F97-C5 Page -1- DEVELOPMENT AND EXPERIMENTAL EVALUATION OF NONLINEAR PHENOMENA IN HIGH-SPEED YARN TRANSPORT SYSTEMS F97-C5. Principal Investigators

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1 F97-C5 Page -1- DEVELOPMENT AND EXPERIMENTAL EVALUATION OF NONLINEAR PHENOMENA IN HIGH-SPEED YARN TRANSPORT SYSTEMS F97-C5 Principal Investigators Bhuvenesh Goswami Team Leader Textiles Clemson University Barrie Fraser Applied Mathematics Sydney University Subhash Batra Textiles NC State University Bill Oxenham Textiles NC State University Tushar Ghosh Textiles NC State University Christopher Rahn Mechanical Engineering Clemson University GOALS This project develops and experimentally validates nonlinear models for high-speed yarn transport systems. The research focuses on models for specific textile processes that involve 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 or ply-twisting); and iii) two-for-one twisting. The computer models provide insight into and promote understanding of the complex process dynamics. The models can also be used to design processes that provide low, uniform tension at high speed. This maximizes the process efficiency by minimizing yarn breaks and maximizing throughput. ABSTRACT During the second year, this interdisciplinary, international research group developed and experimentally validated computer models for ring spinning, twisting, and unwinding. New models for unwinding near the package ends and with conical packages were developed. Several ring-spinning experiments were completed that demonstrate the applicability of low cost proximity sensors for tension monitoring. Improved models for yarn twist in ring-spinning and two-plying enable prediction of system performance. The Unwinding Analyzer has been improved to allow simultaneous capture of high-speed videos, balloon rotation rate, and tension during unwinding.

2 F97-C5 Page -2- INTRODUCTION During the second year of this project, our interdisciplinary, international group of researchers developed 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 conducted ring-spinning experiments. Barrie Fraser at the University of Sydney in Australia developed twist models for ring-spinning and two-plying operations. Under the guidance of Bhuvenesh Goswami (Textiles) and Chris Rahn (Mechanical Engineering), graduate students at Clemson University refined the Unwinding Analyzer for experimental measurement of high-speed video and tension data. UNWINDING THEORY (Batra and Ghosh) Analysis of Package Ends for Cylindrical Packages A computational method [1] to solve the problem of unwinding yarn from a cylindrical package has already been developed. However, the problem of unwinding o 1 v2 from end regions of the package is Point1: Transition point, more complex. It requires b specification of appropriate 2 φu φu->φe and t=0 boundary conditions. The threeregion analysis developed earlier has 4 been applied to examine this φe b problem. The following two v1 equations build the numerical 5 relationship between unwinding Figure 1. The expanded view of yarn path at end of package position along package axis (x) and the end region winding angle (φ e ): 1 y / b φe = tan ((2e 1) tanφu ) y / b x = tanφ ( y b + 2be ) u The expanded yarn path at the end of package is shown in Figure 1. Where t: t is time elapsed between point 1 and 2, b is the distance between the path of winding point and the path of guide point, (x,y) is the position of winding point, φ u is the winding angle in the middle part (constant) and φ e is the winding angle in the (variable). The following conclusions are obtained from our analysis: Yarn Tension varies periodically, with maximum at far end and minimum at near end to the guide eye.

