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2006 76: 559Textile Research JournalZheng-Xue Tang, Xungai Wang, Lijing Wang and W. Barrie FraserThe Effect of Yarn Hairiness on Air Drag in Ring Spinning

  

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Textile Research Journal Article

Textile Research Journal Vol 76(7): 559–566 DOI: 10.1177/0040517506064472 www.trj.sagepub.com © 2006 SAGE Publications

The Effect of Yarn Hairiness on Air Drag in Ring SpinningZheng-Xue Tang, Xungai Wang1, and Lijing WangSchool of Engineering and Technology, Deakin University, Geelong, VIC 3217, Australia

W. Barrie FraserSchool of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia

Ring spinning has been a very important technology forstaple yarns as it produces relatively high quality yarns andthe quality of ring spun yarns has been used as the bench-mark for yarns spun on other systems [1]. Many research-ers have made contributions to the development of thering-spinning system to reduce power consumption andimprove productivity [2−18]. In particular, the effect of airdrag on spinning tension, which relates to ends-down andenergy consumption, has been reported [19–23]. However,for simplification of calculation and modeling, previousstudies often neglected yarn hairiness and used smooth fil-ament yarns.

The concept of hairiness as a quantitative parameter ofyarns was first definitively stated in the early 1950s [24].Since then yarn hairiness and its measurement haveattracted increasing attention. In the last two decades, con-siderable research has gone into the methods of measuringand reducing yarn hairiness [25−35]. Recently, Chang et al.[36] reported the importance of hair length and number ofhairs in determining the power consumption to rotate aring spun yarn package.

This study examines the effects of hairiness on air dragin ring spinning. The air drag arises mainly in two parts –the surface of a rotating yarn package and the ballon. Theauthors first describe the testing of the hairiness effects,and then the development of the models of skin friction

coefficient on the surface of rotating cotton and wool yarnpackages. Finally, they verify the results empirically.1

Experimental

Yarn Samples and their Hairiness IndexesA 38 tex cotton yarn and a 103 tex wool yarn were used inthe experiments. The hairiness indexes of these two yarnswere measured on an Uster Tester 4 under standard condi-tions and at a speed of 400 m/minute. Table 1 lists the hair-iness results, which were used for the further analysesdescribed in the following sections.

Power Consumption on Rotating Yarn Package SurfacesA single spindle rig (see Figure 3 in Ref. [36]) was adoptedto measure the level of power consumption during therotation of a single yarn package. The roving build methodand the 38 tex cotton yarn were used to wind three yarn

Abstract Air drag on yarn and package surfacesaffects yarn tension, which in turn affects energyconsumption and ends-down in ring spinning. Thisstudy investigated the effects of yarn hairiness onair drag in ring spinning. Theoretical models of skinfriction coefficient on the surface of rotating yarnpackages were developed. The predicted resultswere verified with experimental data obtained fromcotton and wool yarns. The results show that hairi-ness increases the air drag by about one-quarterand one-third for the rotating cotton and wool yarnpackages, respectively. In addition, yarn hairinessincreases the air drag by about one-tenth on a bal-looning cotton yarn.

Key words ring spinning, ballooning yarn, yarnpackage, yarn hairiness, air drag

1 Corresponding author: e-mail: xwang@deakin.edu.au

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560 Textile Research Journal 76(7)TRJTRJ

packages with different layers (i.e., package A with 2 lay-ers, package B with 7 layers and package C with 12 layers)and the 103 tex pure wool yarn to wind one package (i.e.,package D with 2 layers). The packages were the sameheight (h = 0.245 m). After winding the packages, thepackage diameters were measured. For each of the fourpackages, the diameter was measured at the two ends andin the middle, and their average was used as the diameterof the package. The cotton yarn packages had averagediameters d1 = 0.0279 m, d2 = 0.0302 m, d3 = 0.0325 m,and the pure wool yarn package had diameter d4 =0.0297 m.

Each of the four packages were tested twice at spindlespeeds ranging from 2000 rpm (i.e. 33 rps) to 16 000 rpm(i.e. 267 rps), in steps of 2000 rpm. For each of the pack-ages at different spindle speeds, the average values of thecurrent and voltage readings were taken from the testdevice and the readings were used to calculate the powerconsumption at a given spindle speed. The experimentalresults are shown in Table 2.

