圆弧齿廓谐波齿轮齿廓设计和啮合侧隙优化

Tooth profile design and meshing backlash optimization of circular-arc harmonic gear

以圆弧齿廓谐波齿轮为研究对象,建立柔轮节曲线上任意点的切向方程和法向方程,并将柔轮节曲线上各点的切向位移与法向位移拟合,计算出装入椭圆凸轮波发生器时的柔轮齿廓曲线。根据柔轮坐标系到刚轮坐标系的变换矩阵及所求出的柔轮齿廓曲线,得到刚轮齿廓上离散点的坐标,从而拟合出与柔轮齿廓共轭的刚轮齿廓。建立了柔轮和刚轮间的侧隙模型,并以啮合侧隙为目标函数,选取柔轮齿面与刚轮齿面接触点的压力角、柔轮齿廓的全齿高、柔轮轮齿的法向转角及柔轮齿面接触线的弧长增量,这4个变量作为侧隙优化的设计变量,使侧隙量在满足约束方程的条件下最小。针对椭圆波发生器的谐波齿轮,通过其圆弧齿廓设计和啮合侧隙优化的实例,验证了理论模型的正确性。

With the circular-arc tooth profile harmonic gear as the research object,the tangent and normal equations on the arbitrary points of flexspine pitch curve are formulated.With the fitting of every point’s tangent and normal displacement of flexspine pitch curve,the curve of flexspine tooth profile is calculated when the ellipse cam wave generator is loaded.Based on the transformation matrix from the flexspine coordinate system to the circular spline coordinate system as well as the flexspine tooth profile curve which has been obtained,the discrete point’s coordinate of circular spline tooth profile is calculated,and the circular spline tooth profile is fitted,which is conjugated with the flexspline tooth profile.The meshing backlash model is set up between the flexspine and the circular spline.With the meshing backlash the objective function,the four variables below are selected as the design variables of backlash optimization,and the magnitude of backlash is minimized under the conditions of constraint equation.The four variables are as follows:the pressure angle of contact point between the flexspine tooth surface and the circular spline tooth surface,the whole depth of flexspine tooth profile,the normal angle of flexspine,and the arc increment of flexspine tooth surface’s contact line.The case study on the circular-arc tooth profile design and the meshing backlash optimization shows that for the harmonic gear of ellipse cam wave generator,the theoretical model is correct and effective.