 45.
single yarns used were of very good quality and ah alike, con
taining twist to the extent of 3"6\/count, per inch. The twofold
twists, per inch, ranged from 2"5\/count to 6*85\/count. Those ]
twisted in the same direction as the single were harder to the
touch and darker in shade, and with the increased twist, their
elasticity, to tensile resistance, increased to an abnormal extent.
Yarns for elastic fabrics and in preparing for sewing threads
have their twist in this direction. Those twisted in the reverse
direction exhibited no abnormal features ; a slightly darkening
shade was noticeable especially in those fullest twisted.
The Influence of Varying Degrees of Single and Folding Twist. —
Fig. 4G was prepared from the breaking strains of yarns con
taining a graduated extent of twofold twist, and made from
AND COSTS OF YARN
219
single yarn containing the following twists per inch : (1) 2"9,
(2) 335, (3) 39, and (4) 45 times the y'counts. The doubling
twist was inserted in the reverse direction to that in the singles,
and the twofolds comprised 20 differently twisted threads,
ranging in extent from v^counts X 2"75 to ^/counts X 595.
The following were the most noticeable differences in features
of these yarns : —
Number (4) gave the best strength when containing doubling
twist to the extent of 5y/count and below. It was small and
pearly.
Number (1) was the most attractive yarn, being softest, most
35
TWIST PER INCH
9 10 11 12 13 14 15 16 17 18 19 20
1
^^
_ 
s.^1 .
^
f^
2^
^
^
^
^^
X^d
r
\
4'
r^
y^
/
\
_^
^
/
V
3*
'
^
>
V
^^
^*
<
\
2
^
X^
~1
r*«i
_ 25 —^^ —
3 4 5 6
TWOFOLD TWIST CONSTANTS
Fig. 46.
cylindrical, and lustrous. In point of strength, however, it is
inferior to the others, up to 49v/counts, turns per inch, but a
little beyond this point its strength is superior to the others. Of
the four types this would be the most expensive yarn to produce.
This figure is useful in indicating the twofold twist most
beneficial in variously twisted single yarns; also the most
serviceable single twist when a given twist is desired in the
twofold.
The Effects of Twisting Two or More Single Threads together. —
When the twist inserted is in the reverse direction to that con
tained in the singles, it displaces an equal amount from each
of them. When the twisting proceeds in the same direction as
220 COTTON SPINNING CALCULATIONS
that contained in the singles, that in the singles is supplemented
to the extent of the doubling twist. Thus, the former procedure
removes the twist in the singles, the fibres being simply re
arranged convolutely, or in what may be termed a spirocorrugate
order. When tension is applied to bodies of fibres so arranged
they are pressed towards a common centre, and this force bonds
them, preventing the fibres from sliding.
It is this change in the arrangement of the fibres, without
necessarily changing their compactness, that is responsible for
the greatly increased strength of doubled yarn as compared
with that of single yarn of a similar weight.
The conditions that would have to obtain in order to utilize
to the fullest extent the available strength of the body of fibres
contained in a doubled yarn, are —
That all fibres be equally outstretched and in alignment, so
that they mutually share the tension applied. That they are
bonded sufficiently to prevent their slippage upon each other
and devoid of individual twist.
This latter state, in so far as twist is concerned, can readily
be obtained. It is in the laying of the fibres equally outstretched
that difficulty arises, that state being only partially possible.
The formation of the fibres about a common centre, twisted,
renders their alignment impossible.
The aims of doubling may be stated as follows : —
(1) To permanently utilize the available strength of the
fibres by preventing their axial movement after the thread is
completed.
(2) To obtain the desired compactness, lustre, and freedom
from ooze, with the fibres bonded in the most suitable manner
for the required size of thread.
(3) To insure definite elastic properties in the yarn when
under tension.
(4) To obtain the desired character of surface, such as
cylindrical, spiral, corkscrew, pearly, crepe, or other effects.
In order to secure the utmost strength, and at the same time
prevent axial movement, the twists in the successive stages
should be arranged so that they balance in the completed
yarn.
AND COSTS OF YARN 221
Compactness is the result of tension and compression applied
during doubling. In order to obtain the smallest thread from
a number of others, as, for example, in sewings and kindred
3'arns, the following procedure is most effective : —
In doubling the singles the fibres should be compressed to
their limit, by twisting in the same direction as the singles, and
to the extent necessary to obtain a balanced state when the final
twisting is completed. Thus, when the final twist is great, that
in the folded singles must also correspond. In the substitution
of the preparing by the final twist the consequent extending
and expanding tendencies are fully absorbed, or counteracted
by their greater radius about a common centre.
Lustre is affected by the angle which the fibres make
with the completed thread. It is greatest when they are in
line with the axis of the individual singles, and vice versa.
Thus, lustre indicates the extent of the twist in the singles
and in the fibres.
Freedom from Ooze. — This is in the main the result of the
rolling action of the yarns against each other in the course of
twisting.
The Tendency to Stretch, under tension, is regulated by the
angle of the singles or strands comprised in the final thread.
The more numerous these are the less their stretching tendency.
Thus, highly elastic doubled yarns are composed of the fewest
singles and strands. The number of strands that can be satis
factorily bound in this way are limited, and hence they seldom
exceed four. Above this number the singles or strands have
insufficient adherence, and hence plaiting is resorted to.
Cylindricity is developed most effectively when the singles
are only slightly twisted and of the best quality.
Pearly Effects are developed by employing highly twisted
singles.
Crepe by twisting in the same direction as the singles,
also by inserting considerable twist in the reverse direction to
that in the singles ; but the effect is not the same in both cases.
Spiral Effects are obtained by slight folding twist.
Where a small yarn with hard effects are required, highly
twisted singles are necessary. For soft effects similar to those
222 COTTON SPINNING CALCULATIONS
required in yarns for mercerizing, the singles should be softly
twisted.
Corkscrew Effects are obtained by doubling —
(a) Yarns in unequal tension.
(h) Yarns unequal in size.
(c) Yarns containing unequal twist.
(d) Yarns twisted in opposite direction.
The Relative Resistance of Yarns to Twist. — Assuming the
CO efficient of resistance to the first twist in a given length of
yarn to be 1, and the resistance, as the twist progresses, directly
proportional to the twist contained, the relative resistance, when
the diameters of the yarns are not alike, being proportionate to
their diameters cubed— then, upon these assumptions, the
relative resistance of a body of untwisted fibres, equal to 60^*
and 40* yarns, are respectively —
When the fibres are twisted, their resistance, when t denotes
the twist contained in them, will be respectively —
.(iYand^(4=f
V\/60/ \v'40/
The above are based on other conditions being equal.
The relative resistance of 60' and 40^ yarns containing twist
to the extent of 3*5>/count, is therefore expressed as follows : —
60% 35v/6o(^y=057
40% 35v/40(^y=0837
When folded threads are required balanced, namely, without
tendency to twist or untwist, it is necessary to insert twist to the
extent that will balance the forces they contain. Thus, a yarn
composed of several single threads should be twisted so that the
force developed by the doubhng twist is sufficient to counteract
those still contained in the singles. When a number of singles
AXD COSTS OF YAEX 223
are bound by twist in tbis manner, the twist inserted adds to, or
reduces, that in each single, to a corresponding extent. This
action reduces or increases the force which the singles exert.
Therefore, when the doubling twist is inserted in the reverse
direction to that in the singles, and to the extent of rendering
the opposing forces equal, the yarn is then in a state of equili
brium or " still." The amount of twist, which is required to
produce the still or balanced state, will be governed by that con
tained in the singles and also by the number of threads
comprised in folding. Hence, the more numerous the twists in
the single and the fewer the folds, the greater the amount of
twist required in doubling the yarn.
