LIBRARY OF CONGRESS 018 446 118 3 * T S l5 7^ .¥3 i VAUGHAN'S Carding Lessons a For the Mill Boy'' BY M. H. VAUGHAN HUNTSVILLE, ALA. 1905 Class : p ^'sill Book V S GpiglttN". COPYRIGHT DEPOSrr. Faugh an s Carding Lessons 4* "For the Mill Boy 4? PRICE POSTPAID $1.23 Per Copy f|? BY M. H. VAUGHAN Huntsville, Ala. 1905 5? i/i.' ^"^ Two Copies rieCSivej JUN 13 J ^05 QuuyriKiit ^.iiry Copyright I go 5 MAT HIS H. FAUGH AN ^ il o5iL CONTENTS PAGE Chapter 1.— The first principles in, mechanical arithmetic as applied to belts and pulleys 2 Chapter 2. —The first principles in mechanical arithmetic as applied to gears and worm gears 3 Chapter 3.— A combination of gears, pulleys and belts. . . 4 Chapter 4. —Belts and pulleys as applied to line shafting and picker beater pulley 7 Chapter 5.— Finding the length of the lap and the draft of the picker 11 Chapter 6. —Getting the speed of card comb from the line shafting, also the speed of the doff er and licker-in 14 Chapter 7. — The draft and draft constant, also production of the card 17 Chapter 8. — Speed production draft and draft constant, with other calculations on the drawing frame 19 Chapter 9. — Drafts between all of the bottom rollers on the drawing frame 22 Chapter 10. — Hank roving; how it is figured by the card drawing sliver, also roving 24 Chapter 11.— Speed of slubber shaft spindle and draft. Twist constant, also other calculations on the slubber 26 Chapter 12. — Intermediate twist constant, production of one spindle, also production of a number of frames. The tension gear and the rule to get the number of coils per inch for hank roving 29 Chapter 13.— Draft constant on the fine roving frame, also twist constant, and many other calculations 32 Chapter 14. — What one tooth change at any preceding process will effect the hank roving of the fine frame frame 34 Chapter 15. — How to figure the weight of lap to produce a certain hank roving at the fine frame, also the weight per yard at any process to produce any hank roving 37 Chapter 16.— Care of the card licker-in 42 PREFACE After writing for several years for different textile papers on calculations in the carding room, I have written a series of articles on calculations for the mill boy whose educational facilities are limited. Knowing the value of such information from my own experience as a mill boy I have decided to put them in book form. I have made every effort to make this work so simple that with a knowledge of the four ground rules of arithmetic most all of the problems can be solved. The repetition of the draft and the twist constant is intended to make them more simple for the learner. M. H. VAUGHAN Huntsville, Ala., Oct. 31, 1904. CHAPTER I. The first principles ii\ mechanical aLrithmetic as applied to belts and pulleys. In the figure given below, A represents a pulley on the main line of shafting, B is a pulley on the countershaft. A is 36 inches in diameter, B is 18. If the pulley A makes 250 revolutions per minute, how many revolutions will B make? A boy in his first conception of figuring speed of pulleys is naturally inclined to the idea that the circumference of the pulley A should be multiplied by its revolutions, and this product divided by the circumference of the counter pulley B. This would give the revolutions correctly, but for prac- tical purposes we take the diameter instead of the circum- ference. Multiply the diameter of A, which is 36 inches, by 250 revolutions of A. 36X250=9000. Divide this product by the diameter of B, which is 18 inches. 9000--18^500. revolutions of the counter pulley. Putting B on main line and A on the counter will make B the driver and A the driven. Then if B makes 250 revolutions, what will A make per minute? Multiply diameter of B by the revolutions of main shaft. 250X18=4500. VAUGHAN'S CARDING LESSONS Divide this product by 36, the diameter of A, 4500^36=125, the revolutions of the counter shaft. If we have a pulley on main shaft 36 inches in diameter making 250 revolutions per minute and wish the counter shaft to make 400 revolutions per minute, what diameter of pulley will be required on the counter shaft? Multiply rev- olutions of main shaft by the diameter, 36 inches. 250X-'^6=9000. Divide this product by the revolutions we wish the counter shaft to make per minute, 9000--400r=22.5 diameter in inches of the pulley required. If we have a pul- ley 30 inches in diameter on the counter shaft which we wish to make 160 revolutions per minute, what diameter of pul- ley will be required on the main line, which makes 250 rev- olutions per minute ? Multiply the revolutions of the counter shaft by the diameter of the pulley, 30X160=4800. Divide this product by the revolutions of main shaft, 4800^-250=19.2, diameter in inches of the pulley required on main line. If the 36 inch pulley on main shaft makes 250 revolutions per minute, how many feet will the belt travel in the same time ? In this case we shall have to get the circumference of the 36 inch diameter pulley. The rule for this is to multiply the diameter of the pulley by 3.1416, which is the constant for figuring the circumference by the diameter and has four figures to the right hand of the decimal point. We get the circumferance as follows: Multiply 3.1416X36=113.0976 inches around the pulley. Multiply this product by the rev- olutions per minute of the pulley, 250X113.0976=28274.4 inches of travel; divide this product bj^ 12 and the quo- tient will be feet. 28274.4^12=2356.2. Knowing the circumference of a pulley we find the diam- eter by dividing by the 3.1416. Take the circumference. 113.0976--3.1416=36 inches in diameter. VAUGHAN'S CARDING LESSONS Now add two more pulleys to the first. In the following example A is on the main line of shafting, B and C are on the same counter shaft and D is on a counter shaft. A and C are drivers, B and D are driven. A is 24, B is 15, C 23 and D 8 inches in diameter. If A makes 250 revolutions per minute, what will D make in the same time'? To show the principle of figuring this example, we will work it by the single rule of three. Multiply A by the revolutions of main line, 250X24=6000. divide this product by B, 6000-^15=400. revolutions counter shaft. Multiply this by the pulley C, which is 23 inches in diameter, 400X23=9200. Divide by the pulley D, 8 inches in diameter, 9200--8=llo0, revolutions of pulley D per minute. The rule for these examples is, multiply the revolutions of main shaft per minute and all the drivers together for a dividend and all of the driven for a divisor, as follows: 250X24X23=138000, then 15X8=120, and 138000--J 20=1150 revolutions of pulley D. Then the statement should be : 250X24X23 =1150. 15X8 VAUGHAN'S CARDING LESSONS CHAPTER II. The first prmciples in mecKanicad aLfithmetic as applied to gears and worm gears. A is a gear wheel on a shaft making 160 revolutions pei minute and has 44 teeth, and B has 26 teeth. How many revolutions will B make in the same time? A is a driver and B a driven. Multiply the number of teeth in A by the revolutions and divide this product by the number of teeth in B. 160X44=7040. 7040-f-26=270.76 revolutions per minute of B. If B is a driver and makes 250 revolutions per minute, what will A make ? Multiply B by its revolutions and divide this product by A. 250X26=6500. 6500-^-44=147.72, revolutions of gear A. If A makes 175 revolutions per minute and has 44 teeth and we wish to make 220 revolutions in the same time, how many teeth will be required in B? 175X44=7700. Divide this by revolutions of B. 7700-=-220=35 teeth required in B. Gear wheels are figured the same as pulleys, except we take the number of teeth instead of the diameter. In the next train of gears, intermediate or carrier gears like B that merely transmit the power from A to C are not considered in figuring the speed. If A makes 150 revolutions per minute, what will C make in the same time? Multiply the number of teeth in A by its revolutions. VAUGHAN'S CARDING LESSONS 150X42=6300. Divide this product by teeth in C. 6300-5-24= 262,5, revolutions of C. If C makes 180 revolutions per minute, what will A make ? 180X24=4320. 4320-^-42=102.85. Will now add two more gears to the first example. If the power is applied to A, A and C are drivers and B and D are driven, but if the power is applied to D then D and B are drivers and C and A are driven. A is a driver and makes 250 revolutions per minute, what will D make in the same time 1 Mutliply the number of teeth in all of the drivers, together with the revolutions of A for a dividend. 