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Torque in Worsted Wool Yarns Abstract

A direct technique developed for measuring yarn torque is explored for the case of worsted wool yarns. The technique balances the torque in a yarn hank against a wire of known torsional rigidity. It is shown that this technique gives a reliable measure of the torque per strand independent of the size of the hank. The torque per strand was found to be linearly dependent on the applied external tension and a finite torque exists even at zero applied tension. This leads to the concept of resolving the torque into two components, (a) the torque due to the applied tension and (b) the intrinsic torque that exists in the untensioned yarn. The torque due to the applied tension does not depend on the yarn history but only on yarn geometric factors such as the yarn twist and linear density. By comparison the intrinsic torque depends on factors such as the level of yarn set as well as the twist and linear density. These components of torque due to tension and intrinsic torque are shown to be consistent with literature models and lead to estimates of yarn specific volume, yarn packing fraction and relative fiber relaxation moduli after steaming.

P. Mitchell, G. R. S. Naylor and D. G. Phillips1 CSIRO Textile and Fibre Technology, Belmont, Victoria 3216, Australia

Key words torque, yarn count, yarn twist, packing fraction, relaxation moduli

During yarn formation by ring spinning the fibers are bent into approximately helical shapes and an unbalanced torque or twist-liveliness is created as a result of the fibres’ attempt to straighten. One obvious manifestation of twistliveliness in singles yarn is snarling; a condition whereby the yarn attempts to relieve the unbalanced torque by wrapping about itself. This undesirable yarn property makes handling difficult and may cause problems in later processing. Another important consequence of torque in knitting yarns is the presence of spirality in plain knitted fabrics [1]. Steaming the yarn can reduce the unbalanced torque or liveliness. Commercially, a steaming operation after spinning is commonly used, so that a yarn that is initially twist-lively after spinning is stabilized. Different types of set have been observed in wool and they can be usefully classified as

either (i) cohesive1 or temporary if it can be removed by cold water (20°C) or (ii) permanent if it remains after a wet treatment at 70°C for 30 minutes [2]. These two types of set can be linked to two molecular phenomena in the wool protein. Cohesive set is related to the glass transition temperature [3], a moisture-dependent transition in the wool matrix material, whereas permanent set is related to the chemical rearrangement of disulphide bonds in the wool protein [2]. Gentle steaming of a freshly twisted yarn raises the temperature above the glass transition temperature and the stresses in the now rubbery matrix of the fiber relax and, on cooling below the glass transition temperature, the yarn is stabi-

Textile Research Journal Vol 76(2): 169–180 DOI: 10.1177/0040517506060909 Figures 2, 5 appear in color online: http://trj.sagepub.com

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1

Correponding author: e-mail: [email protected]

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lized because the cooled matrix becomes glassy and resists any residual strains from stressed disulphide bonds and intermediate filaments. On reheating or wetting of the yarn, that is, above the glass transition temperature, the yarn again becomes twist lively due to the strained disulphide bonds and intermediate filaments. These strains are only reduced by disulphide interchange in the presence of reducing agents or heat. Most commercial worsted yarn steaming operations primarily involve cohesive set and hence during subsequent wet processes such as washing or re-steaming, the cohesive set is released and yarn torque will reappear. A practical solution to the problem of twist-liveliness is the formation of a two-fold yarn. For a balanced yarn, the two-fold twist level is chosen such that the torque created by the ply structure is equal and opposite to the torque remaining in the two individual strands. Commonly the amount of torque in a yarn is not measured directly, but rather the degree of twist-liveliness is estimated. Quantitative measurement can be achieved by either counting the number of turns that form in a length of freely suspended yarn; or by measuring the distance between the two ends of a length of yarn when snarling just begins [4, 5]. Milosavljevic and Tadic [4] and Tao et al. [5] disagree as to which of these techniques is preferable. Although twist-liveliness is a commercially practical quantity, yarn torque is a more basic concept and it is desirable to have a direct measure of this quantity. Steinberger [6], and later Morton and Permanyer [7], introduced a technique whereby the torque in a yarn is determined directly by measuring the torque in a calibrated torsion wire used to counterbalance a twist-lively length of yarn. There are, however, practical difficulties with this technique. Firstly, the level of torque manifested by a single length of yarn is generally small, thus requiring sensitive and often delicate measuring techniques. In addition, it is very difficult to attach the ends of a length of twist-lively yarn to the apparatus without altering the twist and therefore the torque. Recently Tavanai et al. [8] extended the torquemeter concept to the measurement of torque in a yarn hank. In this approach, a hank of yarn replaces the single strand used in the earlier systems and the measurement is of the torque in the whole hank. Using false-twist textured, continuous filament, nylon yarns Tavanai et al. showed that the torque in a single strand could be obtained simply by dividing the measured hank torque by the number of strands; that is, the measured torque of the hank is proportional to the number of strands in the hank. The technique allows a more precise measurement of torque to be made, in compared with measurement of a single strand. The larger value for the hank reduces relative errors and also the hank measurement is sampling a longer total length of yarn. One aspect that Tavanai et al. [8] did not examine was the influence of externally applied tension on the measurement of torque; instead they simply limited the maximum

