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

W.B. Fraser & G.H.M. van der Heijden

In this paper 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 and 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 axial elasticity is essential.

keywords: elastic rods, false twist, internal bending layer, localised buckling, singular perturbation, textile yarn snarling

Journal of Engineering Mathematics (in the press)