The ratio of the amplitude Kr to the average value K0 in the formula is defined as the amplitude coefficient α K of the time-varying meshing stiffness. Figure a) shows the influence of amplitude coefficient α K on gear slapping state. It can be seen from the figure that with the amplitude coefficient of meshing stiffness increasing from 0 to 0.8, the reducer variable speed integrated gear always keeps unilateral impact state. When the speed α 1 of the small cylindrical gear is 140 rad / s, the vibration state of the gear does not change with the amplitude coefficient α K.

When the speed ω 1 of the small cylindrical gear is 160 rad / s, the value of RSV is always 1, that is to say, the reduction and speed change integrated gear always keeps one side impact state. Through further calculation, it is found that under some critical conditions, such as ω 1 = 145rad / s, the change of amplitude coefficient α K of time-varying meshing stiffness may lead to the change of slapping state of reducer variable speed integrated gear. The results show that the fluctuation of time-varying meshing stiffness has little effect on the vibration state of the integrated gear.

Figure b) is the curve of response peak to peak PPV varying with amplitude coefficient α K. As shown in the figure, with the increase of amplitude coefficient of time-varying meshing stiffness α K, the vibration amplitude of reducer variable speed integrated gear will obviously increase, which is the same as that of ordinary circular face gear.