Indian Journal of Fibre & Textile Research Vol. 30, June 2005, pp. t36- 14 1

Torsional rigidity of cotton hosiery yarns

P K Banerjee" & P B hat Department of Textile Technology, Indian Institute of Technology, New Delhi 1 10 0 16, India

Received 9 January 2004; revised received alld accepted 6 August 2004

Torsional properties of eighteen different commercial cotton hosiery yarns in the count range of 1 6s -40s Ne have been studied on a Torsiometer. The mean torsional rigidity, derived from the slopes of torque-twist hysteresis loop, relates very well with relevant fibre and yarn variables. It is observed that the increase in fibre span length and maturity leads to rise in mean torsional rigidity of cotton hosiery yarns while the finer fibres yield lower yarn rigidity. Moreover, the coarser yarns exhibit greater mean torsional rigidity while the yarns of higher tensile modulus show lower values.

Keywords: Cotton yarn, Torsional rigidity, Torque-twist hysteresis

IPC Code: Int.CI.7 D02G3/00, GOIB5/00

1 Introduction During the process of loop formation on a knitting

machine, the yarn undergoes tensile, bending and torsional deformations. The dynamic balance between the resulting yarn tension in the knitting zone and other mechanical forces acting on the needles affect the loop forming point and hence the loop length I . During the course of its relaxation in wet processing stage, the loop changes its shape and tends to assume the one corresponding to the minimum strain energy level. The torsional as well as tensile and bending stresses stored in the loop during its formation on the knitting machine play important roles in this relaxation process. As the yarn rigidities in tension, bending and torsion affect the loop length as also its relaxed shape, it becomes necessary to relate them for manufacturing knitted fabrics of stable and desirable dimensions. Measuring the torsional rigidity of hosiery yarns and developing an understanding of its dependence on critical fibre and yarn variables is an important step in this direction.

By definition, the torsional rigidity is the torque required to produce a unit twist per unit length in a fibre or yarn. There are basically two principles by which the torsional rigidity can be measured, namely the torsion pendulum and torsion balance.

In the torsion pendulum method, a short pendulum is suspended at one end of the sample while the other end is attached to a stirrup. The torsional rigidity of

aTo whom all the correspondence should be addressed. Phone: 26591409; Fax: +91 - 1 1 -2658 1 103; E-mail: pkbt60@yahoo.com

the sample can be calculated from the moment of inertia of the rod about sample axis, free length of sample and period of oscillation of the system. Meredith2 employed the torsion pendulum method for studying a wide range of fibres while Cheng and Duckete used this principle for the study of torsion in a bundle of fibres. Owen4 used double pendulum method to measure the torsional rigidity of fibres.

In the torsion balance principle, a torsion wire of known torsional properties balances the torsion induced in the test specimen. Peirce5, adopting this principle, used suspended magnets while other researchers employed the optical lever method. Skelton6 used a mirror and circular scale to study torsional properties of nylon monofilament yarn. Dhingra and Postle 7 used photo potentiometer to measure torque in mono- and multi- filament yarns. Postle et at. 8 used lamp and scale arrangement to measure the torque in twisted worsted yarns. Okabayashi and Yamazaki9, Freestone et at. 10, Tandon et al. I I and Tavani et al. 12 employed the torsion balance principle for measuring the torsional properties of various types of fibres and yarns.

From some of the plots or data published in the literature, an estimate of torsional rigidity of different yarns can be worked out. Accordingly, a typical value of the torsional rigidity of 1 5 denier nylon monofilament yarn6 is 0. 1 05 x 1 0-7 N.m2, of 206 denier monofilament yarn7 is 1 .0 x 1 0.7 N.m2 while that of 256 tex woollen carpet yarn I I is 3.2 X 10.7 N.m2•

As an instrument to measure the torsional properties of spun single yarns is not commercially .

BANERJEE & BHAT : TORSIONAL RIGIDITY OF COTION HOSIERY YARNS 1 37

available, Mukherjee l 3 initiated the development of torsiometer at the Indian Institute of Technology, Delhi, employing the principle of torsion balance. Godharal4, Kumbharl5 and Holkarl6 improved this instrument further. The software and hardware of this instrument needed to be further improved for conducting computer-controlled experiments with an acceptable degree of accuracy and reproducibility.

Information on torsional behaviour of single cotton yarns and its dependence on various fibre and yarn properties could not be found in literature. Hence, a preliminary investigation on the torsional behaviour of single cotton yarns has been carried out and reported in the present paper.

