Development and Experimental

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National Textile Center Annual Report: November 1999F97-C05

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DEVELOPMENT AND EXPERIMENTALEVALUATION OF NONLINEAR

PHENOMENA IN HIGH-SPEED YARNTRANSPORT SYSTEMS

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Principal Investigators

Bhuvenesh GoswamiTeam Leader – Textiles

Clemson University

Subhash BatraTextiles

NC State University

Tushar GhoshTextiles

NC State University

Barrie FraserApplied Mathematics

Sydney University

Bill OxenhamTextiles

NC State University

Christopher RahnMechanical Engineering

Clemson University

http://ece.clemson.edu/crb/research/yarn/ntc/textile.htm

GOALS

This project develops and experimentally validates nonlinear models for high-speed yarntransport systems. The research focuses on models for specific textile processes thatinvolve rotating balloons such as: i) unwinding from cylindrical (as in texturing) or conical(as in warping and weaving) packages; ii) ring twisting and winding (as in ring spinning orply-twisting); and iii) two-for-one twisting. The computer models provide insight into andpromote understanding of the complex process dynamics. The models can also be used todesign processes that provide low, uniform tension at high speed. This maximizes theprocess efficiency by minimizing yarn breaks and maximizing throughput.

ABSTRACT

During the last year of this project, our interdisciplinary, international group of researchersdeveloped new models for several complex yarn manufacturing processes and new, model-verifying experiments. At North Carolina State University Subhash Batra, Tushar Ghosh,Bill Oxenham, and their students refined models for the unwinding process and conductedring-spinning experiments. Barrie Fraser at the University of Sydney in Australiadeveloped twist models for ring-spinning and two-plying operations. Under the guidanceof Bhuvenesh Goswami (Textiles) and Chris Rahn (Mechanical Engineering), graduatestudents at Clemson University refined the Unwinding Analyzer for experimentalmeasurement of high-speed video and tension data.

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UNWINDING THEORY (Batra and Ghosh)

The governing equations developed in our previous research on cylindrical package havebeen modified to analyze the problem of unwinding from conical package, which is widelyused in the textile processes such as warping and weaving. As shown in Figure 1, the yarnpath can be divided into three regions: the balloon region (OL, region 1) where yarn flies inthe air, the drag region (LU, region 2) where yarn moves on the surface of package, and thestationary region (US, region 3) on the surface of package where yarn tension varies due tothe static friction. The equation of motion of yarn in region1 and 2 can be written as:

FRs

Ts

RkaRkkRDkRDmωωωωωωωωωωω

+∂∂

∂∂=×+××+×+ )(})(2{ 22 ωω

Where, m is the mass linear density of the yarn, R is the position vector of point P, ω is theangular speed of the rotating frame about z-axis, T is the yarn tension and a is the angularacceleration. For region 1, F is the air drag force per unit length of the yarn, and for region2, F is frictional drag force per unit length of yarn.

The above two-region analysis is sufficient to solve the problem when the tension atunwind point is less or equal to the residual tension in the yarn package. However, if this isnot the case, a third region need to be postulated from unwind point to some further point inthe yarn package where yarn tension decayed to residual tension. This point is known asstationary point S in Fig. 1. The tension decay is due to the static frictional force betweenthe yarn and package. The force equilibrium equation on P is:

0sincos =−++

kNeN

ds

RdF

ds

RdT

ds

drs

ϖϖϖϖϖϖ

αα

Where, position vector kzeHzcsR r

ϖϖϖ+−+= )tan)(()( 0 α , N is the normal force exerted

on the yarn element by the package, sFϖ

is the static friction force. sFϖ

equals to zero at the

Hu

Hs

VLUS R

φ

eerr

kkee

αα

H

FFiigguurree 11:: TThhee oovveerr--eenndd uunnwwiinnddiinngg ooff yyaarrnn((OO:: gguuiiddee--eeyyee;; LL:: lliifftt ooffff ppooiinntt;; UU:: uunnwwiinndd ppooiinntt;; SS::ssttaattiioonnaarryy

ppooiinntt;;

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stationary point and mF (maximum friction force in region 3, where frictional coefficient is

µ ) and at an arbitrary point NF ss µ= . Static frictional coefficient sµ at an arbitrary point

in region 3 is proportional to the yarn distance from stationary point S, i.e.:

( ) ( )usss ssss −−= µµ (10)

Where us , s , ss is the distance measured from guide eye to unwind point, a point in the

region 3 and stationary point respectively.

