Cotton Spinning Calculations and Yarn Costs

C OTTO N SPI N NI N G CALC U LATI O N S

AN D YA R N C O STS CO ON W A NG AN D D S IG N B TT E VI E ING . y H T TAY o n n W vin . L C an JO N LOR , late ecturer otto ea g d D i nin in the P n and h T ni a S es g g resto ot er ech c l chools . R i n r n W s d u d the di ti F . K Di e ev e er ec o of IL INSON , r ctor of the T x i and E n in in S B n Wi e t le g eer g chool , olto . th 402 D ia r m C wn 8 vo s . 6d net g a s. ro , 7 . .

L M N TH E E E E TS OF COTTON S PIN NING . W B H M and F W K . it e y JO N ORRIS . IL INSON h a Pr face

i B . . B . Wi i m S r A D C . E 1 6 D by O SON , , th 9 agra s

and I i n C wn 8vo s 64. llustrat o s. ro , 7 .

P N I O D P N N B RI C P LES F W ORSTE S IN I G . y W 1 1 8 l v H A D PR I E STMAN Wi I ti n . 8 c O R . th l ustra o s , 5 6d n 7 . . et .

WI LD A N D CULTIVATE D C OTTON = PLANTS O F TH D : a R i i n the G nu G i m E WORL ev s o of e s ossyp u , framed prim arily with the object of aiding Planters and I nvestigators who m ay contem plate the System atic I mprove i WA m n the C n S . B S r G G e t of otto taple y EOR E TT ,

M . E C M . LL . D Abd . and . , . ( f m B an C U ni i and or erly Professor of ot y , alcutta vers ty, R eporter o n E cono m ic Products to t he G overnm ent of

I ndi Wit P t o f w i are C ed . R a. h 53 la es, 9 h ch olour oyal

Svo 0s . net , 3 .

J ACQUARD W E AVING AN D D ESIG NI NG . B F T B E M d i in n and C e ti d y . . LL , e all st Ho ours r ﬁcate Teacher in Linen Manufacturing and in Weavi ng and ” n D e i nin C i and Gui d L nd n I n i Patter s g g, ty l s of o o st tute . W t it 1 Di m 8vo 1 2s . ne . h 99 agra s . ,

M AN R N AN D LO N G S G CO . , EE ,

D N E W Y K B BAY A N D CALC U ’I‘ TA LON ON , OR , OM , COTTON SPINNING CALCULATIONS AND YARN COSTS

A PRAC TICAL AND COM PREH ENSIVE M ANUAL OF CALC LA O NS A R CO S S AND O H ER U TI , Y N T , T DATA INVO LV ED IN ADAPTING TH E M ACH N ERY IN ALL SEC ONS AND FO R ALL G RAD ES I TI , , O F SPIN NIN G AN D DO UBLING

JAM E S WINTE RBOTTO M

H T H OLOGY MA CH ST R LECT URER I N COT TON SPI NN I NG, M UN I CI PA L SC OOL OF EC N , N E E

M A N G R E E N A N D C O . L O N G S , ,

E RN O S E R RO W ON DON 39 PAT T , L

Y ORK BOMBAY A N D CA C A N E W , , L UTT

A l l r zgglzts r eser ved

P R E F A C E

TH E aim of the author of this work has been to provide the student with particulars of the gearing in all the machines i d in i i wi d cal cu nvolve Cotton Sp nn ng, together th a metho of T m i d i lating the trains of gearing . hese are acco pan e by su table

x nd x e amples a e ercises . E xisting works containing Spinning Calculations appear to deal with this subject in a manner too abstract for the average

d I n i d i d i cal cu stu ent . th s book the eta ls connecte w th the l tion s and i in i di i i a essent al chang ng the con t ons of work ng , are l ful y given . The effects of twi st 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 I nstitute examina

i in S i i t ons Cotton p nn ng.

A u u st 1907 . g ,

C O N T E N T S

TRANSMISSION OF MOTION PAG E — — — — Ascertaining the rate D irection Sizes E ﬁects of changes E x am ples — and ex ercises 1 1 5

COTTON MIXING

— — B ale- breakers or cotton pullers and distributors Their object Types — — ﬂ — — Action s Capacities Speeds D r afts Merits and dem erits E x am ples — and ex ercises N otes on the stack and direct m ethods 1 5 25

OPENING AND SCUTCHING

— — — — — — Openers Gearing Speeds Methods of feeding D rafts Lap weight E x — — — — — am ples and ex ercises Scutchers The gearing Speeds D rafts L ap w i — d i n—L a n m i n —C n in d w i e ght Pro uct o p le gth ot o s ha ges spee , e ght , — and n—E x m and x i i i m i and non - i i cotto a ples e erc ses Pos t ve , se pos t ve — — — — draft conn ections N on stop working Controll ing factors Speed of — — heat er s and fans Sizes of feed rollers Overscut ching and other defec — tive treatm en t 25 56

CARDING

— — - — — Cards The gearing Speeds D rafts Alterations Functions of parts C ndi i n n ll in efﬁcienc — m ﬂt — in o t o s co tro g y Rate of ovem ent of a s Wrapp g — — — N am es applied to cotton in the processes Counting cotton Card in n in i n m n in c it s in cloth g , cou t g, preparat o for ou t g , haracter of po ts E x am ples and ex ercises

PREPARA FOR AND C MB G TION , O IN — — — Sliver lap m achine Object N am es and functions of parts Gearing — — — — Speeds D rafts Production E x am ples and ex ercises 76 80 — — — Ribbon lap m achine Object N am es and functions of parts Gearing — — Speeds D rafts Production - E x amples and exercises V11 1 CONTENTS

PAGE — — — Com bing Alternative preparation of laps Objects of com bing The N asm ith m d D and im i i n in n co ber Spee s rafts , the l tat o s ra ge — — Weights of sliver and waste E x am pl es and ex ercises 84 95 — — The Heilm ann com ber Differences of the duplex and N asm ith Speeds D — A in how d d—D i i n —I m n in rafts ttach g, a juste raft restr ct o s te s co troll g — — the efﬁ ciency E xam pl es and ex ercises 95 1 02

ATTENUATING AN D E QUALI! ING (THE DRAWING PROCESS) — — — draw - fram e Objects N um ber of heads useful Object and m ode of — “ — testing slivers System of putting up Allocating the draft s S in the i —S d d n and d i n—S i pac g sl ver pee s , rafts , cou ts pro uct o u table — — sizes of rollers Analysis of system s of roller gearing The arrangem ent — — of heads A m ode of ascertaining the total draft E x am ples and ex ercises 102

ATTENUATING (THE FLY- FRAME PROCESSES)

Th ﬂ di and —Th e m : in m e objects of the y fra es slubber , ter e ate , rover jack — — n ecessity for repetition The object of twisting The direction of twist in it s infl n — Twi n n The in in m g, ue ce st co sta ts gear g these fra es — The nam es and fun ction s of parts E ffects of al tering the cone train C n in d d n wi an d in E x m and ha ges spee , raft , cou t , t st spac g a ples — — ex ercises Cone dr um s and differentials Reasons for a differential train ﬁx — of ed value 1 1 0 7 1 41 — Analysis of the action of drawing rollers wi th deductions 1 52 1 54

SPECIFICATION OF COND ITIONS IN CARD ING DEPAR TMEN T — Suitable cou n ts and spindle speeds Preparation deﬁned Coun ts pr acti — cable with the available m achinery Factors con trolling the allocation — — of th e total draft E x am ples and exercises Hank indicators 4 — 1 52 1 54 1 1 , Ful l bobbin m easuring m otions

SPINNING — — The m ul e D escription and functions of parts Twist constants Factors n l in l all in —E x m d wi d co trol g the va ue of tra s a ples of spee s , t st , raft , n il d in and d i n— in in m ul D n and cou t , bu er, ga pro uct o Gear g es by obso B w in n P Tr el fal l — J in l w d arlo , Hether gto , latt , ack g, s o roller , ouble

d wi in ni n in - off and in -u and m i ns spee , t st g, haste g, back g tak g p other ot o — — Com parison of actual speeds and productions with calcul ated Losses — — in drivi ng U se of the tachom eter and tachoscope Hauk and other — — indicators Tables of production s 156 204 CONTENTS 1X

PAGE — — — — The ring fram e Gearing Speeds D raft Twist and other changes — E x am ples and ex ercises Com parison of calcul ated with actual speeds — — — and productions L osses in driving Table of production s Condition s — favourable to ring spinning The inﬂuence of twist on the output 204 213

YARNS — — Twi st standards for single E ffects of twist in single Relative breaking resistance in single 21 4 21 6 Twi d d n — The inﬂn st standards for various kin s of folde yar s ue ce of the direction and ex tent of twist l n the singles upon the strength and other — — features of the folded yarn The aim s of doubling E quilibrium in — folded yarns - Features developed in folding To ascertain the suitable twist 21 6—224

DOUBLING — — — The ring doubli ng fram e Gearing Speeds Twist production E x amples — — — — and ex ercises The twiner m ul e Gearing Speeds Twist production — E x am ples and ex ercises 224 230 — — Winding Reeling 247 249

COSTS OF YAR N — — Total and details of expenses E x am ples of costing Com parison of cost

— - Yarn from single and double roving Com bed qualities Ring yarn — — Cotton and yarn price lists Cost of power space Power required — — E x tra cost of com bing D epartm ental costs 231 247

I ND E X

COTTON SPINNING CALCULATIONS AND COSTS OF YARN

TRANSMI SSI ON or MOTI ON

The M hod of l in R of Mo io wh n Too h G is et calcu at g the ate t n, e t ear — employed When wheels are employed in a simple or direct i in Fi . 1 i tra n , as g , the r move in circ ment , teeth or umfer en tiall is i y , al ke . Their axial movement differs only when the wheels are not alike in

i . T i dif is B o s ze h s ference , rela tivel i i y , nverse to the r teeth FI G. 1 . T i contents . h s is proved by

i A B C and D in Fi . 1 i assum ng that the wheels , , , g conta n 1 0 5 50 nd 2 i nd 0 , 7 , , a 5 teeth , respect vely, a that the ﬁrst i d A i . T ment one moves one revolut on hus , the wheel moves x 100 and i its i to the e tent of teeth , s nce teeth gear w th those B and i and wi D of , the latter w th C, these also th , then each of i A nd i them w ll move tooth per tooth of , a therefore each w ll i 100 . i i xi move teeth Hence , the r respect ve a al movements w ll be

1 o o —o_ _ 1 A — 1 01 - - B _ or l 1 0O 7 0 ° ° C = L Q or 2 D = J Q 01 4 O 5 § 5

The preceding results show that the axial movement or revo i d di i i lut ons of wheels , un er such con t ons , are nversely pro i i i and port onal to the r relat ve teeth contents , therefore as follows O t COTTON SPINNI NG CALCULATIONS

Toot contents . Ratios of t eir revo utions h h l .

The Di ion of he Mo m n of Too Wh l s - rect t ve e t th ee . I n simple di i i is i rect tra ns of wheels th s always respect vely alternate . T i is 1 in h s seen on reference to Fig. . By number g the wheels in i i u i d it is i the r respect ve n mer cal or er , seen that those hav ng odd i in di i nd numbers w ll all rotate the same rect on , a reverse to those having even numbers . The following are ex amples in the application of the afore i d i i 1 ment one po nts in respect of F g. — A I . A min A 100 im min at w t EX MPLE ssu g revolves t es per ute, ha rates w d B C and D e in im oul , , rotat that t e — A II . A min B o the t 100 er min t i e EX MPLE ssu g rev lves at ra e of p u e , g v the A C and D in im rates of , , that t e . AM TIL—A min C m 100 i n how m n wo d A B EX PLE ssu g akes revolut o s, a y ul , , and D make — A P . I f D m d 100 vo ti n how m n wou d A B and C EX M LE IV a e re lu o s, a y l , , make ?

A nswers

A P I -The mo m n A x e d in t min te wo d EX M LE . ve e t of e pr sse eeth per u ul be e i n w n m f it con in i 1 0 100 w i R volut o s of heel x u ber o teeth ta s, th s 0 x , h ch AND COSTS OF YARN 3

n m of t et B C and D m i wi e m and t e o e n m u ber e h , , ust l ke s ove , h ref r the u ber of m d er min B di id d n m w ic it on in teeth ove , p ute , by v e by the u ber of teeth h h c ta s, wi i e its i n in im ll g v revolut o s that t e .

13 3 % revolutions per minute of B

Similarly

The revolutions per minute of C 200

400

A II - The n m w i B m er min 1 EX MPLE . u ber of teeth h ch oves p ute 00 i n x 7 5 t and i n m e A C and D m t con e n m revolut o s eeth, th s u b r , , us s que tly ove , and therefore

The revolutions per minute of A

I I — n m f t w i m A I . The e o C ve are 100 50 w i EX MPLE u b r eeth h ch o s x , h ch n m A B and D m o m o and e e u ber , , ust als ve , th r fore

The revolutions of A

200

—' ‘ A I V. 1 he n m of tee moved D are 100 x 25 and EX MPLE u ber th by , e e A B and C wi m i e n m e e o e th r fore , , ll ove a l k u b r ther f r

The revolutions of A

The Relative Rates of Rotation of the Wheels comprised in any — Direct Train are respectively inverse to their Teeth Contents This T in is seen to be the case in all the preceding examples . hus 4 COTTON SPINNING CALCULATIONS

Answer to E xamp le I . A B 10 1 1 : : : 0: 33 39 or

nswer o E x m l I I A t a p e . B A z : 1 00 : 7 5

n w to x m le I I A s er E a p I . C 50 C : B : : 100:

nsw to E xam le I A er p V. D A 100 25

D C 100 50 — Exam l es i n Res ec of the Di c ion of Ro ion. I n E xam I comm n p p t re t tat ple . e ce n m in A 1 B 2 C 3 D 4 t A and C m in o i by u ber g , ; , ; , ; , ; hus ove the opp s te n and D directio to B .

I n Ex m I I . c mm n n m in B 1 A 2 C 2 D 3 A a ple o e ce by u ber g , ; , ; , ; , ; thus n B and D a d C m ove reverse to . — NOTE The reason for numbering A and C the same is because that is their i e d relat v or er .

I n E x m . mm nc n m in C 1 D 2 B 2 A 3 C a ple III co e e by u ber g , ; , ; , ; , thus and A m in the i di i n D and B ove oppos te rect o to . I n E x m I V n m in is D 1 C 2 B 3 A 4 D and B a ple . the u ber g , ; , ; , ; , ; thus m in i di i n C and A ove the oppos te rect o to . . — Direct and I ndirect Trains When wheels are arranged in an indi i d i i rect tra n !(compose of two or more s mple tra ns), as con

tained in Fi . 2 di i g , the con t ons of transmission differ from those obtaining in di i i d in Fi . 1 rect tra ns as conta ne g . h dif 2 T e ference in Fig. consists in the wheels B and C being united and xi T have a common a s . hese must

therefore revolve together . Motion from A to D is imparted to the rim B A of by that of , thence from the r im B its and of to hub , thence to im i r C and rim D . the of , from th s part to the of The effects of B and C being so coupled are that their AND COSTS OF YARN 5 movement in teeth is only alike when they contain the same iff in number of teeth . Their relative movement in teeth d ers

di i i T if in Fi . 2 the rect rat o of the r teeth contents . hus , g , A C D i 40 20 60 and 20 i , B , , conta n , , , teeth respect vely

The i A wlll B 20 40 1 2 revolut ons of be to those of , or as B C : : 1 : 1 C

T i in i h s shows , two only of the three nstances that th e i i i i di i and relat ve rotat on is the nverse of the r mens ons , henc e “ i i i the rule , revolutions of wheels are relat vely nverse to the r ” is i in di i teeth contents , only appl cable respect of rect tra ns of wheels .

Fi . 2 is i di i and i di i g an n rect tra n , compr ses two rect tra ns B Th ff i i i A and CD. e of wheels , namely, e ects of the r comb nat on i d i i ir may be ascerta ne by mult ply ng the separate values , together , thus

2 x 3 = 6 or the movement

f d 20 i I A, therefore , ma e revolut ons , the movement of D n i l d 20 x 6 1 20 A and B i revolut ons wou be , because would 40 and and d move 20 x teeth , therefore B C woul mak e 20 X 40 20 X 40 x 60 i C and D l d revolut ons , wou move teeth ; 20 20 20 60 and i D d 120 therefore the revolut ons of woul be , 2T) 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 Di T ins of W s — rect ra heel 1 . The circumferential or teeth rate of the movement is alike in all the wheels comprised in a direct train of wheels . 2 h i . T e rate of rotat on is relatively inverse to the circum ference or teeth contents of the wheels compris ed in a direct train . 6 COTTON SPINNING CALCULATIONS

h 3 . T e direction of rotation is alternate at each successive and d in d di i wheel , when numbere progressive or er, the rect on of the odd- numbered wheels will be alike and opposite to those i wh ch are even numbered. I ndir c T ins of Wh s — Th i e t ra eel 4. e c rcumferential or tooth rate of the movement is alike only in those wheels comprise d in each of the several direct trains which constitute any indirect train . Th 5. e rate of rotation is relatively inverse to the tooth contents of th ose wheels comprised in each only of the several direct trains of which the indirect train is constituted. h 6 . T e direction of rotation is alternate at each successive wheel in any one only of the several direct trains which con stitute i di i the n rect tra n . The di ion of o ion i 7 . rect r tat is alternate throughout an ind rect i i d tra n when those wheels wh ch are fastene to each other , by a. i d d i shaft or other coupl ng, are regar e , when number ng , as only

: in Fi . 2 A B D d one wheel thus g the wheels , , C, woul be num d 1 2 2 3 i di i B and C bere , , , respect vely, so that the rect on of d i nd D woul be that oppos te to A a .

8 . Th i i i i e c rcumferent al rate as well as the relat ve rotat on , in i di i is i d i n rect tra ns , ascerta ne by treat ng them as so many simple trains as they may comprise . — Classiﬁcation of Wheels When the function of a wheel is to i x rim an convey mot on from hub or a le to , d therefrom to another

it is d dr i . wheel , terme a ver iv im When the motion is rece ed at the r , from another wheel , and its x it is d i d d i en passes thence to hub or a le , es gnate a r v h W eel. When the function of a wheel is merely to convey motion s r im it is d i Whee along it from wheel to wheel , terme a carr er l , but when such a wheel has also to transmit movement to its hub x d i i it d d or a le , for r v ng some other part , woul also be terme a

d i n i . r ven wheel , but only i respect of the latter connect on

la si cation o wheels in Fi s . 1 2 3 E xamp les in the C s ﬁ f g , , i i A D Fi . 1 i g , assum ng the mot on ﬂow ng from to

A is a driver (m otion ﬂowing from the axle to r im).

8 COTTON SPINNING CALCULATIONS

i and in i i di i 2 2 respect vely, therefore the pos t ve rect on ; B , F , E , ,

and 4 i and i . respect vely, therefore negat ve in V u of Wh T ins The Method of calculat g the al e eel ra . A i d i in di i di r i s mple metho , appl cable rect or n rect t a ns , is deduced from the foregoing procedure in ascertaining the

n i 1 and 2. The relative movements of the wheels i F gs . value i in i is d mu i in of the tra ns , each of those nstances , foun by lt ply g the si s of the dri w e s in e h o h for um o ze ver h el , te t , t get er a n erat r, and those of the driven wheels t ogether for a denominator i u i i the resultant be ng the val e of the tra n ; or, the relat on of

n T i su the final wheel i terms Of one of the first wheel . h s re lt, wh n u mu i u n f fi s h in e f rther lt plied by the revol tio s o the r t W eel, a

i i ob ins the o u ions of the ﬁn wh in i . g ven t me , ta rev l t al eel that t me Applying this in ﬁnding the revolutions per minute of 2 3 4 d i in i i an 5 F . shafts , , , respect vely , g 3 , when the s zes of

in ic : 40 20 50 25 100 40 the wheels teeth , alphabet ally , are , , , , , , 3 0 and 1 i i i ; ( ) s assumed to make 500 revolut ons per m nute , the following are the results 1 A is d i B i C is d i w n ( ) a r ver , a carr er, a r ven heel, a d therefore The revolutions per minute of shaft (2) gf g x 500 400 AND COSTS OF YARN 9

2 A nd D dri B is i C and d i ( ) a are vers , a carr er , E are r ven and wheels , hence

Revolutions of shaft (3 ) per minute 8- 8 X X 500 1 00

B dri (3) Here A is a driver and the ven wh eels , therefore

1 8 x 500 1000 revolutions of shaft (4) per minute

4 A nd F d i and B and d i ( ) Here a are r vers , G are r ven wheels , hence

The revolutions of shaft (5) per minute x 500 1 3 3 3 8

— The Effects of changing Wheels The effects of changing the i n I f d i wh s ze of any wheel depe ds upon its f unction . a r ver eel , the ax ial rate of all other Wheels receiving motion from it will be l t d in the di io of the h n a ere rect rat c a ge, because the movement of in i i d in the new wheel , teeth , per revolut on , w ll be altere that ratio ; and this will affect all the others depending upon it for i i in i i A 3 0 and the r mot on l ke terms . Hence , chang ng to , i i A 500 i d tak ng the revolut ons of at per m nute, woul cause The shaft (2) to rotate at

500 X i 88, by gear ; or, , by proport on 400 x 3 00 per minute

The shaft (3) to rotate at

500 x x 2 5 i 88 1 00, by gear ; or , by proport on 1 00 X 3—8 7 5 per minute

The shaft (4) to rotate at

500 x i 88, by gear ; or , by proport on 1 000 x 38 : 7 50 per minute

The shaft (5) to rotate at

500 x 3 — i ,8 X 88 , by gear ; or , by proport on 1 3 3 3 1 x 28 1 000 per minute

I n cas e o a driven wheel bein al ter ed the axial r ate o thos e f g , f wheels de endent u on it or their motion would be a ected in the , p p f , ﬁ I O COTTON SPINNING CALCULATIONS

— invers e ratio to that change Because the rate of movement of its d d i s i teeth woul be unaltere , because the wheel receives t mot on

i I s xi d from the same wheel as h therto . t a al rate woul be i d i and di i i d if ncrease when the new wheel conta ns less , m n she i i n i 40i d t . C conta n ng more , tee h He ce , alter ng the wheel to nstea A i 500 i of the wheel , assum ng the latter to make revolut ons per i d i m nute , woul have the follow ng results Shaft (2) would rotate at

500 x 400 x — 500 i i 588, or 528 revolut ons per m nute

Shaft (3) would rotate at

500 x 3—8 x 1 25 revolutions per minute

S 4 and 5 d d hafts ( ) ( ) woul not be altere . I f d 0 i i B were altere to 3 nstead of C, then the follow ng would be the result

' S 2 and 3 d i d ff d hafts ( ) ( ) woul not have the r spee s a ecte , because C would move at the same tooth rate ; thus Shaft (4) would rotate at

500 x 1000 x 666 i i 88, or 88 8 revolut ons per m nute

Shaft (5) would rotate at

500 x X - 8 88 i i 88 88, or 8 revolut ons per m nute

The foregoing show that increasing the siz e of a driver wheel increases proportionately the speeds of the subsequent

W in i and r ice uer sd i i i heels the tra n , that ncreas ng the s ze of a driven wheel proportionately decreases the speeds of the sub a t o in i nd vice vers . T sequent wheels the tra n , a herefore , determine the teeth contents or size of a wheel when it is required to the s ds d alter pee , the proce ure must be as follows I n the case of driver wheels : the size of the wheel it is decided ti i d d i d and di id d to alter , mul pl e by the spee requ re , v e by the

xi i d i i i d i e st ng spee , w ll g ve the wheel requ re , because the s z e of this wheel must be altere d in the direct proportion of the present rate to the required rate . I n case of driven wheels : the size of the wheel it is decided i i d xi i d and di id d i d to alter , mult pl e by the e st n g spee , v e by requ re AND COSTS OF YARN 1 1

d i i i d s d i spee , w ll g ve the wheel requ re , becau e the r ven wheel must be altered in the inverse proportion of the present rate to i d the requ re rate . To determine the siz es or te eth contents of wheel s to employ in in a tra 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 d f i n wi due d the teeth that affor s su fic ent stre gth , th regar to i i i i d id l ghtness ; the d rection of motion . Th s latter w ll ec e whether d dd the number of wheels to employ shoul be o or even . The The number of wheels should be as few as possible . i i i space ava lable restr cts the r size . The distance apart of the two centres multiplied by will give the sum of the circumferences of the wheels required. This divided by the suitable pitch of the teeth gives of i the sum the r teeth contents , whatever the number of wheels , i i i i when they are arranged w th the r centres in a stra ght l ne . I f i n d i it d the r centres are arra ge otherw se , woul be necessary to d i i d h eterm ne the sum of the r istances apart . T e latter would Th control the sum of their teeth contents . e contents of each wheel would then be decided according to the intermediate axial d i d spee s requ re .

U d di i i i Fi . 2 i in i n er con t ons s m lar to g , where the rat o the tra n is 6 1 and in i di i to , the latter has to rotate the oppos te rect on

Odd d. to the former, an number of wheels must be employe Th A six i i D e following would suffice , t mes the smallest s ze of i nd d i i odd pract cable , a these connecte by a su table carr er , or i I f is id diff in i number of carr ers . there a w e erence the s zes of i is i i A 24 i B and C the wheels th s mpract cable , then , t mes ; , d 25 times D should be employe .

— EXE RCI SE S Ascertain the wh eels convenient to secure the undermentioned values in the following trains 1 A di ct t in n i t of six w e wi x i m i n in i . re ra to co s s h els th a al ot o the rat os of nd e e i 1 2 3 4 5 a 6 . , , , , , r sp ct vely i in to n i t e w e wi xi mo ion in i of 2. A d rect tra co s st of hr e h els th a al t the rat os

1 and 3 iv . , 8, respect ely 3 An indi in six w e m i in e di c in wi . rect tra of h els, co pr s g thre re t tra s, th the

xi i 1 and 8 i . a al rat os , respect vely I 2 COTTON SPINNING CALCULATIONS

4 . An indi in six w m i in di in wi rect tra of heels, co pr s g three rect tra s th the diff n in xi i di i d w m n in 8 ere ce a al rat os equally str bute , the hole a ou t g to .

5. An indi in six w w on ainin i 1 9 one rect tra of heels , the hole c t g a rat o of , of the direct trains to have the value — Rope and Belt Driving Ropes and belts are extensively d in i i i h d employe the transm ss on of mot on . T e metho of — calculating the speeds and sizes of the driving surfaces pulleys and d —is id i i in i rums ent cal w th that wheel gear , the s zes of the pulleys and drums taking the place of the teeth contents in wheels ; the measurem ents usual being in inches or feet di m t i d di i ameter, these measure en s be ng ma e from ametr cally opposite points of contact of the transmitting medium .

FI G. 4 .

— min w A P 1 Fi . At w d B C D E and EX M LE ( g hat rates per ute oul , , , , F , f d ﬂw n in A m 50 i n G rotate i the groove y heel of the e g e akes revolut o s per 9 min was 25 and 5 9 8 125 5 and 6 i ute , feet, the others , , , , , feet respect vely Ans wer s

Revolutions of B per minute AND COSTS OF YARN I 3

Revolutions of D per minute

120

100

The reasons for adopting this method of determining the Speeds of parts when m otion is transmitted by belt or rope gear are as follows The circumference of a drum or pulley or a circle when divided by the n m 3 1416 i its di m t di me in i to m it is u ber , g ves a e er ; the a ter be g eas er easure, customary to ascertain the circumference by multiplying the diameter by that n m e For i o e 2 2 is n id d n n in i ind u b r. pract cal purp s s 7 co s ere ear e ough th s k of work . The rate of the movement of the strap in calculating is generally assumed to me n ce d m T i w i con be the sa as the co tact surfa of the ru . h s, ho ever , var es siderabl m c din w in ndi i n n i n y fro that rate , ac or g to the ork g co t o s, such as te s o , i n and i il it di n n m i cohes ve ess , pl ab y of the belt ; sta ces of the ce tres apart ; ater al , i and e of d m m o n of d T e not u ec ni ed in s zes , shap ru s ; a u t loa . hes are us ally r og z

in c ion w d for in ene i . mak g cal ulat s , but are allo e g ral pract ce The rate of the m oveme nt of rop es is ab out the same as the point of contact n w - n t d d I n i n it i not t m to m i ell co struc e groove pulleys. calculat g s cus o ary ake an ow n e y all a c . The of m m nt n n wi d ﬂA rate ove e of the ropes e gagi g th the groove ywheel will therefore be the same as that of the pulley at the centre of the part in con

wi o . I f t i is 12 5 e m n tact th the r pe h s fe t fro the ce tre of the pulley, or equal to 25 in di m the ci c m n i w d 25 3 1416 feet a eter, r u fere ce of such a c rcle oul be feet x , and therefore this would be the rate which the rope would move per revolution f A I n 60 ev ti n it w d e m o 60 im t o . r olu o s oul , therefor , ve the rope t es tha m o nt or a u , 25’ x 3 1416 x 60

Th mo in i e t the B w i is 5 di m t e rope v g at th s rat abou pulley , h ch feet a e er, or ’ 1 41 6 in i m n e n n m im w i n re re 5 x 3 c rcu fere c , the the u ber of t es h ch the le gth p senting the circumference is contained in the length of rop e passing over the

in i en tim wi the w i it e . T pulley a g v e, ll be rate at h ch revolv s herefore

25 ” 1 60 the rate of rotation of B 300 151212

— inc in o and e t in d m and w wo in i a S e, r pe b l gear g, ru s pulleys al ays rk pa rs — driver and driven and these in calculation are always placed on opposite sides — i n n is n m e is w d n min . of the equat on whe o e the u erator, the oth r al ays the e o ator The n i u in con n 3 141 6 to n e the di m in ecess ty for s g the sta t , co v rt a eter to the ci c m en c t en num e to den min o and it w r u fer ce, o curs jus as oft a ra r as a o at r , al ays I 4 COTTON SPINNING CALCULATIONS

nc . I t is c c i n ence is ca els , therefore , left out of the al ulat o ; h the rule as follows

diam eters of drivers revolutions of 1 st driver the revolutions of the last x d m diameters of driven l { dri ven ru or pulley

because

diameters of drivers x revolutions of 1st driver diameters of the driven x revolutions of last driven

A 2 Fi — i d the i n min D C B A EX MPLE ( g. Requ re revolut o s per ute of F , , , , e i w n wi the in i n in E x m 1 is nd resp ct vely, he , th gear g as g ve a ple , G fou to 1 10 im min revolve t es per ute . — NOTE I t is best in working questions of this kind to assum e the one moving

at n wn d i . T i w im i n a k o rate the r ver h s al ays s pl ﬁes the calculatio , whether

d in wi o a . eal g th r pe , belt, or teeth ge r (1) G is a driver and F driven

13 2 revolutions of F

2 E and A d i A and D d i n ( ) G, , are r vers ; F , , are r ve

_ - 206 25 revoluti ons of D 5 x 25 x 8

3 E and A are d i A and C d i n ( ) G, , r vers ; F , , are r ve

1 10 x 6 x l 2-5 x 25 revolutions of C 5 x 25 x 9

4 E and A d i A and B d i n ( ) G, , are r vers F , , are r ve

1 10 x 6 x 12' 5 x 25 3 30revoluti ons of B 5 x 25 x 5

(5) G and E are drivers ; F and A are driven

1 10 x 6 x 125 66 revol uti ons of A 5 x 25

i —W t i of B C D E and w d i d in EXAMPLE 3 (F g. ha s zes , , , , F oul be requ re in ma B 250 C 214 D 1 87 E 1 50 order that their revolutions per m ute y be , ; , ; , ; , 100 c i el min A m e 60 e tion in im and G, respe t v y, assu g to ak r volu s that t e , to ’ be 25 in diam eter ? h i and of the mo em nt of the o e wi Here A is t e dr ver, the rate v e r p s ll be ’ n 60 x 25 x 3 1416 per mi ute . Since B is required to rev olve 250times per minute 60 x 3 1 416 Circumference of B must be

I 6 COTTON SPINNING CALCULATIONS

d i f h etr mental ef ect u pon the cotton . T ere is a great difference in i i two the pr nc ple of the types of machines named. The has i i and Hopper a coarse comb ng act on , considerable pressures i i Th upon the cotton are el m nated. e productive capacity of a

FI G. 5.

i i lb 55 roller pull ng mach ne ranges up to s . per 8 hours i when worked at the highest pressure . The best results obta nable are when it is run at a high speed for American cotton and at d d i nd I a mo erate spee for Egypt an a ndian varieties . The following are the particulars of the parts in the Roller

Fi . 5 cotton puller, g

a i i 220 i i . , the l ne shaft mak ng revolut ons per m nute ” b d 19 in di i and d i i , a rum , ameter, on the l ne shaft r v ng the i mach ne strap .

0 c i . , are sw ng or gallows pulleys d represents the fast and loose pulleys on the machine shaft ; 1 6" di these are ameter . e d 19 di x d , a groove rope pulley, ameter, ﬁ e upon the i d i i i d i i mach ne shaft , r v ng a rope wh ch r ves the porcup ne i d cyl n er . AND COSTS OF YARN 1 7

- d i i d . f, a groove carr er pulley for the above ment one rope " d 10 di x d i g , a groove pulley, 5 ameter, ﬁ e upon the porcup ne

- shaft and driven by the above mentioned rope . h i in 25 x d i , a wheel conta n g teeth , ﬁ e on the mach ne

shaﬁ . i d i l , a wheel on the shaft of the lower secon pull ng ro ler ,

i i 0 and d i h. conta n ng 4 teeth , r ven by

i i 1 4 and x d i i . j , a wheel conta n ng teeth , ﬁ e upon the ax s of

k i i 6 and d i . , a wheel conta n ng 7 teeth , r ven by j

l i i 1 4 x d xi k. , a wheel conta n ng teeth , ﬁ e to the a s of m w i i i , a wheel on the lo er ﬁrst pull ng roller, conta n ng

6 and d i l . 7 teeth , r ven by li i i 1 n x d . , a wheel ﬁ e on the ﬁrst pul ng roller, conta n ng 7 teeth

0 i i i n and . , a carr er wheel , gear ng w th p i i i 2 p , a wheel on the latt ce roller shaft , conta n ng 0 teeth . d 10 di t d e and q, a groove rope pulley, ameter , at ache to

r driving .

r d 1 5 di . , a groove pulley, ameter

3 x d xi r i i 20 . , a wheel ﬁ e upon the a s of , conta n ng teeth

t i 60 x d i xi u . , a wheel w th teeth , ﬁ e on the latt ce roller a s t i 60 x d i i l , a wheel w th teeth , ﬁ e upon the other vert cal latt ce and d i t shaft engage w th . u and n i i i l a, wheels on latt ce roller shafts , each conta n ng

3 8 teeth . u i i i u d u . z, a carr er wheel , gear ng w th l an g u 24 x d i , a wheel , teeth , ﬁ e to the latt ce roller shaft . 27 i i u , a carr er wheel engag ng with and w. w w z i i 24 di i i , , y , , wheels conta n ng teeth each , str but ng lattice connections . Revolutions per minute of the various parts in the roller i cotton pulling machine (F g .

220x The machine pulleys 12

The feed lattice roller

22 The sur face speed in inches per minute 4 7 x x 7 8 1 2 4 C 1 8 COTTON SPINNING CALCULATIONS

The ﬁrst pair of pulling rollers Revolutions per m inute

Surface Speed 1 1 3 ‘ 7 6 7

The second pair of pulling rollers

220X 1 9 x 25 Revoluti ons per mi nute 1 63 3 1 6 x 40

Surface speed per mi nute 1 6 x 40 7

The porcupine cylinder

1 9 x 21 Revoluti ons per mi nute 1 6 x 1 05

The lower conveyor lattice rollers

220X 1 9 X 10X 20X 60 Revolutions per minute 58 05 1 6 x 1 5 x 60x 60

i in i x x 2 2 1 003 ' 5 Surface rate per m nute nches 7

The right -hand elevator lattice roller

Surface rate 58 05 1003 5

The left - hand elevator lattice roller 23

The ﬁrst overhead conveyor and distributing roller

58 O5

M ' Surface rate 58 05 x 1003 5 7 AND COSTS OF YARN 1 9

The second overhead conveyor and distributing lattice roller

2 2 Surface rate 58 05 x x 7 1 003 5

All the machines used in connection with cotton Spinning The i is contain the power to attenuate the cotton . term wh ch ” m ost generally used in place of the word attenuation is draft . “ ” The e xtent of the draft governs the relative weigh t Of the he x cotton at the difier ent points in the processes . T e tent i in i and i i pract cable each mach ne , also between the var ous po nts in i d d d it is i each mach ne , shoul be well un erstoo , because th s which governs the relation in the weight of the cotton in any part of the machine . I f i it i d t a mach ne , or a part of , conta ns a raf of four, the diff in d its i d erence the state of the cotton , as regar s we ght , woul i i be four t mes . This means that t has become four times lighter and longe r between the parts referred to . The extent of the draft may be ascertained from the relative i i rates of the parts mov ng the cotton , or, from the relat on in the weight Of the cotton as it passes under the influence of the two i in po nts question . A in i in i d i it is pply g th s , respect of the mach ne un er not ce , found that the draft between the feed lattice and the first pair of pulling rollers is surface movement of the 1 1 3 i i surface movement first pa r of pull ng rollers per minute in inches of the lattice per minute in inches so that the cotton under the influence of the rollers will be 1 4 i i i nd 1 4 i t mes l ghter than that upon the latt ce , a therefore t mes longer . The following are therefore the drafts between the

d r in i d in - a jacent pa ts , progress ve or er , the above named machine 20 COTTON SPINNING CALCULATIONS

First and second pair of pulling rollers

3 07 9 1 8 8 5 1 63 3

Second pulling rollers and lower conveyor lat tices

03 26 3 07 9

Lower conveyor and the vertical lattices 1 003 5 1 003 5

Feed lattice and overhead conveyor lattice 1 003 5 1 2 3 5 8 1 2 4

1 — Vhat w d d in i n mi n E . \ EX RCISE oul be the spee s , revolut o s per ute , of the

- n i n d if in - t d i in dr m was 1 6 in in di m u nder me t o e parts, the l e shaf r v g u ches a eter ins tead of 1 9 inches : (a) the m achine pulley ; ( b) the feed lattice roller ; (0) the ﬁ rst pair of pulling roll ers ; (d) the second pair Of pulling rollers ; (e) the porcupine cylinder ; (f ) the lower conveyor lattice roller ; (g) the vertical con vey or lattice rollers ; (h) the overhead conveyor lattice rollers 2 —Wh w l d ff t n d dif n EXERCISE . at ou be the e ec upo the spee s of the fere t parts if the 25 wheel on the machine shaft was changed to 3 0after changing the ? line - shaft dru m to 1 6 inches

The wmking Of the ﬁrst of these e x ercises is as follows

220 x 25 x 1 4 x 14 x 17 _ 40 x 7 6 >< 7 6 x 20 1 6 o i n or, by prop rt o

220 x 25 >< 1 4 x l 4 0" 40 x 7 6 x 7 6

1375 ; or 1375

220 21 x 440 440 , ; or 10,

220 x 10 x 20 x 3 8 15 x 60 x 3 8 AND COSTS OF YARN 21

220 x 10 x 20 488 ; or 1 5 x 60

220 x 10 x 20 x 24 483 ; 0" 488 9 15 x 60 x 24

Answers to E xer cise 2

a ine 220. ( ) Mach pulleys, b 4 7 ( ) 59. (c)

(d) 165.

Fi 6 is i i in g. an elevat on of the gear ng a cotton pulling T i i machine of the Hopper type . h s type of mach ne reduces the

5 d ue .

Fe e d La t t ic e

Lo w e r C o n ve y o r Lat t i c e s

FI G . 6 .

di The d i cotton to a very loose open con tion . a vantages of th s machine over the roller type of machine are

Greater opening and cleaning power . d Less noise and dus t when well constructe .

Less personal attention .

i . i Greater product on , about lbs per hours , w thout pressure . 22 COTTON SPINNING CALCULATIONS

Less risks of ﬁre in this and subsequent machines by its i i el m nating hard substances . ixin id in M g powers cons erable , whereas the roller type they are very limited.

nd - Fewer breakages a up keep less costly. The machine driving pul leys are on the stripping cylinder

and in 1 2 i in di . shaft , the ﬁgure they are shown as nches ameter d i 26 These are driven by a strap from a rum on the l ne shaft ,

i in di nd i 220 i i . nches ameter, a mak ng revolut ons per m nute ( 1) Revolutions per minute of the fast and loose drums of the machine 220 x 26 1 2 Revolutions per minute of the supply lattice roller

220 x 26 >< 7 x 24 x 24 x 24 1 2 x 20 x 90 x 3 0 x 3 0 Rate per minute in feet

x 5 5 x 22 1 2 x 7 Revolutions per minute of the spiked lattice roller 220 x 26 >< 7 x 24 1 2 x 20 >< 90 Surface rate per minute

x 20 x 22 l 2 x 7 Revolutions per minute of the regulating cylinder

220 x 26 >< 7 x 54 _ 1 2 x 20 >< 90 (7) Surface rate

1 00 1 x 1 4 x 22 1 2 x 7 (8 ) Revolutions per minute of the stripping cylinder

220 x 26 1 2

24 COTTON SPINNI NG CALCULATIONS

12 in di m d tw n w When the driving pulleys are ches a eter, the raft be ee lo er is conveyor and elevating lattices 05 . in di m d When the driving pul leys are 1 5 ches a eter, the spee of all the parts ti n and d wi e e o e will be decreased in the same propor o , the rafts ll th r f r be n ed u alter .

