Studies on melt spinning. V. Draw resonance as a limit cycle
Article first published online: 9 MAR 2003
Copyright © 1975 John Wiley & Sons, Inc.
Journal of Applied Polymer Science
Volume 19, Issue 2, pages 557–566, February 1975
How to Cite
Ishihara, H. and Kase, S. (1975), Studies on melt spinning. V. Draw resonance as a limit cycle. J. Appl. Polym. Sci., 19: 557–566. doi: 10.1002/app.1975.070190218
- Issue published online: 9 MAR 2003
- Article first published online: 9 MAR 2003
- Manuscript Revised: 14 AUG 1974
- Manuscript Received: 13 JUN 1974
The exact wave form of draw resonance in isothermal spinning of Newtonian liquids was sought by solving numerically the simultaneous partial differential equations1 of melt spinning in their original nonlinear form without recourse to perturbation. When the draw-down ration of spinning exceeded 20, solution of the equations became a limit cycle, a sustained oscillation having amplitude and period independent of initial conditions. As the draw down ratio was further increased, the amplitude of the limit cycle grew very rapidly, and the wave form became close to a pulse train predicting an extreme thinning of the thread at regular intervals along the thread. The above solution for Newtonian liquids agreed well with experiment with respect to oscillation period. Agreement, however, was poor in amplitude, indicating that possibly the amplitude of draw resonance is affected by deviations of polymer viscosity from Newtonian.