A complete dynamics model of defective bearings considering the three-dimensional defect area and the spherical cage pocket

In current studies of dynamics of the defective bearing, the lumped-parameter model of the rolling element bearing is widely used, which is a simplified bearing vibration model consisting of the rigid masses connected by springs and dampers and is not a complete bearing dynamics model. In this paper, based on Gupta's bearing dynamics model, a complete dynamics model of the defective bearing is developed. The dynamics model includes the translational and rotational motion of all components in the bearing and fully considers the contact and friction forces between each component, especially the interaction between the rolling element and spherical pocket of the cage when the cage is guided by the rolling element. Different from the lumpedparameter model which needs to pre-plan the motion path of the rolling element in the defect area, the dynamics model can solve the motion path directly based on the three-dimensional geometric relationship and mechanical mechanism between the rolling element and defect area. The vibration responses of the defective bearing simulated by the dynamics model are in good agreement with the measured vibration responses in the time, frequency, and timefrequency domain, and the double-impulse phenomenon exists in the vibration response of the defective bearing with either outer or inner raceway defect, and the average value of the dynamically varying cage rotation speed solved by the dynamics model is consistent with the theoretical calculation, which verifies the accuracy of the model. The effect of raceway defects on the cage motion state is also studied, and the cage stability index is given by combining the cage whirl instantaneous angular velocity and cage rotation angular velocity, and the cage stability index is quantified and analyzed. The analysis results show that the bearing with inner raceway defects has worse cage stability than the bearing with outer raceway defects, and there is no obvious regularity for the effect of changes in the geometry of the defect area on cage stability.