2 Materials and Methods

2.1 Torsiometer

Schematic diagram of assembled instrument is shown in Fig. 1 . The framework of the instrument consists of circular plates and three vertical rods. All plates are levelled horizontal and held normal to the supporting rods. Coaxial holes in the center of each plate were drilled to accommodate various components. The base plate is provided with screws to adjust levelling. The power supply system and microprocessor control cards are accommodated at convenient place inside the instrument.

At the centre of plate P2, a stepper motor M is mounted. This is a bi-directional stepper motor with microprocessor and software control to operate it as per the testing requirements. The direction of rotation of motor has several options, such as clockwise, anti­clockwise, oscillation mode and stepwise rotation with pause at certain intervals, at any selected speed for specified amount of rotation or period.

The shaft of stepper motor carries an adapter AD 1 for adjusting gauge length of torsion wire, which, in turn, is linked to a jaw 1 1 . At the centre of this jaw 1 1 , the torsion wire TW is inserted. Another jaw 12 grips the bottom end of TW. The other end of jaw 12 is threaded to a small shaft SH.

A digital encoder EN is mounted on shaft SH while the photo diode, which reads the rotation of encoder, is supported on a metal ring MR. The ring is mounted on an aluminium disc, which, in turn, is screwed to the metal plate P3 . The shaft SH passes through the hole at the centre of plate P3 as well as through that of metal ring MR and aluminium disc. A 'Z' shaped lever LZ supports the base of jaw 12 during loading or unloading of test specimen.

P2

P3

1'4

P I I vi J

AD l - -?H �

TW

SH Q --Ii""�wb.i �N LZ g •• _ .... � _ .......... _. _ MR

I

s 7

H Let) SL

PS J Fig. I-Torsiometer

The bottom end of shaft SH carries an adapter AD2, which is used to adjust the distance between jaws 13 and J4, i .e. the gauge length of test specimen. The other end of adapter AD2 carries the jaw 13 for clamping the yarn.

The axes of the stepper motor M, jaws 11 - 13, torsion element TW, adapters ADl and AD2, shaft SH, encoder EN and test sample are aligned along the same vertical line. They are free to rotate co-axially in any direction, depending on the rotation of testing the torsional properties of spun yarn while maintaining the tension at the desired level.

A solenoid SL is fixed at the center of base plate P4. A core that can slide up and down freely along the axis of solenoid is constrained in such a manner that it cannot rotate about its axis. The top end of core is linked to a load cell LC, which is rigidly connected to the lower end of the jaw 14. These three elements form a single unit which can move vertically but cannot rotate.

The solenoid along with the elements LC and 14 permit testing of torsional properties of spun yarn

1 38 INDIAN J. FIBRE TEXT. RES., JUNE 2005

while maintaining the tension at the desired level. The functions of load cell and solenoid are synchronized. The solenoid applies required tension. During testing, the insertion or removal of twist may change length of sample, which, in turn, may cause change in tension in specimen. The load cell measures this tension and the same is corrected by change in voltage supply to solenoid by microprocessors. For this, a program was prepared in C++ language. Thus, the entire testing can be conducted virtually under constant tension.

The torsional rigidity (r) of the test specimen can be calculated using the following equations:

r (N.m2) = 2 n L K ( <p- e ) / e and

K (N.m) = [4 n2 1 / r] x l O -7

where K is the torque balance factor of the wire that can be determined from a torsion pendulum of given moment of inertia (I) oscillating with a time period of T ; L, the test specimen length (m); ¢ , the rotation introduced by motor; and e, the rotation of the encoder.

Before using this instrument for large scale testing of yarns, its reliability, accuracy and reproducibility were established by conducting various experiments. For estimating the reliability, the torsional rigidity (TR) of a polyester monofilament yarn of l inear density 508 denier was determined on torsiometer as also on a standard torsion pendulum instrument at various gauge lengths. The results are shown in Table I .

While comparing the two sets of data, i t must be underlined that in the pendulum method the sample is subjected to an oscillation that introduces very low number of twists per unit length (low amplitude) over a very short time period (high frequency), whereas in the torsiometer the sample undergoes a considerably larger amount of deformation (high amplitude) in one direction over a much longer duration (low frequency) before being gradually brought back to the original state. The deformation modes of the two instruments in terms of amplitude and frequency are therefore different. However, the results of torsion pendulum and torsiometer show a reasonably good agr'.:!ement. It can also be noted that the gauge length shows no specific trend, a feature observed earlier by other researchers for fibres and filament yarns.

