## 1 Introduction  
In recent years, gear systems have been developed rapidly with new calculation models [1], different materials [2] and new measurement methods [3]. In harmonic drive, a wave generator is used to make the flexspline produce controllable elastic deformation for realizing the transmission of motion and power. The flexspline is a thin-walled shell part, which is also the core part determining the performance of harmonic drive. The complex elastic deformation of the flexspline is generated with the combined action of the wave generator, the rigid wheel and the output shaft, but the basic deformation of the flexspline mainly depends on the type of the wave generator and its profile. The working stress and the service life of the flexspline greatly determine the transmission performance of the whole harmonic reducer. In order to improve the meshing performance and extend the service life of harmonic gear transmission, scholars worldwide have studied the deformation and stress characteristics of the flexspline under the action of different types of wave generators. [PERSON] [4] used the finite element method and experiments to compare and analyze the stress and strain of the flexspline in conventional cam wave generator and the split cam wave generator without assembling the ring gear. [PERSON] [5] studied the stress and related vibration characteristics of the flexspline with numerical analysis. [PERSON] [6, 7] presented the problem of failure of the elastic bearing supporting the generator in a harmonic drive and a solution to the problem of elastic deformation of thin-walled shell structures with complex shapes within the theory of geometrically non-linear shells. [PERSON] [8] proposed a method to calculate the load shared by the contact tooth pairs and the stress of the flexspline by estimating the contact load of multiple tooth pairs. [PERSON] [9] simplified the profile of the gear tooth of the flexspline as two simple shapes, a rectangle and a trapezoid. The influence of gear tooth on the stresses in the flexspline has been studied and analyzed, and two simplified tooth profiles have been compared with each other. [PERSON] [10] derived the deformation equation of the neutral layer of the flexspline in the engagement output harmonic drive and obtained the deformation relationship between the wave generator end and the engagement output end of the flexspline under the action of the wave generator based on the plate and shell theory. [PERSON] [11] analyzed the influence behavior of radial deformation on meshing performance in harmonic drive based on the envelopment meshing theory and obtained the stress distribution of the flexspline under the action of cam wave generator with finite element analysis. [PERSON] [12] analyzed the internal stress distribution and stress sensitivity of the flexspline with multiple geometric structural parameters such as the aspect ratio of the cup, the wall thickness, the round corner radius and the width of the tooth ring in ANSYS software. [PERSON] [13] studied the deformation problem of the flexspline in the harmonic reducer and analyzed the mathematical model of the flexspline's neutral layer in theory. [PERSON] [14] established a three-dimensional CAD model and a finite element model for the short barrel flexspline and studied the influence of geometric parameters on the stress value and distribution of the short barrel flexspline. [PERSON] [15] proposed the problems of wear failure mechanism of flexible wheels and its future research direction of friction and wear mechanism. [PERSON] [16] analyzed the coning phenomenon and the lubrication mechanism. [PERSON] [17] mainly discussed the influence of wave generator shape on the relative motion between the fixed and flexible splines, and the relative motion of flexible spline viewed from fixed splines. [PERSON] [18] deals with the numerical stress calculation in the flexspline tooth rim of the harmonic drive.