200X80X70=1120000. Multiply the number of teeth in all of the driven together for a divisor, 40X24=960. VAUGHAN'S CARDING I^HSSONS then divide the product of the drivers by the driven. 1120000^960=1166.66 revolutions of D per minute. This example should be stated and worked out as follows: 200X80X70 =1166.66. 40X24 We sometimes have an example to work out like the fol- lowing. In this case A is a driver, B and C are intenned- iate carriers used to transmit the power from A to D and are not taken into account in figuring the speed of D from A; and in this example we only take the number of teeth in D as follows: A is a driver and makes 175 revolutions per minute. What will D make in the same time ? 175X24 =105 revolutions of D. 40 We will make D a driver which will make 120 revolutions per minute. What will A make in the same time ? 120X40 =200 revolutiona of A. 24 If A has 24 teeth and makes 240 revolutions per minute and we wish D to make 180 in the same time, how many teeth will be required in D ? 240X24 =32. 180 It happens frequently that we have worm gears to figure. A is a worm, B the worm gear and C is a counter gear. If A makes 308 revolutions per minute, what will C makef In the statement of this example, if the worm is single thread- ed put 1 in its place, or if double put 2 in its place. In this example the worm is single. VAUGHAN'S CARDING LESSONS ^ORM 308X1 ^=14, revolutions of C. 22 If A makes 440 revolutions per minute, what will B make ! 440X1 ■3=15, revolutions of B, 36 If A is double threaded and makes 216 revolutions per minute, what will B make? 216X2 =12, revolutions of B. 36 The rule is, divide the revolutions of the worm, if single- threaded, by the number of teeth in the worm gear. If double, multiply the revolutions of the worm by 2 and divide this product by the number of teeth in worm gear. CHAPTER III A combination of belts, pulleys aivd gears. This example is a combination of belt pulleys and gears. A is a 36-inch diameter pulley on the main line of shafting which revolves 350 times per minute. How many revo- lutions will gear D with 42 teeth make in the same time "? VAUGHAN'S CARDING IvESSONS A is a driver, B is driven 24 inches in diameter, C is a driver with 18 teeth and D is a driven with 42 teeth. Example: 350X36X18 -=225. 42X24 Suppose D 42 teeth to be a driver which makes 160 revo- lutions per minute, what will A make ? Example: 160X42X24 =248.88. 36X18 If the line of shafting makes 350 revolutions at A and we wish the gear D to make 180, what diameter of pulley will be required at A? In this case D is a driver, so we put the revolutions of line shaft in place of A in the example, as follows : VAUGHAN'S CARDING LESSONS 180X42X24 =28.8. 350X18 To show the principle of the solution we will solve it by the single rule of three and make D a driver. Multiply the number of teeth in D by its revolutions per minute, which is 180. 180X42=7560. Divide this product by C, which has 18 teeth. 7560-j-18=420. revolutions of pulley B. Next multiply pulley B, which is 24 inches in diameter, by its revolutions per minute which is 420. 420X24=10080. Divide this product by the revolutions of the line shafting, which is 350. 10080h-350=28.8, diameter of pulley required on main line. The rule to solve these examples is the double rule of three, and the statement should be made by cause and effect. In the first example in this article pulley A on the main line of shafting is the prime driver, or where the power is first applied. The revolutions of this pulley is a cause, the diameter is a cause and pulley B is an effect. Gear C is a cause and gear D is an effect. If the power is first applied to B and C, then they become drivers and B is a cause and C is a cause, then A is an effect and so is D. I mention the cause and effect because the learner will more readily under- stand which terms to place in the dividend and the divisor. In making the statement of the example we should know that all of the drivers are causes and the driven are the effects of the drivers either in a train of belts and pulleys or gears. The revolutions of the main driving pulley is in all cases a cause and so is the diameter of this pulley. And to make the statement more plain will say that the rev- olutions of A is the first cause, the diameter of A is the sec- ond cause and gear C the third cause. Then pulley B will be the first effect and D the second effect. In making the statement draw a horizontal line and place the causes above and effects below the line, thus: Causes, 350X36X18 Effects, 42X24 10 VAUGHAN'S CARDING LESSONS CHAPTER IV. Belts and pulleys as applied to line shafting a^nd picker beater pulley. The three preceding lessons given cover the ground rules for figuring all pulleys and speeds in the mill, and the mill boys who have learned all of the rules and have become fa- miliar with the solution of the examples are now prepared to go with us into the picker room where the next lesson will be given by solving several speed and pulley examples. A is the driving pulley on main line shaft, which makes 240 revolutions per minute, C and B are on the counter shaft of the picker and D is the beater pulley. The diameter of each pulley is marked in inches. What speed will the beater run? 240X40X36 ^1440 revolutions of beater per minute. 24X10 Suppose we wish the beater to make 1,400 revolutions per minute, what diameter of pulley will be required at A? 1400X10X24 =38.88, diameter of pulley at A. 36X240 In this example the beater pulley D becomes a driver. The learner must not become confused because in the first ex- ample the beater pulley is a driven and in this one it is a VAUGHAN'S CARDING LESSONS 11 driver, for if we get the revolutions per minute of the count- er shaft on which B and C are fixed, and figure from C to D, C is a driver and D is a driven, or if we figure from B to A, B is a driver and A is a driven. In this case B and C are both drivers. In the last example we know the revolutions of the beater to be 1,400 and start from this point. Remember that the pulley from which we start to figure the revolutions becomes the first cause and its diameter the second cause, which makes it a driver. It makes no difference whether we figure from the main line or from the beater pulley. For instance, take the first example and find the revolutions of the beater, knowing the main line to make 240 per minute. 240X40X36 =1440 revolutions of beater. 24X10 On the other hand, knowing the revolutions of the beater we make it a driver and find the revolutions per minute of the main line.. 1440X10X24 =240 revolutions of main line shaft. 36X40 On the beater shaft there is a fan pulley 5 inches in diameter, and on the fan shaft is one 8 inches and the line shaft makes 240, what will the fan make per minute ? 240X40X36X5 r900. 24X10X8 If it is desired to run the beater at 1,200 revolutions per minute instead of 1,440 by making the beater pulley larger, what diameter will be required with the conditions the same as in the first example? 240X40X36 =12 inches diameter of pulley. 24X1200 If one picker with a 5-inch diameter feed pulley keeps laps for 11 cards and we add one more card, what diameter of feed pulley will be required for the 12 cards f 5X12 =-5.45 inches diameter. 11 If one picker keeps laps for 12 cards with a 6-inch feed 12 VAUGHAN'S CARDING LESSONS pulley and we wish to cut down the feed so it will keep up for 10 cards, what diameter of feed pulley will be re- quired ? 6X10 =5 inch feed pulley. 12 CHAPTER V. Fiading the length of the la^p aivd the draft of the picker. Will figure the length of the lap from gears on the Kitson picker each having the following number of teeth: Knock- off gear 60, knock-off driver 18, worm gear 35, worm No. 1 calender gear 80, drop shaft gear 13, opposite end of drop shaft 14, large lap roller driver 73, small driver 18, lap roller gear 37, diameter of lap roller 9 inches. Example : 60X35X80X14X18 =66.98 revolutions of lap roller. 18X 1X13X73X37 Multiply this product by the circumference in inches of the 9-inch lap roller, which is 28.27 inches. 66.98X28.27=1893.52. Divide this product by 36 inches and the quotient will be yards in the length. 1893.52^36=52.59 In rolling the lap up under the heavy pressure it stretches the lap and it will be longer than it figures. To make up for this we add 4 per cent, to the figured length which will be 2.10+52.59=54.69 yds., length of lap. If a 60-tooth knock-ff gear gives 54.69 yards, what num- ber will be required to give 48 yards ? 60X48 r=52.47 teeth. 