Vibration Analysis of Ball Bearings with Outer Race Defects: Development of Mathematical Model and Experimental Validation

Abstract

In this paper, the radial vibrations of rigid shaft supported ball bearings are studied. In the analytical formulation the contacts between the balls and the inner and outer races are considered as nonlinear springs, whose stiffness are obtained by using the Hertzian elastic contact deformation theory.For perfect bearings, vibrations occur at the ball passage frequency. All results are presented in the form of Fast Fourier Transformations (FFT). The experimental validation of a mathematical ball bearing model with localized defects is presented here. The bearing is considered as a mass ? spring ? damper system, considering each rolling element as a contact spring ? damper pair, based on Hertz equations for contact deformation, moving along the inner and outer raceways. In accordance with the obtained results, in this work a bearing model is validated with a purpose built test bench. To compare the vibration signals from the real system and the model, spectral and high frequency analysis is used, particularly techniques commonly used on commercially available vibration analysis equipment, such as envelope and Peak Value analysis. The studied model shows a frequency behavior similar to that of the experimental data and the envelope and Peak Value analysis clearly reveal the characteristic frequencies of the studied type of defects.