Tension in a Ballooning YarnThe 38 tex cotton yarn and the roving build method wereused to wind a yarn package with one layer and the hairi-ness on the package surface was removed by singeing. Thesinged 38 tex cotton yarn was then unwound from thepackage. The tensions in the singed and unsinged yarnswere measured using a specially constructed rig (see Fig-ure 2 in Ref. [37]). One end of the yarn, which passesthrough the guide-eye, was attached to the tension sensorand the other end was fixed on the eyelet. When the eyeletstarted rotating, the yarn between the guide-eye and rotat-ing eyelet formed a balloon and generated tension in the

yarn. The tension signal at the guide-eye was digitized bythe computer data acquisition system.

Theoretical

Modeling Skin Friction Coefficient on a Yarn Package SurfaceThe power required to overcome skin friction drag, Pf (W),on the surface of a rotating yarn package can be expressed as:

(1)

where Cf (scalar) is the skin friction coefficient on thepackage surface, V (rps) is a given full spindle speed, d (m)is the diameter and Sp (m2) is the surface-area of the yarnpackage [21].

During yarn winding in ring spinning, the package pro-file varies with winding-on time and is not of a strictly cylin-drical shape. For a full yarn package, the surface area of themain part (with the maximum package diameter) is about90% of the yarn package surface. In order to simplify thecalculation, the skin friction coefficient on the surface ofthe yarn package is considered to be the skin friction coeffi-cient on the surface of the main part of this yarn package.Let d (m) be the diameter of main part of a yarn package,then the yarn package can be taken as a cylinder havingdiameter d and height h (m), and equation (1) becomes:

. (2)

Based on the experimental data in Table 2, the skin fric-tion coefficient on the surface of natural cotton yarn packagewith a diameter of 0.0279 m (i.e., package A) was calculatedusing equation (2), as shown in the right column in Table 3.The skin friction coefficient on the surface of other yarnpackages can be calculated using the same method.

Table 1 Hairiness index of cotton and wool yarns.

Yarn type Cotton Wool

Yarn count (tex)Hairiness index (H)

388.1

10313.0

Pf12---ρ πdV( )3SpCf=

Cf2Pf

ρ dπ( )4hV 3---------------------------=

Table 2 Power consumption on the surfaces of rotating yarn packages at varying spindle speed.

Spindle speed Package A(W)

Package B(W)

Package C(W)

Package D(W)

Empty bobbin(W)(rpm) (rps)

200040006000800010000120001400016000

367

100133167200233267

15.93920.58126.96434.98744.95155.67569.86586.359

18.89223.54729.94738.27348.51559.42573.89690.612

22.19626.89833.39842.41052.49663.42778.46495.130

25.77128.67633.92941.99352.28862.41276.75293.390

5.1389.744

15.72922.84731.77142.05555.56771.431

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The Effect of Yarn Hairiness on Air Drag in Ring Spinning Z.-X. Tang et al. 561 TRJ

The skin friction coefficient [Cf (scalar)] on a rotatingyarn package surface without hairiness depends on the fullspindle speed [V (rps)] and the package diameter [d (m)]:

(3)

where a and b are constants that can be determined fromexperiments [21].

Equation (3) was modified into a general model for theskin friction coefficient on the surface of a rotating yarnpackage:

(4)

where H (scalar) is the yarn hairiness index that can bemeasured; a, b, a1 and b1 are constants that can be deter-mined from experiments.

If equation (4) is applied to a rotating yarn package sur-face without hairiness (e.g. H = 0), then equation (4)becomes equation (3). In equation (3), the constants (a =148 030 and b = –2.575) for the cotton yarn were deter-mined in the previous study [21]. Now constants a1 and b1can be determined using experimental data.

From Table 1, the hairiness index of cotton 38 tex yarnis 8.1. Based on the data in the second and fourth columns(from left to right) in Table 3 and using the principle ofmaking a “best fit” between the theoretical and experimen-tal points, as shown in Figure 2, the authors obtained a1 =384128 and b1 = –3.4316 for the cotton yarn in equation (4).

