An improved dynamic model of defective bearings considering the three-dimensional geometric relationship between the rolling element and defect area

The accuracy of the vibration response simulated by the dynamic model of the defective bearing depends on the precise expression of the interaction between the rolling elements and defect area in the model. An improved dynamic model considering the three-dimensional geometric relationship between the rolling element and the defect area is developed to investigate the abrupt change of contact force and the corresponding vibration response of the bearing system. The geometry parameters describing the defect area are extended to the radius and groove radius of the raceway, the maximum and minimum depths of the defect area, and the circumferential angular extents of defect area on the radial and axial cross-sections for the first time. During a rolling element passes through the defect area, the contact forms between the rolling element and the defect area are classified into different types depending on whether the rolling element is in contact with the top edges or the bottom surface of defect area. The influence of defect size on contact form was investigated, the changes in contact force of the rolling element under different types of contact forms were compared, and the relationship between defect size and vibration response of the bearing system was quantified. The analysis results indicate that the circumferential angular extent of defect area on the axial cross-section has significant influence on the contact force between the rolling element and defect area, as well as the impulse response of the bearing system. Double-impulse phenomenon appears in both the time domain and time-frequency distribution of the vibration response of bearing system, and the simulation results have a good agreement with the experiments. The comparison of the vibration responses at different defect sizes shows whether the double-impulse phenomenon can be clearly observed in the vibration response depending on the rotational speed of the bearing and the size of the defect area.