applied weight to 3 N. It is well known that the application of an axial load to a helical structure causes it to rotate about its axis [9]; that is, a torque is developed. In the case of a yarn, theoretical considerations indicate that this torque, arising from external forces, dominates the total yarn torque under even moderate tensions [1, 10, 11]. In this study we explored the approach of Tavanai et al. to measure the torque in singles wool worsted yarns including the effect of varying the applied external tension to the hank. Torque measurements are presented for yarns both dry [under normal laboratory conditions, approximately 65% relative humidity (RH), 20°C] and wet. The measurement of wet yarns is of practical importance since with wetting, the mechanical properties of wool fibers and yarns can change significantly [12, 13] and this influences the wet finishing behavior of knitwear.

Materials and Methods All yarns used in this study were spun from the same untreated, undyed wool top (21.2 µm mean diameter, 65 mm mean fiber length). After spinning the yarns were given one of the following treatments: no steaming, steaming at 85°C for 10 minutes, and steaming at 110°C (1.43 bar) for 10 minutes. Yarn twist was measured using a Zweigle D312 twist tester in untwist/twist mode as specified in test method AS 2001.2.14 – 87. The reported twist results are the average of twelve measurements. Following the approach of Tavanai et al., a torquemeter was constructed (see Figure 1) to directly measure the torque in the hanks of yarn. An 800 mm (± 2 mm) length of stainless steel piano wire, 0.23 mm in diameter, was suspended from a freely rotating protractor that could measure the angular deflection of the upper end of the wire. A bob of 120 g, with a pointer to locate the zero position, was attached to the lower end of the wire. Yarn hanks were created by initially wrapping yarn around a frame 1 m in circumference, removing the hank and tying the free ends together. The hank was then placed in the torquemeter with its upper end attached to a hook below the center ring on the torquemeter. A tensioning mass was hung from the lower end of the hank and fitted into a slot to prevent rotation while still allowing the mass to hang freely. The distance between the upper and lower ends of the hank, defined as the hank length is then 500 mm. Six different masses between 5 and 200 g were used for each trial in this study. For the measurement of wet hanks, a tube of water could be lifted to cover the lower half of the torquemeter and totally immerse the hank. When the water tube was in place, the change in the applied tension was corrected for the buoyancy forces on the tensioning mass. Torque generated in the yarn strands induced rotation of the upper end of the hank causing a torque in the torsion wire. At equilibrium, the torque in the wire was equal

Torque in Worsted Wool Yarns P. Mitchell et al. MH = MW = θ.S

171 (1)

where θ is the angular deflection between the ends of the wire (read from the protractor on the upper ring) and S is the torque to produce unit angular displacement of the wire [14]. With S known, the torque in the hank MH can easily be found. The torque S is dependent on the torsional rigidity of the wire JG and the length of the wire l according to the equation [14]: S = JG/l

(2)

where G is the shear modulus of the wire and J is its moment of inertia. Tavanai et al. [8] determined the torsional rigidity directly by applying a known torque to the wire. This was achieved by using a weight suspended over a ceramic guide and attached to the pointer, at a known distance from the wire, by a fine line. In our experience, this approach proved to be unsatisfactory due to friction in the pulley used as a guide and the difficulty in maintaining the applied force at right angles to the pointer. Instead, the torsional rigidity of the wire was determined experimentally by using a torsion pendulum. A bronze disc, 50.0 mm in diameter and 200.0 g in mass, was suspended from a length of wire and allowed to oscillate freely. The period of such a pendulum is given by [14]: τ = 2π I ⁄ S = 2π lI ⁄ JG

