Research On The Deformation Characteristics And Structure Optimization Of The Bell-shaped Flexible Wheel Of Harmonic Drive

Harmonic gear has the advantages of large transmission ratio,small volume,high transmission precision and strong bearing capacity,etc.It is widely used in robot,satellite antenna,precision machine tool,aerospace and other fields requiring precision transmission.As the tube length of the cup flexspline is shortened,the deformation will affect the cup bottom,making the cup bottom stress too high.Too short tube body will lead to shape distortion,accelerate gear wear.In order to solve the above problems,a bell-shaped flexspline is proposed.In order to obtain the deformation mechanism of bell-shaped flexspline,bellshaped flexspline is regarded as cylindrical shell,the tube as rotating shell and the cup bottom as disk.According to the cylindrical shell theory,the theoretical deformation of the ring gear is calculated,and the geometric conditions for the plane deformation of the ring gear are obtained by analyzing its geometric equation.Since the cylinder body is a rotating body,the theory of rotating shell based on elastic mechanics cannot be solved directly.Therefore,it is assumed that the deflection of the tube busbar after deformation is a cubic polynomial of the angle between the normal line of the bell curve and the section perpendicular to the axial direction.Then by using the theory of rotating shell deformation,a method for calculating the deformation of bell-shaped flexspine is obtained.Since the circumferential displacement of the cup bottom is very small,it can be neglected.According to the theory of disk,the calculation method of cup bottom deformation is obtained.In order to verify the availability of the deformation calculation method,a parametric contact model of shell was established,and the geometric conditions to realize the plane deformation of the ring gear were iteratively solved according to the conditions for realizing the plane deformation of the ring gear.That is,the relationship between the central surface radius of the ring gear and the ratio of the radius of the bell curve and the central angle of the bell curve is expressed by using the five-spline curve fitting,the comparison with the geometric conditions in the literature verifies the correctness of the geometric conditions in this paper.According to the geometry condition,the finite element model is established to realize the plane deformation of the ring gear,and the deformation and bending stress of the ring gear,tube and cup bottom of the model are solved respectively,comparing with the existing results,the deformation method is verified.This paper presents a new bell-shaped flexspline structure which is easy to be processed.ANSYS software is used to compare the influence of the parameters of the ordinary bell-shaped flexspline and the new bell-shaped flexspline on the maximum equivalent stress,and the structural parameters of the new bell-shaped flexspline are topologically optimized to ensure that the highest stress occurs in the ring gear.Changing the bus shape,to achieve the effect of reducing the length of the cylinder.The results show that:(1)the axial displacement of the ring gear is zero,which ensures the plane deformation of the ring gear.(2)the solution and the finite element solution of the bell-shaped flexspline deformation calculation are in good agreement.The correctness of theoretical deformation calculation of bell-shaped flexspline is explained.(3)among the parameters of flexspline,only the width of the cup bottom film plate affects the distribution of the highest stress of the new bell-shaped flexspline.(4)the bus shape does not affect the plane deformation of the ring gear,but can reduce the axial size.