An Improved Theoretical Model of Unbalanced Shaft-Bearing System for Accurate Performance Prediction of Ball Bearing Due to Localized Defects

In this study, an improved mathematical model of unbalanced shaft supported on two ball bearings has been developed for accurate prediction of the behaviour of system due to the localized bearing defects (spall). In the mathematical formalism, the contact between the balls and races of the bearing is considered as nonlinear spring, whose stiffness is estimated by using Hertzian contact deformation theory and shaft is considered as rotating Timoshenko beam. The four nonlinear factors of bearing are incorporated in modelling, namely localized bearing defects, varying compliance (VC) vibration because of elastic and geometric characteristics of bearing, unbalanced force and radial internal clearance. After the mathematical model for shaft, the governing equations of motion for bearing have been derived. Sixth-order Runge–Kutta method is employed to increase the numerical stability. The effect of the localized defect and bearing speed is analysed. The result is presented in the form of peak-to-peak plot, frequency spectra and phase trajectory diagram.