The variation law of gear vibration state with the eccentricity of reducer variable speed integrated gear is studied. Figure a) shows the influence of eccentricity ε on the rattling state of gears. It can be seen from the figure that as the eccentricity increases from 0 to 0.8, the reducer variable speed integrated gear also successively experiences non impact, unilateral impact and bilateral impact States, which is similar to the previous situation. As the eccentricity continues to increase, the gear will always maintain the bilateral impact state. Eccentricity is the essential difference between non-circular gear and circular face gear. When ε = 0, the non-circular gear is circular, and the increase of ε will lead to the increase of alternating component coefficients B1 and B2, which will cause the gear to produce slapping behavior. It is also found that, under certain parameters, the small amplitude VSR value of eccentricity will cause gear slapping. Therefore, compared with the ordinary circular face gear, the reducer variable speed integrated gear with instantaneous center and meshing stiffness combined excitation is easier to produce slapping behavior than the circular face gear.

Figure b) is the curve of response peak to peak PPV versus eccentricity ε. As shown in the figure, when the reducer variable speed integrated gear experiences non impact state and unilateral impact state, its response peak to peak value PPV increases with the increase of eccentricity ε, and suddenly increases when the double impact phenomenon occurs. With the increase of eccentricity ε, the peak to peak PPV decreases obviously, however, it is still in the state of bilateral impact. The larger the eccentricity is, the easier it is to cause the rattling state of the gear. For the gear with large eccentricity, the rattling phenomenon can be prevented by reducing the input speed or improving the machining accuracy.