The above single pair of tooth stiffness algorithm is used to calculate the comprehensive meshing stiffness of helical gears with normal modulus of 3mm, helix angle of 18.42 °, effective contact tooth width of 35mm and number of teeth of 23 and 51 respectively. The meshing stiffness per unit contact line length of helical gear end face is calculated by romax software, As shown in Figure 1 (a). The meshing stiffness per unit contact line length of the normal surface of a single pair of helical gears obtained by conversion is shown in Figure 1 (b). The meshing stiffness of a single pair of teeth is obtained by calculating the meshing stiffness of contact lines of different lengths of a single pair of teeth, as shown in Figure 2 (a). The comprehensive meshing stiffness of helical gears obtained by superposition according to the coincidence relationship system is shown in Figure 2 (b).

It is basically consistent with the single pair tooth meshing stiffness and comprehensive meshing stiffness of helical gear calculated by helical gear stiffness algorithm, as shown in Fig. 3. Reference [68] is used in Figure 3 (a) In the algorithm, the meshing stiffness of a single pair of teeth adopts the algorithm of multiplying the length of the contact line of a single pair of teeth by a stiffness coefficient. The meshing stiffness of a single pair of teeth in the rising and falling stages changes linearly. The meshing stiffness of a single pair of teeth calculated in this paper changes along the curve. Therefore, the algorithm makes the overall amplitude of the integrated meshing stiffness of the superimposed helical teeth larger, as shown in Fig. 3 (b).

The meshing stiffness of a single pair of teeth before and after helical gear modification is shown in Figure 4 (a). According to the coincidence relationship, the superimposed comprehensive meshing stiffness before and after helical gear modification is shown in Figure 4 (b). Figure 4 (b) shows that the change of comprehensive stiffness curve of helical gear after modification is relatively gentle.