# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 2 Materials and Methods
### Reliability Verification of the Virtual Prototype  
To validate the reliability of the virtual prototype methodology, it is essential to ensure that the transmission accuracy values obtained from the virtual prototype methodology for the RV-40E reducer are closely aligned with the transmission errors measured by the actual prototype test bench. Consequently, a test bench was constructed, and several groups of parts, drives, loads, and other samples were selected for transmission error measurement. The test bench primarily consists of servo motors, torque sensors, a circular grating encoder, etc. The experimental test bench, as illustrated in Figure 7, consists of the following components: two mounting brackets are fixed on the experimental platform, with an accompanying RV-40E reducer, torque sensor, and servo motor mounted on the left bracket, while the tested RV-40E reducer and encoder are installed on the right bracket. The input shaft of the tested reducer is likewise secured to the bracket. Upon activation of the servo motor, transmission error values under varying load conditions can be detected.  
Figure 6: Rigid–flexible coupling model.  
Figure 7: Transmission accuracy test bench for the RV-40E reducer.  
Five sets of RV-40E reducer parts were randomly selected for parameter measurement. After assembling the machine, five sets of transmission error data were obtained. Simultaneously, the corresponding five sets of transmission error data were acquired using the aforementioned virtual prototype. According to the transmission principle of the RV-40E reducer, the authors speculate that the sensitivity to output transmission errors is relatively small due to the runout of the central gear and planetary gear, the spacing between the cycloidal gear holes, and the spacing between the planetary carrier holes at both ends of the input and output. The radius of the central gear ring is selected as 11.094 mm, the radius of the planetary gear ring is 23.094 mm, and the spacing between the cycloid wheel holes and the planetary carrier holes is selected as 72.000 mm. The final transmission errors of the virtual prototype and experimental testing are shown in Table 4.  
Five sets of RV-40E reducers were randomly assembled, and comparative analysis revealed that the average relative error between the transmission errors measured by the virtual and actual prototypes was 2.9%. The experimental results demonstrate that the relative errors of all reducers remain below 5%, confirming a high degree of consistency between the virtual and actual prototype measurements. The error between the numerical simulation results of the virtual prototype and the actual detection results of the experimental device does not exceed 5%, which is smaller than the difference in error when the author conducted multiple reproducibility tests on the RV-40E experimental device. Therefore, the transmission error data obtained from the virtual prototype simulation can be used as a substitute for the measured transmission error data. This approach enables calculating the transmission errors of the RV-40E reducer parts listed in Table 1, thereby reducing reliance on measured data.