First, the differences of gear dynamic characteristics with different friction models are discussed.Figures 1 and 2 show the time and frequency domain signals of pinion displacement in X and Y directions under three friction models respectively.In the time domain signal, the maximum amplitude of the three models’displacements are not significantly different, but the fluctuations of model M1 and M2 are larger than M3. Therefore, in the frequency domain signal, the amplitudes of the first three orders of M1 and M2 are larger than M3, but the amplitudes of the fourth to tenth order are not significantly different.The amplitudes of M1 displacement in X and Y direction are larger than M2, which indicates that the sudden change of friction coefficient increases the excitation to gear vibration.

Fig. 3 compares the time domain signals of engagement and friction forces of three friction models.From the point of view of total friction force, the amplitudes of model M1 and M2 are larger than M3, and the friction direction is always positive, but the friction force of M3 is negative near the joint, which is caused by the difference of friction coefficient values on two teeth engaged at the same time (M3 friction coefficient decreases with the increase of distance from the joint), and the negative direction at the joint increases after friction is cancelled.By comparing M1 with M2, it is found that the abrupt change of friction direction at the joint causes a sharp increase in friction, which is not the case in the smoothing model.From the meshing force of tooth surface, the meshing force of model M3 is greater than that of M1 and M2, and the impact near the joint is obvious.

Fig. 4 shows the time-domain and frequency-domain diagrams of the transmission errors obtained by the three models. It can be seen that the transmission errors of model M3 are the largest due to the maximum meshing force on the tooth surface and the most obvious variation near the joint.The difference of amplitude is mainly in the 1st and 2nd order of engagement, but there is little difference between 3rd and 7th order.