Three-dimensional dynamic analytical modeling and vibration analysis of deep groove ball bearings under multi-source internal fault excitation

Abstract

Abstract Dynamic modeling can greatly inform the study of characteristics of bearing failures. However, traditional two-dimensional dynamic models are not effective in analyzing complex dynamic characteristics of bearing elements, in particular three-dimensional rotations, gyroscopic effects, and lubrication traction under high-speed operations. To address these limitations, this paper establishes a novel three-dimensional bearing dynamic analytical model based on Hertz contact theory. The proposed model considers multiple rigid body degrees of freedom, rotational attitude, dynamic circular motion, and mixed elastic lubrication of the bearings. Dynamic variation of the contact points between bearing elements are described using quaternions. The proposed model is validated by experiments. By introducing a contact stiffness variation coefficient, this paper also demonstrates that replacing time-varying Hertz contact stiffness with a constant Hertz contact stiffness produces insignificant errors in the localized fault region. To further test the effectiveness of the proposed three-dimensional model, Lempel-Ziv complexity (LZC) is adopted. The LZC values of the signals from the three-dimensional model, two-dimensional model and experiment are compared. It is found that the LZC of the three-dimensional model signal is closer to that of the experimental signal, indicating that the proposed model can more accurately reflect actual bearing operations.