In order to accurately simulate the whole process of a certain tooth surface of the driving gear from entering meshing to exiting meshing, the whole meshing process of a single pair of gears is divided into 20 positions for calculation, and each position of the driving gear rotates 1 ° to extract the mechanical results required for the analysis through finite element post-processing.

Taking the meshing tooth surfaces of the driving and driven gears in the three tooth model as the analysis object, the contact force and displacement output are set as the field output variables in the initial analysis step of ABAQUS, and the change of the contact force can be obtained by post-processing. Figure 1 shows the contact force nephogram of the driving gear face at a certain meshing position. It can be seen from Figure 1 that the contact area of the variable hyperbolic arc gear is a slender ellipse when the load is applied, and the contact pressure at the center of the ellipse is the largest.

Figure 2 shows the comprehensive elastic deformation diagram of a single tooth. It is necessary to extract the comprehensive elastic deformation of different meshing positions to calculate its meshing stiffness. When the elastic deformation of the gear pair is not considered in theory, the gear pair is in point contact. According to Hertz contact theory, the maximum deformation of the gear pair occurs at the theoretical contact point, which is the comprehensive elastic deformation of the gear.

The curves shown in Fig. 3 are the comprehensive elastic deformation of driving wheel and driven wheel at different meshing positions and the comprehensive elastic deformation of gear teeth. It can be seen from Figure 3 that the comprehensive elastic deformation of the driving gear tooth surface increases with the increase of the gear angle, and the comprehensive elastic deformation of the driven gear tooth surface decreases with the increase of the gear angle, both of which are nonlinear deformation. The results show that the comprehensive elastic deformation of gear teeth decreases first and then increases with the increase of gear angle. This is because the Hertz contact elastic deformation of gear teeth basically remains unchanged during the contact process, while the bending deformation of gear teeth decreases first and then increases.