3 F97-C5 Page C = 80mm, µ = 0.6, V = 800m/min, H u = 480mm, T res = 0.5gf Yarn tension increases with the increase in the height of the unwind point on the surface of the package. However, at the far end of the package the tension drops slightly due to the decrease of wind angle in the end-region from φ u to 0 (or from -φ u to 0). See figure 2. There is a region in the near end of the package near the guide eye, in which the analysis in its present form may not be applicable because the lift-off point might fall off the package as the unwind point move toward the guide eye. Unwinding from Conical Package Tension at Guide-eye dr/ds at Guide-eye Figure 2. Tension and dr/ds at guide eye with different wind angle φ u The governing equations developed in our previous research on cylindrical package have been modified to analyze the problem of unwinding from conical package, which is widely used in the textile processes such as warping and weaving. As shown in Figure 3, α S U L φ e k e r R H H u H s V the yarn path can be divided into three regions: the balloon region (OL, region 1) where yarn flies in the air, the drag region (LU, region 2) where yarn moves on the surface of package, and the stationary region (US, region 3) on the surface of package where yarn tension varies due to the static friction. The equation of motion of yarn in region1 and 2 can be written as: Figure 3. The over-end unwinding of yarn (O: guide-eye; L: lift off point; U: unwind point; S:stationary point; α: conicity of conical package) ω ω ω ω ω ω ω ω ω ω ω 2 2 m{ D R + 2ωk DR + ω k ( k R) + Dωk R} = ( T R) + F s s Where, m is the mass linear density of the yarn, R is the position vector of point P, ω is the angular speed of the rotating frame about z-axis, T is the yarn tension. For region 1, F is the air drag force per unit length of the yarn, and for region 2, F is frictional drag force per unit length of yarn. The equation of yarn motion can be solved as a boundary value problem if boundary conditions at guide-eye, lift-off point, unwind point and stationary point along the yarn path are defined. Numerical solutions of these problems have been obtained by using shooting method [2]. Most of the observations in cylindrical package are preserved in conical package, such as effects of wind angle, yarn-package coefficient of friction, yarn

4 F97-C5 Page -4- Balloon Shape and Tension ( Nodimensional) Figure 4. Balloon Shape and Tension of Unwinding from Conical and Cylindrical Package Length from Guide Eye (Nondimensional) 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 of conical package changes the balloon shape and tension distribution, and the tension in the yarn path is slightly less than in cylindrical package. Other observation includes that if the balloons have the same loops, the dr/ds value at the guide eye will decrease with the increase of the tension at the guide-eye. See Figure 4. Red: Unwinding from Conical Package with Conicity = 12 o Black: Unwinding from Cylindrical Package P 0 = 8, (c=100mm, m = 155den), V=500m/min, H u = 400, 500, 600, 700mm, φ=20 o, T res = 0.306gf RING SPINNING EXPERIMENTS (Oxenham) Earlier reports have shown that the instrumentation applied to a ring frame has provided experimental validation of theoretical models. Particular emphasis has been placed on the monitoring of tension since this was shown to clearly correlate with observed instabilities in the spinning balloon. While it is believed that this parameter could potentially offer the basis of a control system to enable maximum productivity to be achieved from ring spinning there are currently problems which have to be resolved. The current devices for measuring tension have limitations associated with: Cost - commercial tension meters, which can operate at frequencies required to detect instabilities, are a major capital investment Use most tension meters require physical contact with the yarn and as such usually act as twist barriers. Their use in staple spinning is problematic since they tend to cause yarn breaks. Size the physical dimensions of most tension meters precludes their permanent installation on most commercial ring frames. Alternative approaches to assessing changes in tension were considered. In particular, it was believed that variations in tension should be reflected in changes in traveler speed, however such changes may occur within one revolution of the traveler. To verify this possibility four proximity sensors were mounted at equal intervals around the circumference of the ring (see Figure 5). Each time the traveler passed the sensor, a pulse

5 F97-C5 Page -5- was produced and the traveler speed in each quarter revolution was determined from the interval between successive pulses. This experimental set-up also allowed greater insight into tension variations since it was possible to relate tension values (obtained from high frequency tensiometer) to traveler location and a typical output is shown in Figure 6. It is interesting to note that the tension exhibits a periodic change with traveler position and higher tensions are found when the traveler is at the front of the ring and lower tensions are measured at the ear of the ring. These differences are thought to reflect asymmetry in the configuration of the spinning machine. Left Separator Plate SENSOR 4 Traveler BACK Spindle Bobbin SENSOR 3 Ring Right Separator Plat Yarn tension at the guide-eye(gm) Time (seconds) SENSOR 1 FRONT SENSOR 2 Sensor 1 Sensor 2 Sensor 3 Sensor 4 Figure 5. Schematic sketch of the positions of the traveler sensors around the ring. Figure 6. Influence of traveler rotation on yarn tension. The difference in speed between the spindle and the traveler enable the yarn to be wound on to the bobbin. Traveler speed is thus a function of spindle speed, bobbin diameter and length of yarn being wound. The last parameter is in turn dependent on the delivery roller speed and the balloon dimensions. Figure 7(a) shows the variation in tension and traveler speed (calculated every quarter revolution) with time over 13 traveler revolution (lasting <0.2 s). It can be observed that even within this time frame the traveler shows considerable variation in speed. When viewed over a longer time scale (figure 7(b)) it is interesting to note that instabilities in spinning conditions, which are shown by extreme variations in tension, result in large and easily determined changes in the traveler speed. It is thus believed that the use of low cost proximity sensors to monitor traveler speed not only provide an additional resource for research into ring spinning but may also afford a new approach to optimizing the operation of ring frames.