A ns wers to Ex erci se 5

ns 8 and 9 Un d (1) 47 68 revolutio . ( ) ( ) altere . er s a a; a; (6) (7) 834

The usefulness of this machine is inﬁnitely greater than the id i is d in i roller puller . Ev ence of th s foun the number of m lls which have modiﬁed their mixing arrangements since its i introduct on . The most common practice in using this machine is that of in i in i plac g the cotton from the var ous lots of bales the mach ne , d i i i in the desire proport ons , at a rate perm tt ng only of the i O i and ixi i limited exercise of the r pen ng m ng funct ons . When ixi i i i i in such replaces stack m ng, var at ons are v s ble all the subsequent stages . E xtension in the usefulness of the machine is possible by

d i l . n a opt ng one pu ler per or lbs per week , a d adjusting them so that their maximum opening capacities are i i d in i l ut l ze that t me , the cotton , from the several pu lers , supplied with bale cotton in the usual way but in perfect i i i i rotat on , pass ng nto a common trunk , from wh ch the several i i exhaust openers draw the r suppl es . These latter deli ver to d d O d i hopper fee ers attache to further peners , fitte w th the full width type of heater s . From these the cotton may pass to the Th scutcher or to the card direct . e hopper feeder to the final opener should be fitted with automatic supply control attache d

d i its . B i to fee of the opener respons ble for supply y th s system ,

in i i . a m ll consum ng lbs of cotton per week , the supply d d six i i woul be rawn from t mes the usual number of bales , w th the additional advantages that the hard and soft qualities would be unavoidably mixed in the designed proportions con

in ou sl t u y . To derive the ful lest beneﬁts from the use of the hopper AND COSTS OF YARN 25

ll er - i — cotton pu T as an open ng process it is necessary to bear in i d i and i ff is m n that the open ng , consequently the clean ng e ect, 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 ul i i d i d i and reg at ng cyl n er from those on the sp ke latt ce , the contrasting rates in the movement of these two latter parts . The best Speed of the Spiked lattice is the highest rate at i i The i wh ch it may be worked without undue stra n . rate var es

id in i and i d. cons erably the var ous makes , also w th cotton treate American cotton allows of a higher rate than I ndian or di i d Egyptian . The most beneﬁcial Speed can be rea ly ascerta ne

. T i d id d i i d d d d by test h s ec e , the regulat ng cyl n er shoul be a juste to a point at which the machine produces only the amount of ir i cotton requ ed in the full working time . Where these tems are disregarded the Opening and cleaning utility of the machine is i i only part ally real zed.

TE E OPE NE R .

i i i i and i Fig. 7 conta ns part culars of the pr nc pal parts the r

- connections in a hopper fed compound combined opener . Par ticul ar s of the other parts and their connections are contained h i i i in in i . 8 10 and 1 1 . T e d F gs , 9, , object of g v ng the eta ls i ﬁve instead of in one ﬁgure is to avo d confusion .

The speeds of the various parts in Fig. 7 are

Counter shaft revolutions per minute Beater shaft Cross shaft Side shaft Bottom cone shaft Top cone shaft Porcupine cylinder Fan shaft (1 ) Fan shaft (2) 26 COTTON SPINNING CALCUL ATIONS

r m i . . p e n

C o u nt e r

a n S h a ft 1 Fa n Sh a ft 2

FI G. 7 .

EX AMPLES OF WORKING OUT TH E SPEED S OF TH E AB OVE PARTS .

220 3 6 The counter shaft 12

220 x 3 6 x 27 The beatei 1 6 x 13

220 x 3 6 x 27 x 5 The cross 214 17 1 6 x 1 3 x 24

220 x 3 6 x 27 x 5 x 30 The side 428 34 1 6 x 13 x 24 x 15

220 x 36 x 27 5 x 3 0 >< 40 The bottom cone

5 x 30 x 40 >< 5 The to 61 1 95 sa r 619 p ’ y 16 x 13 x 24 x 1 5 x 20 x 7

The pOI Cupi ne cyli ndei 1 6 x 1 6

1 5 Fan shaft ( 1) 557 X (g

Fan h 2 s aft ( ) 1028 x B 1542 AND COSTS OF YARN 27

A N To 7 EXERCISES REL TI G FIG . .

(1) At what spe eds would the parts contained in this ﬁgure revolve if the line shaft made 250instead of 220revolutions per minute ?

2 I f fan- l 1 was n d to 6 inc e at w t te ( ) the shaft pu ley ( ) cha ge h s , ha ra per minute would it revolve ? (3) At what rate per min ute would the bottom and top cones revolve if the

ttom ne and id - w e l 20 and 40 w e ti ed 24 and 3 bo co s e shaft h e s , , er subs tut by 6 resp ectively (4) What size of driving and driven pulleys would alter the rate of the cr oss 7 shaft from 214 17 to 257 per minute ? “ hat effect would such an alteration have upon the speeds of the other parts ? (5) What changes would alter the sp eed of the heater to 1 113 revolutions per minute if the fan and cross shaft are to remain unal tered? (6) At what rates would the top- cone shaft revolve when the cone strap is working on the extreme right and left ends respectively ?

e i Answer s to E x r cises (F g. 7)

(1) The sp eed of all the: parts would be increased in the same prop ortion as the c n e in eed t : 562 1168 243 3 486 7 973 5 684 500 1 153 8 ha g sp s, hus , , , , , , , , 1 2 e i e 75 r spect v ly . 2 The te of the and wo d he n d and e ( ) surface ra strap pulley ul u altere , therefor the revolutions per minute would be altered in same proportion as the siz e of

n m to 1 100. pulley, a ely,

3 Bo om c n 4589 con 645. ( ) tt o e , top e , — 4 A 6- in d i e on e te or 20inc d i n on the c o ( ) ch r v r the b a r shaft, a h r ve r ss The ide t and ottom and t o con wo d be e ed in the ti shaft . s shaf b p es ul alt r ra o

m 5 6 or to 514 1028 and 734 e i . of fro to , , , resp ct vely (5) The heater pulley to 13 inches ; the pulley driving the cross - shaft pulley 4 in or c o - l 26 in on fan 58 ches , the r ss shaft pu ley ches ; the pulley shaft

68 inches . 1 62 nd 3 527 e ecti e (6) 5 a r sp v ly .

h o i n i o s e d ar i 1 . Calcul at o s r elat ng t t e p e s f the p ts n F g 8 . Revolutions per minute oi

The supply latti ce roller 9 x 7 x 7 8 x 8 5

inches per minute The bottom lattice rollers 61 2 x 4 x 23 x 1 7 x 20x 20 i n the hopper }

inches per minute 28 COTTON SPINNING CALCULATIONS

The spiked lattice rollers 61 2 x 4 x 23 x 1 7 in the hOpper 9 x 55 X 7 9

The d i n 24 47 x 55 X 22 surface spee 4229 8 inches per minute 7

' I l \ 2 i f. l at l g as 5

440 x 6 x 4 x 24 The regulati ng cyli nder 1 2 x 1 2 x 48 AND COSTS OF YARN 29

The surface speed in 3 30x 1 8 x 22 2074 or 17 2 8 ft’ inches per minute} 9 7 , 440 x 6 The i i i d 220 str pp ng cyl n er 1 2

The d in 220x 1 6 x 22 surface spee _ 1 1063 inches per minute } 7

E N A N T 8 . QU STIO S REL TI G O FIG .

m ff d e win e i n and t Na e the parts a ecte by ach of the follo g alt rat o s, calcula e the effects in revolutions and surface speed in feet per minute (7) I f the cone strap was successively placed at both ex treme points on the n d m co e ru s .

- (8) I f the pulley on the top cone shaft was 5 inches diameter instead of 4 . 9 I f on C was n in i m ( ) the pulley cha ged to 9 ches d a eter. ( 10) I f the 86 on the supply lattice roller shaft and the 1 2 driving it were ed to 84 and 1 4 i alter respect vely .

A ns wers to u estions r elati n to F i q g g . 8

(7) When the strap occupies

The l eft - h and The righ t-hand

ext reme osi t ion ex treme osI tion. p . p Spiked lattice roller revolutions revolutions 244 feet 123 8 feet Hopp er lattice roller revolutions 10 84 revolutio ns 423 feet 1 876 feet Supply lattice roller revolutions 1 6 15 revolutions 6 3 feet 279 feet

8 The ff ct d w d in i c be the m e in ue tion 7 ch ( ) parts a e e oul th s ase sa as q s , ea in inc d in to the ex en of or be g rease rate t t g, Spiked lattice roller revolutions 528 72 feet Hopper lattice roller revolutions 918 feet Supply lattice roll er revolutions 13 67 feet

9 I n t i e on the s t ice wo d be ff d and is ( ) h s cas ly upply la t ul a ecte , th to the exte nt of 8 ; thus Revolutions of supply lattice roller Surface speed

10 I n i in n on i w d ffec ed and i ( ) th s sta ce ly the supply latt ce oul be a t , th s to x n x and e o the e te t of 88 pg, th ref re

Revolutions of supply lattice roller 0756 Surface speed 13 67 3 0 COTTON SPINNING CALCULATIONS

d i Calcul ations r elating to the sp eed of the par ts foun n

i . F g . 9 Revolutions per minute of

The latti ce roller 62 x 40 X 3 3 x 20

” The d 58 3 5 x 3 x 22 surface spee of 55 01 5 the lattice in inches 7

r'e r o lle r 3 : e e d r o ne r ﬂ Pr e s s u r e E P 2n d . ﬂp

” 3 Lo we r' Fe e d r o lle dal r o lle r

Sid e Sh a ft

Bo tt o m C o ne

FI G 9 . .

61 2 x 1 The ﬁrst presser roller

” The surface speed of the 4 667 x 3 5 x 22 51 3 3 7 ﬁrst presser roller in ins . } 7 61 2 x 1 x 34 x 27 The lower feed roller 62 x 40 x 3 8

3 2 COTTON SPINNING CALCULATIONS

5 44

2 03 9 x 1 6 x 22 _ 1 02 0 53 7 5 44 Top cage

498 960 _ 1 5528 8 21 3 28

To S i de

' C age 1 6

Pulley C r o s s Shaft

FI 1 0. G.

1 5 528 x 21 x 22 102 4 8 5 7 5 AND COSTS OF YARN 3 3

1 1 ° 72 x 3 x 22 7 220x 3 6 x 27 >< 5 x 1 3 x 1 3 x 24 >< 24 x 40

3 5640 2128

" 1 67 5 x 25 x 22 1 3 1 ‘ 6 7

IN W H 10 EXERCISES CONNECTION IT FIG . . What would be the effects if (a) The 44 wheel driving the bottom cage wheel was changed t o 46 (b) The 1 4 wheel on the bottom feed roller was changed to 16 (c) The 24 wheel on the side shaft was changed to 22 ? A in w s w d m S ed of scerta the heel that oul ake the surface pe s cages, cage o and ed o e n i e c i wi in r llers, fe r ll rs as early al k as pra t cable thout alter g the rate of the latter .

Calculations relating to the sp eeds of the p ar ts found i n

Fi . g. 1 1 Revolutions and surface speed per minute oi

5 3 3 The top cage

22 03 x 21 x 22 S d 1 45 4 5 urface spee 7 220x 3 6 x 27 x 5 >< 1 3 x 1 3 x 27 x 25 x 3 3 The b0ttom cage

2 8 93

2 8 93 x 1 6 x 22 S d 1 45 5 1 urface spee 7 5 The cage rollers

1 57 56 1 57 56 x 3 x 22 S d urface spee 7 First or the top 5 calender } 1 6 x 1 3 x 24 x 65 x 7 1 x 23 Surface speed 3 4 COTTON SPINNING CALCULATIONS

220x 3 6 x 27 >< 5 The second calender

Surface speed

5 The thl rd calender 1 008 4 1 6 x 1 3 x 24 X 65 x 7 1 X 21

1 00 08 4 X 5 a 5 X 2 Surface speed g 1 7 4 ‘ 80

’ C a le d e ns 55D 1a

La p Ro lle r s

S h a ft

F I G . 1 1 .

The fourth or 220x 3 6 x 27 x 5 X 1 3 x 1 3 bottom calender } 1 6 X 1 3 x 24 x 65 x 7 1 Surface speed

220x 3 6 X 27 X 5 X 1 3 X 21 X 1 7 The lap rollers

1 3 ” 7 7 9 x 8 4 x 22 Surface speed 1 97 ‘ 42 7

— Drafts in Openers I n the processes embraced in Spinning is t d in d d the cotton a tenuate a somewhat gra uate manner , until AND COSTS OF YARN 3 5 it is reduced to a specific weight per unit of leng th ; the extent i i d in in of the attenuat on appl e , each as well as the collective d di i processes , epen ng upon the ult mate fineness or count of the The i is i d i yarn required. attenuat on ncrease w th the fineness and it is di i d i i of the yarn , str bute amongst the var ous mach nes n i i i d i i proport ons wh ch pract ce has prove most benefic al . A k d x x di in nowle ge of the e tent most e pe ent each process , as well i i in i as between the var ous po nts each process , s 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 I t is d in x i d various stages . use also e press ng the ifference in the rate of movement of the parts of a machine . It denotes the i i two i i amount of attenuat on occurr ng between po nts , wh ch it i s customary to express in terms of one unit of the preceding of the T if d in two points specified. hus the raft an opener is said to d i in i be three , the rate of the el very terms of one un t of the feed is and is d an x three , therefore the cotton elongate to e tent of i i s i i and in three t mes t or g nal length , consequence becomes at

- i i least one third of the we ght per un t 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 . (b) By comparing the weight of the cotton per unit of length at the respective parts . (0) By calculating the relative movement of the respective parts by means of the connecting gearing . The d a and b i metho s ( ) ( ) are , of course , only pract cable when Th it is convenient to work the machines . e other method (c) i i and necessitates part culars of the gear ng only, the draft can I t i be ascertained at any time . s the method most generally

d and is . it is i i adopte , accurate When nconven ent to obtain i xi particulars of the connect ng gear, an appro mate result may i d i d be quickly arr ve at by e ther of the former metho s .

The i i i d a and c follow ng calculat ons llustrate the metho s ( ) ( ), S d i i d the pee s represent ng the former , however , be ng those alrea y ascertained by calculating from the connection with the driving 3 6 COTTON SPINNING CALCULATION S

i i d i i . x i i i shaft, nstea of by t m ng E amples llustrat ng the appl cat on of the method (b) will follow .

Calculations r elating to the drafts between the t arions eon ti uous ar ts com ri s ed in the o ener as r e r es ented in Fi s g p p p , p g

and 1 1 . 7 , 8 , 9, 1 0, The dr aft between ’ ) The supply and bottom lattice (Fig. 8

" By the calculated 7 3 5 surface Speeds 1 0 94” or, by the connect ins sear

The lower hopper lattice and the spiked lattice 4 2 8 By the calculated surface speeds 3552 48 x 48 x i 5 6 or, by the connect ng gear 7 20 x 20 x 5,

The Spiked lattice and the feed lattice to the porcupine i 8 and 9 cylinder (F gs . )

By the calculated surface speeds 422 98 Ey the connect 1 I ng gear 1 7 x 23 x 4 x 62 x 40x 3 3 x 20x 5;

h T e feed lattice and ﬁrst presser roller to porcupine cylinder F ( ig. 9)

By calculated surface speeds

By the connecting gear

The feed lattice and the ﬁrst lower feed roller to the porcupine

By calculated surface Speeds

By the connecting gear AND COSTS OF YARN 3 7

The ﬁrst lower feed roller and the pedal roller

7 2 9 1 By the calculated surface speed 647 3 3 x 2g By the connecti ng gear di rect 27 X 3

T i n he pedal roller and the ﬁrst bottom cage (F gs . 9 a d 1 02 53 By the calculated surface speeds 1 4 23 7 2 61 By the connecting gear direct

44 x 1 6 3 4 x 1

T he ﬁrst bottom cage and the ﬁrst cage rollers (Fig. 10)

1 105 By d d 1 078 the calculate surface spee s . 1 02 48 1 1 5 x 44 >< 3 69 By the connecti ng gear di rect 44 x 20 x 1 6 64

The nd d ﬁrst cage rollers , a fee rollers to beater 1 3 1 6 By the calculated surface speeds

20 x B the connect ing gear di rect y 1 4 x 3

The feed rollers to beater and the second bottom cage (Figs . 10 and 1 1)

By the cal cu lated Speeds 1 3 1 6 By the connect 28 x 3 0x 24 x 3 8 x 27 x 25 x 25 m l r s se er d ect } 40x 24 x 24 x 7 1 x 21 x 23 x 1 1 5 x 2;

1 1 Second bottom cage and the second cage rollers (Fig. ) 1 43 -55 By the calculated surface Speeds 1 02

1 1 5 x 25 x 3 By the connect i ng gear di rect 3 3 x 1 6 x 1 6 3 8 COTTON SPINNING CALCULATIONS

D r aj ts (continued)

First calender (top) and the second cage rollers

By the calculated surface speeds

1 6 x 21 x 5 5 B the connecti ng gear di rect 1 07 y 25 x 23 x 3

Second and ﬁrst calenders 1 045 By the calculated surface speeds

By the connecting gear direct 1 0 45

Third and second calenders

By the calculated surface Speeds

By the connecting gear direct

Fourth and third calenders

By the calculated surface speeds

By the connecting gear direct

Lap rollers and the fourth calender 1 97 4 2 By the calculated surface speeds

’ 7 1 x 21 x 1 7 x 8 2 By the connecting gear direct

The draft between the lap rollers and the feed rollers to the beater

- By the calculated 1 97 42 surface speeds 1 3 1 6

By the connecting gearing direct

By the intervening x X drafts 1 X X 1 2 25

1 T i s e h d ﬁciency i s d ue to the dr afts between the various p ar ts being i ncomp letely e essed xp r .

4O COTTON SPINNING CALCULATIONS

d x i the length , contracte to the e tent of t mes the length

d d i i i x . T elivere , thereby ncreas ng the we ght to that e tent hus i 1 0 0 the we ght of the cotton d. 1 2 x x O! S' per y 5 7 fed by the pedal roller (x)l

The weight of the cotton at any other points may be similarly d i i xi if is calculate , the we ght be ng only appro mate the loss

unknown . The following answers relate to the weight of the cotton at i i d and i the var ous po nts , the loss between the pe al roller ﬁrst pa r

i d 2 . and 1 . of cages be ng assume as per cent , per cent between n The i i i the ﬁr st a d second pairs of cages . work ng of th s quest on is given so that the student may accustom himself to the ki wor ng of such exercises . The weight of the cotton at d Fee lattice to porcupine ozs . d Pe al roller Ans .

(Working ) Let a weight of the cotton at the pedal roller

(a (93 i 2 we ght of cotton at deli very 1 ozs . draft 27 2

9 7 . A s 1 2 . x 1 2 x 2 x 2 68 A . ozs ge 7 3 3 ozs . ns

i i 2 F Ans . 4 rst pa r of cages 3 ozs .

d A s 1 2 Fee rollers to beaters n . 8

d i Ans Secon pa r of cages .

B w d and 4 A s et een calen ers 3 n .

I t is customary to alter the draft by means of the wheels on id S S i i the s e haft , also l ght alterat ons by adjustments of the cone strap .

I N OF D AF I N TH E As D A I EXERCISES RESPECT R TS OPENER PER ET ILS N FIGS .

7 8 9 10 AND 1 1 N V W H A W A P D D , , , , I CLUSI E , IT NS ERS P EN E .

Find the drafts between the following parts by gear direct 1 1 S i d i and d An 0 1 ( ) p ke latt ce pe al roller . s . 71 . 1 2 S i d ic and d the ( ) p ke latt e fee roller to beater . A ns . 03 1 . 13 S i ed i e and ( ) p k latt c lap rollers . Ans. AND COSTS OF YARN 4 1

14 d to ind and d to . Ans . 1 1 ( ) Pe al roller cyl er fee rollers beater 8 .

15 d ind and nd m e Ans . ( ) Pe al roller to cyl er seco botto cag .

1 m nd A n . 2 38 6 d in and s . ( ) Pe al roller to cyl der botto cale er .

n nd . A ns 1 1 . ( 17) Feed rollers to the beater a d the ﬁrst cale er .

1 d and Ans . ( 8) Fee rollers to the beater the lap rollers . 19 h n n Ans ( ) T e seco d bottom cage a d the lap rollers . .

20 n om nd A ns . ( ) First calender a d the bott cale er . (21) Assuming that this opener produced laps which weighed at the rate of 13 5 d w n in w i w d i e om e c ozs . per yar , hat cha ge that e ght oul ar s fr a h of the foll owing alterations (a) The 3 0 cross - shaft bevel changed to 27 ? b The ini n on the o m n to 22 and d i in it on the Sid ( ) p o b tto co e , that r v g e Shaft to 3 8 (c) The 5- inch pulley on the beater Shaft to 6 inches ?

A ns . . ozs . ; ozs . ; ozs 22 W n w d d w i in 10 d min ( ) hat cha ges oul pro uce a lap e gh g ozs . per yar , assu g wi the e in in m d w i 12 d that th g ar g as the ﬁgures the lap a e e ghs ozs . per yar ?

SCUTCH E RS . — The Particulars of Driving Speeds of the p arts in the Fi scutcher ( g. In this ﬁgure B is driven by a belt from a 25-inch pul ley on and is d i nd a counter Shaft , the latter ﬁtte w th fast a loose 1 5 i in di and d i pulleys , nches ameter , these latter are r ven by a

2- i di d i belt from a 3 nch ameter rum on the l ne shaft , which makes 220 revolutions per minute . Th i i i e revolut ons per m nute of the var ous parts , together i with the calculat ons , are as follows

220 X i Beater Shaft (B) f?2ﬁg

220 x 3 2 x 25 x 5 8 3 8 1 1 5 x 1 0 x 7

220 x 3 2 x 25 x 6 Cross shaft 58 6 0 6 1 5 x 1 0 x 1 2 Driver cone 220 x 3 2 x 25 X 6 X 65 drum (D) 1 5 x 10 x 1 2 x Feed lattice 6 45 x 1 x 3 9 roller (F)

Surface rate 42 COTTON SPINNING CALCULATIONS AND COSTS OF YARN 43

6 x 1 Her 8 3 42 Pedal ” - 1 5 x 1 0x 1 2 x 5 5 x 42 5 x 8 8

Surface rate

2 Lap motion 220 x 3 2 x 5 X 6 x 8 shaft (L) 1 5 x 1 0 x 1 2 x 20

Eottom cage U0 1 5 x 1 0x 1 2 x 20x 7 1 x 74 >< 96 Surface rate

' 2 Top cage (C) 220x 3 2 x 25 x 6 x s 3 1 5 x

Surface rate

6 x 8 x 1 3 x 20>< 1 9 _ TOPcalender (21) 10506 1 5 x 10x 1 2 x 20x 7 1 x 74 x 21 1 05 06 x 5 x 22 Surface rate 1 65 094 7

Revolutions and surface Speed per minute of

Bottom calender 220X 3 2 X 25 X 6 X 8 X 1 3 X 20 1 1 612 revs‘ (1 9- 3 2) 1 5 x 1 0x 1 2 x 20x 7 1 x 7 4 H 1 1 o 61 2 x 5 x 22 Surface rate 1 82 474 7

6 x 8 revs 1 5 x 1 0x 1 2 x 20x 7 1 x 74 I I 6 3 8 7 X 9 5 x 22 Surface rate 1 90 6 96 7

Drafts between

Pedal roller and feed lattice

By gear direct 1 0 25

b d d ( ) By the surface rates, alrea y calculate 4 4 COTTON SPINNING CALCULATIONS

Bottom cage and pedal roller 8 diameter 1 2” diameter 1 45-93 8 2 7 8 4 524 3 5

Top cage and bottom cage 1 54 x 1 2 1 0 1 ” 3 96 x 1 9

1 44 09

Bottom calender and bottom cage 96 x 5

3 2 x 1 2 1 8 24 74 (b)

Lap rollers and bottom calender 74 x 1 1 x 95 20 x 74 x 5 1 906 96 b 1 045 ) - ( 1 8 2 47 4

Lap rollers and bottom cage “ 0 1 3 06 3 2 x 20 x 7 4 x 1 2 1 906 96 b ( ) - 1 45 98 8

Lap rollers and pedal roller 1 1 x 95 ‘ 1 2 1 90 696 52 43 5

Lap rollers and lattice roller

1 3 1 90696 AND COSTS OF YARN 4 5

A I N FI G . 12 EXERCISES I N RESPECT OF TH E P RTS .

1 —W Si of EXERCISE . hat zes (a) Beater pulley would be required to give 1066 revolutions of that part per minute (b) Counter shaft drum (25 inches) would be required to give 1266 revol u tions of beater Shaft per minute (c) Pulley on the fan shaft would be necessary to give 1 173§ revolutions of fan per minute ? (d) Pulley on the beater Shaft woul d be necessary to drive the fan 1 67 5 revolutions per minute ? (e) To what extent would the weight produced by the machine be affected by the alterations (a) and (b) respectively (f) What changes respectively in the gearing would be expedient after m in i n a and b if it was i d wei d d ak g the alterat o s ( ) ( ), requ re that the ght pro uce in a given time remain as before the alteration

— 2 W t wo d d in the m c ine Fi . 12 om if EXERCISE . ha ul the raft a h ( g ) bec e , the following alterations were made in the gearing (a) The 8 - inch pulley on the cross shaft changed to 9 inches and 7 inches successively (b) The 65- inch pulley on the cross shaft changed to 6 inches and 7 inches successively

c The 6 -inc and 8 -inc u ot on the S are c n d to ( ) 5 h h p lleys, b h cross haft, ha ge 7 inches each

EXERCISE 3 a A in the w i t in nd in e of c e a b ( ) scerta e gh , pou s, per lap ach the as s ( ), ( ), Exe i 2 and o the n m of m d in 10 o min rc se , als u ber laps a e h urs, assu g they

m r d 3 6 7 d and d 22 . 15 . wi in easu e yar s, average lbs ozs each , th the gear g

i i 12. A ow 10 n . im . otherw s e as per F g. ll per ce t for lost t e

n in i - in - n h (b) What cha ge the s z es of the 65 ch or 8 inch pulleys o t e cross b n 12 m d wi S w d e e od e oz s . d if t haft oul ec ssary to pr uc a lap per yar , tha a e th

the in er Fi . 12 w i d 10 . d A t diff gear g, as p g , e ghe ozs per yar ? lso, sta e the er n in n and wei in o in n e w i w d be d e ce the le gth ght, b th sta c s, h ch oul cause by the n cha ge. 0 W eff on the of i m in w d om an ( ) hat ect, up output th s ach e, oul result fr alteration in the position of the strap on the cones Assuming the sum of the di me cone o i in 8 in and is on a ters of the s at opp s te po ts are 2 ches , the strap a of d i en con 4 in in di m w w d wei d part the r v e ches a eter, hat oul be the ght per yar

m d if t od d wi in Fi . 12 was 10 . of the lap a e , hat pr uce th the gear g, as per g , ozs per yard ? d I f m de in m ine d r Fi 12 e d 367 d c e . ( ) the lap a a a h , geare as p g , av rage yar s d w i d and an 22 . 1 5 . and in th was 2 er n . e ghe lbs ozs , the loss e process p ce t , the n m u ed d 4 w t should~ be wei t er d of c u ber of laps s at the fee , ha the gh p yar ea h of the latter 4 6 COTTON SPINNING CALCULAT IONS

4 8 COTTON SPINNING CALCULATIONS

Ans wer s to E xer cise 6 (a) Driver 3 1 32 33 34 3 5 36 3 7 38 42 Draft .

3 9 40 4 1 42 43 3 4

Answers to E xer cise 6 (b)

The Hunting Cog Measuring or Length Motion used in Openers

u h s - 14 K and A d and n S I n Fi . a d c tc er . g , represent the calen ers

FI G. 14 . also the connecting wheels ; H is the drop - shaft wheel ; G the d - G i its i is i su rop shaft lever , 1 be ng p vot , g a project on of G p d is i d and porte by the lower part of catch lever F , F p vote on P AND COSTS OF YARN 4 9

D D D i its u m coupled to the lower part of lever by 1 , hav ng f lcru The i I i D i C at E . spr ng presses aga nst , forc ng the wheel , i is d d D i B wh ch loose upon a stu attache to , to gear w th wheel , the latter being ﬁ xed upon the shaft of the calender A. R and i id C and w i B are project ons from the s es of the wheels B , h ch i h i are in gear . When the project ons meet t e wheel C s forced i i i D D and out of gear w th B , th s act on causes the levers , 1 , F and T di i to release g, consequently G falls to , thereby sengag ng H and Si is d i J from J , , nce the latter r ven by the former, ceases

Th di d- i to rotate . e fall of the lever G sengages the fee mot on clutch by r od connections with G Sho wn at point ! . 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

i C. contact w th R , on

The i and C are the least revolut ons of the wheels B , per lap , whole numbers which ex ress the r elation o their tooth contents p f , their r elative r evol utions bein invers e to thos e number s T g . hus , if B is 21 and C d 7 1 8 1 i , range from to teeth respect vely, i l a d i in the revolut ons of these wheels , per p, woul be as g ven I f B h . 50. ad 2 and the ﬁrst part of the table on p 7 , C d 1 8 1 i i d range from 7 to teeth , then the r revolut ons per lap woul I f h be as given in the second part of that table . C ad 80and d B 2 i i i 1 and 40. teeth , then the r respect ve revolut ons woul be Should C be any number which has no common divisor between i nd i if i tself a un ty, then , B conta ns less teeth than C, the revolutions of B per lap would be the same as the teeth contents of C. A i di d 5 i ssum ng the ameter of the calen er nches , then the length of the lap would be

o x revolutions of B per lap yards 3 6

i B x 4 63 d or , revolut ons of per lap 0 3 yar 50 COTTON SPINNING CALCULATIONS

Si z es of the wheels Relative rate of

in tee t h i tat ion. ( h ). t e r ro Length of the l ap in yards as as certai ned by calcul ati on.

A P E — If C is 7 8 and B 41 and di m nd 5 in EX M L , the a eter of the cale er ches , and the draft between this calender and the lap rollers then the approx i mate length of the lap would be as follows The ratio of the tooth contents of C and B cannot be expressed in less w n m and n B wi m 7 8 i n hole u bers, he ce ll ake revolut o s per lap ,

7 8 x 5 x 3 1416 x 1045 length of lap in inches (approximate) inches 1067 feet

I t is nd w n is i x d m w fou that , he the lap very th ck , the lap e cee s so e hat the calculated length but as this discrepancy is the same in respect of each lap of m w i it is n n d and d n n the sa e e ght, ge erally eglecte , the calculate le gth take as the

actual .

The advantages of the hunting- cog m o tion is that it obtains the same length

on and i nn im d in m i n . T i each lap , th s ca ot be cla e respect of the other ot o s h s arises through the slow and irregular disengagement of the knocking- off catch in

the latter . Laps of a length representing any number of revolutions of the op erating nd can m i m i n cale er be ade by th s ot o . AND COSTS OF YARN 51

EXERCISE 7 ( a H ow m n i n wo d B m and w ) a y revolut o s ul ake , hat length of lap would if B and C we 41 n result, re a d 8 1 respe ctively and calender 5 inches diameter

A ns . 106 feet . b W ( ) hat length of lap would be made if B had 42 and C 8 1 teeth when the c nde B i ale r s 5 inches in diameter ? A ns 3 58 . feet . 0 W ( ) hat Sizes of B may be used for a lap of 3 6 2 yards if C had 83 teeth w en the end B is 5 in in di m ? - h cal er ches a eter Ans . 1 82.

’ PLATT S KNOCKI NG - OFF MOTI ON

I n Fi . 1 5 K is d g , the bottom calen er and A is a Single worm d it is d i A secure to ; B a worm wheel r ven by , and C a pinion ﬁxed upon the axis of B ; C drives the

i - off D i knock ng wheel , the project on E on D pulls the catch F and the lever i it is d in i G , to wh ch attache , pass ng i that po nt . This movement moves the lever G to the right on its pivot X until Th G ceases to support H . e latter is the drop - shaft lever and in consequence of i d w G d the w th ra al of the support , the rop

FI G. 1 5. shaft wheel is disengaged from driving the d and i i calen ers other parts dependent upon them for the r mot on ,

and d i i is d. hence , el very ceas ng , the lap complete To is i d i start a new lap , G ra se at a po nt on the left to enable is d the clearance of the catch F from E , F supporte by a i d i i d ﬁnger of the r ght han , wh lst the left l fts the rop lever i d i it H , when the we ghte port on of G , to the left of X , causes to i i i i i move nto a support ng posit on for H . Th s act on engages the

- d nd d i and d in i . rop shaft wheel , a sets the el very fee parts act on The length of the lap will vary according to the revolutions which the calender makes in turning the wheel D one revolution . The —B d i gear may be as follows z ottom calen er , 7 nches

di A 1 B 25 C 1 8 D 48 . ameter ; , ; , ; , ; , The revolutions of A per one of D will therefore be

5 4 a x 3 3 and the length of the 1 200 7 x 3 1 41 6 x lap in yards } 1 8 3 6

This type of length motion tends to the production of laps 52 COTTON SPINNING CALCULATIONS

i i in T i i sl ghtly vary ng length . h s ar ses from the slow move d i its i d and d its ment of part G ur ng w th rawal , the ten ency of d d i supporting surface to wear smooth and somewhat roun e ; th s , i i i assisted by the v brat on , causes the support ng part G to fall

' away at slightly varying intervals measured in revolutions of d the calen er .

8 —C l n EXERCISE . alcu ate the le gth of the laps

a W n C is 16 17 19 and 20 i . ( ) he , , , respect vely

A ns d . . yar s (b) When the following wheels are used together instead of those previously

i n : A 1 B 24 C 17 D 50 Ans . d . g ve , ; , ; , , . yar s W n B i d 4 ? 1 c s 2 Ans . 3 9 d ( ) he altere to yar s .

W n D i 42 d . (03) he s altered to 50? A ns . 5 yar s EXERCISE 9 I f 50 d on is i d w Sin w w d i n t a lap yar s l g requ re , hat gle heel oul g ve the eares

e ? Ans . n in D 9 r sult Cha g g to 5 .

EXERCISE 10

I f 48 d was i ed w Si C S d d? Ans. a lap % yar s requ r , hat ze of houl be use

EXERCISE 1 1 a W n in d w d m d if n in - ( ) hat le gth of lap , yar s, oul be a e the hu t g cog lap length m otion wheel on the top calender contained 82 and the wheel on the

n in - off 83 ? Ans k ock g lever teeth . b ind im d in n ( ) F the t e taken to make a lap yar s le gth . A ns 3 845 min . utes . 0 i f ne and d i n in ( ) What would be the we ght O o lap also the pro uct o lbs . per 10 if 2 n w was x d and im in a in hours , per ce t . aste e tracte the t e lost t k g out the nd in id n n and w i laps a other c e tal stoppages equals 8 per ce t . the e ght of the four i m in d c 1 18 d. A m n laps co pr s g the fee ea h average ozs. per yar ssu e the le gth of

ds . A ns 3 9 6006 the lap yar . lbs . ; lbs . (d) What changes in the gear would be best to reduce the output to a

n m m n 3000 . er 1 0 s wi n in c n or al a ou t, say to lbs p hour , thout cha g g the ou t of the lap ?

Ans . d c i 8 in and in Si 24 in in cor ondin Re u e s ze of ches, crease ze of ches resp g ti n r in in 24 in in o or o o 8 s 6 c 30 . pr p s che to hes, ches to ches

PRACTI CAL OTE S N .

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 facili tate adjustments in i i d d the we ght of the lap , as c rcumstances eman , an adjusting

i is id d. T i nd screw connect on prov e h s latter , a changing the AND COSTS OF YARN 53 d li d and raft gear, are the means of control ng the raft , therefore Th d of the weight and count of the lap made . e range of a just i in r es ect d i is i i d ment pract cable , p of the raft by gear ng , unl m te d is i i d and but that by the a justment of the cone strap very l m te , should only be availed of for temporary adjustments . The i i d is best pos t on for the cone strap , when the fee of the “ T i is . i mean or normal we ght , at the centre of the cones h s secures id and i the w est most useful range of act on of the cone strap , adaptable equally toward light and heavy variations in the feed. W d i d i hen , by temporary a justments , so often necess tate by var a i in and i i t ons the character of the cotton , act ons of the mach ne , in di i d common or nary work ng , the cone strap has been gra ually d and d in i i i move settle a pos t on otherw se than central , steps ought to be taken to alter the draft to an extent which will i i i restore the cone strap to the centre pos t on , or otherw se the fﬁ i i is i e cacy of th s part of the mach ne nterfered with . The i d nd d in system of connect ng the fee a elivery parts , i is i d these mach nes , by belt , be ng superse ed by rope or tooth Th e d i Fi 1 2 i . gear. metho Shown n g. s not always satisfactory Variations in the slippage of the above - named straps affect the d nd dd i i a a i i . raft , to that ar s ng from the cone strap Pos t ve driving reduces the possibilities of such defects without intro ducing any disadvantages . Fluctuations in the draft are al so often occasioned by variation in the slippage of the feed lattice ; too highly tensioned or slack i i i i and i latt ces , latt ce roller bear ngs out of al gnment , obstruct ons i di ti i id about these parts , b n ng of the lat ce aga nst the s es , these are amongst the chief causes of variations in the weight and Th i d i count of the lap . e system of connect ng the fee latt ce roll ers by tooth gear should receive consideration whenever the variations in the weight of the laps is unsatisfactory and i i d cannot be el m nate . P od io s S ds and h i Con o in F o s —I n r uct n , pee , t e r tr ll g act r the spinning of coarse and medium counts of yarn from American and i i and x s m lar lower types of cotton, e haust openers are

x i d I i di i e tens vely use . n these machines the pract ce of spens ng " - i the lap measuring and knocking off motion is extens ve . The d i i i i a vantages of such pract ce are , the el m nat on of the 54 COTTON SPINNING CALCULATIONS

i n i i and in th ck a d th n place , usually follow ng the stoppage , creased production ; it is also a deterrent towards dilatoriness d i i i on the part of the attendant . Pro uct ons rang ng as h gh as 55 d lbs . per week of 5hours are not uncommon un er such

conditions . d 0 mi and The rate of elivery ranges up to 3 feet per nute , the

- The i rate of the feed about one third of that amount . we ght of d i the cotton deliver ed ranges to oz . per yar per nch of

and d 2 5 . d i id . width , that of the fee ozs per yar per nch of w th The Sizes of j eed rollers are from 2} inches to 3 inches in

diameter . The highest surface rates of beating instruments range up to i 1 000 i . i feet per m nute Cre ghton porcup nes up to , i i d 1 1 00 i di 900 small porcup ne cyl n ers up to , porcup nes ( scs) ,

i i n d 600 - d d large porcup nes (3 6 nches a d upwar s) to , three bla e

1 250 - d d 1 500 i beaters to , two bla e beaters up to revolut ons per

° minute .

Fans range up to 2500 revolutions per minute . The on in F s in s f the P s and S ds N m d C troll g actor re pect o art pee a e . Small feed rollers are only adapted for light feeds at low rates and i i f i i pressures . Feed rollers wh ch have nsu ﬁc ent hold ng d i i i i “ i power eprec ate the open ng act on by allow ng pluck ng . — Overweighting in order to secure increased pressure better di — i d n hol ng power has the same tendency . H gh rates of fee a d i d i d beat ng, as well as heavy fee s , requ re larger fee rollers i i T uick n rrespect ve of the length of the staple . oo q a d over di d x d i d i fee ng pro uces an e cess of goo cotton w th the ropp ngs , and i i i i Th i nterferes w th the open ng and cleaning act ons . e S zes of feed rollers are from 2 inches to 3 inches diameter 24 inches i d is i and are only su table when the fee l ght , slow , the pressure

d . i d i d d n mo erate H gh spee s , accompan e by a heavy fee a d i 2 ° i i di 2 pressure , necess tate rollers 15 nches to 3 nches ameter ; 4 i d T nches are only a apted for moderate conditions . oo close i d i i i sett ng of these ten s to weaken ng the ﬁbres , wh lst the oppos te i d in causes a str ngy ten ency the appearance of the cotton . 3 When large rollers are used 1 3 inch would be satisfactory for i the heav est feed. With small feed rollers distances less than i a e d 3 nch r oubtful .

56 COTTON SPINNING CALCULATION S

16 Dr — C the d w n win EXERCISE ( afts). alculate rafts bet ee the follo g parts in Fi 13 g.

i L and d Ans . att ce pe al rollers . (

d nd A ns . Pe al roller a bottom cage . ( B m n a d A ns . otto cage cage rollers . ( t o nd A ns p cale er . ( . ir and S nd nd A ns F st eco cale er . ( . d and i n S n d d A ns . eco th r cale er . ( T i d and nd Ans h r fourth cale er . ( . nd and Ans . Fourth cale er lap rollers . ( ’ d i n in nds in 10 nin d w in min Pro uct o pou hours u terrupte ork g, assu g the lap

w i 2 in Ans . e ghs 5 50 gra s per yard. (

A d w n d i and Ans . lso , the raft bet ee the fee latt ce lap rollers . ( A w i d n fed min la d d lso , the e ght, per yar , of the cotto , assu g the p pro uce to

w i 5250 in d win 2 n . in w . e gh at the rate of gra s per yar , allo g per ce t for loss aste

A ns . r in ( g a s .)

CARD CAL CULATI ONS .

i i F g. 1 6 represents the gear ng common in cards of the I n dif revolving ﬁat type . the ferent makes of these machines and in di i d wheels other parts of vary g mens ons are a opted, to d di i d i a apt them for the con t ons un er wh ch they work . The subtended calculations relate to the Speeds of all the parts which i d in i i they conta n ; they are arrange the follow ng nstances , i in i d . as far as conven ent , progress ve or er Slippage and thick nesses of belts and ropes have not been taken into consideration in i it is d i do in these calculat ons , but a v sable to so practice . I n d bad di i i d i , , is i id belt r ves un er con t ons th s somet mes cons erable , but under fair conditions should not amount to more than two

. i in i i or three per cent at each po nt transm ss on . The actual d i he spee s w ll , therefore , somewhat less than the calculated. The Speeds given are those in common use in treating ordinary i and A i Egypt an the better classes of mer can cotton .