54.69 Will figure the draft of the picker from the following gears and diameters: (1) (2) (3) (4) 9X14X39X85X3XX54X30X14X14X18 37X73X76X24X40X10^1X20X26X1.81 (5) (6) (7) (8) (9) Performing these operations of multiplication and divis- VAUGHAN'S CARDING LESSONS 13 ion we obtain for a result 4.18 draft. The figures above and below the fraction are explained as follows: 1. Diameter of lap calender, 2. Worm Gear. 3. Diameter of cone. 4. Feed roller gear. 5. Lap calender gear. 6. Draft gear. i 7. Diameter of cone drum, ' 8. Worm, 9. Diameter of feed Roller. These gears and diameters are taken direct from the pick- er as it is made at present. In figuring the draft of any ma- chine, if the feed or back roller and front or lap calender were of the same diameter we should leave them out of the calculation. The learner will get confused as to where to put the diameter of these two rollers in the example. On the picker the front roller is larger than the back and in this case the larger the front and smaller the back roller the more draft it gives. Therefore we put front roller diameter in the dividend and the back roller in the divisor. If the rollers were reversed so as to have the larger one in the back this would make a less draft. Then we should place the diam- eter of the two rollers in the example the same way as men- tioned above, but most machines in the cotton mill have the front roller larger than the back one. In figuring for the draft constant, we take the above ex- ample and leave out the draft gear, which has 24 teeth. A short way to get the draft on the picker is to get the revo- lutions per minute of the feed and lap calender rollers. Multiply each diameter by its revolutions and divide the larger by the smaller product, as follows: Diameter of feed roller 1.81 inches, revolutions per minute 7, diameter lap calender 9 inches, revolutions 5.89. 1 .81X7=12.67. 9X5.89=53.01. This product. 53.01-^12.67=4.183, draft. There is another way to get the draft. If there are 4 laps on the feed apron, get the ounces per yard of one, multiply the ounces in one yard by four, and divide by the ounces per yard of the finished lap. Any of these methods are near enough for practical purposes. 14 VAUGHAN^S CARDING LESSONS CHAPTER VI. Getting the speed of card comb from the line shaft- iti^, also speed of the doffer and Hcker-in. A is a pulley on line shaft making 275 revolutions and 12 inches in diameter. B is a pulley 20 inches in diameter on the card cylinder shaft. If line shaft makes 275 revolutions per minute what will the cylinder make in the same time? Example : 275X12 ^165, revolutions of cylinder. 20 If A makes 275, what will D make in the same time? Example : 275X12X18 =495, revolutions of pulley D. 20X6 VAUGHAN'S CARDING I.ESSONS 15 If A makes 275, what will F make in the same time? Example : 275X12X18X12 -1485 revolutions of F, 20X6X4 A is on the line shaft, B is a pulley on card cylinder shaft, D and E are doffer comb pulleys, and binder F is a comb pulley. In practice where the V-grooved pulleys and the round bands are used, one diameter of the band should be added to the diameter of each pulley as the center of the band governs the speed of the pulleys. Will figure the speed of the doffer from main line from the following pul- leys and gears: Line shaft 275 revolutions per minute, di- ameter of pulley on line shaft 12 inches, pulley on card cylinder 20 inches, licker-in driver on cylinder shaft 18 inches, licker-in pulley 7 inches, barrow pulley driver on licker-in 4 inches, barrow pulley 18 inches, doffer change gear 28 teeth, doffer gear 214 teeth. Example: 275X12X18X4X23 :=12.38 20X7X18X214 Find the constant divisor from the following: Doffer gear 214 teeth, leave out the doffer change gear, barrow pulley 18 inches, small pulley on licker-in 4 inches, large pulley on same 7 inches, cylinder pulley 18 inches, revolutions of cylinder 165. Example : 214X18X7 ^2.269 165X18X4 Dividing the number of teeth in the doffer change gear by 2.269 will give the revolutions of the doffer per ininute. How many revolutions per minute will a 28-tooth gear give the doffer? Example: 28.000^2.269^12.33 revolutions of the doffer per minute. If a 28-tooth doffer change gear gives 12.33 revolutions per minute, what will 30 give ? Example : 12.33X30 =13.21 revolutions of doffer. 28 If a 30-tooth gear gives 13.21 revolutions per minute, what will 22 teeth give*? Example: 16 VAUGHAN'S CARDING LESSONS 13.21X22 =9.68 revolutions 30 If the cylinder makes 165 revolutions per minute and the doffer makes 12 revolutions per minute, how many inches of cylinder surface will pass one inch of doffer surface, the cylinder being 50 inches and doffer 27 inches in diameter? We first get the circumference of cylinder, 157 inches, and doffer, 84.8 inches, and multiply the circumference of each by its revolutions per minute. Cylinder 157X165=25905. Doffer 12X84.8=1017.6 inches of surface speed. Take surface speed of the doffer from the cylinder, 25905—1017.6=24887.4, pud divide this product by the surface speed of the doffer, 24887.4 =24.45, 1017.6 the number of inches of cylinder surface that would pass one inch of doffer surface. If the doffer makes 12 revolutions per minute, what will the feed roller make in the same time with the following gears, — gear on doffer pulley 45 teeth, gear on side shaft doffer end 40, draft gear 20, feed roller gear 120 teeth? Example : 12X45X20 -=2.25 revolutions feed 40X120 If cylinder makes 165 revolutions per minute, what will the licker-in make in the same time with the following pul- leys, — cylinder pulley 18 inches, licker-in pulley 7 inches in diameter? 165X18 =424.2 revolutions of licker-in. 7 With the licker-in making 424.2 and the feed roller 2.25 revolutions per minute, how many inches of licker-in surface will pass one inch of feed roller surface? The licker-in is 9 inches and feed roller 2.25 inches in diameter, circum- ference of licker-in 28.27 inches, circumference of feed rol- ler 7.06 inches. Multiply each circumference by its revo- lutions. VAUGHAN'S CARDING LESSONS 17 Licker-in 28.27X424.2=11992.13 inches of surface. Speed of licker-in 2.25X7.06=15.88 inches of surface speed of roller. Divide licker-in surface speed by the feed roller speed. 11992.13 =755.17. 15.88 The quotient is the number of inches of licker-in surface that would pass on one inch of stock delivered. CHAPTER Vll. The dr^Lft ^nd droAt coAstaLi\t, also production of the card. Get the draft of the card from the following gears. The card is the Pettee make with the twenty-seven inch diameter doffer, coiled calender roller 2 inches diameter, feed roller bevel gear 120 teeth, gear on side shaft doffer end 40 teeth, doffer gear 214 teeth, gear on card calender roller driver coiler 27 teeth, feed roller diameter 2.25 inches, draft gear 20 teeth, gear on doffer pulley 45, card calender roller gear 21 teeth, gear on coiler upright shaft 17 teeth. Example : 2X120X40X214X27 =76.73 draft 2.25X20X45X21X17 Get the draft constant with the same conditions as the last example with the draft gear left out 2X120X40X214X27 =1534.56 draft constant. 2.25XXX45X21X17 Divide the constant by the number of teeth in the draft gear, the quotient will be the draft of the card; or divide the constant by the draft of the card and the quotient will be the number of teeth in the draft gear. What is the production of the card with doffer making 12 revolutions per minute and the sliver weighing 50 grains per yard? First get the revolutions of the coiler calender roller by the following gears: Revolutions of doffer 12, doffer gear 214, card calender roller 21 teeth, card calender roller that drives coiler 23 teeth, gear on coiler upright shaft 17 teeth, gear on top upright coiler shaft 21 teeth, coiler 18 VAUGHAN'S CARDING LESSONS calender gear 18 teeth, diameter of coiler calender roller 2 inches. Example : 12X214X23X21 :193 revolutions of 21X17X18 calender roller per minute. The circumferance of the roller is 6.28 inches. Multiply this by the revolutions per minute 193X6.28=1212 inches of sliver delivered per minute. Multiply this by 60 minutes, 1212X60^=72720 inches in one hour. Divide this by 36 inches in a yard. 72720^36=2020 yards per hour. Multiply yards per hour by 50 grains sliver. 2020X50=101,000 grains. Divide this by 7,000 grains in a pound. 101,000^7000=14.42 lbs. per hour. Multiply by 11 hours, 14.42X11=158.62 pounds per day, nothing deducted for stoppage. A short way to get the production of a card is to multi- ply the revolutions of the doffer per minute by the weight in grains of one yard of card silver, for the 24 inches di- ameter of doffer divide by 5.49 and for the 27 inch diameter by 4.57, which will come near enough for all practical pur- poses. Will take a 24 inch doffer making 12 revolutions per minute with a sliver weighing 60 grains. 