# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 2 Materials and Methods
### Analysis of Factors Affecting Transmission Accuracy and Manufacturing Costs  
The transmission accuracy and manufacturing cost of the RV-40E reducer are influenced by the accuracy levels of the purchased bearings as well as the width and position of the tolerance zones of eight types of self-manufactured parts. As the bearings and other purchased parts are constrained by their rated load capacity, the available types and accuracy levels are significantly restricted. By conducting multiple replacement tests and performing a basic cost analysis, it is relatively straightforward to determine the types and accuracy levels of these purchased parts, and it will not be discussed in detail later. However, determining the tolerance zone width and position of the eight types of self-manufactured parts remains challenging due to the complexity of influencing factors, making the rationality of the selected values difficult to justify. Therefore, this study employs orthogonal experiments and virtual prototype simulations to determine the values of these parameters. Following the orthogonal experiments on the influencing factors and key determinants of the RV-40E reducer's output transmission accuracy and based on the sensitivity analysis of accuracy influence and the cost-effectiveness of the manufacturing process, this study proposes recommended values for the tolerance zone width and position of the eight types of self-manufactured parts. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Proto. or** & **Needle** & **Eccentric** & **Ring** & **Equi Dist. ** & **Moved** & **Simu. ** & **Meas. ** & **Diff. ** \\
**Test No. ** & **Radius** & **\(r_{p}\)** & **Dist. ** & **\(e\)** & **Radius** & **\(\pi_{rp}\)** & **Dist. ** & **\(\Delta r_{p}\)** & **Result** & \(\Delta\varphi\)**1** & **Result** & \(\Delta\varphi\)**2** & (\(\Delta\varphi\)1-\(\varphi\)2)/\(\Delta\varphi\)**2** \\ \hline
1 & 2.999 & 1.248 & 66.000 & 0.012 & 0.021 & 1.185 & 1.232 & 3.81\% \\
2 & 3.000  
Based on the working principle and structural composition of the RV-40E reducer, this study conducts a reverse analysis of the tolerance values of eight parts from the output transmission accuracy. The primary factor directly affecting output transmission accuracy is the rotational error of the output-end planet carrier, followed by the accuracy levels of two angular contact ball bearings supporting the output-end planet carrier, and then the installation errors of the planet carrier itself. Other contributing factors include the installation accuracy of four tapered roller bearings connecting the planetary carrier, four cylindrical roller bearings supporting the cycloid wheel and pin wheel, as well as the cycloid transmission accuracy, crankshaft transmission accuracy, and planetary gear transmission accuracy. Thus, multiple factors influence the output transmission accuracy and manufacturing cost of the RV-40E reducer. Apart from enhancing transmission accuracy and reducing manufacturing costs through selecting externally purchased bearings, it is also essential to optimize the tolerance levels of the eight self-manufactured parts to further enhance transmission accuracy and reduce manufacturing costs. Since the first stage of planetary gear transmission accuracy primarily affects the instantaneous speed variation in the crankshaft, and the planetary gear speed is more than 40 times that of the planet carrier or the output speed, the radial runout and other errors of the input shaft in the first stage and the planetary gear have a negligible impact on output accuracy and can thus be disregarded. Likewise, the influence of the dimensional errors in the holes and shoulders of the angular contact ball bearings supporting the planet carrier, the tapered roller bearings supporting the crankshaft, and the cylindrical roller bearings supporting the cycloid wheels can be temporarily negligible or not considered based on the rough calculation by virtual prototype.