The extent of the twist required in folding yarns to balance
that in the single yarn may therefore be ascertained in the
following manner : —
Let ci = the count of the single.
02= ,, ,, folded yarn.
Ti = the twist in the single yarn.
T2 = ,, required in the folded yarn.
The relative twist required to develop a balance of the forces
in the completed thread, when twofold, is as follows ; —
The force in the singles before folding is :
'Hvm
The force due to the twist remaining in the singles when
doubling is completed is :
'b'^  <37)1
The force due to the doubling twist in the thread is
Therefore, the forces in a balanced thread are :
224 COTTON SPINNING CALCULATIONS
The above formula, when applied to twofold 50* with
ti = 3"5\/ci, gives the following results : —
t.2 = 109
This method of ascertaining the twist is applicable to all
kinds of yarns. It enables that necessary, in the singles, to
balance a certain folding twist to be ascertained, or vice versa.
Adherence to this method would necessitate considerably more
twist, in the single yarn, than it is customary to apply, and
hence it would increase the cost and this without commensurate
return. In certain classes of yarns it is applied to some extent.
The application of the above formula is further illustrated by
the following example : —
Let the count of the single be 50, and twofold is made containing the usual
turns ^^2 X 4 = 20. "What twist would be necessaiy in the singles in order that
the completed twofold be in perfect balance ?
.•.[(x,/6020)(.y> = ^
_ , 20
V50y J V25
a;V50 = 465
X = 6*58, the single twist coefficient
or constant
The Eixg Doubling Fra^te.
Fig. 47 represents the gearing common in ring doubling
frames, A, Ai being the rollers, and L the driving pulleys, J the
tin roller, and I the tin roller shaft wheel, the train I, H, G,
E, El, D, Di, Ci, B, and Bi, being the trains of wheels con
necting the front rollers to the tin roller. K and K are the
spindles.
The following twist is obtained when the smallest sizes
of the change wheels are employed : —
The revolutions of the spindle per one of the roller, with the
smallest sizes of change wheels, are —
AND COSTS OF YARN
225
75 X 60 X 120 X 8
20 X 20 X 20 X IJ
= 480
and therefore the twist per inch inserted in the yarn, on the left
side of this machine, would be —
lii V 22 = 8727
whilst that on the right side would be —
480
21 X ^^ ~ ^^
The range of twist with 2060 the available sizes of top
Fig. 47.
change wheels, when the tin roller and the lower twist wheels
are both 20, is —
On the left side, from 8727, to 8727 X §!] = 2909 ■
On the right side, from 61, to 61 x fB = 203
With the available sizes of wheels for G, when the tin roller
wheel is 20 and C is 60, the twist per inch procurable, ranges
from
On the left side, from 2909, to ^^'^^ ^ ^^
On the right side, from 203, to
60
203 X 20
60
= 969
= 677
226 COTTON SPINNING CALCULATIONS
With the tin roller 40 and the other change wheels 60 and 60,
the twist would be —
On the left side, ^n = 4*89 twist per inch
On the right side, j^ = 338 twist per inch
r„, , ,. .. » ,. revolutions of spindle (actual)
The production per unit of time = 1—^, — ■ — r^ '
^ twist required
= inches per unit of time
Therefore with the spindles making 8000 revolutions per
minute (actual), and the counts 272* and twist coefficient 1'5,
the rate of production in hanks and ounces per spindle per
10 hours, no allowances, would be —
8000 X 60 X 10 = revolutions of spindle per 10 hrs.
8000 X 60 X 10 . , • ;n • 1A 1
=^^ = inches per spmdle in 10 hrs.
8000 X 60"x 10 , • ;ii • iA I
= = yards per spindle m 10 hrs.
45 vZ'g X 36 "
8000_x 60 x 10 ^ j^^^j^g , ^ .^^^^ .^ jQ j^^.g^
45 ^/l^ X 36 X 840
8000x60x10x16 ^ ^^^^^^ .^^1^ .^^ 10 1^^.^
45 V^X 36 X 840 X ^2_
This is assuming the yarn does not contract.
= revolutions of the roller per
45 \/^2 X If X ^ minute on the left side
= revolutions of the roller per
45 x/^2. X 2i X 2^ minute on the right side
"With the particulars of the frame as given in the figure, the
different top change wheels that would be applicable, in order
that the same turns may be put in the yarn made on both sides
of the machine, are as follows : The ratio of these change
wheels, left to right, should be as ^ : 1^, or 10 : 7, or 1 : 7.
The following exercises are based on the conditions obtaining
in Fig. 47 :—
AND COSTS OF YAKN 227
Exercises 1. What size of wheel Bj would give twist identical to that on the
left side with top change wheels 20 ?
2. Assuming B, and B 107 and 75, respectively, with the top change wheels
C, Cj alike and G, 60, whilst the yarn doubled is 260' ; what sizes of G would be
suitable for iising 270', 280% 290", the same twist coefiScient in each instance ?
3. Assuming the tin roller wheel 20 and bottom change wheel G 20, what
size of C and G^ would be necessary for 2120' on both sides, the twist constant
being 4'5 ?
4. Assuming that 2120', containing 35 turns per inch, is being doubled on
both sides, at what rates per minute should the rollers rotate ?
5. What twist per inch would be inserted when the 2^ inch roller is observed
to make 1 revolution per 70 of the spindle ?
6. If the twist is 80 turns per inch with a 60 lower change wheel, what size
of wheel will give 24 turns? Also, at what rate must the roller rotate per
minute in both instances, assuming the spindle makes 600 revolutions per minute ?
7. The top and bottom change wheels are 60 and 40 respectively, and the
present twist is 248 turns, but 258 are required : which change wheel would alter
to get the nearest to this, and what size of wheel would be necessary ?
8. If the twist per inch was 24*8 and the top and bottom change wheels, 60
and 40 respectively, are each changed for wheels three teeth less, what would be
the alteration in the twist ?
9. Give several sets of top and bottom change wheels which would give
identical twists to those obtained with : 20 top and 60 bottom, 21 top and 56
bottom.
Changes in the sizes of the tin roller shaft and bottom
change wheels, affect both sides equally.
Alterations in the twist by means of the top change wheels
must be made, on both sides, inversely to the changes in the
twist required.
The rate of the production is altered, by changes in any of
those wheels, in the direct proportion to the alteration. When
changing counts of yarns, and the twist, required, involves the
same twist coefficient, then the sizes of the wheels required are
inversely as the v'counts. Thus, if changing from 230' to
2 40% prese nt wheel : required wheel : : v^intended count :
V^present count.
When the wheels required for carrying out the change desired
at one or two of these points are not available, the results
desired may be obtained by changing at the other points in the
same proportion.
The speed of the spindles applicable for various counts
228
COTTON SPINNING CALCULATIONS
range from 3000 to 8500, according to the class of work. When
changing, ahvaj^s consider whether the new circumstances will
admit of or require a change in the speed of the spindles. Such
is made by altering the frame shaft pulleys or their drivers,
whichever be most convenient.
Slippage in Doubling Frames. — In doubling frames there is
usually considerable slippage in driving the spindles from the
tin roller, and this often results in undesirable variations in the
twist which the yarn contains. An idea of the extent of this is
contained in the following observed speeds in a ring doubling
frame in good working condition. This frame contained one
tin roller making 838 revolutions per minute and 8 inches in
diameter, the spindle wharves being 1^ inch in diameter. The
following were typical records of their speeds per minute : 5186,
5100, 5416, 5265, their calculated rate being 5950, and hence
the loss was 12*8, 14"3, 9"0, 11*5 per cent, respectively. This
is when neglecting the size of the spindle band. It will be
noticed that when the size of the spindle band is allowed for
in this instance, the loss will be almost «?7.