12X60 =131.14 lbs. per day. 5.45 Or take 27 inch doffer making 13 revolutions per minute and a 54 grain sliver. 13X54 =153.61 lbs. per day. 4.57 If one yard of lap weighs 12 ounces and one yard of dof- fer sliver weighs 50 grains, what draft has the card? One ounce contains 437.5 grains 437.5X12=5250 grains. Divide by the 50 grains sliver. 5250^50=105, draft of card. There is nothing allowed for waste. If the lap weighs 12 VAUGHAN'S CARDING I.BSSONS 19 ounces per yard and the draft of the card is 85, what will the sliver weigh in grains ? 437.5X12=5250. Divide this by the draft of the card 5250--85=61.76. grains per yard of sliver. If the card has a draft of 95 and the card sliver weighs 54 grains, what weight of lap per yard will be required? Multiply the weight of sliver in grains by the card draft and divide by the grains in one ounce. 54X95=5130.0-^437.5=11.72 ozs. per yard of lap. CHAPTER VIIL Speed production, dra.ft, a^nd draft constdLivt, with other calculations on the drawing frame. On the line shaft is a pulley 11 inches in diameter making 280 revolutions per minute, on the main drawing shaft is a pulley sixteen inches in diameter, the pulley on the same shaft that drives the front roller is 16 inches in diameter and on the front roller is a pulley 10 inches in diameter. What speed will the front roller make per minute? Ex- ample : 280X11X16 =308. 16X10 If the front roller makes 308 revolutions per minute, what will the production be per day with 54 grains per yard of drawing sliver? We get the revolutions of coiler calender roller which is two inches in diameter, gear on front roller 20 teeth, coiler shaft 31 teeth, bevel gear on coiler shaft 18 teeth, gear on upright 16 teeth, and the gears on top of up- right shaft and coiler calender have the same number of teeth. Example : 208X20X18 =223.5 revolutions of coiler calender per minute. 31X16 The circumferance of calender roll is 6.28 inches. Multi- ply this by the revolutions. 223.5X6.28=1403.58 inches per minute. 20 VAUGHAN'S CARDING LESSONS Multiply this by 60 minutes. 1403.58X60=84214.8. Divide this by 36 inches. 84214.8-^36=2339.3 yds. delivered per hour. Multiply yards per hour by 54 grains in one yard of sliver. 2339.3X54=126322.2. Divide by 7,000 grains. 126322.2^7000=18.046 pounds per hour. Multiply pounds per hour by 11. 18.046X11=203 lbs. per day for one delivery of drawing. There should be about 20 per cent, deducted from the fig- ured pounds for stoppage. Find draft of the drawing from the following: Back roller gear 60 teeth, crown gear 100, gear on front roller 20, bevel gear on side shaft 18, bevel gear on top coiler upright 16, diameter of coiler 2 inches, draft change gear 45 teeth, gear on end of front roller 24, gear on end side shaft 32, bevel gear on bottom of coiler upright 16, bevel gear on coiler calender 16, diameter of back roller 1%. Change the diameter of the rollers to eighths of an inch which would be, back roller ll-8ths, cal- ender roller 16-8ths. Example: 60X100X20X18X16X16 =5.68 draft. 45X24X32X16X16X11 To get the draft constant we will use the same example as the above with the draft gear left out. Example : 60X100X20X18X16X16 =255.68 draft constant. 24X32X16X16X11 Divide the constant by the draft and the quotient will be the number of teeth in draft gear required; or divide by he teeth in the gear and the result will be the draft of the drawing. If the drawing sliver weighs 60 grains per yard with a 48 draft gear and we wish the sliver to weigh 54 grains, what draft gear will be required? 54X48 =43.2. 60 If 45 draft gear makes sliver that weighs 50 grains per yard, what will 48-tooth draft gear make it weigh? VAUGHAN'S CARDING LESSONS 21 50X48 =53.33. 45 If there are six slivers up on the back of drawing with a 44 draft gear on and we wish to take out one and have but five, and want the front sliver to weigh the same, what draft gear will be required? 44X6 =52.8 draft gear. 5 If the sliver from the coiler weighs 54 grains and the draft 5.5, what weight will be required per yard of each of the six slivers on the back? 54X5.5 =49.5 wt. of sliver on back. 6 If one yard of sliver on the back weighs 60 grains wdth six double and the drawing has a draft of 6.5, what will the sliver weigh per yard at the coiler? 60X6 =55.38. 6.5 22 VAUGHAN'S CARDING LESSONS CHAPTER IX. DrdLfts between 8^11 of the bottom rollers on the draiwing fraLme. The above cut represents the four bottom rollers of the drawing frame with the diameter of the rollers and the number of teeth in each gear marked on them. They are taken from the catalogue and the diagram is given in order to figure the draft between each set of rollers. First get draft of the front and second roller. Example; 32X37X11 =-2.584. 20X28X9 Next get the draft between second and third. This is quite a long example as we figure from the third roller around through the draft gear to the second, and as each roller has the same diameter, leave them out of the example. 20X24X60X100X20X28 =1.732 draft. 28X26X45X24X37X32 Get the draft between third and back roller. 26X28X9 =1.240. 20X24X11 VAUGHAN'S CARDING LESSONS 23 These three different drafts if run far enough into frac- tions should get the draft of the drawing when multiplied together. 2.584X1.732X1.240=5.5496 draft. Wlill figure the draft from the front to the back roller. These rollers have the same diameter, so leave them out of the example and figure the gears only. Example: 100X60 i5.555. 24X45 If we were to run the fractions till there would be no re- mainder the draft in the two examples would be the same. Figure the draft between the front roller and the coiler calender from the following gears and diameters: Front roller 1% inches, diameter front roller gear 17 teeth, coiler shaft driver 31, gear on coiler shaft 18, gear on bottom of upright shaft 16, gear on top upright and calender have the same number of teeth, diameter of coiler calender 2 inches. 17X18X16 =1.025 draft. 31X14X11 If a 30-tooth gear is put on side coiler shaft instead of the 31, what draft will this give between the front and coiler calender rollers? 17X18X16 =1.059. 30X14X11 If the card sliver weighs 60 grains per yard and the first drawing doubled 6 times and the second 5 times, and we wish the finish drawing sliver to weigh 54 grains and wish each process to have the same draft, what will be the draft ? Mul- tiply the doublings at each back together, 6X5=30. Multiply this product by 60 grains, 30X60=1800. Divide last result by 54 grains, 1800^54=33.33. Extract the square root of the last result: The square root of 33.33=5.773, draft oi each drawing frame. Will see how this example 24 VAUGHAN'S CARDING LESSONS proves out. If the card sliver weights 60 grains, double 6 into 1, draft 5.773, multiply sliver by doublings, 60X6^=360. Divide by draft, 360^5.773=62.359 grains per yard from first drawing. Multiply this by doubling at back of second drawing, 62.359X5=311.795 Divide by draft, 311.795--5.773=54 weight of sliver from second drawing. As the next calculations will be on roving frames, the next lesson will be on hank roving. CHAPTER X. Hank roving; Kow it is figured by the card and drawing sliver, also roving. In cotton mill parlance, eight hundred and forty yards is denominated one hank, whether it be lap, card or drawing sliver, slubber or fine frame roving, or yarns, and the num- ber is fixed by the weight of one hank. If one hank weighs two pounds, it is one-half hank; if one pound, one hank, and if one-half pound, it is two hank. If twenty hanks of yarn weigh one pound, it is No. 20 yarn. Seven thousand grains make one pound avoirdupois weight, or is called one cotton pound. Divide 7,000 grains by 840 yards and it will give 8 1-3 grains per yard for one-hank roving or yarn, and the weight in grains of one yard of one-hank roving or yarn form the basis for calculating all*hank sliver, roving or yarn. It is not practical to reel off one hank of sliver or roving, but more convenient to take so many yards, twelve yards from each (this is the standard given by most books and catalogues in the tables for numbering roving), from four to eight bobbins and reel twelve yards from each and weigh each separately and add the weights together and the yards cf each together. The rule to find the hank is to multiply the number of yards of the several weighings by 8 1-3 for VAUGHAN'S CARDING LESSONS 25 a dividervd, and take the grains of the several weighings added together for a divisor and the quotient will be the hank. Take four slubber bobbins and reel 12 yards from Bach. The first 12 yards weigh 202, the second 198, third 199, fourth 201, what will be the hank roving? Example: 12X4=48 yards Multiply the yards by grains per yard. 81^X48=400, dividend Add the gi-ains of each weighing. Example: 202-1-198+199+201=800, divisor Example: 400-^800=. 