# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 2 Materials and Methods
### Single-Factor Experiment Analysis of Reducer Part Tolerances
Given the constraints of existing processing equipment, it is recommended to temporarily maintain the original width and position of the tolerance zone for the crankshaft. The modifications to the moved distance and equidistant parameters of the cycloidal wheel must be strictly controlled at 0.012 mm and 0.020 mm, respectively, as even slight deviations can cause significant variations in the output transmission error. Therefore, it is advised to maintain the original width and position of their tolerance zones. The pin-wheel ring radial runout of the pin-wheel housing and the pin-wheel radius error are also highly sensitive to transmission error, with their variations either amplifying or compensating for each other to some extent. Therefore, efforts should be made to control these two errors by improving the machining accuracy of the pin-wheel radius while appropriately relaxing the machining difficulty associated with the runout tolerance of the pin-wheel housing's pin center circle. Meanwhile, the original tolerance designs for the pin-wheel ring radial runout and the pin-wheel radius should be temporarily maintained. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Part Name** & **Char. Param. (Rep. Value)** & **Char. Values** & **Error \(\mathbf{\Delta\varphi}\)** & **Extr. Diff. R** \\  & & **Value)** & **(Minute of Arc)** & **(Minute of Arc)** \\ \hline
1 & input shaft & pitch circle & 12, 11.098, 11.096, 11.094, & 1.135, 1.171, 1.096, 1.164, & 0.075 (insensitive) \\  & & \(r_{1}+\Delta r_{1}\) (=11.094) & 11.092, 11.090, 11.088 & 1.125, 1.160, 1.142 & 0.075 (insensitive) \\ \hline
2 & planetary gear & pitch circle & 24, 23.099, 23.097, 23.094, & 1.360, 1.316, 1.286, 1.292, & 0.077 (insensitive) \\  & & \(r_{2}+\Delta r_{2}\) (=23.094) & 23.091, 23.088, 23.085 & 1.312, 1.299, 1.283 & 0.077 (insensitive) \\ \hline
3 & crankshaft & eccentric distance & 1.253, 1.252, 1.251, 1.250, & 1.387, 1.351, 1.321, 1.280, & 0.118 (sensitive) \\  & & \(e+\Delta e\) (=1.250) & 1.249, 1.248, 1.247 & 1.269,1.318, 1.325 & 0.118 (sensitive) \\ \hline
4 & cycloid wheel & moved distance & 0.013, 0.0125, 0.012, & 1.213, 1.128, 1.013, & 0.200 (sensitive) \\  & & \(r_{p}+\Delta r_{p}\) (=0.012) & 0.0115, 0.011 & 1.185, 1.211 & 0.200 (sensitive) \\  & & equidistance & 0.022, 0.021, 0.020, 0.019, & 1.222, 1.121, 1.118, & 0.204 (sensitive) \\  & & \(r_{rp}+\Delta r_{rp}\) (=0.020) & 0.018 & 1.110, 1.018 & 0.204 (sensitive) \\  & & bearing hole distance & 72.006, 72.003, 72, 71.997, & 1.206, 1.203, 1.190, & 0.016 (insensitive) \\  & & \(a_{c}+\Delta a_{c}\) (=72) & 71.994 & 1.197, 1.194 & 0.016 (insensitive) \\ \hline
5 & pin-wheel & pin-wheel ring runout & 66.003, 66.002, 66.001, 66, & 1.303, 1.302, 1.001, 1.010, & 0.202 (sensitive) \\  & housing & \(r_{p}+\Delta r_{p}\) (=66) & 65.999, 65.998, 65.997 & 1.081, 1.198, 1.297 & 0.202 (sensitive) \\ \hline
6 & pin wheel & rolling needle radius & 3.001, 3.0005, 3, 2.9995, & 1.125, 1.175, 1.225, & 0.116 (sensitive) \\  & & \(r_{r}+\Delta r_{r}\) (=3) & 2.999 & 1.232, 1.241 & 0.116 (sensitive) \\ \hline
7 & input-end & hole distance & 72.006, 72.003, 72, 71.997, & 1.206, 1.203, 1.199, & 0.15 (insensitive) \\  & planet carrier & \(a_{k}+\Delta a_{k}\) (=72) & 71.994 & 1.997, 1.214 & 0.015 (insensitive) \\ \hline
8 & output-end & hole distance & 72.006, 72.003, 72, 71.997, & 1.203, 1.214, 1.192, & 0.028 (insensitive) \\  & planet carrier & \(a_{k}+\Delta a_{k}\) (=72) & 71.994 & 1.175, 1.197 & 0.028 (insensitive) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Transmission error results based on virtual prototype and single-factor experiment. In summary, the results of the single-factor experiment indicate that the tolerance values of the 8 parts of the RV-40E reducer are reasonable.