The i S i dr i i l ne haft from wh ch the strap v ng the card, in the is d i is d 220 , i mi ﬁgure r ven assume to make revolut ons per nute , d d it 1 2 i in di an the rum upon to be nches ameter . The dimensions given refer to the diameters in inches in in respect of pulleys , or teeth cases of wheels . AND COSTS OF YARN 57 58 COTTON SPINNING CALCULATIONS

Sur ace s eed er minute f p p . t i s f ca cu ion De a l o l lat .

I n inches . I n eet f .

Lap roller

220x 12 x 18 x 5 x 28 >< 40 x 40>< 14 x 17

l 5x 7 x 10x 100x 216 x 40x 1 20x 48

04 848 x 6 x 22 9 1413 07 6 17 7

" The feed roller ( 120 x 17 x zé )

220>< 1 2x 1 8 x 5 x 28 x 40 x 40>< 14

1 5 x 7 x 10x 100x 216 x 40x 120

" 1 3 69 x 24 x 22 08 06 7

" The l ickerin (7 x 5

452 57

127869 8 1 0655 8

The cyl inder ( 15 x 18 x 50 x 64 220 x 12 1 5

17 6 x 50 x 22 27607 23047 5 7

The 40 h in im in flats ( x ere, est at g c m m n it is m d the surfa e ove e t, assu e that the dis tance from centre to centre of the flats m r 1 in and d i n w easu es 4 ches . are r ve by a heel c n inin 1 2 w i n o ta g teeth, each of h ch e gages a flt ” T m a . he w d i in w m w l or , r v g the or hee has d d a ouble threa .

220 x 1 2 >< 6 §x 1 x 2 15 x 1 2 x 24 x 40 143 x l 2 x 1§ 7 20 x 1 x l

e no h wn The d i in B ru sh s : t s o . r v g gear for the brushes that clean the flats is not con tained in The d the figure . spee of that part varies ; under ex ceptional circumstances it is d i 3 00 r i n mi worke as h gh as evolut o s per nute . The normal rate of the ordinary brush is about m A n 40 revolutions —per inute . pate t com binatio—n brush which gives encouraging results i s worked as l ow as 5 revolutions per mi nute The stripping brush u sed in cleaning ‘ i nd and dofier i s d i n d in the cyl er r ve , ur g that AND COSTS OF YARN 59

Sur ace s eed er minute f p p .

Det ai s of ca cu ation l l l .

I n h et I n inches . .

O i n m r in o perat o , fro a g oove the l ose pulley on the ind s the di m in cyl er haft, a eter be g 1 5 1 6 in whi on or ches, lst that the brush i m 5 10 in i in var es fro to ches, thus g v g From

220 x 1 2 x 1 5

1 5 x 10

220} 12 15 x 5

' The doﬁer (216 x 9 x 40) 5 x 28 x 40 1 5 x 7

17 6 X 26 X 22 958 -78 7 98 98 1 5 7

The bottom calender (3 0 x 3 1)

84 48 1 5 x 7 — [ Nata The doffer wheel is here a carrier]

x 4 x 22 l 062 03 7

The coiler delivery rollers ( 16)

220x 12 x 1 8 x 5 x 28 x 40x 3 1 x 20x 1 6

1 5 x 7 x 1 0x 100x 3 0x 1 5 x 20x 1 6 17 4 5 7 x 2” x 22 1 097 423 91 4 52 7

The coiler ( 106) 220x 12 >< 18 x 5 x 28 x 40x 3 1 >< 20x 3 8 1 5x 7 x 1 0x 100x 3 0x 1 5 x 20>< 1 06

The radius of the centre of the coiler tube at the point of ex it is 3 inches The distances traversed by this point 98 1 6

The can table wheel ( 8 2) 220x 12 >< 1 8 x 5 x 28 x 40x 3 l x 20x 1 6 l 5 x 7 x 10x 100x 3 0x 15 x 20>< 48 6 0 COTTON SPINNI NG CALCULATI ONS

n Surface sp eed per mi ute .

D t o ca cul ation e ails f l .

n inches I n eet . I . f

The number of coils laid per revolution of the can

Occasionally an alteration in the rate Of the can i s necessary through considerable he iv I f the change in thickness of t sl er . d can is in i n d n spee of the sufﬁc e t , the a jace t i in I f coils adhere instead Of fr eely unco l g . the rate of the delivery is gr eater than the e i i n the i i id Of c l g rate , sl ver st cks to the s es ‘ c n n r v rz a the a , a d ice e . ' The doﬁer comb 220 x 1 2 x 1 8 x 12

" 1 5 x 6 x 4

I t is now usual to furnish this part with a d d i i is ik steppe pulley, also the r ver of th s l e wi d d Of the mb se steppe , so that the spee co ' m a d d the Of the doﬁer y be a apte to rate . The indin di on the gr g sc, or roller, " cyl inder (5 X 220 X 1 2 x 1 8

63 3 6 x 7 x 22 7

The indin di on doﬁer gr g sc, or roller, the : ' the doﬁer during grinding is driven from the 1 8 - inch pulley on the cylinder during this i n in di onn d act o , the other gear be g sc ecte , the speed being

The direction Of the cylinder when grind in i s O i the n m w in di i n g ppos te to or al ork g rect o . ' The doﬁer in m di c i rotates the sa e re t on . This dir ection is opposite to that indi cated by the nd d wi in in be of the car re both stances . The di i n the m di i rect o of e ery scs, or rollers, s Opposing the movement Of the parts to be ground .

An increased or diminished rate Of any of these parts may O i d i i Of Of be bta ne by alter ng the s ze any the wheels or pulleys , AND COSTS OF YARN 6 1

in i i i ff i in di not a carrier , the ntercept ng tra n , the e ect be ng rect nd i d i ratio in case of drivers , a nverse when r ven wheels or pulleys . The grinding of the ﬂats is done at a similar speed to that

Of i d i d di i . the cyl n er , rollers be ng preferre to scs for th s work — To alter the Speeds of the Various Parts The speed of the lap i 48 d i rollers may be altered by chang ng the , r ven wheel , on the

- nd 1 d i d lap roller shaft , a also by the 7 , r ver wheel, on the fee

roller shaft . The speeds of the lap and feed rollers may be altered by i 1 20 d i W d 1 4 chang ng the , r ven heel , on the fee roller ; the , d i id 40 d i id r ver wheel , on the s e shaft ; the , r ven , on the s e shaft

and 40 d i doﬁer . the , r ver , on the shaft h d i d i i and T e speeds of the calen er, co ler el very rollers , co ler d i the doﬁer 216 can wheels may be change by alter ng , , or the

3 0 d . , calen er shaft wheel The d d ff d and d and spee s of the o er , fee lap rollers , calen er i d i and i and co ler el very rollers , also the co ler can wheels , may be changed by altering the 5- inch driver pulley on the lickerin

1 0- i d i 28 d i shaft, the nch barrow pulley ( r ven), the r ver wheel on Of 1 00 and 40 d i nd d the hub the latter , the the r ven a river ll i respectively . A these are connect ons in the train driving th e

doffer from the licker in. The speeds of all the above parts may be changed by any i i i d lickerin alterat on wh ch ncreases the spee of the . 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 d i i , woul be necessary to alter the connect ng tra n at some

' i e lickerin and doﬁer i po nt b tween the the wheel , nversely to the former change . Alteration in the movement Of the ﬂats may be effected by

i 6 -i d i i d 1 2 chang ng the 5 nch r ver on the cyl n er shaft , or the i d i ﬁat- i d nch r ver pulley on the mot on shaft , or the ouble , for a treble , worm . 62 COTTON SPI NNI NG CALCULATI ONS

E T RATI N F SPE E D S OF ARTS EXERCISES R AL E O O VARIOUS P .

—I f the d ind m 178 i n min w n EXE RCI SE 1 . car cyl er akes revolut o s per ute he 16 in in di m w w d its fast and loose pulleys are ches a eter, at hat rate oul each of its parts work after changing the fast and loos e pulleys to 18 inches diameter ? Answer s

C ind C i yl er, o ler,

Lickerin 4022 . Can w , heel, ‘ '

Doﬁer D oﬁer m 1408 . , co b, — d S i in 235 470. Fee roller , tr pp g brush,

La indin di c 563 . p roller, Gr g s s ,

C nd D ff w n indin 3 13 . ale er, o er ( he gr g), C i d i o in min o ler el very r llers, Flats ( ches per ute),

E — a i n w d be n to e d of E XERCI S 2. What lterat o s oul ecessary restor the spee s all im i d in the i n ex in inde to o i in the parts pl e last quest o , cept g the cyl r, the r g al rates Answer s

- d i in i k rin 2 2 in 1 8 inch pulley r v g l c e to 0 5 ches .

< in d i in w in 7 ch pulley r v g barro pulley to ches .

1 - in l on ind d i in the d ff m inc 6- in 8 ch pu ley cyl er r v g o er co b to hes, or ch in pulley to 53 ches .

' - i i n ﬂ on nd d i 3 1 in 65inch pulley the cyl er r v g the ats to 7 ches .

- on indin di 4 in 5 inch pulley the gr g sc to 3, ches .

I E 3 —A d in doff in di m t m in 1 EXE RC S , car hav g a er ches a e er, ak g 8

n min t d 550 lbs . s i w h i in revolutio s per u e, pro uces of l ver per eek . T e dr v g 16 in di m and ind m 180 i n pulleys are ches a eter, the cyl er akes revolut o s per W i of w d n d d d d 1 60 minute . hat s ze pulleys oul be ee e to re uce the spee to revolutions per minute ? What effect would this change have upon the revo ' ﬂr i lutions per minute of the do e as well as upon the length and we ght produced per week l 18 in e n 488 . Ans. ch s ; less le gth ; 5, lbs per week .

The D ft s be ween the V ious P s how s e in d —T ra t ar art , a c rta e he draft may be ascertained by comparing the weight per unit of length of the cotton at the different points in the machine ;

i i d i and o also , by t m ng the spee s of the respect ve parts as er i i i i i and i i ta n ng from th s the r rat o ; aga n , by calculat ng the mechanical value of the connecting train of gear and dimensions of surface . It is preferable wherever possible to do this by the latter i i d Th t t i . e o system , as furn shes the most rel able ata tw o her v in i i xi and ways serve ery well ascerta n ng appro mate results , in i also check ng the calculated draft .

4 6 COTTON SPI NNI NG CALCULATI ONS

Calenders and coiler delivery rollers

1 062 03

1 5 x 20 x 1 6 x 4

‘ The D f s be w n the V ious P s ho d —I i ra t t ee ar art , w altere . t w ll be seen fr om the foregoing that the drafts between any Of these d i i d i parts may be altere by chang ng the s ze of any r ver , or I i d i i d in i i . r ven wheel , compr se the r connect onal gear ncreas ng the Size of a driver increases the rate of the part nearest the d d and d d t fee , of the two parts concerne , therefore re uces the raf , ct i i and vice vers . Alter ng the driven wheels has the nverse of i d ff the aforement one e ects . 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 d together the intervening drafts between the parts involve . Thus The d and i d i total raft , between the lap co ler el very rollers

(a) 1 04 X 1 3 32 X X 00 346 X X 1 033 1 18 4

By comparison of the surface Speeds Of these two parts 1 097 -428 1 20 9 1 41 3

By the connectional gear and sizes Of parts

l 7 x 1 4 3 0

' The draft between the feed roller and the doﬁer

(a) 1 298 X X 00346 97 958 7 8 (b) 99 04

” 1 20 X 40 X 26 14 x 40 x 24 AND COSTS OF YARN 6 5 — 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 f i i I f i is x d d more than su fic ent to keep the lap stra ght . th s e cee e i in f d i irregular ty the cotton e w ll result . Smooth lap rollers are i i i Of i i and l able to cause sl pp ng the lap , caus ng fluctuat ons , d i h nd i d a greater raft than that est mated. T e corrugated a r bbe i i i forms of lap roller el m nate th s tendency . The draft between the feed roller and lickerin varies con l I is r sider ab y . t customa y to alter the speed of the former part n i d T whenever a change i the draft is necess tate . hat of the is i d i i latter part rarely nterfere w th , be ng generally about one i d i i d . A i at half the rate of the cyl n er lter ng the raft th s po nt , i d therefore , changes the rate at wh ch the fibres are presente to i Of lickerin and d i the act on the , therefore controls the urat on of its i i i comb ng act on upon any g ven fibre . The draft between the flats and the cylinder is regarded x d i f A i generally as fi e for d fferent classes O cotton . lterat ons i The in th s are made by varying the Speed of the flats . rate of movement of the flats in the main governs the duration of the ’ i d i d and cyl n er s act on upon a given bo y of fibres , also the Of di d d and it is amount clean car ng surfaces intro uce , hence proper to vary their Speed according to the exigencies of card

in . i ne di n d i g W th ppy , rty , a d matte cottons a h gher rate of i is x di I di and i . l o A i th s part e pe ent For w mer can , n an , l ke i i d d in qual t es of cotton , they are worke at about ouble the rate vogue for the clean qualities Of American and Egyptian . Th ﬂr is i d e d nd do e raft between the cylinder a also var e ,

i x I n i d d probably more than s e pedient . th s the spee of the offer The is Often regarded as subordinate to the count Of Sliver . i Of i i Th d w propr ety th s s discussed elsewhere . e raft bet een the d f and It S d o fer the calender is only varied slightly . houl always ” u i d x be s ch that the sl ver , or web , oes not sag to an e tent i is d i d if d is wh ch etr mental . On the other han , the raft too

i i i i . The much , rregular ty through overstretch ng w ll result draft between the calender and the coiler delivery rollers should be sufficient to maintain a slight tension at all times . 6 6 COTTON SPINNI NG CALCULATI ONS — Condi ti ons contr olling the Output of a Card General 00n — i d d i in ditions . When c rcumstances eman an alterat on the d i i i Of quantity Of the output , a knowle ge of the l m tat ons each action are essential in deciding the best manner Of procuring d i d i i i the same . This knowle ge cannot be ga ne w thout nt mate A i Of association with the work . ss stance a general character nd i is d in i may be afforded, a th s attempte the follow ng state ments . d Of di Greater the contrasting Spee s the car ng parts , longer the fibres are desired to remain in the carding action ; greater d di the length Of the fibres treate , closer the car ng surfaces ; m ore 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 di fficulty involved in their separation . The more numerous the body Of fibres present in the carding

d i i i : d Of influences , beyon a certa n l m t the greater the ten ency i n x i i T i damage to them by roll ng a d e cess ve strain ng . h s occurs whenever the quantity Of fibres are in excess Of the capacities of i di and in i Of the ava lable car ng surfaces , results some port on the weight Of the flats being borne by the body of fibres instead T i d i of by the bend. h s ten ency ncreases as the crowding becomes T i r i d more intense . h s becomes appa ent through the ncrease power required to drive the card. Such conditions are more

i i in i i ﬁbr ed . l kely to ar se treat ng long than w th short , cotton I nconsistent increases in the power consumed by these i i Of i d d mach nes , after alterat ons th s nature , may be regar e as s igns Of overcrowded carding surfaces and straining of the

ﬁbres .

is tinct conditions i n r es ect o the actio th a in a ts D p f ns Of e c rd g p r . — The functions Of the lickerin are to straighten the ﬁbres i i Of i i i compos ng the fr nge the lap , el m nate fore gn 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 l ickerin i Of i Of d , to carry them nto the range act on the car flats , h i whereupon the latter arrest t es e fibres otherw se than straight . AND COSTS OF YARN 6 7

The i i i act on of the cyl nder , about this latter port on of the i is di and mach ne , rectly upon those fibres held by the flats , i i i d i part ally project ng n the carding action . The gra ual stra ght enin and i d f i d g w th rawal O these , ntro uces others more or less i I n i the cont guous to the carding action . th s way super abundance Of fibres which the flats receive during the earlier i d i i i and d per o of the r act on are held n reserve , gra ually i A d r d brought nto the action . s the fibres are gra ually sepa ate

and i d i d ff i d . stra ghtene , they are carr e O by the cyl n er The i i i di funct ons Of the flats are to rece ve fore gn bo es, 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 d i i Th i f and d i efin te per od. e fac lity O the flats to arrest eta n foreign bodies and to retain and present the fibres requiring di d d f i i these car ng, epen s upon the e ficacy of the po nts , compos ng and surfaces , 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 tinu all i d i i f i y pass ng into action . Shoul th s latter be nsu fic ent the imperfectly carded cotton from the lickerin would be carried d i i d and in i forwar by the act on of the cyl n er , pass ng the d d Of i d d d thes e crow e surface po nts of the flats , woul ten to embe

d i i . T d fibres alrea y engag ng the w re hose fibres , brought forwar , which cannot be accommodated by r eas on of the crowded character Of d i d the surfaces , are subj ecte to the pressure prev ously referre and i d d and ne ed di to , are thus stra ne , rupture , pp accor ng to the d egree of overcrowding . To guard against the fibres becoming embedded care Should be observed to ensure that the proper inclination Of the bend in i is T i i d d i i w re preserved. h s s Often epresse through the str pp ng i i di i its i brush be ng used n an unclean con t on , also by be ng Th S d set too deep . e wire on all surfaces houl have a fine i and i u d i i d in i keen po nt , th s sho l be ma nta ne as un form a con dition as possible . — The Rate of Movement of the Flats I t would seem that if the 6 8 COTTON SPI NNI NG CALCULATI ONS

d i d i d wire surfaces act as heretofore escr be , a per o very much less than forty minutes would more than suffice for the selection Of all the desirable fibres from those received by the flat whilst d occupying the first position on the ben . Such may be the i in i i i case , but s nce the flats when even the r last pos t on arrest — fibr es proved by passing a little coloured cotton in with the — i i its x x d lap , th s mak ng appearance on the ne t flat e pose the best way in deciding the proper speed Of flats is to recognize the x The d d d d strips from them as the inde . spee shoul be a juste i TO to give the lightest strip that will strip sat sfactorily . adjust the percentage of strip by manipulating the front stripping i i i is i i plate s wrong in pr nc ple . There only one correct pos t on t and is and i d for tha part , that as near the flats cyl n er as i I i its di pract cable . ncreas ng stance from the flats causes the detachme nt Of portions Of the entangled fibre and impurities selected in the carding action from the flats as they move out Of i and i i e act on , thus pollut ng the work otherw se a com lished p .

' I n id i Of f doﬁer its cons er ng the rate movement O the , functions as well as the length or the weight must be kept

in mind. The function of the doffer is to take the ﬁbres fr om the

The . cylinder . more completely this is accomplished the better Should the cylinder be only partially cleared Of the fibres it its i in di i i d i borne upon , nfluence car ng w ll be nterfere w th to that extent ; because it reduces the extent Of the surface of carding points at liberty to act upon these fibres presented by i k rin n T i l c e a d . he a m in i the flat surfaces , therefore , work ng the doffer Should be to clear the cylinder as completely as i and i its poss ble , to ensure th s surface rate should be as high as T i p ra cticable . h s rate cannot be specified only in general terms Of id i i in i i i on account the w e var at ons the work ng cond t ons . Li i bad d uns atis ght sl vers , poor staple , laps , poor selve ges , doffin d d S i factory g combs , ba ly constructe l ver easements , d d i d f raughty rooms , all ten to restr ct the speed at wh ich the o fer d can be run . Un er favourable conditions 1 6 revolutions per minute can be attained. Th e rate of the flats is as high as 3 per minute . AN D COSTS OF YARN G9 — The rate Of cylinders is 1 70 1 80 revolutions per minute for

low American and like cottons . The rate Of cylinders is 1 60- 1 7 5 revolutions per minute for i n iti E gypt an a d American better qual es . — The rate Of cylinders is 1 20 1 60 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 doffer and Sid nd Si id i e shaft a feed roller. nce the s e shaft transm ts i d d i i i the mot on to the fee parts , a r ver wheel w ll nﬂuence the d in di i and d i i rate of the fee the rect rat o the raft nversely, wh lst

d i i i f I t is ~ a r ven wheel w ll have the nverse e fect . customary to d Of id d i i alter the raft by means the s e shaft wheel , r v ng that d and i is d d n l on the fee roller, hence t calle the raft cha ge whee . W i is i i Of i i in i henever th s mpract cable , on account the l m ts s z e Of i it is d wheel appl cable , customary to alter that on the fee roller to an extent providing a more convenient range Of drafts i i O i id S nd d ff w th the wheels ava lable . ccas onally the s e haft a o er d i i x d bevels are altere , but usually these are nconven ently ﬁ e for i th s purpose .

E XE RCI — W t n in Of SE 4. ha cha ges each the wheels forming the draft gea r in Fi . 16 w d i 1 60 Of d min n d f 120? g oul g ve a raft, assu g the prese t ra t

Wor king and Answer s

' Bevel wheel on doﬁer Shaft

Bevel on Side shaft

Side - Shaft change wheel

Bevel wheel on the feed roller 1601

— - EXERCI SE 5. W d w d win id n w i hat rafts oul the follo g s e shaft cha ge heel g ve , i min d n in 12 n respect vely, assu g the car co ta s 0 of a draft whe n that wheel contai s 18 : 14 1 5 1 6 1 7 19 teeth , , , , , and 22 ? Ans 1 44 13 5 1 . 27 1 1 3 6 108 102 8 i . , , , , , , respect vely — EXE RCI SE 6 Si - , What zes Of side shaft change wheels would be required to

1 U n — sually cha ged to secure fresh range of drafts for the available Side shaft n w cha ge heel . 7 0 COTTON SPI NNI NG CALCULATI ONS

in in d min 14 d Of 120: 1 12 105 99 obta the follow g rafts , assu g gave a raft , , 93 5 88 5? ,

A ns 15 1 6 1 7 1 8 19. . , , , ,

E XE RCI SE 7 — \Vhat Si d o w wo d n min . ze of fee r ller heel ul be ecessary, assu g that card drafts rangi ng from 1 12 to 1 60 are required with the side - shaft change w 14 20in i and 14 Side- c n w d i in 120 on heels to clus ve, a shaft ha ge heel r v g a the feed roller give 120 Of a draft ?

A ns . 160.

What drafts would the various Sizes Of Side - shaft change wheels give after making the alteration referred to in the last question

A nswer s

VVith the Side - Shaft change wheel 14 1 5 1 6 17 1 8 19 20 The draft would be 160 1 493 140 13 18 1244 1 18 1 12

WRAPPI NG .

i S i and i i is d For measur ng l ver roves a spec al mach ne use , i i i is called a wrapp ng mach ne . Th s arranged to measure one i I n i i i yard per revolut on . us ng th s nstrument care must always be taken to secure the movement Of the cotton in a straight i and i i and i l ne also at a un form tens on , at the same t me pre i i i ix d i caut ons taken against sl ppage . F ve or S yar s w ll be fﬁ i nd i d d i d su c ent length , a the sl ver teste shoul be Obta ne from diff Of and m Of d in erent parts the can , fro several the car s the ” i in d i di i preparat on , or er to get prec sely the con t ons pre

i i . The i d S d va l ng cotton , after be ng measure , houl be compactly d in O i i i woun the form of a ball to bta n accurate we gh ng.

XE I E 8 —W S d i t in in E RC S . hat houl be the we gh gra s per yard of the Sliver d d in d n inin win d i : 1 60 1493 pro uce car s co ta g the follo g total rafts respect vely , , 1 40 if in in , the loss the process each case amounted to

c n . and fed w i d 437 5 in d per e t , the lap e ghe gra s per yar ?

Ans . 3 3 2 3 5 3 6 8 i , , respect vely .

EXE RCI SE —W d S i w i h 5 d i i 9. e w hat shoul the l ver e g , per yar s, resp ct vely, th d n w n in m 15 22 in i if 5 d of i raft cha ge heels ra g g fro to clus ve , yar s the sl ver Weigh 13 4 grains with a 14 wheel ? 5 A ns 5 dwts 2 6 d ts 9 d 1 . . 3 . w . . 6 wts . 9 . 8 dwts . 4 8 dwts . grs , grs , grs , grs . , 14 8 dwt 23 . s . rs s 9 9 dwts 1 . . 9 dwt . . 8 grs , g , grs , . grs

EXE RCI SE 10— d n . What raft cha ge wheel would give slivers weighing

9 dwts . 6 9 dwts 20 . . . 10dwts . 1 1 1 1 dwts 2 1 1 dwts 1 grs , grs , grs ., . grs . , . 7 grs . i 6 d if wi 14 d n 6 d Of i i respect vely, per yar s , th a raft cha ge yar s the sl ver we ghs 203 grains ?

A ns . 1 5 1 6 , ,

7 2 COTTON SPI NNI NG CALCULATI ONS

00 . d . Of O 1 5 b ank ds . 60 s N . Alea 1 , or y y ) grs

1 1 2 7 0 n

The above are the fractions of a b ank usually measured when testing the count of the cotton in the various stages of its preparation . I n connection with the weight table a difﬁculty is experienced

1 . To in remembering that l 8i dwts . make oz remember that

000 . l lb . and 24 . 1 dwt . 7 grs make , that grs make , also that in 1 6 . 1 . d dif x i d in ozs make lh , re uces the ﬁculty e per ence recall g Of i the number pennywe ghts per ounce , because the penny d i n weights m ay then be re uced to gra ns a d the grains to pounds . I f a similar difﬁculty occurs with the number Of grains in an

i 000 . i d in 1 . Of 1 6 . ounce , by not ng that 7 grs are conta ne lb ozs , 1 00 43 i in . I n i then 793 7 6, the gra ns an ounce th s way the di ﬁ i x i d i f cult es so Often e per ence by beg nners are overcome . I n order to ascertain the count when the weight Of a given is w d is di id i i length kno n , the proce ure to v e the we ght nto that f i i f N 1 x i O O O. i d d a s m lar length count , each e press on be ng re uce to common weight terms . Thus

E XAMPLE S

For r easons see a e 73 . , p g

(a) Required the count when 1 lea 50 grains

1 lb .

1 hank grains AND COSTS OF YARN 7 3

i (f ) Required the count when 1 hank 24 gra ns

(9)

1 yard 1 lb .

grains

s Notes on the wor ki ng of the p r eceding E xamp le . l —00—Q the n m The i 1 l ea Of NO. 1 15 or . (a) we ght of 4 , 7 grs ; thus, u erator n m 0 is 1000 and the de o inator 5 . w i h n m is Of enn w i in 1 lb . c it is (b) T e u erator 4 the p y e ghts , be ause the e ght i n d n min o f 1 l ea Of . 1 in enn w i w i t x O No p y e ghts, the e gh e press o of the e o at r in i used th s case . 1 x 7 000 h n i f 1 T e pen ywe ghts in o lb . 4 7 x 24

T n ted in 1 9 941 1 hese co ver to gra s 7 000 and 1 d t in in 24 w . gra s 417

m e is f 1 in o n and d nomin to 1 (c) The nu erator h re 1 O lb . u ces the e a r

h n me in i c e is in 4 Of 1 lb and th i (d) T e u rator th s as aga ; . e denom nator l

e I n i in t nc the n m to is 1 lb . 16 and d n min to ( ) th s s a e u era r , or ozs . , the e o a r 1 1 — 1 6 or 1 oz . e ec i e and n the c n or i . 1 6 lb . r sp t v ly, he ce ou t 1 3 respect vely T6

(f ) The weight of pounds and ounces can always be more conveniently x d in in t n in nn w i and n the n me to is ed ed e presse gra s ha pe y e ghts , he ce u ra r r uc

000 . and the d n min o 24 to 7 grs , e o at r to grs . ; 1 999

it One ve 840 is n m it is w i t Of d Of ( ) o r the u erator, because the e gh yar 1 x d in o nd and 1 d n min o No . e presse p u s, the e o at r . — E XE RCI SE 11 . What are the counts Of 1 4 dwts 4 ( a) lea . grs .

b 60 d 2 dwts . 2 ? ( ) yar s grs . 7 4 COTTON SPI NNI NG CALCULATI ONS

c 95 d 50 ? ( ) yar s grs . d 2 125 ? ( ) % leas grs .

e 4 1 dwt 16 . ? ( ) leas . grs

1 d 1 dwt 1 r. ? (f ) yar . g

5 d dwts . 12 (g) yar s 7 grs . ? h 1 d 12 d ts ( ) yar w . ?

What should be the weight in grains Of 1 1 (i) yard of No . (j ) 1 lea Of (1c) 30 yards of (!) 60 yards Of (m) 6 yards of (n) 15 yards Of o 1 d 003 40 in o nce ? ( ) yar , , u s

— t wo d the c nt and i in oun d Of EXE R CI SE 12. Wha ul be ou we ght ces per yar the laps fed in cards containing each 120 Of a draft if the amount lost in waste

i 5 n . and the co nt and w i of the S i ar s per ce t , u e ght l ver e

Respective count 02 67 02 41 Respective weight in grains per yard 3 1 2

A ns Co n : 0002225 00020 8 00016 000138 . u t 8 Ounces per yard 9 10 124 1 5

EXE RCI SE 13 —W w d b th n h i and its w i in in . hat oul e e cou t of t e Sl ver e ght gra s d if d in the d was 1 2 nd i d 8 d per yar the raft car 5 a the lap we ghe 0ozs . per yar , the in w te ein 5 n ? loss as b g per ce t .

Ans C nt . ou W i e ght grs .

EXE R CI SE 14 —W t w i i in in d e i w d . ha e ght of sl ver, gra s per yar resp ct vely , oul n d to d 00 i w 55 be necessary to e able a car pro uce 8 lbs . of sl ver per eek of " in u wi doﬁer 126 L in di m w n run 1 6 15 14 13 work g ho rs th a i ches a eter he at , , , , and 12 revolutions per minute respectively ?

Ans 52 56 617 . . , ,

E XE RCI SE 1 5 - W t w d n and w i of i in in . ha oul be the cou t e ght the sl ver, gra s d in d n inin 1 20 d if fed d 10 1 1 12 per yar , car s co ta g of a raft, the lap average , , ,

13 and 14 oz s . d c i and w in c din was 5 er c n , per yar respe t vely, the aste ar g % p e t .

O° 202 086 n cou t. w i in in r d e ght gra s pe yar . — E XE RCI SE 1 6. W o d be w i t of i in in d hat sh ul the e gh the sl ver, gra s per yar , d d d c n inin 120 Of d t if the w i 1 oz s d pro uce by a car o ta g a raf , lap e ghs 0 . per yar and the waste extract ed is 5 per cent ?

A ns . . grs AND COSTS OF YARN 7 5

— d w i the it c d if E XE RCI SE 1 7 . What shoul be the e ght of lap su able for a ar is n d in 120 and the i is i d the loss in waste 5 per ce t . , the raft be g sl ver requ re r d to weigh 3 6 g s . per yar

An . 4547 . . s grs , or ozs

XE RCI SE 1 8 —At w t in e o ion er min e o d dof in E . ha rate, r v lut s p ut , sh ul the fer

d 4 i of . d a card be worked in order to pro uce 00 lbs . of sl ver grs per yar ’ n in o in if d ff is in in di me and in 54 hours co t u us work g, the o er ches a ter the draft between this part and the coiler delivery roller is i n A ns . . revolut o s

n h f Fill it ui d t o Cl o h the C ind i Su f s The Le gt o req re t yl r cal r ace . I n i Of fillit i d it is calculat ng the length the requ re , necessary n di i to allow one coil extra i ad t on to that sufficient for holding . T i d 50 i di 3 8 i id hus , a cyl n er nches ameter , nches w e , to be d i fillit 2 i in id d i 3 8 i 1 covere w th nches w th , woul requ re 5 co ls , and di 6 the length for hol ng , say, about feet

?g X X feet 6 feet 268 feet

D ff 24 i di 3 8 i id d i 1 i o ers nches ameter , nches w e , clothe w th 5 nches ﬁllit i 4 di and , requ re about feet for hol ng , 22 49 4 1 3 0 2% X 7 X 2 feet feet feet

' The wi is d in i S i d follo ng the proce ure form ng the p rals , terme

- and d i d i . The is half lap tapere ta l en s , respect vely latter commenced the width Of one staple and increased gradually to id in the full w th a length equal to the ﬁrst coil . The former is

d - i d - id and i commence one th r or one half the w th , the sp ral i d in and i i i obta ne one a half or two co ls, the fin sh ng ends i i terminat ng n the inverse manner . “ ” Ex m of in H a1f-1a — a ple prepar g p. Assuming the fillit contains six in id id i columns the w th , half the w th w ll be convenient for i i i id i and the commencement ; ma nta n th s w th for half a co l, d t o add i - d id i then procee a column , on the r ght han s e , at po nts idi i x equ stant n the ne t half coil . I n doing this it is necessary to have the commencement Of the last row Of each col umn a 1 di x Of Of Of stance from the first row of the ne t column 4, 7, Athe i Of i c rcumference the cyl nder . Thus three columns would be

dd d in Of i . A d a e the latter half the ﬁrst co l fterwar s , com m encem ent is i d end f on the r ght han , the left half of the O the “ ﬁrst coil must be secured to the jump - end of the beginning 7 6 COTTON SPI NNI NG CALCULATI ONS

Of i and d i is d i the ﬁrst co l , the secon co l commence w th the

i - The - d i is d r ght hand half. left han port on prepare 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 left -hand Side in the same manner and at the same rate as with the d i Of i Of tapere port on the first co l , but from the commencement d i O i i id i the secon co l , thereby bta n ng the full w th at a po nt O i in i ppos te the commencement of the taper the first co l . This i i completes the preparat on for cutt ng . odd in i When the columns are number , for nstance , seven , commence with the width Of three columns to extend o ver ? Of i and d the c rcumference , then procee to make the tapered portion i i i and in i i over the rema n ng 8 of the first co l , put the rema n ng

' i d S i in ° cf three columns requ re to complete the p ral , the ﬁrst 7 I n i the second coil . the former nstance the spiral extends over 1 1 i end and in 1 . 2, co ls at each , the latter over 9 — — The tapered tail end completed in one coil is defective in that the terminals cannot be sufﬁciently tensioned for satis i n i The i d factory gr nding a d work ng . taper ng shoul always be i id and id i i on the ns e not on the outs e , th s be ng the most com

x di in - mon method. E ten ng the taper half lap over the whole Of i i x d d i the ﬁrst co l , necessar ly e ten s the taper over the secon co l . This would largely reduce the number Of wire points over these

- i i id a Of i . The ﬁnishin ff port ons , mak ng w e g ps absent po nts g O preparation is exactly the inverse of the commencement . R emember th at uniformity in the character Of the point is d d i r esil ence i and i epen ent upon un form of the w re , th s support it Obtains through the medium Of the tension at the i foundat on .

H T E SLI VE R LAP MACH I NE .

1 Of i i n Fig. 7 represents some the pr nc pal parts a d the i in i i gear ng the sl ver lap mach ne. The Object of this machine is to prepare a ribbon Of ﬁbres Of i id i and i i un form w th , we ght , , as far as pract cable , w th the and di i i T i ﬁbres laid parallel str buted un formly . h s latter is i d nd i O a di . only part ally bta ne , hence the succee ng process AND COSTS OF YARN 7 7

The machine consists Of parts having the following functions

1 6 D ie .

FI G . 1 7 .

a Th d S in x d ( ) e fee parts , not hown , for present g a ﬁ e number i i and d of the carded slivers in uniform tens on , al gnment , place as 7 8 COTTON SPI NNI NG CALCULATI ONS

A f i i close as practicable . lso means for the detection O m ss ng n in i slivers a d stepp g the mach ne . (5) The rollers ( 1 5X X for attenuating the above d i i x i is name sl vers to the most beneﬁc al e tent , th s generally up 2 to about . (e) The calenders (5 X 5 ) for smoothing and pressing the

attenuated ribbon of fibres . (d) The lap rollers (1 2 X 12 for winding the continuous i ribbon Of fibres t ghtly upon a wood roller . ns in to he Sli La M hi n — i Calcul atio relat g t ver p ac e (Fig. Th s machine is driven by a strap from a 9-inch drum on a line shaft 2 i making 20 revolut ons per minute . The calculated revolutions per minute Of the various parts are as follows Machine shaft fl 1 23 7 5 — — , or , (1 6 1 3 29) 1 6 First drawing roller 9 X 29 X 21 X 50X 4 1 X 3 3 r 8 4: 2 (64—26—1 g) , Second dr awing 9 ” 99 5 01 22—1 ’ ’ roller ( 92

22 Thirddrawing roller 9 X 29 X 21 X 5OX 41 1 63 3 , or,

i and d F rst secon 220X 9 X 29 d 498 calen ers , or , 1 6 x 2 (50 (7 2—5 7 22DX 9 X 29 X 21 1 6 x 7 2 >< 21 Lap rollers 22C X 9 X 1 3 — — 22 04 01 1 2 7 3 3 0 , ” ( ) 1 6 x 7 3 220X 9 X 1 3 X 3 0 1 6 X 7 3 X 3 0 Draft s Between second and 26 X 8 ﬁrst rollers , or, Between third and second rollers 26 X 3 3 X

8 0 COTTON SPI NNI NG CALCULATI ONS

E XE R CI SE S I N CH ANGI NG THE SLI VE R LAP M ACH I NE .

EXE R I SE 1 —Wi d in w ff w d c n in C . th the spee s as the ﬁgure hat e ect oul ha g g w i f i m 3 0 3 6 in d e n the e ght o the sl ver, fro to gra s per yar , hav upo the laps i im produced (a) The weight per yard ? (5) The weight produced per u n t of t e

20 . 90 n . 252 . 26 (c) The length produced in hanks Ans . grs lbs ; ha ks E R E — n w d n if S i d was d XE CI S 2. What cha ges oul be ecessary the l ver use altere m 30 in 3 6 in d in d the w i t and n t ni fro gra s to gra s per yar , or er that e gh le g h u ts , d i ed un ff d ? el ver , be a ecte

n w to in the draf 30 3 6. Ans . Alter the draft cha ge heel crease — n w d e e m w i nit im E XE R CI SE 3 . What cha ges oul s cur the sa e e ght per u of t e , 1 i Ans A in d . and at the same time alter the we ght of the lap £3 ? . lter g the raft 1 5 I — d w i d and Of 10 EXE RC SE 4. What woul be the e ght per yar , laps per hours , if each lap m easured 280yards and one minute is lost at the completion of each ?

The in f i i n in the and m 20 i n lap rollers be g o the s ze g ve ﬁgure , ake revolut o s i in er d and per minute ; each of the fourteen slivers fed we gh 28 gra s p yar , the draft in the machine is

TH E RI BB ON LAP MACH I NE .

i i nd Fig. 1 8 represents some of the pr nc pal parts a the i gearing in a ribbon lap mach ne . The object of the machine is to prepare from the Sliver laps one which has the ﬁbres arranged in the most suitable manner i i i in i for comb ng to make the r bbon of ﬁbres un form th ckness ,

id and i and i . w th , we ght throughout , w th all the ﬁbres parallel This machine consists Of parts having the following functions

a The d : La ins . di and ( ) fee parts p rollers 3 ameter , the detector of missing and light laps the latter is not shown .

5 The 1 1 - 1 1 i ( ) rollers ( 3, X 32 X 5X 4) for attenuat ng the i b x r bbon of fi res to the e tent necessary, to lay the fibres parallel , n i a d to make the r bbon the desired weight . 0 The d di id i i ( ) curve fol ng plate C gu es the r bbon , pass ng di D i i from the rollers , on to the fol ng table , plac ng t upon the i n latter at r ght angles to the rollers . I the figure only one

d is . The i is i s ix d hea shown mach ne usually made w th hea s , six i and d to treat sl ver laps , hence the rollers are constructe to d i . T Six d di eal w th that number here are , therefore , curve fol ng and di i plates , the fol ng table s continued to the left accordingly . The i and i 3 ins di carr er compress ng rollers , . ameter, are placed at intervals along the folding plate to move forward the d d fol e ribbons . AND COSTS OF YARN 8 1 8 2 COTTON SPI NNI NG CALCULATI ONS

” (e) The calender rollers (5 X 5 for smoothing and pressing the ribbons and completely uniting them . ” (f) The lap rollers (1 2 X for winding the continuous i i d r bbon of ﬁbres , or lap , t ghtly upon a woo roller . The machine is driven by a strap from a 9 -inch drum on the line shaft which makes 220 revolutions per minute and drives

16 - i the inch pulleys on the mach ne Shaft . The revolutions per minute of its various parts are as follows 220X 9 X 7 2 X 25 54 3 0 d 1 3 5 X X Fee lap rollers (3 , or, 1 6 x 68 x 1 00x 7 0x 56 The ﬁrst draw roller 220 X 9 X 7 2 X 25 x 54 25 3 01 — - , " (3 7 40 70) 1 6 x 68 x 1 00 x 70 The r d 22C X 9 X 7 2 fou th raw roller 1 3 1 — — " , or , (68 25 1 5 1 6 x 68 The carrier and com 220 X 9 X 3 1 X 22 1 7 or, pressing roller (22 1 6 x 54 x 22 220 X 9 X 2O X 1 5 The calenders (21 44 25 or , , 1 6 X 4O X 21 220 X 9 X 2O X 1 5 X 21 The 12 - 1 2 lap rollers ( or, 1 6 x 40 x 21 x 50

Drafts Between ﬁrst roller and the feed lap roller 3 7 X 3

Bet ween second roller 3 7 X 12“ or and the first roller 30 X 1 ; Between third roller and 3 0 X 40 X 01' d ’ the secon roller 3 7 X 22 X 1 7} Between third roller and or the first roller x l é B and 0 1 00 r 1 etween fourth roller x 7 X X 2 2. 8 6 01' i d 4 the th r roller X 54 X 25 x l g Between four th roller and x l OO X l -g 5 18 , or the first roller X 25 x l —g Between carrier and the X 3 1 X 22 X 3 or fourth roller X 54 X 22 X 1§ Between calender and X 54 X 20 X 1 5 X 5 . ’ 1 03 , 01 carrier roller X 3 1 X 40 X 21 X 3 AND COSTS OF YARN 8 3

Between lap rollers and 21 X 1 2 or , the calenders 50 X 5 Between delivery lap rollers and the feed lap rollers 7 6 x 7 0 x 1 00 x 68 x 20 x 1 5 X 2l x l 2

’ 3 7 x 54 X 25 X 7 2 X 40 X 21 X 50 X 3

P odu ion —Th i i d r ct e we ght , per un t of length of the lap ma e , is d i fed and controlle by the we ght of the laps , by the total in draft . Any alteration in the latter items affect the former di and i i i the rect nverse proport ons respect vely, namely a The i d i and vice cers . heav er the fee , the heav er the lap ,

The d i and vice versa. greater the raft, the l ghter the lap, The length delivered is only affected by the alteration of i speed of the mach ne shaft . I t is customary to regulate the weight of the lap by altering f the draft but sometimes by altering the weight of the lap ed. The draft can be altered to a very considerable extent with i out inﬂuenc ng the quality of the work . The customary changes are made through : The pinion (54) or the back- roller wheel (70) for the draft ; the machine pulleys 1 6 i d ( nches) for spee . The restrictions in altering the draft and weight of the feed i i i d ar se from the gross we ght of the laps gthat are requ re for the combing machines .