50 hank roving which is one-half hank. Take 12 yards of slub- ber roving which weigh 180 grains, what hank is it? Ex- amx)le : 12X8 1^=100-^180=. 555 hank Take four bobbins of intermediate roving and reel 12 yards which weigh as follows in grains: 85+88+84+86=343 grains. Yards, 12X4=48X8^=400-^343=1.166 hank. For 12 yards 100 is the constant dividend and for every 12 yards added add one hundred to the dividend. If 48 yards of roving weigh 130 grains, what will it hank? Ex- ample : 48X8^=400^130=3 07. Where four bobbins are used to weigh from and 12 yards are taken from each the multiplication by 8 1-3 can be dis- pensed with by using 400 for the dividend; or if eight bob- bins are used 800 will be the dividend. If 12 yards from each of eight bobbins weigh 560 grains, what will it hank? 800-^560=1.42 hank. If one yard of drawing sliver weighs 60 grains, what hank is it? Example: 8>^-r-60=.138 hank If one yard of card sliver weighs 52 grains, what will be the hank? Example: 8>^--52=.160. If four yards of card sliver weigh 220 grains, what will it hank ? Example : 26 VAUGHAN'S CARDING LESSONS 4X8K=33>^^220=.151 hank. If three-hank is wanted from fine frame, what hank will be required of two into one at the back with a draft of six? Example : 3-^6=.50X2=1.00 one hank. Divide the draft by the hank and multiply the quotient by the doublings at the back. Take one-hank roving in the back with two into one and a draft of five, what will be the hank from fine frame? Example: 1.00^-2=50X5.5=2.75 hank. In this case divide by the doublings at the back and multi- ply by the draft and the quotient will be the hank roving produced. If we have .60-hank at the back of the interme- diate and two into one, what draft will it take to produce 1.20 hank? Example: 1.20 .60-^2=.30 =4 draft. .30 If we have on the backs of the intermediate 48-hank and two into one and a draft of five, what hank will be produced ? Example : .48-^2=.24X5=1.20 hank. If one yard of drawing sliver weighs 60 gains, what hank is it? Example: 8K--60=.138 hank. If at the back of the slubber we have .138-hank sliver, single, what hank roving will be produced with a draft of four ? Example : .138X4- .552 hank roving. The expression should be 552 hank 1000 CHAPTER XL Speed of slubber shaft, spmdie, and draft. Twist constant, also other calculations on the slubber The main line of shafting makes 290 revolutions per minute with a pulley 15 inches in diamter, which drives the main shaft of a slubber having a pulley 16 inches in VAUGHAN'S CARDING IvKSSONS 27 diameter; how many revolutions will slubber shaft make per minute? Example: 290X15 =271.8 revolutions slubber shaft. 16 If the main line makes 290 revolutions per minute, what will the spindle make with the following pulleys and gears: Main shaft pulley 15 in., pulley on slubber shaft 16 in., gear on main slubber shaft 50 teeth, gear on end of spindle shaft 46 teeth, gear on spindle shaft 55 teeth, gear on spindle 27 teeth ? Example : 290X15X50X55 =601.77 revs, of spindle. 16X46X27 If the slubber is on one-half hank roving, requiring a 59 twist gear and the spindle making 602 revolutions per min-^ ute, what will the front roller run from the following gears: Spindle gear 27 teeth, spindle shaft gear 55 teeth, gear on end of spindle shaft 46 teeth, gear on main shaft 50 teeth, twist gear 59 teeth, gear on top cone shaft 46 teeth, gear on cone shaft inside of head 71 teeth, front roller gear 130 teeth ? Example : 602X27X46X59X71 =190.45 55X50X46X130 With the front roller making 190 revolutions per minute, what v/ill the back roller make in the same time with the following gears: Front roller gear 33 teeth, gear on stud 100 teeth, draft gear 50 teeth, back roller gear 56 teeth? Example : 190X33X50 =:55.96 revolutions of back roller. 100X56 The front roller is 19-16 inches in diameter and makes 190 revolutions, and the back roller is 1 inch in diameter and makes 55.96 revolutions, what draft will this give? Ex- ample : 190X19 =4.030 draft. 55.96X16 We will see how this will figure out by the rule to get the draft. Example : 28 VAUGHAN'S CARDING LESSONS 100X56X19 =4.030 draft. 83X50X16 Rule : Multiply all of the drivens together with the diam- eter of front roller for a dividend, and all of the drivers with diameter of back roller for a divisor. The draft con- stant is figured by the same example with the draft gear left out. Example: 100X56X19 =201.515 constant. 33X0X16 Divide the constant by the draft desired and the quotient will be the number of teeth in draft gear, or divide by number of teeth in gear and the quotient will be the draft. How many turns will the spindle make to one of the front roller with the following gears : Front roller gear 130 teeth, cone shaft 71 teeth, center cone shaft 46 teeth, twist gear 59 teeth, gear on main shaft 50 teeth, gear on end spindle shaft 46 teeth, gear on spindle shaft 55 teeth, gear on spin- dle 27 teeth ? Example : 130X46X50X55 =3.1638 turns of spindle to one of roller. 71X59X46X27 To get the turns of twist per inch divide the turns of the spindle to one turn of the front roller by the circumference of the front roller, which is 3.731 inches. Example: 3.1638h-3.731=.847 turns per inch. To get the twist constant will use the above example with the twist gear left out and the circumference of the front roller put in its place. Example : 130X46X50X55 =49.9837, constant. 71X3.731X46X27 Divide constant by number of teeth in twist gear and the quotient will be turns per inch of twist in the roving, or divide by the number of turns of twist desired per inch and the quotient will give number of teeth in the twist gear. In figuring the draft gear to change from one hank to another. Rule: Multiply the number of teeth in draft gear on by the hank roving being made and divide by hank desired and the quotient will be the answer. If a draft gear with 50 teeth gives one-half hank roving^ VAUGHAN'S CARDING IvESSONS 29 what number of teeth will it take to make .60 hank? Ex- ample : 50X50 =^41.6 draft gear .60 Or if a .70 hank requires a 45 draft g«ar, what will .60 hank require? Example: .70X45 =52.5. .60 To find the twist gear when changing from one hank to another. Rule: Square the twist gear on and multiply this product by the hank being made and divide by the hank to be made. Extract the square root of the last product and the quotient will be the number of teeth in twist gear de- sired. One-half hank has a twist gear with 59 teeth, what num- ber of teeth will it take for .60 hank ? Example : 59X59X.50-^.60=V2900=53.5. Another rule is to multiply the gear in use by the square root of the roving being made and divide by the square root of the roving to be made. CHAPTER XII. lAtermediate twist constaivt, production of one spindle, also production of a number of frames. The tension gear and the rule to ^et the number of coils per inch for hank roving. The intermediate roving frames have the same size diam- eter of front and back rollers and the same draft gears, and the draft and draft constants are the same as the slubber. But there is some difference in the number of teeth in the gears from the top cone to the spindle, that makes a dif- ferent twist constant, which is figured by the following gears: Front roller gear 130 teeth, on end of cone shaft gear 71 teeth, gear in center of cone shaft 39 teeth, gear on main shaft 42 teeth, gear on end spindle shaft 35 teeth, gear on spindle shaft 44 teeth, spindle gear 23 teeth, cir- cumference of front roller 3.731 inches. Example: 30 VAUGHAN'S CARDING LESSONS 130X39X42X44 =:43.937, twist const. 71X5.731X35X23 If the spindle makes 746 revolutions per minute, what will the front roller make with a 37 twist gear on, the other gears being as follows: Front roller 130 teeth, gear on end of cone shaft 71 teeth, gear at center of cone shaft 39 teeth, twist gear 37 teeth, gear on main shaft 42 teeth, gear on end of spindle shaft 35 teeth, gear on spindle shaft 44 teeth, spindle gear 23 teeth ^ Example : 746X23X35X37X71 =168.37 rev. of front roller. 