Stress Optimization And Meshing Characteristics Analysis Of Double-arc Tooth Profile Harmonic Drive

Harmonic gear transmission,based on the theory of thin-shell elastic deformation,is widely used in aerospace vehicles,radar communication antenna mechanisms,intelligent bionic robots,CNC machine tools,precision medical equipment and other fields for its incomparable advantages such as high load bearing,high precision,large reduction ratio,miniaturization,and light weight.As the key transmission component of the harmonic reducer,low stress means long life and high rigidity determines the large load about the flexspline.This article harmonic gear transmission using the non-common tangent double-arc tooth profile as the research object,and designs the structural parameters of the key components of the harmonic reducer according to the mechanical design method and the non-common tangent double-arc tooth profile by using the basic mathmatical theory of the harmonic gear transmission and the improved kinematics method,using MATLAB simulation and finite element analysis to study the mechanical characteristics,meshing characteristics and other questions of the harmonic drive.(1)The mechanical characteristics of the harmonic flexspline are analyzed,and the design method of the harmonic drive plane tooth profile is introduced.Based on the theory of the smooth cylindrical shell,the stress characteristics of the flexspline are calculated.The equation of the micro-element section of the elastic ring gear of the flexspline is established and revised.The contour equation of the deformation and the calculation of the rotation angle of the flexspline is established by adopting the improved kinematics method and the mathematical relationship among all the elements of the harmonic drive.The meshing invariant matrix(B matrix)is geted.Finally,the method how to design the double-arc tooth profile and check the common interference situation of the tooth profile are introduced.(2)A finite element analysis model of the three-dimensional multi-body by nonlinear elastic contact of harmonic gear transmission is established,and its characteristics at the stress and deformation are calculated.In view of the mechanical design method,the structural dimentions of the components of the harmonic reducer are settled.Based on the improved kinematics method and the theory of the harmonic transmission,the noncommon tangent double-arc tooth profile is devised.The method of the finite element analysis is adopted to study the stress and deformation of the flexspline when the wave generator is assemblied,and the result is basically consistent with the actual.The influence on the stress and deformation of the flexspline is discussed by changing the position of the wave generator.The results tell us that the position of the maximum stress of the flexspline is mainly concentrated at the end of the inner wall of the short shaft,the long shaft gear ring and the rounded corners of the cup bottom under the action of waves and the deformation mainly occurs in the long and short shaft ring gears,which are all symmetrically distributed.(3)Three kinds of stress relief structures are proposed,and their mechanical properties are compared by adopting the finite element analysis.According to the deformation mechanism of the harmonic flexspline,three stress relief structures are proposed: large fillet structure,draft characteristics and surface fillet settings.The influence by changing fillet radius and draft angle on the stress of the flexspline is analysed.The influence of the fillet size on the bottom surface of the cup on the stress of the flexspline is studied.The research and analysis of the meshing of circular splline and flexspline tooth profiles and the loading of the flexspline are carried out for the three structures with the smallest stress.The results tell us that the effect of releasing stress of the surface fillet setting is much better than the large fillet and the draft feature,and the rigidity of the draft structure is the largest,while the large fillet structure is similar to the surface fillet setting.(4)Three options for the modification of tooth profile of the circular spline and flexspline are designed,and the meshing characteristics are compared and analyzed.In view of the complete meshing of the main section of tooth profile of the circular spline and flexspline and the interference of other sections,three types of options of the modification of tooth profile were proposed when they are compared and analyzed through MATLAB simulation and finite element method.A method of simultaneous modification of tooth profile of the circular spline and flexspline is proposed which has much better meshing characteristics.We can get the influence on the amount of modification,the stress and deformation of the ring gear of the flexspline by changing the position of the main section of the tooth profile meshing under the condition of keeping the meshing characteristics,.The results tell us that the sensitivity of the modification of the rear-end of the tooth profile of the flexspline is lower than that of the front-end of the circular spline,and the sensitivity of the stress of the bottom of the flexspline is higher than that of the end of the ring gear with the change of the main section of the tooth profile.