Nonlinear Dynamic Analysis of an Unsymmetrical Generator-Bearing System

Considering both nonlinear oil film force and unsymmetrical stiffness, this paper presents a mechanical model of a generator-bearing system. The complex mode synthesis method is used to reduce the linear degrees of freedom of the high order model in the rotating coordinates, and one-order modal differential equations are obtained which may not be solved directly by Newmark-$β$ method. To solve this problem, a modified Newmark-$β$ method is presented to investigate dynamic effects of the asymmetry of rotor stiffness, the viscosity of oil, the rotor unbalance and the ratio of length to diameter of bearings. Three-dimension diagrams and unfiltered vibration curves are used as tools to examine the dynamic behavior of the system, and some insights into the dynamic behavior are given. Numerical results show that instability of the system may be improved by modifying these parameters.