44X42X39X130 If the front roller makes 168 revolutions per minute and the roving one hank, how many pounds Tvdll one spindle take o^ in ten hours if it is run without stopping, diameter of roller 1 3-16? Multiply the revolutions of the roller per minute by 60 minutes and by 10 hours and by the circum- ference of the roller. Example: 168X60X10X3.731=376084.8. This product is inches which have been delivered in the ten hours, and we divide by 36 inches, which makes yards, and by 840, which makes hanks. Example: 840X36X30240. Then divide. Example: 376084.8^30240=12.43. Divide this product by the hank roving and the quotient will be pounds. The roving is one hank, which will make 12.43 pounds in ten hours. To get the pounds per day taken off one frame, multiply the number of hanks registered by the indicator by the number of spindles on the frame and divide by the hank roving being made. Take a frame with 68 spindle on 1.25 hank and run 12 hanks per day, what num- ber of pounds will be produced? Example: 68X12 =652.8 pounds. 1.25 Where there are several frames with the same number of spindles and on the same hank roving, take the number of hank run on all the frames and multiply by the number of spindles on one frame and divide by the hank roving made. Take 12 intermediate frames with 92 spindles on each mak- ing 1.40 hank, and all of the hanks from each added to- gether amounts to 132 hanks in one day, what is the produc- tion in pounds'? Example: 132X92 =8674.28 pounds. 1.40 VAUGHAN'S CARDING IvBSvSONS 31 We get the lay gear constant as follows: Multiply the square root of the hank roving being made by the number of teeth in the lay gear in use. What is the lay constant with a 28 lay gear making 1.10 hank roving, the square root of 1.10 hank^ being 1.049? Example: 28X1-049=29.372, lay constant. If we change this frame onto 80 hank what lay gear will be required? Divide the lay constant by the square root of the hank to be made. The square root of .80 hank is .894. Example : 29.372 =32.85 lay gear. .894 The tension gear is figured for the constant the same as the lay. To get the coils per inch to be laid on the bobbin for different hank roving, get the number of coils per inch on one hank that will make the best bobbin of roving, usually 11 or 12. This number of layers per inch on one hank rov- ing forms the basis for figuring the coils per inch for all numbers or hank roving, and from the fact that the coarser the roving the smaller number of layers to the inch. Unlike the twist and lay gear, in which the coarser the roving the larger the gears, we reverse the terms in multiplying and di- viding. Rule: Multiply the coils per inch of the roving being made by the square root of the hank roving to be made and divide by the square root of the hank roving being made. If one hank roving has 11 coils per inch, what will be required for two hank? Example: 11X1.4142 =15.5562 coils per inch. 1.000 If one hank has 10 coils per inch, what will I/2 hank re- quire ? Example : 10X.7071 =7.07 coils for >^ hank. 1.000 If three hank has 17 coils per inch, what should six hank have? Example: 17X2.4494 =24.0414 coils per inch. 1.7320 32 VAUGHAN'S CARDING lyBSSONS CHAPTER XIII. Calculatioas on the Fine Roviag Frame, Which is the Biddeford, 3 1-2 inch Flyer by 8 inch Traverse. The draft gears are the same as the slubber and interme- diate, but the front roller being smaller in diameter, the draft constant is different, and is figured as follows: Gear on front roller 33 teeth, gear on stud 100 teeth, draft leave out, back roller gear 56 teeth. Diameter of front roller 1^/^ or 18-16, back roller 1 inch or 16-16. Example: 18X100X56 =190.909 draft constant. 16X56 The gears and diameter of front roller being different, the twist constant will be different from the coarser frames, and is figured from the following: Gear on front roller 130 teeth, gear on end of top cone shaft 71 teeth, gear on cen- ter of cone shaft 39 teeth, twist gear leave out, gaar on main shaft 53 teeth, gear on end of spindle shaft 33 teeth, gear on spindle shaft 44 teeth, gear on spindle 23 teeth, cir- cumference of front roller 3.534. Example: 130X39X53X44 =62.0826 twist constant. 71X3.534X33X23 Circumference of the front roller is put in the place of twist gear in the above example. If the frame is on two hank roving, what number of coils should be laid to the inch on the bobbin? (See rule given for intermediate frame.) One hank has 11 coils per inch and the square root is 1.000; the square root of two hank is 1.414. Multiply the 11 lay- ers on one hank by the square root of two hank and divide by the square root of the one hank. Example : 11X1-414 =:15.554 layers. 1.000 How many turns of twist per inch should two hank rov- ing have by the standard? Multiply the square root of the hank roving by 1.20; the square root of two hank is 1.414. Example : 1.414X1.20—1.6968 twists per inch. What number of teeth will it take in the twist gear for two hank? Divide twist constant by the number of turns per inch required. Example: 62.0826^1.6968=36.58 twist gear. If the frame is running on two hank roving with 15.5 VAUGHAN'S CARDING IvESSONS 33 layers per inch on the bobbin, 1.69 turns of twist per inch with 37 teeth twist gear, 55 teeth tension gear and a 40 teeth lay gear, what number of layers and twist per inch and number of teeth in each gear will be required for three hank roving*? First get the layers, multiply the square root of three hank by the two hank layers, divide by the square root of two hank. Example: 1.732X15-5 =18.98 layers per in. for 3 hank. 1.414 Second, twist per inch. Multiply square root of thr«e hank by 1.20. Example : 1.732X1-20=2.088 twists per inch. Third, divide twist constant by twist per inch in the three hank for the twist gear. Example: 62.0826-j-2.088=29.73 twist gear. Fourth, multiply lay gear by the square root of the roving being made and divide by the square root of the roving to be made, for the lay gear. Example: 40X1.414 ^=32 lay gear. 1.732 Fifth, the tension gear is figured like the lay gear. Ex- ample : 55X1.414 =44.9 tension gear. 1.732 In changing from one number of roving to any other num- ber the layers, twist per inch and number of teeth in the gears are figured as above and will apply to any of the rov- ing frames. On three hank roving, with the front roller lYs inches in diameter and making 145 revolutions per min- ute, how many hanks will one spindle produce in 10 hours, if the frame runs without stopping? Multiply the revolu- tions per minute of front roller by 60 minutes, by 10 hours, and by the circumference of front roller, and divide this product by 36 inches and 840 yards and the quotient will be hanks. Example: 145X60X10X3.534 =10.16 hanks per day. 36X840 If the frame has 160 spindles and runs ten hanks of three 34 VAUGHAN'S CARDING LESSONS hank roving, what will be the production in pounds'? Ex- ample : 10X160 =533 pounds, 3 Rule: Multiply the number of hanks by the number of spindles on one frame and divide by the hank roving. There are twenty frames of 160 spindles to each frame, all ininning on 2.75 hank roving, and the hanks from all of the frames added together amount to 210. What is the production per day in pounds^ Example: 210X160 =12218 pounds per day. 2.75 Ten per cent, should be deducted from the above pro- ducts for stoppage. CHAPTER XIV. What 03\e tooth cKaLnge at aLivy preceediiv^ process will effect the hank roving on the fine frame. In this case we leave off the weight in grains and hank rov- ing, and figure from the gears, except at the fine frame, we use only the hank roving. For an example, take the fine frame which has a 34 tooth draft gear and making 3 hank roving; the intermediate has 45 teeth draft gear and slubber 60 teeth. Suppose we build up one tooth on the slubber and one tooth on the intermediate. Fiut find what the one tooth on the slubber will change the three hank. Example: 60X3.00 =2.95 hank. 61 Second, find what the one tooth change on the intermediate will change the 2.95 hank on the fine frame. Example: 45X2.95 =2.88 hank, 46 which the two changes will make in the three hank on the fine frame. But after making these two changes we wish to change the draft gear on the fine frame so the roving will remain three hank, which calls for the draft gear on the VAUGHAN'S CARDING LESSONS 35 fine frame in the example, as follows: 34X2.88 =32.64 draft gear. 3.00 Suppose we heavy up two teeth on the draft gear on coarse drawing and change one tooth lighter on the fine drawing, how will these two changes affect the three hank roving on the fine frame? The coarse drawing has on 47 draft gear; put on a 49 gear and find what this will make the three hank. Example : 47X3.00 =2.87 hank. 49 The fine drawing has on 47 draft gear; put on a 46 gear and find what this will change the 2.87 hank on the fine frame. Example : 47X2.87 :2.93 hank. 46 What draft gear will be required on the fine frame to bring the roving back to three hank with a 34 tooth gear on the fine frame. Example: 34X2.93 =33.20 draft gear. 3.00 The rule for figuring a change like the above example is simple and the same as the rule used to figure the same changes on the fine frame, which is, multiply the draft gear on by the hank roving being made and divide by the gear put on whether the change is made on the intermediate, slubber, drawing or card. Where a change is to be made from a certain hank to another hank roving, multiply the hank being made by the draft gear on and divide by the hank to be made. Take the fine frame on three hank and change to four hank by changing the draft gear on the card which has a 20 tooth draft gear on. Example: 3.00X20 =15 draft gear. 4.00 Or say 60 grains card sliver makes three hank roving, how many grains must sliver weigh for four hank? Ex- ample : 36 VAUGHAN'S CARDING LESSONS 60X3.00 r=45 grains. 