An analytical method to calculate the time-varying mesh stiffness of spiral bevel gears with cracks

Time-varying mesh stiffness (TVMS) is one of the main dynamic excitation sources of gear transmission systems. The accurate calculation of TVMS is the foundation to comprehensively investigate the vibration of powertrain. Compared with the spur gear, the meshing process of spiral bevel gear is spatially time-varying, which makes the analytical calculation of TVMS more difficult. In this paper, the meshing relationship of spiral bevel gears is first established by extending the slice method of spur and helical gears to spiral bevel gear. Secondly, the analytical models of perfect and cracked spiral bevel gears are presented to evaluate TVMS. Meanwhile, the effects of crack length and depth on mesh stiffness are investigated. Thirdly, the influence of crack length and depth on the dynamic response are simulated based on the 8-DOF dynamic model of spiral bevel gear. Finally, the experiments are conducted to verify the effectiveness of the analytical model. Experimental results demonstrate that the existence of tooth crack fault makes the response characterized by periodic impact with the rotating frequency of cracked pinion.