Research On Deformation Of Flexspline Of Harmonic Gear Considering Clearanc

For advantages of large transmission ratio,small volume and high transmission accuracy,harmonic gear reducer is widely used in industrial robots,precision machine tools,and aerospace and other precision transmission fields.The flexspline is the core component of harmonic gear,and its assembly deformation of tooth ring is the basis of tooth profile design and meshing analysis.Therefore,the assembly deformation of the tooth ring has become the research focus of harmonic gear.The design tolerance,machining error and circumferential elongation of the tooth ring as well as the flexible bearing clearance will seriously affect the deformation of tooth ring.In this paper,the existed deformation model of tooth ring is improved,and a contact mechanical model and calculation method of the deformation and internal force of tooth ring are proposed.To accommodate the large deformation characteristics,taking double roller wave generator as an example,the strain energy based on the internal forces after first-order deformation is derived,and an improved method for solving the deformation and internal forces of the tooth ring is proposed.A finite element model of flexspline tooth ring is established to solve the internal forces and deformation of the tooth ring under different deformations to verify the improved method and Ring theory.The research shows that the improved method is closer to the finite element results with large deformation option than Ring theory and finite element results with small deformation option.Taking elliptical cam wave generator as an example,considering the fit clearance caused by clearance between the inner wall of flexspline and the outer surface of wave generator,and the clearance of flexible bearing and the elongation of neutral line,a contact mechanical model of flexspline tooth ring is established.The wrap angle after deformation is introduced as an unknown parameter,and the neutral line of flexspline tooth ring after deformation is divided into contact and non-contact interval.The neutral line of the tooth ring in contact area is represented by an elliptic equidistant line.The segment in non-contact area is treated as a curved cantilevered beam fixed at the wrap angle,and Energy Method is applied to solve the wrap angle as well as the deformation and internal force of non-contact area iteratively.Finite element models of tooth ring with shell element are established under different fit clearances and solved to verify the theoretical results and tooth positioning.The results show that the contact model of tooth ring deformation considering the fit clearance parameters can obtain more accurate deformation of tooth ring,internal forces and tooth positioning.Based on planar deformation of tooth ring,formulae for spatial deformation of the flexspline tooth rim are derived using straight generatrix assumption.A finite element contact model containing a cam,flexible bearing and flexspline is established and solved for large deformations.Obtained deformation data of the tooth ring generatrix,and the theoretical results are compared and verified.The experimental measurement of the assembly deformation of a flexspline tooth ring without tooth is carried out by using CMM,and curve fitting is performed with the spatial discrete points in several cross sections of the tooth ring.Comparison and analysis with the theoretical results and finite element results reveal the spatial deformation characteristics of the tooth ring.The research shows that the theoretical results and finite element simulation results considering the fit clearance parameters are in good agreement with the test datum.