(3)

where I is the moment of inertia of the mass. Thus, from the measured period and the length of the wire, the torsional rigidity of the wire JG can be determined and hence, the value of the torque S in equations (1) and (2). To determine the period τ the time for 50 oscillations was measured for five trials and the mean value used. The torque of all yarn samples was measured in both normal ‘dry’ laboratory conditions (approximately 20°C and 65% RH) and wet (20°C in water). The hanks tested in water were allowed to equilibrate for at least 30 minutes in a beaker of water before transfer to the torquemeter. With the water tube on the torquemeter in place these yarns were kept wet throughout testing. Figure 1 A schematic diagram of the torquemeter used in this study.

and opposite to the torque in the hank. To return the hank in its original straight configuration, the upper ring was rotated until the bob and pointer were returned to their original positions. Then the torque or torsional moment in the untwisted hank, MH, equals the torque in the torsion wire, MW and this is given by:

Results and Discussion Evaluation of the Instrument and the Technique Calibration Using the approach described in the previous method section, the period of a torsional pendulum was used to characterize the torsional properties of the wire. The average

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Table 1 Angular deflection in degrees for torque trials using: (A) ten separate hanks and (B) ten repeated trials on a single hank, each with ten strands. Measurements on dry hanks Applied tension (mN) Mean (A) Standard deviation Mean (B) Standard deviation

1946 217.6 9.90 211.5 5.28

976.0 117.6 4.22 115.6 1.58

490.6 75.2 3.08 73.3 1.16

198.3 49 2.54 47.6 1.65

98.8 40.7 2.26 38.5 1.43

period was found to be 11.70 ± 0.009 s for a 990 ± 2 mm pendulum. This length of wire included the 800 mm section subsequently used in the torquemeter. The moment of inertia of the rotating mass was (62.49 ± 0.03) × 10–6 kg m2 which, using equation (3), gives a value of (17.83 ± 0.07) × 10–6 N.m2 for JG. For the torquemeter l = 800 mm and, from equation (2), the torque value S is (22.28 ± 0.14) µN.m/rad. At the end of the experiments reported in this paper (about 5 months after the initial calibration) the torsional rigidity of the 800 mm length of wire used throughout was re-measured. The measured value (17.82 ± 0.07 µN.m2) indicated that there had been no significant change in the properties of the wire during the course of the experiments.

Sensitivity and Reproducibility To test the sensitivity and reproducibility of the torquemeter, trials were made on ten identical hanks. Each of these hanks consisted of ten strands (five wraps) of 81 tex yarn with a metric twist factor of 142 previously steamed at 85°C for 10 minutes. Each hank was hung in place and the torque measured in the dry state (conditioned state in laboratory at 20°C and approximately 65% RH) for each of six different tensions, beginning with the largest (Table 1). The experiment was then repeated using the same hanks wet (Table 1). Ten repeated measurements were also made on a single hank in the dry state. This hank was removed from the torquemeter and left untensioned for at least 5 minutes between repeats (Table 1). The same hank was also tested ten times while wet, resting in a beaker of water (i.e. removed from the torquemeter) for about 5 minutes between trials (Table 1). The results in Table 1 show that, except for the results from the repeated trials on the single wet hank, the deflection given by the torquemeter could be used with an accuracy of approximately 5%. (As noted previously, the applied tension values in Table 1 for measurements on wet hanks have been corrected for buoyancy effects.) The results from the repeated trials on the single wet hank showed a consistent decrease over the ten trials. A similar decrease was found in a hank left in water under tension for approximately 16 hours. In both cases the measured deflection dropped by about 20%. It is assumed that this phenomenon is related to time-dependent relaxation processes in the wet fibers. Since the established procedure takes less than 5 minutes and each sample hank was only

Measurements on wet hanks 48.4 35.1 2.13 33.5 1.08

1718 231 9.03 197.4 14.98

861.1 142.6 8.13 121.5 7.12

434.3 105.1 8.18 88.4 6.42

176.3 82.5 5.28 69.5 5.36

87.9 74.8 4.92 62.9 4.98

43.7 69.5 4.14 58.1 4.15

measured once, these relaxation effects are not significant in the rest of this study. To test that the sensitivity and reproducibility are not dependent on a particular hank size, the same exercise (i.e. Table 1 data) was repeated with hanks from the same yarn but containing four strands each. Similar results were achieved.

