A 3D finite element-based model order reduction method for parametric resonance and whirling analysis of anisotropic rotor-bearing systems

A generalized and efficient model for rotating anisotropic rotor-bearing systems is presented in this paper with full considerations of the system’s anisotropy in stiffness, inertia and damping. Based on the 3D finite element model and the model order reduction method, the effects of anisotropy in shaft and bearings on the forced response and whirling of anisotropic rotor-bearing systems are systematically investigated. First, the coefficients of journal bearings are transformed from the fixed frame to the rotating one. Due to the anisotropy in shaft and bearings, the motion is governed by differential equations with periodically time-variant coefficients. Then, a free-interface complex component mode synthesis (CMS) method is employed to generate efficient reduced-order models (ROM) for the periodically time-variant systems. In order to solve the obtained equations, a variant of Hill’s method for systems with multiple harmonic excitations is developed. Four dimensionless parameters are defined to quantify the types and levels of anisotropy of bearings. Finally, the effects of the four types of anisotropy on the forced response and whirl orbits are studied. Numerical results show that the anisotropy of bearings in stiffness splits the sole resonant peak into two isolated ones, but the anisotropy of bearings in damping coefficients mainly affect the response amplitudes. Moreover, the whirl orbits become much more complex when the shaft and bearings are both anisotropic. In addition, the cross-coupling stiffness coefficients of bearings significantly affect the dynamic behaviors of the systems and cannot be neglected, though they are often much smaller than the principle stiffness terms.