6 F97-C5 Page -6- Controlled balloon Tr. 3 (0.2 grams) Yarn tension at the guide-eye (gms) (a) Traveler speed (100 rpm) Yarn tension at the guide-eye (gms) (b) Traveler speed in (100 rpm) Time (seconds) Figure 7. (a) Relationship between traveler speed and yarn tension; (b) Variation of traveler speed with yarn tension TWISTING THEORY (Fraser and Stump (U. Queensland)) Introduction The application of the theory for bending and twisting of thin elastic rods to model yarn twisting process has a long history. References can be found in the paper by Batra [3]. In the current project elastic rod theory was used to develop a better theory of the three problems described below: Twist Variation in the Ring-Spinning Balloon The application of the elastic rod equations to model twist variation in the ring-spinning balloon is reported in reference [8] below. The main results are as follows. 1. The equations that determine the shape of the balloon are independent of the torsional and bending stiffness of the yarn and therefore also of the twist. 2. The equation governing the rotation of the yarn cross-section derived by Miao and Chen [7] for a straight strand is independent of the curvature of the yarn path. Thus the twist is almost independent of the balloon shape, except where the yarn path curvature becomes large (eg. where the yarn passes over a guide) and the path tortuosity makes a significant contribution to the yarn rotation. 3. Torsional vibrations in the balloon between the guide-eye and the traveller could be a source of twist variation in the finished yarn. These vibrations cause twist variation at the traveller which could pass through the traveller and be locked into the yarn. A Dynamical Theory of Twist Trapping in Two-Plying In 1982 Emanuel and Plate [5] and [6] reported an investigation into the mechanism by which twist is trapped in the plied strands in the Sirospun two-ply yarn manufacturing system for wool fibres. They set up an experimental model of yarn plying in which two rubber strands of uniform circular section, initially untwisted, were twisted together in order to measure the twist in the strands above and below the ply convergence point. They

7 F97-C5 Page -7- also produced a theoretical model to analyse the experimental results. Their theory was essentially a kinematical model based on the assumption that the torsion in the strands is continuous across the convergence point. This assumption must be abandoned to obtain the the new results in references [8] and [9] below, in which elastic rod theory has been used to derive new formulae for the strand twist above and below the convergence point in two-plying operations as a function of the ply twist. Reference [8] gives the result for the `static' case considered by Emanuel and Plate, and reference [9] gives the result for the dynamic case. The dynamic theory has been derived on the assumption that the convergence point remains stationary during the plying process, and this leads to the result of zero twist trapping. Even a casual observation of the plying operation in a ring-frame shows that the convergence point is not stationary but oscillates with a fairly regular period. Clearly the result we have obtained in [9] is unstable and the next steep in the analysis is to examine the stability of this solution theoretically. In order to do this we will need to be guided by experimental measurements made during actual plying operations. We propose therefore that an experimental programme is set up to measure the frequency spectrum of the oscillations of the convergence point in ringplying operations. This should be accompanied by simultaneous measurements of the tension in the plied strand at the guide-eye. Twist in the Balanced Ply The easiest way to demonstrate what is meant by a balanced two-ply yarn is to take a strand of singles yarn and twist it while it is held under sufficient tension to prevent it buckling. If this twisted strand is now carefully folded lengthwise upon itself, and then allowed to writhe into a plied structure, of opposite twist to the initial twist inserted in the strand, a stable piece of two-ply yarn is produced. That is, it remains plied without the application of external tension or torque. Such a structure is called a balanced ply. New formulae for the relationship between the strand twist and the two-ply twist have been derived and are given in reference [10]. Figure 8: Unwinding Analyzer UNWINDING EXPERIMENTS (Goswami and Rahn) Introduction A mechatronic system is designed and constructed in order to collect data from the over-end unwinding process. A variety of sensors are used in conjunction with a personal computer (PC) and real-time data capturing boards to monitor and trigger