4.00 If we are making two hank roving with a 14 ounce lap and change to 2.50 hank by making the lap lighter, what ounce lap will be required? Example: 2.00X14 =11.2 oz. per yd. of lap. 2.50 If the intermediate has a 45 tooth draft gear on, the slubber 60, the fine drawing 46, coarse drawing 47 and card draft gear 16 teeth, and we change one tooth heavy at each process, how will these changes affect three hank roving on the fine roving frame? First, the intermediate has 45 and we put on 46 tooth draft gear. Example: 45X3.00 =2.93 hank. 46 The slubber has 60; put on 61 draft gear and find how much this will change the 2.93 hank. Example: 60X2.93 hank. 61 The drawing has 46 teeth; put on a 47 tooth draft gear. Find what this will change the 2.88 hank. Example: 46X2.88 =2.818. 47 The coarse drawing has 47; put on a 48 draft gear and see what this will change the 2.818 hank. Example: 47X2.818 i2.755 hank. 48 The card draft gear has 16 teeth; put on a 17 tooth gear and find what it will change the 2.755 hank on the fine frame. Example : 16X2.755 =2.59 hank roving on the fine fiame. 17 The one tooth change at the five different processes makes a change on the fine frame three hank roving from three hank to 2.59 hank. The above example demonstrates the fact that the smaller number of teeth the draft gears have, the greater change one VAUGHAN'S CARDING LESSONS 37 tooth will make in the weight or number of the roving, and the more teeth the less one tooth will change the number. This is why I make my changes in keeping numbers on the large gear on the draft gear stud, in place of changing the draft pinion. This gear on the Biddeford frame has 100 teeth, and one tooth change on this gear makes one pound in the hundred pounds in the cloth room, while the change pinion has about 33 teeth, and one tooth change will make three pounds in the hundred. CHAPTER XV. How to figure the weight of lap to produce a certaiix Kaivk rovii\g ai the fine frame, also the weight per yaLfd at any process to produce any haak roving. The two most important questions to decide before we can solve this problem are the drafts and doublings on each pro- cess; and to make the solution as simple and plain as pos- sible, I will take the schedule of drafts and doublings as are used in the new Dallas Mills, which are as follows: Card draft 95, drawing draft coarse head 6 and double 6, fine drawing draft 6 and double 6, slubber draft 3.50, inter- mediate draft 4.50 and double 2, fine frame draft 5.50 double 2. By this schedule we will find the requisite weight per yard of lap to produce three hank roving on the fine roving frame. In figuring from the roving frame back to the card, mul- tiply the weight in grains of one or more yards by the draft and divide by the doublings. First, 12 yards of three hank weigh s 33 1-3 grains with two doublings and 5.50 draft; what will 12 yards of intermediate roving weigh in grains? Example : 33^X5.50 -=91.66 grains weight of 12 yards. 2 Secondly, 12 yards of intermediate roving weighs 91.66 grains and with two doublings and a draft of 4.50, what will 12 yards of slubber ro\dng weigh in grains? Example: 3K VAUGHAN'S CARDING LHSBON'S 91.66X4.50 =206.23 grains. 2 The slubber has a draft of 3.50 and no doublings. We multiply the 206.23 grains by the draft and divide by 12' yards; this Avill give what one yard of drawing sliver will- weigh in grains. Examples 206.23X3.50 — -" =61.41 grs. per yard of fine drawing sliver^ 12 As the two processes of drawing draw six times and double- si± times, this will make the card sliver the same weight per yard as the fine drawing sliver, which is 61.41 grains, Thereis no doubling on the card. Multiply the weight of sliver by the draft of the card; this will give the grains in one yard of lap; divide this product by 437.5, which are the grains in one ounce, and the quotient will be ounces per yard of lap. Example: 61.41X95=5833.95^437.5=13.33 ounces in one yard of lap. There is no deduction made in the above for waste nor any allowance for contraction. By the above schedule of drafts and doublings will be found the required weight per yard of the fine drawing sliver to produce four hank roving on the fine roving frame. Twelve yards of four hank roving weighs 25 grains, draft of fine roving frame 5.50 double two times, draft of intermediate 4.50, double two times, draft of slubber 3.50 and no doubling. Example : 25X5.50X4.50X3.50 — - — = =541.40 grains in 12 yards drawing sliver. 2X2 Divide by 12 yards and the quotient gives grains in one yard of sliver. 541,40-^12=45.11 grains in one yard. Rule: Multiply the weight in grains of 12 yards of fine roving and the draft of each process together for a dividend and the doublings of each process together for a divisor, and the quotient will give the weight in grains of 12 yards, which divided by 12 will give the weight of one yard. I will change the schedule of the drafts on each process aiid use whole numbers, to eliminate fractions, which will simplify the operation. Card draft 90, coarse drawing draft 5, fine drawing draft 5, slubber draft 4, intermediate draft 5, TAUGHAISrS CARDING LESSONS 39 line frame draft 6, tlie doublings the same as in the first •schedule. "What weight per yard of lap will he required to produce two hank roving on the fine ro^dng frame by the last schedule? Multiply the 12 yards by the doublings to give one yard of lap in gi'ains. Twelve yards of two hant roving weighs 40 grains. Example : 40X6X5X4X5X5X90 —6250 grains in 1 yard of lap. 12X2X2X0X6X6 Divide by grains in one ounce, wliich is 437.5. Example: 6250.0-^437.5=314.28 oz. per yard of lap. When figuring from the card to the roving frame multiply the weight in grains of one yard of lap and all of the doub- lings and 12 yards together for a dividend and all of the drafts together for a divisor, the quotient will give the weight in grains of 12 yards of fine roving from the last schedule of drafts and doublings. Will find what a 12 ounce per yard of lap will give in hank roving on the fine roving frame. Twelve ounces of lap contains 5250 grains. Ex- ample : 5250X12X2X2X6X6 —33.6 grains in 12 yards of fine roving. 90X5X5X4X5X6 Divide 100 by the last results and it will give the hank roving. Example : 100-^33.6=2.97 hank roving. From the present schedule we will find what the roving and sliver at each process should weigh to produce a given hank roving with a draft of 6 on fine roving frame. What will the intermediate roving have to weigh to produce two hank roving? Twelve yards of two hank weigh 50 gi'ains and double two times. Example: 50X6 =150 grains per 12 yards. 2 With six draft on fine frame and double two times, and 5 draft on the intermediate and double two times, what will 12 yards of slubber roving have to weigh to produce 2.50 hank roving on the fine frame? Twelve yards of 2.50 hank weigh 40 gi-ains. Example: 40X6X5 =300 grains per 12 yards. 2X2 40 VAUGHAN'S CARDING I.EvSSONS With 6 draft on fine roving frame and double two times, 5 draft on the intermediate and double two times, and a draft of 4 on slubber, what weight of fine drawing sliver per yard will it take to produce three hank on fine roving frame? Twelve yards of three hank weigh 33 1-3 grains. Example : 33JX6X5X4 =:83.33, one yard of sliver. 12X2X2 With 6 draft on fine frame, 5 draft on intermediate, 4 draft on slubber and 5 draft on fine drawing, what weight must coarse drawing sliver be to produce two hank rov- ing? Twelve yards of two hank weigh 50 grains. Example: 50X6X5X4X5 =104.16. 