Studies on melt spinning. V. Draw resonance as a limit cycle



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.