The Twiner Mule. — Fig. 48 contains particulars of the gear for
driving the spindles and drawingout scroll shaft in a twiner.
Fig. 48.
N, N are the strap driving the rim pulley M ; L is the rim pulley,
and LK the rim band driving the tin roller pulley J, K being the
rim band carrier pulley. The tin roller B drives the spindle
wharve A ; C and Ci are the tin roller wheels, shown in two
sizes, for driving the train D, E, F, G, H ; H is the drawingout
shaft clutch wheel. The other particulars of the above gear are
AND COSTS OF YARN 229
as follows :— Revolutions per minute of run shaft, 770. Rim
L, 1224 inches ; B, 6 inches ; J, 11 inches ; A, i inch diameters
respectively. C and Ci, 15 and 25; D, 80; E, 2040; F, 90;
G, 15; H, 68, teeth respectively. H makes 3;]^ revolutions
per draw in moving the creel out 72 inches. The twist change
wheels are : the tin roller 15 and 25, and the wheel E 20 to 40.
The rim pulley is seen, on inspection of this gear, to be the
medium for adjusting the speed of all the productive parts, and
the twist change wheels for altering the rate at which the yarn
IS introduced to the twisting influence.
If the examples relating to the spinning mule have been
understood, the following calculations will be understood.
Hence only one example is given in each set of these
calculations.
ExEKCiSE 1 Calculate the revolutions of the spindles per minute with con
secutive sizes of riras ranging from 12 to 24 inches in diameter.
diaiSter'''~'^'''°^"^'°"' ^''' """'"^^ °^ 'P'^^ ''''"' ^^'^ ''"^ '^ ^ '"<^^^«^ "^
11 X i
Size of rim . 12" 13" U" 15" 16" 17" 18" 19" 20" 21" 02" 93" oi"
Revs.ofspindle5760 6720 7680 8640 9600 10,560 "^ 11^520
permmute / 6240 7200 8160 9120 10,080 11,040
chan^rSstTStst^^ ''' '^''' ''' ''''' ''^^ ''' ^'^'S^ ''^^ ^^^
^^Emmj^IcBeyolntions of spindle per one draw and per 3f revolutions
3iix 68 X 90x 80x 6 , .
lE~x~W^<r25x^^ ~ l*^^ "^'^'^^ °^ '' inches
.. the twist per inch = ^ 58 x 68 x 90 x 80 x 6 x 8 _
68 X 15 X 40 X 25 X 72 X 7 ~ ^
When the tin roller wheel is ^
25 and the twist change is/ ^^ ^^ ^^ 37 36 35 34 33 32
The twist per inch is / ^'^'^ 127 1.34 143
I 118 124 1305 138 147
31 30 29 28 27 26 25 24 23 22 21 ^o
157 168 181 196 214 03 x
152 162 174 188 205 224
{
Exercise 3.Calculate the twist change wheel that will give the nearest to
23 5 turns per mch when the tin roller wheel is 15.
230 COTTON SPINNING CALCULATIONS
ExEKCisE 4. — Calculate the twist per inch with consecutive sizes of twist
change wheels ranging from 20 upwards, with the tin roller wheel 15.
Alls. Twist change wheel . . 20 21 22 23 ... 30
n, • , 1 / 375 342
Twist per inch. . . (3^.^ 3^.3 ^6 3
, 258 X 68 X 90 X 80 X 6 X 1 ^^ ,
Jiixamine. jr^ ^= ^77. ^^ ^5 _ = 39*4
^ 68 X 15 X 20 X 15 X 72 X I
Exercise 5. — If the twist change wheel 35 and the counts doubled 4,"', what
sizes of wheels would be required for 4f', "o"', ^', ^"% 1^^', when the same twist
constant is used ?
35 V^^
Example. — =^ = wheel suitable for ^\!^'
ExERCiSE 6, — Estimate the production in hanks per spindle and in pounds
per twiner of 1000 spindles per 10 hours ; the spindles to develop a speed of
11,000 revolutions per minute, and baching off and winding to occupy 5 seconds ;
the counts doubled are ^Q', "f', 5^', ^% "#', i^^^% and the twist constant 45 is
used. Allow 15 per cent, for loss of speed during twisting, and 15 minutes per
doff, the cops weighing 2 ozs. each.
Example. — 4f'.
/45a/^*x72\ 100
Seconds taken twisting per draw = I — tiaaa /^O of = 1004 seconds
Seconds per complete draw = 1004 + 5 = 1504
Time to make a cop in seconds = — "^^ ^^^ = 1504 seconds
^ 72 X 85
The above numerators = contents of a cop in inches
Time taken to make a cop and) _ 1 x 25 x 840 x 36 x 1504 15
doff in hours / ~ 8 x 72 x 60 x 60 60
= 5 hrs. 29 mins. + ~ hrs. = 5733 hrs.
bO
10 X 2 X 25
.'. production in hanks per spindle = K:noo tc. f = ^'45
.". i>roduction in pounds per twiner = ^.^ =218 lbs.
Changing the size of the rim affects the speed of all the
parts concerned in twisting and introducing the yarn, and there
fore alters the time occupied, in making this movement, in direct
proportion ; the time taken to back off and wind remaining
unaffected.
Changing the twist change wheel alters the twist through
affecting the rate of movement of the carriage, in the direct
proportion to the change made in the wheel. This alters the
AND COSTS OF YAPyN 231
rate of the carriage movement inversely to the twist, the pro
ductive rate being affected in the proportion which this altera
tion affects the period of twisting.
ExAMPLK.— Assuming a draw is made in 1504 seconds, when the twist
change wheel is 35, and of this 50 seconds is the time occupied in backing
off and winding ; the following alteration would arise in the event of employing a
23 twist change wheel : —
1004 X 35 . .
20 ~ ^^^^ ^^^ seconds occupied in twisting
/. time per draw = 1757 + 5  2257
The rate of production is therefore altered in the terms of
15'04 : 2257 = 0'666, and not in proportion to the change in
the wheels, 0657.
Costs of Yarn.
The following are given as representing about the average
costs of the various items of expenditure in SouthEast
Lancashire mills in the production of mule yarns of medium
count from uncombed cotton when spun from single roving :
Cost in pence per
spindle per annum.
Banding — Twine — Rope 05
Carriage on cotton and other materials 2*3
Coal 375
Taper 015
Cleaning cloths — Engine packing — Brushes 0*25
Leather and cloth for rollers 05
Belting and its accessories 025
Lubricants 0'9
Repairs : Mill buildings — Machinery and upkeep : basis )
1 per cent, at 24s. per spindle per annum j'
Gas and water lO
Rates and taxes 20
Stationery — Telephone — Exchange — Railway tickets — ■!
Stamps — Printing and sundry office expenses J
Sundry stores 05
Insurance 045
Interest at 5 per cent, at 25s. per spindle 150
Depreciation at 4 per cent, on 24s. per spindle .... 1152
Wages 360
8064
Percentage of wages to other expenses ... 45
232 COTTON SPINNING CALCULATIONS
In order to ascertain the cost of producing yarn wben the
production and the inclusive expenses per spindle are known,
the following is the course usually followed : —
To the cost of the cotton at the card delivery add the cost
of production, per pound, and deduct the sum received, per
pound of yarn spun, for the waste.
The rate of the production per spindle in the SouthEast
Lancashire district does not vary considerably. The range is
given on p. 204.
In costing it is usual to disregard the loss arising from
waste after the card, because this item is about balanced by the
regain in conditioning. The value of the waste is assessed at
2^ per cent, of the cotton price ; this is considered a fair value.
Example of the cost of 28" T. made from Middling American cotton at 6d.
per pound.
