Stability analysis of an anisotropic rotor partially filled with viscous incompressible fluid based on Andronov-Hopf bifurcation

Abstract

Instability of a rotor partially filled with viscous incompressible fluid is a common issue in rotary machines, which leads the amplitude of perturbations to increase exponentially. Currently, different models of an isotropic rotor partially filled with fluid are established to investigate its stability, but the research on the stability of an anisotropic rotor is rarely reported. To explore the instability of an anisotropic rotor partially filled with fluid, a continuous model is established to represent an isotropic rotor system partially filled with fluid and dimensionless hydrodynamic forces are calculated, and then D-decomposition method is introduced to obtain stable and unstable regions of this isotropic rotor. The transitions of different regions are called as Andronov-Hopf bifurcation. Then, a novel predicting model, where the elliptical motion of a rotor partially with fluid is assumed, is established to obtain the same unstable regions, comparing with the results from D-decomposition method. The correctness of this novel predicting method for an isotropic rotor partially filled with fluid is verified by this comparison. The influence of dimensionless damping coefficient on the stability is also analyzed. Last, this novel predicting model is applied to an anisotropic rotor partially filled with fluid, the unstable regions of rotational frequencies are analyzed. The results show that dimensionless damping coefficient and dimensionless stiffness coefficient have significant influences on the stability of a rotor partially filled with fluid, there especially exist two unstable regions for a lower dimensionless damping coefficient. In addition, the asymmetric degrees of an anisotropic rotor have great influences on the unstable low boundary.