Application of topological conservation to model key features of zero-torque multi-ply yarns

Abstract

During yarn formation by ring spinning, fibres are bent into approximately helical shapes and torque or twist-liveliness is created. The yarn torque causes yarn instability, manifested as snarling or entanglements, and this instability must be controlled during manufacturing processes. Generally, the torque depends on yarn geometric factors such as the yarn twist, linear density and the fibre properties. A practical solution to the problem of twist-liveliness is the formation of a two-fold yarn. This twisting or plying process produces a yarn structure where the energy of the system is determined by purely geometrical constraints of the plied structure and consequently when an energy minimum is reached the plied yarn obtained from the process is torsionally balanced and torque-free. In the present paper, the stability of plied textile yarns will be evaluated using the Topological Conservation law (Fuller, F. B., 1971, Proc.Nat. Acad. Sci. USA, 68, 815–819.) developed to study the post-buckling behaviour of twisted rods by Van der Heijden et al. (Int. J. Mech. Sci., 45, 161–196, 2003).The present work considers the equilibrium configuration of a series of multi-ply twisted yarns (2, 4, and 6 strands) of finite length. Several structural and mechanical properties are highlighted: (i) the influence of structural properties (the number of strands, the strand linear density and strand twist) and the ratio of the torsional and bending stiffnesses of the strands on the balance point in multi-ply yarns. The topological invariant of the twisted yarn (link) is used to calculate the ply and strand properties (writhe) and compared with experimental results obtained at CSIRO. The inter-strand pressure between strands of a multi-ply yarn, a feature of interest for fibre interactions in yarn structures, is also calculated at the balance situation across a range of structural and mechanical conditions.