Cost in pence
per pound.
Working costs per spindle per annum SOGi \
Production per spindle per annum, based on 50 „.;, k^ [ = 1413
working weeks per year and 32 hanks per week " „ —
Cost of the cotton delivered at the card delivery,
allowing 10 per cent, for loss, ^ — "'"'
8083
Less value of the waste 015
,, cost of raw cotton 60
615
Nett cost of spinning 1 933
Add : cost of selling and discounts 3i per cent on selling price.
Example 36' T. from F. Middling American cotton at QWd. Production,
30 hanks per spindle per week.
Cost in pence
per pound.
Working costs per spindle per annum, 8064 ^ _ 80*64 x 36 _ i.qok
Production per spindle per annum, 50 x 30 hanks / 30 x bO
Cost of the cotton at the card delivery, allowing
10 per cent, loss 6*844
8*779
Less value of the waste 0*154
„ cost of the cotton 6*16
6314
Nett cost of spinning 2465
AND COSTS OF YARN
233
Example 60' T. Fair Br. Egyptian at dd. per pound.
Working costs per spindle per annum 80'64
Production per spindle per annum ^ X 50
Cost of the cotton delivered at the card 10 per
cent, wasted, ' — ^t, —
Cost in pence
per pound.
= 4032
100
14032
Less value of the waste 0*225
,, cost of cotton 00
9225
Nett cost of spinning 4 807
The Approximate Costs of Yars when Spun from Single Koving, the Basis
BEING 8064 Pemce Cost per Spindle per Annum = 161 Pence per Spindle
PER Week.
t
a>
<» 1
a>
<D
^
^tn
1
°.S
fcoS
CO
"(G
a
a°
II
la
=3 OJ
P.5
"I.
Count and
description
of yarn.
at
.2 c
II
■30
2 &
Suitable cotton and
grade.
Price of cotton at t
of compilatio
=1 ■
?^ S "
If
" 3
aa
l§
*" is
Jl
II
•a s
P
1 °
to o
■£ s
o o
Prime cost of yarn i
per pound.
Margin between
cost of yarn and
the raw cotto
1
^ G.O. American!
16 W.
34
, /G. Broach >
2\G.Tinnevelly)
555
12
631
0137
076
6933
1383
16 T.
34
G.O. American
571
12
648
0142
076
7098
1388
16 T. super.
33
s.L.M. „
595
11
668
0149
0783
7314
1364
20 T.
34
b.
586
11
6o8
0147
095
7383
1523
20 W.
34
G.O.
571
12
648
0142
095
7288
1578
24 T.
34
s.L.M. ,.
595
11
668
0149
114
7671
1721
24 W.
34
f.G.O.
581
12
66
0145
114
7595
1785
SOT.
32
b.M.
605
11
68
0151
115
7799
1749
30 W.
32
s.L.M. „
595
11
668
0149
115
7681
1731
32 T.
30
M.
609
10
677
0152
172
8338
2329
36 T.
29
f.M.
62
10
69
0155
20
8745
2545
36 W.
31
b.
605
11
68
0151
188
8529
2524
40 T.
285
G.
631
10
70
0158
220
9102
2792
42 W.
285
8. „
615
10
683
0154
238
9056
2906
50 T.
26
M.F.
655
10
728
0164
31
10216
3666
50 W.
26
G.M.
631
10
70
0158
31
9943
3633
GOT.
23
j Special select
I grades only
60 W.
24
M.F. American
655
10
728
0164
403
11146
4596
In those spinning mills preparing the yarn from double roving,
at the spinning machine, the cost of the working expenses are
234
COTTON SPINNING CALCULATIONS
greater than those previously given. This has been ascertained
to approximate VI 2(1. per mule spindle per week.
Thus, 50^ T. from double rove, and produced at the rate of 25*5
hanks per mule spindle per week, will cost in working expenses —
1 72 X 50 „.^_ , ^
— ^^ — = 3"37f<. per pound
and 60' T. at 23*5 hanks per spindle per week —
172 X 60
235
= A' id. per pound
The AppiixiMATE Cost of Yarn spun from Double Eoving as per Data
PREVIOUSLY GIVEN.
is
o
o
ai
<U 1
.3 c
t>
a
lid
a,
a
cu .
t .
■"SS
.
13
U
IM □ ^
0! B
CO ^
0) >>
12°
Count and
description
of yarn.
5
as,
Suitable grade of
cotton.
^ .2
c a
o r:;
8S
»* o
o
a 0.
2 =>
If
o2?
13S§
.£"S
1 p.
Jog
■3Ss
a; M
SI P.
9
1
CM
(
0^
° S
V
2
PM
S^2
1 G.O.American
16 \V.
34
, /Broach G. >
* \Tinnevelly G.
555
12
631
0137
080
6978
1428
1
16 T.
34
G,0. American
571
12
648
0142
0805
7143
1433
16 T. super.
33
8.L.M. „
595
11
668
0149
083
7361
1411
20 T.
34
b.L.M. „
686
11
658
0147
101
7443
1583
20 W.
34
G.O.
571
12
G48
0142
101
7348
1638
24 T.
34
s.L.M. „
595
11
668
0149
122
775
18
24 W.
34
f.G.O.
581
12
66
0145
122
7675
1865
SOT.
32
b.M.
605
11
68
0151
161
8209
2209
SOW.
32
s.L.M. „
595
11
668
0149
161
8141
2191
32 T.
30
M.
609
10
677
0152
184
8458
2368
S6T.
29
f.M.
62
10
69
0155
2 35
905
2875
S6 W.
31
b.M.
605
11
68
0151
20
865
26
40 T.
285
G.M.
631
10
70
0158
241
9252
2942
42 W.
285
s.M.
615
10
683
0154
253
9206
3056
50 T.
26
M.F.
655
10
728
0164
331
10426
3876
50 W.
26
G.M.
1 Peeler, Baders,!
631
10
70
0158
331
10152
3842
60 T.
23
JBoweds, or super >
I Orleans or Texas)
—
10
—
—
—
—
60 T. super
( Ditto (double j
\ rove) j
American.
60 W.
24
M.F. American
655
10
728
0164
403
11416
4866
50 T.
255
Egy. G.F.
9
11
101
337
0225
1324
424
50 W.
26'5
U. Egy. F.
8/5
11
92
325
0204
1225
407
60 T.
235
Egy. G.
lOJ
10
1125
44
0253
1540
527
60 W.
25
U. Egy. G.F.
9fB
11
103
413
0229
1420
502
TOT.
205
jEgyG. )
\i „ F.G.F./
lOi
10
1153
588
0259
1715
677
AND COSTS OF YAKN
235
■i
, J
P4
<a
*■§
•K 3
5S
p< .
0. •
^8^
Count and
description
of yarn.
S
Suitable grade of
cotton.
as
•o .
§1
sa
ble percentage
up to carding h
f the cotton pas
ding head per po
ated value of
made up to and
iided in carding.
S 3
13
cost of yarn s
pence per pounc
n or difference
the price of the
d prime cost of y
1
s
II
Cost
the car
Estim
waste
cl
^1
§2
III
TOW.
225
U. Egy. F.G.F.
^
10
110
535
0247
1610
622
SOT.
185
Egy. G.
ni
10
125
744
0281
1966
841
SOW.
195
U. Egy. G.
10^
10
1136
705
0253
1816
629
90 T.
170
Egy. F.
111
9
1305
91
0297
2185
997
90 W.
190
U. Egy. F.
lOi
10
114
815
0256
1930
905
100 T.
150
Egy. F.
lOi
10
1305
114
0297
2422
1334
Combed Qua
lities
—
Cost of cot
at the com
head.
*
*
SOT.
19
Egy. F.