Properties of the Torque per Strand Figure 2 shows the measured deflection as a function of tensioning weight for ten different hank sizes (10, 20, 30 etc, up to 100 strands per hank) using an unsteamed 76 tex yarn with a metric twist factor of 81 tested dry about 10 months after spinning. It can be seen that, for each hank size, the relationship is close to linear. For a given absolute tensioning weight, the deflection increases as the number of strands in the hank increases. When these results are plotted as the torque per strand as a function of the tension per strand, all data points in Figure 2 collapse into one line depicted by the open circles in Figure 3. [The measured deflections have been converted into a torque value using equation (1).] This demonstrates that the technique can be used successfully to measure the torque per strand independent of the size of the hank. This validates the approach of deducing the torque in a single strand from the torque in a hank. Figure 3 also includes the results of repeating this experiment with wet yarns. This confirmed that the measured torque per strand for a given applied tension per strand is also independent of hank size for the wet yarn. Figure 4 shows the results for a similar experiment using a higher twist yarn (81 tex with a metric twist factor of 140). In this case it can be seen that, at low values of tension per strand, the curve deviates from linearity. This deviation coincided with the observation that the hank was no longer being held straight by the applied tension but rather some buckling and minor localized snarling was occurring. This will reduce the net torque and explains the phenomenon in Figure 4 where the data points fall below the line for very small values of tension per strand. The regression coefficients for the low twist factor dry yarn in Figure 3 and high twist factor dry yarn in Figure 4 were the same, r2 = 0.96, indicating that the method was independent of twist level.

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Figure 2 Hank torque is plotted against the applied tension for an unset 78 tex yarn of twist factor 80 measured dry using hanks of different sizes. The bottom line corresponds to a hank with 10 strands and each subsequent line corresponds to increasing the hank size by 10 strands up to a maximum of 100 strands.

Figure 3 A plot of torque per strand as a function of tension per strand for an unset 78 tex yarn with a twist factor of 80. The open circles represent all the data from Figure 2 (i.e. dry yarns) and the closed circles represent the corresponding data for wet yarns.

It is interesting to note that, at a tension per strand in the region of 5 mN, the low twist factor dry yarn in Figure 3 has a similar measured torque as the high twist factor wet yarn in Figure 4 but does not show the same non-linear behavior. Snarling is dependent, not only on yarn torque but also yarn stiffness and thus the wet yarn, with a lower stiffness, is more prone to snarling and hence the non-linear behavior. Another estimate of the error of each data point was made using the following approach. In some instances, independent measurements of the torque per strand at the same tension per strand can be obtained from different combinations of number of strands and the applied strand weight. For example using different weight (in grams) and strand number combinations of 20 : 10, 100 : 50, 200 : 100, respectively, the

same tension per strand is obtained, namely, 2 g/strand. Single factor analysis of variance of the corresponding torque per strand has been made to estimate the error in the individual results. This shows that the mean coefficient of variation across 42 data sets for the torque per strand to be 4.6% (dry) and 5.4% (wet). These independent estimates are in good agreement with the ten replicate measurements described in the previous section.

Effect of Hank Length The effect of hank length was investigated using 10 strand hanks of 80 tex unsteamed yarn with a twist factor of 80 and measured dry, 12 months after spinning. Figure 5 shows that, as expected theoretically, the measured torque

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Figure 4 The torque per strand as a function of tension per strand for an unset 81 tex yarn of twist factor 140. Open circles represent the data from dry yarns and closed circles represent the data from wet yarns.

Figure 5 The effect of changing hank length on the measured torque per strand of a dry 78 tex unsteamed yarn with a twist factor of 80. The different lines relate to the six tensions used in Figure 2.

per strand is independent of hank length. This is an important result for the experimental protocol since after mounting the hank on the torquemeter, there will inevitably be some variation in the lengths of individual strands.

