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本文讨论空间啮合理论——线接触共轭曲面理论的一般问题。文中提出研究啮合问题的直接法,并应用旋转矩阵作为主要运算工具,从而使公式的推导较为简捷。文中对空间啮合曲率干涉的一般条件作了严格证明,并给出较便于应用的形式。此外,文中得出滑动线的微分方程、共轭曲面退化的条件、以及滑动线向径一阶导数的公式。后者是酒井高男所得公式的推广形式。最后,文中举了两个实例,得出渐开线斜齿轮传动节点综合曲率的准确公式,以及G.Niemann蜗杆传动的根切界线方程、滑动率公式等。
This article discusses the theory of spatial meshing - the general problem of the theory of conjugate surfaces in linear contact. In this paper, we propose a direct method to study the meshing problem, and use the rotation matrix as the main computing tool, so that the derivation of the formula is simpler. In this paper, the general condition of space meshing curvature is strictly proved, and a more convenient form of application is given. In addition, the paper derives the differential equation of sliding line, the condition of the degradation of conjugate curved surface, and the formula of the first derivative of sliding line radial. The latter is the promotion of Sakai tall men’s formula form. Finally, two examples are given in this paper, and the exact formula of the involute helical gear node’s total curvature is obtained, as well as the equation of root cut-off line of G.Niemann worm drive and the sliding rate formula.