The effect of bearing cage run-out on the nonlinear dynamics of a rotating shaft

This paper presents an analytical model to investigate the nonlinear dynamic behavior of an unbalanced rotor-bearing system due to cage run-out. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact forces and cage run-out, and the resulting transition from a state of no contact to contact between the rolling elements and the races. The contact between the rolling elements and races is treated as nonlinear springs and the system is analyzed for varying numbers of balls. The results are presented in the form of fast Fourier transformations and Poincaré maps. The results show that the ball passage frequency is modulated with the rotational frequency. The response falls into three regimes: periodic motion, quasi-periodic oscillations, and chaotic response.