Abstract: In view of the influences of cross sections with cone or sphere on the mechanics properties of the engagement points of the cross-groove equi-speed output mechanisms, a cross-groove structure of the cross section with a double arc of equal radius of curvature was proposed. The accurate formulas of the axial micro displacement was obtained according to the Hertzian contact theory by the geometrical relationship between normal deformation at the engagement points and the axial micro displacement. A four-point-contact mechanics model of the cross-groove was established, and the engagement normal forces of the cross-groove were obtained by the axial force balance equation and torque balance equation. The influences of parameters on the engagement normal forces and the stress of contact zone were analyzed. The results show that engagement normal forces of the cross-groove are changed periodically. The most important factor affecting the engagement normal forces is the quantity of steel balls, and the least important factor affecting the engagement normal forces is the input shaft eccentricity. The normal stresses and the peak values of the shear stresses in the contact zones may be reduced by increasing the radius of steel ball, and may be reduced by the radius coefficients.

Key words: cross-groove equi-speed output mechanism, four point contact, axial preload, engagement normal force, contact stress

摘要： 针对锥形或球形槽截面对十字槽等速输出机构啮合点力学性能的影响，提出等曲率半径双圆弧的十字槽结构。利用啮合点法向变形量与轴向微位移的几何关系，根据赫兹接触理论推导出轴向微位移计算公式。建立了十字槽四点接触力学模型；通过轴向力和力矩平衡方程，求得十字槽啮合点的法向力；分析了参数对法向力和接触区应力的影响规律。结果表明：十字槽啮合点的法向力呈周期性变化，钢球数对法向力的影响最大，输入轴偏心距对法向力的影响最小；增大钢球半径可减小接触区正应力以及切应力峰值，减小半径系数可减小接触区正应力以及切应力峰值。

关键词: 十字槽等速输出机构, 四点接触, 轴向预紧, 啮合法向力, 接触应力