# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 2 Materials and Methods
### Flexibility Treatment of the Virtual Prototype  
To incorporate dynamic factors into the subsequent transmission error analysis, the relevant transmission parts must be treated as flexible bodies. Based on the structural characteristics of the transmitting gear train, the first-stage planetary gear transmission part rotates at a higher speed and bears a smaller impact on the output transmission error compared to the second-stage pin-cycloid gear transmission part, so that local deformations are relatively negligible. In order to add dynamic factors to the subsequent transmission error analysis, it is necessary to consider the relevant transmission parts as flexible bodies. According to its structural characteristics, the first-stage planetary gear transmission part rotates faster, and the torque it bears is smaller compared to the second-stage pin-cycloid gear transmission part, resulting in relatively negligible local deformations. The second-stage pin-cycloid gear transmission part transmits a larger torque and features a compact structure. The output part of the planet carrier is closely connected to the second-stage pin wheel, crankshaft, and cycloid wheel, which are treated as flexible bodies. Figure 3: Exploded view of the three-dimensional model of the RV-40E reducer. Figure 2: Three-dimensional model of the RV-40E reducer. (**a**) RV-40E reducer input-end view; (**b**) RV-40E reducer output-end view. The primary steps for establishing the rigid-flexible coupling model of the RV reducer in RecurDyn are as follows:  
1. To enhance simulation efficiency, the three-dimensional model in SolidWorks (SW) was simplified without compromising the research results. This simplification involved ignoring fine structures such as chamfers and bolt holes, omitting gaskets, seal rings, and other non-critical parts, while retaining roller bearings and replacing them with bearing sleeves. 2. The interference-free assembly is saved in the parasolid (x_t) format and imported into RecurDyn dynamics software. The resulting virtual prototype model is illustrated in Figure 4.
3. The material properties of the rigid body parts are defined. In RecurDyn software, the rigid body properties are specified based on the material properties and mass values. The material properties of each part of the RV reducer are listed in Table 2, where \(\rho\) represents density, \(E\) represents Young's modulus, and \(\
u\) represents [PERSON]'s ratio. 4. The constraints are defined, including kinematic pairs and contact pairs, as detailed in Table 3. The crankshaft and the planet carrier are coupled by simulating the support bearings using the virtual bearing constraints provided by the software. Special attention is given to the positioning of the revolute joint in the eccentric section. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parts** & **Material** & \(\rho\)**(103 kg/m3)** & \(E\) **(1011 N/m2)** & \(\
u\) \\ \hline input shaft & 20 CrMnMo & 7.87 & 2.07 & 0.254 \\ planetary gear & 20 CrMnMo & 7.87 & 2.07 & 0.254 \\ crankshaft & 20 CrMnMo & 7.87 & 2.07 & 0.254 \\ cycloid wheel & 20 CrMnMo & 7.87 & 2.07 & 0.254 \\ pin wheel & GCr15 & 7.83 & 2.19 & 0.300 \\ pin-wheel housing & QT500-7 & 7.25 & 1.68 & 0.240 \\ output-end planet carrier & ZG65 Mn & 7.85 & 1.98 & 0.230 \\ input-end planet carrier & ZG65 Mn & 7.85 & 1.98 & 0.230 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of RV reducer parts. Figure 4: Rigid body virtual prototype modeling. * Based on the applied constraints, the mesh function in RecurDyn is utilized to discretize the pin wheel, crankshaft, and cycloid wheel. Material properties are assigned to the corresponding parts, and the patch function is employed to establish surface contact, thereby completing the flexible body conversion. Finally, the rigid-flexible coupling model of the RV reducer is obtained as shown in Figure 5.
* Setting the overall contact parameters of the model too high will slow down the calculation speed, while setting them too low will cause penetration between components.