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Melt Spinning: Optimal Control and Stability Issues

In: Recent Advances in Computational and Applied Mathematics

Author

Listed:
  • Thomas Götz

    (TU Kaiserslautern, Department of Mathematics)

  • Shyam S. N. Perera

    (University of Colombo, Department of Mathematics)

Abstract

A mathematical model describing the melt spinning process of polymer fibers is considered. Newtonian and non-Newtonian models are used to describe the rheology of the polymeric material. Two key questions related to the industrial application of melt spinning are considered: the optimization and the stability of the process. Concerning the optimization question, the extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first-order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. Concerning the stability with respect to variations of the velocity and temperature of the quench air, a linear stability analysis is carried out. The critical draw ratio, indicating the onset of instabilities, is computed numerically solving the eigenvalue problem for the linearized equations.

Suggested Citation

  • Thomas Götz & Shyam S. N. Perera, 2011. "Melt Spinning: Optimal Control and Stability Issues," Springer Books, in: Theodore E. Simos (ed.), Recent Advances in Computational and Applied Mathematics, chapter 0, pages 123-141, Springer.
    • Handle: RePEc:spr:sprchp:978-90-481-9981-5_5
    DOI: 10.1007/978-90-481-9981-5_5
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