Research on assembly deformation of flexspline and mechanical characteristics of flexible bearing in harmonic drive

JIA Lupeng; XING Jingzhong; CHEN Xiaoxia

doi:10.16578/j.issn.1004.2539.2026.06.010

Abstract：[Objective]Aiming at the problem that the flexspline tooth positioning method based on cam isometric lines in harmonic reducers lacks mechanical basis,a contact mechanics model of flexible bearing and flexspline was constructed to reveal the deformation and positioning mechanism of flexspline tooth ring under discrete ball loads.[Methods]Firstly,considering the synergistic deformation of bearing outer ring and flexspline tooth ring,bearing clearance and cage constraint,the mechanical equations describing the boundary conditions of outer ring and the relation between ball force and radial displacement were established based on superposition principle and energy method to provide support for solving ball forces.Secondly,an iterative algorithm was adopted to solve the distribution range and amplitude of discrete ball forces and clarify the ball contact state.Then,the influence laws of deformation coefficient and clearance coefficient on contact characteristics were discussed by using finite element analysis software to verify the theoretical model.Finally,the theoretical results of radial deformation of flexspline tooth ring were verified by coordinate measuring machine tests.[Results]The results show that the proposed method has significantly higher accuracy in predicting the radial deformation of flexspline tooth ring than the traditional isometric line method,and the maximum deviation is reduced by 84%.The measured data prove that affected by the discrete ball contact characteristics,the flexspline tooth ring only presents obvious quasi-elliptical characteristics in the long-axis ball contact area,while the bending moment remains continuous in the non-contact area.Reference is provided for the structural optimization of flexible bearings and the accurate positioning of gear teeth.