111
10+18
164
/ 725
1 + 09026
2951
+107 /
231876
113151
90 T.
175
"
Hi
10+18
164
f 885
1+09026
02951
+107 /
247876
129151
100 T.
160
>»
Hi
10+18
164
/ 1075
1+09026
02951
+107 /
266876
148151
The plus items in columns marked * refer to the extra cost through the combing pro
cess. The particulars of these are given on p. 239.
The productions per spindle are given on p. 204.
Costs of producing Yarns by Ring Spinning. — The cost of
preparing the cotton up to the roving for ring spinning is
greater than for mules. In the roving stage the cost is from
25 to 33 per cent, more on account of finer roving required.
This necessitates more machinery for preparing the roving.
The costs of labour in the spinning process, when producing the
classes of yarn for which ring frames are most adapted, is in
some cases as much as 50 per cent, less than in mule spinning
process. Besides the extra preparation, a better class of cotton
has to be used, and even then the yarn is not in a convenient
form for transport when it leaves the spinning machine. The cost
for winding the yarn in a convenient form for sale is consider
able. This latter item is dealt with in another part of this work.
The following are the yarn and cotton quotations for
June 29, 190G. These are given for comparison with the
estimated costs contained on the foregoing pages.
236
COTTON SPINNING CALCULATIONS
From the
"Manchester Guardian," June 30, 1906.
Good Bhow
nuggar.
Per pound.
20^ water
twist.
Per pound.
Middling
American.
Per pound.
32" cop
twist.
Per pound.
Fully good
fair Egypt.
Per pound.
60' twist
Egypt.
Per pound.
1905.
d.
d.
d.
d.
d.
d.
September 1
5
8i
583
S^
^li
13
8
4i
8i
556
8i
7i
ISg
„ 15
4ii
8i
550
8i
7i
133
22
413
8i
564
8i
7}i
13i
29
4i
8i
574
8i
vii
13i
October 6
4U
8J
541
8^
7}^'
131
„ 13
^W
8
532
8J
7}i
13J
„ 20
^W
8J
542
8J
7ii
13i
,, 27
m
8i
571
Si
8
131
November 3
4ii
8i
591
8i
81
131
10
4{i
8^
616
8J
Si •
in
17
4}i
81
593
8
81
14J
2i
4{i
SI
611
9
81
14J
December 1
4i
m
616
81
81
141
8
5
9
642
9^
8ft
14i
15
47
8?
629
%
81
14i
„ 22
4}i
8f
631
9
81
141
29
H
8U
624
9
81
141
1906.
January 5
Iji
81
623
9
8k
141
12
^
81
609
m
8tI
141
„ 19
4
8i
630
»i
81
141
„ 26
4i
8i
612
8f
8i
14i
February 2
^
8i
599
8i
8?,
14
9
45
8.1
587
8i
8\h
15J
16
^
8i
591
8i
81
15i
23
4
8i
573
81
81
15i
March 2
41
8,^B
578
8i
9V8
15i
9
^
8t*8
592
8
9
151
„ 16
^
8t^s
577
81
91
15i
„ 23
n
8.1
584
81
9,'b
16^
„ 30
n
8i
603
8
91
15i
April 6
41i
81
610
9
91i
161
„ 12
4{i
8i
616
9
101
i6i
» 20
4U
81
604
9^
lOi
16i
„ 27
4^
8}^
607
9J
lOi
16i
May 4
m
8?
608
9
101
16i
„ 11
43
8
618
9J
101
16i
„ 18
4i
8Ji
625
%
101
i6i
„ 25
43
8?
620
91
101
i«i
June 1
4^4
8?
602
91
10
16i
» 8
41^
8
601
91
10
16i
„ 15
4^
8
607
9i
101
16^
„ 22
^
8^
612
n
IOi'b
16^
„ 29
^
8:1
610
9i
lOi
16J
AND COSTS OF YAEN
237
From the "Cotton Factory Times," June 29, 1906.
PRICE of medium tarns IN PENCE PER LB.
Count.
416
1028
20
30
32
36
34
40
50
60
70
80
AVeft.
89
013_Q 9
9i'69H
9^610
1213
1415
17H8i
Twist in cop. gea^j.
^T6 ^'iS
9TV10i
9ft
12^
lOi
llf
13i
Bundle.
8F9i
9=110'
lOJlll
llM2i
1 Twofold.
Bundle.
Cop.
—
—
9H0i
9f'B10^
loiiii
10tV"t^b
11H2^
lli12i
Uf^li
13^131
—
EGYPTIAN YARNS.
60
15A1G^
—
—
17121
17i 20^
70
16H7i
— —
—
19i24
19I23J
80
171 18i
— —
—
21i26f
21126^
90
18i20i
—
—
—
23^30
23^29^
100
20i22J
—
25H3i
25i32i
Cotton, Official Quotations.
June 29, 1906.
American
G.o.
573
American.
L.M. Md.
593 611
G.M.
G33
F.G.M.
643
M.F.
661
M.F.
Fair.
G.F.
Pemain
Ceara
Paraiba
Maceio
578
585
577
*o79
618
623
615
*617
644
645
639
*639
Fair.
Egyptian.
G.F.
F.G.F.
Gd.
Egyptian, brown . .
Ditto, upper . . . .
! 8?
91
8}i
lOi
9e
*9i
Egyptian, brown, fine, 11^.
Ditto, upper, fine, *10.
Egyptian quotations do not refer to Bamia or Upper Egypt cotton.
Nominal.
238
COTTON SPINNING CALCULATIONS
Tnd
ian.
F.F.
G.F.
F.G.F.
Gd.
F.G.
Fine.
Broach ....
_
_
5i
5U
5Vb
Bhownuggar . . .
—
*4i
*ik
*4i
*43
HI
No. 1 Oomra . . .
—
*n
*41
*4
*43
HI
Bengal
—
m
Q2S
^35
3§i
ii.
i^%
Tinnivelly . . .
—
5A
K3
^8
5^
—
Bengal, Superfine, 4.
* Nominal.
The Costs of Power available at the Machines, in a Spinning Mill.
Basis : EDgine and all plant connected therewith to develop
1000 I.H.P.
Engines, boilers, and economizers — Pumps and all the
necessary connections — Shafting and ropegearing — Keservoirs,
land, buildings, and approaches at £15 per I.H.P. = ^£15,000.
Piatio of above costs —
(a) Engines, 35 per cent.
(b) Boilers and economizers, 20 per cent.
(c) Shafting and ropegearing, 15 per cent.
(d) Reservoirs, land, buildings, and approaches, 30 per cent.
Woi'king Expenses ; — £ «. d.
Depreciation and upkeep inclusive on (a), {b), (c), at 10
per cent, per annum 1050
Depreciation and upkeep on (fZ), at 2i per cent. ... 112 10
Interest at 4 per cent, per annum on (a), (b), (c), {d) . . 600
Stores at £0*25 per I.H.P. per annum 250
Coals : 2 lbs. per I.H.P. per hour, at 7s. Qd. per ton . . 1 47G
Insurance (fire, accident), at 10s. per cent, on £12,000 . 60
Labour 400
3948 10
Cost per I.H.P. per hour in pence (50 X 55 working hours) —
39485 X 240
50 X 55 X 1000
The inclusive j)ower required in spinning mills, is about
AND COSTS OF YARN 239
1 I.H.P. per 63 spinning spindles in mills containing all mule
spmdles, and about 1 I.H.P. per 44 spinning spindles in mills
contammg all ring spinning spindles.
The power required to drive the various machines
Hopper cotton pullers and feeders . . 1 LHP. per machine
Simple Creighton opener 2^
ylfW ; For each extra cylinder or beater 2
For each lap machine . . 2
Jb or automatic feeders . l
T7I • • • • ^ J) ,,
i^ or pneumatic cleaning trunks. 1^
Other types of openers as above.
