# Transmission Performance Analysis of RV Reducers Influenced by Profile Modification and Load
## 2 Analytical Model of RV Reducer with Tooth Profile Modifications
### Transmission Error Calculation
#### 2.2.2 Transmission Error Measurement Experiment  
A physical prototype of an RV reducer is produced according to the parameters in Table 1. Several tests were conducted to measure the transmission performance of the RV reducer prototype to validate the analytical model. These tests were conducted on a rig composed of a servo motor, two torque meters to measure the input and output torque, two round gratings to measure the input and output rotation angles, the tested reducer, and a magnetic brake acting as a load equipment. The rated torque of the magnetic brake is 2000 N-m. The test rig is shown in Figure 8. The control system is shown in Figure 9. The input and output round gratings are mounted on the end of the RV prototype. To avoid the influence of eccentricity on the accuracy of the output grating, the thin reed structure is adopted to connect the output shaft and the round grating. The measurement accuracy of the test rig is 2  
The forward and backward TEs were tested in one loop to obtain the backlash of the RV reducer. Moreover, the TE in one direction was tested twice continuously to verify the repeatability of the test results. It can be seen from Figure 10a that the TE is consistent. The backlash of the RV prototype is 31.03 arcsec. In addition, the analytical backlash is 28.12 arcsec, as calculated using Equation (29), which is smaller than the experimental value because small influencing factors are ignored. The forward transmission error is 40 arcsec, and the backward TE is 42 arcsec. Figure 10b shows the harmonic spectrum of the forward TE as the output shaft rotates one round. Figure 10c,d show an enlarged view of the forward and backward TEs, respectively, as the cranks rotate six rounds.  
As the cranks rotate one round, the TE curves generate a large peak. There are 40 main peaks as the output shaft rotates one round, which is the same as the crank rotation period. This fully demonstrates that the cycloid drive is the main factor affecting the transmission performance of the RV reducer, which also indicates the correctness of the simplified model. Most of the other harmonics are multiple frequencies of the cranks, as shown in Figure 10b. The details of the main harmonic components are listed in Table 4. Because the cycloid gear generates 39 meshing cycles in one crank revolution, it can be concluded that the 1560 th harmonic is caused by the cycloid tooth profile [27]. The TE amplitude is 0.47 arcsec, whereas the analytical result is 0.49 arcsec. The percentages of differences between the analytical method and the test results are presented in Table 5. The analytical and test results are in good agreement.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Type** & **Range** & **Accuracy** \\ \hline Torque sensors & HY-G33/HY-G32 & \(\pm\)10 N-m/\(\pm\)1500 N-m & \(\pm\)0.25\% Fs \\ Round gratings & REXM & 360\({}^{\circ}\) & \(\pm\)2\({}^{\prime\prime}\)/\(\pm\)1\({}^{\prime\prime}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter list of sensors.  
Figure 10: Test results of RV prototype: (**a**) transmission error (TE) including backlash, (**b**) harmonic spectrum of a TE as output shaft rotates one round, (**c**) enlarged view of forward TE in the dashed frame of (**a**), and (**d**) enlarged view of backward TE in the dashed frame of (**a**).