We have re-analyzed the dynamics of the ring spinning process as a coupled set of subproblems and have obtained the solutions numerically. The analyses in Parts I and II of this series deal with the case of an uncontrolled balloon. In Part I we ignore the effects of air drag as well as gravitational and Coriolis accelerations. In Part II we include the effects of air drag. These analyses differ from the earlier ones in their choice of the relevant boundary conditions; those used here we presume are more realistic. The shapes of the spinning balloons are derived from the conditions of dynamic equilibrium of the yam, from pigtail to wind-point, as well as that of the traveler. Nondimensionalization of the problem is based on two physical lengths, allowing easy comparison of the balloon shapes for widely different dynamic conditions (including collapsed balloons) on the same plot. Tension distributions along the yarn path can be predicted. Similarly, the mass of the traveler required for a specified yarn tension at the pigtail can be calculated. Air drag is particularly useful in controlling the shape and size of the balloon. The numerical solution procedures we have developed can be used to explore the regions of instability of the balloon.

The tensile and tear strengths and hence the durability of a cotton fabric are greatly influenced by the length and strength of cotton fibers in addition to the fabric structure. This is so because fiber length to a large extent determines yam strength, which ultimately contributes to fabric strength. Also, fiber length and its distribution affect fiber processing and hence yarn performance during subsequent mechanical processing, including knitting and weaving. Therefore, fiber length distribution and its ultimate effect on the yarn strength are important. To better understand the length-strength relationship in cotton fibers, we have tried to model the strength of fibers assemblies in a yarn, based on some simple assumptions. In this model, we address an important issue of friction among adjacent fibers in a yarn structure and also introduce and derive a new parameter called the "strength efficiency" of fibers in a yarn, which may contribute to an understanding of the yarn failure mechanism. The paper should be helpful to the scientific community involved in improving the properties of cotton fibers, yarns, and fabrics.Although fiber migrations and the resulting entanglements are very important in yarn formation, fiber length, fineness, and strength and their respective distributions/ consistencies are even more critical parameters in determining the effectiveness of the ultimate fibrous assembly (yarn). For decades, textile scientists worldwide have been studying the mechanics of flexible fiber assemblies and investigating the effect of fiber properties on yarn properties, especially tensile properties [1][2][3][4][5][6][7][8][9][10][11]. Several models have been developed to understand the mechanics of yarn formation and failure [2,5,8,10, 111. For example, a semi-empirical expression developed from work by Grosberg and Smith on worsted rovings to predict the breaking strength of low-twist woolen-spun yarn reveals the relative importance of the contribution of fiber length and fiber strength to estimated yarn strength [ 10]. They examined the effect of carbonizing in altering fiber strength and entangling and showed that fiber length has the most marked influence on yarn strength. Tests have also shown that fiber slippage is an important part of the yarn failure mechanism. Van Luijk et al. developed a model for the long-gauge behavior of staple-fiber yarns based on Hearle's work incorporating fiber migration and slippage [ 11 ]. The tensile strength of the model stems from frictional forces, which are calculated using the Grosberg theory of fiber-withdrawal force from a sliver. The governing equations of the staple fiber/yarn model have been formulated and solved using the finite element method.Since fiber length and strength greatly influence yarn , strength, we have tried to develop a model to express yarn strength as a function of the accumulated strengths of the individual fibers in the yarn cross section. In this research approach, we use the following simplifying assumptions: First, the fibers are quasi...

A simple analysis of the local linear density of a yarn yields an equation of its overall variance, which has three components: variance of the number of fibers per cross section, variance of the mean local fiber fineness, and that of the mean parameter of fiber inclination relative to yam axis. Further mathematical analysis of the component variances reveals a set of determining factors: the sequence of the fiber ends along the yam, the distribution of the fiber length, fiber fineness and its irregularity, the irregularity of the fiber configuration relative to the yam axis, and the blend uniformity along the yarn. To help in this analysis, a representation of the yarn, free of any structural hypothesis, is derived from the way the yam emerges from a ring spinning process: a superposition of elementary strips, each resulting from an initial sliver. This represen tation demonstrates that inverse proportionality between the squared CV of the yarn and its mean number of fibers in cross section holds for any yarn, including those idealized by Poissonian or other similar models.

The dynamics of the ring spinning process has been re-analyzed as a coupled set of subproblems; the solutions are obtained numerically. The analyses in Part I and II of this series deal with the case of an uncontrolled balloon. In Part I the effects of air drag as well as gravitational and Coriolis accelerations are ignored. In Part II the effects of air drag are included. These analyses differ from the earlier ones in their choice of the relevant boundary conditions; the ones used here are presumed more realistic. Shapes of the spinning balloons are derived from the conditions of dynamic equilibrium of the yam, from pig-tail to wind-point, as well as that of the traveler. Non-dimen sionalization of the problem, is based on two physical lengths, which allows easy comparison of the balloon shapes for widely different dynamic conditions (including collapsed balloons) on the same plot. Tension distributions along the yarn path can be predicted. Similarly, mass of the traveler required for a specified yam tension at the pig-tail can be calculated. Air drag is found to be particularly useful in controlling the shape and size of the balloon. The numerical solution procedures developed can be used to explore the regions of instability of the balloon.

Based on large data sets from three consecutive cotton crop years, linear models for SFW and SFN in terms of the HVI length parameters have been developed. The necessity of modifying the Suter-Webb array distributions is justified. The results are discussed in light of the concept of "similarity" related to fiber length distributions, as defined in Part I. Using normalized regression equations, UI is demonstrated to have a stronger influence on SFC than the range parameters (UHM, ML). The terms UI, UHM, ML are standard measurements of the HVI instruments and have been defined in the text. The models developed in this study have been compared with the one developed by Preysch in 1979, and the relative improvement over Preysch's method is discussed.