Bending stress analysis of hypoid gear tooth root

Submit the established model to abaqus/standard solver, and finally get the finite element analysis results, as shown in Figure 1 (a) and (b), which are the mise stress of small and large gear pairs in the meshing process of hypoid gear. It can be seen that the mise stress of tooth surface is distributed on the adjacent three teeth. Theoretically, the meshing process of large and small gears of hypoid gear is point contact, but due to the elastic deformation of tooth surface, the deformation of support bearing Under the influence of axle housing deformation and other factors, the tooth surface appears an approximate contact ellipse. The bending stress at the root of the tooth will be further studied, and the change law of the bending stress at the root of the hypoid gear tooth in the whole meshing process will be analyzed. Figure 2 shows the definition of tooth blank contour. In order to better observe the change of tooth root bending stress of hypoid gear in a meshing cycle, the fillet transition surface of a single tooth is mapped to a rectangular plane. The length direction of the rectangle is from left to right, from the small end to the large end of the tooth, and the width direction is from the fillet starting position (st) to the contact starting position (ED) of hypoid gear.

Figure 3 (a) shows the cloud diagram of the instantaneous maximum principal stress change at the concave root of the pinion gear during the whole meshing process. For convenience of display, five positions in the meshing process are selected from top to bottom in the figure, and the horizontal axis and vertical axis in the figure are normalized relative to the tooth width and the size of the gear fillet transition respectively. During the meshing process, the meshing line of the hypoid gear moves from the big end to the small end, and the maximum principal stress at the tooth root also changes. Because the overall model of the drive axle takes into account the influence of the meshing of the hypoid gear due to the flexible deformation of the axle housing, bearings, main reducer housing and so on, the maximum value (about 530mpa) is reached when the pinion enters the meshing, that is, when the big end of the pinion begins to contact, This point is the dangerous point of small gears in the meshing process of hypoid gears. Figure 3 (b) shows the time history of the three-dimensional principal stress change of the corresponding unit at the dangerous point of the maximum principal stress at the pinion root. It can be seen from the figure that the first principal stress and the third principal stress are dominant in the meshing of this tooth. Here, the unit is first subjected to compressive stress (the third principal stress) and then tensile stress (the first principal stress) in the whole meshing process. In the meshing process of the pinion, the position where the tooth root is close to the concave surface is first stressed. This compressive stress is due to the compressive stress generated at the root of the tooth during the meshing process of the previous tooth. Then the tensile stress, which is due to the bending of the pinion gear teeth when the current gear teeth mesh, and the tooth root near the concave surface of the pinion is pulled. Therefore, if a virtual strain gauge is pasted at this position, the stress change process of the strain gauge here is shown in Figure 3 (c).

Similarly, we can get the cloud diagram of the first principal stress change at the root of the gear tooth convex surface during the whole meshing process, as shown in Figure 3 (d). In the figure, five positions corresponding to the above positions of the gear and pinion during the meshing process are selected from top to bottom. From the figure, it can be seen that since the overall model of the drive axle takes into account the influence of the deformation of other components of the drive axle, The maximum principal stress at the root of the big gear appears near the small end, and the maximum principal stress is 600MPa, which is the dangerous point of the root of the big gear in the meshing process of the hypoid gear. The difference between the maximum principal stress nephogram of large and small gears is mainly caused by the different geometry of the tooth surface and tooth root of hypoid gears.

As shown in Figure 3 (E), the time history of the first principal stress, the second principal stress and the third principal stress of the location unit at the dangerous point of the gear root during the whole meshing process is shown. From the figure, it can be seen that the first principal stress and the third principal stress are dominant in the meshing process of the hypoid gear, but unlike the pinion, the unit at the gear root is first stressed in tension and finally stressed in compression. This is mainly due to the tensile stress at the root near the convex surface of the big gear, which is caused by the tension at the root due to the current tooth meshing. Then it is subjected to compressive stress, which is caused by the compressive stress at the root of the tooth during the meshing process of the next tooth. If the virtual strain gauge is pasted at this position, the stress change process of the strain gauge here is shown in Figure 3 (f). Comparing the stress change law of the tooth root of the large and small moving gears in the whole meshing process, it can be concluded that in the meshing process of the hypoid gear based on the integral drive axle studied in this paper, considering the influence of the deformation of the main reducer, halfshaft, bearing and other components of the integral drive axle housing, the hypoid gear has edge contact, which makes the bending stress of the concave tooth root of the pinion reach the maximum value when entering the meshing (that is, the big end of the gear), The tooth root is first subjected to compressive stress and then tensile stress. When the convex tooth root of the big gear leaves the mesh (i.e. the small end of the gear), the bending stress reaches the maximum value, and the tooth root is first subjected to tensile stress and then compressive stress.

Compared with the tooth root bending stress distribution obtained by considering only the hypoid gear alone, the hypoid gear of the drive axle will be affected by the support stiffness of the drive axle, the support stiffness of the main reducer and other components of the drive axle during the actual loading operation, so the meshing of the hypoid gear is different from that when considering the meshing of the hypoid gear alone, Therefore, when designing the hypoid gear of the drive axle, not only the meshing of the hypoid gear should be analyzed separately, but also the meshing state of the hypoid gear installed on the drive axle and under load.