谐波齿轮传动共轭齿廓求解方法的研究∗

摘要

Based on meshing principle of harmonic drive, a method of solving conjugate profiles is pro-posed. The initial deformation of flexspline could be figured out by Abaqus. Radial deformation and tangen-tial deformation of the deformed points on neutral surface of middle section would be collected. Combined with curve fitting toolbox of Matlab and taking sum of sin functions as fitting function, deformation function of the flexspline were got. Substitute theoretical deformation function with it, and after completing the mo-tion simulation of engaging-in and engaging-out for a single tooth, fit the envelope curve of the flexspline’ s motion trail by least square method. The tooth profile of rigid spline would be worked out. The result shows that based on the envelope theory, combined with finite element method and motion simulation, con-jugate profiles can be worked out and it can provide reference for design of harmonic gear drive.%在谐波传动啮合原理的基础上，给出一种共轭齿廓求解方法。利用Abaqus求解柔轮的初变形，提取齿圈中截面中性层节点的径向变形位移和切向变形位移，结合Matlab曲线拟合工具箱，以子项为正弦函数的多项式作为拟合函数，求取柔轮的变形函数。以此代替理论变形函数，完成柔轮单齿啮入啮出的运动仿真，对其运动轨迹的包络曲线进行最小二乘拟合，得到刚轮齿廓曲线。结果表明：基于包络理论，结合有限元法和运动仿真，对于求解共轭齿廓是可行的，为谐波齿轮传动的设计提供了参考。