Tooth Profile Optimization Calculation And Strength Analysis Of Harmonic Reducer

Harmonic reducer has the advantages of large transmission ratio,strong bearing capacity,low noise and high precision,which is widely used in aerospace,robot and other general machinery fields.The tooth profile of harmonic gear is one of the decisive factors that affect the transmission performance and service life of harmonic reducer,so the research on the tooth profile design and optimization of harmonic reducer is of great significance.Aiming at the design and optimization of harmonic gear tooth profile,this paper systematically carried out the following research:Firstly,the meshing theory of harmonic drive is analyzed based on the kinematic assumptions of planar harmonic drive.The conjugate tooth profile of flexspline is solved by envelope method,and the rigid tooth profile is fitted according to the principle of least square method.At the same time,the meshing assembly simulation of flexspline and rigid wheel is completed in MATLAB.It provides a theoretical basis for the design and optimization of tooth profile in the next part.Secondly,the meshing characteristics of the harmonic gear with double circular arc tooth profile are analyzed.In order to increase the dual-conjugated interval of the harmonic gear with double circular arc profile,an optimization model of the harmonic gear with double circular arc profile based on genetic algorithm is proposed.The optimization model is used to optimize the tooth profile parameters of the flexspline,and the single parameter sensitivity analysis and multi parameter sensitivity analysis of the optimized tooth profile design parameters are carried out.Through single parameter sensitivity analysis,it is found that the objective function is sensitive to two longitudinal distances of the common tangent and the public inclination angle,but has low sensitivity to the convex arc radius,the concave arc radius and the tooth thickness ratio.Through the multi parameter sensitivity analysis,the allowable range of each tooth profile parameter within the allowable range of the objective function value is obtained,which provides a reference for the accuracy requirements of flexspline manufacturing.Thirdly,the stress and deformation of the flexspline under the action of wave generator are analyzed in ANSYS.At the same time,the variation of the maximum radial deformation of the neutral curve of the flexspline along the axial direction is studied,and the maximum radial deformation function of the neutral curve of the flexspline is obtained in MATLAB.According to this function and envelope method,the spatial tooth profile of the rigid wheel is designed,and the meshing backlash of the spatial tooth profile is calculated.It is found that compared with the plane rigid tooth profile,the spatial tooth profile of rigid wheel can increase the conjugate interval and contact area of harmonic gear meshing,and improve the stability and load capacity of harmonic gear transmission.Finally,the rigid wheel model with spatial tooth profile is established in 3D software.Finally,according to the above design of the rigid wheel model with spatial tooth profile,the finite element contact models of harmonic reducer with spatial profile rigid wheel and plane profile rigid wheel are established respectively.The stress and deformation of the two contact models under no load and load are compared by finite element analysis.The results show that the rigid wheel with spatial tooth profile can improve the interference between the flexspline and the rigid wheel due to deformation,reduce the maximum equivalent stress of the flexspline,and improve the service life of the flexspline.