The equation of yarn motion can be solved as a boundary value problem if boundaryconditions at guide-eye, lift-off point, unwind point and stationary point along the yarn pathare defined. Numerical solutions of these problems have been obtained by using “shootingmethod” [2]. Most of the observations in cylindrical package are preserved in conicalpackage, such as effects of wind angle, yarn-package coefficient of friction, yarn

length in the balloon and residual tension on the balloon shape and tension distribution.Bifurcation phenomenon exists in conical package as well. However, the conicity ofconical package changes the balloon shape and tension distribution, and the tension in theyarn path is slightly less than in cylindrical package. Other observation includes that if the

Balloon shape and tension distribution

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Length from gudie eye

Sh

ape

and

ten

sio

n

mmc 450 = , ο6=α , ο20=φ , 0.1=µ , .,100denM = min,/1000mV =,450mmH u = gTres 78.0=

Figure 2: Length from Guide Eye (Nondimensional)Red: Unwinding from Conical Package with Conicity = 12o

Black: Unwinding from Cylindrical Package

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balloons have the same loops, the dr/ds value at the guide eye will decrease with theincrease of the tension at the guide-eye. See Figure 2.

RING SPINNING EXPERIMENTS (Oxenham)

Earlier annual reports have shown the derivation of the theoretical models. Studies arebeing conducted to validate the theoretical models in different spinning conditions andparameters. Experiments are being conducted with different yarns and defects and thebehavior of the balloon is being studied. This will enable us to a better understanding thevalidity of theoretical models.

Emphasis has been placed on the tension monitoring methods since this was shown clearlyto correlate with the observed instabilities in the spinning process (Punitha, 1998). It isunderstood that the variations in yarn tension during spinning causes proportional variationin traveler speed. It is also understood that this parameter could potentially offer basis of acontrol system to enable optimum productivity. The conventional devices to measure thevariation of tension are costly and difficult to use. In order to overcome the deficiencies ofthe conventional devices a new device was set-up. Four proximity sensors were mounted atequal angular intervals around the circumference of the ring (see Figure 3). Each time thetraveler passes the sensor, an electric pulse is produced. The time elapsed between thepresence of the traveler in front of the sensors is recorded. The traveler speed in eachquarter revolution is then determined from the interval between successive pulses. Thiscould ultimately be used as the basis of a control system to maximize the productioncapabilities of the ring frame.

This approach will be further pursued by mounting additional sensors and coupling this to amore sophisticated image capturing system. This system will analyze two perpendicularimages to develop a 3D profile of the balloon and this will be compared with datagenerated by the traveler speed measuring system. The data obtained from thesemeasurements will be used to clearly define unstable operating conditions.

Ring spinning experiment results

The figure 4 shows five consecutive captured frames for an experimental balloon profilefor M of 23 (traveler mass), spindle speed of 12,500 rpm, yarn count of 29 Tex, and ringradius = 25 mm, at maximum bobbin diameter. The theoretical balloon shape (obtainedfrom the theoretical model) predicts the formation of one and a half balloons withminimum radius less than that of the bobbin radius. This would cause the yarn to wraparound the bobbin and ultimately lead to an end-break. The experimental evidence from thephotographs clearly supports this proposal.

