Analysis of Yarn Structure of Crimped Fiber Assemblies

Abstract

This article concerns the structure of yarns composed of crimped fiber assemblies. A theory to derive the diameter of a yarn is presented if the yarn is composed of helical coils having the same lead length. The positions of fibers in a yarn cross section are determined as follows: When three helical coils having different phase lags gather together to come in touch with one another, then the positions of the axes of these three helicals can be detemined. This procedure is repeated many times until covering all fibers in the cross section. The theoretical analysis clarifies that, when the phase differences are uniformly distributed random variables, the yarn diameter takes the maximum and this model is adapted for a high crimped yarn; and that a model of exponentially distributed random variables with larger density at the side of small phase difference conforms to a middle or low crimped yarn.