The Meshing Stiffness Analysis And Meshing Force Distribution Law Research Of Harmonic Gear Transmission

Harmonic drive gears are widely used in industrial robots and aerospace with the advantages of high precision,large gear ratio,high load-carrying capacity,light weight and small in size.The distribution of meshing stiffness of flexspline and meshing force are important index for evaluating the harmonic tooth profile and structural parameters.The circumferential stiffness of the meshing point is the basis of the meshing force analysis of harmonic drive gears.Firstly,the theoretical formula for calculating the circumferential deformation of the meshing point under the action of circumferential force is derived,and the torsional deformation of the cylinder cup of flexspline,the gear ring and the ring connection part,the tooth body bending,shear deformation and the rotational deformation of the involute tooth shape are calculated respectively.On this basis,the theoretical formula for calculating the circumferential stiffness of the meshing point is derived.Secondly,in order to verify the correctness of the theoretical formula of the circumferential deformation,the FEM model of flexspline with solid element is established.In the assembly state,the centralizing force and the uniformly distributed circumferential force are respectively applied to the teeth on the long axis of the flexspline to calculate the tooth deformation and verify the theoretical calculation results of tooth deformation.Then the unassembled deformation and the assembled deformation under the action of wave generator are calculated.The flexure cylinder body deforms under the action of circumferential concentrated force of the two models,and the correctness of the theoretical formula is verified.The stiffness matrix reflecting the mesh stiffness of the flexspline is obtained by the finite element contact analysis,and the influence of different loads and different wrap angles on the mesh stiffness is analyzed.Finally,the circular spline FEM model with solid element is established,and the contact relation between circular spline teeth surface and flespline teeth surface are defined.The load backlash and meshing force are calculated by applying the rotation angle to the circular spline step by step.In order to reflect the change process of gear engagement,the contact pressure of the meshing surface under different loads are calculated.The radial displacement of the neutral layer of the flexspline under load is analyzed.The research findings are as following:(1)The deformation of cup and toothring of flexspline under the action of circumferential force are good agreement with the results of finite element model.The theoretical solution of tooth deformation under uniform circumferential force is good agreement with the results of finite element model.But the deformation result under concentrated force has difference,because the theoretical formula does not include the elastic deformation of mesh point.(2)The theoretical formula is only suitable for small meshing forces.For large meshing force,the mesh stiffness of the mesh point in the mesh area decreases obviously with the increase of meshing force,and is less than the theoretical value.The wave generator with large wrap angle can obviously improve the mesh stiffness of the biting area.(3)With low load,the front section enters into engagement and the engagement area is small.With the increase of load,the middle section and the back section mesh gradually and the meshing area of the middle section is larger.