## 5 Results and Discussions
### Effect of Manufacturing Errors
Additionally, the MTE and MB have an approximate linear relationship with the upper deviation of \(F_{\alpha}^{\text{c}}\) and the \(\delta_{\text{RP}}\), and the slopes of the TE and backlash curves are used to evaluate  
Figure 11: MTE and MB with different (**a**) profile deviations and (**b**) pin center circle diameter deviations. Figure 10: Results with MEs: (**a**) TE and (**b**) backlash. their influence on the MTE and MB. The slopes of the TE and backlash curves in Figure 11a are 4.1848 and \(-\)8.4004, respectively, and the slopes of the TE and backlash curves in Figure 11b are \(-\)2.6029 and 4.7578, respectively. This indicates that the profile deviation has a greater effect on the MTE and MB than the pin center circle diameter deviation. In addition, the number of contact pins and the load distribution on the pins with different types of MEs (corresponding to Figure 10) are calculated, as shown in Figure 12. As shown in Figure 12a, when the pitch deviation is considered, the number of contact pins varies from three to ten, instead of periodically changing between six and seven pins when the MEs are not considered. This shows that the early contact (e.g., \(\theta_{\rm f}=80^{\circ}\)) or the instantaneous mesh-apart (e.g., \(\theta_{\rm f}=180^{\circ}\)) of the pins occur due to the influence of the pitch deviation. The irregular changes of the number of contact pins in a large range are the main reasons for the changes in the waveforms of the TE and backlash and the increase in their peak-to-peak value (see Figure 10), and this will also cause the vibration of the transmission system and worsen the force condition of the pins. Figure 12b shows that the load on some of the pins is significantly increased when the pitch deviation is considered (e.g., the 11 th pin when \(\theta_{\rm f}=60^{\circ}\)), which will greatly increase the MCS. Since the upper deviations of the profile deviations \(F_{a}^{\rm c}\) and \(F_{a}^{\rm P}\) are 3 \(\upmu\)m and zero, respectively, the initial gap between the tooth surfaces is reduced, which leads to an increase in the mean value of the number of contact pins, as shown in Figure 12c. Additionally, due to the influence of the profile deviation, the minimum initial gap between the tooth surfaces of each pair is different, which leads to the irregular changes in the number of contact pins, and this is also another reason for the slight fluctuations in the curves of the TE and backlash in Figure 10. Compared with Figure 12a,c, the number of contact pins changes more regularly and periodically under the influence of the pin center circle diameter deviation, as shown in Figure 12e. Since the pin center circle diameter deviation is 4 \(\upmu\)m in this case, the initial gap between the tooth surfaces increases, which leads to a decrease in the mean value of the number of contact pins. As can be observed by comparing Figure 12b,d,f, the profile deviation and the pin center circle diameter deviation have much less influence on the load distribution on the pins than the pitch deviation. To summarize, the pitch deviation is the main factor that affects the TE and backlash in the MEs. It is suggested that the pitch deviation should be strictly controlled in the gear manufacturing process to achieve a smaller PPTE and PPB, and a smaller MTE and MB can be obtained through different tolerance allocation of the profile deviation and the pin center circle diameter deviation during the installation of the gear pair.