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FRONT

BACK

SENSOR 1

SENSOR 4 SENSOR 3

SENSOR 2

RightSeparator Plate

LeftSeparator Plate

Traveler

RingBobbin

Spindle

Figure 3: Schematic of the traveler speed monitoring system

Figure 4: Theoretical and experimental balloon profiles

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TWISTING THEORY (Fraser and Stump (U. Queensland))

During this period the the theory for the dynamics of twist in the ring-spinning balloon wasbeen further developed to model strand twist variation in yarn plying processes (see paperscited below). The major progress has been in the inclusion of the effect of twist in the yarnpackage unwinding balloon theory. This work, by Clark, Fraser and Stump, has just beenwritten up and submitted for publication. The main new result from this work is the morerealistic model for the forces that hold the yarn in the package surface and resist theunwinding. At present we are looking at the stability of unwinding balloon configurations.Preliminary results from this work are expected by November next.

UNWINDING EXPERIMENTS (Goswami and Rahn)

The magnitude and uniformity of the withdrawal tension during over-end unwindingdepends on the coefficient of friction between the yarn and the package. Currently usedfriction measurement techniques are not adequate for measuring package surface roughnesscharacteristics such as yarn-on-package friction at high speed. In research conducted thisyear, a new measurement technique for yarn-on-package friction has been developed thatuses simultaneously captured tension data and images of the yarn sliding on the packagesurface during actual unwinding. An algorithm combines a mathematical model of thesliding motion with experimental data to produce estimates of the coefficient of friction ofthe yarn/package. Packages of equivalent denier textured and fully drawn polyester yarnsare tested with measurement uncertainty of less than 10%.

Figure 5 shows a schematic diagram of the Unwinding Analyzer used for experimentalmeasurement. Yarn is withdrawn from a fixed horizontal package by a yarn drive attransport speeds of up to 1000 meters per minute. A tension sensor installed on the standnear the eyelet measures the yarn tension. A video camera and stroboscopes capture theyarn path. The system is controlled and synchronized by Windows-based software on aPC. The software package integrates data display, control and image processing functionsin one graphical user interface. The image captured by the video camera is transferred tothe PC by the video capture board and displayed. The Digital Signal Processor (DSP)board receives signals from the speed sensor, tension sensor, and synchronization sensor.The tension data sampled by the tension sensor is filtered and displayed on the PC.Synchronization pulses are generated by an optical synchronization sensor at every halfrevolution of the balloon and used to measure the rotation speed and control the capturingof the image by the video camera and flashing of the stroboscopes.

The unwinding analyzer data is processed through a friction algorithm to estimate theyarn/package friction coefficients of fully drawn and textured polyester yarn packages.The solid curve in Fig. 6 shows the coefficient of friction for FDY packages with radii of110 ± 3 mm over a range of withdrawal speeds. The coefficient of friction shows markedincrease from 500 to 800 m/min that tapers off above 800 m/min. Although it is difficult todifferentiate between the effects of tension and speed because both are increasing duringthe experiment, the relative insensitivity of friction coefficient to tension in previous

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experiments indicate that speed is responsible for the increasing friction. Figure 6 showsthe increase in the textured yarn coefficient of friction with increasing speed. Again, therate of increase seems to decrease above 800 m/min.

This research develops the first in-situ measurements of yarn/package friction during over-end unwinding. The method combines measurements from the Unwinding Analyzer with acomputational algorithm based on the mechanics of the yarn sliding on the packagesurface. The experimental results are reasonable with an overall uncertainty of less than10%. The FDY coefficient of friction is relatively insensitive to normal force but sensitiveto withdrawal speed, increasing from 0.23 to 0.35 over the speed range of 500 - 1000m/min. The TY packages have higher coefficients of friction than the FDY packages. TheTY coefficients also increase with speed from 0.37 to 0.48 in the range of 400 - 1000m/min. The slopes of the coefficient of friction versus speed curves decrease above 800m/min for both materials. We have also developed a simple measurement method using anInstron Tensile Tester can be used for comparative coefficient of friction measurements butprovides quantitative agreement with the in-situ measurements only at low tension.

