The effect of ball size variation on nonlinear vibrations associated with ball bearings

An analytical model to predict nonlinear dynamic responses in a rotor bearing system due to ball size variation has been developed. In the analytical formulation the contacts between the rolling elements and the races are considered as nonlinear springs, whose stiffnesses are obtained using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained using Lagrange's equations. The implicit type numerical integration technique Newmark-β with the Newton-Raphson method is used to solve the nonlinear differential equations iteratively. A computer program is developed to simulate the effects of ball size variations. Results are presented in the form of fast fourier transformation and Poincarè maps. The highest radial vibrations due to ball size variation are at a speed of the number of balls times the cage speed (ω =kω c Hz). The other vibrations due to ball size variation also occur at VC ± kω cage , where k is a constant.