A multi-objective optimal model of a K-H-V cycloid pin gear planetary reducer is presented in this article. The optimal model is established by taking the objective functions of the reducer volume, the force of the turning arm bearing, and the maximum bending stress of the pin. The optimization aims to decrease these objectives and obtains a set of Pareto optimal solutions. In order to improve the spread of the Pareto front, the density estimation metric (crowding distance) of non-dominated sorting genetic algorithm II is replaced by the k nearest neighbor distance. Then, the improved algorithm is used to solve this optimal model. The results indicate that the modified algorithm can obtain the better Pareto optimal solutions than the solution by the routine design.

The factors influencing rotate vector (RV) reducer dynamic transmission error were studied using virtual prototyping technology, which contained the elastic deformation, working load, part manufacturing error, and assembly clearance. According to the error transmission relationship of the RV reducer, 15 influencing factors were selected to design an orthogonal simulation test. The virtual prototype of the RV reducer was built using CREO and ANSYS, and imported into ADAMS for multi-body dynamics simulation. The simulation method reliability was verified via experiments. The results show that the circle center radius error of the pin gear, the amount of equidistant modification of the cycloid gear, the amount of radial-moving modification of the cycloid gear, the clearance between the support bushing and planet carrier, and the clearance between the crankshaft and the support bushing were positively correlated with the RV reducer dynamic transmission error. Among these, the circle center radius error of the pin gear has the greatest influence on the dynamic transmission error of the RV reducer followed by the amount of equidistant modification of the cycloid gear. The elastic deformation of the part and the load fluctuation show a certain gain effect on the transmission error, the elastic deformation of the cycloid gear has a great influence, and the elastic deformation of the pin gear has the least.

This paper proposes a new method for predicting rotation error based on improved grey wolf–optimized support vector regression (IGWO-SVR), because the existing rotation error research methods cannot meet the production beat and product quality requirements of enterprises, because of the disadvantages of its being time-consuming and having poor calculation accuracy. First, the grey wolf algorithm is improved based on the optimal Latin hypercube sampling initialization, nonlinear convergence factor, and dynamic weights to improve its accuracy in optimizing the parameters of the support vector regression (SVR) model. Then, the IGWO-SVR prediction model between the manufacturing error of critical parts and the rotation error is established with the RV-40E reducer as a case. The results show that the improved grey wolf algorithm shows better parameter optimization performance, and the IGWO-SVR method shows better prediction performance than the existing back propagation (BP) neural network and BP neural network optimized by the sparrow search algorithm rotation error prediction methods, as well as the SVR models optimized by particle swarm algorithm and grey wolf algorithm. The mean squared error of IGWO-SVR model is 0.026, the running time is 7.843 s, and the maximum relative error is 13.5%, which can meet the requirements of production beat and product quality. Therefore, the IGWO-SVR method can be well applied to the rotate vector (RV) reducer parts-matching model to improve product quality and reduce rework rate and cost.

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