The comparisons between skin friction coefficients onthe surface of yarn packages obtained from the experi-ments and the predictions obtained from equation (4) areshown in Table 4.

Table 3 Skin friction coefficients on the surfaces of natural yarn package and singed yarn package (package diameter = 0.0279 m).

Spindle speed (V)Skin friction coefficient (Cf ) on package surfaces (scalar)

(rpm) (rps) Hairiness singed* Natural hairiness

200040006000800010000120001400016000

3367

100133167200233267

16.93212.66660.93330.44690.25390.16080.10900.0778

33.55944.20881.29290.58940.32760.19590.12950.0906

* Data obtained from [27].

Cf0.025

d--------------aV b=

Cf0.025

d-------------- aV b a1HV

b1 +( )=

Figure 1 Modelling skin friction coefficient on the surfaceof a rotating natural cotton yarn package (package diam-eter = 0.0279 m).

Table 4 Comparison of skin friction coefficients on yarn package surfaces between experiments and predictions.

Spindle speed (V)

Cotton yarn package B(d = 0.0302 m, H = 8.1)

Cotton yarn package C(d = 0.0325 m, H = 8.1)

Wool yarn package D(d = 0.0297 m, H = 13.0)

(rps) Cf-experimental Cf-theoretical Cf-experimental Cf-theoretical Cf-experimental Cf-theoretical

3367100133167200233267

31.19313.91301.19430.54670.30380.18240.12120.0850

29.99523.88341.22050.54510.29400.17830.11720.0816

28.90073.63291.10880.51790.28090.16760.11310.0784

27.87243.60861.13410.50650.27320.16570.10890.0758

50.13665.75051.63790.72690.39880.22900.15010.1042

42.49325.13271.55220.67610.35820.21440.13940.0963

d, diameter of a yarn package; H, hairiness index of a yarn.

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562 Textile Research Journal 76(7)TRJTRJ

Modeling Air Drag Coefficient on a Ballooning YarnConsider the yarn tension at a material point P(r, θ, z) for afree-balloon (no control ring) spinning, as shown in Fig-ure 3. Let Fd be the air drag, the quantity of air drag actingon the yarn segment ds at P on a ballooning yarn owing toair-resistance can be evaluated by [36]:

(5)

where ∆Fd (N) = |∆Fd|, ρ (kg/m3) is air density, ∆CD (sca-lar) is the drag coefficient at P, ∆A (m2) is the projectedfrontal area of the yarn segment ds, i.e., ∆A = yarn diame-ter × the length of ds, and υ (m/s) is the linear velocity ofthe ballooning yarn at P.

Since the velocity at point P on the ballooning yarndepends on the balloon radius at P and the rotational speedof the yarn which is constant, the drag coefficient at Pdepends on the yarn velocity at P. Therefore, ∆CD and υvary with balloon radius.

For simplicity, however, the authors assume that the airdrag coefficient ∆CD is constant along the whole length ofthe yarn in the balloon, and it takes on a value appropriateto the velocity of the yarn at the maximum balloon radius.From equation (5), the quantity of air drag acting on thewhole ballooning yarn can be estimated by:

(6)

where ρ = 1.197 kg/m3, dy (m) is yarn diameter, sl (m) isyarn length in balloon, rmax (m) is the maximum radius ofthe balloon, V (rps) is the spindle speed and CD (scalar) isthe air drag coefficient on the ballooning yarn.

From equation (6), the effects of yarn hairiness on airdrag, (i.e., the percentage of air drag increased due to yarnhairiness) on a ballooning yarn can be estimated once theair drag coefficients of the natural (hairy) yarn and thesinged (hair free) yarn of the same diameter are known.

Figure 4 shows the comparisons of the curves of tensionat the guide-eye against yarn length in the balloon, wherethe experimental data came from simulated spinning experi-ments and have been converted into a normalized form, andthe theoretical curve came from simulation with normalizedair drag coefficients, which were estimated by making a“best fit” between the theoretical and experimental turningpoints. The normalized air drag coefficient p0 equals 5.0 forthe natural 38 tex cotton yarn and p0 equals 4.6 for singed 38tex cotton yarn.

