Nonlinear dynamic analysis of rolling element bearings due to cage run-out and number of balls

This paper presents an analytical model to investigate the nonlinear dynamic behavior due to cage run-out and number of balls in a rotating system supported by rolling element bearings. 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 the Hertzian contact force and cage run-out resulting transition from no contact to contact state between rolling elements and races. The contact between the rolling elements and races is treated as nonlinear springs. The nonlinear stiffness is obtained by application of Hertzian contact deformation theory. The implicit-type numerical integration technique Newmark- β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of fast Fourier transformations (FFT) and phase trajectories. It is implied from the obtained FFT that due to the non-uniform spacing the ball passage frequency is modulated with the cage frequency.