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

  • Yongzhen Liu
  • Yimin ZhangEmail author
  • Zhihua Wu
Technical Paper


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.


Rotor–bearing system Stochastic dynamic Orthogonal polynomial Bernoulli distribution Edgeworth series Random clearance 



We would like to express our appreciation to the Chinese National Natural Science Foundation (U1708254) for supporting this research.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina
  2. 2.Equipment Reliability InstituteShenyang University of Chemical TechnologyShenyangChina

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