# Calculation and Discussion on meshing stiffness of gear transmission system with single pitting

According to the schematic diagram of pitting section in Figure 1, the section at the node is selected to study and analyze the influence of different pitting characteristics and pitting positions on the section area and moment of inertia. The standard involute profile of the basic parameters (module 6.5mm, gear 24 and pressure angle 20 °) of the pinion of gear pair 1 is selected as the research and analysis object, and the calculation equation of the geometric characteristics and position parameters of the pitting pits is derived according to the above section. In order to study the independent influence of various factors on the characteristics of pitting pits, firstly, the rectangular shape of pitting pits is selected to be symmetrical about the y-axis in the YOZ plane, where LS + WS / 2 = L / 2 exists. The simulation results are shown in Figure 2. The curve drawn in Fig. 2 (a) shows that the cross-sectional area decreases with the increase of pit depth at the same pit width WS, and the deeper the pit depth is, the more obvious the reduction of cross-sectional area is; at the same pit depth HS, the cross-sectional area decreases with the increase of pit width, and the wider the pit width is, the more obvious the reduction of area product is. The change of section moment of inertia in Fig. 2 (b) is consistent with that in Fig. 2 (a), and decreases with the increase of width and depth.

The influence of pitting location on cross-section area and cross-section moment of inertia is studied under the fixed value of pitting geometric size (HS = 1 mm, WS = 5 mm). The simulation results are shown in Figure 3. It can be seen from the figure that the cross-section area and the cross-section moment of inertia are consistent with the change of the pitting position, and are invariable with the change of the pitting position, which indicates that the cross-section area and the cross-section moment of inertia do not change with the change of the pitting position from the perspective of mathematical simulation. It can be seen from the formula that the calculation expression of cross-section area is only related to the geometric characteristic parameters of pitting (depth HS, width WS), but has nothing to do with the location parameter ls of pitting. Similarly, it can be seen from the formula that the cross-section moment of inertia A is related to the distance of the centroid along the y-axis, while the change of the pitting position parameter LS changes the distance of the centroid of the pitting pit along the z-axis. It can be seen that the change of LS has no effect on the cross-section moment of inertia IZ, thus explaining that the cross-section area product and the cross-section moment of inertia shown in Fig. 3 remain unchanged.

According to the description of the causes of pitting and the pitting characteristic diagram shown in Fig. 4, pitting is easy to occur on the lower side near the pitch line. The basic parameters of gear pair 1 are still selected to further analyze the changes of cross-sectional area and moment of inertia of the region from the tooth root of involute profile to the pitch line. Since the location of pitting has no effect on the cross-sectional area and moment of inertia, the location of pitting along the tooth width is not considered in the analysis. Figure 5 shows the change of cross-sectional area and moment of inertia curve with the change of meshing angle under different pitting depth. In Fig. 5 (a), it can be seen that with the increase of pit depth, the cross-sectional area decreases under the same pit width, and the cross-sectional area also decreases along the tooth root pitch line. The moment of inertia of the cross section plotted in Fig. 5 (b) has the same effect on the pitting depth. The influence of different pitting width on cross-sectional area and moment of inertia is shown in Fig. 6. The change form of the curve in Fig. 6 is similar to that in Fig. 5, which shows a decreasing trend. 