## 5 Application of the Elastic TE Compensation Method for the RV Speed Reducer
### Validation of the TE Compensation Method and Comparison between the Initial and Modified Prototypes  
After TE compensation, the TE of the modified RV speed reducer is simulated by using Adams. The simulated input shaft rotation angle of the modified RV speed reducer prototype model after running 0.4 s is 826.2996\({}^{\circ}\). The simulated output shaft rotation angle of the modified RV speed reducer prototype model after running 0.4 s is 8.2429\({}^{\circ}\). The TE of the modified RV speed reducer prototype model has accumulated twice and its value for a period is 0.8538\({}^{\prime}\). TE simulation results of output shaft rotation angles of the initial and modified RV speed reducer prototype models are shown in Figure 9. By comparing the TE of the modified RV speed reducer prototype model with that of the initial RV speed reducer prototype model, the TE of the modified RV speed reducer prototype model is reduced by 41.35%.  
The contact force and deformation of the modified RV speed reducer prototype and those of the initial RV speed reducer prototype are calculated based on the tooth contact analysis method for cycloidal gear transmissions. The maximum contact force \(F_{\max}\) and normal deformation \(\delta_{i}\) of the modified RV speed reducer prototype can be obtained after 17 iterations, as shown in Tables 7 and 8, respectively. To transfer the same torque \(T_{c}\), the maximum contact force \(F_{\max}\) between a cycloidal gear and a pinwheel of the modified RV speed reducer prototype is 1435.9 N. After TE compensation, the maximum contact force \(F_{\max}\) of the RV speed reducer prototype is reduced by 24.83%. The maximum normal deformation \(\delta_{\max}\) of the cycloidal gear after modification is 0.0088 mm. After TE compensation, the maximum normal deformation \(\delta_{\max}\) of cycloidal gear of the RV speed reducer is reduced by 24%. The initial clearance \(\Delta(\varphi)_{i}\) and contact deformation \(\delta_{i}\) of the modified RV speed reducer prototype are shown in Figure 10. After TE compensation, the number of meshing teeth of the cycloidal gear increases from 9 to 17.  
In order to analyze the proportion of the elastic TE in the total TE, a rigid RV speed reducer prototype model is simulated by using Adams. The simulated input shaft rotation angle after running 0.4 s is 826.2977\({}^{\circ}\) and the simulated output shaft rotation angle after running 0.4 s is 8.2056\({}^{\circ}\). The TE of the modified RV speed reducer prototype model has accumulated twice after running 0.4 s and its value for a period is 1.22195\({}^{\prime}\). Output shaft rotation angles of the modified RV speed reducer prototype model are shown in Figure 11. By comparing TEs of the initial and modified RV speed reducer prototype models, the elastic TE accounts for 25.28% of the total TE. Hence, simulation results  
Figure 9: Output shaft rotation angle of the initial and modified RV speed reducer prototype models.  
Adams simulation results of the contact force between cycloidal gears and pinwheels of the modified RV speed reducer prototype model are shown in Figure 12. Changes of the contact force can be observed. The simulation result of the maximum contact force \(F_{\text{max}}\) is 1428 N, which is similar to that of \(F_{\text{max}}\) of the modified RV speed reducer prototype model. The maximum contact force result of the cycloidal gear that is obtained by the tooth contact analysis method shows acceptable agreement with the Abaqus simulation result.  
The TE of the modified RV speed reducer prototype model is obviously reduced. This is due to the decrease of normal deformation \(\delta_{i}\) and the contact force caused by the increase of meshing gears. Therefore, it can be indicated that the proposed TE compensation method effectively improves the transmission accuracy of RV speed reducers.