Internal Mechanics of Twisted Yarn 1

Abstract

Part I: Theoretical Model

The equilibrium of the yarn element is defined on the basis of a cylindrical model of yarn formation. The fibrous system is considered a continuum. The stress-strain relationship is solved for the element of this fibrous continuum. A mathematical model is proposed which is based on the idea of effective elastic bonds including nonlinearity and finite strains. Through substitution of this model in a differential equation of equilibrium, a differential equation is found which can be solved numerically. Also, the effect of fiber migration is taken partly into consideration. A method of calculation is deduced for the course of the radial fiber packing density.

Part II: Application

A new method of experimental determination of the course of the fiber packing density is described. The method is based on mathematical evaluation of tracer fibers from photographs produced on the OMEST Tester. A modified evaluation of experimentally determined yarn diameters is proposed. Results obtained with carded cotton yarns are specified. The theoretical model is processed numerically. The input parameters of the numerical solution are discussed. Theoretical results are compared with the results of the fiber packing density and yarn diameter measurements. The findings are discussed from the viewpoint of the physical aspects of the internal mechanics of yarn.

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