The Expression Of The Midplane Curve Of Harmonic Gears And The Research On Gear Tooth Positioning

With the transformation and upgrading of manufacturing industry in China,the demand for high-precision transmission equipment in various industries is increasing.For advantages of high transmission accuracy,compact structure and large transmission ratio,Harmonic drive is widely used in industrial robots,aerospace,medical equipment,machine tools and other fields.In the research of fluctuation deformation in harmonic drive,the deformation of tooth ring is the basis of tooth profile design and meshing analysis,so it becomes the research focus.The maximum radial deformation of tooth ring is mostly close to its own thickness,which belongs to the large deformation problem.The deformation of gear ring under the action of cam-like wave generator is a large deformation contact problem,and the results of Ring Theory are difficult to meet the increasingly stringent design requirements.In this paper,a new calculation method is proposed to improve the existed deformation calculation method.Taking the double-disk wave generator as an example,a geometric method of fitting the neutral line deformation curve according to the geometric conditions is proposed.Setting the wrap angle as an unknown parameter,and the neutral line inside the wrap angle is determined according to the equidistant line of the wave generator.A polynomial function of the neutral line outside the wrap angle is constructed,and the wrap angle and polynomial coefficients are determined with the slopes,curvatures and continuity conditions at the wrap angle and at the short axis,and the arc length conditions of the non-contact segment.In the condition of arc length,the influence of elongation of the neutral line can be ignored,or the increment of arc length can be taken to be equal to the elongation caused by circumferential force.Finally,the neutral line and gear tooth positioning after deformation can be determined according to the polynomial function and arc length relation.Based on the geometric method,mechanical method for solving the assembly deformation of tooth ring is proposed.Taking double-disk wave generator as an example,the wrap angle of contact area is set as an unknown parameter,and the contact process of large deformation of the ring bending is simplified as a bending deformation of the non-contact segment translated and rotated to the boundary point of the wrap angle.Considering the strain energy caused by circumferential force and bending moment of the non-contact section,the wrap angle and non-contact deformation are solved by Energy Method.Based on large deformation curved beam theory,a calculation model of gear ring deformation under the action of double-disk wave generator is established.According to the deformation characteristics of flexspline,the boundary conditions at the wrap angle and the short axis are set,and the neutral line deformation of the non-contact section is numerically solved by Shooting Method,and the tooth position on deformed flexspline is determined.Finally,a parametric finite element model of shell element is established with APDL of ANSYS,and the neutral line deformation and flexspine tooth positioning of the aforementioned methods are numerically verified.The methods in the paper provide an accurate calculation way for the neutral line of flexspline and gear tooth positioning.