EXAMP LE 1 —I f thi m in six e ds and the fed w i . s ach e has h a , laps each e gh at the rate of 202 grains per yard ; what weight oflaps in pounds would be produced ’ in 10 o nin e ted wo in and w t wo d be the w i t of h urs u t rrup rk g, ha ul e gh these in grains per yard

202 X 6 200 grains per yard

12 22 10 x 60 x 200 -— —— 18 55 X X X 333 lbs . 36 7 7000

EXAMPLE 2 —W t wou d be the wei of the d if the d , ha l ght laps per yar raft inﬂn change pinion 54 was changed to 3 6 ? H ow would this change ue ce the weight and length produced in ten hours ? A ns The d wo d e d in in e o i n to c n e . raft ul be alt re the v rse prop rt o the ha g w and n heels, he ce 8 4 COTTON SPI NNI NG CALCULATI ONS and the weight per yard of the lap produced would become lighter in direct i n in i w and t e e prop ort o to the change th s heel, h r fore

133 grains per yard

And the w i d d in 1 l d ff d in m m e ght pro uce 0 hours wou be a ecte the sa e ter s , 54 : 3 6 the n m i nin n d. , le gth re a g u affecte

EXE RCI SE S.

1 The d n i six d and w i t d is 240 . fee co s sts of hea s, the e gh per yar of the laps

in d i d in 5. W w i d and 10 gra s, the raft requ re be g hat e ght of lap , per yar per d d ed win 2 nt ? A w hours , shoul be pro uc , allo g 3 per ce . for stoppages lso, hat d ini n w wo d n d the m in ot e i raft p o heel ul be ecessary to a apt ach e , h r part culars in Fi 18 ? be g as per g.

2. I f m in was od in wei in 240 in d d the ach e pr uc g laps gh g gra s per yar , geare

in Fi . 18 w t wo d th w i t er d fed ? as g , ha ul be e average e gh p yar of the laps 3 U n in w i f d d o nd 224 in . po test g the e ght o the laps pro uce , they are f u gra s per yard instead of 240 gr ains : what sizes of draft pinion or back - roller wheel d e o e d d i w i ? A o i e woul r st r the laps pro uce to the r proper e ght ls , g v the pro portional alteration that this change would make in the weight of laps produced ni im per u t of t e . 4 I f the d ini n 54 was c n ed to 60 w eff ct wo d it u n . raft p o ha g , hat e ul have po the drafts between (a) the ﬁrst and second ; (5) the second and third (c) the third and fourth rollers respectively ? 5 I f w i d d c d m n in . the e ght per yar of the laps pro u e beca e 240grai s stead 200 w wo d ou and w wo d ou do ? of , hat ul y suspect, hat ul y 0

OMBI C NG MACH I NE S. i 1 F g. 9 represents the gearing in the Nasmith combing machine . The Object of this machine is to comb the ﬁbres and reject d i and S i d those that are efect ve below a pec ﬁe length . The cotton for treatment in this machine is prepared from d S i i and i i the car l ver, by the sl ver r bbon lap mach nes , an alternative to these processes being one head of drawing followed

D D . The is d by the erby oubler former the mo ern system, and d has many a vantages over the latter, the chief of these d i d i in d a vantages be ng a re uct on the goo 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 OF YARN 8 6 COTTON SPI NNI NG CALCULATI ONS

G i i . , a crank on the osc llat ng shaft H HI i O i d and , the oscillat ng shaft for perat ng the fee the i advancing and receding movements of the n ppers .

d H I I . J , a lever couple to the Shaft at

K i s d and id O . , a crank ; t stu Sl e perate the lever J

L i d i i . , the mach ne r v ng shaft

U i d S . , a cam on the comb cyl n er haft T d d H I and d , a qua rant rack lever centre on , actuate by a

d and i i U. stu bowl , the latter project ng nto the cam R n i n a d 3 0 is the quadrant rack p nion a d Spindle . 4 is d ti i 7 an escapement clutch , the left toothe por on be ng d S i d i i i secure to the p n le R, the r ght port on be ng loose upon and d and di d i i i R, engage sengage w th the left port on to Obta n

movement of the wheel containing 47 teeth . for i P , a cam controll ng the clutch Q. d i d i V are the etach ng rollers connecte by a tra n of wheels ,

4 20 1 8 1 it . 7 , , , 7 w h the clutch

i d . M, the comb cyl n er

N i d . , the brush cyl n er

0 d i d . , the car cyl n er W d d is d , the hea calen er ; there one for each hea . ” - - 3 0 25 1 20 d b ox. The d , , 7 , , are the raw raw rollers are

in d i . four number , to attenuate the combe sl vers

- d box d . Y, the raw calen er ! i d i nd i and , the co ler el very rollers , a the co ler can wheels are Shown beneath . The speed of the comb cylinder in this machine ranges from 1 0 i i 0 0 d i d. T 9 to , accor ng to the qual ty of staple treate h s machine is especially adapted for combing the shorter staples i i i nd . from the equ valent of G . M ddl ings Amer can a upwards Another feature of the machine is the wider range of selection in i d respect of the length of the ﬁbres rejected. W th goo staples this can be reduced to as low as 12 per cent . without interfering i i with the thoroughness of the combing. The p ecing s aecom lished i i nd d p on a much better pr nc ple , a the a justments are all much Simpler than in the machines constructed on the Heilmann

Th i is . system . e product on also considerably greater The following are the speeds Of the variou s parts and manner

8 8 COTTON SPI NNI NG CALCULATI ONS

in i . forward, respect vely Hence , these movements result the ﬁrst 4 0 9 hm I l b ad mard and d detaC g d er movmg ’ forwar , 3 0 ii25 95i 25

i i i d . T i respect vely , per revolut on of the comb cyl n er h s amounts to the following rates per minute 1 00 X 9 X 47 B d 705 i ackwar , revolut ons 3 0 x 20 1 00 1 7 X 47 X Q 1 d 1 3 3 i Forwar , 6 revolut ons 3 0 X 20

—9 the forward progress per minute amounting to ( 13 3 4 7 5 2 2 X 7 The second detaching roller exceeds the movement of the f ﬁrst as 18 1 7 on account O the gear. T d d x d d hese amounts must be regar e as ﬁ e , as a justments of n this gearing are not arra ged for . 2 The i d d 2 i in di nd comb ng hea calen ers are 5 nches ameter, a make revolutions per minute

1 00 x 48 x 43 x 40 x 1 6 x 1 7 x 3 3 x 20 24 x 40 x 50 x 25 x 43 x 7 2 x 20

The revolutions per minute of the ﬁrst draw roller 58 645

1 00 x 48 X 43 X 40 X 1 6 x l 7 24 x 40 x 50 x 25 x 3 0

The revolutions per minute of the second draw roller 703 74 1 00 X 48 X 43 X 40 X 1 6 X 1 7 24 X 4O X 50 X 25 X 25

The revolutions per minute of the third draw roller : 1 10 1 00 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

1 00 X 48 X 43 X 40 24 X 40 X 3 1 AND COSTS OF YARN 8 9

The revolutions per minute of the draw -box calender : 1 26 1 00 x 48 x 43 x 40 x 20 24 x 40 x 3 1 x 44

The revolutions per minute of the coiler delivery rollers

1 00 x 48 x 43 x 40 x 7 0 x 20 x 20 24 x 40 x 55 x 61 x 20 x 20

The revolutions per minute of the coiler can 1 00 x 48 x 43 x 40 x 7 0 x 20 x 1 3 x 1 8 x 1 8 24 x 40 X 55 x 61 X 20 X 3 6 X 3 6 x 8 4

The drafts between the parts in progressive order work out as follows : Th (a) Lap and ﬁrst detaching roller by gear direct . e progressive movement in respect Of the detaching roller amounts 1 8 8 47 to 7 9 teeth of the quadrant wheel , or 3 5 of the i d i i clutch wheel wh ch r ves that roller, per revolut on of the m b i d and co cyl n er , therefore 8 x 47 the progressi ve movement or the amoun t gai ned i n 3 0 X 20 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 i 5 i from a pawl mov ng the ratchet wheel , 7 , a certa n number i d of teeth each nip ; the extent of this movement can be var e , nd is di The d is a one me um of tensioning the lap . fee roller S it is and not hown , but also worked by a pawl ratchet , the i d ni and is pawl be ng operate each p, the ratchet wheel d d secure upon the feed roller . The movement of the fee roller is d d in is d a juste altering the draft . I f the pawl move four ni i d teeth per p or revolution of the comb cyl n er , the movement of the lap rollers per nip will be the denominator in the di succee ng calculations . Hence the draft 90 COTTON SPI NNI NG CALCULATI ONS

(a) By gear direct

" 8 x 47 X 9 3 0x 20X 1 0 8 X 47 >< 9 x 7 5 X 8 0x 47 x 4 _ 4 X 4 2 X 3 5 3 0X 20X 1 0X 4 X 42 X 3 5 X 1 1 7 5 X 8 0X 47

(0) By calculated surface speeds per minute 1 7 7 -2 9 0 8 3 6 1 8 02

The draft between the ﬁrst and second detaching rollers 1 8 X 1 058 9 1 7 X 1 6 1 8 7 68 1 7 7 2 7

The draft between the second detaching rollers and the combing head calenders

8 X 47 X l 8 X 9 3 0x 20x 1 7 X 1 0 48 x 43 x 40X 1 6 X 1 7 x 3 3 x 20X 1 1 X 30X 20X 1 7 x l 0 24 x 40x 50x 25 x 43 x 7 2 x 20x 4 X 8 X 47 X 1 8 X 9 09 1 6 1 7 2 4 0 91 8

The draft between the combing head calenders and the ﬁrst draw - head roller 20x 7 2 x 43 X 14 a ( ) 20 X 3 3 X 3 0X 22; 207 -8 5 (b) 1 2 1 7 24

The draft between the ﬁrst and second draw - head rollers

3 0X 9 X 8 _ 28 X 8 X 9 248 8 2 207 3 5

92 COTTON SPI NNI NG CALCULATI ON S

(6)

By proportion

By proportion X 4

The percentage of waste at this machine is rarely lower than d and i Of f 1 5 . 1 4 per cent . I per cent be allowe , the we ght the d 28 dwts . i i 4 laps per yard be each taken as , a mach ne w th hea s

d. when the feed pawl moves 4 teeth per nip grs . per yar 28 4 n d is ni A d when the fee actuated 5 teeth per p,

8 5

d. X grs . per yar 100

T —The n fed ni w n the w m o e 8 te wo d NO E . le gth of lap per p h e pa l v s eth ul be 3 6 4

0 3 604. 103

The latter length would prove in most cases an impracticable amount in this machine . I t would make the combing action i d very severe , throw ng a great eal more work on the top comb it i i A d i than s capable of accompl shing . nother way of a just ng the draft in this machine is by changing the wheel compounded with the feed ratchet wheel ; this may be called the draft A i d in change wheel . ltering th s wheel will alter the raft the i i i i d d it is nverse rat o, because t w ll re uce the length fee when d n i nd re uced in size . Changes i the we ght of the Sliver a the output of the machine may be accomplished by (a) The draft is altered by the wheel coupled with the ratchet

i i di . wheel , or by ncreas ng the ra us of the pawl lever

OTE —ThlS w can n d imi d x n win N . heel o ly be altere to a l te e te t, o g to its alter in i w n and e d o e n w g the rat o bet ee the lap the f e r ll rs ; u less the pa l lever, Operating e is t d m e tim The is i e n the latt r, al ere at the sa e . lap l abl to be u duly stretched if i is n t d n or puckered th s o o e . AND COSTS OF Y ARN 9 3

(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 in n i d machine gear ed as the ﬁgure a d hav ng four hea s , the

i d i 100 i i i 28 dwts . comb cyl n er mak ng n ps per m nute , us ng laps d d 625 8 1 5 i in i per yar , the raft , per cent . be ng lost str ps ,

i 1 0 . i i 55 d t me lost per cent , eng ne t me hours per week, woul be computed as follows

55 X 90 X 60 minutes worked per week 1 00 less allowances ” 55 X 90X 60X X 2 X 22 i nches delivered per week by 1 1 0 7 the coiler delivery rollers 55 X 90X 60X X 2 X 22 hanks delivered per week by 1 00X 8 40X 3 6 7 the coiler delivery rollers

Per cent. Revs . P. M . Di H rs Mins . . d e; yar ds delivere by the 90 X X 2 X 22 X 55 X 60 coiler delivery rollers 1 00 X 3 6 7 er week l es s p , stoppages

Grs . Dwts La s Per cent . . p . 24 X 28 X 4 X 8 5 weight Of the sliver in x 100 { grains per yard Dra t f .

Weight in pounds of the Sliver delivered by the machine per 55 week of hours , no allowance

24 x 28 x 4 x 8 5 X 1 7 9 ° 43 x 2 x 22 x 55 X 90 X 60 62 58 x 1 00 x 3 6 x 7 x

The d i in d d 5 ni pro uct on , case the fee pawl move teeth per p i d 4 d be nstea of , woul Weight of the sliver per yard when pawl moved 4 teeth

4 X 28 X 24 8 5 X 3 6 5 grai ns 625 8 1 00

Weight of the Sliver per yard when the pawl moves 5 teeth

3 6 ' 5 X O 4 94 COTTON SPI NNI NG CALCULATI ONS

Production in pounds per week of 55 hours 48 53 X 5 606 5 . 4 lbs

d d i d The length elivere after the alterat on woul be the same , f d d and but the length e woul be one quarter more , therefore the i weight delivered would be proport onately increased. i if d d The product on per week , the fee pawl move the lap 8 d be rollers teeth , woul 8 X 06 lbs . 97 4

EXE RCI SE 1 —A min the ed the com c ind 100 e tion r . ssu g spe of b yl er r volu s pe min t and the m c in l 14 inc e in di m e c n ed to 12 inc u e , a h e pul eys h s a et r are ha g ; hes , what would be the speeds of each of the parts of the machine ?

Answer Lap rollers with the pawl m oving 4 teeth 5 3 3 3 5

i d t c in l w d 7 89 6 F rst e a h g rol er, back ar forward backward forward l 57 ° 92 Cam shaft 1 12 Comb cylinder 1 12 6 Machine shaft 4389 3 B c inde 4045 rush yl r . Card Combing head calenders 23 9 3 6 First drawing roller 65 682 Second Third Fourth Draw- box calender Coiler delivery roller Coiler Can

E XE RCI SE 2 —W t wo d be the con m ti n of and d c ion i . ha ul su p o laps pro u t of sl ver, ’ in n and ound 50 o nin d w in of asmith m ha ks p s , per h urs u terrupte ork g a N co ber, and wei er d o the e centa the w te ex d the ght of the lap p yar als p r ge of as tracte , under the following conditions

S ive od ced in 1 min te 1 117 in l r pr u u , gra s . S i 292 in tr ps gra s .

9 6 COTTON SPI NNI NG CALCULATI ONS

i d i in i only subm tte to once comb ng, whereas the He lmann they i d i i i d i are subm tte a number of t mes , the r ntro uct on to that

The ff i is i action being graduated. e ect of th s that the He lmann AND COSTS OF YARN 97 wields greater powers Of discrimination in respect of the length and other features of the fibres selected by it. i d n Th The respect ve parts are name as given i the figure . e i revolutions of the comb cyl nder range from 60to 90per minute . T i is O in i i d i h s ften spoken of terms of n ps nstea of revolut ons , there being one nip or complete cycle of actions per revolution i d in i i of the comb cyl n er the s ngle act ng type . I n 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 i i i d i d var ous parts , for th s purpose the comb cyl n er be ng assume to make 8 0 revolutions per minute i 8 0 8 0 Revolut ons of machine 1 6 X 3 04 — 01 pulley per min ute 2 1 , , 21 R i 8 0X 1 X 18 X 21 X 2OX 3 0 evolut ons of lap rollers 1 7 7 ’ or , per minute 5 X 8 8 >< 20X 55 X 49 Revolutions of feed roller 8 0X 1 X 1 8 or , per minute 5 x 88 R i d 8 0X 8 0X 2 x 20 evolut ons of comb hea 1 1 43 , or, calenders per minute 80X 1 4 X 20 i Revolut ons of first roller 8 0X 25 X 14 in d - x the raw bo per or , 25 X 48 minute i n i d Revolut o s of th r roller 8 0X 41 in d - box 1 04 5 the raw per , or , 2?z22i 3 2 minute

Revolutions of draw - box 8 0X 25 X 50X 40X 22 a or , calender per minute 25 X 45 X 3 4 X 40

R i i de 8 0X 60X 22 X 1 8 evolut ons of co ler ° 8 1 4 or, livery rollers per minute 59 x 22 x 1 8 Revolutions of brush 8 0X 3 4 X 8 0 414 4 , or , cylinder per minute 25 x 21 Revolutions of card cylin 2 5 , or , der per minute

Drafts B and d 1 1 66 etween lap fee rollers , 49 X 55 X 20X 9 3 0x 20x 21 x 2g- 9 8 COTTON SPI NNI NG CALCULATI ONS

Between lap and comb head calenders 49 X 55 X 20X 3 8 X 5 X 8 0X 2 X 20X 2§ ’ 3 0x 20x 21 X 1 8 X 1 x 80X 1 4 x 20X 2§§

Between lap and ﬁrst draw roller 49 x 55 x 20x 3 8 x 5 x 25 x 1 4 x 13

Between lap and third draw roller

n - x d 3 2 5 Between lap roller a d draw bo calen er , 49 x 55 x 20X 3 8 x 5 x 25 X 50X 40X 22 X 2§ 3 0x 20x 21 X 1 8 X 1 X 25 X 45 x 3 4 X 4OX 2§

B nd i d 3 3 4 etween lap a co ler elivery rollers , 49 x 55 x 20x 3 8 x 5 x 60x 2 >< 22 3 0x 20x 21 x 1 8 x 1 x 59 x 22 x 22 Between ﬁrst and second draw rollers 3 1 x 1 3 25 X 13 Between ﬁrst and third draw rollers

1 4 x 45 x 3 4 x 13

Between second and third draw rollers

25 X 48 X 50X 40X 1% _ 3 1 x 1 4 x 45 x 3 4 x 1§

Between third draw roller and draw -box calender 22 x 29 40x 13 Between draw -box calender and the coiler delivery rollers

22 X 40X 50X 25 X 59 X 22 X 18 X 2§

The movement of the detaching rollers is derived as follows The quadrant rack is a part of a lever actuated by a bowl pro ectin i i Th i i j g from t nto a cam . e r s ng and falling movement

1 00 COTTON SPI NNI NG CALCULATI ONS

Feeding a considerable length of lap generally results in i and d greater waste ; hence, l ght laps low rafts together are i not benefic al . — 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 d i the count of the combe sl ver. The d d length of the staple ecides the suitable Spee . Results must always decide the weight Of the lap as its state i diff as well as that of the mach ne er so much . h d di T e waste made ranges from 1 5 per cent . upwar s , accor ng i to the state of preparat on of the laps , the amount of short fibre

i it i and i . wh ch conta ns , the sett ngs i i i 240 i d i W th laps each we gh ng gra ns per yar , a mach ne , i i Six i d and d 3 4 conta n ng comb ng hea s a total raft of 3 , the loss

in i 18 . d i i i waste be ng per cent , woul make sl ver we gh ng

240 X 6 8 2 X 3 6 5 grams per yard 1 00

The percentage of the waste is always based upon the weight of the feed. The i and S i d i d we ght of the waste of the l ver , el vere per f i i fed in unit O t me, together , equal the we ght of the cotton that time . i i six i i d These mach nes usually conta n or e ght comb ng hea s , and therefore the amount fed is always that number multiplied i i fed i by the average we ght per un t of length of the lap , wh lst d i d x d fed in d in the length el vere e cee s that , one hea , the terms of the total draft.

— E XERCI SE l l The sliver and the waste produced in a given tim e weigh 520 and 130 in the w di c d six m in respectively gra s, aste s harge by the co b g

d w i in 20 20 21 22 23 and 24 in . Gi indi id and hea s e gh g , , , , , gra s ve the v ual total d percentage of the loss at each hea . E 2 —The i d ced m in m in in si E XE R CI S . sl ver pro u by a co b g ach e hav g x heads

is 8 . d 10 . The d is 32 and w at the rate of lbs per hea per hours total raft , the aste i 1 2 W is n d in i d w 0 . the e m d ma e that per o e ghs lbs hat the perce tage of wast a e, t h i in nd and en in d of the con med e we ght pou s , the l gth yar s laps su ? AND COSTS OF YARN 1 01

cc 1 4 10 O b 90 G) O 1 02 COTTON SPI NNI NG CALCULATI ONS — EXE RCI SE 12. I f m in l in ion 15 in in the ach e pul eys the last quest , ches di m t n d 16 in in di m dif en in i a e er, are cha ge to ches a eter, what fer ce the we ght of c m d s i e w and w d ? o be l v r, aste, laps oul result

ME THE DRAWI N G FRA .

The Object of this process is the elimination of the irregu

l ar ities d in i i i . T i is , foun the we ght of the sl ver , at th s stage h s accomplished by repeating the process of aggregation and

i . I n i i i attenuat on th s process there are usually three repet t ons , i two d d in and b ut somet mes or four are a opte , the former coarse ,

in . i i d the latter ﬁne , work Repet t on of the process Shoul be di i d d i d d d i i i scont nue when the es re stan ar of un form ty is atta ned. The heads are numbered corresponding with the repetitions T d d respectively . hus a raw frame of three hea s means that the is d i and i i cotton treate to aggregat on attenuat on three t mes ,

in d and i d d . I t is namely : the ﬁrst, secon , th r hea s necessary S i d and to test the l ver , preferably at the last hea , at frequent x d i i da an d i i ﬁ e ntervals , four t mes per y at least , so that y ev at on d i d d nd d i Th from the stan ard We ght may be etecte a ealt w th . e tests should be recorded along with the precautionary or correc

i in i i i . I n t ve measures taken nstances of var at on these tests , i d i 5 6 15 d f . The , , or yar s w ll be oun conven ent lengths to wrap sliver tested Should be taken in a manner ensuring correct i i i di i i representat on of the preva l ng con t on , the best way be ng

i t d i off . The to take a l t le from each el very, but not full cans weight is liable to frequent variation at this stage the cause of The i i this is not always apparent . var at ons foreshadow the working qualities of the cotton and irregularities in the treat i i ment pr or to th s Stage . i i di d d di When var at ons are sregar e , more than correspon ng dif x d in and ferences may be e pecte the subsequent processes , Often complications of an involved character arise through these fau lts being unchecked. During very dry weather the wrappings tend to the heavy in i side . A sudden change the atmosphere w ll sometimes i i i in necess tate an alterat on of qu te a few teeth the change wheel . Changes in the mixing which result in the cotton differing are i t u ld similarly liable . Cottons wh ch are sof er than us al sho u

1 04 COTTON SPI NNI NG CALCULATI ONS

1 nd 2 NOS. a draw rollers

1 8 X 13

N08 . 2 and 3 draw rollers

m x 47 x g 25 X 1 6 X 1 ig

1 nd 3 d Nos . a raw rollers 47 x l 4 1 6 x 1 3

3 nd 4 d NOS. a raw rollers

1 6 x 1 00 x 100 x 1§ 4 2 7 x 60 X 0 X 1 2};

NOS. 1 and 4 draw rollers

60 X 20 X 1 3

nd i d i No. 4 draw roller a co ler el very roller E

22 x 3 48 X 1§

Li i and i d i A nd ft ng roller co ler el very rollers , a draft 3 —" 2l x 60 x 20 X 48 X 1i

There is much difference of opinion in regard to the system of allocating the draft in the draw rollers of drawing frames i i The i d d wh ch g ves the best results . follow ng has prove a goo and is in d i i di i ° rule , accor ance w th the work ng con t ons

Draft between ﬁrst and s econd draw rollers : not more than 1 2 second and third

draft between ﬁrst and fourth

third and fourth draw rollers : (draft between d n i 2 the secon a d th rd rollers) .

EXAMPLE —T if d in d w ac and t tw n hus , the total raft the ra rollers , tha be ee AND COSTS or YARN 1 05

n nd t we n the c nd and i d and w n the ﬁrst a d seco 931 , tha bet e se o th r that bet ee i n x in 8 3 3 th rd a d fourth x3 ( the ﬁgure )

en 90 ac x 93 03 th , 1 2 x 3

in x s ce 1

an 8 3 3 “ 2 X 303 “

The d 90 is in i incon raft 2 , most makes of these mach nes , enient i v for chang ng . Changes in this are only necessary when i i the total draft referred to becomes abnormal . W th th s draft £13 d d x d d d m 2 regar e as ﬁ e , the efects arising are through the raft g

approaching in amount that of mg when the total roller draft is

d d 43 8 x and 56 i . re uce to , then 2 3 are al ke I t must not be inferred from the latter statement that a change of the draft between the ﬁrst and third rollers is I is advocated whenever the total roller draft is altered. t only desired to point out the error arising when considerable change is d 1n d and x di ff di i ma e the total raft, the e pe ency of a or ng rel ef i i i n d and i d in by a sl ght alterat on the raft between the ﬁrst th r , order to redistribute the drafts in reasonable proportions . I t is necessary also to draw attention to the desirability of

i d i v idi . us ng change wheels of mo erate s ze , a o ng small ones

The r evol ut1ons of 22 x 1 8 x 42 3 20 x 8 3 8 4 the coiler per minute} 46 x 20 x 69

The revolutions of 22 x 1 8 x 1 8 x 10 X 20 3 20 x the can per mm ute } 46 x 20 x 3 4 x 3 6 x 1 04

d d i Whenever raw frames are change from heavy sl vers ,

x i ill - to the other e treme , the co ls are frequently spaced in the nd r ic t a e er sé . can , This may be remedied by remembering i i and i d that heavy sl ver requ res more space , hence h gher spee s i i of the can than l ght ﬁne sl vers . When the sliver is coiled too widespread it i s liabl e to be trouble some through too much tension caused by binding in the T i can . h s may be overcome by slightly increasing the rate l O6 COTTON SPI NNI NG CALCULATI ONS

i On i is . d of the co ler the other han , when the sl ver not fully — distributed indicated by a wide space between it and the can id — i T i s e the cans cannot contain as much as des rable . h s may i W be overcome by sl ghtly reducing the rate of the coiler . hen the unoccupied space in the centre of the can is greater than “ ” d i d it is due i i i es re , to the can be ng too eccentr c w th the

i . d i i and i co ler By re uc ng th s , at the same t me the rate of the i i i co ler , th s object on may be removed. The quantity of the production in draw frames varies accord i n d and i . g to the spee , the system , the efﬁc ency of the workers

I n i i 90 . d i some m lls , as h gh as per cent of the pro uct on , caleu d d i d i i i late from the actual spee s , are obta ne w th sl vers as h gh 0 i as 7 gra ns per yard. The above may be considered practicable under the best con ditions . T i d i i d i in h s woul g ve the follow ng, per el very, a week of 55% hours

PRODUCTI ONS FOB SPE E DS RANGIN G FROM 3 20 UP TO 3 8 0 RE VOLUTI ONS PE R MI NUTE

- LLE R OF l gI NOH FRONT R O .

R evol utions of front Weight of s liver in Production in pounds per

ro er er inute rains er ard. wee ll p m . g p y k .

I di 503—805 n me um ﬁne ( ) counts , the former of the above i d id d and i speeds and product ons woul be cons ere ample , the sl ver 0 d d d di would range from 5 grains per yar ownwar s , accor ng to

1 08 COTTON SPI NNI NG CALCULATI ONS

N o tes in r esp ect of this System of Gearing R ollers .

a T i P is i ( ) hat , s nce the customary change wheel for vary ng the total e xtent of the attenuation and the weight unit of the i d d i P sl ver pro uce , any alterat on of or of the back roller wheel di d 2 and 3 and if sturbs the raft between rollers only, the total d d i d 3 68 raft be altere by th s means gra ually to 9 , that between 2 and 3 d d di i i d i d woul be gra ually m n she , no attenuat on woul and if d then take place between those rollers , altere to less than that amount contraction instead of attenuation of the sliver must result between those points . b The d 3 nd 4 d d ( ) raft between the rollers a woul , un er the i i d in a c rcumstances ment one paragraph ( ), always be constant , and hence should the wheels be altered to exercise a greater d 6 ° C d d and ir d raft than , the raft between the secon th rollers

d i d. T in d only woul be ncrease hus , case the total raft was raised to 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 i i i T i id po nt wh ch s not the best . h s also may be sa of system X F i . i i ddi i is in cal cu ( g w th th s a t on , that there room for error lation by overlooking that the two trains— eight wheels— are i d in i A nvolve the calculat on of the total draft. nother feature in these systems of gearing (Y and X) is the backlash due to i the ncreased number of wheels and indirectness of the gear . This is b eSt understood when the effects upon the sliver are C id d i n ons ere w th the wheels loosely geared or worn . O refer i it i 3 ill 4 and ence to the gear ng w ll be seen that w start after , 2 id i in cons erably after th s , because the former there are only i i in three or four wheels aga nst e ght 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 I t i dr t over X and Y. ensures the var able af between those i i i i i rollers hav ng the l ghtest work to perform , greater fac l t es for nd i i i i changes a calculat ons ; occup es less space , s mpl ﬁes the i d an d i parts , fewer wheels are requ re , perm ts the use of larger wheels . AND COSTS OF YARN 1 09

— 1 w n EXE RCI SE S Calculate the drafts in Fig . 2 bet ee a 1 and 2 2 and and 4 1 and 3 1 and 4 2 and 4 w n com nd ( ) , , , , , he the pou wheel between 1 and 2 is 20 and 3 0. b 1 and 2 w n w m d 20is 21 22 23 and 24 i ( ) he the heel arke , , , respect vely .

0 1 and 4 w n w m d 20 is 21 22 23 and 24 c i . ( ) he the heel arke , , , respe t vely d 1 and 4 w n P is in i i m 4 60 ( ) he the clus ve s zes fro 0 to . n w n P i in i i m 40 60 (e) 2 a d 3 he s the clus ve s zes fro to .

1 and 4 w n the 60 on 2 is 40 50 7 0 80. (f ) he the roller , , , W d wei in in d and o nt i (g) hat shoul be the ght, gra s per yar , c u of the sl ver d iv d in of in i n if n m i el ere , each the three types of gear g g ve , the u ber of sl vers fed d i w e in e c e six and e c of e e w i d at h per el very er ach as , a h th s e ghe t e rate of 48 grains per yard ?

h i i e ed m chine d in Fi . 21 w i ed 54 (k) If t e sl ver del v r by a a , geare as g , e gh in d w o d it w i if the w e P was ce i 40 45 gra s per yar , hat sh ul e gh h el suc ss vely , , 50 and 55 c i e , respe t v ly (4) What would be the production in p ounds per delivery per week with P

40 45 50 and 55 e e i if wi 60 1152 . we e od ced? , , , r sp ct vely, th a , P, lbs r pr u

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 i i d di dacing more or less than s requ re by the succee ng machine . I t is the most common practice to have the same number d i i in d and in of el ver es each h ea , also for the front rollers these “ i to revolve at the same rate . Pract ce has proved this most

“

x di . To d di i e pe ent get the best results un er such con t ons , 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 i id i in d occas on cons erably more loss of t me the ﬁrst hea , through i i 1 0 and i in stoppages , tak ng th s at , 7 , 7 per cent . respect vely d and i the three hea s , the revolut ons of the front roller at 3 20 er i and 1 i in di d Sli 3 p m nute 3 nches ameter , the car ver at 6 i d and d 60 i gra ns per yar , that at the last hea at , say , gra ns T d i i i d per yard. hen the pro uct ve capac ty of the th r head would amount to

” 55 . sox 3 20x 1 2 so 93 hrs g 3 1 0 d i x X 00 lbs . per el very 3 6 x 7 000 7 1 1 00

in d d d i Hence , the front roller the secon hea woul requ re to d d i d i d pro uce sliver at the same rate per yar , wh lst that el vere 1 1 O COTTON SPI NNI NG CALCULATI ONS by the ﬁrst head would require to be heavier to the extent of the diﬁer in i and ence the loss of t me , therefore

60 X 93 62 grains per yard 90

The draft in the respective heads on the assumption that d i 6 in the oubl ngs are , each case must therefore be I n the ﬁrst head

And in the second head

62 X 6 draft

draft

And in the third head

draft

FLY FRAME S.

i in — i di The pr mary obj ect fly frames slubber , nterme ate , and — is i i d rover, jack to attenuate the sl ver obta ne from the drawing frame to the extent necessary to prepare it for the spinning machine . It wou ld be possible to dispense with fly frames if drawing d d i D i rollers were perfectly a apte for attenuat ng cotton . raw ng d rollers , as at present constructe , cannot attenuate perfectly bodies of fibres varying in length . Cotton cannot be obtained

d in its . I n which oes not vary the length of ﬁbres consequence , the relative sequence of the ﬁbres is altered during attenuation in a degree proportionate to those variations and the extent of

i d. T i i the attenuat on attempte h s means , that a sl ver or rove with its ﬁbres uniformly distributed would have its ﬁbres

1 1 2 COTTON SPI NNI NG CALCULATI ONS 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

5 . to the proper extent varies from count x 08 to count X 1 Cottons which are long and harsh and lie compactly require i w i and do lie least , wh lst those h ch are short not compactly

i i . requ re most , tw st

The following is a table of the normal twist constants . i i d i These , when mult pl e by the counts of the actual rove , w ll give the t wist per inch suitable under most conditions .

S u er I nter. Rover . l bb . from 09 Sea I sland and Egyptl an cottons to :

from : 1 0 1 2 i n m i n and imi co ton Braz lia A er ca , s lar t s , to : 12 1 3 from 12 1 4 I ndi an and S1m1lar cottons to :

The G in in Fl F m s Fi — The i in ear g y ra e ( g. gear ng ﬂy i in I t i frames is ident cal all the principal makes . cons sts of d i a principal shaft calle the frame shaft, and from th s 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 D C d i i i wheels , F , E , , , B , name , respect vely : the tw st , the tw st i d end and carr er or compoun , the top cone , the of top cone , the end of the front roller wheels ; a compound wheel instead of E i being necessary when cons derable range of twist ar e necessary . The back and middle rollers are connected with the front in the i : i 28 0 40 56 and follow ng manner a tra n of four wheels , , 9 , , , named respectively the front roller the crown the pinion and the back roller wheels these i i and compr se the connect on to the latter roller, the crown Th pinion being compounded. e middle roller is connected with di 25 18 the back through the me um of three wheels , , C, they are d d i i and idd name the back roller ( r ver), carr er, m le roller wheels . The S indl s —The d i i is p e shafts r v ng these , one only shown , d i 3 3 in are connecte by a tra n of three wheels , , H , 3 3 , 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 1 1 3

i 60 and These spindle shafts are furnished w th skew bevels , , Th u i 21 i d . e these drive the bevels , , on the sp n les val e of th s

x train is ﬁ ed. — (0) Winding The B obbins are driven from two points upon i T.W. and i the frame shaft , M , the mot on from these two po nts i 1 4 in diff being brought together at the term nal wheel , , the er i d i 0 is d i ential . The bobb n riv ng shaft ( ) connecte w th the diff i N sleeve wheel of the erent al , by means of four or ﬁve wheels W B . R. .

Ra t ch e t Wh e e l

F I G. 22.

and 45 C 40 in of I n case of the front , three or four , , , , case the back bobbin shaft. These wheels are known as the swing

i . The N i its i m t i tra n sleeve acqu res mot on fro the wo po nts , i i x d i i and i rece v ng a fi e contr but on from one , M ; a var able con ribu i n A i x d i t t o from , the other of these two po nts the fi e port on here referred to being contributed by that part of the differential is which is fixed to the jack shaft . I n some cases that part a i i wheel . The variable contr bution is received by the different al

i T. . S i from the tw st wheel , W , on the frame haft , the mot on i and o and pass ng through the top b ttom cones , thence through a 1 1 4 COTTON SPI NNI NG CALCULATI ONS

i i i i d tra n cons st ng of a vary ng number of wheels , numbere on the

3 6 3 6 46 50 46 1 06. The x d i is d ﬁgure , , , , , ﬁ e contr butor arrange to supply the movement necessary to rotate the bobbins at the same rate as the Spindle ; the variable contributor communi eating only that necessary to obtain winding at the desired i B i tens on . y th s arrangement , the cones completely control

i di . i i di the w n ng When they cease to contr bute , w n ng ceases , h i d The through the bobbins then assuming the rate of t e sp n les . wheels in this latter connection are known by the following

: i di diff names the bottom cone , change shaft , w n ng shaft , er ential diff i s i i s and , erent al sleeve , w ng, bobb n shaft , kew bevels , i bobb n wheels . The Cons u n s of a in th u of n in — eq e ce lter g e Val e the Co e Tra . The

i i x d i i value of the wheel tra n , connect ng the ﬁ e contr butor w th i S d and d the bobb ns , houl be a constant , therefore any eparture from the above - named conditions will result in imperfect wind in h i i g. T e value of the wheel train connect ng the tw st wheel i di i i i Th w th the fferent al should l kew se be constant . e 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 di i in i di d i d two con t ons respect of w n ng , referre to , are bobb n lea

nd flr d. I n i di is i a ye lea the former of these the w n ng occas oned x in i i fl by the e cess the rotat on of the bobb n over that of the yer ; d i I n fld vic vers n fler d. er i and e y lea y lea the bobb n must be accelerated to the extent coincident with the proportional change in the Size of the bobbin at the commencement of each i in i i new layer of co ls , but only respect of that port on of the r motion supplied through the medium of the cones . I n bobbin i lead retardation takes the place of accelerat on . The connection i i is of the front roller w th the bobb ns , therefore , such that the latter creates a winding rate coinciding with the rate of delivery An in i by former . y change the rate of rotat on of the front di n in i i roller obtains a correspon ng cha ge the w nd ng rate . The cone dr ums are constructed to comply with the require i i i i i d ments of certa n s zes of bobb ns , each port on be ng a apted

i and . A in for a certa n size , that only lter g the value of this

1 1 6 COTTON SPI NNI NG CALCULATI ONS

ct Fi Subj e . Details of calcul ation ( g .

3 50 x 39 3 5 Assuming the strap on the parts 6 top cone and bottom cone 3 50 x 3 1 x 6 3 5 x as Assuming the strap on the parts 3 } diameter top cone and 6 diameter bottom cone

56 x 90 >< 1 40 x 28 >< 1

35o x s9 >< 6 x 3 6 x 1 3 >< 1 0 x 14

x 3 6 x 1 4 50 x 90 — Note The above is when cone strap is ” assumed in positions 6 in diameter ” driver cone and 3 1 in diameter driven

cone . And w n n is in i i n he co e strap pos t o s, ” i v 6 respect el y , 1 0 x 1 4 3 5 x 6 3 6 x 14 X 50 x 90 B bin To wind wi in min ob thout stretch g, assu g ” the winding circle 1 5 i n d1ameter and bobbin lead 000 1 1 084 3 30 in ex cess fi er I f flr of y pres ye lead 3 30 8 3 3 1 000 91 6 33 0 , slower 1 , 22 x than flyer Max imum size of bobbin that the cbnes pressure are adapted for 6 x 6 1 1 x 4 25 , 3 , x 3 , W n in is the m xim m i he the bobb a u s ze, and bobbin load 3 3 0 1000 1 0247 ‘ 22 44 . fl x 7 I f yer lead 3 30 1000 4 2, , x 7 For calculations of the speeds of the in in see 1 2 bobb s as per gear g, p . 7 . AND COSTS OF YARN

The Ch n Wh s in the fo -m n ion d T ins s i a ge eel a re e t e ra re pect vely . The following are the customary change wheels (a) For altering the rate of the rollers relative to the Spindles and i — i d and thereby the tw st tw st , compoun , top cone shaft

in d d. wheels, the or er name For altering the total draft or the attenuating powers of the — i i and rollers p n on , back roller , crown , front roller wheels . i d i di id For alter ng the rafts between the n v ual rollers , the id small wheels on the back or m dle roller . b N in i i d ( ) one of the wheels th s tra n are altere . i i T i (c) For altering the tens on of w nding . h s should be done by the ratchet wheel or adjusting the position of the cone The i i strap forks . pract ce of chang ng one of the wheels in this iﬂn l i i i i d ere tia s i d tra n , connect ng the , wh ch generally recogn ze , i i i i d in i s open to ser ous object ons , wh ch are state the sect on

d i i i di . 1 2 . eal ng w th w n ng, p 7 d i i i ( ) For controll ng the spac ng of the rove upon the bobb n . The lifter change shaft wheel and strike bevel are the usual i change po nts . — Alterations in the Draft Alterations in the draft are neces i i sary when the count , or the we ght per un t of length, are not d i d Al is d in d nd as es re . so , when a change ma e the fee , a a in d i is i d corresponding change the el very not requ re . Th i d is e formula when chang ng the raft or the counts , Present draft count desired count of present feed draft present count count of distended feed irequired

i l it is When the we ght takes the p ace of the count, necessary i i i i to bear in m nd that the we ght s nverse to the count, and that i i i i d i th s necess tates the nvers on of the two terms , es red and in i present , the above equat on . 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

. The i i is i d front roller p n on wheel the recogn ze change wheel , and the back roller wheel is changed when the limits in respect h d i i of the former ave been reache . When the l m ts of the two x l is d i former are e hausted the crown whee change , but th s is not often necessary . 1 1 8 COTTON SPI NNI NG CALCULATI ONS

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 . in i d i in d i Changes the s zes of the r vers , the raft tra n of i i in d t and and wheels , obta n nverse changes the raf count , 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 . Al ions in the D f how m de — d terat ra t , a Changes in the raft , or in d d do ff x the count pro uce , not a ect the e tent of the length d i n el vered by the front roller . Such cha ges always affect the i d i i in i we ght of the el very , per un t of length , nverse terms . The d i d in raft , as conta ne the present roller gearing (Fig. is as follows

Between the ﬁrst and second rollers 1 2 1 6

second and th1r d 25 x 40 x 28 x 1

56 x 90 >< 1 ﬁrst and third 40 x 28 >< 1

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 45 i d would be t mes ﬁner than the fee . The feed in the slubber generally consists of one end per d i d i in i di and it rove el vere , wh lst the nterme ate , rover , jack

i d . T in 02 is always compr ses two en s hus , the case where the d in i 45 d 45 count of the fee a slubber hav ng of a raft , x d d i d di i 09 woul be the count el vere . An interme ate w th 9 9 45 d i i 09 d d — X raft , treat ng slubb ng of count , woul pro uce 2

. A i i i d i count rov ng frame , w th a l ke raft, us ng that 2 25 i di d d x 4 5 45 56 count of nterme ate rove , woul pro uce 2 count .