The accuracy and reproducibility of torsiometer were evaluated by operating the instrument without

Table I-Comparison of torsional rigidity

Instrument Torsional rigidity x 10 -7 . N. mC

Torsiometer Torsion pendulum

" Gauge length in em

3" 1 7.55 16.57

5" 15.2 1 16 .43

8" 1 7.59 1 5 .46

test specimen and turning the motor repeatedly for specified number of rotations, namely 5 , 1 0, 1 5 and 20 rotations. The corresponding rotations of encoder were recorded for the analysis of error factor and reproducibility. Ideally, the encoder should not display any lag and should always yield the same value. However, an error ranging from 0.3% to 0.4% was observed accompanied by 92% reproducibility for 5 rotations and 98% for 20 rotations. Apparently, the inertia of the system suspended at the end of the torsion wire, consisting of Jaw 12, encoder EN, shaft SH, adaptor AD2 and jaw 13, plays a role in the lag. The effect of this inertia is more pronounced for lower number of rotations, suggesting that this aspect would influence the initial part as also the turning zones of the torque-twist hysteresis profiles of test specimens.

2.2 Testing of Yarn Samples

The yarn samples were collected directly from manufacturing stage of mills that produce hosiery yarns of 5% level Uster standard. A total of 1 8 different samples covering 7 different counts ranging from 1 6s to 40s Ne from 8 different sources were collected. In four cases, mixing and process line were same but count was different, in another four the nominal count was same but collected from three or more different sources, and in three cases the yarns were only carded. By this, an attempt has been made to cover a wide variety of hosiery yarns for the study.

To investigate the role of fibre properties on torsional behaviour of spun yarns, the fibres were tested for properties that are likely to have influence on the former. The cotton yarns were also tested for certain general yarn quality parameters . The fibre and yarn properties tested are listed in Table 2 .

The torsional properties of yarns were tested in standard atmospheric condition. The yarn samples were fixed on windows, which were cut out from chart papers. While mounting the yarn samples on windows, a pretension of 0. 1 cN/tex was applied and care was taken to avoid any loss of twist in handling. The mounted samples were conditioned for 24 h before testing. The gauge length on torsiometer was set to

BANERJEE & BHAT : TORSIONAL RIGIDITY OF COTION HOSIERY YARNS l 39

Table 2-Methods of testing

Property Method of testing Standards

Fibre Fibre length HVI ASTM 0-5867-95 Uniformity ratio HVI ASTM 0-5867-95 Fibre fineness HVI ASTM 0-5867-95 Bundle strength HVI ASTM 0-5867-95 Maturity coefficient HVI ASTM 0-5867-95

Yarn Count ASTM 0- 1 907-97 Irregularity Uster Tester III ASTM D- I059-97 Twist Auto twist tester ASTM 0- 1422-99 Tensile strength Statimat ME ASTM 0-2256-97

lOmm by inselting suitable adapter at the base of the upper jaw of yarn. As the present work is aimed at investigating the influence of torsional property on loop dimensions, testing at comparable lengths was thought to be proper. Incidentally, the reports in literature of independence of torsional properties on gauge length are mainly centered on the more homogenous fibres and filaments. Accordingly, the minimum gauge length possible on this instrument ( l Omm) was selected. The torsional properties of all the 1 8 yam samples were tested at this gauge length in hysteresis mode . . In this mode, the yarn samples were subjected to 5 rotations in Z (clockwise) direction (twisting operation) fol lowed by 1 0 rotations in S (anti­clockwise) direction (detwisting operation) and finally given another 1 0 rotations in Z (clockwise) direction (retwisting operation), by which one cycle of hysteresis loop was completed. The typical hysteresis curve for a 33 tex cotton yarn is shown in Fig 2. The torsional rigidity and other torsional properties were calculated from such plots.

In this work, the rigidity during twisting has been termed as torsional rigidity (TR), calculated from the

. slope of GB in Fig.2. However, the average of two linear parts of the hysteresis curve is termed as average torsional rigidity (ATR), i.e. average of slope of JB and EH. Interestingly, the slope of detwisting (HE) for spun yarns is different from that during twisting (GB) or retwisting (JB), because the energy stored in the spun yarn gets released during detwisting and hence the slope of HE is always lower than that of GB or JB. The two rigidities (TR and A TR) are different and their selection should depend on the requirement of property in analysis.

