From the above analysis, it can be seen that the gear error and the loaded deformation of the gear teeth cause the actual meshing point to deviate from the theoretical meshing point, which makes the normal velocity of the two gears near the actual meshing point different, resulting in the velocity difference, that is, the meshing impact velocity vs. The diagram shows the principle diagram of the impact velocity outside the line.

In the figure, the normal velocity VP and VG of the driving wheel and the driven wheel at the actual meshing point D are not collinear, which can be divided into two directions: the instantaneous meshing line and the vertical line of the instantaneous meshing line. The difference of the components of VP and VG on the instantaneous meshing line of the gear is the meshing impact velocity vs. According to the geometric relation, we can get the following results

The instantaneous base circle radius r’g of the driven wheel can be expressed as:

The center distance of gear pair can be expressed as follows:

When the formula is combined, the meshing impact velocity can be obtained as follows:

Among them,