Nonlinear Dynamics Analysis for a Model-Reduced Rotor System with Nonlinear Galerkin Method

Rotor-bearing systems are important components of aircraft engines of which vibration response must be analyzed under normal and disturbed conditions. Due to the existence of strong nonlinearity from squeeze film dampers and ball bearings, it is often very time consuming to evaluate the vibration of the rotor excited by unbalanced mass, which makes efficient and reliable modeling reduction is pivotal to rotordynamic analyses. In this paper, the nonlinear vibration and dynamical behavior of a twin-spool rotor assembly supported on bearings and squeeze film dampers with centralizing springs is investigated through the post-processed nonlinear Galerkin method. The rotor is spatially discretized with the finite element method, and the nonlinear governing equation of motion of the system is derived. To reduce the scale of the full-sized model, the post-processed nonlinear Galerkin method is employed to project the original system onto a low-dimensional sub-manifold with a relatively smaller number of degrees of freedom. The convergence of the nonlinear Galerkin method is verified through comparisons energy between the original and the reduced systems. The optimal choice of the number of master modes is determined to form the reduced model for nonlinear vibration analyses. Through the NGM the vibration of the system is solved, and the amplitude-frequency response, bifurcation and the Poincaré map are obtained to demonstrate the complexity in the rotor dynamics.