1 20 COTTON SPI NNI NG CALCULATI ONS

W kin 3 —C d i d 55 5 5 or g . ount el vere x ;

Dra t ear . Diam eters o f F. R f g . and Bac R a ike k . i PAV B R l V . . . .

Change to the latter of these condi

tions . From these condi tions change to t he latter.

60 From these condi tions change to 9 “ 28 90 the latter .

P- 1 0 l 25 0 h ﬂn 25 50 w 25 1 00 56

a x 25 1 00 50 o

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 . d (1 ) and (2) determine the raft.

(1) and (3) determine the twist . The Rate of the Winding and Spacing of the Coils cannot be acc urately ascertained by calculation on account of the dis s imi i The i din u l arity in the Size of rov ngs . w n g m st be regulated i i Th by adjusting the pos t on of the strap on the cones . e rate of the vertical m ovement 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 i in This is useful as a bas s the absence of other data . AND COSTS OF Y ARN 1 21

22 The twist per inch Obtained by the gearing as per Fig.

A din d . 1 1 2 i i inches . ccor g to ata on p , the tw st ng would be adapted for

I f Sea I slands cotton

I f Brazilian cotton

I f Indian cotton 47 to 4 1

Thus ﬁve fram es employed as above stated with the draft 45 : the count of the feed and that in the creel would be respectively

X 2 4 04

X 2

1 2 x 2 2 4

X 2

09 1 x 2 1 8 2

d i ﬂ A change in the pinion wheel woul have the nverse e ect d d and d i i upon the counts pro uce , woul nﬂuence the we ght per

- unit of length in the direct proportion . Therefore a 30 draft i i i d 4 d d wi p n on nstea of 0 woul pro uce the follo ng counts , assum in g the feed as in the above instances 1 22 COTTON SPI NNI NG CALCULATI ONS

1 2 1

6 4 x 40 8 5 3 0

6 4 x 40 3 0

X 40 30 4 7 X 40 3 0

A change in the back roller wheel would have the inverse i i effect to that of the p n on . W t is d it u d henever the coun change , wo l become necessary

- i to r e adjust the tw st per inch to co unt t wist constant . The rate of the front roller would need altering in the pro

i i i . T i i port on nverse to the tw sts hus , assum ng the tw st wheel in d in - i d x each of the frames, referre to the last ment one e amples , 3 9 in d i i , the changes count woul necess tate the follow ng altera tions in the twist wheel

For (a)

— Nora The twists are in the direct prop ortion of the square root of the co n and n tt m a i m . u ts, he ce the la er y subst tute the for er

3 9 x x/6 ° 4 For (5)

For (c)

For

For ( e)

Assuming a: the size of the ratchet wheel and 3! that of the i d d in as and lifter change wheel , the follow ng proce ure woul obta

1 24 COTTON SPI NNING CALCULATI ONS

and o nce S ind 10 nd the win ndi i n in in u s per p le per hours, u er follo g co t o s a rov g m i n . min : S ind 1 150 F R . 1 20: di m 1 in fra e Revolut o s per ute p le , ; . a eter, % ch ; d 5 c n fed : two nd 3 5 n in e m di im raft, , ou t e s of ha k t r e ate rove ; loss of t e , 8 n per ce t .

A in - 3 . rov g frame is required to produce 9 hank rove containing twist equal

n x 1 4 and ind m in 120 i n min to cou t , the sp les ak g 0 revolut o s per ute ; the di m n is 1 in At w n a eter of the fro t roller } ch . hat rate must the roller be drive ? 4 At w m in in d indin d rin . hat rate ust the bobb s rotate to obta goo w g u g the ﬁrst layer under the following conditions : Gear from the front roller to the frame m m t ind 11 di m shaft, gs, that fro the fra e shaf to the sp les, 42, gg ; a eters, of n 1 in in 1 5 in e i n min e the m fro t roller , 4 ch , of the bobb , 5 ch r volut o s per ut of fra e 30 ? shaft , 0

- . A ﬂm in n n w 5 y frame ak g a 6 ha k rove has the foll owing cha ge heels D ini n 42 wi 6 4 i i 3 0 d i 26. W raft p o , ; t st, ; ratchet , ; l fter ( r ver), hat s zes of these wheels respectively would be required for a 5- hank 0 9 37 29 Ans . 5 3 . , , .

The ind in m in - 6 . sp les a slubber ak g a hank rove are Observed to rotate 45 im 1 n w i is in in i m the n t es per of the fro t roller, h ch ch d a eter : cha ge w — wi 40 1 9 i 26 d ini n 42 : and the S ind heels are t st, ; ratchet, ; l fter, ; raft p o , p les n wn m k 550 i n min t A in : a nt are k o to a e revolut o s per u e . scerta ( ) the prese

wi in b wi in i - n and n e t st per ch ; ( ) the t st per ch su table for ha k , also the cha g wheels required ; (0) the rate of production in both cases in hanks and ounces

im . ind 10 u min 1 5 n . n o per sp le per ho rs , assu g per ce t represe ts the l ss of t e

A ns 49 32 63 173 358 . . , or }g, , ; ; W i w w d m i in in m n foI° 7 . hat l fter heels oul be ost su table us g the sa e cotto 10 and for 05 n if it was n wn 6 i in was m o i ha k , k o that co ls per ch the st sat s factory Spacing for 1 bank and a 28 lifter wheel (driver) gave 7 coils per

A n 24 17 . inch ? s . ; W t i Of w w d m i in in m 8 . ha s zes ratchet heels oul be ost su table us g the sa e n 1 0 and 05 n if it was n wn 1 4 was m o i a cotto for for ha k , k o that a st su t ble for 1 7 12 hank ? A ns . ; .

The ind in in me d in 7 - n o in m 1 120 and 9 . sp les a rov g fra pro uc g ha k r v g ake ,

n 100 i n minu is 1 in in di m . the fro t roller , revolut o s per te ; the latter § ch a eter What twist per inch should the rove contain ? Give the twist constant and the ’ n Ans . hanks produced in 10hours uni terrupted working . 10 Th d in in m is 6 and the in m di . e raft the rollers of a rov g fra e ter e ate banks and two d d : w co n wi roving is 2 6 , of these are ouble hat u t of rove ll be ? h n in d n d and d w m ade I f t e cou t , ascerta e , has to be cha ge to the raft heels

0 4 B W di m F R. 1 W. 8 P W 0 . R 60 R W 20 C . . . . n F W . a d rollers are , , , ; a eters , g i w w d and w x n ? in h B R. 1 in w c c , % ch, h h of these heels oul you alter , to hat e te t ° — ns 7 8 P W 52. A . . . to

1 1 in m is m in 7 8 n - in wi win w : . A rov g fra e ak g ha k rov g th the follo g heels i 2 W w wo d ini n 40 wi w 38 46 t 8 . Draft p o , ; t st heel , ; ratchet, ; l f er, hat heels ul be needed for 6 ? What effect would these changes have upon the length and w eight produced A ns 52 43 40 32 in in n th 3 8 43 in in w i . , , , crease le g , to ; crease e ght, 6 to AND COSTS OF YARN 1 25

S acin Wind p g Cou nt Twist . Ro er ear 1 ft ll g . 1 11 . fed g b i . w ez.

— Winding in Fly Frames is obtained by the Bobbin Winding in these frames is due to the bobbin rotating at a slower i S i d I n or qu cker rate than the p n les . the former case the “ ” ﬂer d and in i d . Th y lea s the latter the bobb n lea s e rates i i d and i i di is of rotat on of the sp n les rollers be ng constant , w n ng obtained by that of the bobbin differing from the former of these to an extent sufﬁcient to wind the amount delivered by G i . n i i is the rollers enerally, the range the s ze of the bobb ns

i d 6 i . I from nch upwar , empty , to below nches when full t is not Often that full bobbins exceed more than four times i their s ze when empty . i di is d in i i W n ng arreste , these mach nes , when the bobb ns i i d ﬂr T assume the same rate of rotat on as the sp n le or ye . hus x d vice versd iﬂer ence if d the latter e cee s the former , or , the i d i represents the co ls woun . However large the bobb n becomes — i di is i d— i its when w n ng requ re the rate of rotat on must , as i d i d i s ze evelops , approach that of the sp n le , but never atta n

d it . T if i d and the same spee equal to herefore , the bobb n lea s i d 1000 i i the sp n le makes revolut ons per m nute , however large the

i c its i 1 000. bobb n may be ome , rate must be someth ng more than I n the i i 1 i in di the case of bobb n be ng 5 nches ameter , empty , and 6 i di and d nches ameter when full , the length woun equal to 1 20 i i m i i t mes the c rcu ference of the former s ze , then the bobb n 1 26 COTTON SPI NNI NG CALCULATI ONS

120 x 1 4 — —3 must revolve at the rate of 1 000 1030 revoluti on s 6

i 1 000 1 20 . when full , as aga nst empty The Use of Con D ums — d i e r . Cone rums are used to g ve the i i in d i T i necessary var at ons the spee of the bobb ns . he r work consists of contributing toward the driving of the bobbin an amount sufﬁcient only to ensure winding at the desired i i d i is the tens on , the rema n er an amount wh ch always equal to

i d i O i d x d i rate of the sp n le be ng bta ne from a ﬁ e contr butor . he Use of Diff n i s —Dif i 1 d i T ere t al . ferent a s a m t of the trans mission of the motion from the two above - named sources with i the most satisfactory results . A simple way of calculat ng the motion transmitted through the differential gear is as follows Let n d the i i i i m i enote mot on ssu ng from t ; , that port on n d i d x d i a i of er ve from the ﬁ e contr butor ; , that port on of n d i d i i nd A er ve from the var able contr butor ; M a , the rates of those parts of the differential responsible for m and a

FI G. 23 .

i t i i i respect vely , the values of the respect ve connect ng tra ns connecting M and A with n then n consists of m i a d diff i Fi 2 Applying this to the Hol sworth erent al gear ( g. 3) i and i is i d A When M s at rest mot on mparte to ,

At in di i revolutions of n A 1 ( the same rect on).

128 COTTON SPI NNI NG CALCULATI ONS

i i i and the revolut ons of the bobb n per m nute , when the bottom d w wi is 0 c one is stoppe , or hen the t st wheel

4o x 6o M‘X 40 x 21

in i and Since the two wheels the sun wheel are carr ers , the wheel on the frame shaft driving them is 3 6 and that driven by this

3 6 t 1 . a train is also a , therefore equals 32 Hence the revol

' 40 x 60 tions of the bobbin per minute 400 x 1 x 40 x 21

d nd in di i i or the same Spee a the same rect on as the Sp ndle . i i i The revolut ons of the bobb n per m nute, when the bottom in nd wi is 50 cone is work g a the t st wheel , are

40 x 60 — - (A + At i Mt) 40 x 21

23 x 1 9 23 x 1 9 1 1

4o x 6o X 40 x 21

t 1 and Here , the sun wheel moves in the opposite direction and i is to M, , therefore , the s gn hence

1 X 3 5 X 55 X 1 revolutions of bobbin per minute 7 6 60 400 x 1306 8 1 98 ) 21

the revolutions of the bobbins in excess

1 142 8 1 64

The d length of rove woun upon the bobbin per minute , i v is i and neglect ng the facts that the ro e wound sp rally, also that the actual winding radius is greater than the radius of i i the bare bobb n , s

612 inches per minute AND COSTS OF YARN 1 29 the revolutions per minute Of the front roller being and the length delivered by it in that time

400 x 50 >< 3 5 605 i 1 nches

Upon this basis the bobbin is shown to wind 7 inches more than the actual length delivered by the front roller . When the due i in i wi amount to contract on the rov ng , by reason of the t st i d in it is dd d diff due i dis nserte , a e to the erence to the sp ral i and dif posal of the co ls , also to the ference between the actual di i and i i ra us of these co ls that of the bobb n , the tens on of winding must be considerably more than is represented in the calculation . i The i d in Fi . 24 i f part culars conta ne g are of a rov ng rame ,

R. 1 d l F .

T W . . 3 9

FI G. 24 .

d the differential in this instance being of the Curtis and Rho es type . i 23 Proceeding to deal as with F g. n = m i a

i l x i i i When M is at rest it w l be seen , upon e am nat on of th s if is d differential , that, the bottom cone rotate ,

a At n , or n and in the same directio . 1 3 0 COTTON SPI NNI NG CALCULATI ONS

A is and is d When at rest M rotate ,

m Mt , or M and and A i when M revolve in the same direct on ,

m — t + a, or M Mt + A T di i herefore when M and A revolve in Opposite rect ons ,

= m — — t —At n a, or M M

The value of t in each of the above instances is the same , being 3 0 x 18 >< 14 25 x 3 0 >< 90

A di i d in it i ccor ng to the part culars containe the ﬁgure , w ll A is be seen that when at rest ,

71. 3 08 3 08 t

zs x so x so

The i n d d a di port on of enote by , when the ameters of the i O i — 5 cones at the po nts ppos te the centre of the strap are top , 2, bottom 3 4 inches ; equal s

46 l — 0 3 5 x 3 z x 3 6 x 50 x 106 x 25 x 3 0 x 9

M and A are indicated in the ﬁgure as working in the same di i ﬂr n i in rect on, the ye a d the bobbin are also revolv ng the same di i i m and rect on, the latter leading ; the connecting S gn between a must therefore be plus

3 08 x 3 0 x 1 8 x 1 4 25 X 3 0 >< 90)

46 3 5 x 3 4 x 3 6 x 50 x 1 06 x 25 >< 3 0 x 90 Under these conditions the revolutions of the bobbin per minute will equal

45 x 60

1 3 2 COTTON SPI NNI NG CALCULATI ONS

Under these conditions the inches Of rove delivered by the r d 3 3 9 1 f ont roller per minute would be stretche to 7 , or to the e xtent of 3 3 97 1 493 1 i i 1 th s be ng 7 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 T i when the cone drum ceases to b e a contributor. h s makes T d i i . the correct a justment of w nding imposs ble hus , when the is cone stopped, the revolution of the bobbin per one of the spindle is

49 45 >< 60 26250 - 2940 45 X 60 x X 1 250] 40 X 21 7 5000 40 X 21

23 3 10 X 45 X 60 999 7 5000 X 40 X 21 1 000

The bobbin moving slower to the extent of 0001 per revol ution of i d and i is d if the i d the sp n le, thus , wh lst the cone stoppe , sp n le 8 8 0 i i d makes revolut ons , the bobb n woul make 8 8 0 x 09 99 87 9 1 2 revolutions

T . W 4 6

FI G. 25.

25 particul ars given in Fig . are taken from an AND COSTS OF YARN 1 3 3 i di Th di . ﬂ nterme ate frame e er ential in this case is of the T d D i i ex wee ale type . eal ng with this as with the prev ous amples

n m i a

is and m is d When M at rest the botto cone actuate ,

n a At , or and in di i . A i the same rect on When s at rest ,

m Mt , or M

and A in di i When M revolve the same rect on , m — + a, or M Mt + At

W and A v in i di i hen M revol e oppos te rect ons ,

n = m - a — — , or M Mt At

The value of t in this case is

1 8 x 1 6 3 0 x 48 Taking the speed of the frame shaft at 2563 revolutions per minute with the bottom cone at rest

2563 x 1 8 x 1 6 n 256% 3 0 x 48

T i n m m his be ng the portion contributed to , fro source , when M and A are both in action together . T n a hat portion of contributed from source , 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 s i and a i i i be e, nches s nches respect vely , w ll

—— 48 x 8 g x 68 x 3 4 x 3 0 x 48 therefore when the M and A are working together

the revolutions of the bobbins being 50 x 55

42 x 3 0 1 3 4 COTTON SPI NNI NG CALCULATI ONS

The revolutions of the bobbin per minute are therefore

51 5) 27 3]x

50 x 55 - _ (205 3 27 3 ) x 42 x 3 0

The revolutions per minute which the bobbins would make if the bottom cone was stopped would be

50 x 55 (256 6 51 6) x 448 -146 42 x 3 0

The revolutions of the spindles per minute would be

40 x 55 2563 448 148 42 x 3 0

T i i i d he revolution of the bobb n per 1 revolut on of the sp n le , di i is accor ng to the above work ng, therefore

448 148 448 148

i di i i Work ng rectly from the spindle to the bobb n , th s last result is proved as follows

revolutions of bobbin per 1 of Spindle

1 revolution of bobbin per 1 of Spindle

The revolutions per minute of the front roller are

46 x 48 2562 X 48 x 1 30

The length of rove delivered by the front roller per minute 48 2563 x 285 m ehes 48 x 1 30 x 1 x 7

1 3 6 COTTON SPI NNI NG CALCULATI ONS

k in i i i wor s an obl que pos t on, and this is m aI nt ained by the Of i id pressure the cam aga nst the s es of the disc . Under these

conditions W1 and W2 act as a compound wheel toward motion i pass ng from M to N. Under these conditions the value of the train would be M W2 X w1 N

The ﬂ A is is e ect of the movement of , when M at rest, that

the cam would compel the gearing points of W1 and W2 to cir cu of i and i late , the teeth the former enter ng emerg ng from the

teeth contained in M as A revolves ; therefore if Wl contains i i i the same number of teeth as M, no c rcumferent al mot on T i i i in i i of W1 or W2 could accrue . h s reason ng appl es a s m lar 7 d and W i diff manner to “ 2 and N. Shoul M 1 conta n erent i i i i i d numbers of teeth , then c rcumferent al mot on w ll be mparte W nd W in di i i A W to 1 a 2 the rect on oppos te to that of , when 1 i and in di i W conta ns less , the same rect on when 1 has more , W W W . T d teeth than 2 hus , the movement of 1 woul be 1 M , in and its d teeth per revolution of A, rotary movement woul be

W1 M

The in d W in im d movement teeth ma e by 2, the same t e , woul b e 7 W1 M “ 2 x W. 1

nd if N i d a , therefore , conta ne the same number of teeth as W2, d the movement of N woul be the same as W2. I f in W and N i the number of teeth 2 were not al ke , the movement would be further affected by reason of the cam A i in W and caus ng all the teeth 2 to enter, emerge from , as many in N i d in T i n i of those as are conta ne W2. hus , the act on i th s is case must be, when M at rest and A makes one revolution

W1 M W2 N W2 x w1 N

i diff i t two I n the i I n th s erent al has values . respect of mot on from M its value is AND COSTS OF YARN 1 3 7

i is A its is Let this be termed t1 . When the mot on from value

W1 M W2 N W2 x W1 L et this latter be denoted by ta. I t will now be possible to proceed to deal with this in the same manner as with previous examples

m i “ a under all conditions . Therefore when A is at rest

n Mtl in di i the same rect on .

When M is at rest

71. Afg the resultant direction depending on the diﬁer ences in the

i d in W and N. number of teeth conta ne the wheels M , W1 , 2, T i i i di d h s w ll be n cate by the Sign being either plus or minus . When M and A revolve in the same direction together

72, Mil Afg T i i i F d in i . 26 and ak ng the part culars of the gear as conta ne g , the diameters of the cones at the points opposite the middle of

is i d w the cone strap , when the ﬁrst layer be ng woun , as follo s 7 i 3 i and in top 3, nches , bottom 3 nches , that of the bare bobb inch ; then : the revol utions of the bobbin per minute when i is 0 is d the tw st wheel , or when the bottom cone not engage , u d di wo l be , accor ng to the formula

The revolution of the bobbin per minute with a 50 twist

i . i A is in i wheel , assum ng M to be at rest wh lst mot on 3 6 3 2 3 6

4 X GS X 5O — 8 5 95 1 Therefore the revolutions per minute of the bobbin the winding of the ﬁrst layer would be 3 063 66 3 923 1 6 1 3 8 COTTON SPI NNI NG CALCULATI ONS

63 x 50 x 3 92 3 16 58 x 25

The revolutions of the spindle per minute are

1 65 x 56 x 50 3 06 3 66 1 X 58 x 25

The number Of coils of rove wound upon the bobbin per minute are therefore 3063 66

The following will therefore represent the length of rove wound X 22 X inches per minute 7

The in i front roller, that t me , makes 1 65 X 46 X 40 revolutions 24 X 1 1 5 or delivers

l 65 x 46 >< 40 3 88 928 inches of rove 24 x 1 1 5 >< 7

T is d if is d herefore that length stretche , the rove assume to

i i x have no th ckness , to nches , or to the e tent of 1 3 265 inches more than the rollers deliver ; this is equal to nearly per cent . The i i d in Fi 2 part culars conta ne g . 7 are those of a slubber dif i i ’ B and . frame , the ferent al be ng that known as rooks Shaw s

The i i dif i is di act on of th s ferent al rea ly understood. Applying the formula as in the previous examples

n m i n di i i i i i for all con t ons of work ng , the revolut ons wh ch the bobb n d i if ste ed if woul make per m nute , the bottom cone was pp , or i was 0 the tw st wheel , are

( 771 i a) X

l 40 COTTON SPI NNI NG CALCULATI ONS

i d therefore , of these the bobb n woul make

C i di i d i a alculat ng rectly from the sp n le to the bobb n , the revol tions of the latter per one of the former would be

52 x 24

The i i i revolut ons of the bobb n , assum ng the bottom cone to rotate whilst M is at rest and the diameters of the top and

i i r bottom cones , at po nts oppos te the centre of the cone st ap i in i i i i i i 6 i and 3 i wh lst the n t al pos t on , be ng } nches 5 nches i d b e respect vely , woul

[1 62 1 62 x

7 4 x 50

The rate at which the coils are wound during the ﬁrst layer laid upon the bobbin is therefore 48 07 7 1 00 5 per minute The rate at which the rove i s wound 1 0 1 —1 22 4 3 i i 05 X 2 X 7 7 7 8 nches per m nute

The rate at which the front roller revolves

46 x 65 2 200 X revoluti ons per mm ute 1 43 3 2 X 1 8 0 1

The length delivered per minute by the front roller is

’ 46 x 65 1 95 x 22 200 >< 4800 inches s x rso 7

The amount of rove which the bobbinwinds in excess of d i d i that el vere by the front roller , assum ng the radius of the winding circle of the rove inch 48 0 47 3 7 8 62 2 inches or per cent . less than that delivered. The S d in Fl F m s —Th pee y ra e . e speed at which the most satisfactory resul ts are obtained vary with the working AND COSTS OF YARN 1 4 1

di i : i d f i i con t ons the k n of work , the e ﬁc ency of the mach nes , i and i i i sk ll organ zat on of the operat ves .

D i d d d i xi ata on th s subject shoul not be regar e as nfle ble, but should be subjected to modification such as experience and d in i i evelopments , the appl cat on , suggest . The rates of spindle speeds attainable in modern makes d i of these frames , fitte w th long collars , are

Kind of cotton S u er . Intermedi at e . Rover l bb .

E gyptian 450- 500 050- 800 950- 1 050 1000- 1 1 50

— — American 550 7 00 7 00 850 1050- 1 200

— — I ndian 600 7 00 7 50 8 50 1050- 1200

Adopt the highest beneficial speed and fix other conditions so that the whole of the machinery is continuously occupied in i i d produc ng the requ re amount . P o o ions of M in in the C din D tm nt — Th fl r p rt ach ery ar g epar e e y i i frame processes usually cons st of three stages , but somet mes

t o nd d d. T d i w a four are a opte hey are name respect vely slubber , di i di interme ate , rover ; slubber , rover slubber, nterme ate ,

r over ack. , j The number of these processes expedient depends upon the

x i d i d i i in and e tent of the attenuat on es re pr or to sp nn g, also , to

x . U i d some e tent , upon the character of the cotton n form staple cottons are inﬂuenced less detrimentally by high drafts . Beyond a certain count the roving can be more economically prepared by

i i T i i x d. I t an add t onal process . hat l m t cannot be ﬁ e ranges Th dr upwards from between 1 5 and 20. e aft necessary to attenuate the drawing sliver to the desired extent for s pinning is di i d u in str bute amongst these two , three , or fo r processes certain proportion (see p . I n the machinery from the card onward to Spinning it is customary to arrange the machinery in what are termed pre ” ” i “ f nd parat ons . A preparation consists o one slubber a all the other machinery necessary to prepare as well as to deal i its d x d w th pro uct . Such may be literally e presse as a slubber 1 42 COTTON SPI NNI NG CALCULATI ONS and its The complement. following are the proportions of the machinery forming one preparat ion ih

Cards . m ers w r Co r me . . D a a s u . t Rovers b f Sl bbers I ntermedi a es . .

Mule s in p 9 t0 1 5 6 130 1 0 One frame o f One frame of Two frames Four frames in n g 1 8 to 24 8 0 to 1 00 of 1 20 to of 1 68 to 200 d di i indl 140 l i n d l s els . v sp es spd es . s p e ded n i to each each . three heads Ringfr amcs D itto D itto D itto D itto

The following are therefore the proportions of the above d i i i d i name mach nes per slubb ng sp n le , respect vely

( deliveries ) ( s pindle) ( s pindles) ( spindles) 007 5- 001 1 0 27 2—3 0

These proportions are those ruling in the bulk of spinning i and it is r e re m lls , therefore reasonable to assume that they p s ent what is found most useful . — Draft s 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 ) E xtent of the combined attenuation required ; (4) E fﬁcaciou s twist constant at each stage Ti (5) me lost at each stage . T d id d x i i hese ec e , for e ample , as g ven below, the respect ve drafts are arrived at as follows

n m inute . S u e 50 I nte e i t 8 0 ver S eed of s i d es er r 5 . rm d a e 0. Ro 1200. p p l ( p ) l bb , , ,

im x Per cent . t e lost (appro ) Twist constant Proportions of spindles Count at each stage D raft at each stage

This i s always ﬁxed by the count of roving Total draft m these ﬂy decided upon for spinning and by the weight of frames i m i d win m . sl ver, ost su table , at the ra g fra e

1 44 COTTON SPI NNI NG CALCULATI ONS

: 02 and 0 i d di i frames 6 respect vely . Un er these con t ons the d i in i di total raft or the attenuat on the slubber , nterme ate , —6 and i d - X (2 X the latter allow rov ng frames woul be 0 2 2 for the two doublings i n each of the latter stages ; 1 0. Therefore the weight produced per roving spindle per 55 hours

55 60 X 1 200 X 93 X 8 3 lbs .

n x 8 40 ds . 6 1 00 3 6 i s . y

(03) (C3)

3 The weight produced per intermediate § X S 8 3 lb ’ spindle per 55 hours 3

55 x 60 x 8 00 x 90 s x 3

55 x 60

0 23 3 the i di 2 , count of the nterme ate rove

The weight produced per slubbing X spindle per 55 hours

X 8 lbs .

CI X CI 0 61 5 V ' 3 6 x 840 x 8 3 x 8 x 1 00 0 0 25 i i 1 7 , count of the slubb ng sl ver

The drafts in the respective ﬂy frames may be now as oer f i d and a ne from the above counts , they are as follows Draft in the rover count of roving X 2 count Of intermediate

Draft in the intermediate i count of nter . rove X 2 X 2 count Of slubbing AND COSTS OF YARN 1 45

Draft in the slubber

count Of slubbing count of sliver 02

I t is r i du i seen , f om th s proce re , that the drafts n these

i d d i S i d mach nes epen not only upon the proport ons of p n les , but d i i d 142 and also on the other pro uct ve factors ment one on p . ,

d 2 3 4 5. numbere , , ,

ARTI C LARS OF FLY FRAME S P U .

Loss Of ume due t o oi in l g, c eanin and Us ua s iz es l g, l s M ine . i ncidenta of u s ua i t ach l f ll U l l f . sto a es o i ns pp g b bb . apart from doﬁi ng .

" 3 5 an 1 min 5 5 d 8 8 1 12 . Rover § § to 3 2 to 4 7 to ozs . s

" ' I n m di 4 4 6 9 and 10 18 24 ter e ate 6 to 5 to to ozs .

2 Slubber 10 to 1 2 4 to 3 0ozs .

— The Production in Fly Frames TO estimate the production of

- n d i . i d i 1 1 50 the above ame mach nes Rover , sp n les mak ng — i i u d 55. A w 5 . revolut ons per m n te ; hours worke , llo ,5per cent i d u and d for loss occas one thro gh breakages , procee as follows Weight of contents the weight that would be delivered of full bobbin in X in the period required to make a d if a ounces off, no stoppages ( ) the weight in ounces 1 1 50 X 1 6 delivered by the roller in i u ni nter twist per inc h X 3 6 X 8 40 X count one m nute , rupted w orking (y)

minutes required to ﬁll a set Of bobbins

minutes taken to ﬁll and + t1m e l ° st m dOf-ﬁn g doff Of bobbins z y a set ( ) 55 x 60 weight Of contents of production per spindle in X { } { z a bobbin in ounces ounces per week 1 4 6 COTTON SPI NNI NG CALCULATI ONS

T i d d i 6 i herefore, w th the count pro uce by the rov ng , the tw st 2 n Of 1 a d i 1 0 . constant , the contents a full bobb n ozs , the d i i d in and b anks 55 pro uct on per sp n le ounces per hours , i d be respect vely , woul 55 X 60 1 00 545 1 1 2 x 0 103 5 2 ozs . 1 1 50 x 1 6

Hanks

With the count produced by the intermediate the twist

1 2 and i 22 . constant , the contents of a full bobb n ozs , the production per spindle in ounces and hanks per 55 hours i d respect vely, woul be

55 x 60 9 22 x 9 94 5 1 2 x 22 ozs . 8 00 x 1 6

x 1 2 x 3 6 x 8 40x 23 3

Hanks 42 8

i d d 0 1 5 W th the count pro uce by the slubber 7 , the twist 1 2 and i 28 constant , the contents of a full bobb n ozs . , the production per week in ounces and hanks per 55 hours i d be respect vely , woul

55 x 60 100 28 X T ‘ 5 28 9 1055 . 12 X ozs 550 X 1 6 x 1 2 x 3 6 x 8 40 x 07 25

COTTON SPI NNI NG CALCULATI ONS

I f - i d d all 53 hank rov ngs were pro uce , the total weight would be 28 1 60 X “ 4 ; X 45 lbs . lbs . lbs . “ 55 X 55

1 ! i r e u l r ed The amount of 4 ,, hank rov ng q per week is

lbs . i d i The number of roving s p n les requ red to prepare lbs .

- Of 575hank must be 50280 i i d 4 2 42 total rov ng sp n les X 7 7 , say frames 7 1057

Leaving 18 frames for the 4% b ank.

Another way of arriving at the number of roving spindles to engage on each count is

Of 5 n lbs . 5hank ha ks f 4 lbs . O 5

T if 60 Of 1 7 6 i d d herefore , frames sp n les pro uce the above , and the respective productive ratios are

S 4 - 4 X in F , hanks or length or 5, ; 5 5 5 4 1 5 , 5X V 2 then the number of frames required for 20 hanks of 459 /4 5 x 1 8 1 frames V55

5 and for hanks Of 55

60 X 42 frames

The d i d i nd d pro uct on of the ﬂy frames , raw ng frames , a car s , in d w i . poun s , must be as follo s , allow ng per cent for waste at each stage

51 d i in d 2 hank Pro uct on , poun s , per roving spindle 5028 0 X 1 00

42 x 1 7 6 x 9a; AND COSTS OF YARN 1 49

4 d i in d in i d 5hank Pro uct on , poun s , per rov g sp n le

218 60 x 1 00 1 8 X 1 7 6 x 995

d i in d i di i d . All Pro uct on , poun s , per nterme ate sp n le these frames making the same count

7 8 440 x 100 3 360 x 99

d i in d i i d Pro uct on , poun s , per slubb ng sp n le 7 8440 X 1 00 691 2 1 1 52 X 98 5

d i in d d Pro uct on , poun s , per raw frame delivery 7 8440 X 100 8 34 lbs . 96 X 98

d Weight per car (see later).

° The S ds of he S ind s in m s — pee t p le in the Rov g Fra e . Talu ng the i 1 2 in and tw st constants at each of the ﬂy frames , the and i di d d i stoppages allowances as n cate , procee to ascerta n i i d the rate of rotat on of the sp n les . Q in : The d ff Rov g, 55hank o s per week 6 8 34 X 1 6 1 1

The time to complete a set of bobbins and doff

i d fﬁn (555 (m ns . per o g) hours

Speed of spindles ; revolutions per minute

1 1 X 55 X 8 4O X 3 6 X /55 X 1 ' 2 \ 107 3 5 x 60

R i 4 The d ff ov ng , 5hank o s per week

s -sé x 1 6 1 1 1 50 COTTON SPINNI NG CALCULATI ONS

The time to complete a set Of bobbins and doff

97 1 5 12 i . (555 25) 12 993 x m ns 1 00 hours 1 2 993

— The Count of the I ntermediate Roving The weight on an intermediate bobbin 22 ozs . i d i t 8 0 : 1 2 Revolutions Of sp n le per m nu e , 0; allowances

i d and 2 . 2 i . m nutes each off, 5per cent after 5hours for clean ng

1 x 1 6 2 Time lost in dofﬁng 22 X 1 206 mins . 1

N i . 2 i i i . 2 x ett t me work ng 53 hrs 06 m ns $38 8 87 m ns .

the count

x \/C x

The count

count

— The Count of the Slubbing Rove The weight of the slubbing

bobbin 28 ozs .

i Of i d 6 0 : 14 i Revolut ons sp n les , 0 ; allowances m nutes per

d ff and 2 . 2 i . o , 5per cent after 5hours for clean ng h d T e pro uction required per spindle per week lbs .

Time lost in dofﬁng X 14 553 mins .

N i i 53 i ett t me work ng hrs . 553 m ns . X 2547 mins .

1 52 COTTON SPI NNI NG CALCULATI ONS

— W i of Car d the Sli e . N Of d 1 20 4 e ght v r umber car s , ; allow for

i di . d 55 2 . gr n ng Hours worke , actual , , less 5per cent

7 8440 1 00 X 69 . 0 7 lbs , say 7 0 1 1 6 97 i d ﬂr 1 mi 2 n . Revolut ons of o e 5 per nute 6 i ches diameter Weight of sliver per yard

7 000 x 700 26 22 X X 55 X 36 7

ANALYSI S OF T E D A I NG OLLE H ACTI ON OF R W R R S.

Provided it is reasonable to assume that top rollers move i i in at the rate of the cotton w th wh ch they are contact, then i F gs . 28 and 29 are records of the action Of the dr awing rollers in i i d i d di i . the var ous frames , un er or nary work ng con t ons

Fig . 29 gives the particulars Of the Observed relative move in i nd i i di i a i . ment slubber, nterme ate , rov ng, sp nn ng mach nes

04 5—9 4 —5 57 Dr af t — — 9 4 6 4 L4 »

Re vs

Re vs :

Dr a ft

FI G 28A FI G . 28B . . .

T i d S. W. i hose , subsequently g ven , marke be ng of the self

i d i e. i i d. we ghte type , . only the front top roller be ng we ghte The rest are Of the ordinary weighted type .

i . 28 A 28 13 S Of i i d . F gs , , how the manner obta n ng the ata The revolutions given are exclusively in respect Of each pair b n The i i Of of rollers ( ottom a d top). relat ve rotat on th e dif ferent lines are contained in th e draft . In these ﬁgures the rollers are arranged in the order of their AND COSTS OF YARN 1 53

T i i i r . sequence , from left to r ght , back to f ont he r c rcumference , d l acéd i i revolutions , and raft are p oppos te the parts to wh ch

they refer . in ﬁ s O d i in The top line of numerals , g , are the bserve rat o d in in i in the movement , or raft , the top rollers , each nstance T 1 0 is d . 03 terms of one Of the prece ent roller hus , 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

S LUBBE R I NT ERME D IAT E ROV E R 1 5 4 3 2— — — — 1 P 04 5 5 7 - — — — F T 7 r ) F > T T1 01 3 79 3 9 8 1 01 5 1 07 0 9 8 2 1 008 1 : 1 205 70

' L1 21 s - —3 -9 7 — — i 21 5 — J J L1 9 L3 3 1 J

R W O E R ( S . IN M W V R G FRA E ( S . ) 1 OO3 —6 4 — 8 — — — F T 7 r 1 0 Tg 7 05 1 1 ( 1 1 28 7 1 005 1 02 1 1 25 1 01

L - > L J L i e 3 6 —J

FI 2 . G. 9

i in i in d l nes of rollers , each nstance , terms of one of the prece ent roller . The i 2 i i in features most not ceable , fig. 9, are the var at ons the i i di d f i sl p of the cotton , n cate by the movement O the respect ve i id . x in i i is top rollers E cept the slubb ng frame , th s sl p cons er i able . W th that e xception the effect of the action of the first and s econd pairs of rollers appears to be only that attributable to the i i i 4 ° 5 in i di : . elast c ty of the rove , be ng per cent the nterme ate , 1 3 i . d n an 0 3 . in per cent one ro ver per cent the other rover , i it is i i 8 . n wh lst almost per cent the r ng frame . — The Functions of the Re spective Lines of Draw Rol lers There are no reasons for suspecting that the ratios given in the last iff i T paragraph d er from those generally obta ning . hose results imply that the functions Of the middle and back top rollers Of i i i i in t i are , first , that obta n ng a un form tens on tha port on 1 54 COTTON SPI NNI NG CALCULATI ONS

Of w m d i d the rove bet een the ; secon , that of controll ng the bo y I f of ﬁbres not within the nip Of the front pair Of rollers . i it d c these nferences are true , cannot be an a vantage to pla e idd and id in i the m le back rollers w ely apart , also hav ng a draft greater than that whic h covers the possible variations in i and i i tens on natural ela st c ty of the rove . For these reasons the draft between the ﬁrst and second lines Of rollers should always be l ow and in accordance with the last -named

' di i n i con t ons . The difference in the c ondition i wh ch the is d in cotton presente the slubber, accounts for the almost complete realization of the draft between the ﬁrst and second i Of in l nes rollers that machine .

H ANK I NDI CATORS.

i 3 n Old and F gs . 3 0 and 1 contain the gear common i the new

i di d in d i and i . types of hank n cators use raw ng , ﬂy, r ng frames 1 00 and i I n Fi . di i d 0 g 30 the al s numbere from to , th s part is connected with the front roller by the following train of wheels : A single worm d i o nt ”o ne, on the front roller r ves 51 a worm wheel of teeth , the subsequent gear being dri vers

5 4 5" j “ 5 _ - . ? ’ : , ’ the 6 0 6 0 6 0 6 0 driven latter denominator being

the dial wheel . This form Of indicator does not admit of reliable di and fractional rea ngs , for this reason is being

discarded. The above gear is only applicable to frames containing a front roller 15 inch in diameter . is d An allowance of 25 per cent . always ma e for breakages , so that the indicator registers 25 per cent . less than the actual length delivered.

1 56 COTTON SPI NNI NG CALCULATI ONS

E XE R CI E - W n in n d 100 d d if S 5. hat le gth ha ks would be delivere per recor e 36 w m w i n the or heel s cha ged to 37 Ans . EXE RCI SE 6 —W n in bank w d d i d 1 0 d d if . hat le gth s oul be el vere per 0 recor e 3 6 and 3 w m w Ans the 4 or heels are changed to 3 5 and 25? . EXE RCI SE —W w i Of ° in wi l d d in m 7 . hat e ght 4 rov g l be pro uce a fra e

n inin 200 S ind 52 n d d an in i as in Fi . 3 1 co ta g p les per ha ks recor e by d cator, g ,

umin i n s 2560lbs . e s 2 An . ass g the l ss actually 5per ce t .

LE R NGTH O F ULL BOBBI N STOP MOTI ONS .