Components of Yarn Torque The testing of the instrument over the range of different conditions presented above indicates that it is experimentally a robust technique for measuring and analyzing the torque characteristics of yarns. This section of the paper will now focus on how the technique can be used to gain a fuller understanding of the physical mechanisms associated with yarn torque.

The Concepts of Torque due to Applied Tension and Intrinsic Torque The linear relationship between the torque per strand and the applied tension per strand (as seen in Figure 3) provides a useful insight about the origins of yarn torque. The slope of the line represents the change in torque with a corresponding change in yarn tension and therefore provides a measure of the component of torque due to external forces. The intercept of the line with the vertical axis gives the value of the yarn torque at zero tension and therefore represents the residual or intrinsic torque in the yarn due to the bending and twisting of the fiber during spinning. It is clear from Figure 3 that the component of the yarn torque due to

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Figure 6 The torque due to applied tension (i.e. the slope of plots similar to Figure 3) as a function of yarn twist factor. Circles show unset 40 tex yarns and squares show the set yarns (110°C for 10 minutes). Diamonds indicate 78 and 81 tex yarns with three different steaming histories (Table 2). Open points represent dry yarns and closed points represent wet yarns.

the application of an external tension can easily be similar to the intrinsic torque at low levels of applied tension; for example, for the dry yarn in Figure 3, the torque developed by a 0.1 N/strand external load is equal to the intrinsic torque. Previous workers [15, 16] had to estimate the residual or intrinsic yarn torque in continuous nylon filaments due to fiber bending and twisting (called the net torque) by subtracting a theoretical calculated value of the yarn torque due to tension from the total torque measured experimentally. The technique described here is a significant improvement and allows the intrinsic (or net torque) to be measured directly.

Analysis of the Two Components of Yarn Torque Nine 40 tex yarns with metric twist factors between 60 and 140 were examined. The torque generated by these yarns, both when unsteamed and when steamed at 110°C (1.43 bar) for 10 minutes, was measured about 1 week after spinning. For each experiment the torque per hank as a function of the tension per hank was obtained for 48 data points [hank sizes of 4, 8, 12, and 16 strands for six different applied tensions as in Figure 2 (performed twice)]. For each yarn a plot of torque per strand as a function of tension per strand was obtained and the best-fit straight line determined (r2 > 0.96 in all cases), similar to Figure 3. As explained above, the gradient is interpreted as the component of torque due to applied tension and the measured intercept as the intrinsic torque.

Torque due to Applied Tension Figure 6 plots the gradient data, namely the incremental change in strand torque per unit applied external tension, as a function of twist factor. The data from the four different experimental series of 40 tex yarns (unsteamed, steamed, dry, wet) all fall on the same straight line in Figure 6. This

demonstrates that the torque generated by a given applied external tension increases with increasing twist factor and is independent of the level of set and physical state of the yarn. This is also apparent in Figures 3 and 4 where the fitted lines for both wet and dry yarn results are parallel. A smaller data set was formed from 78 and 81 tex yarns with metric twist factors of 82 and 142 respectively, processed in three ways (unsteamed, steamed at 85°C for 10 minutes, steamed at 110°C for 10 minutes) and tested both dry and wet. These 12 results shown in Table 2 are also plotted on Figure 6 and again this data demonstrates clearly that the torque due to applied tension at a given twist factor is independent of the history or environment of the yarns and directly related to twist factor. The theoretical calculations of Bennett and Postle [10] indicate that the torque due to applied tension is purely determined by yarn geometry. In the case of a staple fiber yarn with perfect fiber migration, their equation has the solution:  sec 3 β – 3sec β + 2 LP ------ = R  --------------------------------------------- P  3tan β ( sec β – 1 ) 

(4)

where LP is the torque arising from an applied tension, P is the applied tension, R is the yarn radius and β is the helix angle of the surface fibres. Note that in the original paper, Bennett and Postle mistakenly included a factor of 2 in the right-hand side of equation (4) [personal communication: R. Postle]. (While both R and β are dependent on yarn extension, for the current experiments using the torquemeter, the maximum observed extension is less than 2% and this will not significantly alter the value of the right-hand side of equation (4).) From equation (4) LP ------ = R f { β } P