Scutchers, single with lap machine .31
Cards ^~
Sliver lap Q.g
Eibbon lap I'O '
Comber, per combing head .... 01
Drawing frames, 5 dels, per .... 1
Slubbing frames, 45 spindles per . . 1
Intermediate frames, 60 spindles per . 1 '^
Eoving and ring frames, 80 spindles per 1
Mules, 110120 spindles per .... 1 '
The Cost of Spaces in Spinning MiUs.This works out at about
2s. per square yard per annum, inclusive of lighting and rates
The Extra Cost when the Process of Combing is introduced.—
The productive capacity of a machine of the Heilmann type, as
made by the principal makers, ranges from 300 to 500 lbs. per
machine of eight heads.
In the following estimate moderate working conditions have
been assumed, the production being taken at 400 lbs. per week
of 551 hours per machine, and the waste extracted at 18 per cent.
The quantity of cotton required for treatment would there
in , 400 X 100
fore be ^ — = 488 lbs.
Assuming a wastage of 2^ per cent, between the combing
and carding stages, the amount of carded cotton required per
400 lbs. of combed would be 500 lbs. If a loss of 5 per cent is
240 COTTON SPINNING CALCULATIONS
allowed for in the card, then '^ — ^  — = weight of cotton
required in card laps, 527 lbs.
And if 5 per cent, loss be allowed for in opening and scutch
,, 527x100 ^^^,, , ,, . , ,^^„
mg, then, ~ = 555 lbs. of raw cotton required per 400 lbs.
of combed cotton.
When combing is not in vogue this amount would be less
to the extent of
.^. /400 X 100 X 100\ ^^. ,,. ,,, „
Assuming the production of the card 350 lbs. per week, the
extra carding machinery per 400 lbs. of combed sliver would be—
(500  400 = 100 lbs.) = ^^
Taking the productive capacity of a scutcher at 8000 lbs., and
that of the opener at 16,000 lbs. per week, respectively, the loss
being 2 and 3 per cent, respectively, then the extra scutching
and opening machinery would be —
106 . 109
scutchmg,gQQQ; opening, jg^
The extra labour involved, upon the following basis, would
cost as follows : —
Cost of treating 16,000 lbs. of scutched cotton.
Mixing, opening and scutching, wages inclusive, £3 15s.
The cost, therefore, of treating the extra cotton required (106
lbs. scutcher lap) would be —
375 X 240 X 106 _ . q ,
16000 ~ ^*^''
Therefore the extra cost on account of labour under this head
would be —
5*9
Tjrx = 0"01475(7. per pounds of combed cotton
AND COSTS OF YARN 241
Taking the labour in carding at 28s. per 14 cards inclusive,
the cost per pound of combed sliver would be —
— — ^^ = 0*01701(?. per pound of combed sliver
350 X 14 X 400 ^ ^
The costs of labour involved in preparing the cotton for and
in combing :
One person, at 18s. per week, to attend the sliver and ribbon
lap machines. Production, 2450 lbs. per week.
— r— — ^^ — ~r— = 0108fL per pound of combed cotton
2450 X 400 ^ ^
One person, at 20s., per six combing machines inclusive of
cost of overlooking —
20 X 12
n 77^ = O'l^^ per pound of combed sliver
b X 400 ^ ^
Other expenses :
Costs on account of the machinery —
Approsimate Proportional cost
coat. per combing
machine.
£ £
Cotton puller 140 0*92
Opener 300 197
Scutcher 180 236
Card 100 286
Silver lap 60 120
Kibbon lap 140 280
Comber 170 170*0
Total . . . £24385
Eepair and upkeep at Ti per cent, per annum oii\ _ n,Q o
£24385 ~ j  ^1«'289
Depreciation at 7i per cent, per annum on £243*85 = 18'289
Interest at 5 per cent, per annum on £243*85 . . = 12192
£48770
Cost, under this head, per pound of "1 4877 x 240
I = Z^\/\"r = 0585^/.
combed sliver j 50 X 400
242 COTTON SPINNING CALCULATIONS
Extra stock of cotton in process through combing, say 400
lbs. per combing machine of 8 heads.
Value of this at 8d per lb. = £133.
Interest on £13'3 at 5 per cent, per annum = £0'665
Therefore cost per pound of combed sliver = ^ 77^ = 0008
^ ^ 50 X 400
Extra cost on account of space, at 2s. per square yard per
annum —
Proportional area :
square yards.
Space per combing machine (400 lbs.), 15 square yards = 150
ribbon lap ,, (2450 lbs.), 15 „ = 2*5
sliver „ 12 „ =20
195
19"5 X 2 X 12
Cost per pound of combed sliver = — 7^ ,^^ = 0*0234f/.
^ ' 50 X 400
Extra cost on account of power, at 0"344(/. per I.H.P. per
hour —
Proportional
power.
Comber (400 lbs.)  I.H.P. 075
Eibbon lap machine (2450 lbs.) 1 ,, ^
Sliver „ ,, h „ f
The extra cost on account of the waste extracted —
Waste at the combing stage, 88 lbs.
Extra waste at the previous stage, not returnable to mixing,
555  444 = 111 lbs.
Therefore 111 + 400 = 511 lbs. the amount of raw cotton
required per 400 lbs. combed, and therefore the cost of the
cotton per pound at the combing head on this account is —
Sd. X 511
400
= 10'22(^?. per pound
AND COSTS OF YARN 24
Summary of Costs.
Per pound of
combed sliver.
Labour : On account of extra mixing, opening, and scutching . 0'01475
carding 001715
„ Preparing the comber lap 0"108
„ Combing 0*1
Machinery and upkeep, repairs, and stores 0'585
Extra stock of cotton 0008
Space 00234
Power 00473
Tlie total expenses nominally unaffected by changes in cotton
values 09026
Value of the cotton at the combing head 1022
111226
Cost of raw cotton 80
Extra cost of combing (value of the waste reserved) .... 31226
Allow for value of the waste I'O
Nett extra cost of combing 21226
80^ — The cost of combing, when the raw cotton costs 11,^':/.
per pound and the waste at this stage is 18 per cent., and
10 per cent, previous, allowing 50 per cent, of the cotton value
for comber waste sold —
11"(/
Value of the waste = 18 per cent. 1 lb. at — ^' = 1'07(/. per pound
The extra waste made in scutching and carding will be
worth about 2.} per cent, of the cotton price per pound —
The cost of the cotton at the combing head is therefore
HZ X 100
72
= 164(?.
The cost of spinning 80' uncombed on the basis of 19 hanks
produced per spindle (see p. 235) —
244 COTTON SPINNING CALCULATIONS
172 X 80 _.,,.,
The other expenses of combing —
09026fL per pound
Hence, assuming the waste made at the comber is sold at a
price per pound equal to half the cost price of the raw cotton,
then the extra cost of combing in this case would be —
18 per cent., 1 lb. x 'Tjd. = 0'T2d.
The cost of combing = 111226  B'O  072 = 25026(/.
per pound 11*1226
1022
The expenses exclusive of the loss in waste .... 0"9026(Z.
1022
80
The cost on account of the waste extracted, assuming
it has no value 2*22
Costs of 80' combed as per tabulated data on p. 235. The
cost of combing and spinning when the raw cotton costs llld.
per pound.