There is a relationship between the normalization form[p0 (scalar)] and dimensional form [CD (scalar)] of the airdrag coefficient on a rotating yarn as below:

(7)

where ρ = 1.197 kg/m3, d (m) is yarn diameter, a (m) isring radius and m (kg/m) is linear density of yarn [20].

Figure 2 Yarn tension T, drawing force Fp, air drag Fd andcentrifugal force Fc acting on a material point P on a bal-looning yarn in a free-balloon ring spinning.

∆Fd12---∆CD ρ ∆A υ2⋅⋅ ⋅=

Fd 2π2ρdys1rmax2 V 2CD≈

Figure 3 Modelling air drag coefficients (p0) on balloon-ing 38 tex cotton yarn at 5300 rpm: p0 = 5.0 for naturalyarn and p0 = 4.6 for singed yarn.

CDm

8ρda------------- p0=

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The Effect of Yarn Hairiness on Air Drag in Ring Spinning Z.-X. Tang et al. 563 TRJ

Results and Discussion

Difference in Hairiness Effect on Wool and Cotton Yarn Package Surfaces

The data in Table 3 show that the effect of yarn hairinesson skin friction coefficient on the surface of a rotating yarnpackage is inversely proportional to spindle speed. Specifi-cally, the skin friction coefficient increases about 98% at aspindle speed of 2000 rpm and about 16.5% at spindlespeed of 16 000 rpm for cotton yarn package.

Table 4 shows that the results from equation (4) were ver-ified by experimental data very well for cotton yarn packagesB and C (e.g., the average relative error is less than 2.3%).However, for wool yarn package D, the experimentallydetermined skin friction coefficients were greater than thosecalculated from equation (4) and the average relative erroris about 10%. One reason for this may be that the hair fiberson the wool yarn are much coarser and longer than the hairfibers on the cotton yarn (e.g., the average diameter of woolfibers is about 24 µm whereas the average width of cottonfibers is about 13 µm).

Equation (4) was modified into a new model that canmore accurately predict the skin friction coefficient on thesurface of a rotating wool yarn package as below:

(8)

where d (m) is the diameter of a wool yarn package, V (rps)is a given full spindle speed, H (scalar) is the hairinessindex of the wool yarn, a, b, a1 and b1 are still equal to 148030, –2.575, 384 128 and –3.4316, respectively.

Figure 5 displays a comparison of skin friction coeffi-cients on the surface of the wool yarn package betweenexperiments and model prediction from equation (8).

Effects of Yarn Hairiness on Air Drag on a Rotating Yarn Package SurfaceA yarn package, being a circular-cylinder with diameter ofd (m) and height of h (m), rotates at a given full spindlespeed V (rps), the air drag Fd (N) on the package surfacecan be obtained by [38]:

(9)

where ρ = 1.197 kg/m3, Sp (m2) is surface area and Cf (sca-lar) is the skin friction coefficient on the surface of the cir-cular-cylinder.

Let Cfs and Fds be the skin friction coefficient and airdrag, respectively, on the package surface of singed yarn;similarly, let Cfn and Fdn be the skin friction coefficient and

air drag, respectively, on the package surface of un-singednatural yarn. Two cotton yarn packages wound by the 38tex cotton yarn and another two wool yarn packages woundby the 103 tex wool yarn were considered. All four pack-ages had the same diameter of 0.045 m and the sameheight of 0.245 m, and the surfaces of one cotton packageand one wool package were singed. Table 5 shows the com-parison of air drag for the singed and un-singed cottonyarn packages rotating at different speeds, where Cfs wascalculated from equation (3), Cfn was calculated fromequation (4), Fds and Fdn were calculated from equation(9). Table 6 lists similar results for the wool yarn packages.

Tables 5 and 6 show that yarn hairiness contributed a25% air drag (average value) on the surface of a rotatingcotton yarn package and a 35% air drag (average value) onthe surface of a rotating wool yarn package.