(5)

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Table 2 Summary of torque measurements on twelve yarns (two levels of linear density, two twist factors, three steaming treatments) all produced from the one parent wool. The torque/tension and intrinsic torque values were derived from the gradient and intercept of the line of best fit to the torque per strand versus tension per strand graph (n = 48 and r2 > 0.98 for all data). Linear density (tex)

78

78

78

81

81

81

40

40

40

40

40

40

Metric twist factor

80

80

80

140

140

140

140

140

140

87

87

87

85oC

Steaming treatment (10 mins)

none

85oC 110oC none

110oC

none

85oC

110oC

none

85oC

110oC

Torque/tension gradient dry (µNm/N)

16.56

18.29 18.62 36.18 34.34 34.88

25.13

26.21

22.32

12.44

13.31

13.97

Intrinsic torque dry(µNm)

2.635

0.634 0.437 4.621 1.186 0.176

2.854

0.568

0.13

0.947

0.251

0.205

Torque/tension gradient wet (µNm/N)

17.42

18.41 18.71 34.24 34.58 36.80

25.02

23.32

23.70

14.41

13.08

14.73

Intrinsic torque wet (µNm)

0.426

0.363 0.183 2.643 2. 371 1.598

1.569

1.259

0.634

0.280

0.224

0.071

1

0.8

0.4

1

0.8

0.25

Normalized intrinsic torque values

1.0

0.85

0.43

1.0

where  sec 3 β – 3sec β + 2 f { β } =  ---------------------------------------------  3tan β ( sec β – 1 ) 

(6)

For worsted yarns, the surface angle of twist β is less than 45° for the range of worsted yarns used [17] and a simple plot of equation (6), (not displayed here), shows that for β < 45° f{β} = 0.482 tan β

r2 = 0.999

(7)

where T is the yarn twist in turns/metre, vy is the yarn-specific volume in m3/g; that is, vy = (packing fraction × fiber density(σ))–1 and R, the yarn radius, is measured in m, see [17]. Hence it can be shown that tan β = 2 π1/2 vy1/2 α

0.6

the slopes in Figure 6 are in the ratio of Tex1/2 and this is also observed in the data in Figure 6; that is, the ratio of the slopes is 1.43, which is close to that predicted from the square root of the ratio of the 78 and 81 tex yarns with the 40 tex yarns, approximately √2. Furthermore by substituting for α, equation (10) becomes L -----P- = 9.64 × 10–4 vy T Tex P

(11)

L -----P- ÷ Tex = 9.64 × 10–4 vy T. P

(12)

and

Also on the basis of yarn geometry, tan β = 2 π RT, and Tex = π R2 vy–1 1000

0.9

(8)

where α is the metric twist factor, α = T(Tex/1000)1/2. Furthermore by combining equations (5), (6), (7) and (8) LP ------ = 0.964 π1/2 vy1/2 R α P

(9)

LP ------ = 0.964 vy (Tex/1000)1/2 α P

(10)

or

Equation (10) predicts that the data sets for constant linear density in Figure 6 form straight lines passing through the origin, as observed. Further, equation (10) predicts that

LP To test equation (12), Figure 7 is a plot of ( ----P ÷ Tex) against twist for all the 42 experiments from Figure 6; that is, the sets of 40 tex yarns (unset and set, dry and wet) over a range of twists and the nominally 80 tex yarns (actually 78 and 81) with two twist factors (80 and 140), unset and set, dry and wet (as shown in Table 2). This combined data set plotted in this manner forms one straight line through the origin as predicted by equation (12). The slope of the line of best fit through the origin, (r2 = 0.94) was 8.05 × 10–10 tex–1 m(tpm)–1 and from equation (12) the yarn-specific volume was estimated as 0.835 × 10–6 m3/g. Using a fiber density of 1.31 × 106 g/m3 for wool gives a packing fraction of 0.91, somewhat higher than the literature values of about 0.45–0.65 for worsted yarns [17]. One possibility is consolidation of the packing of the fibers due to the effect of applied tension or twist. This seems unlikely because, interestingly, the linear relationship in Figure 7 suggests that the packing of fibers does not change over the range of twist factors used. Similarly the effect of tension in Figures 3 and 4 indicate no effect of tension on packing density. Interestingly the packing fraction value of 0.91 equals that expected when uniform circular cross-section fibers are

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Figure 7 The incremental torque due to applied tension is normalized by tex and plotted against twist as per equation (12) using all the data in Figure 6.