2 Fig. 3 represents a length stop motion applicable in ﬁne work when a number Of sets of bobbins are required containing x T i i i e actly the same length . h s mot on s very D = 5O convenient in the preparation of special rove 1 i i and i i and 0 for sp nn ng samples small quant t es, when not more than the roving necessary to

is i d. F= 25 make the yarn requ re A is B a worm on the front roller , a worm FI G 3 2 w d i in D D is heel , C a worm on the latter , r v g ,

m E dri compounded with the wor ; E ves 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

42 5 9 yards .

E XE RCI SE 1 —W i Of n i d to m . hat s ze cha ge wheel (3 5) would be requ re ake

in n inin 21 7 3 d Ans 27 . bobb s co ta g leas , yar s . E XERCI SE 2 —A in m n inin 20 ind i i d . rov g fra e co ta g 0sp les s requ re to prepare 8 500lbs Of 20 in m n n 1 0 ind . . rov g for a ule usi g double roving and containi g 00 sp les What change wheel will give the nearest approach to the necessary le ngth on in 3 4 each bobb Ans . .

EXE R I E - n C S 3 . What lengths of roving will be delivered by the fro t roller per action of this part with change wheels ranging from 25 to 45 respectively ?

MULE CALCULATI ONS.

The G in in Mul s —The d d i S i i ear g e . parts engage ur ng p nn ng receive their motion from the r im shaft . These parts that are engaged whilst spinning is in abeyance AND COSTS OF YARN 1 57 receive their motion through the shaft designated the backing

- OH and taking up motions shaft. The rim and the backing - off and taking- up motions Shaft i receive their movement from the l ne shaft , usually through the i f d i medium Of a counter shaft . Th s system O riv ng obtains d i di i better control than when r ven rect from the l ne shaft . The draft gear in these machines is identical with that in

ﬂn i . these i the a d y , r ng frames Reference to w ll make clear all that can be said respecting drafts and changes in the counts in

i in i i . mules . E xamples are g ven later th s sect on (a) The spindles are connected with the rim shaft by an di i i i di i and d in rect tra n , compr s ng two rect tra ns of pulleys ban s , the rope from the pulley on the rim shaft being guided to one

T - on the tin roller shaft by suitable carriers . he last named is d i d tin Shaft couple to a ser es of long rums known as rollers , these drive bands conveying the motion to grooved pulleys or The r im ul is wharves on the spindles . p ley the usual change i I n i part in this tra n . some makes sl ght changes are also d in i tin it is arrange for , the s ze of the roller pulley then made i in two detachable portions . When a change n the Speed of the

i x di i is d i Sp ndle is e pe ent , th s change use for alter ng the rate of i Of i d and its i i rotat on the sp n le relat on w th other parts . b The i rim ( ) connect ng gear from the shaft to the front roller , in Of i i di i six most makes mules , cons sts of an n rect tra n of wheels , arranged in three direct or simple trains . These are conveniently mounted to enable at least one driver and one driven wheel to n A in Of i i be cha ged. change the value th s tra n is necessary when an alteration in the relation Of the rollers with the rim

is i d. A in Shaft requ re lso , when a change the speed of the i d is d i d i i sp n le es re , but w thout any alterat on in the relation between this part and the rollers . (e) The front r oll er is connected with the back roller by an i di i i i di i n rect tra n of four wheels compr s ng two rect tra ns . These d d and i wheels are name the raft wheels , respect vely , the front i i and Th roller , crown , p n on , back roller wheels . e two latter i d i i are conven ently mounte for chang ng, be ng the medium of i in d alterat ons the raft . The idd d di i m le back rollers are connecte by a rect tra n , 1 58 COTTON SPI NNI NG CALCULATI ONS

i i in in fl compr s ng three wheels , the same manner as y frames . d The i i d is d d ( ) carr age , of sp n les , rawn outwar by two sets d h of ropes attached to rums secured upon the back Shaft . T e latter being connected with the front rollers by an indirect train i di i T of ﬁve wheels , these compr se two rect tra ns . hose wheels are conveniently arranged tO enable a driven and a driver to be

“ d T w i n i change . hey are kno n as the ga n a d ga n boss wheels i d d i i respect vely, the last name r v ng the wheel on the back T di i shaft. hese wheels are the me um of alterat ons in the rate i i of movement of the carr age , relat ve to that of the front roller and therefore they control the tension in the yarn during I n i i spinning . sp nn ng the poorer classes of yarn gain is Often “ ” “ ” i i . The i i i a m nus quant ty j ack ng , ratch ng , or stretch ng i i s i a i d d i mot on the means by wh ch y rns may be mprove , ur ng i i i f f k S i in O so t i i . The m otion p nn g , by the el m nat on th c port ons is d d it not usually a opte for other than ﬁne work , because d d i id i i re uces the pro uct on cons erably , thereby ncreas ng the cost Of i i I t is di i k h f i sp nn ng. the me um for actuat ng the bac s a t tra n and d i i i r ol ler s at 5to 5 the normal rate , ur ng th s act on the are i i e ither at rest or moving at an almost impercept ble rate . Th s action has the effect of moving the carriage at from 5to 5Of the S d and is d and d normal pee , hence the yarn stretche ma e more i i i d I n uniform by the th cker port ons be ng attenuate . a ecom plishing this successfully it is necessary that the yarn should i its i i i i The only receive a port on of tw st pr or to th s act on .

x d it i in x e i e act amount cannot be state , because var es e t nt , w th i Of i d i in the c rcumstances , from gto 5 that requ re , be ng lowest

- d and - d the best prepare long staple cottons . When the com

l eted i d d i i i is p yarn conta ns above the stan ar tw st, much tw st ng “ ” d. T i if d di necessary at the hea h s , complete at the or nary d Of i d in id l ess i spee the sp n le , results a cons erable of t me . The i d in i i i in di gearing , compr se th s mot on , var es the fferent

. T i d in i 3 4 3 6 3 and 38 . makes hree types are conta ne F gs . , , 7 , ” e The i di i i d ( ) slow roller turn ng , or rece ng , mot on , conta ne

in i . 3 4 and 3 6 i Of i in i d F gs , cons sts a tra n of wheels un nterrupte i r m T i connect on with the i shaft . h s prevents the front roller from being at rest whilst the rim Shaft is rotating in the

1 60 COTTON SPI NNI NG CALCULATI ONS

i d d carr age front ; an a justable number of teeth per raw , through

di Of and . The the me um a pawl pawl lever pawl lever , at is d rior i i d each passage , p ushe p to the term nat on of each outwar h x i i movement of the carriage . T e e tent of th s movement s d d in i i i d n a juste by vary g the ncl nat on of the curve bracket , a d d ff i i . R also , by the use of screws of erent p tch atchet wheels are d d d di wi i ma e a stan ar ameter by each maker , but th vary ng i numbers Of teeth . Whenever convenient the wheel s moved one tooth per draw only . — The Ro l D i Mo i n u in Windin l er el very t o , d r g g This motion i di i d usually cons sts of a rect tra n , compose of three wheels , for d i i d i i d i r v ng the front rollers ur ng the nwar run of the carr age .

T i is f d . The h s ef ecte from the back shaft wheel on the latter , is i d i or that on the front roller , furn she w th an escapement that allows Of the front roller being driven by the major movement i act ve . The winding motion is similar in construction in all the I t i i types of mules in general use . cons sts of an actuat ng i and i i di i i cha n cha n barrel , w th a rect tra n connect on to a wh eel

tin . T i i on the roller Shaft h s generally cons sts of two wheels , one Of these communicating the movement to the shaft through an escapement that allows the tin roller to be always under the The i i inﬂuence of the m aj or movement . rate at wh ch the cha n i d The is unwound from the barrel controls the Sp n le . rate of the u nwinding of the chain is determined by the radius described i T i is d by the other end of the cha n . h s secure to a nut on a i i d i d in screw w th n the qua rant arm , the screw be ng actuate one di i and i i di d i d rect on only , th s ncreases the ra us escr be by the nut . T i i i f i d i i h s s the funct on O the automatic w n er govern ng mot on . — The backing- OS and taking in motion is shown in each of the

3 and 4 . T i i in x Figs . 3 3 h s s the same all types of mules e cept that the value of the train and rate of movement are varied. During recent years considerable improvement has been d in i i The i ma e th s mot on . change enables the tens on , to i is d d d in d i wh ch the yarn subjecte , to be a juste the most es rable d i i i i i egree . Th s is Obta ned by the ntroduct on of parts wh ch

i - Off i i and i control the engagement of the back ng fr ct on , allow th s to be deferred until the momentum of the rim Shaft is reduced to AND COSTS OF YARN 1 6 1

Th ff i - the desired degree . e e ects are that back ng Off fr ictions nd m or e i may be run at slower rates a are rel able . They can be i adjusted more definitely to the requ rements . — The Hastening Motion The usefulness Of self- acting mules for the finest counts has been improved by the introduction I ts i of figure 3 5 type Of this motion . a ms are to secure the desired adjustment in the number and spacing of the coils d i i i i d u on i d . A woun p the sp n le at the term nat on of w n ng lso, to relieve thereby the strain u pon the yarn during the action i - ff of back ng e . — ’ Twist The following are the common twist constants standards in connection with the ordinar y qualities of Single yarns :

The Condi ti ons governing the Various Changes in the Wheel Train Values in Mules The speed Of the Spindle should be i i i i i d nd the h ghest cons stent w th the qual ty of yarn requ re , a 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 T i i d d i . i stan ar s g ven above h s controls the s zes of the r ms , 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

nd d i i Of the d . i d run , a eterm nes the s ze spee wheel F ve raws 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 d i es red. “ “ (5) The gain or drag must be governed by circum stances ; generally it is beneﬁcial in attenuating the thick soft and i A break ng the weak parts Of the yarn . t the same time it M 1 62 COTTON SPI NNI NG CALCULATI ONS

i i and is i d t x el m nates snarls , usually appl e to the greates e tent i i i pract cable . Th s governs the relat on between the movement

of the carriage and rollers . (6) Jacking ” or “ ratch can only be adopted when time nd i d d a other circumstances permit . Generally it s only a opte to a very limited extent in other sections than the production of I i ﬁne yarns . t is essent al in the production of yarns of a superior quality ; sometimes it is applied to the extent of as 4 much as 5inches in a draw of 60 inches . ” (7) The shaper wheel governs the thickness of the cep . I n i i i d d chang ng , the follow ng precaut ons shoul be note (1) Avoid changing the twist by means of either the speed wheel or r im pulley before ascertaining whether a change in the i d i d i i and sp n le or carr age spee w ll be most beneﬁc al, to what

extent each of these may be altered to advantage . 2 i i id ( ) Before chang ng the tw st wheel, cons er whether the pr epesed alteration can be accomplished to greater advantage by ri d means of the m or spee wheel . (3) Always notice and collect data Of the difference between d nd T the calculate a actual results . hese vary very considerably in - i i and i i the non pos t ve gear , can only be sat sfactor ly deter i n i m ned i th s 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 d Of d d en i d en s , a stan ar length , to able the counts to be ascerta ne . 5 The diff in S i d ( ) erences the rate of p n les vary very much , and in i i i ascerta n ng the actual tw st , several tests should be made .

CALCULATI ONS AND OTH E R PARTI CULAR S OF THE VARI OUS RA T I NS OF GE ARI NG.

Fi 3 3 i g. s a plan of the gearing as found in the Hetherington and di mule for coarse me um counts . The particulars relating to the driving of the rim shaft in this ﬁgure are Li S 23 5 i in di f d ne haft, revolut ons per m ute ; ameter O rum ,

3 2 inches .

C : and 1 6 i dr m ounter shaft fast loose pulleys, nches ; l v g d 28 i i rum , nches d ameters .

1 64 COTTON SPI NNI NG CALCULATI ONS

Siz e of rim 1 8 P 12 T R. . Size of .

S ind min. Revs . of p le per

— h wil diff on id m t d S d The NOTE T e actual l er c s erably fro the calcula e pee . d ind n rim S an wi om 5 n . w d loss betwee the haft the sp le ll be fr per ce t up ar s, when the diameters of the surfaces in the train are measured in the customary a w y . (b) The rate of rotation of the front roller relative to the i in d O i d i d i Th spindles is var ed or er to bta n the es re tw st . e train connecting the front roller with the rim shaft is provided with Th suitable change gear for that purpose . e length delivered by d i d i i the front roller ur ng the outwar run of the carr age , var es “ ” is d i d to i Th with the amount that the latter es re ga n . e i is 68 i 58 i movement by the carr age from nches to 5 nches , the and in former in mules for coarse , the latter those for ﬁne , work . ” i Of Assuming no ga n , the surface rates the movement of the

i d. T i rollers and carr age correspon hus , w th the front roller i and d 64 i 1 inch in d ameter the raw nches , the front roller makes 20 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 i d d i nd rim shaft to the sp n les , the smallest r vers a the largest

. T i driven change wheels are necessary hus , neglect ng the i i in i i d slippage ar s ng respect of the connect on to the sp n les , the i d 20 5 i revolutions of the Sp n le per 1 , revolut ons Of the front r oller would be 3 8 x 3 5 X 40 X 1 2 X 6 2 A 412 5 01 1

This represents the least twist per draw under the i d cond tions name .

The twist per inch Of yarn is therefore 64

T d i and d i in i i hus , r ver wheels r ven pulleys th s connect on AND COSTS OF YARN 1 6 5

d i i in i i il d i re uce the tw st nversely to changes the r s ze , wh st r ven

nd d i i . T wheels a r ver pulleys have the nverse effect herefore , the revolutions of the spindles per draw and the twist inserted i i e per nch of yarn spun , w th other chang wheels than those i in i i g ven the prev ous calculat ons , are as follows

Si of w on rim 3 0 29 28 27 26 25 24 (bl ) ze heel the Shaft ind d w 412 426 441 457 47 5 494 515 Revs . of sp le per ra Twist per inch

Size of wheel on the rim shaft 23 22 21 20 19 1 8 1 7 S ind er d w 537 562 588 618 650 687 7 28 Revs . of p le p ra Twist per inch 8 4 92

The revolutions of the Spindles per draw possible with the

in d- 40 iﬁ d and range spee wheels ( as spec e , the rest of the s d x i 1 3 0 pee gear, e cept ng that a wheel of 7 teeth replaces the r im i in i i as on the shaft , as g ven the prev ous calculat on , are — foll ows z The train from the rollers to the r im shaft when 3 8 X 3 5 X 40 Obtains 7 28 revolutions of the Spindl e per draw 20 X 3 5 X 1 7 20 4 i h i of 1 , revolut ons of the front roller . T e 40 in this tra n is the speed wheel and therefore increasing the size of this i du d and w ll cause a re ce rate of movement , by the rollers i i in and carr age , nversely to the change these wheels , hence proportionately more twist in the following amounts

(b Size Of speed wheel 40 41 42 43 ind w 2 74 7 64 82 Revs . of sp le per dra 7 8 6 7 Twis t per inch 1 19 122

Fur ther increases in the twist may be Obtained by increasing T i i d d i the value of this train . h s may be accompl she by re uc ng the number of the teeth contained in the wheel on the same axis as the speed wheel and also the b evel wheel d i i h s d r v ng that on the front roller shaft . T e latter i name the u i i 2 and 1 front roller cl tch bevel . By replac ng these w th 7 7

i wi i 60-S d respect vely , the range of t st obta n able when a pee is d wheel also employe , becomes

5333 3 5 X 60 X 1 2 1 670 i i 204 X 5 revolut ons of tw st per 1 1 draw 1 6 6 COTTON SPI NNI NG CALCULATI ONS

Thus : when the spee d wheel is altered to 40 the twist per draw becomes

i f i d d and Hence , the revolut ons O the Sp n les per raw the twist per inch obtainable by using the various sizes Of speed wheels comprised in the range will be b Si ( 3 ) ze of speed wheel 40 45 ind Revs . of sp le per dra w 1 112 1 250 Twist per inch 1 95

A i the - d in ssum ng that , after above state changes , the range Si x d the zes of the speed change wheels e hauste , further altera tion in the twist would only be practicable by changes in the i and nd d i i rim t tra n of rope ba r v ng gear, from the shaf to

i d . S d i S d the sp n les uch woul , at the same t me , alter the pee

i d a Th in i of the sp n les as per paragraph ( ). e changes tw st i i i as obta nable w th the range in sizes of rim pulleys ava lable , s i d pec ﬁe , are

Size of rim in inches 12 Twist per inch with the 40 17 ° 3 appended Speed wheels }60 26 ° 1

Size of rim in inches 17 Twist per inch with the 40 24 5 appended Speed wheels }60 37 ° 0

B is as 64 inches draw.

It is tin in customary, also , to make the roller pulley halves in order to admit of its being changed : the range is from 1 0 i 1 I n i n is in nches to 2 inches. the present nsta ce the latter i n use . Altering this would affect the tw st a d at the same time d r r i n the spee of the Spindles in the inverse p Opo t o . e Gain Chan — h in i ( ) ges T e back Shaft , pull ng out the car

ria e is d t o x d . T i i x g , assume make a ﬁ e movement h s s not e actly i i i the case , because th s movement must be subject to var at ons arising through differences in the tension of the ropes and matters inﬂuencing the resistance to the movement of the i f i i i carr age . For the purpose O calculat on it s conven ent to

1 68 COTTON SPI NNI NG CALCULATIONS most applicable with low spindle speeds and when the yarns are wi d du i not fully t ste r ng the movement of the carriage . — Changes in the Builder Wheel The approximate size of suit i d i d i able bu l er wheel , may be ascerta ne as follows , when the s ze of cop required is known

suitable builder wheel

5 in i the length nches of the yarn contained in the cop . d d in i the length woun nches per draw . 0 the revolutions of the copping screw necessary in i complet ng the cop . b is i d m i n , ascerta ne fro the we ght of the cop i grains , di id d i t in i and l i v e by the we gh of one hank gra ns , mu t plied by i the nches per hank . Thus

0 is t i d i i , ascer a ne by mark ng upon the sp ndle the length i 00 wh ch the p 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

d in d i . T i d i marke on the sp le , oppos te h s must be one wh lst the i is i i carr age at rest , w th the tra l lever bowl on the ridge of the i i and i d copp ng ra l , the revolut ons of the screw counte . As inin the Sui b Bui d Wh in n in C un s certa g ta le l er eel cha g g o t . Changing the counts affect the weight of the cops in the inverse i and i i proport ons , , assum ng the tens on of the yarn during i di i di w n ng proport onal to the area of the yarn , the ameter of the cop would be affected in the inverse proportion to the

T d i i in d \/counts . hus , the mo e of calculat ng th s wheel , or er to i d obtain a cop of constant s ze , shoul be as follows

Present wheel X “ required count required wheel x/pr es ent count

TE —A diff n in i the 00 m w w en the n NO . ere ce the s ze of p ust al ays result h yar is wound at other tension than inversely proportional to the difference in the area AND COSTS OF YARN 1 6 9

n n. A w n the t i n in an wa of the yar lso , he cha ge al ers the qual ty of the yar y y , the difﬁculty of adjusting the tension in the correct order is such that the above i c nn e i d n. The ow n wi nd mo e e i rule a ot be r l e upo foll g rule ll be fou r r l able, but must not be regarded as accurate in all cases

present wheel J required count present wheel required cou nt Reqaired wheel + n n 2 X n o n 24/prese t cou t prese t c u t

Ascertaining the suitable builder wheel in changing the size of the 00ps only Present wheel (diameter of required cop)2

The following are exercises in calculating the alterations

i in Fi . 3 3 i necessary to adapt the gear ng g for the work g ven . They are given in tabulated form because it is more convenient i in d i i i Allow 10 per cent . for sl ppage the r v ng of the Sp ndles rim and i from the shaft , use the customary tw st constants where i the tw st is not given . — h E xp lanation of the tabulated exer cises . T ose columns h numbered 1 to 1 6 are separate exercises . T e data required is signiﬁed by Base the calculations for the builder wheel on that given in E xercise 1 . The items referred to in each column are contained opposite in the ﬁrst two columns on the left hand.

1 7 2 COTTON SPINNING CALCULATIONS

I N AG 1 - 1 EXAMPLES I N CALCULATI NG TH E E XE RC SES O P E 70 .

3 3 The following changes would b e necessary to adapt the gear in Fig. for the conditions stated E X ERCI 1 —T d i in a 000 e o i n er min te ct SE . o r ve the sp dles t 6 r v lut o s p u , a ual , with a 1 2-inch mm : 6000 10° The calculated rate of the spindles will 3 6666 and the — 9 Revol utions of Rim Shaft With the minimum and maximum siz es of driver and d i n n i c v a . 1 63 r ve ha ge pulleys respect ely (see par . ( ), p )

Revolutions Of the rim shaft per minute 834 — S eed and Twi s Chan es . The n o if 1 in in di me and e is p t g fro t r ller, ch a ter, ther 64 x 7 n in 4 o wi be e i d t m n d w. D in ga , ll r qu re o ake 20 o io 22 1 1 rev lut s per ra ur g this movement the spindles are required to insert twist to the extent of

8 106 er in 3 ° 7 5 8 64 in d w 7 53 and p ch, or J X ( ches per ra ) , actual ; 7 53 129 e o the c d i n ind d w are - 837 th ref re alculate revolut o s of the sp le per ra 527 ,

3 3 1 13 1 t d wi inc or 3 4 calcula e t st per h .

The in nn . a b tra of gear co ecting the spindle and the front roller (see pars ( ), ( ), 83 7 1 1 1 6 — h pp . 3 4) must therefore have t e following value if); 222 Ac din to the n in n w e i n in Fi 33 the owe cor g ra ge the cha ge h els g ve g. l st x 12 v e of i t in is alu th s ra ° 07 5 x 12 x 3 0 x 3 5 x 20

n e e in e an of the w c nt ined in i t in He c , alt r g the valu of y heels o a th s ra , to in i i 202 to wi h i ed m c n in crease the r rat o ll have t e effect des r . Na ely, ha g g d the twist to 13 1 calculate . (driven)

3 m t be te ed in e to Therefore the wheels 38 1 us al r valu (dri ver) 54 2 7 20

n rim t 20 and eed w e 54. Therefore the required wheel o shaf , the sp h el

“ - Whe l s ee . 166 7 . For Gain e , pp to tt n t l The Draft required in the rollers is that necessary a e ua e g to 8 1 8 _ in h d t n inion nece 8 o n or 55 By assum g t e raf cha ge p ssary, c u t, f ; 1 a

' owin i n is in d a, the foll g equat o obta e

130 1 54 — 51 x 3 (b n l

can be ccommod d is The range of siz es Of draft pinion wheels that a ate , The om 30 60 and on the c m 40 60. w approxim ately, fr to , ba k roller fro to heel AND COSTS OF YARN 1 73

82 is o t oo e and en e it is n c a to d e the i i , theref re, larg , h c e ess ry re uc s ze to w thin r vet 82 the n of c omm d ion The io e two w e is i ra ge a c o at . rat of thes he ls gri ven 54 or

n an the owin ir of w e w d be it f He ce , y of foll g pa s h els oul su able or the 47 56 59 i ion . pos t ’ ’ 3 1 3 7 39

EX RCI 6 —I h i in t n e en t n to be w nd e c d E SE . th s s a c the l g h of yar ou a h raw is 64 4 in an n the twi in ed m be in cc d n e ches , d he ce st sert ust a or a c therewith .

T i in i d in n wo n 1 4 w st per ch requ re the yar u d 4/24 x 8 Twist per draw 68 inches x 18 4 1 250 — Acco din to . . 163 the o d be cin the tr in m rim r g par p , gear sh ul tra g a fro the

F R. : 17 dri in 45 27 d i in 35 17 d i in 8 1250 ion shaft to the . v g , r v g , r v g 3 revolut s rim d w and e o e l i Q 184 wi in i in wi of per ra ; th ref r % 8 t st per ch, th s be g th a

12- in nd Of 2 in min ch rim pulley a at the rate 75 0revolutions of the sp dl e per ute . — The Siz e of Rim The rate of the spindle required is 9500 revolutions per min c n wi rim m kin 940 o i n min ute, a tual ; he ce , th the shaft a g rev lut o s per ute ,

and the i e the rim a: and 10 er c n . wed for i the owin s z of , p e t allo sl ppage , foll g equation is obtained

940 X a: x 6 9500 x 100 10555 12 x if

The o i n of ind er d w 1250 rev lut o s the sp les p ra , actual A win for li c c ed e i n in r 1 llo g s ppage, the al ulat r volut o s Of Sp dle pe draw 3 90

Proof that the ab ove is satisfactory — The Speed Tr ain of Wheel s The train connecting the r ollers with the spindles 1390 must therefore have a value of 68 3 20 4 1 T This means that the spindle must be calculated to m ove revolutions

er 1 the F .R. and en e owin e ion w n e d w e p of , h c the foll g quat , he the sp e he l has the value ac

6 x 17 >< x x 3 5 x 3 8

Alternative sizes of suitable wheels The smallest sp eed wheel practicable b eing 40(40 and the ratio required 1 e we n t i and the w ee on the eed in the l owin e b t e h s h l sp shaft be g , fol g oth r 3 574 w l wi in n e of c omm d i n wi i e oxim the de i d hee s , th the ra g a c o at o , ll g v , appr ately, s re 23 24 25 26 wheel on rim shaft results ’ ’ ’ ’ 48 50 52 54 speed wheel

° The draft requir ed in the rollers is that necessary to attenuate 3 roving 1 7 4 COTTON SPINNING CALCULATIONS

“ 2 4 i n h in in 24 8 . B min a the d t c n e in o t e ow to 3 y assu g raf ha g p , foll g equation is Obtained

54 X I 3O X 1 54 X l 3O _ 8 _ 55 D inion , raft p w X 1 6 X 1 8 X 16 12 24 12 2 _ X ¢ x 4 Bul lder wheel 104 18 say 28 27 8 2 X 8

“ ’ EX RCI 7 —The d 28 W m 3 in o in E SE , raft for , fro s gle r v g A min a; d c n e ini n and 54 the th win i n ssu g the raft ha g p o , e follo g equat o is obtained

54 3 x 130

“ 47 D t inion x , raf p m x 1 6 x 1 w a 1 6

The i e of rim n e o t in te of ot tion of the ind s z ec ssary to b a the ra r a sp les,

10 en . ma be O in d m h win e ti n w n per c t for loss, y bta e fro t e follo g qua o , he a; the siz e Of the rim in inches —a 6 10500 X 100 940 X x 1 1680 1 2 I 90

940 x 6 1 1 680 X 12 X 25 1 1 680 X 1 2 X 2 19 I n Ri m say ches, 940 x 6

The twist per inch J 28 X 3 25

Therefore the twist per draw (68 inches) X 68 inches 1 170

h nt m e 20 e u i n er d w and ed Assuming t e fro roller ak s ﬁ r vol t o s p ra , the spe o owin e ion con in the v ac owin wheel contains ac teeth, the f ll g quat ta s alue of , all g n i 10per ce t . for sl ppage 19 X 6 1 170 X 100 90

20ﬁ x 3 8 x 3 5 x 19 x 6

T i w e ein too i w of i iz a b t in h s h el b g large , a pa r of heels su table s e m y e ob a ed m he io o id d e e c n w e o e fro t rat pr v e by th s ha ge h els, theref r driver 20 ’ say driven 53

“ The gain wheels necessary to give 3 inches gain are

z 64 - 3 § o i n of the f on e 194 60 rev lut o s r t roll r

here a the value of the change wheels

X x :

1 7 6 COTTON SPINNI NG CALCULATIONS

The pair of wheels within the range speciﬁed having the nearest to this gain rati o are 12 x 80 The builder wheel x 2J 8 2 X 8 (l i )2

E X R 1 —The d e i ed in the ol E CI SE 6. raft r qu r r lers

Th d n w e tio a m e raft cha ge h els ra , , ust be

4 3 9 X m = 10 1 6 10 x 16 160 w 1 30 130

Therefore the suitable draft wheels are 53 54 B .E .W. 48

’ ’ P . W. 39 43 44

The twist per inch required 4/100 draw 64 X 2035

in for 10 c nt. the c c ted ev tion of the ind e Allow g per e loss , al ula r olu s sp l s per 2035 x 10 d w e i d 2238 . ra r qu re 9 The actual revolutions per minute of the spindles required 8000 8000 x 10 c t d alcula e 9

With the siz e of rim required 570 x x {g g 8888 x 10 x g say 570 x 6 60 4 — The revolutions of the front roller per draw required 178 7 8888 X 10 X 33 The revolutions of the rim shaft per draw , 143 195 X 6

n w ee tio 96 is t e The speed cha ge h ls ra , , her fore

60 3 5 143 x 1 7 x 27 1 7 8 X — X - x x — 143 _ 17 Q7

Therefore any of the following pairs of wheels would be suitable

speed wheel 42 44 49 51 ’ ’ rim shaft wheel 24 28 29 AND COSTS OF YARN 1 7 7

nd ont i d d w ain —The revol utions of the back shaft a fr roller requ re per ra , G . f in 3 3 8 and owin e tion i e the O x respectively, be g the foll g qua g v s value the gain change wheels ratio

X X a; a; g?)

i e And hence the following pair of these wheels are most su tabl

105 gain wheel 1 5 gain boss wheel 12 X 100 The i de w X bu l r heel 2 X 8

’ — d Mu Fi . 34 Particulars of Gearing in Dobson s or . le g shows

FI G. 34 . the arrangement of the gearing in mules for medium and d D n medium ﬁne counts as ma e by obson a d Barlow. The following are particulars of the various trains and the range in the size of the wheels shown 1 7 8 COTTON SPINNING CALCULATIONS — (a) Tr ain to Sp indles Revolutions of the rim shaft (H G)

4 0 8 50 i . Rim D 1 2 per minute from 0 to per m nute pulley , , 2 in D 1 0—1 2 i tin U 2 inches ; t roller pulley , 3 , nches ; roller, , — 6 i i d h u 3 4 i . nches ; sp n le w arves , l , nches

° - - b T r ain to the ROlle7 s . J 1 9 K 58 L 3 0 56 C 60 ( ) , ; , ; , ,

1 00 3 2 25. ; R , ; S, — — 0 d : k 20 l 180 A 30 60 on 30 7 0. ( ) Roller raft gear , ; , ; , , : 1 i idd i Diameters of rollers front , nch ; m le , nch ; back , i 1 nch . ain h ack ha t rom the F ront R oller Sha t — T (d) Tr to t e B S f f f , — — — 1 55 0 55 0 8 1 6 20 68 1 5 : N 55. 5 ; , ; E , 7 7 ; P , ; Q, ; M , , Revolutions of the back shaft per draw : 3 5 for 64- inch

- 6 -i d draw for 60 inch draw for 5 nch raw .

e Train or Slow Roller Turnin s ometi mes called the ( ) f g, — 4 R ecedin M otion U 20 40 W 1 3 0 24 ! 2 . g , ; V, ; , ; X , ; Y, ; ,

i Roll er D eliver durin th I nwar d R un —i Tr a n f or y g e , — 1 4 1 40. 7 ; j ,

- - akin in and B ackin O M otion Gear . a 14 i e 1 T g g f , nches , 7

24 1 4 h 40 c 10 cl 7 3 . f, ; g, ; , ; , ; , — - i a 1 i in : 0 3 50 i . Tak ng mot on shaft , 7 per m nute

i ki - in i ( l 4 - i 6 d . Revolut ons of ta ng mot on shaft per nch raw , 3 a n — 2— n uildin or h er M otio . 1 0 a d B g S p Wheel, 7 , various pitch of screws . ' — — Twis t Wheel . 40 1 20. — XE RCI SE S. A ce t in the owin om the rt ic s con ained in E s r a foll g, fr pa ular t i 3 4 z F g. 1 The n in the te er min te at w i the ind ma i n . ra ge ra s p u h ch sp les y be dr ve . 2 The n in wi t m a b e inse d in rn . ra ge the t st tha y rte the ya .

3 The n in the d . . ra ge raft n in n wi nd i n d 4. The t a we w c m i i t ra ge the cou ts, t s ft, h h the ach e s adap e for n wi in wi n m wi c n n i the respect of t st g th the or al t st o sta ts .

5. The i in m m n c i and nd inﬂn e rat o the ove e t of the arr age before u er the ue c in m o i n min d in m m in of the jack g t o , assu g that ur g the for er ovement the draw g out band is on the full- sized portion of the scroll ; and at the termination of the m em n on the - i d i n latter ov e t, half s ze port o of that part . 6 The i and i m m n d in i n . rat o of the roller carr age ove e ts ur g tw sti g at th e n in din i n head and whe or ary act o .

The a i in S ind d in innin and w - 7 . r t o the rates of the p les ur g sp g hen backing off. The im in e ond en m e i -in a 8 . t e, s c s, tak to ov the carr age , t the slowest and

quickest rates . in in d i d b h l 9 . The n c e e e t e d in in n le gth, h s, el v r y ro lers ur g the ward ru .

1 8 0 COTTON SPINNING CALCULATIONS

a n r s ect o E xercise 9 — A min m E x mp le i e p f . ssu g the back shaft akes revolutions during the drawing in of the carriage and the 17 wheel is in use on he c the n d iv d e t ba k shaft, le gth el ere , quals

1 7 1 x 22 3 3 9 X x 4 52 i nc E 7 hes

EXERCI SE S —A c in od i n in n 55 r wi . s erta the pr uct o ha ks per hou s, thout allowances for stoppages ; and the various change wheels necessary to adapt the

in c n ain d in Fi . 3 4 nd m n i n d n and ndi i n gear g, as o t e g , for the u er e t o e cou ts co t o s i n of product o . Allowances : i in dri i n ind m rim ft 10 For sl ppage, v g the sp les fro the sha , per i in nt . d w 60 4 in d d d in inw d run ce ra , 5 ches, the latter el vere ur g the ar ; back g - d due n 1 0 n off and r un ia 5 n d . to occupy seco s ; loss of spee to cha ges, per ce t 1 60 W r m 10 n d vin E i n : d rim and . . f o ha k ouble ro g , gypt a actual spee s of ind 859 and 10000 i n min in 1 in in 1 in sp les, , revolut o s per ute ; ga , ch ; jack g, ch ,

5 n wi in in d t in . per ce t. of t st be g serte af er jack g

2 60 T f m 12- n d vin E i n : rim and ind d 840 . . ro ha k ouble ro g, gypt a sp le spee s, and i n min u in in in 1 in 12 revolut o s per ute act al ; ga , ch ; jack g, ch ; per

n wis in in . ce t . of t t g after jack g

- 3 . 80 W. m 14 n d in E i n : r im and s ind d fro ha k ouble rov g, gypt a p le spee s, 840 and 9000 i n min t ct u in 2 in in 1 in revolut o s per u e a al ; ga , ches ; jack g, % ch ; 8 n wi in in per ce t . of t st g after jack g .

- in E i n : ri m and indl ds 4 . 80 T m 1 6 n d . fro ha k ouble rov g, gypt a sp e spee , 840and 9500 i ns min in 2 in in 2 in h revolut o per ute actual ; ga , ches ; jack g, c es ;

1 2 n wi in kin . % per ce t . of t st g after jac g 5 94 W m 1 6— n d in E i n : rim and ind e d . . fro ha k ouble rov g, gypt a sp le sp e s, 840 and 8700 e ti n mi n e in 2 in c in 2 in r volu o s per ut actual ; ga , ches ; ja k g, ches ;

1 0 n f in in . per ce t . O twis t g after jack g

- k d in E i n rim and in 6 90 T. m 1 6 n : dl d . fro ha ouble rov g, gypt a sp e spee s, 8 40 and 8700 i n min tu in 1 inc c in 2 in revolut o s per ute ac al ; ga , h ; ja k g, % ches ;

12 r n wi in in . } pe ce t . of t st g after jack g

— The ind d E xamp le of worki ng E xercise 1 . sp le spee will be attained by using a rim and tin roller pulleys of the following diameter Let x the Spindle speed change ratio

10000 X 10

9. then 850 X x X 6 1 2 2$ 9

in R P . and 1 1 in e T in i i 18 . R .P. o i t . ches ch s or, thers g v g h s rat o

The revol utions of the rim shaft per draw must be

6 4 0 § x = 135 1 8 b 90 x x 1 1 2 100 AND COSTS OF YARN 1 8 1

The sp eed change gear must be arranged to Ob tain the delivery Of 60 2 inches X 59 w i t the is m in the c i out 59in e and e e h ls back shaft ov g arr age ch s, th r fore the 60

i n i i th m i d D in i mo revolut o s of the back shaft are requ red n e sa e p er o . ur g th s ve ment the spindles are required to insert twist in accordance with the state

i d w . 1 00 n 5 n n i in in in . t . x . w d spec ﬁe per ce t . per ce per ce t t st g ur g jack g D in in i is m d m n m and ur g jack g the carr age assu e to ove at 3 the or al rate , there fore requires a period equal to that required to move the carriage 3 5inches at the

. n 95 n Of wi in i d i d latter rate He ce , per ce t . the t st g equals the per o requ re for 59 3 in m m n n m and t e o e the e i n of ; ches of ove e t at the or al rate , h ref r r volut o s the rim d in e 9 in e m be , ur g the abov 5 ch s, ust

9 en of 13 5 1 20 v ion rim 8 5per c t . re olut s of

D in the i the ont e is i d to d i ur g the run out of carr age, fr roll r requ re el ver 58 in and e o it m m ches , ther f re ust ake 58 revolutions 1 x

The Speed change gear ratio (x) is therefore

1 8 ‘43 X 58 X 25

9. 120 x 1 x x x 3 2 1 8 43 w 5 8 0 5 . o 120 x 19 x 3 2

The ed n w ee wi in the n in i spe cha ge h ls, th ra ge hav g th s value , are

driver 3 4 3 5 3 6 37 3 8 3 9 40 ’ ’ ’ driven 101 104 107 1 10’ 1 1 3 ’ 1 1 6’ 1 19

“ x 59 The gain change gear must be arranged to impart revolutions 60

f i n n e in to the back sha t per revolut o s of the fro t roller, b fore jack g mm n T e in co e ces . herefor the ga change wheel ratio (x) must be

- 55 _ 3 28 x 59 8 l 8 43 x ‘ x x _ i85 60

The change wheels nearest to this value are

— T he dra t and dra t chan e wheels A - n ce itate f f g . 10 hank double rove would e ss 6 0 d t 12 if the d du e to in and in is n ct d. a raf of 121 , raft ga jack g egle e 2 T in in o o n it ak g the latter t acc u t , woul d be 1 82 COTTON SPINNING CALCULATIONS

The draft change wheel ratio (x) to give the latter draft must be

X 20 X x 11 6 1 80

The d n e w ee wi in n e i d raft cha g h ls, th the ra ge sp c ﬁe , containing this value driven 58 53 49 ’ ’ ’ dri ver 48 45 41 ES

Twist wheels are necessary when the rim shaft is required to rotate a “ ” d ni m n i d d it is eﬁ te a ou t after the carr age has reache the hea . Usually m n ni n to r n m m one two tion d w ost co ve e t a ra ge the to ake or revolu s per ra , and in i in t n in 13 5 is not i 6 therefore, th s s a ce, s ce ava lable , say 8 . 13 5 Ti m d w X e per ra Q T)

Hanks per spi ndle per week 27 8 X 36 x 840

E xam le o wor kin E xer cise —The i d d of ind e wi p f g 6. requ re spee sp l ll be Obtained when the change pulleys in the gear from the rim to the Spindles have the ratio x in the foll owing equation

8700 " 10 8 40 x x x 9 9666 9

rim 44 nearest T R P T e l u i n rim d w if the d ted her fore the revo t o s of the per ra , latter are a op

90 ﬁ x ; X

— 3 0 1 OTE . The is the i N 4 4 sl ppage . The speed change gear must be arrangedto obtain the delivery Of60 34inches w i i m o 57 in O w d and e the m h lst the carr age ves 4 ches ut ar , therefor back shaft akes 3 28 x 57 4" 3 14 o i n in i m m nt The S ind rev lut o s dur g th s roller ove e . p les 60

i d to in t twi m n in to the o win in the s m e iod are requ re ser st a ou t g f llo g, a e p r ,

210 x 87 x 57 4 4 1 revolutions of rim per draw 59.

— is the c ion 87 n . 210 e o tion d in w i tim géf fra t of 4per ce t of r v lu s, ur g h ch e the i i n m in no m t T i is ined om car age a d rollers are ov g at the r al ra e . h s ascerta fr the 1 t kin oc edin at w n n m the in ra e of jac g pr e g 3 1 slo er tha the or al rate , jack g rate 1 b eing from to the no m d ndin n ext n c o d o i n 73 4 r al epe g upo the e t of the s r lle p rt o of he d win - out e on f 1n tion t ra g barr ls , the back sha t, ac ,

1 8 4 COTTON SPI NNI NG CALCULATI ONS

The revolutions of back Shaft for 624- inch draw 3 4 60 3 -65 584 535 6

8 A i n c n 100 m do 1 n ea I slands R ve min lterat o s for ou ts fro uble 8 ha k S o , assu g n d ind i the prese t spee of sp le su table . The present speed of Spindl e

800 X 6287 7 revolutions per minute

Twist constant 3 6 per inch 3 6 T ” " ” wi d w 62 ut u t . e 58 3 62 1 3 6 2232 st per ra of p p, . 4 4 X J 00 X

The revolutions of the rim must be such as will give 223 2revolutions of spindle d per raw. A min f 5 r n in t n mi in n ssu g a loss o pe ce t . ra s tt g the motion to the spi dle m rim n e i n the rim er d w o d fro the shaft, the the r volut o s of shaft p ra sh ul be 223 2 X 100 X 1 1 X ? ” 95 6 say

The duty of the twist wheel is to control the revolutions per draw of the rim I n i c e the twi t w e di id d 2 the o i n ofthe rim shaft. th s as s he l v e by equals rev lut o s

2 Q2 i 1 1 § tw st wheel 0

I f there were no gain between the m ovement of the carriage as compared i n n n o m d i d in w th the le gth delivered by the fro t roller, the the r llers ust el ver , ur g tw d run c i 58 inc and e e the ont e m the ou ar of the arr age, 4 hes , ther for fr roll r ust m ake

e i n r volut o s , say

The present gear would deliver 21 x 60 x 15 revolutions of front roller instead of

60 X 303 f d ed w ee 104 w Therefore I the change be ma e at the spe h l , a heel

n would be ecessary . im i U the d i Such a large wheel would probably be pract cable . sually r ver of i i n w in w i c x n the speed wheel s const tuted a cha ge heel , h ch ase the e te t of the n in n i in the d w and i d w d differe ce the cha ge pract cable, spee heel, that requ re , oul i be possible at the dr ver wheel . in 0 i Si d w n Assum g that up to 9 are the ava lable zes of spee heels , the the Speed wheel driver would need to contain

52 teeth AND COSTS OF YARN 1 8 5 — N. B I n c e it wo d nne e twi t w e a . such a as ul be u c ssary to use the s h el , s the fact of the carriage getting out to the head would control the revolutions of the rim cc e , but less a urat ly . — N o Gain The gain wheel and its train controls the ratio in the movement The o m t ne e i d i of the carriage relative to the Spindle . r llers us c ssar ly el ver 584 in and the c i m m mo n . ches , arr age ust ove that a u t Cl he m ovement of the back Shaft in drawing the carriage out 624-inch draw i 4 - s i n at 3 i n . T e e for 58 in ion m m n g ve revolut o s h refor , 4 ch, proport al ove e t 3 > 58 ? 3 ° wil be e i d — 3 56 in t d of 3 8 l r qu re , or , s ea . 6 2 1 S o l d t i c en the on o e m t m e h u h s be the ase, th fr t r ll r us ak revol a

‘ “ “ 1 7 i n w i t t m e o ion th t o s , h ls the back shaf akes r v lut s ; therefore e revolutions of the front roller

— - NOTE Variations in the tension and size of drawing Out bands will cause i i in i n f d w var at ons the revolut o s o the back shaft per ra .

