Obtaining Precise Critical Draw Ratio of Draw Resonance in Polymer Processing by Numerical Simulation of Difference Equations
Jinan Cao
Swinburne University of Technology
Australia

Keywords: Melt spinning, Drea resonance, Critical draw ratio

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Direct difference methods have been used to solve the simultaneous non-linear partial differential equations for melt spinning and file casting without recourse to linearisation or perturbation approximation. The stability of each difference schemes is studied by error analysis using the Taylor series, and by comparison of the results obtained from numerical simulation with the logical value in melt spinning. The most stable difference method is then applied to simulate the critical draw ratio over which draw resonance in melt spinning of polymer fluids occurs. It is found that the precise critical draw ratio of draw resonance in an isothermal and uniform tension spinning of Newtonian fluids is in between 20.218 and 21.219, a figure consistent with 20.218 which was obtained by a linear perturbation approximation method by Kase and Denn.