An analytical method for dynamic analysis of a ball bearing with offset and bias local defects in the outer race

Ball bearings are the critical essential bodies in different industrial machinery. An in-depth recognition of the vibrations of defective ball bearings can be useful for the progress of defect detection approaches of the machinery. In this paper, an improved time dependent displacement excitation (TDDE) model is proposed to consider the parallel, offset or bias local defects in the outer race of ball bearing. The contact relationship between the parallel defect and ball, that between the offset defect and ball, and that between the bias defect and ball are deeply analyzed. The TDDE model for the parallel, offset, and bias defect cases is established by using a piecewise function model including the rectangular and half-sine functions. A dynamic model in the previous study is improved to consider the effects of the offset and bias local defects. The Hertzian contact theory is adopted to calculate the bearing contact stiffness. The effects of defect sizes, defect offset distance, and defect bias angle on the vibrations of a ball bearing are analyzed. Comparison results among the parallel, offset, and bias defect cases show the advantage of established method in this study. The obtained results show that the given method can provide a more accurate and reasonable analytical method for studying the vibrations of ball bearing with a local offset defect.