A vectorial modification methodology based on an efficient and accurate cycloid tooth profile model

Abstract

A cycloid gear is the central component of a rotate vector reducer, and cycloid profile design has served as the basis for manufacturing modification research. The previous cycloid tooth profile equations are complicated to derive and not efficient to calculate. Moreover, the current tooth modification method only allows for uniform correction of the overall profile. This work presents an efficient calculation and high accuracy model of the cycloid profile which is designed in dual quaternion space by introducing assembly and machining error parameters. Moreover, we propose a vectorial modification method to achieve a single-point partial modification instead of simultaneous modification of all tooth profile points. With the meshing characteristics as the optimization objective, the optimal solution of the error term is obtained by means of the response surface method, which is the maximum error tolerance in the design process. Finally, verification is carried out by the finite-element method. The new cycloid tooth profile model provides the basis for a modification vector calculation of large-scale scatter points. The synchronization of the design error tolerance maximum and tooth profile design will also effectively improve the manufacturing accuracy of the whole machine and shorten the design cycle.