Dynamic stability and bifurcation in a bundle flow

In roll draft operation mechanisms, the behavior of floating fibers is known to cause the thickness variation in output fiber bundles. Despite the significance of this phenomenon, few studies have sought to explain the underlying mechanism theoretically. We analyzed the dynamic characteristics of bundle flow in roll draft systems, based on a model of bundle flow. By applying both linear stability and phase plane analyses, we investigated an occurrence of draft waves. Our results suggest that the principles of linear stability can be applied to analyze bundle flow dynamics. The nonlinearity of bundle flow, however, reveals that the stable fixed point disappears when draft ratio changes, which in turn implies that the topological structure of the phase portrait changes as the process parameter is varied: a bifurcation property. As the process parameter increases above certain critical values, fixed points are destroyed and oscillations within the limit cycle occur. Also the system oscillates at a critical draw ratio harmonically, indicating the onset of a Hopf bifurcation, which corresponds to the draft wave. The phase portrait converges to a shell-shaped curve if the process parameter increases further. The results of this study also show that there is a specific draft ratio below which flow is always stable.