# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 4 Discussion  
This article systematically validates the methodology for component accuracy selection and tolerance design in the newly developed RV-40E reducer. The research focuses on two key aspects: accuracy class selection for purchased components, such as bearings, and tolerance design for manufactured parts, such as gears. A multi-software virtual prototype \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Part Name (qty.)** & **Char. Parameter** & **Tolerance Value** \\ \hline
1 & input shaft (1) & pitch circle runout tolerance \(\Delta r_{1}\) & 0.012 (\(12^{0}_{-0.012}\)) \\ \hline
2 & planetary gear (2) & pitch circle runout tolerance \(\Delta r_{2}\) & 0.015 (\(24^{0}_{-0.015}\)) \\ \hline
3 & crankshaft (2) & eccentric distance tolerance \(\Delta e\) & 0.004 (\(1.25^{+0.002}_{-0.002}\)) \\ \hline  & & mov. dist. modify. tolerance \(\Delta r_{p}\) & 0.002 (\(0.012^{+0.001}_{-0.001}\)) \\
4 & cycloid wheel (2) & equidistance modify. tolerance \(\Delta r_{rp}\) & 0.004 (\(0.020^{+0.002}_{-0.002}\)) \\  & & bearing hole dist. tolerance \(\Delta a_{c}\) & 0.012 (\(72^{+0.006}_{-0.006}\)) \\ \hline
5 & pin-wheel housing (1) & wheel ring runout tolerance \(\Delta r_{p}\) & 0.004 (\(66^{+0.002}_{-0.002}\)) \\ \hline
6 & pin wheel (40) & needle radius tolerance \(\Delta r_{r}\) & 0.002 (\(3^{+0.001}_{-0.001}\)) \\ \hline
7 &
\begin{tabular}{c} input-end planet \\  & carrier (1) & bearing hole dist. tolerance \(\Delta a_{k}\) & 0.012 (\(72^{+0.006}_{-0.006}\)) \\ \hline
8 &
\begin{tabular}{c} output-end planet \\  & carrier (1) & bearing hole dist. tolerance \(\Delta a_{k}\) & 0.012 (\(72^{+0.006}_{-0.006}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Tolerance values after optimized design for RV-40E reducer parts. was developed through the integration of SolidWorks, RecurDyn, and Adams platforms to predict transmission errors with \(\leq\)5% deviation from experimental measurements. Experimental validation using five physical prototypes confirmed the virtual model's accuracy, with simulation results deviating \(\leq\)5% from the measured transmission errors. Building on this validation, single-factor and orthogonal experimental analyses were conducted. Single-factor analysis provided the preliminary identification of key parameter sensitivities and their spatial influence distributions, while the orthogonal experiment enhanced sensitivity discrimination accuracy by compensating for measurement uncertainties. For externally purchased components, such as bearings, a transmission-error-driven accuracy selection strategy was developed. Bearing accuracy classes (C, D, E, and G) were evaluated through application-specific selection criteria: Class C/D bearings for high-accuracy applications and Class E/G bearings for standard applications. Trial assembly and error testing validated the appropriateness of these selections. For manufactured components such as cycloidal gears, sensitivity-based tolerance optimization was implemented through the simulation-guided optimization of both tolerance bandwidth and position. Current limitations include incomplete manufacturing cost data acquisition (due to proprietary process/equipment constraints), which partially constrained the tolerance optimization outcomes presented in Table 9. Future work should enhance virtual model fidelity and incorporate production cost data for cost-constrained accuracy/tolerance co-optimization. Conceptualization, methodology and project administration, S.J. ; writing--original draft and developing software, J.S., B.W. and F.Y. ; supervision and data curation, Y.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the National High-tech R&D Program of China (Grant. No. 2025 AA043002) and the National Natural Science Foundation of China (Grant No. 51605442). Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to corporate data privacy.