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)