连续共轭啮合的双圆弧谐波齿轮齿廓设计及运动仿真验证

摘要

Based on a common tangent double-circular-arc tooth profile expressed with parametric Heaviside function, the influence of the original tooth profile on the envelope existent domain and feasibility of the conju-gated tooth profile are studied with an exact conjugate algorithm using assembly deformation of the flexspline, and a design method is presented to make the double conjugate phenomenon available. The tooth profile orienta-tion on the deformed neutral curve of the flexspline is determined by a rotation angle caused by circumferential displacement on the neutral curve, and a rotational angle of the symmetric line of the tooth profile relative to the radial vector. Then, the movement trace of the tooth profile on the flexspline is plotted, and the tooth profile of circular determined with a series moving tooth profiles on the flexspline is obtained, which verifies the double conjugate phenomenon and the feasibility of the conjugated tooth profile. The illustration example shows that the harmonic drive with double-circular-arc tooth profile can realize continuous conjugate transmission in the whole meshing range by reasonable design parameters of the original tooth profile, and makes more teeth in meshing, which leads to higher transmission capability and stable location accuracy.%基于分段函数表达的参数化公切线双圆弧齿廓，利用柔轮装配变形的包络精确算法研究双圆弧齿廓原始齿廓参数对包络存在区间大小的影响及其共轭齿廓的可用性，提出使二次共轭现象成为可用齿廓的设计方法。首先按照柔轮中性层周向位移引起的转角及其轮齿对称线相对于径矢转角的精确计算方法，确定变形后柔轮轮齿的位置和方位，获得一系列柔轮齿廓相对于刚轮齿槽的啮合运动轨迹；然后从计算机图形学角度获得用柔轮齿廓外包络表达的刚轮齿廓，验证二次共轭现象及其可用共轭齿廓的存在性。实例结果表明，双圆弧齿廓谐波齿轮可以通过合理的参数设计实现在整个啮合区间上的连续共轭传动，使更多齿对同时参与共轭啮合，从而提高谐波齿轮的承载能力和传动精度。