# Analysis of simulation results of coupling dynamic model of helical gear modification and friction excitation

Based on the 8-DOF coupling dynamic model of helical gear system, the Runge Kutta method is used to solve the dynamic response of helical gear system with and without friction after helical gear modification, in which the friction coefficient is 0.1. The vibration displacement and vibration velocity of the driving wheel in X, y and Z directions are shown in Fig. 1, Fig. 2 and Fig. 3 respectively. The vibration displacement and vibration velocity of the driven wheel in X, y and Z directions are shown in Fig. 4, FIG. 5 and Fig. 6 respectively. Where, X direction is the friction direction, Y direction is the meshing line direction of helical gear system, and Z direction is the axis direction of helical gear system. Figure 1 ~ 6 shows that when friction is not considered, the vibration displacement and vibration velocity in X direction are zero, and the vibration displacement and vibration velocity in Y and Z directions change periodically. When considering friction, the amplitude of vibration displacement and vibration velocity in X, y and Z directions increase obviously.

The dynamic meshing force and friction of helical gear system are obtained by simulation calculation, as shown in Figure 7. Figure 7 (a) shows that the fluctuation amplitude of dynamic meshing force of helical gear increases obviously when friction excitation is considered. When friction excitation is not considered, the mean value of dynamic meshing force is close to 9253.7n calculated by theoretical formula, indicating the correctness of dynamic model.

Figure 8 shows the dynamic transmission error of the helical gear system obtained by analysis, Figure 8 (a) and figure 8 (b) It shows that when friction is not considered, the fluctuation of dynamic transmission error curve is very small, while when friction is considered, the fluctuation of dynamic transmission error curve increases significantly. When friction is not considered, it is basically consistent with the static transmission error waveform of helical gear system calculated by romax software as shown in Figure 9. When friction is considered, the dynamic transmission error vibrates due to friction excitation The swing amplitude increases.

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