Nonlinear vibration prediction of cylindrical roller bearing rotor system modeling for localized defect at inner race with finite element approach

Abstract

In this paper, an analytical model is proposed to study the behavior of defective bearing and rotor system. An overhung rotor system and defective roller bearing are considered for the study. Rotor is considered with unbalanced mass and bearing is taken as the cylindrical roller bearing having localized surface defect. To analyze all the system components’ effect at one node, finite element method is used to predict exact system vibrations. Euler–Bernoulli’s beam element is used to discretize the shaft. Gyroscopic effect of overhung rotor is also taken into account and governing equations of motion have been modified according to our system. Hertz contact stress theory is used for every roller–race contact to calculate the overall nonlinear bearing force. Governing differential equation is solved by Newmark-β time integration method. Nonlinear matrix equation, which is generated at each time-step in Newmark’s method, is solved by Broyden’s method. Results for defective bearing are obtained and plotted in the time and frequency domain. Poincare map has been plotted to view the system’s minimum stability time. An experiment has been carried out to validate the proposed analysis work. In this paper, it has been shown how rotor dynamic analysis can be achieved numerically with minimum calculations.