## 4 Effects of Different Factors on Dynamic Meshing Force
### Influence of Different Deviations on Dynamic Meshing Force  
Here, we still take the tooth profile deviation as an example to analyze the changes of the dynamic response and the dynamic meshing force under different profile form deviations and profile slope deviations. Let the profile form deviation \(f_{f\alpha 1}\) be \(0,\ 0.005,\ 0.015,\)\(0.025\) mm, respectively, and the corresponding meshing errors can be obtained based on the meshing error solution algorithm. Substitute them into the dynamic equation and let \(\overline{\zeta}=0.04,T_{1}=500\ \text{N}\cdot\text{m},\Omega_{h}=0.6\). By solving the dynamic equations, we can obtain the time history diagram and the FFT spectrogram when \(f_{f\alpha 1}\) is \(0,0.005,0.015,0.025\) mm, respectively, as shown in Figure 10. When \(f_{f\alpha 1}\) increases from \(0\) to \(0.005\) mm, the change of dynamic response is not obvious. With \(f_{f\alpha 1}\) increasing from \(0.005,0.015\) to \(0.025\) mm, the amplitude of dynamic transmission error (displacement) \(q\) and the dominant frequency increase obviously, which shows that the increase of \(f_{f\alpha 1}\) leads to the aggravation of vibration of the whole system. Figure 8: Dynamic mesh force based on new dynamic model under different meshing errors: (**a**) dynamic mesh force based on Figure 5c; (**b**) dynamic mesh force based on Figure 5d. Figure 9: Load sharing ratio based on new dynamic model. By bringing the solution results of the dynamic equation into the formula of the dynamic meshing force, the variation of the total dynamic meshing force and the single pair of teeth meshing force with the meshing cycle can be obtained when \(f_{fa1}\) is equal to \(0,\ 0.005,\ 0.015,\ 0.025\) mm, respectively, as shown in Figures 11 and 12. As can be seen from Figure 11, with different \(f_{fa1}\), the total dynamic meshing force will be different due to the different meshing state of each pair of teeth, which can be seen more clearly from Figure 12. It shows the change of dynamic meshing force of a single pair of teeth from meshing in to meshing out. It can be seen that as the profile form deviation \(f_{fa1}\) increases from \(0.005,\ 0.015\) to \(0.025\) mm, the difference between the corresponding dynamic meshing force curve and the dynamic meshing force curve with \(f_{fa1}=0\) mm becomes more and more obvious. It should be noted that, in the rear double-tooth meshing region, the dynamic meshing force of the pair of teeth is reduced to \(0\) when \(f_{fa1}\) is \(0.025\) mm, which means that the pair of teeth are in the state of tooth disengagement and the load is completely borne by the other pair of teeth. To further illustrate the load distribution of a single pair of teeth in a meshing cycle, the curve of the load sharing ratio varying with the meshing cycle is drawn, as shown in Figure 13. When \(f_{fa1}=0\) mm, in the front and rear double-tooth meshing regions, the load sharing ratio increases or decreases smoothly with the change of meshing cycle and the load sharing ratio curves in the two double-tooth meshing regions are symmetrically distributed relative to the middle single-tooth meshing region. When \(f_{fa1}=0.005\) mm, the load sharing ratio curve fluctuates to a certain extent, the fluctuation state of which mainly depends on the shape of tooth profile deviation. As \(f_{fa1}\) increases from \(0.005,0.015\) to \(0.025\) mm, the amplitude of the fluctuation of the load sharing ratio curve increases  
Figure 10: The dynamics characteristics with different \(f_{fa1}\): (**a**) time history diagram; (**b**) FFT spectrogram. gradually. When \(f_{fa1}\) is 0.025 mm, a section of meshing region with the load sharing ratio equaling to one appears in the front double-tooth meshing region, which indicates that another pair of teeth are out of meshing at this time and the load is completely borne by the pair of teeth.