Subsurface stresses analysis of flexible ball bearing with bendable races in a harmonic reducer by superimposition method

The bending of races of the flexible ball bearing in a harmonic reducer inevitably results in significant hoop stresses, which leads to the bearing working under a complex stress state. Studies show that hoop stresses can affect bearing life considerably, and subsurface stresses are the fundamental nature of the bearing failure mechanism. This paper established a simplified theoretical model of subsurface stresses for flexible ball bearing by considering bending deformation and contact deformation. First, the plane curved bar theory was used to solve the hoop stresses of the races caused by bending deformation. Second, the hoop stresses were superimposed on the Hertzian principal stresses generated by the contact load to calculate the maximum shearing stress of the raceway. Then, the influence of hoop stresses on subsurface stresses of both the inner and outer races was analyzed based on the proposed model. The results indicated that the subsurface stresses of the inner race calculated by the model were in good agreement with that of the cam-inner race-single ball contact finite element model. In addition, hoop stresses of the inner race increase the maximum shearing stress but decrease its depth to the contact surface, making the inner race more prone to spalling failure, while the outer race is the opposite. At last, the influence of the design parameters of flexible ball bearing on the subsurface stresses of races was studied to provide a theoretical basis for the optimization design of flexible ball bearing and its fatigue failure analysis.