Deformation Characteristics And Meshing Performance Of Variable Mid-plane Radius Harmonic Gears

Flexspline is the main component to transfer force and motion in harmonic gear.In order to enhance the load transmission capacity,the radial modification of the flexible gear can improve the load engagement between the tooth surfaces,thus a flexible gear structure of variable thickness ring rear is formed.In this paper,takes variable thickness ring gear flexspline as the research object.A series of research are developed,which is based on the research of flexible gear ring deformation,focusing on the analysis of backlash and meshing force under different load conditions,and finite element numerical simulation as the tool.The deformation of flexible gear is the basis of tooth profile design,and the premise of meshing analysis of no-load and load.Firstly,detailed analysis of the formation process of variable thickness ring gear structure,then based on the neutral line deformation equation of the ring gear design cross-section under the action of the elliptic wave generator.Based on straight generatrix assumption,a theoretical calculation method for the spatial deformation of flexspline with variable thickness ring gear structure is established,which provides a theoretical basis for the tooth positioning in the spatial tooth profile design.To verify the theoretical method,a full-featured solid element cup-shaped flexspline model containing the true arc tooth profile is established and solved.Three circumferential paths are defined in the front section,middle section,and back section of the ring gear,and the radial displacement,circumferential displacement and angular displacement of the neutral line in each section are extracted,which verifies the correctness of the theoretical calculation method.Compare the neutral line displacement results of the equal thickness ring gear and the variable thickness ring gear.Analyze the influence of the thickness change of the ring gear on the neutral line deformation law after the radial modification.The axial path is defined at different polar angle positions in the major axis area,45°,and minor axis area of the flexspline gear ring,and the radial displacement on each path is extracted.Use the displacement difference change law to reveal the actual deformation characteristics of the generatrix.To research the no-load meshing performance,based on the node position of the flexspline tooth surface after deformation,a finite element assembly model of circular spline that meshes with the arc tooth profile is established.An algorithm for calculating the backlash between teeth of segmented circular arc tooth profile with the shortest circumferential distance along the tooth height is established.The no-load backlash in the front section,middle section and back section of variable thickness ring gear is calculated.Compared with the theoretical backlash,the change trend of the backlash along the axial and circumferential direction is analyzed.To analyze the load meshing performance,based on the finite element assembly model,the contact relationship between the flexspline tooth surface and the corresponding tooth surface of circular spline is defined in the form of different real constants.Apply gradually increasing rotational displacement load to the circular spline to simulate different load conditions,and numerically solve the load backlash and meshing force.Through load backlash,contact specific pressure,tooth surface circumferential meshing force and other indicators to reveal the load meshing process.