Wb. Fraser et al., EFFECT OF YARN NONUNIFORMITY ON THE STABILITY OF THE RING-SPINNING BALLOON, Proceedings - Royal Society. Mathematical and physical sciences, 449(1937), 1995, pp. 597-621
This paper extends the results of W. B. Fraser and D. M. Stump on the
stability of a ballooning yarn of uniform mass linear density to allow
for non-uniformities in the yarn. A two-variable perturbation expansi
on procedure (two-timing) is used to show that the effect of a slub (d
efined as a thick place or lump in a thread) on the stability of the r
ing-spinning balloon can be analysed as a sequence of quasistationary
balloons for yarn of variable mass linear density as the slub travels
slowly through the rapidly rotating balloon. The slub is modelled by t
he addition of a mass linear density term, in the shape of a gaussian
or cosine distribution function, to the uniform mass linear density. C
omputational results are given for a ring spindle and yarn combination
with representative geometry, air drag, and frictional parameters. Th
ese results show that even a slub that in practice would be considered
quite small can have a significant effect on the stability of the yar
n balloon. The results in this paper show how such effects can be quan
tified.