Research on Tooth Positioning and Mechanical Properties of Flexspline Tooth Rings with Harmonic Gear Clearance Assembly - Xing Jingzhong; Yang Ziyu; Chen Xiaoxia; Yao Yunpeng (Jixie chuandong)
The current theory considers that the shape of the deformed flexspline tooth ring neutral line is an isometric line of the cam, which ignores the effect of fit clearance and neutral line's elongation. To reveal the mechanical properties and the tooth positioning on deformed flexspline tooth rings with fit clearance, taking elliptical cam wave generator as an example and considering the fit clearance caused by the clearance between the inner wall of flexsplines, the outer surface of wave generators, the clearance of flexible bearings and the elongation of neutral lines, a contact mechanical model of tooth rings is established. The wrap angle after deformation is introduced as an unknown parameter, and the internal forces in tooth rings in the wrap angle is determined according to the curvature of the neutral line of tooth rings represented by the elliptic equidistant line and the equilibrium equations of the forces. The size of non-contact area, and the internal forces and deformation of tooth ring is solved iteratively with Energy Method according to the displacement conditions on minor axis and the curvature condition at wrap angle and arc length relationship. Based on the results of finite element model, the theoretical results and tooth positions are compared and verified. Both the theoretical analysis and the numerical simulation show that the actual wrap angle of zero clearance fit is far less than 90°, and the full round fitting cam is not true because of the elongation of the neutral line. Reducing fit clearance can effectively increase the contact area and reduce the radial load and the wear of flexible bearings. Considering the wrap angle and the circumferential elongation, more accurate tooth positioning may lead to a more accurate foundation for structural design and meshing analysis of harmonic gears.