A theoretical model for studying vibrations of ball bearing with localised defects on inner race using cubic hermite spline

The paper deals with the analysis of vibration behavior of a ball bearing under the influence of localized defects on the inner race. In the mathematical model, the calculation of contact force is based on Hertzian contact deformation theory. Using the blending functions of cubic hermite spline, the pulse generated by the ball striking the defect is modeled. The model predicts the effect of size of the defect (bearing deterioration), the effect of intensity of load and the effect of multiple defects present on inner race on the vibration amplitude. MATLAB programming environment is used for realizing the vibration response of the ball bearing under study. The simulation is different from defective outer race since the defect on inner race does not remain stationary and as such the rolling elements try to catch the moving defect. The governing equations of motion are solved by Euler´s method. The numerical results of the analysis are presented as a function of variation of the geometry of the inner race due to the impact at the defect and normal race contact w.r.t. time and the conclusion about the health of the bearing is determined by the spectral analysis.