## 4 Effects of Different Factors on Dynamic Meshing Force
### Influence of Different Deviations on Dynamic Meshing Force
It can be seen that the profile form deviation can affect the meshing state of gear teeth, resulting in the change of dynamic transmission performance and dynamic meshing force to a certain extent. Moreover, if the profile form deviation is too large, the phenomenon of tooth disengagement will occur, which should be paid attention to in gear design and processing. In order to analyze the influence of profile slope deviation on dynamic response and dynamic meshing force, we select \(f_{Ha1}=0.015\) mm and let \(f_{Ha1}\) be \(-0.010,0,0.01\) mm and \(0.020\) mm, respectively. Similarly, after calculating the meshing error, the corresponding time history diagram and FFT spectrogram can be obtained when \(f_{Ha1}\) varies from \(-0.010,0,0.010\) to \(0.020\) mm, as shown in Figure 14. We can see from Figure 14a that, when \(f_{Ha1}\) is different, the curve of displacement \(q\) with the meshing cycle will deviate to a certain extent, but the overall fluctuation trend of each curve is similar. In Figure 14b, as \(f_{Ha1}\) increases from \(-0.010,0,0.010\) to \(0.020\) mm, the amplitude of the dominant frequency increases to some extent. However, when \(f_{Ha1}\) continues to increase, the amplitude of the dominant frequency does not increase significantly. It can be seen that the vibration and noise can be reduced by properly adjusting profile slope deviation. 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 \(f_{Ha1}\) is equal to \(-0.010,\ 0,\ 0.010,\ 0.020\) mm, respectively, as shown in Figures 15 and 16. From Figure 15, we can observe that, with different \(f_{Ha1}\), the total dynamic meshing force will be different due to the different meshing state of each pair of teeth. With the increase of \(f_{Ha1}\) from \(0\) to \(0.010,\ 0.020\) mm, the fluctuation amplitude of the total dynamic meshing force increases accordingly, and the fluctuation curve gradually moves to the left. When \(f_{Ha1}\) changes from \(0\) to \(-0.010\) mm, the amplitude of the total dynamic meshing force will also increase, but the fluctuation curve moves to the right. As can be seen from Figure 16, as \(f_{Ha1}\) increases from  
Figure 14: The dynamics characteristics with different \(f_{Ha1}\): (**a**) time history diagram; (**b**) FFT spectrogram. 0 to 0.010, 0.020 mm, the dynamic meshing force of a single pair of teeth increases in the front double-tooth meshing region and decreases in the rear double-tooth meshing region. Moreover, when \(f_{Ha1}=0.020\) mm, the dynamic meshing force of a single pair of teeth decreases to 0 near \(\tau/\tau_{z}=99.4\), that is, the pair of teeth are in the state of disengagement at this time. When \(f_{Ha1}\) changes from 0 to \(-0.010\) mm, the single tooth dynamic meshing force gradually decreases, and increases in the rear double-tooth meshing region. However, when \(f_{Ha1}\) is equal to a different value, the fluctuations of the corresponding dynamic meshing force of a single pair of teeth are very similar. Figure 17 shows the curve of the load sharing ratio varying with the meshing cycle. In the whole double-tooth meshing region, especially in the meshing in and meshing out positions, the load sharing ratio curves under different \(f_{Ha1}\) have a certain offset, which is different from that reflected in Figure 13.  
It can be seen that both the profile form deviation and the profile slope deviation will have a certain effect on the dynamic characteristics and dynamic meshing force, but their effects are different. Therefore, in order to accurately analyze the dynamic response and  
Figure 16: Dynamic mesh force of a single pair of teeth under different \(f_{Ha1}\). Figure 8:0 Dynamic mesh force of a single pair of teeth under different \(f_{Ha1}\). Figure 8:1 Total dynamic mesh force under different \(f_{Ha1}\).