The cost of spinning (uncombed) as per tabulated data on
p. 235—
172 X 80 _^ „ „ ,
— = 7 25 per lb. of yarn
The cost of the cotton at the combing\
head, through waste loss, neglect[= 164 ,, ,,
ing value derived from sale ]
The expenses of combing, excluding] aoaoa
waste f ^"^^^^ " "
AND COSTS OF YAEN 245
Less the value of 18 per cent, waste)
made in combing (at half price of = 107 per lb. of yarn.
raw cotton per pound) I
Less the value of waste made prior to )
combing (at 2^ per cent, on the = 0295
raw cotton price) J " »»
Cost per pound of yarn = 231876f?.
Example of the method adopted in estimating the cost given below
Cardincj : 850 lbs. per card —
Cost per pound
Labour: 2s. lid per card, inchisive of over .s. d. y'^"'"*!'""
looking and card head tenter 2 11 = 0043^
Power: 1 H.P. per card at 034rZ. per hour . 1 GT = OQ^^O
Machinery: £100 per card, 10 per cent, for
loss, depreciation, and upkeep 4 1 = 0057G
Space : 1058 square yards per card at 2s. per
y^'"^ 518 =00061
8 1188 01289
The cost at the drawing and subsequent stages is given per
productive unit, on account of the wide range of variation in
then production. In order, therefore, to estimate the cost per
pound, the production per delivery or per spindle is required.
The production can be ascertained in the manner explained in
other parts of this book.
The Departmental Costs in Spinning Carded aualities of Yarn —
In estimating these costs uptodate conditions have been taken
as the basis. The cost of space has been assessed at 2s. per
square yard per annum, inclusive. But no allowance has been
made for waste.
MixhujCotton and W.ufe StormjeOpenh.g—ScutcU
ruj
Cost in pence por pound
T , of yarn spun.
L'ibonr ^,^^^
l^'^f. 00255
^^^^^^'"^^•y 00144
^"^^^^ 000317
007007
246 COTTON SPIKXIXG CALCULATIONS
Carding —
Cost in pence per
card per week.
Labour 35'0
Power 187
Machinery 490
Space 5'18
10788
Drawing —
Cost in pence per
delivery per week.
Labour 12'5
Power 3'75
Machinery 160
Space 07G
0. 9,.
01
Fly Frames :
Sluhber —
Cost in pence per
spindle per week.
Labour 3'25
Power 0415
Machinery 087
Space 0195
4730
Intermediate —
Labour 175
Power 031
Machinery 0575
Space 01
2735
Roving —
Labour 088
Power 0268
Machinery 04
Space . " 0067
1615
Mules —
Labour 045
Power 0156
Machinery 015
Space 0075
0831
AND COSTS OF YARN 247
Rings —
Cost in pence per
ppindle per week.
Labour 0*25
Power 0235
Machinery 0216
Space 0029
0730
Twining —
Labour 066
Power 0113
Machinery 012
Space 0067
0960
In twining the waste and costs of steaming and unpacking
and packing the yarn must be added.
The waste is sometimes a considerable addition to the cost.
Twice the labour cost should always more than cover all
expenses.
Ring Doubling —
Cost in pence per
spindle per week.
Labour 05
Power 0312
Machinery 025
Space 0044
1106
Other expenses — namely, waste, travellers, grease, spindle
banding, bobbins — are considerable. The "waste" should
always be considered as a separate item ; 0*25 is a reasonable
allowance for the rest.
Doubling Winding, or Winding.— The production per spindle
is considered good at 75 per cent, of the calculated without
allowances.
The number of spindles attended by one person may be
estimated from the rate the winder can piece up as follows:
Assume the winder can piece up at the average rate of 12
ends per minute, and that in the course of unwinding each
ring bobbin end breaks twice, allowing 25 per cent, for the
spindles stopped through incidental breakages.
248 COTTON SPINNING CALCULATIONS
On this assumption the production per winder will be —
55 hrs. X 60 mins. x 12 x ounces contained on each bobbin
2 X 16
= pounds per winder
Number of spindles per winder
_ pounds per winder j_ ok
~ 75 per cent, calculated production per spindle ^
A Method of Ascertaining the Production of Reels. — The pro
duction of 40hank reels in 55 hours when worked at 250
revolutions of the swift per minute, allowing two stops per
bobbin unwound, and 5 seconds for each stop, the bobbins
containing 0*75 oz. of counts 20^ the time lost in tying and
doffing being 3 minutes.
The time taken to fill the reel (40 hanks) if no stoppages
80 X 7 X 60
= ?r^rpr seconds
ZoO
The number of stops in filling the reel
840
075
^ X 840 X 20
lb
X 2
The time lost in filling the reel through stopping
840
^ X 840 X 20
lb
X 2 X 5 X 40 seconds
The time taken to fill and doff, allowing two stoppages per
bobbin unwound
^ 80 X 7 X 60 840x16x2x5 xJO
250 "^ 075x840x20 + ^^^
= 1344 + 427 + 180 seconds = 1237 minutes
The production per week in pounds
55 X 60 , _„^ ,,
AND COSTS OF YARN 249
The weekly earnings of winders and reelers vary from 14.s.
to 24s. per week, and the cost per pound of yarn treated,
varies, in this work, comparing districts, more than in any
other section of the spinning mill.
The numerous departmental wage lists and the difference
in these, in the various districts, do not admit of the costs in
wages being treated, in a work of this kind, in any other manner
than that adopted.
Although these lists differ on paper, competition has resulted
in this difference in the costs— being that approaching the
vanishing point, when reduced to a basis embodying quantity
and quality of production.
INDEX
Attenuation. See Draft
Backingoff and takingin motion, 157,
IGO, 178
Bale breakers or cotton pullers, 1525
gearing in, 15, 21
hopper type of, 15, 2125
Belt and rope driving, 12
Brooks and Shaw's type of differential
(slubber frame), 138140
Builder wheel in mule, 168
ascertaining suitable, in
changing counts, 168
changes in, 168
in ring frame, 210
Building motion, 159, 178
Card calculations, 56
conditions controlling output of, G6
Carding department, proportions of
machinery in, 141
parts, conditions respecting actions
of, G(J
functions of lickerin, cylinder,
flats, doffer, 6668
Combing machines, 84101
detaching rollers, 87
drafts in, 89, 97
adjustment in, 99
lap rollers, 87
Nasmith and Heilmann ma
chines compared, 95
Nasmith's, gearing in, 848(5,
9597
productive, 93
Cone drums, use of, in fly frames, 126
Constants for twist —
normal, for roving, 111, 112
standards for single yarn, 161, 214
for folded yarn, 216
crochet, 217
fish netting, 217
knitting yarns and embroidery, and
for mercerizing, 217
sewings, 217
Costs of yarn, 231247
by mule spinning, 231
by ring spinning, 235
Cost of yarn extra when combing intro
duced, 239
departmental, 249
winding and reeling, 247, 248
of power available in mills, 288
of space in spinning mills, 209
Cotton, names applied to. in its prepara
tion, 71
system of counting, in its stages of
preparation, 71
Cotton pullers or bale breakers, 1525
gearing in, 15, 21
■ hopper machine, 15, 2125
Count, 71, 117
changes in, in mule, 157
~ in ring frame, 209
of laps made by openers and
scutchers, 52
— — changing, ascertaining suitable
building wheel in, 168
of intermediate roving, 150
of sliver at the drawing frame, 151
of slubbing rove, 150
Counting cotton, system of, 71. See aho
Count
Curtis and Rhodes type of differential
(roving frame), 129
Differentials, principal types of, 127140
Brooks and Shaw's (slubber
frame), 138140
Curtis and Rhodes (roving
frame), 129
Fallows motion (slubbing
frame), 135
Tweedale (intermediate frame),
133
use of, in fly frames, 120
Dobson's ord. mule, 177
gearing in, 177, 195
doublespeed and hastening motion,
190
Draft, 19, 35
between various parts, how ascer
tained, 62
how altered, 64, 65
changes in total, 69
in combing machines, 89, 97
252
INDEX
Draft in drawing frames, 103, 107, 109
iu fl} frames, 142, 151 i
in mules, 157
in openers, 3i40 '
in ribbon lap machines, 82
in ring frames, 209
in scutchers, 4347 ]
in shver lap machines, 78
Drawing frame, 102
calculations relating to, 103
coiling of sliver, spacing, 105
count of sliver at, 151
drafts, 103, 107, 109
effect of atmospheric changes,
102
system of gearing rollers, 108
rollers, analysis of action of, 152
functions of, 153
I)river and driven wheels, eflect of
chaoging, 9, 10
Driving, rope and belt, 12
speeds and sizes of driving
surfaces, 1215
Equilibrium, state of, in yarn, 223
Fallows t\'pe of differential (slubbiug
frame), 135
Fillet, length and preparation of, re
quired to cloth cylindrical surface, 75
Flats, in cards, functions of, 67
rate of movement of, 67
Fly frames, 110152
■ — consequences of altering value
of cone train, 114
cone drums, use of, 126
count, 150, 151
changes in. 118
draft, 142,151
alterations in, 117, 118.
