Journal of Engineering Mathematics

, Volume 61, Issue 1, pp 81–95

On the theory of localised snarling instabilities in false-twist yarn processes

Article

DOI: 10.1007/s10665-007-9180-4

Cite this article as:
Fraser, W.B. & van der Heijden, G.H.M. J Eng Math (2008) 61: 81. doi:10.1007/s10665-007-9180-4

Abstract

A theory for the twist-induced localised snarling instability observed in whirling and transported yarn in textile manufacturing processes such as false-twisting is developed. The buckling of the yarn can occur in two modes. At a critical level of the tension the straight yarn path bifurcates to a whirling ballooning mode. The localised snarling bifurcation can be triggered either from the straight line path prior to whirling or from the post-whirling configuration depending on the transport speed of the yarn through the system. The yarn is modelled as a pre-tensioned elastic rod. A perturbation analysis is carried out in which the small parameter measures bending relative to dynamical forces. The whirling bifurcation is captured with a regular perturbation analysis and the snarling bifurcation is captured with an internal bending layer in a singular perturbation analysis. This localised snarling is a subcritical bifurcation that occurs at a critical combination of yarn torque and tension. Critical conditions, as well as the position along the yarn where the snarling instability occurs, are obtained by matching the internal layer to the outer solutions. To accomplish this matching yarn axial elasticity is essential.

Keywords

Elastic rodsFalse twistInternal bending layerLocalised bucklingSingular perturbationTextile-yarn snarling

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of SydneySydneyAustralia
  2. 2.Department of Civil and Environmental EngineeringUniversity College LondonLondonUK