Non-linear dynamic behaviors of rolling element bearings due to surface waviness

An analytical model to predict non-linear dynamic responses in a rotor bearing system due to surface waviness has been developed. In the analytical formulation the contacts between the rolling elements and the races are considered as non-linear springs, whose stiffness are obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained by using Lagrangeʹs equations. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the non-linear differential equations iteratively. A computer program is developed to simulate surface waviness of the components. Results presented in the form of fast Fourier transformation with agreement of various authorʹs experimental researches.