To simulate the condition of knitting, where the yarn in a loop is subjected to twisting of one loop arm and detwisting of the other, the mean torsional rigidity (MTR) has been calculated by averaging the twisting

� ' 0 ; -600 :0 " {2

800 8 J

S' 600

-800 Twist (tpm)

Fig. 2-A typical hysteresis loop

slope (GB) and the latter half of the detwisting slope (DE). It has been found that the detwisting slope over HE is less than that of DE. This is because during the first half of the detwisting action the energy stored in the parent yarn supports the process whereas this effect weakens in the latter half (DE), resulting in a higher value of slope. The calculated values of these three rigidities are given in Table 3 .

The torque i n yarn and torsional rigidity are frequently used to indicate the torsion related state of yarn. However, some more related properties, as shown in Table 3 , could be obtained from torsional hysteresis curve.

The residual twist (RTPM) is the deformation that remains permanently in the yarn after removal of the applied torque. This property indicates the amount of permanent deformation that the yarn undergoes on application of twist. It is calculated as half of the intercept of the hysteresis loop (Fig. 2) on the shear strain axis. Thus,

Residual twist = Mean of absolute values of shear (RTPM) strain at zero torque value of yarn

OC + OF 2

Similar to residual twist, torsional recovery (TREC) is also dependent on twist. It is the ratio of difference between strain at maximum and at zero torque to strain at maximum torque, expressed in percentage. Thus,

Torsional recovery = { (OB' - OC)/OB ' } x I 00.

Coercive torque (CET) is the iorque remaining in the yarn as stored energy at zero strain value of deformation. The average of hysteresis loop intercepting point on the torque axis is considered as coercive torque. This property indicates the relative ease with which a material can be torsionally deformed.

140 INDIAN J. FIBRE TEXT. RES., JUNE 2005

Table 3--Torsional properties of cotton yarn

Yarn codea TR xlO'7 ATR x 10'7 MTR X 10'7 Coercive torque x 10'7 Torsional recovery Residual twist N.m

2 N.m2 N.m2 N.m % tpm

AI6K 0.874 0.439 0.555 152 1 0 1 .23 230 B 1 8C 0.866 0.497 0.550 225 1 45.08 1 25 C20K 0.5 19 0.409 0.43 1 233 40.73 365 D20C 0.625 0.465 0.490 153 69.45 288 E20K 0.62 1 0.447 0.482 220 74.28 288 F20C 0.930 0.428 0.589 200 G20C 0.659 0.4 1 1 0.420 1 88 100.00 240 H24K 0.57 1 0.422 0.390 194 67.48 305 124C 0.57 1 0.447 0.458 2 1 0 75.46 285 J24C 0.565 0.387 0.429 228 108. 17 268 K26C 0.5 16 0.350 0.387 187 93.88 230 L30C 0.523 0.389 0.401 304 1 40.08 150 M30C 0.42 1 0.359 0.369 3 1 5 6 1 .22 325 N30C 0.492 0.3 1 5 0.340 1 70 152.85 1 15 030C 0.505 0.323 0.352 1 19 164.9 1 85 P40C 0.409 0.292 0.3 19 132 Q40C 0.358 0.340 0.364 96 95.95 200 R40C 0.393 0.3 19 0.326 156 1 63 .0 1 90

aValues consist of a running alphabet followed by the yarn count and then either K (carded) or C (combed). TR-Torsional rigidity, ATR-Average torsional rigidity, and MTR-Mean torsional rigidity.

Table 4-Nature of dependence of torsional properties on independent variables

Variable Torsion property

TR MTR TREC RTPM CET Fibre bundle strength ./ ./ Fibre elongation Fibre count in tex ./ ./ ./ ./ Fibre maturity ./ ./ ./ ./ 2.5% Span length ./ ./ ./ ./ Number of fibres in yarn Twist factor of spun yarn ./ ./ Twist factor after 5 rotations in testing ./ ./ Yarn thickness ./ ./ Yarn breaking force Yarn modulus ./ ./ ./ Yarn count in tex ./ ./ ./ ./ Value of R2 0.83 0.94 0.69 0.79 0.56

TREC - Torsional recovery, RTPM - Residual twist, and CET - Coercive torque

Coercive torque = Mean of absolute values of (CET) torque at zero strain of yarn.

= OA + 00 N.m

2

For each of the 1 8 yarn samples, a set of data on fibre and yarn properties and a corresponding set of data on torsional properties evolved out of the tests described above. It then became necessary to identify the torsional property that relates well with the fibre and yarn properties. Therefore, the general linear model (GLM) was adopted for generating multiple regression equations relating the two sets, while

taking care of the influence of multicollinearity and about the selection of variables 1 7 . The Systat 1 0 software was employed for this purpose.

