Theoretical model to predict the effect of localized defect on dynamic behavior of cylindrical roller bearing at inner race and outer race

Abstract

The dynamic response of bearing under load and speed often determine the performance limitations of the machines and it is necessary to be able to predict bearing dynamic performance as an integral part of machine design analysis. In this paper, a mathematical model has been developed to investigate a nonlinear dynamic behavior of a rotor-bearing system due to localized defects of inner race and outer race. In the mathematical formulation, the contacts between rolling elements and inner/outer race is considered as nonlinear springs whose stiffness is obtaining using Hertz contact stress theory. Here nonlinear damping is also taken into consideration for cylindrical roller bearing. The governing equations of motion are formulated by using energy approach. Contact force and contact stiffness having nonlinearity and is calculated by using Newton–Raphson method for n-unknown nonlinear simultaneous equation. The new mark implicit integration technique is coupled with the Newton–Raphson method to solve the differential equations. A computer program is developed to simulate the defect on inner race and outer race and all the results are represented in the time and frequency domain. Equations of motions are solved by using Newmark-β method for phase plot/Poincare map. The proposed mathematical model is also compared with experimental results having radial and axial load condition. From the results obtained from the predicted model for frequency spectrum and phase plot at various speeds, the mathematical modeling and experimental results are found quite similar.