119
dififerentials, principal tvpes
of, 127140
use of, 12G
drawing rollers, action of,
analysis, 152
gearing in, 112115
hank indicators, 154
" preparations," 141
■ processes, three stages, 141
■ production in, 145
rate of winding and spacing
of coils, 120
speed of spindles, 149
speeds, 115, 140
twist constants, 111
twisting in, object of. Ill
winding in, obtained bv bob
bin, 125
Gain, or drag, 161, 164
changes, 166, 186
Gearing iu bale breakers, 15, 21
in carding machines, 56
in Dobson's doublespeed and
hastening motion, 190
in draw frames, 103
in fly frames, 112
in mules, 156
— — Dobson and Barlow's, 177,
195
Piatt's, 183, 191, 192
various trains, 162, 177190
in Nasmith combing machine, 84
iu openers, 25
in Piatt's knockingoff motion, 51
in ribbon lap machines, SO
in ring frames, 204
doubling frames, 224
rollers, 108
in scutchers, 41
in sliver lap machines, 76
in twiner mule, 228
various trains of, calculations and
other particulars of. 161177
Halflap, 75
preparing, 75
Hank indicators, 154, 200203
Hastening motion, 161
Dobson's, 190
Hetherington mule, 162
Hopper type of cotton puller, 2125
gearing in, 21
usefulness of, 24
Hunting cog measuring or length
motion, used in openers and scutchers.
48
advantage of, 50
Indicators, hank, for frames and mules,
158,200203
length, 200
speed, their use, 198
Jacking or ratching motion, 158. 162
Piatt's, 191
t Trelfall'e, 193
' Knockingoff motion in scutchers, Piatt's,
I ^^
Laps, 71
i changes in weight and count of,
made by openers and scutchers,
52
' length of, 4951
rollers, 87
Length and hank indicators, 200203
1 stop motion, 150
INDEX
253
Motiou, rate of, calculating, when tooth
gear employed, 1
transmission of, 115
Motions —
backiugoflf and takini'in, 157, 1(J0
178
building, 159, 178
doublespeed, 159, 19U
hastening, 161, 190
jacking or ratching, 158, 162, 191, 193
knockingoff, 51
length stop or full bobbin, 156
receding, 158, 178
roller delivery, 160
twisting, 159
Movement of tooth wheels, direction of,
Mules, 156204
calculations, 156, 183
compared with ring frame, 213
costs of yarn, 231
counts, changes in, 157
drafts in, 157
Dobson's and Barlow's, 177,190, 194
gearing in, 150
various trains of, 162167
Hetheriugton, 162
losses in driving in, 194, 196
motions, 157161
Piatt's, 183, 191, 192
productions in, 204
proportion of machinery forming a
"preparation," 142
Trelfall's, 193
twiner, 228230
twist per inch, 197
wheel train values in, conditions
governing changes in, 161
various, and range in
size of wheels, 177190
Openers, 1540, 4856
changes in weight and count of
laps made by, 52
drafts in, 3440
gearing in, 25
hunting cog measuring or length
motion used in, 48
productions, speeds, and controlling
factors, 54
Overscutching, 55
Piatt, Bros., jacking motion, 191
Piatt's knockingoff motion, 51
■ gearing in, 51
Plucking from feed rollers, 54
"Preparation," 70, 141
proportion of machinery forming a,
in mule spinning and ring frame
spinning, 142
Productions, and their controllintr fac
tors, 53, 54
Keceding motion, 158, 178
Revolution of wheels, law, 1
Ribbon lap machines, 80
drafts in, 82
— ; production in, 83
Ring doubling frames, 224228
gearing in, 224
production in, 226
slippage in, 228
twist obtained, 224
■ winding, 247
Ring frames, 204224
builder wheel (ratchet), 210
compared with mule, 213
costs of yarn, 235
counts, changing, 209
gearing in, 204
looses in driving spindles,
212
productions in, 213
proportion of machinery form
ing a " preparation " in, 142
speeds of spindles, 206, 212
twist per inch, 207
Ring spinning. See Ring frames
Roller delivery motion, 160
Rope and belt driving, 12
calculating speeds and sizes
of driving surfaces, 1215
Rotation, direction of, 6
of wheels in any direct train, rela
tive rates of, law, 3
Scutchers, 4156
changes in weight and count of
laps made by, 52
draft in, 4347
gearing in, 4143
hunting cog measuring or length
motion used in, 48 ^
particulars of driving, 41
productions, speeds, and controlling
factors, 54
Sliver, or web, 65, 71
coiling of, 105
■;;;— weight of the card, 152
Sliver lap machines, 76
drafts in, 78
production in, 79
• to alter, 79
Speed indicators, 198
Speeds in scutchers and their control
ling factors, 53, 54
altering, 61
Stop motions, length. 156
254
INDEX
Tachometer, the, 198, 199
Toothgear, calculatiug rale of motion
wlien, employed, 1
wheels, direction of movement of, 2
Transmission of motion, 115
Trelfall's jacking motion, 19:>
Tweedale type of differential (later
mediate frame), 133
Twiner mule, 228230
gearing in, 228
Twist, constants, for roving, normal,
111, 112
standards for single yarns,
161,214
■ doubling, aims and effects of, 220
constants used in, 216
in roving direction and usefulness,
111
effects of. 211
in single yarns. 21.3
influence of direction of, in folded
yarns, 218
object of, 111, 2U1
obtained in ring doubling frames,
224
per inch and per draw, 197
in ring frames, 207
relative resistance of yams to, 222
■ standards, for folded yarns, 216
for 6in,(,'le yarns, 214
state of equilibrium, 223
influence ou breaking strength, 215,
216
twisting two or more threads
together, 219
Wheel trains, 411
calculating value of, 8
direct and indirect, 46
effects of changing wheels, 9
values of, in mules, conditions
governing changes in, 161
various, particulars of, 177
See Gearing
Wheels, classification of : driver, driven,
carrier, 6
direction of rotation, 6
effects of changing, 9
law of revolution, 1
relative rates of rotation, 3
Winding in fly frames, how obtained,
125
Wrapping, 70
Yarn, 71
costs of (q.v.), 231247
doubling, aims and effects of, 220
folded, twist standards for, 216
influence of direction of twist
on strength of, 218
relative resistance of, to twist,
222
singli', twist standards for, 214
. effects of twist in, 214, 215
state of equilibrium, 223
t'ltal length of. per draw, 197,
2J3
testing for breaking strength, 215,
216
».©•
THE END
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FSIKTED Br WILLIAM CLOWES ASD SOKS, LIMITED, LOKDOX AKD BECCLES.
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