Newtonian glass fiber drawing: Chaotic variation of the cross-sectional radius

A model of Newtonian glass fiber drawing at fixed temperature in the unsteady range (the draw ratio E>20.22) is considered. In this range under steady boundary conditions, as is well known, the draw resonance instability sets in, resulting in self-sustained oscillations. These oscillations lead to a periodic variation of the cross-sectional radius of the fiber. In the present work we consider the case where the spinline radius varies periodically. Such a variation may result from flow oscillations in the fiber forming channels in the direct-melt process, or from the variation of the preform cross-sectional radius in drawing of optical fibers. When this variation takes place in the range E >20.22, the self-sustained periodic oscillations of the draw resonance are replaced by quasiperiodic and periodic (mode-locked) subharmonic or (under the appropriate conditions) chaotic oscillations (strange attractors). The routes to chaos found in the present work include (1) smooth period doubling bifurcation of (any) mode-locked periodic solution, (2) abrupt explosions of quasiperiodic solutions. The predicted chaotic variation of the spinline radius at the winding mandrel may result in a similar variation of the cross-sectional radius of the solidified fibers.