# Research on meshing stiffness of gear transmission system with randomly distributed pitting corrosion

According to the randomness of the pitting formation area, the pitting physical model under the random distribution shown in Figure 1 is established. In order to facilitate the analysis and modeling, the regular rectangle is still used for pitting simulation. According to the section analysis method, the section expansion diagram of the random distribution pitting corrosion model along the tooth width at any meshing point along the tooth profile direction in Figure 1 is shown in Figure 2.

The three selected sections in Fig. 2 are expanded, and it can be seen that the complex random distribution pitting model is actually the distribution effect of the fixed-point section of the single pitting model and the multi pitting model along the tooth width direction. When meshing to Section 1, the calculation method of section area and moment of inertia of section 1 is the same as that of single pitting corrosion model; when meshing to Section 2 and section 3, the calculation method of section area and moment of inertia is the same as that of multi pitting corrosion model. Compared with single pitting model and multi pitting model, the main difference of random distribution pitting model is that the value range of pitting pits along the tooth profile direction on the x-axis, the corresponding tooth width direction cross-sectional area and moment of inertia change more frequently, and there are more variable parameters, so the simulation is more complicated. But only from the simulation ideas and methods, the idea is relatively clear. If we can accurately obtain the geometric characteristics of pitting, according to the proposed physical and mathematical model, we can approximately simulate the time-varying meshing stiffness of gears.

Due to the complexity of random pitting distribution, the geometric characteristics of any pitting pit are independent. In order to calculate and analyze the time-varying meshing stiffness of gears under random pitting, the following simulation conditions and examples are set for simulation analysis. Firstly, the geometric dimensions of three pitting pits are set, and the pre fabricated pitting pits in B2C section, CP section and PD section are still selected. The local set pitting in Section C is composed of pitting Pit 1 and pitting Pit 2, the set pitting in CP section is composed of pitting Pit 1, pitting pit 2 and pitting Pit 3, while the set pitting in PD section only contains pitting Pit 1 Cloth effect.

The time-varying meshing stiffness curve of gear with random pitting is drawn in Fig. 3. It can be seen from the figure that the stiffness value in the pitting setting area is lower than that in the non pitting setting area. At the same time, the stiffness difference curve under the non pitting and random pitting characteristics is drawn. From the difference curve, the stiffness of gear with different pitting number and geometric size in different meshing sections is shown The difference of degree is different. The average stiffness is still selected to study the reduction percentage of stiffness difference, and the reduction percentages calculated at the three locations are 0.69%, 3.22% and 0.54% respectively. The reduction percentage of stiffness indicates that the more the number of pitting pits or the larger the geometric characteristics of pitting, the more obvious the reduction of gear time-varying meshing stiffness. 