Linear modification is adopted, and the value range of modification amount is [0, 0.05mm], and the value interval is 0.002mm. The value range of the modification length is [1.4mm, 8.4mm], and the value interval is. Among them, the first four modification lengths are short modification, and the last two are long modification. The change trend of dynamic load coefficient with the modification amount under different modification length is shown in the figure. It can be seen from the figure that with the increase of the modification amount, the dynamic load coefficients all change in the form of “V”, but the optimal modification amount, the critical modification amount and the minimum dynamic load coefficient corresponding to different modification length are obviously different. For four kinds of short modification, the optimal modification is less than the deformation of the highest point of single tooth engagement under the action of the average torque of the engine. With the increase of the modification length, the optimal modification is 0.006mm, 0.014mm, 0.012mm and 0.008mm, respectively. The corresponding minimum dynamic load coefficients are 2.23, 1.87, 1.79 and 2.03, respectively, which are 7.8%, 22.7%, 26% and 16.1% lower than that of the unmodified gear %。

At the same time, four kinds of short modification have critical modification amount, corresponding to 0.016mm, 0.034mm, 0.026mm and 0.024mm respectively. It can be seen from the comparative analysis that when the modification length is 1.4mm, the vibration reduction effect of the system is the smallest, and the critical modification amount is the smallest, indicating that the modification length should not be too short. For the two kinds of long modification, the optimal modification is 0.036 mm, which is significantly larger than the optimal modification in the case of short modification. The minimum dynamic load coefficients corresponding to the two long modifications are 1.69 and 1.57 respectively, which are obviously smaller than the minimum dynamic load coefficient of 1.79 under the short modification. At the same time, there is no critical modification for both long modifications. The above analysis shows that the long modification can reduce the vibration of the gear transmission system more effectively, and the larger modification can be used.

It can be seen from the above analysis that for short modification, when the modification length is 4.2mm and the modification amount is 0.016mm, the dynamic load coefficient is the minimum; for long modification, when the modification length is 8.4mm and the modification amount is 0.036mm, the dynamic load coefficient is the minimum. Further analyze the meshing force and meshing stiffness time-domain curves under the above two modification parameters and compare them with the gear without modification, as shown in the figure. It can be seen from figure a that, compared with the gear without modification, under the above two modification parameters, the maximum meshing force of the gear is significantly reduced, among which the long modification is the largest. It can be seen from the time-domain curve B of meshing stiffness that in the case of short modification, the coincidence degree of the gear is basically unchanged, while in the case of long modification, the coincidence degree of the gear is reduced near 0.252s. Combined with the analysis conclusion of the time-domain curve and node of meshing force, it can be seen that the reduction of the coincidence degree is mainly caused by the reduction of the meshing force between the gears.