Study on three-dimensional elastic deformation characteristics of flexspline in harmonic drive based on Rayleigh-Ritz method with accelerated convergence strategy

Abstract

The 3D deformation mechanism of flexspline (FS) is the foundation of harmonic drive. In this paper, a novel methodology based on Rayleigh-Ritz method (RRM) is proposed to solve the three-dimensional elastic deformation of FS. First, the analytical model of RRM for 3D elastic deformation is formulated. A three-dimensional displacement trial function is designed according to the structure and constraints of FS. The RRM improves the accuracy of the solution by increasing the number of terms of the trial function. According to the completeness of the trial function, the real elastic deformation state can be approached arbitrarily in theory. The convergence efficiency of the actual iteration process is greatly affected by the iteration strategy. Therefore , an accelerated convergence strategy is proposed to overcome the drawback of poor convergence rate in the general iterative process. The elastic deformation characteristics of FS are studied by the new method, and a sensitivity analysis of structural parameters is performed. The results demonstrate that the new method is highly accurate and efficient. The radial deflection is slightly arch-shaped along the axial direction, reaching the maximum value near the axial position of the displacement constraint. The tangential deflection is 0 on the symmetry plane, and the value is smaller when it is farther away from the symmetry plane, which reflects the tendency of the gear tooth deflecting towards the major shaft section of the wave generator. The descending order of sensitivity of structural parameters affecting taper deformation is cylinder length (Pl), radii difference (Pd), cylinder thickness (Pt), hole radius (Ph), fillet radius (Pf) and gear rim width (Pw). The descending order of sensitivity of structural parameters affecting tooth skewness is Pl, Pd, Ph, Pf, Pw and Pt.