In China, there are few studies on the bending stress of the hypoid tooth root of the drive axle, mainly focusing on the contact analysis of spiral bevel gears, hypoid gears and the bending stress analysis of the spur gear tooth root. Professor Fang Zongde of Northwestern Polytechnic University solved the contact problem of hypoid gears with friction by using the combination of finite element and linear programming in 1999. In 2002, Fang Zongde and others used the numerical simulation method to solve the contact points and edge contact points in the meshing process of spiral bevel gears. In 2003, Deng Xiaozhong, Fang Zongde and others used the finite element method to analyze the multi tooth contact of spiral bevel gears, and obtained the contact state and change law of the teeth. At the same time, many scholars in China have studied the contact of hypoid gears, such as Professor Tang Jinyuan of Central South University, who used the finite element method to analyze the dynamic meshing characteristics and static meshing stiffness of hypoid gears in 2011. In 2012, Tang Jinyuan and others also used the finite element method to analyze the dynamic meshing characteristics of spur gears. In 2013, Zhao Xiaobo and others compared and analyzed the influence of the contact area of spiral bevel gears on the root stress, and the results showed that the change of the contact area of gears would affect the distribution of gear bending stress. In 2015, Zhang Hongtao established the geometric model of spiral bevel gear and analyzed the contact and bending stress of the gear by using the finite element method. In 2016, zhuoyao studied the static contact of spiral bevel gears and obtained the variation law of gear root stress with load by using the finite element model. It can be seen that the above research mainly analyzes the single spiral bevel gear pair, without considering the deformation of the gear support shell. In 2017, sun Yuehai et al. Proposed a spiral bevel gear processing method, established the tooth surface equation, and carried out the tooth meshing simulation contact analysis. The results showed that the gears processed by the spiral deformation generation method can eliminate the tooth diagonal contact, thereby improving the gear contact quality.
Comparing the research status at home and abroad, it can be seen that the most widely used finite element method in these studies is to establish the meshing model of hypoid gear. In order to simplify, only one tooth or one segment of hypoid gear is considered. When defining the boundary conditions, it is mainly through artificial constraints and external load loading at a specific gear position to predict the gear contact. These models have two main shortcomings: first, they have to define boundary conditions to simulate the operating conditions of the whole gear, and second, they have to define the load loading mode. Because the stress state of the actual meshing gear pair is uncertain in advance, defining boundary conditions on these simplified models and loading loads at specific positions cannot truly reflect the actual load conditions. During the real operation of the gear, such as the deformation of the axle housing and support bearing in the drive axle, it will also affect the contact of the hypoid gear, thus affecting the fatigue life of the gear. Therefore, the whole finite element model of the drive axle will be established, and this model will be used to predict the bending strength of the gear root of the drive axle.
The bending fatigue of hypoid gear tooth root can be divided into two stages: crack initiation stage and crack propagation stage. Generally, the gear pair is designed with relatively low tooth root stress, and the deformation of the gear is still in the elastic region of the material, so that most of the fatigue life of the gear is spent in the crack propagation stage. In foreign countries, stress life (S-N) method is widely used to predict the bending fatigue life of gears. Of course, some scholars use the strain life method to predict the bending fatigue life of hypoid gears. For example, Ural et al. Proposed a finite element method to predict the crack shape and fatigue life of spiral bevel gears, using commercial software (FRANC3D) and FE contact analysis model to simulate 3D crack propagation, taking into account the movement of load in the meshing process of spiral bevel gears.