With the present gear the revolutions of the front roller per revolutions

the c see . 192 of ba k shaft, are ( p )

i n f of F.R. X 20 o F R o s . . X X 60

4x 6 4x x 3 0 56 6

X 5 x n f R x revolutio s O F. .

The in w e m t t e e be t ed i ev tion and ga h el us h refor al er to g ve r olu s , therefore

X 45

o 1 8 6 COTTON SPI NNI NG CALCULATI ONS

3 6 45 3 56 x X 6 60 w G. .

6 X 60 1

3 4 W. 6 X 5 G. W 3 6 X 45 G . . X 9

” 6 X 60 1 X 2

88 5 89 or 88 , say

” h n es —The 3 6 in c m in d wi an 885 i Gain C a g ga b oss wheel o b e th , g ves ,

in t o vi i n d i n o 58 5 in . accord g pre ous calculat o s, a el very by fro t r ller of ches in i i m n in in d i d the on o Tak g th s as a bas s, the a ou t, ches, el vere by fr t r ller per i n the S f wi i o e iz e Of in w ee is as revolut o s of back ha t, th var ous th r s s ga h ls , follows

Variations in count Gain w ee h l . re u tin s l g .

— 58 83

1 8 8 COTTON SPI NNI NG CALCULATI ONS

(2) To obtain the right speed Of the carriage and roll ers relative to the ind it wi n n d w sp les, ll be ecessary to cha ge the spee heel . eed Wheel —l f n i S . 90 X 52 d i n and d i n w p co st tute the r ve r ver, cha ge heels , din ind m n wi in i and the spee g of the sp les ea s that t st g takes place qu cker, there m t be m d d i i fore the rollers us a e to el ver qu cker in like proportion. 90 16 7 0 80 d w 12 3 spee heel

The Tate of the production would be the time taken to twist 62 inches of

n win 5 n . in t n mi i n wi ind m in yar , after allo g per ce t for loss ra s ss o , th the sp le ak g 6287 ion min e revolut s per ut .

22 x 32 x 100 x 60 22 418 95 X 6 X 287 The time in seconds taken to backing- off and run in 4 5 Time per draw 269 18

The d c ion in i 4 in t d n i . e e i n Of S nd e to 707 pro u t after cha g g, . r volut o s p l s s ea of 6287 16 Time twi in 199 27 ec st g s s .

Time twisting backing- Off and run in 4 5 Total time 24 427

od ction in n er we 55 in 18 - in rim Pr u ha ks p ek of hours, case of ch

60 X 60 X 55 X 62" hanks per Spindle 24 427 X 3 6 X 840

Production in case of 16- inch rim : when the rate of spindle in revolutions per minute with 18 -inch rim is

1 1 X 28 X 24 >< 18 X 6 _ 7074 and

” 60 X 60 X 55 X 62 production in banks with 16- inch rim on 269 18 X 3 6 X 840 i and spindle revolving 6287

— “ E XE R I SE 2 A m e m in 50 T. has the win n e w C . ul ak g follo g cha g heels W t n in ini n 40 rim 18 in d 80 ui d 50. Draft p o , ; , ches ; spee , ; b l er, ha cha ges these would alter the counts to 3 6“ with (a) The speed of Spindles unaltered ? (5) increased 4?

Ans a'er s

i n on 1 68 is d . Rule g ve p . here use AND COSTS OF YARN 1 8 9

E E RCI SE 3 -A m n inin 1000 ind e and innin d w X . ule co ta g sp l s sp g the ra

in in and 1 100 d w m d in min set Of . ind be g ches , ra s are a e for g a cops F

h w Of c win 2 n . . Ans . 48 8 . t e eight of the set ops , allo g 4per ce t for breakages lbs — i 8 W is n wn m E E The i in m od n 46 . o X RCI SE 4. carr age a ule , pr uc g , k o to ve

- 6 er n w n nt o e in 6 n o e in d. ind p ce t . slo er tha the fro r ll r, s gle ha k r v be g use F

A ns . the draft required in the rollers . E —A m m 5 d w Of 64 4 in e in 68 ond E X RCI SE 5. ule co pletes ra s ch s each sec s “ w n innin 40 T The im i d in in - Off and windin is 4 nd he sp g . t e occup e back g g 4seco s . What will be the calculated and ma ximum actual rate Of revolutions of the ind min i and Of im due to e in is n sp les , assu g the sl ppage loss t e , r vers g, k own

25 n T the i nd d Am i n c t n. to be per ce t . ake t w s t sta ar for er ca ot o

A ns wer .

68 (5 X 44) 4645 Time per draw 5 5 seconds

nd i n Of ind d w Twist a actual revolut o s sp le per ra 3 7 54/40X 68 1 612

C d i n Of S ind d w 40 X 68 3 09 alculate revolut o s the p le per ra J X 7 5 2150

m xim m f u Actual a u rate o revol tions of spindle 4/40 X 68 X 60 10620 per minute

Calculated rate Of revolutions of spindle per 10620 X 100 13720 minute 7 5

EXE RCI SE 6 —W t wo d od ti n in banks and o n . ha ul be the pr uc o p u ds, per week Of 55 ind and m 1200 S ind w n 4 hours , per sp le, per ule of p les, he the following allowances are made : 8 minutes per doff ; 94 hours for cleaning ; 24 per i ent . co w in th 1 c for other stoppages , the ps e gh g at e rate of 0per pound R e u ir ed : wi in min ime d w and th q the t st per ch us t per ra , e production in n s and nc S ind 55 o in m m in ha k ou es per p le, per 4h urs, a ule ak g cops that weigh 1 0 nd and wo kin nd win ondi i n : im w d per pou , r g u er the follo g c t o s Nett t e orke , 53 w 2 n for dofﬁn 8 min hours ; allo 4 per ce t . for breakages ; g, utes per doff n 1 2 ” W m m d i E i n 0 . e n wi n t n cou ts, fro co b spec al gypt a cotto , (t st co s a t, S ind w in t wo e Of eed—ﬁrs t 5880 and e ond 9000 p les ork g at rat s sp , , s c , revolutions

- min . i ei the wi t on is in at d Th - per ute F ve ghths of t s ly put ﬁrst Spee . e backing Off and run in occ i 5 econd and the en of the d w is 58 3 in e up es 4 s s, l gth ra 4 4 ch s .

Ans wer

Twist per inch 3 ° 18 J 1 20

Twist per draw X 62 2160

2160 x 5 x 60 2160 x 3 x 60 Time per draw in seconds

13 8 5 4 54 24 7

2 x 840 X 3 6 D w er doll 1 X 2 _ ra s p 10 1 90 COTTON SPI NNI NG CALCULATI ONS

Tim doﬁ in din 1 4 e per , clu g do tting 120 X 8 0 X 3 6 X 8 hrs in minutes 10 62 60 X 60 60 402 0133 £3 l 53 X 60 X 7120 Doﬁ per week

l ﬁ W i er w in o nc : 1 22 X = 1 95 e ght p eek u es 1 0 1 95 120 Hanks per week x 16 1

Do son D u S d and H s ni n Mo ion — 5 b o ble pee a te g t Fig. 3 shows the ’ arrangement in Dobson and Barlow s ﬁne mules for driving the i d sp n les at two speeds . A and B are drums of different size on the line shaft ; the s e are connected to the counter shaft by belts under control of

M o t i o n S h aft

FI G. 35.

d . The r od i forks attache to the same bar stop , operat ng the is d i i straps , notche to occupy the three pos t ons as follows 1 i d 2 d B d i i ( ) Mach ne stoppe ; ( ) ﬁrst spee , strap r v ng ; 3 d d A d i i ( ) secon spee , strap r v ng . This r od is operated in its second and third movements by d and i i Th d the movement outwar nward of the carr age . e spee may be changed from the second to the third at any point in the

d i d . outwar run of the carr age , by a justments

1 92 COTTON SPI NNI NG CALCULATI ONS

m nd a 4 that motion . (60 40) a ( 0 3 4) are compound wheels S i d NX and d i M and A loose on the p n le , they are r ven from on M is the front roller . loose i d on the front roller sp n le ,

Ba c S h a k ft whilst A is fastened to it . Movement of NX is therefore Gain Wh ee l n Bo s s w h ee l i d A nd obta ne from a M, one half being expende d in turning i 2 the wheels w th 7 teeth , upon i x and i the r a es , caus ng them T to roll upon the two 3 4 . hus one - half of any motion con tributed to a or m passes to In cal cu the T arms of NX. f i is lat ng , the formula F. R. C l ut ch

FI G. 37 .

T i d and i 1 00 hus , w th the front roller clutch close mak ng i i d be revolut ons per m nute , the rate of the back shaft woul

1 00t1 1 00t2 45 X 8 6 100 X 1 1 00 X 4 = 1 X 3 2 2 ( 90 x so) 3 20 . i (66%)T6 revs per m nute

I f d the front roller clutch was Opened, then the rate woul

5 revolutions per minute

The rate of the carriage during the j acking is thus one -fourth and in ddi ti i ti the normal , a on that due to the s ze of the por on n of the back shaft scroll i action . AND COSTS OF YARN 1 93

To ﬁnd the revolutions of the front roller when the r evol u tions of the back shaft are 34 per draw of 624- inch draw

Let a: revolutions of front roller . Then

493 1 9 x 1 0 1 90 x 6

’ 6 5 x 3

6 7— 1 u i 4 9 revol t ons of front roller

I n d i i i i is mules not arrange w th th s mot on , the ga n wheel d i r ven by a wheel on the front roller . ’ I n Trelfall s Jackin Mo ion Fi i nd t g t ( g. the r ght a lef clutch 1 3 0 i wheels , teeth , are loose upon the shaft ; the central port on

Back S haft

7 0 S e d c h a nge 53 p e w h e e l

Ro l le r' m o t io n ‘f C Iut c h

Fr o n t r o lle r

FI G. 3 8 . is d S d connecte to the haft upon a feathere key or the equivalent . The clutch is now shown with the carriage driven at the normal Th rate . e movement of the clutch towards the back shaft to 1 3 0 i engage the other part of th s clutch , would set the back shaft i mov ng at the slowest rate , namely 7 0 normal rate 50 X 1 80 2 T3 the normal 6 5 COTTON SPINNI NG CALCULATI ONS — 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 non positive gearing . The i i 23 5 and revolut ons per minute of the l ne shaft was , the 5 i rim nd S i d i connect on to the shaft a p n les , respect vely , 44 X 43, 1 3 3:f The t i me taken to draw the carri age out to a head 8 I l a was gsecs .

Rim shaft Tin roller Spindle n i I n d i i n from z Perce tago e of sl ppage r v g The rim to spindles

Th rim tin 1 . e to rolle . The tin I oll er to the spindles

The in i d is i i and r e r e loss shown the th r column nclus ve , p x i diff sents the e tent wh ch the actual ers from the calculated. D du ions — The in i i and e ct allowance calculat ng the t me taken , d d i i i d t 25 the spee , ur ng tw st ng , shoul be abou per cent . when the conditions are normal . i d i i 5 I n 3 . d arrang ng the r v ng gear , from to per cent shoul d i The i be allowed for each band r ve . losses not ced in belt — drives when the conditions are good ti e. rational sizes of drums id and i — and w ths of pulleys , when not revers ng are only very

i and d i . sl ght, nee scarcely be taken nto account I n i d i cases of very h gh spee s the losses w ll be greater . Con siderabl e variation existed in the loss recorded at different i d due diff in i sp n les , most probably to erences the r resistance i i d and in the tens on of the r ban s . The slippage in the gear bet ween the rim and line shaft is i Th only sl ght when the best systems are adopted. e chief loss i is that due to revers ng. x in d i i l Further e amples of loss r v ng mules fol ow .

P i u s in to the D i in of the P s in Fi art c lar relat g r v g art g. 3 5, ’ Dob son and B ow s Mu for Fin Numb s arl le e er .

1 96 COTTON SPI NNI NG CALCULATI ONS

The rates of rotation per minute of Spindles

4060 d 3 ﬁrst spee 20 >< 1 6 x l 0 X 2;

7 21 9 second speed 20 x 1 6 x 1 0 X 2~ 9 >< 1 6 X 6 high speed during the actio n of the hasten ing motion 23 5 x 1 8 >< 1 2 x 9 X 1 6 >< 6 974 6 low Speed di tto . 1 x 20 x 20 x 1 5 x 1 0 X 4

— 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 ) 22 5 per cent (2) 23 5 per cent ; 3 4 ( ) per cent . ( ) per cent . F i i d 2 n 2 urther , the tw st wheel conta ne 7 teeth , a d moved revolutions per draw ; during twisting the movement was 1 40 and i i d in d teeth , the revolut ons of the sp n le , the correspon in i d 1 454 . T i 1 8 g per o , h s shows a loss of 8 per cent . , the calculated speed being as follows

1 40 1 6 6 x x _ 1 0 x 2

i S i d or 3 3 8 revolut ons of the p n les more than the actual . The time occupied in making this movement was 124 seconds d and 8 d d d in i d at ﬁrst spee , 4 secon s at secon spee , these per o s i i d i i 2 the actual revolut ons of the sp n les be ng, respect vely, 67

and 7 82.

T S d i i hese pee s represent , respect vely, the follow ng average rates per minute

3 1 n 5 20 50, a d 5

i ri di d The loss of t me by the m shaft, as in cate by the above d is spee s , therefore as follows AND COSTS OF YARN 1 97

rim S in 8 . d d 8 00 Calculated revs . of haft 4 secs at secon spee 1 24 ﬁrst 67 5

T 140 i i i 14 i hus , revolut ons requ re the t me of 7 5 , or t me lost rim by the shaft p er cent .

i it is 1 8 . From th s seen that per cent . of the 8 per cent is rim and d i i i between the the r v ng Shafts , the major port on , 1 3 . i n i . per cent , be ng between the spindl es a d r m shaft — Twi st per I nch The length wound per draw was as follows

Distance moved by the carriage each draw

L - l F.R. d r i ength de . by uring the run in of the ca r age

The approximate length wound 64 0

; 4 4 : 1} A i i s 22 7 ctual tw st per nch a 2 : : 1 i - C d i i h 28 alculate tw st per nch C 2

The 608 i actual count spun was , so that the actual tw st

- co efﬁcient as against calculated.

The front roller made the following movements each draw

F R . 1 D i . ( ) ur ng the engagement of the clutch , 1 64revolutions

(2) During the jacking and twisting at the head i i act ons , 4 revolut on 3 D i i d i ( ) ur ng the nwar run of the carr age , 1 revolution

Total length delivered per complete draw 600 Length wound per draw 64

he i d is T total stretch ng of the yarn per raw , therefore ,

60 4 i . Of i i d d i 64 nches th s , the amounts obta ne ur ng the above -named periods are 1 9 8 COTTON SPI NNI NG CALCULATI ONS

( 1) the movement of the carriage being 56 = 56 546 2 3 ” 3 ” 1 2 5 ( ) 4 4 ,

3 9 Length not accounted for

The actual revolutions of the rim shaft after the disengage i nd i i i . i a F . R. e. d ment of the clutch , ur ng jack ng tw st ng at the d i d d 3 . T i d hea , were 7 herefore the length wh ch shoul be el vere

F . R . d i i i d i by the ur ng th s per o , by reason of the act on of the

i i is slow roller turn ng mot on ,

1 I nches 58 X 40 X 3 0 X 24 X 7

The actual length obser ved was 1 inch . The difference was d d due in i un oubte ly to the backlash the mot on .

OTE —The di f nc n d in and d ind N . f ere e ote the actual calculate rates of the sp le emphasize the importance of not relying on the calculated revolutions of the Spindle unless due allowances have been made for slippage in the belt and band d i in The m is w n n in the r v g gears . use of a tacho eter very helpful he arra g g

in . The i i en w in d cc and ex edi i gear g part culars g v ere ascerta e , a urately p t ously, aid in m n by the of that stru e t.

SPE E D I NDI CATOR S.

Loss s in T nsmission of Mo ion and how As in e the ra t , certa ed. The most convenient mode of ascertaining the e xtent of losses arising in the transmission of motion is by the aid of a sel f im - is in m d t e reg ter g tacho eter . The or inary tachometer is defective in i i nd that the attachments for connect ons are mperfect , a in addition the timing has to be done either by a second person or the attentions of the operator divided between the timepiece nd a the tachometer. I n either case the work is not altogether i sat sfactory .

The i i Fi . 3 9 is n i llustrat on ( g ) of a tachometer , a d su table n I t n i attachments for spi ning m achinery . co s sts of a recording

200 COTTON SPI NNI N G CALCULATI ONS

commences upon pressure being applied to the recording S i d 2 di m 60 d p n le , the centre ﬁnger recor ng fro 4 to secon s ,

and the lower finger the minutes . The lower projecting milled i i and S i head is for sett ng back the m nutes finger , the l ght projection on the left hand is the fiy- back release for the

The i - d d i di seconds . large r ght han eal ﬁnger n cates the v i u 1 00 and i re olut ons p to , the small one on the nner left d d i i i d the hun re s , wh lst that on the nner r ght recor s the d The i d id Of i di thousan s . project on on the un ers e the r ght al

is - i - d d the fly back release for the un t tens ﬁnger, the hun re s and thousands ﬁngers being reset by means of milled heads at

the back . d d d i d F , H, are rubber cuppe etachable en s for the sp n le of

the tachometer. and i d d E , that on the left of centre are rubber p vote etach d able en s for the spindle of the tachometer . That on the right of centre is a pyramidal recessed end for

the Spindle of the tachometer . K id d in n i i d J , are pyram al en s for ﬁtt g to mule a d r ng sp n les for use in connection with those found on the left and right of

centre . T i i i d d I n h s nstrument s hel by the etachable handle D . its is h it d in d and use great feature t at can be hel one han , with this exception the whole of the attentions of the operator i i Th are ava lable for other work throughout the observat ons . e di d i als recor the results , the range of speed be ng up to i revolut ons per minute .

LE GT A D ANK I NDI CATO N H N H RS.

Fi 40 g. shows the gearing in an indicator for registering the d in The number of raws mules . segmental wheel is driven by a worm placed upon the back Shaft of the mule (drawing- out — . The b b d a shaft) sector lever , l , secure to , operates the star

0 3 - d d is n wheel to the latter a trea e worm secured, a d this d i d i d d — d i di i r ves the worm wheel on the sp n le l g . F ve al d scs are d i S i d and d i d mounte on th s p n le , these recor un ts , tens , hundre s , d and d i thousan s , tens of thousan s respect vely . Each of these AND COSTS OF YARN 201

d in i 1 d i i 4 are connecte , sequence , by a tra n r v ng a , th e latter i d d i 8 i d i 20 d be ng compoun e w th an , wh ch r ves the secure to the — x di . The di is ed 61 61 and ne t al ﬁrst al secur to 1 2, the rest are i free upon it. Thus this nstrument records from 0 to 99999

FI 40 G. .

d i d d in i i raws , the object be ng to recor the work one a g ven t me i i i and for est mat ng the earn ngs for other purposes .

Th d i x e s i . T recor e act , as shown by calculat on hus

20 X 4 X 20 X 4 X 20 X 4 X 20 X 4 X 10 X 3 — h nkS I OO’OOO a

d d di its i 00000 99999 and recor e on the als by mov ng from to ,

- 00000 i d di . then , or one complete revolut on of the left han al

41 i in i di d in Fig. shows the gear ng a hank n cator as use i n d d d i mules . These nstruments are arra ge to recor the pro uct on i d in i and of the whole of the sp n les the mach ne , hence the gear is varied to adapt them for the different numbers of spindles i n I n which the mules conta n a d the length of the draw. the ﬁgure the particulars are of one designed for a mule containing 202 COTTON SPI NNI NG CALCULATI ONS

1 8 4 S i d and i d 58 i p n les only , mak ng a raw of 4 nches . I t records 0 from up to hanks , the customary allowance for los s i 2 through breakages be ng 4 per cent . The action in this case is as follows

a al (12 a3 (14 d i is d , , , , are attache , th s part actuate by a worm , d x S . a a , place upon the back haft By that means , l , a2, i d and osc llate , each raw, the sector lever a3a4 moves the star

I) . b is d d i c wheel one tooth compoun e w th , 3 0 this latter

FI G. 41 .

d i cl 1 5. ( l is d d i e i r ves , the compoun e w th the worm wh ch d i f is d d i i and r ves j compoun e w th the s ngle worm g, the

d i h. The i 75 is d x h latter r ves lever , , fastene upon the a le of , and i is A x i th s loose on the central spindle . t the e trem ty of i is 21 d d and its th s lever the wheel , mounte free on a stu , teeth 79 and MO i It i d engage two wheels , 3 9 respect vely , be ng secure

and . I i is d revolu cannot rotate , be ng free , move one tooth per i i 5 Th i d x k is its . e t on of the lever , , upon centre n e ﬁnger 1

204 COTTON SPI NNI NG CALCULATI ONS

R OD I E S P U CT ONS I N MUL .

Production in Produ ctio n in Production in Production in hanks p er s pindle hanks per Spi ndle hanks per s pindl e hanks p er spi ndle Count er 55 h u s nt h r s er 55 hours . p 4 o r per 55 hours Cou p er 554 ou p l sn inc usive. inc us ive i nc usive . inc u e. l l . l

6 1’—80

—20

1 6—19 7

1 55—19 3

1 8—21 9

The Rin F me — 42 n 4 g ra Figs . a d 3 represent the gearing i i common n r ng frames . A The back roller and its wheel for driving that on the i d m d le roller . B The carrier wheel connecting the back and the middle rollers . C The u idd wheel pon the m le roller . D The d raft change wheel on the back roller . E The d raft change pinion driving the back roller wheel . F The crown wheel compounded with the draft change i i and in i p n on gear g w th the front roller wheel . G The d i i wheel on the front roller for r v ng the above gear . H The wheel on the front roller gearing with the train

I and K. , J , AND COSTS OF YARN 205

K The twist change wheel . T i d and MN i i L he tw st stu wheel , the connect ng tra n from the tin roller shaft .

: h in i is d N T e t roller Shaft wheel , th s change when an extension in the range of the twist is desired beyond that procurable by altering the twist wheel . P The tin d i i i d d P , I rollers r v ng the sp n le ban s . The i d Q The spindle wharve . Sp n les are arranged in he d i di d rows on either Side . T ban n cate by the dotted lines Shows the driving when double tin rollers are use d for one id s e only . i Fig. 43 shows the driv ng of the cam W for reciprocating

FI G. 43 . FI G. 42.

i i is d i i the ring rail , the rate at wh ch th s r ven controls the p tch of the coils contained by the bobbin .

i i W i I . W S, T, U, V, are the tra n of wheels connect ng w th produces the reciprocation of the ring rail through the medium i d and i i . The of a series of levers, ro s cha n connect ons relat ve positions of their movement is advanced through the agency n i d of a ratchet wheel a d a pawl , the ratchet wheel be ng terme the builder wheel . The number of teeth in the builder wheel and the value of i T U V and its driving tra n , S, , , , control the length , therefore 206 COTTON SPI NNI NG CALCULATI ONS

i the weight of yarn placed upon the bobb ns . When the rate i i is i f i and of rec procat on nsu ﬁc ent , other means have been

x d d i is d i d i e hauste , the spee of th s part change by ntro uc ng a

i d T. The s ngle , ouble , or a treble worm at movement of the pawl operating the ratchet is adjustable to the e xtent of the

varying sizes of the teeth in the builder wheels applicable . D d i i l i , E , F , G , are the gear for r v ng the ro lers on the r ght

d Sid and d i id . han e , these are a upl cate of those on the left s e is d i i d i R , the r v ng pulley connecte by belt or rope w th the i l ne shaft .

' The speeds of the Spindles in these machines usually range

i . The i from 6000 to per m nute , actual usual s zes of 1 i and i i rollers are from 4 to 4 nch for the front back pos t ons , and 4 less for the middle roller ; 4 inch is used for short and

- 14 inch for long stapled cottons .

The i d i for i is 4 u recogn ze tw st r ng yarns ( /co nt per inch . T i is i id d d x i i d h s not r g ly a here to , e cept ons be ng ma e when it secures better spinning and the amount of the twist has not i been st pulated. — The Speeds of Spindles The circumstances that govern the best speeds of the Spindles are quality and count of the roving i x and yarn condition of the mach ne e pertness of the workers . di i d Under the most favourable con t ons , a spee of revo i d i 3 — 3 lutions actual may be atta ne w th counts 3 0 3 6 . For other d di i i i counts , un er the best con t ons , the follow ng revolut ons per minute of spindle are given as a guide For counts below 3 08 intended count 30 For counts above 3 65

10000V/3 6

x/intended count When the conditions are identical but not satisfactory for above For counts below 3 68 known satisfactory speed X “ I ntended count

x/count

208 COTTON SPI NNI NG CALCULATI ONS roller wheel is 25 and the fr ont roller is inch in diameter

Size of t wist wheel 25 26 27 28 29 30 3 5 Twi in 63 7 612 590 68 st per ch . 5

Size of twist wheel 46 47 48 49 50 T i in 3 3 9 3 32 3 25 3 18 w st per ch .

The above are ascertained in the following manner Revolutions of spindle per inch delivered by the front roller 8 0 1 20 1 0H 1 X X X " "

T . T. R. . x . W W 8 8

nd in and 50 wi a hence with a 25 t roller wheel , a t st wheel , the revolutions of the spindle per inch delivered by the front roller

so mo o _ x x l >< 25 59 8 — These results may also be ascertained as follows z Assuming tin 25 and i i d that the roller wheel was , the tw st wheel conta ne

i i d 63 7 25. T i only one tooth , the tw st per nch woul be X ( h s is called the twist change wheel constant number for a 25 tin

and i in di . roller wheel , the front roller 4 nch ameter ) 63 7 X 25 the twist per inch when a 26 Wheel is used 26

T . . W constant the twist per inch intended wheel

W. T. constant required wheel twist per inch

W i i in i i is d hen the l m t the range of s zes of tw st wheels reache , they may be rendered again available by altering the size Of tin in i i the roller wheel , the proport on wh ch the range of

. The i i in i is d wheels represent l m t the present nstance reache , i 25 tin i is 50 i w th a roller wheel , when the tw st wheel , the t w st in is 1 8 i the yarn 3 per nch . By adopting the Size of tin i 25 i i d roller wheel that , together w th a tw st wheel, w ll pro uce 3 1 8 i i i i i tw sts per nch , the range of tw st wheels are aga n ava l T able . hus AND COSTS OF YARN 209

63 7 X 25 the tin roller change wheel constant number for a twist change wheel of 25 teeth 63 7 X 25 the required tin roller wheel 50 3 1 8

and i 50 tin and i , therefore , w th a roller wheel , w th the d i i i i state range of tw st wheels , the follow ng tw sts w ll be Obtained

Size of twist wheel 25 26 27 30 3 4 3 5 26 5 Twi in 18 306 29 4 . . . 229 st per ch . 3 . Size of twist wheel 46 47 48 49 50 in h 17 3 169 1 65 162 159 Twist per c .

Twist change wheels are usually drivers in the train to the n i i i i i front rollers , a d therefore ncreas ng the r s ze ncreases the i d i in di i n length of yarn subm tte for tw st rect proport on , a d hence the twist is reduced inversely. To h n the Coun s — T i is d in c a ge t . h s one the same way as in the previous machines a ( ) By altering that of the feed. i (6) By altering the e xtent of the attenuat on or draft . The results are directly proportional to alterations in either T case . hus wei ht uni d the g of the fee i i d i ’ the we ght un t of the el very , d1 itt a and vi ce ver sct

of d d d i and vice the count the fee X the raft that of the el very , ver sd

The d is d i d in . A i raft also eterm ne the same manner ssum ng, d i and d i d the smallest r ver, the largest r ven , of the raft change d and and i in i wheels are use , the back front rollers al ke s ze , then 1 05 the draft 48 X 4 4 10

i 60 i i Hence , w th the back roller wheel , the range of p n ons , i d d i d appl cable , woul pro uce the follow ng rafts

Draft pinion 30 3 1 32 3 3 34 3 5 Draft 9 1

Draft pinion 56 57 58 59 60 Draft 21 0 COTTON SPI NNI NG CALCULATI ONS

I t is thus seen that the fractional change in the draft d i ti in and correspon s w th the frac onal change the wheel , hence d d large wheels comman a finer a justment of the count , and for this reason the u se of small change wheels should be i avoided as far as pract cable . i i i i d is i Whenever the s ze of p n on requ re not ava lable , alter in i i the back roller wheel the nverse proport on , or change in its Si x i the back roller wh eel , alter g ze to the e tent that w ll i i i The i enable the use of the ava lable wheels , as p n ons . follow ng is then the procedure R back . W. R i i i and and at o of p n on back roller wheels , any pinion two wheels which give a near enough ratio will be satisfactory . Always remember that the back roller wheel has the inverse i i m f i d in di effect to the p n on , the for er a fect ng the raft the rect ratio and the latter inversely . — The Bu d W l . I n i il er hee (Ratchet) chang ng the count , the is ff d in i i if weight of the yarn a ecte the nverse proport on , so that i i d i i the bobb ns are requ re to conta n the same we ght , then the d in di i ratchet wheel must be change rect proport on to the count . This is not always admissible in practice on account of the i i d i bobb ns be ng fille too full for the r ngs , through the yarn not f i h n i being wound su fic ently compact . T e rule i calculat ng the builder wheel is Builder wheel X count required wheel suitable count Spun When the size of the empty bobbins are changed or a diff i u i is i d S d erent s ze of f ll bobb n requ re , the wheel houl be altered in direct proportion to the area of the cross - section i d of the yarn conta ne on the full bobbin . The relative area of a cross - section of the yarn (diameter of full bobbin diameter of empty bobbin)? th e wheel X area of section of yarn on bobbin required area of section of yarn on present bobbin

W i i f i d and hen the bobb ns are nsu ﬁc ently har , the traveller is i i S di i the heav est pract cable , pee ng up the traverse of the r ng i i T U i ra l by the most conven ent of the wheels S, , , V, w ll have i ff a beneﬁc al e ect .

21 2 COTTON SPI NNI NG CALCULATI ONS

KI NG F TH E E XE RCI SE S ON AGE 21 1 EXAMPLE S I N TH E WOR O P . 3 2 1 EXE R I 1 —The d 9 5 n the C SE . X raft 44 4 1 ; the cou t of rove ; 222112 7 95 ' ' ° n th tw1 st m m e 4 cou nt tWI St whccl ’ the ha ks pro e p h J , 4 ¢count i i n F R . 10 X F . R . revolut o s of . per hours c rcle of duced I nches per hank

I E — The d 8 ini n 93 is n in d in i EXE R C S 2. raft g the p o wheel ( ) co ta e th s 1 05 i n Q wi w as in win X 8 ; , or, as the follo g equat o 7 1 the t st heel 322 £ 20 19 3 6 40 ti n 29 1 X — 25 3 i d w equa o , X ; the bu l er heel 50 7 3 25 4

— Losses in driving the Spindles in Ring Frames The following are instances of the observed and calculated speeds of the S i d i i i i p n les , together w th the losses ar s ng from sl ppage i i tin i R ng frame w th two rollers , one of these be ng ﬁxed to i nd d i i d the mach ne shaft , a the other r ven by the Sp n le bands .

Driver T. E . s ide. Driven T. R . side . A i n T E 565 55 ctual revolut o s of . . 5 Actual revolutions of spindle 6250 5824 Calculated revolutions of spindle 6460 63 42 Perce ntage of loss 8 1

The following were recorded after r ebanding the spindles on d i tin id d i d i the r ven roller s e, these ban s be ng r ven by the driver tin roller

i A n T R. ctual revolut o s of . Actual revolutions of spindle Calculated revolutions of spindle Percentage of loss

The following were recorded in a frame having' the rollers connected by an endless rope drive

Driver side. i n T E . 658 Actual revolut o s of . Actual revolutions of spindle 7 184 Calculated revolutions of spindle 7 500 Percentage of loss 42

The d i in i id pro uct ons r ng frames vary cons erably, depending AND COSTS OF YARN 21 3

S d i d i in 1 t t upon the pee of sp n les , tw st per ch , s reng h of the yarn , i sk ll of the operatives and their management. The spindles are run at rates as high as revolutions i i i x i i and ti per m nute , th s be ng e cept onally h gh , only prac cable d d un er the most favourable con itions . The production ranges i 96 d as h gh as per cent . of the calculated when base upon the S i d actual p n le speed. 3 The highest speeds are only practicable with about 8 6 408 d i to counts un er normal cond tions .

ROD CTI N S I N I NG SPI NNI N G P U O R .

Cou nt . Count . er p 555hours .

— Productions in Ring Spinning I n spinning yarns from single i i i d t i i i d rov ng , w th a h gh raf , or from an nfer or or rregular staple n x di w S d or soft cotton , or i e posed buil ngs , lo er pee s are

necessary . The ring spinning machine cannot be as proﬁtably em ployed in the production of yarns other than the best descrip i in i i d d in t ons , when compet tion w th those pro uce the mule i i i sp nn ng mach ne . Ring frames require better cotton and ﬁner roving for the di i i d in or nary classes of yarn . They are pr nc pally employe , i in d i i th s country, the pro uct on of the follow ng 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 u i s bsequent requ rements . I n i i d d all these , th s mach ne can pro uce to greater a vantage i i i when the counts are w th n a certa n range .

1 See ff wis in in n . 215. e ects of t ts s gle yar s, p 2] 4 COTTON SPI NNI NG CALCULATI ONS

TWI ST STANDARD S FOR SI NGLE YARNS.

The object in applying twist in spinning yarn is to secure a d ﬁ and e i common bon amongst the bres , thereby create a c rta n i i n Th i tens le res sta ce to tension . e purposes for wh ch the yarn is required will therefore control the e xtent of the twist applied. The ordinary standards in use are as follows Mu ns le Yar . Turns per inch i n Egyptian weft American weft Egyptian medium American medium Egyptian twist American twist

Rin a ns g Y r . Soft weft count X 3 2 5

Medium weft \/count X Soft twist count X count X 4 0 Ordinary twist

\/count X 42 5 Water twist

x/count X 4 5 H ard twist i \/cou nt X 47 5 E xtra hard tw st

l \/count X Crepe

The d i above twists are not rigidly adhere to . Sl ght modi ﬁcations i i are made in them by the sp nner , such as c rcumstances connected with the operation of spinning render expedient . A d ﬁ i di knowle ge of the e ects of tw st , apart from the or nary

d d is i in i i . stan ar s , most essent al sp nn ng The inﬂuence wielded by twist varies with the character of n I i i the cotto . t is greater in those ﬁbres wh ch are long , un form I n The i nd i in x u and d. the r length , a s lky te t re , well prepare d i i d i i Sha e of the yarn is always darkened w th ncrease appl cat on ,

nd i . d id d i is a the touch s also hardened A ec e curl , or shr nk, d d i d is in also thereby evelope . Th s latter ten ency greatest yarn which is irregular in diameter or m ade from harsh cotton .

21 6 COTTON SPI NNI NG CALCULATI ONS

in i di i d us ng the or nary strength testers , w th those har est i i i d and O d . tw ste , the results bta ne were unrel able U i i d i i lt mately, the tests were accompl she , sat sfactor ly, by

using the Mos cr op patent single thread tester made by Messrs . h in C h . T e d ook of Manc ester whole of the tests , ma e use of i i di x d i . plott ng th s agram , were e ecute on the same mach ne The diagram gives the strength developed in terms of i i i and in s an ncreas ng tw st constant , also trength per turn of i T . he u and indi tw st pper curve shows the former , cates the i i i add and po nt at wh ch tw st ceases to to the strength , the lower curve shows that obtaining the greatest value in strength

per turn of twist inserted. The i d and i i nferences rawn from these tests , from nspect on Of the / yarn , are (a) That in the best yarns the strength contributed per turn wi of t st becomes gradually less at \/count X 8 . (b) That in the best yarns the strength ceases to increase i d w th the a ded 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

and after 5\/count it becomes very appreciably darkened. ( e) A coincidence was that the twist constant realizing the i greatest strength per turn of tw st was count . That adopted by the trade generally in spinning weft from Egyptian cotton is count .

Twis S nda ds for Fo ded n — Th t ta r l Yar . e following are the twist c onstants used in doubling Twofolds XXXX Soft XXX XX X AND COSTS OF YARN 21 7

Lisle Double spun Hard

SE WI NGS CONSTANT OR CO

- Si n e arn Twofold. SI X cord. gl y .

As l ow as possible

CROCH ET .

- Sin e arn. w Six cord. gl y T ofold.

Weft to twis t turns

YARN S FOR FI SH N ETTI NG .

- Sin e arn . Two o d . Si x cord gl y f l .

Common

x 6 5

KNI TTI NG YARNS AND E MB ROIDE RY AND FOR M E RCE RI ! I NG.

Sin es gl .

A s l ow as practicable x 3 0 to 3 2 5 21 8 COTTON SPI NNI NG CALCULATI ONS

TH E I NFLUE NCE OF DI RE CTI ON OF TWI ST I N FOLDE D YARN .

The di Fi 45 i di i agram ( g. ) Shows the nﬂuence of the rect on i i T i of tw st upon the strength n the twofold yarn . h s ﬁgure was plotted from the breaking Strains of two series of twofold

i i d r i d yarns , one set be ng tw ste eversely and the other tw ste in di i i The the same rect on as that contained in the s ngles .

TWO - FO LD TWIST C O NSTANTS

FI G. 45.

d d i nd i single yarns use were of very goo qual ty a all al ke , con d i x i . The taining tw st to the e tent of count , per nch twofol

i i d 2° 5 t TE ? tw sts , per nch , range from \/coun to ( twisted in the same direction as the single were harder to the and d in d and i i d i i touch arker sha e , w th the ncrease tw st , the r

i i i i i d x . elast c ty , to tens le res stance , ncrease to an abnormal e tent Yarns for elastic fabrics and in preparing for sewing threads i i in i T i d in have the r tw st th s direction . hose tw ste the reverse direction exhibited no abnormal features ; a slightly darkening d shade was noticeable especial ly in those fullest twiste .

The I nﬂn f V in D s f Sin and Fo din Twi s . ue ce o ary g egree o gle l g t

46 r d i i Fig . was p epare from the break ng stra ns of yarns con

i i x d i and d ta n ng a graduated e tent of twofol tw st , ma e from

220 COTTON SPI NNI NG CALCULATI ONS

i d in Si in i is d that conta ne the ngles , that the s ngles supplemente

x d i i . T d to the e tent of the oubl ng tw st hus , the former proce ure i in i i i r e removes the tw st the s ngles , the ﬁbres be ng s mply

d in d i - arrange convolutely , or what may be terme a sp ro corrugate d i or er . When tens on is applied to bodies of fibres so arranged d d m and i d they are presse towar s a com on centre , th s force bon s i idi . them , prevent ng the fibres from sl ng I t is i in i th s change the arrangement of the fibres , w thout i i i is i necessar ly chang ng the r compactness , that respons ble for the greatly increased strength of doubled yarn as compared i i i w th that of s ngle yarn of a similar we ght . The conditions that would have to obtain in order to utilize to the fullest extent the available strength of the body of fibres i d in d d conta ne a ouble yarn , are T d and in i hat all fibres be equally outstretche al gnment, so that they mutually share the tension applied. That they are bonded sufficiently to prevent their slippage upon each other i di i i and devoid of n v dual tw st . T i in i is d di h s latter state , so far as tw st concerne , can rea ly i I is in i d be obta ned. t the lay ng of the fibres equally outstretche

dif i i i i . that ficulty ar ses , that state be ng only part ally poss ble The i i d format on of the fibres about a common centre , tw ste , d i i ren ers the r alignment imposs ble . 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 i d i d and d ( ) obta n the es re compactness , lustre , free om i d d in i from ooze , w th the fibres bon e the most su table manner for the required Size of thread. (3 ) To insure definite elastic properties in the yarn when under tension .

