Loaded tooth contact analysis and meshing stiffness calculation for cracked spiral bevel gears

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Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment. In this study, an accurate and efficient loaded tooth contact analysis (LTCA) model is developed to predict the contact behavior and time-varying meshing stiffness (TVMS) of spiral bevel gear pair with cracked tooth. The tooth is sliced, and the contact points on slices are computed using roll angle surfaces. Considering the geometric complexity of crack surface, a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points. According to the positional relationship between contact point and crack path, each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness. Then the compliance model of the cracked tooth is established to perform contact analysis, along with TVMS calculations utilizing three different models. By employing spiral bevel gear pairs with distinct types of cracks as examples, the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis (FEA) outcomes. Furthermore, the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs, including not only cracked tooth pair but also adjacent non-cracked tooth pairs. Hence, the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.