An analytical prediction method for the bifurcation of an asymmetric rotor system partially filled with viscous incompressible fluid

Instability of a rotor partially filled with viscous incompressible fluid will cause the amplitudes of perturbations to increase exponentially. Many models of an isotropic rotor partially filled with fluid have been proposed to investigate its stability. However, the bifurcation of an anisotropic rotor partially filled with viscous incompressible fluid is complicated, which has rarely been studied. To investigate this problem, a continuous model is first established for the isotropic case and the hydrodynamic forces are calculated. The D-decomposition method is then used to determine the stable and unstable regions of the isotropic rotor. An analytical prediction method is then proposed in this paper, and the results for stable and unstable regions are the same as those obtained with the D-decomposition method. Then, this novel analytical prediction model is applied to an anisotropic rotor partially filled with viscous incompressible fluid, and the stable and unstable regions are analyzed. One isotropic and two anisotropic conditions are compared to verify the correctness of the proposed analytical method. The results show that the dimensionless damping and stiffness have significant effects on the stability of an anisotropic rotor partially filled with viscous incompressible fluid; in particular, it is found that there exists a single stable region for low values of the dimensionless damping coefficient and stiffness. Furthermore, the bifurcation law of different anisotropic parameters is first explored, which can provide theoretical guidance for the chosen external stiffness and damping coefficients.