Stochastic dynamic analysis of the rotor–bearing system considering the randomness of the radial clearance

Abstract

A stochastic dynamic model of the rotor–bearing system considering the randomness of the radial clearance is established in this research. Orthogonal polynomial approximation method is chosen to solve the stochastic dynamic equations. Taylor series expansion is used to approximate the nonlinear restoring force derived via the Hertz contact theory. The determination coefficient of equivalent Hertz contact is supposed to follow Bernoulli distribution. Then the probability of the contact between the jth ball and the raceways is solved. The first four order moments of the maximum displacement are obtained. And the CDF of the maximum displacement are calculated according to the Edgeworth series expansion theory. The effects of the factors such as the mean and the coefficient of variation of the radial clearances, eccentricity and the rotating speeds are discussed in time domain and frequency domain, respectively. Monte Carlo simulation verifies the effectiveness of the study.