Applied Mathematics Seminar

Rotating yarn loops, referred to as yarn balloons in the textile industry, play an important role in establishing yarn tension in textile manufacturing processes such as ring-spinning, two-for-one twisting and over-end unwinding. Recent theoretical work has brought the computational simulation of these processes to a high degree of refinement.

In this talk a simple experimental system, consisting of a loop of yarn rotating about a fixed axis, without twist insertion, is described. This system (dynamically similar to the textile processes listed above) exhibits a rich variety of bifurcation behaviour as the length of yarn in the loop is varied.

It will be shown that bifurcation curves derived from the theory (which plot tension versus the unstretched yarn length in the rotating loop) can be fitted to experimentally obtained curves using an appropriate choice of the air-drag and yarn elongation parameters. In particular, it is shown that `fluttering' oscillations observed in the experimental balloon results can be identified with the limit-cycle behaviour of the theoretical balloon profiles.

Finally (time permitting), a video will be shown illustrating the dynamical similarities between the experimental yarn balloon system, and the theoretical yarn balloon model. Matlab (theory), real time video sequences (experiment) and Prisms (modelling a virtual ring-spinning frame) are all used to capture the complex behaviour of the yarn balloon motion in time.