Objective : As a core component in robots, the RV reducer and its transmission accuracy play an important role in the robot performance. Complicatedly, the RV-reducer structure includes cycloidal gear, planetary gear, central gear, and cycloid pin among others. Furthermore, the transmission accuracy will be affected by errors between different components and the meshing interval. Naturally, building equivalent models can help improve the transmission accuracy of RV reducers. To continue this equivalent-model research on RV reducers in previous works, here we analyze the transmission-accuracy effect of six contact stiffness parameters in designed equivalent models and utilize the improved genetic algorithm to optimize three essential parameters.
Methods : The equivalent-error model of transmission errors of RV reducers is established based on Teruaki’s pioneering works. The correlation between six stiffness’s in equivalent error models and transmission errors is analyzed, and three parameters are chosen to be solved by stiffness empirical formula. Then, the theoretical transmission error of the reducer is obtained. An optimization model is built based on the least square method, and the square difference between the predicted transmission error and the actual measurement ones is taken as the optimized objective. Finally, an improved genetic algorithm based on dynamic model is used to optimize these parameters of empirical formula in the method.
Results : An experiment platform is built so that the actual transmission error of RV reducers can be obtained. Here, the angular displacement of RV reducer input is measured by the input circular grates, and the output angular displacement after reducer decelerating can be obtained through the circular grates as the output. The RV20E reducer is selected as the experiment object with the pin gear distribution round radius = 52 mm and the eccentricity = 0.9 mm. The actual transmission error recorded from the experiment platform lies between -25.91"~13.93". The theoretical transmission error optimized by the proposed model in this paper lies approximately between -27.88"~14.84". A small difference is observed between actual and theoretical transmission error peak-to-peak values. Then the improved genetic algorithm is compared with the traditional genetic algorithm under the parameter settings as population size of 100, group iteration of 100, crossover rate of 0.8, mutation rate of 0.2 and elimination rate of 0.2. Test results indicate that the traditional one will approach premature convergences and cannot reach the optimal objective. In some experiments, the optimal objective will be found with 35 iterations or more. By contrast, the improved one will obtain the optimal result within 20 iterations, demonstrating the effectiveness of the proposed method in dealing with the premature-convergence problem and in requiring shorter computation times. Stiffness parameters and fitness V index after optimization are smaller than those prior to the optimization, revealing that the improved genetic algorithm is effective. Results show that the optimized error is reduced by an average of 10.09% compared with the calculated error, indicating that the cooperation of equivalent error modeling and the improved genetic algorithm optimization can effectively improve the design accuracy of RV reducers.
Conclusions: The equivalent-error modeling not only can help analyze the correlation between the components in RV reducer and transmission error, but also can simplify the computation and complex structure of real RV reducer. The equivalent-error model built in this study is inspired by the work reported in the literature and can effectively simulate the contact pressure of different RV reducer components under the equivalent operation as spring models. Through various comparable experiments, it is proved that the proposed equivalent error model and the improved genetic algorithm optimization method can effectively improve the transmission accuracy and reduce the transmission error, so that the design and the optimization of RV reducers in actual applications can be guided. However, room for improvements of the RV-reducer efficiency remains. First, the equivalent-error model can be improved based on different versions of RV reducer. Then, the genetic algorithm can be further improved according to dynamic crossover rates and mutation rates. Furthermore, a deep network parameter space exploration mechanism based on intelligent optimization calculation can be constructed by an online real-time learning optimization, and a deep neural network dynamic model can be built by utilizing the motion-error compensation.