12X2X2X6 With 6 draft on fine roving frame, 5 draft on intermediate, 4 on slubber, 5 on fine drawing, 5 on coarse draAving, what must card sliver weigh per yard to produce four hank on fine roving frame? Twelve yards of four hank weigh 25 grains. Example : 25X6X5X4X5X5 ^=43.40, 1 yard card sliver. 12X2X2X6X6 When starting a new mill it is necessary to have a sched- ule of drafts and weights for each process, and as the stock is put through each process the sliver or roving should weigh the same as scheduled or be made to do so by chang- ing the drafts. VAUGHAN'S CARDING LESSONS 41 CHAPTER 17. Care of ''■'' *.: «o.D 1 J-a.j: iQr t ''O i ;: tU' i- I'-. () j lO.i: : <>()<: <: i-' <. I (. : OOft 1- h' i i-bt i (^)L^£• 8'^ ■:f,<; ; 80(i.<: 08 H i (JOJ: ^ 8'5:.l: ^<' ■ ' f <'•; !rff)i! ^Kf) i u).^ TJ'i- i' ()<' <:!•() L- 88.0 '6b.2 f?f:£-.<: (in r^^B.!: S:0.() Ui) i: r42 1" r<- .' • ... >[;() i: (^■■l OT.S k"l' !. ri.j; Mi-O.i: OO.T ii-.i: 1 :.■)!: '. Hi.:\ o(l).l: Mi.T K-.i: <■-<. <. or.r; [f>().!: 8ii.T i- ^ (*XL: i' <»<: Of,T r.i. «'" V '.'>'.'■ >• ' *■ wt ■:u,i U" <-.>■: 1 Oi- (>;vr •■'(" [ 01-. ; (■ tf ' 1 ui-.r k-':~ ('-8. 1 , . - . <• r ■ -. . i -<■ • o'; I >.' ! : ('. ; .1. }■-: I ii'/H <(}'.[ ?Xi. \ (10. f hi ; t( -' • -f" » . r 81 n no.] 3K.? i-';.i ( .' !^ . . <:',;. (if.l^ i(?T.r i::(: Tl) I KuR. 1 1 (>. r rsr \ 0>>i' ;)f i- (ioR I t <■ <• Si). I 0{>i.i .*)(].[ ■•IL 1 nio.. T • '■ - ' ' 7< <; {>0 I T«^t.r ,HM L*: , ! OS'O 1 ^r i: ' ^'•; ; ()<-.;; : [ (■ <; r. iT.r rS.-l-.r 10 t ;>f!.] (.'M!.f ll:.i' f:H r (.';'*. <'; L-T.I iU-. I (.!(> £• Vi.? Ht'o.f <•',' <• 0(8. r tv- v. ?T [ :Ml Hn.v ^ Hv.r 800 r !■':..'■ ~ '.■■', ! <-\.v. l-T.I OU F or.s: (?[:.r TTO. [ : i' !j •'■'''. r ' r . ', > oT . [ ()c'i-.f iril: (>M [ Or-IM ri: 1: > . I c J . i iG.a <)T.f rri ' '-f -i- • !■: ' ."rii i «i:,L- r«8 I :t-G.8 OT.i Tl' L' (?'-!M f ^fl.f" ?"■ i l-I ! 8K. : Oo XNA^ISX OR ROVING as oi _ 1^ ae a£ a: M 1 1 i 2: i 1 .1 1 i J? 1 1 1 1 i 1 1 2! •1 1 1 2: i 7.20 2.683 3.22 9.55 3.090 3.71 12.18 3.490 4.19 14.98 3 870 4.64 18.20 4.266 5.12 21.68 4.656 5.59 7.25 2.693 3.23 9.60 3.098 3.72 12.24 3.499 4.20 15.05 3.879 4.65 18.27 4.274 5.13 21.76 4.665 5.60 7.30 2.702 3.24 9.65 3.106 3.73 12.30 3.507 4.21 15.12 3.888 4.67 18.34 4.283 5.14 21.84 4.673 5.61 7.35 2.711 3.25 9.70 3.114 3.74 12.36 3.516 4.22 15.19 3.897 4.68 18.41 4.291 5.15 21.92 4.682 5.62 7.40 2.720 3.26 9.75 3.122 3.75 12.42 3.524 4.23 15.26 3.906 4.69 18.48 4.299 5.16 22.00 4.690 5.63 7.45 2.729 3.27 9.80 3.130 3.76 12.48 3.533 4.24 15.33 3.915 4.70 18.55 4.307 5.17 22.08 4.699 5.64 7.50 2.739 3.29 9.85 3.138 3.77 12.54 3.541 4.25 15.40 3.924 4.71 18.62 4.315 5.18 22.16 4.707 5.65 7.55 2.748 3.30 9.90 3.140 3.78 12.60 3.550 4.26 15.47 3.933 4.72 18.69 4.323 5.19 22.24 4.716 5.66 7.60 2.757 3.31 9.95 3.154 3.78 12.66 3.558 4.27 15.54 3.942 4.73 18.76 4.331 5.20 22.32 4.724 5.67 7.65 2.766 3.32 10.00 3.162 3.79 12.72 3.567 4.28 15.61 3.951 4 74 18.83 4.339 5.21 22.40 4.733 5.68 7.70 2.775 3.33 10.05 3.170 3.80 12.78 3.575 4.29 15.68 2.960 4.75 18.90 4.347 5.22 22.48 4.741 5.69 7.75 2.784 3.34 10.10 3.178 3.81 12.84 3.583 4.30 15.75 3.969 4.76 18.97 4.355 5.23 22.56 4.750 5.70 7.80 2.798 3.35 10.15 3.186 3.82 12.90 3.692 4.31 j 15.82 3.977 4.77 19.04 4.363 5.24 22.64 4.758 5.71 7.85 2.802 3.36 10.20 3.194 3.83 12.96 3.600 4.32 1 15.89 3.986 4.78 19.11 4.371 5.25 22.72 4.767 5.72 7.90 2.811 3.37 10.25 3.202 3.84 13.02 3.608 4.33 i 15.96 3.995 4.79 19.18 4.379 5.26 22.80 4.775 5.73 7.95 2.820 3.38 10.30 3.209 3.85 13.08 3.617 4.34 16.03 4.004 4.80 19.25 4.387 5.26 22.88 4.783 5.74 s.oo 2.828 3.39 10.35 3.217 3.86 13.14 3.625 4.35 16.10 4.012 4.81 19.32 4.395 5.27 22.96 4.792 5.75 8.05 2.837 3.40 10.40 3.225 3.87 13.20 3.033 4.36 16.17 4.021 4.83 19.39 1 4.403 5.28 23.04 4.800 5.76 8.10 2.846 3.42 10.45 3.233 3.88 13.26 3.641 4.37 16.24 4.030 4.84 19.46 4.411 5.29 23.12 4.808 5.77 8.15 2.855 3.43 10.50 3.240 3.89 13.32 1 3.650 4.38 16.31 4.039 4.85 19.53 4.419 5.30 23.20 4.817 5.78 8.20 2.864 3.44 10.55 3.248 3.90 13.38 3.658 4.39 16.38 4.047 4.86 19.60 4.427 5.3J 23.28 4.825 5.79 8.25 2.872 3.45 10.62 3.259 3.91 13.44 3.666 i 4.40 16.45 4.056 4.87 19.67 4.435 5.32 23.36 4.833 5.80 8.30 2.881 3.46 10.68 3.268 3.92 13.50 i 3.674 1 4.41 16.52 4.064 4.88 19.76 4 445 5.33 23.44 4.841 5.81 8.35 2.890 3.47 10.74 3.277 3.93 13.56 1 3.682 4 42 16.59 4.073 4.89 19.84 4.454 5.34 23.52 4.850 5.82 8.40 2.898 3.48 10.80 3.286 3.94 13.62 i 3.691 4.43 16.66 4.082 4.90 19.92 4.463 5.36 23.60 4.858 5.83 8.45 2.907 3.49 10.86 3.295 3.95 13.68 I 3.699 4.44 16.73 4.090 4.91 20.00 4.472 5.37 23.68 4.866 5.84 8.50 2.915 3.50 10.92 3.305 3.97 j 13.74 1 3.707 4.45 16.80 4.099 4 92 20.08 4.481 5.38 23.76 4.874 5.85 8.55 2.924 3.51 10.98 3.314 3.98 1 13.80 3.715 4.46 16.87 4.107 4.93 20.10 4.490 5.39 23.84 4.883 5.86 8.60 2.933 3.52 1 11.04 3.323 3.99 i 13.86 3.723 4.47 16.94 4.116 4.94 20.24 4.499 5.40 23.92 4.891 5.87 8.65 2.9a 3.53 1 11.10 3.332 4.00 ! 13.92 3 731 4.48 17.01 4.124 4.95 20.32 4.508 5.41 24.00 4.899 5.88 8.70 2.950 3.54 1 11.16 3.341 4.01 1 13.98 1 3.739 4.49 17.08 4.133 4.96 20.40 4.517 5.42 24.08 4.907 5.89 8.75 2.958 3.55 1 11.22 3.350 4.02 : 14.04 i 3.747 4.50 17.15 4.141 4.97 20.48 4.525 5.43 24.16 4.915 5.90 8.80 2.966 3.56 i 11.28 3.359 4.03 14.10 i 3.755 4.51 17.22 4.150 4.98 20.56 4,534 5.44 24.24 4.923 5.91 8.85 2.975 3.57 j 11.34 3.367 4.04 14.16 1 3.763 4.52 17.29 4.158 4.99 20.64 4.543 5.45 24.32 4.932 5.92 8.90 2.983 3.58 ll 11.40 3.376 4.05 14.22 3.771 4.53 17.36 4.167 5.00 20.72 4.552 5.46 24.40 4.940 5.93 8.95 2.992 3.59 !l 11.46 3.385 4.06 14.28 3.779 4.53 17.43 4.175 5.01 20.80 4.561 5.47 24.48 4.948 5.94 9.00 3.000 3.60 1 11.52 3.394 4.07 14.34 3.787 4.54 17.50 4 183 5.02 20.88 4.569 5.48 24.56 4.956 5.95 9.05 3.008 3.61 ! 11.58 3.403 4.08 14.40 3 795 4.55 17.57 4.192 5.03 20.96 4.578 5.49 24.64 4.964 5.96 9.10 3.017 3.62 ; 11.64 3.412 4.09 14.46 3.803 4.56 17.64 4.200 5.04 21.04 4.587 5.50 24.72 4.972 5.97 9.15 3.025 3.63 ' 11.70 3.421 4.11 14.52 3.811 4.57 17.71 4.208 5.05 21.12 4.596 5.52 24.80 4.980 5.98 9.20 3.033 3.64 j 11.76 3.429 4.11 14.58 3.818 4.58 17.78 4.217 5.06 21. 2-.) 4.604 5.52 24.88 4.988 5.99 9.25 3.041 3.65 1 11.82 3.438 4.13 14.64 3.826 4.59 17.85 4.225 5.07 21.28 4.613 5.54 24.96 4.996 6.00 9.30 3.050 3.66 11.88 3.447 4.14 14.70 3.834 4.60 17.92 4.233 .■).08 21.30 4.622 5.55 25.04 5.004 6.00 9.35 3.058 3.67 11.94 3.455 4.15 14.76 3.842 4.61 17.99 4.241 5.09 21.44 4.630 5.56 25.12 5.012 6.01 9.40 3.066 3.68 12.00 3.464 4.16 14.84 3.852 4.62 18.06 4.250 5.10 21.52 4.639 5.57 25.20 5.020 6.02 9.45 3.074 3.69 12.06 3.473 4.17 14.91 3.861 4 63 18.13 4.258 5.11 21.60 4.648 5.58 25.28 5.028 6.03 9.50 3.082 3.70 1 12.12 2.481 4.18 ! This table u.sed by permission of Draper Co., Hopedale, Mass. 1 4{Vi: (U-. ' {10 f { ii', 1 I M ' r i i '■; i i (• r ■ ; - ; , r ix ''- - <.i .1. (■''■: 1 8i r: (?<). i X:^A 1 ' . ^r.e KJ-.r Itl: T() I KuO. 1 ffi.f rs' - ;)f w! (H)P, I ii:?^ •Si). I 001-. r mA ■aI I : ■ I- ■. , ~ r (• >. >;, r ^L C (I'd I Tt^ivf ,HM L£.i 81"' ' }■.'■ '' Ti'.a.i 04^. J> IT. I 04-i- f or.s; f?2!r TT(*. L li.'i o08. r 8i-;8 oT . r (k'i-.I i't I- , ■ (/a I O.^'O.l . f r.i- 2 av^.r to. a (!".)■ ;,;.; ' '. 1 '• ■ '■ : /I'll i 1 ; r- T- ry.> r 1-.: :: I:" I 8K. OS. f •g c^ ^ ^ £ f^ .^ fO ^ £ J- 7.20 2.683 3.22 7.25 2.693 3.23 7.30 2.702 3.24 7.35 2.711 3.25 7.40 2.720 3.26 7.45 2.729 3.27 7.50 2.739 3.29 7.55 2.748 3.30 7.60 2.757 3.31 7.65 2.766 3.32 7.70 2.775 3.33 7.75 2.784 3,34 7.80 2.793 3,35 7.85 2.802 3.36 7.90 2.811 3,37 7.95 2.820 3,38 8.00 2.828 3,39 8.05 2.837 3.40 8.10 2.846 3.42 8.15 2.855 3,43 8.20 2.864 3.44 8.25 2.872 3.45 8.30 2.881 3.46 8.35 2.890 3,47 8.40 2.898 3.48 8.45 2.907 3.49 ! 8.50 2.915 3.50 8.55 2.924 3.51 8.60 2.933 3.52 8.65 2.9 a 3.53 8.70 2.950 3.54 i 8.75 2.958 3.55 8.80 2.966 3.56 8.85 2.975 3.57 8.90 2.983 3.58 1 8.95 2.992 3.59! 9.00 3.000 3.00 1 9.05 3.008 3.61 i 9.10 3.017 3.62 1 9.15 3.025 3.63 1 9.20 3.033 3.64 1 9.25 3.041 3.65 1 9.30 3.050 3.66 9.35 3.058 3.67 1 9.40 3.066 3.68 ! 9.45 3.074 3.69 9.50 3.082 3.70 1 £ 9. 9. 9.<1 9 9 9.^ 9 10.' 10.1 10. 10. 10. 10.1 10.: 10 10 10 10 10 lO.i lOj lo; lO.i 10 10.^ 10.^ 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11.6 11 11 11 ll.a 11 12.( 12.( 12 This table used by per id to bO lO to 2 ^ "" o to to to W 05 CO CO >4^ rfi. t^ in Oi w< O -J -J 00 O t-i i4i^ ^J CO -Vi Oi O 4^0lCX)K^OiO:>00*-'COaiOWOOCOO-4ii.>fi.03WCO ^^K K^^K ^^K ^^>N ^^K ^;^K 2 2 3 I- ? ?D«D— ''>0 04^000000 |_iH-'K-'»-'l-*»-'>-'l-'l-*»-*l-l|-'l->h-*tOtO MOOOOOOOO?DX'«DOOOt-'^tOtOC'5**i.f^Cn05^000i-' ^OtOf^^lOCOOiOCOMtOCSF— -JCOO