In consideration of the sources of nonlinearity such as inner and outer race surface waviness

Hertzian elastic contact force and internal radial clearance

an analytical model of rolling bearing was presented.The governing differential equations of motion of a rolling bearing-rotor system were solved by Runge-Kutta-Felhberg algorithm.The nonlinear dynamic behavior of the system with variations of parameters was analyzed by means of bifurcation diagrams

poincaré maps and spectrum diagrams.Simulation results show that the severe vibration occurs when the number of balls is equal to the number of waves.The main route to chaos is doubling bifurcation.There is a definitely functional relationship between the number of waves and frequencies of vibration produced by inner race waviness.