Figure 5: The Unwinding Analyzer

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REFERENCES

1. X. Ma, “Dynamic Analysis of Unwinding from Cylindrical Package”, Aug, 1997.Ph.D. Theses, Burlington Textile Library, NCSU

2. W. B. Fraser,, T. K. Ghosh, S. K. Batra, “On unwinding yarn from a cylindricalpackage,” Prod. R. So. Lond. (1992) 436, 479-498.

3. Fraser, W.B.and Stump, D.M., 1998, “Yarn twist in the ring-spinning balloon.” Proc.Roy. Soc. Series A, vol. 454 pp. 707--723.

4. Fraser. W.B. and Stump, D.M., 1998, “Equilibrium of rhe convergence point in two-strand plying.” Int. J. Solids and Structures. vol. 35, pp. 285--298.

5. Stump, D.M., and Fraser W.B. 1998, “On the dynamical theory of twist in yarnplying.” Mathematical Engineering in Industry, vol. 7, pp. 41--56.

6. Stump, D.M., and Fraser W.B. and Gates, K.E., 1998, The writhing of circular cross-section rods: Undersea cables to DNA supercoils. Proc. Roy. Soc. Lond. 454, 2123--2156.

Figure 6: Coefficient of friction versus withdrawal speed: FDY(solid) and TY (dashed). Error bars indicate the uncertaintyassociated with the measurement.

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7. Fraser. W.B. and Stump, D.M., 1998, “Twist in balanced ply structures.” J. Textile Inst.vol. 89, pp. 485--497.

8. Clark J.D., Fraser, W.B., Sharma, R, and Rahn, C.D., 1998, “The dynamic response ofa ballooning yarn: Theory and experiment.” Proc. Roy. Soc. Lond. Series A vol. 454,pp. 2767--2789.

9. Stump, D.M. and Fraser, W.B., 1999, “Bending boundary-layers in a moving strip.”Nonlinear Dynamics, (in press).

10. Champneys, A.R.and Fraser, W.B., 1999 “The “Indian rope trick” for a parametricallyexcited flexible rod: Linearized analysis.” Proc. Roy. Soc. Lond. (in press)

11. Stump. D.M. and Fraser, W.B., 1999, “Multiple solutions for writhed rods: implicationsfor DNA supercoiling.” Proc. Roy. Lond. (in press).

12. Clark, J.D., Fraser, W.B. and Stump, D.M., 1999, “Simulation of tension in anunwinding yarn.” Mathematical Engineering in Industry. (submitted)

13. Zhu, F., Sharma, R., and Rahn, C. D., “Vibrations of Ballooning Elastic Strings,”ASME Journal of Applied Mechanics, Vol. 64, No. 3, pp. 676-683, September1997.12.

14. Zhu, F., Hall, K., and Rahn, C. D., “Steady State Response and Stability of BallooningStrings in Air,” International Journal of Nonlinear Mechanics, Vol. 33, No. 1, pp. 33-46, 1998.19.

15. Sharma, R., and Rahn, C., “An Experimental Study of Ballooning Yarn with a ControlRing,” Journal of the Textile Institute, Part 1: Fibre Science and Textile Technology,Vol. 89, pp. 621-634, 1998.22.

16. Kong, X., Rahn C., and Goswami, B., “Steady State Unwinding of Yarn fromCylindrical Packages,” Textile Research Journal, Vol. 69, No. 4, pp. 292-306, March1999.24.

17. Zhu, F., and Rahn, C., “Limit Cycle Prediction for Ballooning Strings,” InternationalJournal of Nonlinear Mechanics, (accepted, April 1998).25.

18. Wu, R., Yu, J., Rahn, C., and Goswami, B., “Measurement of Yarn/Package FrictionDuring Over-end Unwinding,” Textile Research Journal, (accepted, March 1999).

19. Punitha J.H., Experimental Study of Ring-Spinning, Ph.D thesis, North Carolina StateUniversity, August (1998).

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