Approximation of Periodic and Quasi‐Periodic Motions of a Rotor System with Visco‐elastic Seal Support by Using a Fourier‐Galerkin‐Method

Abstract

In this contribution a Fourier-Galerkin method is used to calculate the periodic and quasi-periodic motions of a rotor-seal system. The system consists of a classical Laval-rotor, a visco-elastically supported rigid seal rigid and a turbulent fluid flow through the seal gap. The Fourier-Galerkin method uses one-and two-dimensional Fourier series to approximate steady-state periodic solutions due to rotor mass unbalance and quasi-periodic solutions due to unbalance and self-excitation stemming from the seal fluid forces. The method is applied to continue solution-branches of the rotor-seal system which show periodic/ quasi-periodic solutions, resonance, multiple Neimark-Sacker bifurcations as well as synchronisation (Torus-breakdown).