The Sensitivity and Stability of Spinning Process Using Frequency Response Method

The sensitivity and stability by frequency response of the final filament to several sinusoidal disturbances have been investigated in viscoelastic spinning by using various novel numerical algorithms. Amplitudes, or gains of the spinline cross-sectional area at the take-up, show resonant peaks, which are frequently encountered in hyperbolic systems. To effectively solve the complex system of the frequency response equation, alternative ways have been performed and compared. Interestingly, in the one-dimensional systems considered, integrating the linearized equations over the spinline length to shoot at the take-up boundary condition using two initial guesses ("two-shot" method) proved far more efficient than modal analysis using eigenfunction data or solving the matrix problem from the entire length by a direct method or an iterative one (GMRES). Also, the methodology to determine the stability of the system by using frequency response data, as suggested in Kase and Araki [1982], has been revamped to viscoelastic spinning system.