4 To i d i d ( ) obta n the es re character of surface , such as

i d i i w e ff . cyl n r cal , sp ral , corkscre , pearly , cr pe , or other e ects I n d and i or er to secure the utmost strength , at the same t me xi i in i prevent a al movement , the tw sts the success ve stages should be arranged so that they balance in the completed yarn . AND COSTS OF YARN 221

Comp actness is the result of tension and compression applied I n d O i d during doubling . or er to bta n the smallest threa from x in i and i d a number of others , as , for e ample , sew ngs k n red i d is ff i yarns , the follow ng proce ure most e ect ve I n doubling the singles the ﬁbres Should be compressed to i i i in di i i and their lim t , by tw st ng the same rect on as the s ngles , to the extent necessary to obtain a balanced state when the ﬁnal

d. T wi is twisting is complete hus , when the final t st great , that d I n in the folded singles must also correspon . the substitution of the preparing by the final twist the conseq uent extending d i d d and expanding ten enc es are fully absorbe , or counteracte by their greater radius about a common centre . Lustr e is affected by the angle which the fibres make I t is with the completed thread. greatest when they are in

i xi i di id i and vice vers é line w th the a s of the n v ual s ngles , . i di x wi in i Thus , lustre n cates the e tent of the t st the s ngles and in the ﬁbres . — Fr eedom fr om Gaz a This is in the main the result of the rolling action of the yarns against each other in the course of twisting . he Tendenc to tr etch d i is T y S , un er tens on , regulated by the i d i d in angle of the s ngles or stran s compr se the ﬁnal thread. i i The more numerous these are the less the r stretch ng tendency . T i i d d d hus , h ghly elast c ouble yarns are compose of the fewest The d Singles and strands . number of stran s that can be satis factoril d in i i i d and y boun th s way are l m te , hence they seldom i i exceed four . Above th s number the s ngles or strands have

f i d and i i is d . insu ﬁc ent a herence , hence pla t ng resorte to Cylindr icity is developed most effectively when the Singles i i d and i are only sl ghtly tw ste of the best qual ty . P ear ly Ef ects are developed by employing highly twisted singles . Cr e e i i in di i i p by tw st ng the same rect on as the s ngles , also by inserting considerable twist in the reverse direction to in i ff is in that the s ngles but the e ect not the same both cases .

S ir al E ects in d i di i p f are obta e by sl ght fol ng tw st . i d ﬂs i W e ect d here a small yarn w th har are requ re , highly i d i ff i tw ste s ngles are necessary . For soft e ects sim lar to those 222 COTTON SPI NNI NG CALCULATI ONS

i d in i i i d requ re yarns for mercer z ng , the s ngles shoul be softly i d tw ste . Cor ks cr ew Ej ects are obtained by doubling

( a) Yarns in unequal tension . i Yarns unequal in s ze . i i (c) Yarns conta n ng unequal twist . Y i d in i di i (d) arns tw ste oppos te rect on . — The Relative Resistance of Yarns t o Twist Assuming the coefficient of resistance to the first twist in a given length of 1 and i i di yarn to be , the res stance , as the tw st progresses , rectly i i i d i i proport onal to the tw st conta ne , the relat ve res stance , when di i i i the ameters of the yarns are not al ke , be ng proport onate to i di d— i the r ameters cube then, upon these assumpt ons , the S i i d i d u 6O relat ve res stance of a bo y of untw ste fibres , eq al to S i and 4O yarns , are respect vely

1 3 3 (7 6- 0and (ﬁ )

i d i i t d When the ﬁbres are tw ste , the r res stance , when enotes i d in i i the twist conta ne them , w ll be respect vely

1! and t < \

d di i i The above are base on other con t ons be ng equal . S 8 The relative resistance of 6O and 40 yarns containing twist to the extent of is therefore e xpressed as follows

1 3 605 3 , > x/60

40s 3 08 3 7 , 7 40)

d d d i d d i When fol e threa s are requ re balance , namely, w thout i i it is i i tendency to tw st or untw st , necessary to nsert tw st to the

x il i . T e tent that w l balance the forces they conta n hus , a yarn composed of several single threads should be twisted so that the force developed by the doubling twist is sufﬁcient to counteract i those still contained in the singles . When a number of s ngles

224 COTTON SPI NNI NG CALCULATI ONS

3 The i d d 50 i above formula, when appl e to twofol w th t 8 5 c i i 1 \/ 1 , g ves the follow ng results

as c [ ( x/ l (wgf a 1 09

This method of ascertaining the twist is applicable to all

i d . I t in Si k n s of yarns enables that necessary, the ngles , to

i di i i d vice ver sé . balance a certa n fol ng tw st to be ascerta ne , or Adherence to this method would necessitate considerably more i in i it is and tw st , the s ngle yarn , than customary to apply, hence it would increase the cost and this without commensurate

i i is i d x return . I n certa n classes of yarns t appl e to some e tent . The application of the above formula is further illustrated by the following example

un the in e 50 and w d is m d con inin Let the co t of s gl be , t ofol a e ta g the usual W wi w d n in h in in n 4 20. t e d tur s 4 ez X hat t st oul be ecessary s gles or er that the completed twofold be in perfect balance ? 1 3 “ 9 - v 07 011 dxl

5 8 the in i n x 6 , s gle coefﬁc e t or constant

TH E I N D R G OUBLI NG FRAME .

Fi 4 i in i d i g. 7 represents the gear ng common r ng oubl ng f A A in and L d i i rames , , I be g the rollers , the r v ng pulleys , J the tin and I tin i I H G roller , the roller shaft wheel , the tra n , , , E D D C and B in i E , 1 , , 1 , l , B , 1 , be g the tra ns of wheels con n K and K necti g the front rollers to the tin roller . are the

Spindles . The following twist is obtained when the s mallest sizes of the change wheels are employed The i i d i revolut ons of the sp n le per one of the roller, w th the i smallest s zes of change wheels , are AND COSTS OF YARN 225

7 5 X 60 X 1 20 X 8

20 x 20 x 20 x 1 -g,

nd wi i i d in a therefore the t st per nch nserte the yarn , on the left id i i d be s e of th s mach ne , woul 480 whilst that on the right Side would be

— The range of twist with 20 60 the available sizes of top

F I G . 47 .

in and i change wheels , when the t roller the lower tw st wheels 20 i are both , s On id 8 ‘ 2 2909 the left s e , from 7 7 , to X % 3 On i id 61 61 — 203 the r ght s e , from , to X 8

i i tin W th the ava lable sizes of wheels for G, when the roller is 20 and is 60 i i wheel C , the tw st per nch procurable , ranges from

On i 2909 96 9 the left s de , from , to

On i id 20 3 the r ght s e , from , to 226 COTTON SPI NNI NG CALCULATI ONS

i tin 40 and 60 n 60 W th the roller the other change wheels a d , the twist would be

On id the left s e , twist per inch

On i id the r ght s e , twist per inch revolutions of spindle (actual) The production per unit of time twist required inches per unit of time

Therefore with the spindles making 8 000 revolutions per S i and 2 - 2 and i m nute (actual), the counts 7 tw st coefficient the rate of production in hanks and ounces per spindle per 1 0 d e hours , no allowances , woul b

8 000 X 60 10 i i dl X revolut ons of sp n e per 1 0 hrs . 8 000 X 60 X 1 0 i i d in 1 0 nches per sp n le hrs . 5 2 V 9 8 000 X 60 X 1 0 d S i d in 1 yar s per p n le 0 hrs . 4 5 1 2 3 6 V 2 X 8 000 X 60 X 1 0 hanks per spindle in 1 0 hrs . 4 7 2 8 40 5 V 2 X 3 6 X 8 000 X 60 X 1 0 X 1 6 ounces per spindle in 1 0 hrs . AIr 1 2 3 6 8 40 1 2 a/ 9 X X X 2

This is assuming the yarn does not contract . 000 revolutions Of the roller per 5 3 2 2 1 " X 1 x/ 2 22 X 7 minute on the left side 000 revolutions of the roller per 7 5 1 2 2 — 2 X " 9 ? 7 minute on the right Side

i i in W th the particulars of the frame as g ven the ﬁgure , the dif d i in d ferent top change wheels that woul be appl cable , or er that the same turns may be put in the yarn made on both sides i The i of the mach ne , are as follows rat o of these change

i d 2 1 10: 7 1 07 . wheels , left to r ght , shoul be as 5 a, or , or The following exercises are based on the conditions obtaining 4 in Fig. 7

228 COTTON SPI NNI NG CALCULATI ONS

i 3 000 8 500 d . range from to , accor ng to the class of work When i id i i chang ng , always cons er whether the new c rcumstances w ll d i i in d i d a m t of or requ re a change the spee of the sp n les . Such is d i S i d i ma e by alter ng the frame haft pulleys or the r r vers , i whichever be most conven ent . — Slippage in Doubling Frames I n doubling frames there is u sually considerable slippage in driving the Spindles from the tin and i in d i i i in roller , th s often results un es rable var at ons the

i i i n x tw st wh ch the yarn conta ns . A idea of the e tent of this is contained in the following observed speeds in a ring doubling in i i T i i frame good work ng cond tion . h s frame conta ned one tin roller making 8 8 8 revolutions per minute and 8 inches in di i d i 1 i in di Th ameter , the sp n le wharves be ng 4 nch ameter . e i i d i d i 518 6 follow ng were typ cal recor s of the r spee s per m nute , 5100 541 6 5265 i d i 5 50 and , , , the r calculate rate be ng 9 , hence

1 28 1 4 3 90 1 1 5 . i T i the loss was , , , per cent respect vely . h s is i i i when neglect ng the s ze of the sp ndle band. I t will be noticed that when the size of the spindle band i s allowed for

in i i i 7217 . th s nstance , the loss w ll be almost The Twin Mu e — 48 i i er l Fig. conta ns part culars of the gear for d i n i d n d i - r vi g the sp n les a d raw ng out scroll shaft in a twiner .

F 8 I G. 4 .

N N d i i rim L is rim , , are the strap r v ng the pulley M ; the pulley K i and LX the rim band driving the tin roller pulley J , be ng the h in B d i i d r im band carrier pulley . T e t roller r ves the sp n le n in wharve A ; C and 01 are the ti roller wheels , shown two i d i i i D G is d i - s zes , for r v ng the tra n , E , F , , H H the raw ng out h i shaft clutch wheel . T e other part culars of the above gear are AND COSTS OF YARN 29 — R i r un 0. Rim as follows evolutions per m nute of shaft , 7 7 , L 12—24 i B 6 i 1 1 i A i di , nches , nches J, nches , g nch ameters i nd 25 D 8 0 20—40 90 . and 1 5 a respect vely C Cl , , ; E , ; F , ; i n 1 5 6 h i . a t G , ; H , 8 , teet respect vely H makes gg revolu o s The i per dra w in moving the creel out 7 2 inches . tw st change

: in nd 25 and 20 40. wheels are the t roller 1 5 a , the wheel E to The rim i i i i pulley s seen , on nspect on of th s gear, to be the di ll d i and me um for adjusting the speed of a the pro uct ve parts , the twist change wheels for altering the rate at which the yarn is i ntroduced to the twisting inﬂuence . If the examples relating to the spinning mule have been

d d i i i d d. un erstoo , the follow ng calculat ons w ll be un erstoo Hence only one example is given in each s et of these i calculat ons .

EXE R I — i n f th ind min wi on C SE 1 . Calculate the revolut o s o e Sp les per ute th c secutive i im n in m 1 2 24 in in di m s zes of r s ra g g fro to ches a eter.

E xam le - i n min d ri i 1 in in p . Revolut o s per ute of spee when the m s 2 ches di me a ter,

Size of rim 12 13 1 4 15 16 17 18 19 20 21 22 23 24 ind Revs . ofsp le 5760 6720 7 680 8640 9600 per minute 6240 7200 8 160 9120

EXE RCI SE 2 — i . Calculate the twist per inch when the largest driver tw st n e w in cha g heels are use . — 1 E xamp le Revolutions of spindle per one draw and per 355 revolutions of H 3 g§ X 68 X 90 X 80X 6 twist per draw of 72 inches 15 X 4O X 25 X § 258 x 68 X 90 X 80 X 6 X 8 _ 68 X 15 X 4O X 25 X 72 X 7

W n the tin he roller wheel is o 40 39 3 8 3 7 3 6 3 5 3 4 3 3 3 ~ 25 and the twis t change is

The twist per inch is

3 1 30 29 28 27 26 25 24 23 22 21 20 15 7 1 68 18 1 196 214 23 5 16 2

E XE R E 3 —C i i CI S . alculate the twist change wheel that w ll g ve the nearest to n er in w n in i 1 tur s p ch he the t roller wheel s 5. 23 0 COTTON SPI NNI NG CALCULATI ONS

E XERCI SE 4 — C wi in wi c n c i i i , alculate the t st per ch th o se ut ve s z es of tw st n w n in m 20 w d wi tin 1 w e 5. cha ge heels ra g g fro up ar s , th the roller h el

Twi n w 2 A ns . st cha ge heel 20 1 22 23 30 3 7 5 342 Twist per inch

2 8 68 5 x X 9O X 80 X 6 X 1 _ E x m le a p . 68 X 1 5 X 2O X 1 5 X 7 2 X %

EXE RCI SE — f i n w and n d d w 5. I the tw st cha ge heel 3 5 the cou ts ouble hat Si w w d i d l —Q' w n m wi t zes of heels oul be requ re for g , he the sa e t s co nstant is used ?

“ E m le e i for ﬁ xa p . wh el su table g

EXER CI SE - E im n in b nks ind and in o nd 6. st ate the productio a per sp le p u s per twiner of 1000 spindles per 10hours ; the spindles to develop a speed of u i n er min and in off and windin c 5 nd revol t o s p ute, back g g to oc upy seco s n d d L 11“ and wi n n 4 5 is the cou ts ouble are 3 , the t st co sta t

d. A w 15 n d d in wi in and 1 5 min use llo per ce t . for loss of spee ur g t st g, utes per d ff w i in 2 o , the cops e gh g ozs . each .

E xam le p .

4 5 /f’ l ' 100 A g x 7 2 Seconds taken twisting per draw seconds 1 1000 8 5 Seconds per complete draw 1004 5 1504 25 840 56 T2 x x x Time to make a cop in seconds seconds 7 2 x 8 5 The above numerators contents of a cop in inches Time taken to make a cop and 1 X 25 X 840 X 3 6 X 15 04 15 dotf in hours } 8 x 7 2 x 60 x 60 60

9 min . 33 5 . 2 5 7 . hrs s 233hrs . hrs

10 X 2 X 25 producti on I n hanks per spi ndle x 1 6 x 1 1000 x d i n in nd win pro uct o pou s per t er 218 lbs .

Changing the size of the rim affects the Speed of all the d in i i and i and parts concerne tw st ng ntroducing the yarn , there i i d in i i m in di fore alters the t me occup e , mak ng th s move ent , rect proportion ; the time taken to back off and wind remaining unaffected. Changing the twist change wheel alters the twist through i i in di affect ng the rate of movement of the carr age , the rect T i proportion to the change made in the wheel . h s alters the

23 2 COTTON SPI NNI NG CALCULATI ONS

I n order to ascertain the cost of producing yarn when the d i and i i x i d pro uct on the nclus ve e penses per Sp n le are known , the following is the course usually followed To the cost of the cotton at the card delivery add the cost d i d and d d s u m i d of pro uct on , per poun , e uct the rece ve , per d poun of yarn spun , for the waste . The rate of the production per spindle in the South - E ast L i di i is ancash re str ct does not vary considerably . The range

i . 2 4 g ven on p 0 . I n costing it is usual to disregard the loss arising from w d i i is d aste after the car , because th s tem about balance by the i in i h is d rega n cond tioning . T e value of the waste assesse at

2 i . % per cent . of the cotton price this is considered a fa r value

“ E XAMPLE of 2 T m de m idd in Am i n c n at 6d . the cost of 8 . a fro M l g er ca otto r nd pe pou . Cost in pence per p ound. Working costs per Spindle per annum

d i n ind nn m d on 50 Pro uct o per sp le per a u , base 3 2 x 50 working weeks per year and 3 2 hanks per week

C of the n d i d the c d d i r ost cotto el vere at ar el ve y , 6 x 100 owin 10 er ent o all g p c . for l ss, 90

Less val ue of the waste cost of raw cotton

Nett cost of Spinning 1 9 3 3

Add : cost of selling and discounts 3% per cent on selling price .

’ ' m idd in Am ic n c t n at 6 1 6d. d c i n EXAMPLE 3 6 T. fro F . M l g er a o to Pro u t o , ind er w 30banks per sp le p eek .

in ind e nn m 806 4 Work g costs per sp l per a u , d i n S indl nn m 50 X 30 banks Pro uct o per p e per a u , n d d i win Cost of the cotto at the car el very, allo g n 10per ce t . loss

Less value of the waste cost of the cotton

Nett cost of spinning AND COSTS OF YARN 23 3

3 EXAMPLE 60 T. i Br. E i n at 9d. nd Fa r gypt a per pou .

\V01 king costs peI spindle per annum Production per spindle per annum Cost of the cotton delivered at the card 10 per 9 X 100 cen w d t. aste , 90

1 4 032 Less value of the waste cost of cotton

Nett cost of Spinning

TH E APPROXI MATE COSTS OF YAR N WHE N SP N F ROM SI NGLE O I NG TH E B ASI S U R V , B E ING 8 064 PE NCE COST PE R SPI NDLE PE R ANN UM 1 6 1 P E NCE PE R SPI NDL E WE K P E R E .

Sm tabl e cot ton and rade g .

W : 3 4 12 6 3 1 01 3 07 6 6 933 1 3 83 1 6 . 7

1 0 7 28 01 64: 4 03 1 11 46 45 96

I i d i n those Sp nning mills preparing the yarn from ouble rov ng , i i i i x at the sp nn ng mach ne , the cost of the work ng e penses are 23 4 COTTON SPI NNI NG CALCULATI ONS

i T i i d greater than those prev ously given . h s has been ascerta ne

° xi 1 2d. S to appro mate 7 per mule pindle per week . 8 T 50 T. d v and d d 25 5 hus , from ouble ro e , pro uce at the rate of i d i i x hanks per mule Sp n le per week , w ll cost in work ng e penses X 50 3 3 7d. per pound

5 T 2 5 i d and 60 . at 3 hanks per sp n le per week 60 X 4 4d d . per poun 23 5

TE E APPOXI MATE COST OF YARN SPUN FROM D OUBLE R oe G AS PER D ATA P RE I S Y I E N V OU L G V .

Suitable grade of

cott on .

0137 080 69 8 1 4 28 1 6 W. 63 1 7

B d r, a ers , ds or su er , p or Tex as Ditto (double rove) M F Am i n . . er ca E G F gy . . . F U . E gy . .

E . gy . G

. E G F U gy . . . E gy . G .

23 6 COTTON SPI NNI NG CALCULATI ONS

“ RO MAN E TE R G AR A 0 1906 M TH E CH S D I N J NE 3 . F U , U ,

5 S 8 Good Bhow 20 water Middling 3 2 cop Fully good 6 0 t wist

nu ar . t w ist Am erican. t wist . ai r E t . E t gg . f gy p gy p

Per ound. Per ound Per ound . Per ound. Per ound . Per ound. p p . p p p p AND COSTS OF YARN 23 7

“ FR M TH E COTTON ACTORY TI ME S J NE 29 1 906. O F , U ,

E E R P RI CE OF M DI UM YARN S IN PEN CE P LB .

w T ofold .

Twist in co . W t . p Bund e e Beam . . Count . f l

Bund e l .

Sig

3 —10 1 0 —1 1 1 05 —1 1 5 91 6 5 3 3 1 3 16

1 03- 1 13 101- I I I

EGY I AN YARN PT S. 17;- 21 1 73 203 — — } 1 9§24 1 9; 23 I 211. 26 233 3 0 23229; 253- 331 255- 3 23

COTTON F I T N , O F CI AL QUO ATI O S.

J n 29 1906 . u e ,

American.

L. M . Arnerican

E t gyp ian .

P .G. P .

E i n wn gypt a , bro D i tto , upper

E ian wn ﬁne 1 1 . gypt , bro , , 3 D i ﬁne * 10 tto, upper , , . E gyptian quotations do not refer to B ami a or Upper E gypt cotton .

N ominal . 23 8 COTTON SPI NNI NG CALCULATI ONS

I ndian .

G F. F . .

S B n n 4 . e gal , uperﬁ e, g

in Nom al .

The Cos s of Pow a i b the M hin s in S innin Mi t er va la le at ac e , a p g ll . Basis : E ngine and all plant connected therewith to develop

I . H P 1 000 . .

i i and i — u and Eng nes , bo lers , econom zers P mps all the

i — i and - i — i necessary connect ons Shaft ng rope gear ng Reservo rs , P d i di and £ 1 5 I . H . . lan , bu l ngs , approaches at per Ratio of above costs

a n i 3 5 . ( ) E g nes , per cent d i 2 6 i an 0 . ( ) Bo lers econom zers , per cent

- S i nd i 1 5 . ( c) haft ng a rope gear ng, per cent d i d i di and 3 0 ( ) Reservo rs , lan , bu l ngs , approaches , per cent .

Worki n E x enses s g p . d .

i i n and in i e on a b c 10 Deprec at o upkeep clus v ( ), ( ), ( ), at n nn m per ce t . per a u .

D i ion and on d 2 n . eprec at upkeep ( ), at 5per ce t

I n 4 n . nn m on a b c d terest at per ce t per a u ( ), ( ), ( ), ( ) I H n m £ 02 5 . .P n Stores at per . per a u .

° Goal s : 2 . eI I .H .P. 7 3 . 6d. ton lbs p per hour, at per i n 1 I n n d 3 . n on sura ce (ﬁre , acc e t), at 0 per ce t . Labour

3 948 10 0

I H . P . in 50 5 i Cost per . per hour pence ( X 5 work ng hours)

3 948 5 x 240 0 3 44 50 x 55 x 1 000

Th i i in i i i is e nclus ve power required sp nn ng m lls , about

240 COTTON SPI NNI NG CALCULATI ONS

d in d i allowe for the car , then we ght of cotton

in ir d d 52 . requ e car laps , 7 lbs n f 5 in i and A d i per cent . loss be allowed for open ng scutch 527 X 1 00

i d 400 . in 555 . g, then , lbs of raw cotton requ re per lbs 95 of combed cotton . When combing is not in vogue this amount would be less to the extent of

400 x 1 00 x 100 4 1 555 44 1 1 lbs . ( 95 X 95

A in d i Of d 0 ssum g the pro uct on the car 3 5 lbs . per week , the e e xtra carding machinery per 400lbs . of combed sliver would b

1 00 500 400 1 ( 00 lbs . ) 3 50

T i du i i 8 000 . and ak ng the pro ct ve capac ty of a scutcher at lbs , the i that of opener at lbs . per week , respect vely , the loss i i 2 and 3 . i x be ng per cent respect vely, then the e tra scutch ng and opening machinery would be

1 06 1 09 i i open ng , scutch ng , 8 000 1 6000

The x i i d e tra labour involved, upon the follow ng bas s , woul cost as follows

Cos t o tr ati s o s cutched cotton . f e ng l b . f

ixi i i i £ 3 1 5s . M ng , opening and scutch ng , wages nclus ve, The i x i d 1 06 cost, therefore , of treat ng the e tra cotton requ re (

lbs . scutcher lap) would be

3 7 5 240 X 1 06 X ° 5 9d‘ 1 6000

d Therefore the extra cost on account of labour under this hea would be

° d d O 01475d. per poun s of combe cotton AND COSTS OF YARN 241

28 3 14 d i u i Taking the labour in carding at . per car s ncl s ve , the cost per pound of combed Sliver would be

28 1 2 100 X X ° 0 01d d d S i 0 17 . per poun of combe l ver 3 50 X 1 4 X 400

The costs of labour involved in preparing the cotton for and in combing :

n 1 8 3 . d i and i O e person , at per week , to atten the sl ver r bbon

d i 2450 . . i . l ap mach nes Pro uct on , lbs per week

18 1 2 490 X X ’ cl d d 0 108 . per poun of combe cotton 2450 X 400

six i i i i One person , at per comb ng mach nes nclus ve of cost of overlooking

20 x 1 2 ° d d o l . per pound of combe sliver 6 X 4OO

Other expenses Costs on account of the machinery

£ 243 8 5

i and Repa r upkeep at 7 5per cent . per annum on £ 1 8 28 9 £ 243 8 5 } D i i eprec at on at 7 2per cent . per annum on £ 243 8 5 I nterest at 5 per cent . per annum on £ 243 8 5

£ 48 7 7 0

C d i d ost , un er th s hea , per pound of 0° 58 5d combed sliver . 242 COTTON SPI NNING CALCULATI ONS

x in i 4 0 E tra stock of cotton process through comb ng , say 0 i i 8 d lbs . per comb ng mach ne of hea s .

Value of this at 8d per lb . £ 13 3 .

I 13 5 0 nterest on £ 3 at per cent . per annum £ 6 65

Therefore cost per pound of combed Sliver 0008

x 23 . d E tra cost on account of space , at per square yar per annu II I Proportional area s ua e ards q r y . S i i 400 lbs 1 5 d 1 pace per comb ng mach ne ( ), square yar s 5 0 i 2450 lbs 1 5 r bbon lap ( ), sliver 1 2

1 9 5 X 2 X 1 2 d d shver 0 023 4ol Cost per poun of combe . 50 x 400

° x 0 3 44d. I . H . P . E tra cost on account of power , at per per hour Proportional owe p r. P I H . . Comber (400 lbs . ) g .

Ribbon lap machine (2450 lbs . ) 1 Sliver

° 0 0473 d.

The extra cost on account of the waste extracted

W i 8 8 . aste at the comb ng stage , lbs x i ixi E tra waste at the prev ous stage , not returnable to m ng ,

555 444 1 1 1 lbs . T 1 1 1 4 herefore 00 51 1 lbs . the amount of raw cotton

i d 400 . d nd requ re per lbs combe , a therefore the cost of the cotton per pound at the combing head on this account is

COTTON SPI NNING CALCULATIONS

‘ 7 25d.

The other expenses of combing

' 0 9o26d. per pound

i d is d Hence , assum ng the waste ma e at the comber sol at a i i pr ce per pound equal to half the cost pr ce of the raw cotton , then the extra cost of combing in this case would be

° d 1 8 . 1 1h. et. 0 2 . per cent , X S 7

° Th : e cost of combing 07 2 2 5026d. per pound

Th x ' e e penses exclusive of the loss in waste 0 9026d.

The x d i cost on account of the waste e tracte , assum ng it has no value

8 d d . 2 Th Costs of 80 combed as per tabulate ata on p 3 5. e i n i i l l d cost of comb ng a d sp nn ng when the raw cotton costs g . per pound. The cost of spinning (uncombed) as per tabulated data on 2 p . 35

d .

7 2 5 per lb . Of yarn

The cost of the cotton at the combing d hea , through waste loss , neglect ing value derived from sale The x i x e penses of comb ng , e cluding ) O9026 waste I AND COSTS OF YARN 24 5

Less the value of 18 per cent . waste

i - ' in i . made comb ng (at half pr ce of 1 O7 per lb . of yarn r aw cotton per pound) Less the value of waste made prior to 2 » combing (at 5 per cent . on the raw cotton price)

2 ° 18 6d Cost per pound of yarn 3 7 .

EXAMPLE of the method adopted in estimating the cost given below

in : 850 er d Card g lbs . p car Cos t per pound of s un yarn p .

L o : 2s . 1 1d. c d inc i e ab ur per ar , lus v of over looking and card head tenter d ° w 1 . c 03 4d . hOur Po er : H P . per ar at per in : er d 10 er n Mach ery p car , p ce t . for

o d e i ion and u e . l ss, epr c at , pk ep S c : 10' 58 e d d at 2s er pa e squar yar s per car . p yard 0 00061

8 0 1289

The cost at the drawing and subsequent stages is given per d i i id i i in pro uct ve un t , on account of the w e range of var at on

i d i . I n d f i the r pro uct on or er , there ore, to est mate the cost per d d i d i d i i d poun , the pro uct on per elivery or per Sp n le s requ re . The production can be ascertained in the manner explained in i other parts of th s book . e D m n l s f n Th epart e ta Co ts in Spinning Carded Qualities o Yar . I n estimating these costs up -to- date conditions have been taken

i . T 23 as the bas s he cost of space has been assessed at . per d i B square yar per annum , nclusive . ut no allowance has been

made for waste .

' l - — / — I l icrcng Cotton and II as l c IStorage Op en IIg Scu tclnng

' Cost I n p ence per pound of arn s un y p . 0027 00255 00144 0003 17

007007 246 COTTON SPI NNI NG CALCULATI ONS

Carding

D rawing Cost in pence per v r er w e deli e y p e k . 1 2 5

Fly Frame s Sl ubber

I ntermedi ate Labour Power Machinery Space

27 35

Roving

Il fules

248 COTTON SPI NNI NG CALCULATI ONS

On this assumption the production per winder will be

i hr s 6 i . 1 2 u d 55 . X 0m ns X X o nces conta ne on each bobbin 2 X 1 6 pounds per winder Number of spindles per winder pounds per winder

25 . d d i per cent 7 5 per cent . calculate pro uct on per spindle — A Method of Ascertaining the Production of Reels The pro duction of 40- hank reels in 55 hours when worked at 250 i i i i revolut ons of the sw ft per m nute , allow ng two stops per i d and 5 d i bobb n unwoun , secon s for each stop , the bobb ns 3 i . 20 i i contain ng oz of counts , the t me lost n tying and dofﬁng being 3 minutes . The time taken to ﬁll the reel (40 hanks) if no stoppages 8 0 X 7 X 60 S d 250 econ s

The number of stops in ﬁlling the reel

8 40 07 5 840 20 1 6 X X

The time lost in ﬁlling the reel through stopping

8 40 X 2 X 5 X 40 seconds X 8 40 X 20 1 6

The i and d f i t me taken to ﬁll o f, allow ng two stoppages bobbin unwound

8 0 X 7 X 60 8 40 X I 6 X 2 X 5 X + 18 0 250 X B4O X 2O 427 1 80 s econds minutes

production per Week in pounds

55 x 60 AND COSTS OF YARN 249

The weekly earnings of winders and reelers vary from 143 .

24s . and d d to per week , the cost per poun of yarn treate , i in i w i di i in var es , th s ork, compar ng str cts , more than any other section of the spinning mill . The numerous departmental wage lists and the difference in in i di i do d i in these , the var ous str cts , not a m t of the costs i d in i i d in wages be ng treate , a work of th s k n , any other manner than that adopted. A i diff i i d lthough these l sts er on paper , compet t on has resulte — in this difference in the costs being that approaching the i i i d d i d i i van sh ng po nt , when re uce to a bas s embo y ng quant ty and quality of production .

252 I NDEX

D in d win m 1 03 1 07 1 09 in d 1 61 1 64 raft ra g fra es , , , Ga , or rag , , r m 142 1 51 h n 1 66 1 86 ﬂy f a es , , c a ges , , i n m 157 in in 1 5 21 ules, Gear g bale breakers, , in n 34 4 0 in din m in 56 ope ers , car g ach es , ’ in i n m in 8 2 in D n d - d and r bbo lap ach es, obso s ouble spee in i n m 209 ni n m i n 190 r g fra es , haste g ot o , in 43—47 in d w m 1 03 scutchers, ra fra es , i n li l a m c in 7 8 in m 1 12 s ver p a h es, ﬂy fra es , D win m 1 02 in m 1 56 ra g fra e , ules , ’ a i n in 1 03 D n and B w 17 7 c lculat o s relat g to, obso arlo s , , i in i in 1 05 1 95 co l g of sl ver, spac g, ’ o n i 151 1 83 1 91 1 92 c u t of sl ver at , Platt s, , , d r 1 03 1 07 1 09 i in 1 62 1 77—1 90 afts , , , var ous tra s, , ff m i n in N asmith m in m in 8 4 e ect of at ospher c cha ges , co b g ach e , 1 02 in n 25 ope ers , ’ m in 108 in n i n -off m i n 51 syste of gear g rollers, Platt s k ock g ot o , na i i n 1 52 in i n l a m in 80 rollers , a lys s of act o of, r bbo p ach es , n i n 1 53 in in m 204 fu ct o s of, r g fra es, D i v and d i n w ff d in m 224 r er r ve heels, e ect of oubl g fra es , n in 9 1 0 1 08 cha g g , , rollers , D i i n and e 1 2 in 41 r v g , rope b lt, scutchers, d and i d i in in i m in 7 6 spee s s zes of r v g sl ver lap ach es , 1 2—1 5 i n win m 228 surfaces , t er ule, i in i n and var ous tra s of, calculat o s h i 16 1—1 7 7 E i i i m i n n 223 ot er part culars of, qu l br u , state of, yar ,

- l a 7 5 Half p, F w diff n i in in 7 5 allo s type of ere t al (slubb g prepar g , m 1 3 5 n indic o 154 200—203 fra e), Ha k at rs, , Fi n and i n r e nin m i n 1 61 llet , le gth preparat o of, Haste g ot o , ’ i d ind i 7 5 D n 1 90 qu re to cloth cyl r cal surface , obso s , F in ds n i n 67 h in n m 1 62 lats , car , fu ct o s of, Het er gto ule, m m n 67 n 21—25 rate of ove e t of, Hopper type of cotto puller, Fl m 1 1 0—1 52 in in 21 y fra es , gear g , n n in s l n 24 co seque ces of alter g value u efu ess of, n in 1 14 n in co m in n of co e tra , Hu t g g easur g or le gth n dr m u se 1 26 m i n d in n and co e u s , of, ot o , use ope ers scutchers n 1 50 1 51 48 cou t , , n in 1 18 d n 50 cha ges , a va tage of, d 1 42 1 51 raft, , a i n in 1 17 1 18 I ndi an m and mu lterat o s , , , cators , h k , for fra es les , 1 1 9 - 203 diff n i in i n 200 ere t als, pr c pal types le gth , 1 27 —1 40 d i 1 98 of, spee , the r use , 1 26 use of, dr win i n k n in m i n 1 58 1 62 a g rollers , act o of, J ac i g or ratch g ot o , , n i 1 52 ’ 1 91 a alys s, Platt s , ’ in in 1 1 2—1 1 5 Trel fal l s 1 9 gear g , , n indi 1 54 ha k cators, ” ' ’ i n 141 - ﬂi n in cutchers Pl att s Kn in o m s preparat o s , ock g ot o , , c r 1 41 1 pro esses , th ee stages , 5 d i n i n 1 45 pro uct o , a windin and in L 7 1 r te of g spac g aps , il 1 20 n in w i and n of co s , cha ges e ght cou t of, d ind 149 m d n and s spee of sp les, a e by ope ers scutcher , d 1 1 5 1 40 52 spee s , , wi on n 1 1 1 n 49—51 t st c sta ts, le gth of, wi in in 1 1 1 l 87 t st g , object of, rol ers , windin in in d L n and n indi 200- 203 g , obta e by bob e gth ha k cators , bin 1 25 m i n 1 56 , stop ot o , I NDEX 253

M i n in w n d i n and h i n in ot o , rate of, calculat g, he tooth Pro uct o s , t e r co troll g fac m d 1 53 54 gear e ploye , tors, , n mi i n 1—15 tra s ss o of, Motions ' din m i n 1 58 1 7 8 n - ﬂnd in -i n 1 57 1 60 ece ot o , , i o a R g back g tak g , , i n w l aw 1 1 7 8 Revolut o of heels , , i n l a m in 8 0 i din 159 17 8 R bbo p ach es , bu l g, , d in 82 d - d 1 59 1 90 rafts , ouble spee , , d i n in 83 nin 161 1 90 pro uct o , haste g, , in d in m 224—228 in in 158 1 62 19 1 1 93 R g oubl g fra es, jack g or ratch g, , , , in in 224 n in - off 51 gear g , k ock g , d i n in 226 n in 156 pro uct o , le gth stop or full bobb , i in 228 din 1 58 1 8 sl ppage , rece g, , 7 wi in d 224 d i 1 0 , roller el very, 6 t st obta e windin 247 wi in 1 59 g, t st g, Rin m 204—224 M m n o w di i n g fra es , ove e t of t oth heels , rect o of i d w 210 2 bu l er heel (ratchet), — m d wi h m 1 M 1 56 204 , 2 3 ules , co pare t ule n 23 5 i n 1 56 1 83 costs of yar , calculat o s , , n n in 209 m d wi in m 213 cou ts , cha , co pare th r g fra e, g g in in 204 n 23 1 gear g , costs of yar , l i n dri in ind n n in 1 5 ooses v g sp les, cou ts , cha ges , 7 d in 1 57 21 2 rafts , ’ ’ d i n in 213 D n and B w 17 190 1 94 pro uct o s , obso s arlo s, 7 , , in in 1 50 i n m in m gear g , proport o of ach ery for — in i n i n 1 42 i in 162 1 67 g a preparat o , var ous tra s of, d ind 206 212 in n 1 62 , , Hether gto , spee s of sp les wis in 207 in d i in in 194 196 t t per ch , losses r v g , , in innin ee in m i n 1 —1 6 1 . S m ot o s, 57 R g sp g R g fra es ’ l d i m i n 1 60 l 1 83 1 91 192 , P att s , , , Rol er el very ot o and d i in 1 2 d i n in 204 , pro uct o s , Rope belt r v g in d nd proportion of machinery forming a calculat g spee s a sizes ” i n 142 d i in s 1 2- 15 preparat o , of r v g surface , ’ i n di i n 6 Trel fal l s 193 Rotat o , rect o of, , — of w in an dir in win 228 230 y t , t er, heels ect ra rela i l wi in 1 9 , aw, 3 t st per ch , 7 t ve rates of w l in in i i n hee tra values , cond t o s nin h n in 1 61 gover g c a ges , i and n in S 41—56 var ous, ra ge cutchers , i w 17 7—190 n in w i and n s ze of heels, cha ges e ght cou t of m d b 52 laps a e y , O n 15—40 48—56 d in 43—47 pe ers, , raft , n in w i and n in in 41—43 cha ges e ght cou t of gear g , m d 52 n in m s in n laps a e by, hu t g cog ea ur g or le gth d in 3 4—40 m i n d in 48 rafts , ot o use , in in 25 i d i in 4 1 gear g , part culars of r v g, h n in co m in n d i n ds and n in u t g g easur g or le gth pro uct o s , spee , co troll g m i n d i n 48 54 ot o use , factors , d i n d and n in S i web 65 7 1 pro uct o s , spee s, co troll g l ver, or , , 54 i in 1 05 factors , co l g of, Overscutchin 55 w i d 1 2 g , e ght of the car , 5 S i l a m in 7 6 l ver p ach es ,

B . in m i n 1 91 d in 7 8 Platt, ros , jack g ot o , rafts , ’ n in - off m i n 51 d i n i n 7 9 Platt s k ock g ot o , pro uct o , in in 51 gear g , to alter, 7 9 l in m f d 54 S d indi 1 98 P uck g fro ee rollers , pee cators, ” r i n 7 0 1 41 S d in and Prepa at o , , pee s scutchers their control i n m in min in 53 54 proport o of ach ery for g a , l g factors, , in m innin and in m in 6 1 ule sp g r g fra e alter g , innin 1 42 S m i n n 156 sp g, top ot o s , le gth, 254 I NDEX

T m e 1 98 199 W in 4—1 1 acho et r, the, , heel tra s, T - in rate m i n in 8 ooth gear, calculat g of ot o calculat g value of, w n m d 1 di and indi 4- 6 he , e ploye , rect rect , w dir i n m m n 2 ff n in w 9 heels , ect o of ove e t of, e ects of cha g g heels , T n mi i n m i n 1—1 5 i n m s ndi i n ra s ss o of ot o , values of, ule , co t o s ’ Trel fal l s in m i n 1 93 nin n in 1 6 1 jack g ot o , gover g cha ges , ‘ Tw d dI fle en ial i n i i u 1 r t 77 ee ale type of ( ter var ous , part c lars of, m di m 133 See G in e ate fra e), ear g Twin mu 228—230 W i i n d i d i n er le , heels , class ficat o of r ver, r ve , in in 228 i 6 gear g , carr er, Twi n an in n m di i n i n 6 st, co st ts, for rov g, or al , rect o of rotat o , ff s n in 9 e ect of cha g g, s nd d in n l aw i n 1 ta ar s for s gle yar s , of revolut o , 1 61 214 i t i n 3 , relat ve ra es of rotat o , d in im and 220 Windin in flm how in d f oubl g, a s ef ects of, g y fra es, obta e , n n d in 216 1 25 co sta ts use , i n vi n dir i n and n W in 7 0 ro g ect o useful ess , rapp g, 1 1 1 ff 214 e ects of, in in n 21 5 s gle yar s , infl Y n 7 1 n di i n in d d ue ce of rect o of, fol e ar , n 218 t 231 - 247 yar s , costs of (g ), 2 0 O 1 1 1 204 d in im and ff , 2 bj ect of, , oubl g, a s e ects of

in d in in d in m d d wi nd d , 21 6 obta e r g oubl g fra es, fol e , t st sta ar s for 224 inﬂuence of direction of twis t n 2 in and dr w 1 97 on , 18 per ch per a , stre gth of in in m 207 a i s i n wis , r g fra es , rel t ve re sta ce of, to t t i si n n 222 222 relat ve re sta ce of yar s to, 14 nd d d d n 216 s in wis nd d , 2 sta ar s , for fol e yar s , gle, t t sta ar s for n 1 in n 21 4 eff wi i , 2 4 21 5 for s gle yar s , ects of t st , i i m 223 s ili i m 223 i , tate of equ br u , state of equ l br u o d w 197 nﬂn on i n n 21 5 t tal n , , , i ue ce break g stre gth , , le gth of per ra 21 6 213 in a in n h 21 5 twisting two or more threads test g for bre k g stre gt , , 219 21 6 together ,

TH E E ND

‘ n l A - l .

LI I TED LONDON AND BECCLE S. P R I NTE D B Y WI LLI AM CLOW‘ES AND SONS, M ,