Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Abstract

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile. Considering the tooth influence on the position of equivalent neutral layer, a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper. Firstly, a mechanic model of a ring of uniform thickness in contact with a rigid cam is established. The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium relationship, respectively. Meanwhile, the wrapping angle is solved according to the boundary conditions. The assembly forces are derived to investigate the circumferential elongation and strain. Then, considering the tooth effects on the neutral layer of flexspline, the tooth is positioned on the equivalent neutral layer, which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer. The equivalent neutral layer is positioned by the empirical formula of the offset ratio, which is summarized by the orthogonal simulation on finite element models of racks. Finally, finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method. The results show that, compared with the geometric method, the tooth positioning deviation calculated by the piecewise method can be reduced by about 70% with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Assembly and dynamic operation simulation research of tooth-locked-output harmonic gear reducer

“…The tooth-locked-output is the most commonly used one among all the connection methods of the harmonic reducer [5]. Its structure is shown in the figure 1, consisting of a wave generator (1), a fixed circular spline (2),an output circular spline(3) and a ring shape flexspline (4).Under the action of the wave generator, there is a relative motion with a transmission ratio of 1:1 i = between the output circular spline and the ring shape flexspline.The ring shape flexspline is a thin-walled external gear ring, and its structure is shown in the figure 2.where δ is the wall thickness of cylinder, d is the inner diameter, a d is the addendum circle diameter, and f d is the dedendum circle diameter.…”

“…In recent years, with the advancement of computer technology and the maturity of finite element analysis theory, the research of harmonic reducer based on finite element analysis has developed in many aspects and in depth [1][2][3][4].In this paper, the research on the ring shape flexspline harmonic reducer with less research but obvious advantages is carried out, and a relatively complete analysis process is established to solve the problems of pre-simulation processing and solution setting caused by the special structure of the ring shape flexspline. An example is demonstrated, and the rationality and correctness of the simulation analysis process in this paper are verified by experiments.…”

Modeling harmonic drive with small deformation of flexspline and assessment of tooth wear by sliding coefficient

“…17 Yao et al presented a piecewise method for calculating the deformation of FS assembled with a cam WG. [18][19] Due to the FS deformation, the involute tooth profile is no longer the best one of HD. For this reason, studies focused on tooth profile optimization, structural modifications and so on.…”

Calculation of tooth thickness errors and its influence on meshing backlash of harmonic drive

“…Gravagno et al [24] discussed the influence of the shape of the WG on the pure motion error of HD, and quantitatively evaluated it. Considering the influence of gear teeth on the position of equivalent neutral layer, Yao et al [25] proposed a piecewise deformation calculation method of FS with cam WG. Jia et al [26] used a special experimental device to verify and explain the pure motion error, and proposed a new structure of WG which can improve the transmission performance.…”