Subhash K. Batra

On unwinding yarn from a cylindrical package

The over-end unwinding of yarn from a stationary helically wound cylindrical package is considered. The motion of the yarn between the unwind point (where it first starts to slip across the package surface before flying into the unwinding balloon) and the guide eye located on the package axis is analysed. The motion is periodic as the unwind point moves backwards and forwards along the length of the package surface. In 1958 D. G. Padfield argued that, provided the helix angle is small, the time derivative terms in the equations of motion can be neglected and the problem can be reduced to a stationary (relative to rotating axes) balloon problem subject to a modified boundary condition at the unwind point. The problem of yarn slipping across the package surface has also been investigated by D. G. Padfield and by H. V. Booth. In the present paper a regular perturbation expansion is used to provide a theoretical framework for Padfield’s ideas and to remove the time dependence from the zero order equations of motion. To this order of approximation the time dependence appears in the ‘moving’ boundary condition at the unwind point. A new derivation of this boundary condition is given and a set of continuity conditions between the yarn slipping on the package and the yarn in the balloon is used to splice the two solutions together so that the package can be unwound through a complete period of the unwinding cycle.

An Integrated Approach to Dynamic Analysis of the Ring Spinning Process Part I: Without Air Drag and Coriolis Acceleration

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 equi librium of the yam, from pigtail to wind-point, as well as that of the traveler. Non dimensionalization 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.

An Integrated Approach to Dynamic Analysis of the Ring Spinning Process Part II: With Air Drag

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.

Sperm transport through vas deferens: review of hypotheses and suggestions for a quantitative model.

Study of the mechanism of sperm transport through the vas deferens stems from the need to develop acceptable male contraceptive devices or procedures. The object of this paper is to review all the hypothese related to the innervation structure and function of the vas. Also considered are the experimental data and theoretical analyses necessary for understanding seminal fluid transport through the vas. Similarities in structure and function of the ureter are noted. Histologically the vas deferens lumen is bounded by a 3-layer musular wall. The inner and outer layers of smooth muscle wall are arranged longitudinally. The middle layer is circumferential. The vas deferns epididymis prostate and seminal vesicles have only an autonomic nerve suppply via the inferior hypogastric plexus. Studies of the fine details are described as they occur in man and experimental animals. Experiments suggest that the innervation of the vas is seriously damaged by local anesthesia used for vasectomy or reanstamosis when attempted. However the mechanisms of veurotransmission in the vas remain controversial. The various theories of muscular activity of the vas are reviewed. These data may be useful in the design of reversible vas occlusion devices. The improved understanding may suggest simple and effective methods of reversible vasectomy.

Micromechanics of three-dimensional fibrewebs: constitutive equations

This paper extends the fibre–network theory of Cox to three–dimensional anisotropic fibrewebs. It presents a micromechanical model employing fibre axial deformation as the elemental deformation mechanism giving rise to assembly stress as a result of applied normal and shearing strain field. This model predicts the elastic constants of an assembly in terms of fibre linear density, fibre elastic modulus, fabric bulk density and the first 15 spherical harmonic coefficients of direction distribution function. A computer simulation has been performed to study the effect of structure on the initial elastic moduli of fibrewebs. This simulation shows that: (a) Youngs modulus evaluated for each fabric axis is directly dependent on the fibre orientation distribution density (FODD) along the same axis; (b) shear modulus in any reference plane is maximized when orientation distribution function is isotropic in that plane and it decreases with increasing FODD along the direction normal to that plane; and (c) Poissons ratio, &ngr;ij, increases as the FODD along the i–axis decreases and the FODD along the j–axis increases, but the effect of FODD along the k–axis is minimal.

An Integrated Approach to Dynamic Analysis of the Ring Spinning Process Part IV: Inherent Instability of the Free Balloon

This paper will show that the theory of ring spinning developed by Batra et al. and subsequently by Fraser can be used to explain recent experimental results obtained at the SRRC. In particular, Fraser showed that the quasi-stationary, nonlinear equations of motion relevant to ring spinning, including the effect of centripetal acceleration and air drag force, developed earlier by several investigators exhibit a bifurcation phe nomenon typical of many other nonlinear systems in mathematical physics. This investigation shows that the bifurcation analysis applied in a way that simulates for mation of the bobbin, even a chase of the bobbin, reveals meta-stability in parametric space, which can be used to explain the instabilities in free (no control rings) balloon profiles observed experimentally.

Computer-assisted Structural Design of Industrial Woven Fabrics Part III: Modelling of Fabric Uniaxial/Biaxial Load-Deformation

This is the third of a three-part series describing an attempt to develop a comprehensive computational framework for aiding the engineering design of woven industrial fabrics. The main aim of this work is to develop a generalized knowledge-based CAD system for fabric design. The present status of this research has been described in [3]. Completing the CAD system entails detailed development of an analytic phase comprised of a set of computational models for simulation of fabric behaviour under external stimuli, and for the predictive estimation of some important properties. Toward that end, an analysis of uniaxial/biaxial load-deformation of a plain woven fabric has been developed under certain restrictive conditions. Part III describes, in detail, the theoretical and practical aspects of this analysis (model). A brief literature review of previous work on this subject is followed by a description of the mathematical model, its computational expression, and the experimental tests performed to validate th...

A New Perspective on Yarn Unevenness: Components and Determinants of General Unevenness

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.

Computer-assisted Structural Design of Industrial Woven Fabrics Part I: Need, Scope, Background, and System Architecture

This is the first of a three-part series describing an attempt to develop a comprehensive computational framework for aiding the engineering design of woven industrial fabrics. The work has two major aims. The first is to develop a generalized knowledge-based CAD system for use in fabric design. A detailed analytic phase will then follow, which will comprise a set of computational models for the simulation of fabric behavior under external stimuli which will be used for the predictive estimation of some important properties. Accordingly, the second focus of this work is to develop an analysis of the uniaxial/biaxial load-deformation behavior of a plain woven fabric. Part I provides the rationale for choosing this domain of industrial fabric design, and discusses the characteristics and the limitations of current design procedures. It examines the requirements for a computer-based system intended to provide decision-making support for a generic design task. There is a short review of such CAD systems withi...

Dynamic Analysis of Yarn Unwinding from Cylindrical Packages. Part I: Parametric Studies of the Two-Region Problem

In recent years, the interest in studying balloon formation during unwinding has been rekindled by recent publication of several significant papers on the dynamic analysis of moving yarns in rotational modes. The renewed interest can be partially attributed to the availability of powerful computing tools needed to solve problems of this kind. This paper is the first of a series of papers reporting results of ongoing research at NCSU. In this paper, apart from a critical evaluation of some recently published work, the physics of unwinding as proposed by earlier publications is examined through extensive parametric studies. That is, two parameters of high practical importance, balloon shape and unwinding tension, are calculated as functions of the direction of unwinding (from front-to-back and back-to-front), wind angle, residual tension in the yarn on the package, and the coefficient of yarn-package drag. In addition, limitations of a two-region analysis are addressed.