3 Results and Discussion The multiple regression equations obtained by

relating the six different parameters of the torsional hysteresis plots with the twelve different variables of fibres and yarns exhibit widely varying coefficients of determination (R2 ) as also varying extent of influence of the independent variables. Table 4 provides an overview of the outcome of this exercise.

The tick marked boxes indicate significant effect of corresponding variable on the torsional property given

BANERJEE & BHAT : TORSIONAL RIGIDITY OF COTTON HOSIERY YARNS 1 4 1

0.6

0.5

0.4

0.3 0.30

Y=3.47E-03+1 .004 1 7x

R'

=O.965

0.35 0.40 RFIYM

0.45

-- Regression • • • • 95% CI

0.50 0.55

Fig. 3--Estimated MTR (RFIYM by considering combined fibre and yarn properties) liS. experimental MTR

in the respective column. :\s the properties TR and ATR exhibit very similar dependence, only one has been reported in the table. It may be pointed out that the twist factor of yarn and the twist factor after five rotations of the stepper motor of the torsiometer are two different variables, as during twisting/detwisting on the instrument, the fibre migration is not affected.

It is also observed from the table that the property defined as MTR exhibits the best relationship with the relevant fibre and yarn variables. The corresponding regression equation is as follows:

MTR = -0.5 1 9 +0.027*Fibre span length+0.373*Fibre maturity - O.0003*Yarn modulus +0.000 1 27*Y arn tex* Twist factor after 5 rotations in testing -0.0472 *Fibre tex* Fibre bundle strength *Fibre maturity . . . ( 1 )

The accuracy of this equation i s demonstrated by Fig.3, i n which the experimental values of MTR have been plotted against those estimated (RFIYM) by the regression equation.

The equation of the best-fit l ine passing though these points works out to be:

MTR = 0.0035 + 1 .00 RFIYM

The regression coefficient in this equation is unity and the regression l ine almost passes through origin. The confidence limit l ines are also very close to the regression l ine. These factors clearly show that the estimated and experimental MTR values match very closely, and the regression equation [Eq ( 1 )] describes

accurately the role of fibre and yarn properties on MTR.

4 Conclusions Extensive multiple regression analysis of data on six

different types of torsional properties derived from torque-twist hysteresis loops of eighteen different cotton hosiery yarns measured on torsiometer shows that the mean torsional rigidity can be predicted very accurately from some fibre and yarn variables. An increase in fibre span length and maturity leads to rise in mean torsional rigidity of cotton hosiery yarns while an increase in tibre count (tex) studied here lowers the rigidity. The coarser yarns exhibit greater mean torsional rigidity while yarns of higher tensile modulus show lower values.

For the cotton hosiery yarns, the role of fibre and yam variables in torsional properties is best manifested in mean torsional rigidity. Hence, i t i s proposed that the mean torsional rigidity be employed as the torsional property for characterizing the cotton hosiery yarns. It is also suggested that an improved torsiometer with lower inertia of the oscillating system might reveal better dependence of the other torsional properties, namely torsional recovery, residual twist and coercive torque, on the fibre and yarn variables. References I Banerjee P K & Ghosh S, J Text [nst, 90 Part I (2) ( 1 999) 187. 2 Meredith R, J Text lust, 45 ( 1954) T489. 3 Cheng C C & Duckett K E, Text Res J, 4 1 ( 197 1 ) 298. 4 Owen J D, J Text [nst, 56 ( 1965) T329. 5 Peirce F T, J Text [nst, 15 ( 1924) Sal . 6 Skelton J, J Text Inst, 56 ( 1965) T443. 7 Dhingra R C & Postle R, J Text Inst, 65 ( 1974) 126. 8 Postle R, Burton P& Chaikin, J Text Inst, 55 ( 1964) T448. 9 Okabayashi M & Yamazaki C, Text Res J, 46 ( 1976) 429. I O Freestone W D, Platt M M & Butterworth G A M, Text Res J,

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Torsional Properties of Yams, M. Tech. report, Indian Institute of Technology, Delhi, 1984.

14 Godhara R, Design and Fabrication of Modified Torsiomeler. B. Tech. report, Indian Institute of Technology, Delhi. 1993.

15 Kumbhar P, Development of Modified Torsiometer, M. Tech. report, Indian Institute of Technology, Delhi, 2000.

1 6 Holkar J, Modification alld Further Developll1el1l of Torsiometer, M. Tech. report, Indian Institute of Technology. Delhi , 2001 .

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