Figure 8 The intrinsic torque as a function of yarn twist factor for the same 40 tex yarns as in Figure 6. Open circles represent unset yarns and open squares represent set yarns.

hexagonally close packed. This ideal result may be a consequence of the model used and needs further evaluation. For example, Bennett and Postle [10] show in their theoretical analysis that yarn torque is significantly affected by fiber migration and predict a fivefold decrease in torque between a 68 tex yarn of 600 tpm, a metric twist factor of 114, with perfect migration compared with no migration. The discovery described in this paper of a direct means to measure the torque/tension relationship will allow a more detailed evaluation of these theoretical models and alternative estimates of the yarn structural parameters.

Intrinsic Torque Figure 8 plots the intercepts of the torque/tension relationships, namely the intrinsic torque, as a function of twist factor for the nine 40 tex yarns either unsteamed or steamed at 110°C for 10 minutes. For the dry unsteamed yarn the

intrinsic torque increases linearly with the twist factor and if extrapolated the curve passes through the origin, as seen from Figure 9. The intrinsic torque for the dry, steamed yarn in Figure 8 is very low and shows no dependence on twist factor. The steaming treatment results in both cohesive and permanent set and when the wool yarns are heated by steaming, the wool exceeds the glass transition temperature [3] and some set can occur through thiol-disulphide interchange while in the rubbery state. Subsequent cooling of the yarn back to the glassy state leads to the stabilization of any residual torque with cohesive set sufficient to stabilize the yarn in its twisted configuration. The fibers are unable to straighten and no intrinsic torque will manifest in the yarn. The observed small constant value of torque can be explained as a consequence of the sample preparation for the torquemeter. In preparing the hanks for measurement, the yarn is drawn off the top of the bobbin and, for a package of approximately 3 cm diam-

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Figure 9 A comparison of the dry and wet intrinsic torque for the unset 40 tex yarns in Figure 8. Open diamonds are the dry values and the closed diamonds are the wet values.

eter; this will introduce an additional twist of approximately 10 turns per meter. By extrapolation of the dry unsteamed curve in Figure 8, the torque corresponding to this additional twist can be estimated to be approximately 0.1 µNm, which is in good agreement with the measured values. The work of Platt et al. [18] can be applied to the phenomenon of intrinsic torque identified in this study. Platt et al. [18] modeled the torsion in a yarn due to fiber bending and fiber torsion and derived the expression for yarn torque due to fiber bending MB and fiber torsion MT as: N f E f I f  log e sec 2 β – sin 2 β -  ---------------------------------------------- M B = --------------tan β Ry  

(13)

N f G f K f  sin 2 β M T = ------------------ -------------- R y  tan β 

(14)

and

where Nf, Ef, Gf, If and Kf are the number of fibers, the fiber bending and torsional moduli and the bending and torsional moment of inertia of the fibers, respectively, or Nf Ef Kf - ( f1 { β } + w f2 { β } ) M Total = -----------------Ry

(15)

where w is the ratio of the torsional rigidity Gf Kf to the bending rigidity Ef If and f1{ß} and f2{ß} are the two trigonometric factors in equations (13) and (14), respectively. Figure 9 of the paper by Platt et al. [11] graphs the influence of w on MTotal as a function of yarn surface helix angle. In the case of wool, w is expected to be about 0.71 in the dry state [18] in comparison with about 0.17 in the wet state [19] (i.e. equation (15) shows that the torsional contribution to the total torque is higher in the dry condition). Figure 9