Effect of Yarn Hairiness on Air Drag on a Ballooning Yarn Let CDs and Fds be the air drag coefficient and air drag,respectively, on a ballooning yarn which has been singed;similarly, let CDn and Fdn be the respective air drag coeffi-cient and air drag on a ballooning natural yarn. If theeffects of hairiness on the diameter and mass of yarn in theballoon are ignored, from equation (6):

(10)

and

Cf0.025

d-------------- aV b 1.4a1HV

b1 +( )=

Fd12---ρ πdV( )2SpCf=

Figure 4 A comparison of skin friction coefficients on thesurface of wool yarn packages between experiments andmodel prediction.

Fdn 2π2ρdys1rmax2 V2CDn=

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564 Textile Research Journal 76(7)TRJTRJ

(11)

where ρ = 1.197 kg/m3, dy (m) is the yarn diameter, sl (m)is the yarn length in the balloon, rmax (m) is the maximumradius of the balloon, V (rps) is the spindle speed and CD(scalar) is the air drag coefficient on the ballooning yarn.

From equations (7), (10) and (11), and p0n = 5.0 andp0s = 4.6 for the 38 tex cotton yarn, one gets:

(12)

Equation (12) shows that the hairiness on a ballooningcotton yarn increases the air drag by around 9%. This canbe considered to be skin friction drag increase due to hairi-ness when the effects of hairiness on the diameter andmass of yarn in balloon are ignored.

Conclusions

Models for predicting skin friction coefficient on the surfaceof rotating cotton and wool yarn packages were developed.

The effects of yarn hairiness on air drag on the surface of arotating yarn package and on a ballooning yarn were exam-ined. The results indicate the following conslusions.

1. The effect of yarn hairiness on skin friction coeffi-cient on the surface of a rotating yarn package isinversely proportional to spindle speed; specifically,for the cotton yarn package, the skin friction coeffi-cient increased from about 16% at a spindle speed of16 000 rpm to about 98% at a spindle speed of 2000rpm;

2. The air drag on a ballooning yarn and the averageair drag on the surface of a rotating yarn packageboth increased with an increase in yarn hairiness.For instance, singing the surface hairs off the cottonand wool yarn packages reduced the average air dragon the rotating packages by about 26 and 33%,respectively; similarly, air drag on the ballooningcotton yarn was reduced by about 9% when the yarnwas singed to remove surface hairs.

This research highlights the significance of yarn hairinessin ring spinning. Realistic models of ring spinning shouldincorporate the effect of yarn hairiness on air drag actingon the rotating package surface as well as on the balloon-ing yarn.

Table 5 Comparison of air drag between packages of natural and singed cotton yarns at different rotating speeds.

Spindle speed (V) Natural package surface Surface without hairiness (Fdn – Fds)/Fds

(%)(rpm) (rps) Cfn (scalar) Fdn (N) Cfs (scalar) Fds (N)

200040006000800010000120001400016000

3367

100133167200233267

20.13012.60620.81910.36580.19730.11970.07860.0548

9.26674.79893.39342.69442.27051.98301.77361.6133

9.85521.65390.58220.27760.15620.09770.06570.0466

4.53673.04542.41212.04441.79821.61921.48191.3724

5137292421181615

Table 6 Comparison of air drag between packages of natural and singed wool yarns at different rotating speeds.

Spindle speed (V) Natural package surface Surface without hairiness (Fdn – Fds)/Fds

(%)(rpm) (rps) Cfn (scalar) Fdn (N) Cfs (scalar) Fds (N)

200040006000800010000120001400016000

3367

100133167200233267

24.24002.98710.91380.40110.21370.12840.08380.0580

11.15865.50033.78602.95442.45942.12851.89031.7097

9.85521.65390.58220.27760.15620.09770.06570.0466

4.53673.04542.41212.04441.79821.61921.48191.3724

5945363127242220

Fds 2π2ρdys1rmax2 V2CDs=

Fdn Fds–( ) Fds⁄CDn CDs–

CDs-------------------------

p0n p0s–p0s

-------------------- 8.7%≈= =

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The Effect of Yarn Hairiness on Air Drag in Ring Spinning Z.-X. Tang et al. 565 TRJ

AcknowledgementsThis work was funded by a grant from the AustralianResearch Council (ARC) under its discovery project scheme.The authors would like to thank Mr. Chris Hurren at DeakinUniversity for assisting with the experimental work.

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