Non-linear Vibration Analysis of a Ball Bearing Having an Outer Race Defect Using 2-DOF Mathematical Model

A mathematical model helps in simulation and prediction of the effects of defects in bearings, where the traditional experimental methods are expensive and time-consuming. This paper presents a 2-DOF mathematical model of a SKF ball bearing having a local outer race defect to simulate the effects of change in shaft speed and radial load on vibration responses of the bearing. In the model, the bearing elements are modeled as mass-spring-damper system. This model considers Hertz’s classical contact theory for calculating the non-linear contact forces between the balls and the races, and also considers the additional radial deflection of the balls due to the radial clearance and defect geometry. The maximum possible deflection of the ball in the defect is obtained from the ball-race-defect geometry. A MATLAB code is developed for modeling the bearing with and without a defect and to solve the equations of motion by applying Runge–Kutta method. Defect is modeled using a half-sine wave function. Vibration responses are represented by orbit plots, time waveforms, and frequency and envelope spectra. Different frequencies obtained from this model match with the analytically calculated frequencies and with the frequencies obtained by the researchers earlier, which validates the model. The results demonstrate that the vibration amplitudes of defective bearings increase considerably with increase in speed and radial load.