Piecewise Modification of Cycloidal Gear in RV Reducer: Application of Spline Interpolation Theory and Comparison with a Combination Modification Optimization Method

Abstract

Rotate vector (RV) reducers are typical deceleration elements with the outstanding characteristics of small size, compacted structure, strong load-bearing capacity, and low transmission error, which are widely applied in the fields of industrial robots, aerospace, and measurement instruments. The cycloidal gear, as the core component in the second-stage drive of RV reducer, its tooth profile directly determines the general performance of RV reducer such as meshing precision, load-bearing capacity, and riding stability. Therefore, it is necessary to explore the feasible methods and parameters for modification of cycloidal tooth profile. In this paper, taking the CRV-20E reducer as an object, firstly, a mathematical model for analyzing contact stress and load distribution on meshing surface was established. Secondly, based on genetic algorithm, a multi-objective optimization for cycloidal profile was applied with maximum contact stress and load distribution coefficient as objective functions, the optimal combination of modification parameters was obtained. Then, with the idea of piecewise modification and spline interpolation method, the cycloidal profile was separated into three segments of dedendum, working, and addendum, which ensures conjugated meshing in working segment, and the reserved gaps in dedendum and addendum can also be remained flexibility according to the specific requirements. The mechanism performance with cycloidal profiles modified by two proposed methods were systematically compared and discussed. Finally, the finite element simulation verification was carried out. The results indicated that both modification methods have specific advantages. This study provides a theoretical reference for designers in the field of gear profile optimization and underscores the critical implications for improving the overall efficiency and reliability of RV reducers in applications.