Considering the random error interference, the vibration characteristics of spur gear transmission in two cases are compared and analyzed: ① the influence of random error on tooth surface friction is not considered, and the tooth surface friction coefficient and meshing radius are assumed to be fixed values; ② Considering the interference of random error, the friction coefficient and meshing radius of tooth surface are assumed to be random variables disturbed by random error, as shown in Figure 1.
| Parameter | The friction parameters of tooth surface are random | The friction parameters of tooth surface are fixed values | |
| Numerical characteristics of acceleration response | Mean square deviation | Mean square deviation | Growth rate |
| X direction (/ mm / S2) | 6.989 6 | 5.512 7 | 26.79% |
| Y direction (/ mm / S2) | 19.200 8 | 15.134 2 | 26.87% |
| Torsion (/ rad / S2) | 0.159 1 | 0.125 4 | 26.84% |
In Figure 1, the acceleration curve considering the randomness of the friction parameters of spur gears fluctuates more violently than the acceleration curve with the friction parameters of the tooth surface set as a fixed value. Based on the analysis shown in Table 1, when the tooth surface friction parameter is a random quantity, the randomness of the vibration acceleration of the spur gear increases, indicating that the randomness of the tooth surface friction parameter interferes with the vibration characteristics of the spur gear transmission to a certain extent.
Through the spectrum analysis of the vibration acceleration response of Spur Gear Considering the randomness of tooth surface friction parameters, it can be seen from Fig. 2 that the vibration acceleration of spur gear when the tooth surface friction parameters are random and fixed values appear peak at 1100 Hz and 2200 Hz. The meshing frequency of the cylindrical gear and the frequency of 860 Hz are superimposed at the meshing frequency of the cylindrical gear. As shown in Table 2, at the peak value, the amplitude of vibration acceleration of spur gear with random tooth surface friction parameter is higher than that of spur gear with fixed tooth surface friction parameter.
| Parameter | Parameter | |
| 1 100HZ | 2 200HZ | |
| X direction | 40.6% | 53.3% |
| Y direction | 40.7% | 53.3% |
| Torsion direction | 40.7% | 53.3% |