谐波传动轮齿的相对运动在柔轮壳体空间弹性变形条件下属于空间共轭运动，空间共轭理论是决定其运动与力的传递及综合性能的核心因素. 为此，提出了一种基于相伴方法的谐波传动空间共轭运动模型. 通过壳体的半无矩理论及各构件间的运动关系，建立壳体中性层母线的直纹面运动方程；根据准不动线条件与中性层母线的直纹面运动，推导出谐波传动轮齿的瞬轴面方程.采用空间运动的相伴方法研究瞬轴面与共轭齿面之间的内在联系，以瞬轴面为原曲面、刚/柔轮齿面为相伴曲面，推导出刚性齿面空间相伴运动的共轭条件式，形成空间相伴运动的共轭模型. 将啮合点的相对运动转化为绕瞬轴的螺旋运动，分析瞬轴与啮合点法矢的关系特性；将空间共轭运动退化为平面共轭运动，分析空间共轭与平面共轭的约束特性；将啮合面约束为准不动面，分析准不动面条件下的空间共轭运动特性. 从实例仿真分析可知，谐波传动刚性轮齿的平面运动是空间运动退化后的一种特殊运动，谐波传动退化后的空间运动与平面运动一致，这验证了本文所述空间共轭模型与运动特性的正确性.
The relative motion between the gear teeth of harmonic drive belongs to the spatial conjugate motion under the spatial elastic deformation condition of the flexspline shell, and its spatial conjugate theory is the core factor that determines its motion and force transmission and comprehensive performance. For this purpose, a spatial conjugate motion model for harmonic drive is proposed based on adjoint approach. By means of the semi-moment theory of the shell and the kinematics between the components, the ruled surface motion equation of the neutral layer generatrix of the shell is established. According to the quasi-fixed line condition and the ruled surface motion of neutral layer generatrix, the axode equation of the gear teeth in harmonic drive is derived. The internal relationship between the axodes and the conjugate tooth surfaces is studied by the adjoint approach. Taking the axodes as the original surfaces and the tooth surfaces of the circular spline / flexspline as the concomitant surfaces, the conjugate condition formula of the spatial concomitant motion of the rigid tooth surface is derived, and the conjugate model of the space concomitant motion is formed. The relative motion between the meshing points is transformed into the spiral motion around the instantaneous axis, and the relationship between the instantaneous axis and the normal vector of the meshing point is analyzed. The spatial conjugate motion is degenerated into the planar conjugate motion, and the constraint properties of the spatial conjugate and planar conjugate are analyzed. The plane of action is constrained as a quasi-fixed surface, and the spatial conjugate motion characteristics under the condition of quasi-fixed surface are analyzed. Finally, through the simulation analysis of an example, it can be seen that the plane motion of the rigid gear teeth of harmonic drive is a special motion after the degradation of spatial motion, and the spatial motion after the degradation of harmonic drive is consistent with the plane motion, which verifies the correctness of the spatial conjugate model and motion characteristics described in this paper.
董博 ,董惠敏 ?,王德伦 ,张楚.谐波传动空间相伴运动的共轭理论与特性分析[J].湖南大学学报：自然科学版,2022,49(10):166~174复制