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Multi-body vibration modelling of ball bearing–rotor system considering single and compound multi-defects

Vibration modelling is a key link to explore the cognitive rules in fault diagnosis. In order to foresee the vibration characteristics accurately, the dynamic contact among joint interfaces and vibration transmission path of ball bearing are well studied. A novel methodology for multi-body vibration modelling of ball bearing–rotor system with bearing inner race–balls–outer race–pedestal is presented. Additionally, the mathematical formulation is derived with consideration of the nonlinear spring at the contact point between ball and raceway. Then, the progressive processes of single and compound multi-defects are described by using bearing practical kinematics and the vibration responses are systematically analysed. Compared with the experimental results, the fault frequency and its harmonic components are clearly observed and achieved better consistency. Moreover, for compound fault, an important observation is that the strength imbalance and mutual restraint of the vibration amplitude due to the vectors superposition of different frequency components. Further, the Lempel–Ziv complexity measure is also employed to investigate the response of signature variations. The results show that the Lempel–Ziv complexity measure used as a quantitative criterion can effectively evaluate the single and compound fault of ball bearings.