The theoretical modeling and experimental validation for distributed defect on inner race of ball bearing under radial load

Abstract

This article presents the theoretical model to study the vibration characteristics of ball bearing. The vibration analysis is accounted for peripheral motions of rolling elements as well as inner and outer races using the Lagrangian approach. In this mathematical model, the contact between the balls and the bearing races is considered as nonlinear springs, whose stiffness is obtained using the Hertzian elastic contact deformation theory. The nonlinear equations of motions are solved by the Runge–Kutta method iteratively. The effects of extended defect on the inner race of the bearing at different speeds and defect sizes have been studied for predicting the vibration response of the bearing. The fast Fourier transformation shows that the vibration characteristic of the ball bearing changes when the ball interacts with the defect as a result of nonlinear load–deflection relation. The analysis implied that defect size and speed of ball bearing are the influencing parameters affecting the dynamic behavior of the ball bearing.