8 F97-C5 Page -8- collection. Figure 8 shows the block diagram of the Unwinding Analysis System (UAS). A Pentium PC is interfaced to real-time Digital Signal Processing (DSP) boards in order to measure eyelet tension, balloon rotation rate and withdrawal speed. Simultaneous High Speed Video and Tension Measurement With a high speed digital camera loaned by the E. I. DuPont de Nemours and Company, video footage of the over-end unwinding process was obtained in order to illustrate yarn motion and its relationship to the eyelet tension. The camera collected image data at a rate of 500 frames per second, fast enough to give a good resolution of rotation at a relatively low storage cost. Capture was initiated using a trigger signal from the UAS so that tension and video data could be synchronized at a later time. The recorded video and tension data represent one full cycle of motion of the lift-off point as it moves from the back of the package, to the front and returns. Figure 9: Tension data (top) and corresponding video images captured by UAS: 200 denier textured yarn, 450m/min, 0.053m package radius.

9 F97-C5 Page -9- As an example, Figure 9 shows a close-up view of the developed balloon of a package of 200 denier textured yarn with a radius of 0.053m. Figure 9(a) clearly shows a single balloon with an unwind point at the back of the package, Figure 9(b) shows a multiple balloon of unknown order and Figure 9(c) highlights the possible existence of a half balloon. At a time of 0.2 s the tension increases sharply indicating that the balloon has changed back from a multiple balloon to the single balloon as shown in Figure 9(d). The data represented in Figure 10 is similar to that of Figure 9, but video images show both the package and balloon. Figure 10(b), as in Figure 9(c), clearly shows the one-and-a-half balloon and at a time of 0.23 s the transition from multiple to single balloon can be seen. Figure 10: Tension data (top) and corresponding video images captured by the UAS: 200 denier textured yarn, 450m/min, 0.053m package radius. References [1] X. Ma, Dynamic Analysis of Unwinding from Cylindrical Package, Aug, Ph.D. Theses, Burlington Textile Library, NCSU. [2] W. B. Fraser,, T. K. Ghosh, S. K. Batra, On unwinding yarn from a cylindrical package, Prod. R. So. Lond. (1992) 436,

10 F97-C5 Page -10- [3] Batra, S.K. (1973) The normal force between twisted filaments Part I: The-fibre-oncylinder model-analytical treatment. J. Textile Inst. Vol 64, [4] Fraser, W.B. and Stump, D.M. (1998) `Yarn twist in the ring-spinning balloon.' Proc. Roy. Soc. Lond. A Vol. 454, [5] Emanuel, A. and Plate, D.E.A. (1982a). An alternative approach to two-fold weaving yarn Part II: The theoretical model. J. Text. Inst. Vol. 73, [6] Emanuel, A. and Plate, D.E.A. (1982b). An alternative approach to two-fold weaving yarn Part III: Testing the theoretical model. J. Text. Inst. Vol 73, [7] Miao, M., Cai, Z., and Zhang, Y. (1993) Influence of machine variables on twostrand yarn spinning geometry. Text. Res. J. Vol. 63, [8] Fraser, W.B. and Stump, D.M. (1998) `The equilibrium of the convergence point in two-strand yarn plying.' Int. J. Solids and Structures. Vol. 35, [9] Stump, D.M. and Fraser, W.B. (1998) `The dynamical theory of twist in yarn plying.' Mathematical Engineering for Industry, (in press). [10] Fraser, W.B. and Stump, D.M. (1998) `Twist in balanced ply structures.' J. Textile Inst. (in press).