# 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  
Using the virtual prototype of the RV-40E reducer, the 10 quality characteristic parameters listed in Table 5 were sampled with Latin hypercube sampling within their respective interval ranges to compute the output transmission error. The corresponding results are presented in Table 6 by a single-factor design of experiment (DOE). For each of the ten quality characteristic parameters of the parts, a single-factor experiment is performed to determine the sensitivity of each parameter to transmission error or transmission accuracy. When employing the virtual prototype to compute the output transmission error, the quality characteristics of the experiment factors are assigned values based on the data in Table 6, while those of the remaining factors are assigned representative values. The representative value corresponds to the median value of the existing tolerance range of the RV-40E reducer, and the final results of the single-factor experiment are presented in Table 7. The virtual prototype calculates the transmission error \(\Delta\varphi\) value and range R value for the input shaft, planetary gear, and crankshaft, and pin-wheel housing 7 times each, and for the cycloid wheel, pin wheel, input-end planet carrier, and output-end planet carrier 5 times each. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Part Name** & **Char. Param.** & **Char. Values** & **Rep. Value** \\ \hline
1 & input shaft & pitch circle & 12, 11.098, 11.096, 11.094, 11.092, 11.090, 11.088 & 11.094 \\ \hline
2 & planetary gear & pitch circle & 24, 23.099, 23.097, 23.094, 23.091, 23.088, 23.085 & 23.094 \\ \hline
3 & crankshaft & eccentric distance & 1.253, 1.252, 1.251, 1.250, 1.249, 1.248, 1.247 & 1.250 \\ \hline  & & moved distance & & \\  & & modification & 0.013, 0.0125, 0.012, 0.0115, 0.011 & 0.012 \\  & & \(r_{p}+\Delta r_{p}\) & & \\
4 & cycloid wheel & equidistance & & \\  & & modification & 0.022, 0.021, 0.020, 0.019, 0.018 & 0.020 \\  & & bearing hole distance & & \\  & & \(a_{c}+\Delta a_{c}\) & 72.006, 72.003, 72, 71.997, 71.994 & 72 \\ \hline
5 & pin-wheel housing & pin-wheel ring & & \\  & & runout & 66.003, 66.002, 66.001, 66, 65.999, 65.998, 65.997 & 66 \\  & & \(r_{b}+\Delta r_{b}\) & & \\ \hline
6 & pin wheel & rolling needle radius & 3.001, 3.0005, 3, 2.9995, 2.999 & 3 \\  & & \(r_{r}+\Delta r_{r}\) & & \\ \hline
7 & input-end planet carrier & hole distance of tapered bearing & 72.006, 72.003, 72, 71.997, 71.994 & 72 \\  & & \(a_{k}+\Delta a_{k}\) & & \\ \hline
8 & output-end planet carrier & hole distance of tapered bearing & 72.006, 72.003, 72, 71.997, 71.994 & 72 \\  & & \(a_{k}+\Delta a_{k}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameter values of quality characteristics using single-factor DOE (mm). The results indicate that the radial runout of input shaft gear, the radial runout of planetary gear, the hole center distance of the cylindrical roller bearing of the cycloidal wheel, and the center distance error of the input and output planet carrier bearing holes have a relatively minor influence on the output transmission error or exhibit insensitivity to it. Moreover, no consistent regular variation in the output transmission error is observed with changes in the input parameter values. Therefore, it is recommended to maintain the original width and position of their tolerance zones. However, the crankshaft eccentric distance error, the modification of the moved distance and the equidistant parameters of the cycloidal wheel, the radial runout of the center circle of the pin wheel within the pin-wheel housing, and the radius error of the pin wheel exert a more pronounced and sensitive effect on the output transmission error. When the eccentric distance error of the crankshaft is zero, the output transmission error remains low. However, as the eccentric distance error of the crankshaft increases, the transmission error rises significantly.