plots the observed dry and wet intrinsic torque for the 40 tex unset yarns in Figure 8, as a function of metric twist factor. The similarity in the form of the observed data to the curves plotted by Platt et al. for a w value of approximately 0.71 and 0.17 is clear (In this region of twist, β is approximately linearly related to the metric twist factor α.) The full application of Platt’s model to the yarn torque data will be described in more detail in a subsequent paper with analysis across a wider range of yarns. Another feature consistent with both the torque model in equation (15) and wool physics is seen in Figure 10. The wet intrinsic torque is shown for the unset yarn and the steamed 40 tex yarns. After steaming at 110°C (1.43 bar) for 10 minutes, the wet intrinsic torque decreases and this is consistent with stress relaxation of the disulphide bonds within the intermediate filaments. Consequently the restoring force decreases and this is equivalent to a decrease in the bending and torsional moduli. If the fractional decay in these relaxation moduli after steaming, that is setting, is equal then equation (15) would predict that the shape of the intrinsic torque curve with twist factor would be similar, because w remains constant but the overall value of intrinsic torque will decrease as influenced by E in the factor, (Nf Ef Kf)/Ry, see equation (15). These features are evident in the wet data shown in Figure 10. Similar behavior can be seen in the wet torque data given in Table 2, for four sets of yarn, unsteamed and steamed under two conditions for setting. The effect of the steaming treatments on the relative wet fiber relaxation moduli is shown when the intrinsic torque data for the steamed yarns is normalized against the wet intrinsic torque for the unsteamed yarn. For example the 81 tex, 140 twist factor yarns show relative wet relaxation moduli of 1, 0.9 and 0.6. This trend is consistent with stress relaxation in the fiber during setting as a consequence of the rearrangement of disulphide cross-links and a reduction in the bending and torsional fiber relaxation moduli.

Torque in Worsted Wool Yarns P. Mitchell et al.

179

Figure 10 The effect of setting on the wet torque. Squares are the unset values and diamonds are the set values.

This approach to measuring the torsional properties of yarn has potential to be applied to yarn quality and longstanding problems of the dimensional stability of knitwear [20]. Further studies will apply this technique to a wider range of yarn structures and evaluate the effects on the problem on spirality in knitwear.

Conclusion

Literature Cited 1.

2.

3.

4.

The technique of measuring the torque in yarn hanks reported by Tavanai et al. [3] has been shown to be suitable for measuring the torque in single worsted wool yarns. The torque per strand, for a given strand tension was found to be independent of hank size and length over a wide range of hank sizes. In extending the approach of Tavanai et al. by measuring the torque as a function of applied tension for the first time, it was possible to directly resolve the measured torque into two components: the torque due to the applied tension and the intrinsic torque due to fiber bending and twisting. The torque due to applied tension was observed to depend only on the yarn geometry; that is, the twist and count of the yarn consistent with theoretical studies. Analysis of a wide range of wool yarns has lead to the estimate of the yarn-specific volume and a packing factor of 0.91 for ring spun yarns. The intrinsic yarn torque is related to the yarn history and physical state of the fiber, for example, level of set and moisture content, as well as the yarn geometry. This has been shown to be consistent with an existing model of yarn torque with components due to fiber bending and twisting. The method for measuring the yarn intrinsic torque allows the relaxation modulus of the fiber after various setting treatments to be estimated.

5.

6. 7.

8.

9. 10.

11. 12.

13. 14.

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15. Dhingra, R. C., and Postle, R., The Measurement of Yarn Torque in Continuous Filament Yarns, Part I: Experimental Techniques, J Textile Inst. 65, 126–132 (1974). 16. Dhingra, R. C., and Postle, R., The Measurement of Yarn Torque in Continuous Filament Yarns, Part II: the Effect of Yarn Tension, J Textile Inst. 65, 171–181 (1974). 17. Hearle. J. W. S., Grosberg, P., and Backer, S., Structural Mechanics of Fibers, Yarns, and Fabrics, Wiley- Interscience, 1, 61–100 (1969).

18. Platt, M. M., Klein, W. G., and Hamburger, W. J., Mechanics of Elastic Performance of Textile Materials, Part XIII, Textile Res. J. 28, 1–14 (1958). 19. Speakman, J. B., The Rigidity of Wool and its Change with Adsorption of Water Vapour, Trans Faraday Soc. 25, 92–103 (1929). 20. Tao, J., Dhingra, R. C., Chan, C. K., and Abbas, M. S., Effects of Yarn and Fabric Construction on Spirality of Cotton Single Jersey Fabrics, Textile Res. J. 67, 57–68 (1997).