Application of topological conservation to model key features of zero-torque multi-ply yarns
C.D. Tran, G.H.M. van der Heijden & D.G. Phillips
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 twisted textile yarns will be
evaluated using the Topological Conservation law (Fuller, 1971) which has
been developed to study the post-buckling behaviour of twisted rods by Van
der Heijden et al. (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 on strands
of a multi-ply yarns is also calculated at the balance situation across a
range of structural and mechanical conditions.
keywords: spinning twist, writhe, twist, link, topological conservation,
torsion, bending, multi-ply yarn, instability, balance, inter-strand pressure,
total pressure, pilling
The Journal of the Textile Institute 99, 325-337 (2008)