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作者在本文将多元函数的极值理论应用于齿轮啮合原理的研究,得到一个定理:共轭曲线上到瞬心距离为极值的点必是接触点,从而指出了一条求啮合方程的新途径,只需按平面两点距离公式构成一个多元函数再求一次偏导数即可得到啮合方程。它不仅能解决平面啮合的一般问题,而且能解决空间啮合的特殊问题。在平面啮合的范围内,这种方法与国内外现有三种方法相比,一个明显特点是无需套用复杂公式,且直观性强。与其中的运动学法及包络法相比功能相同,但涉及的概念少、运算步骤少;比齿廓法线法的功能强,即能适用于变速比场合,因此它较易于理解和使用,尤其容易记忆。文章并举了实例,说明这种方法是解决平面啮合问题的较好的方法。
In this paper, we apply the theory of extremum of multivariate functions to the study of gear meshing theory, and get a theorem that the point where the distance from the instantaneous center to the extreme on the conjugate curve must be the contact point points out a new way to find the meshing equation , Just according to the plane two points distance formula form a multivariate function and then ask a partial derivative can get the meshing equation. It not only solves the general problem of plane meshing, but also solves the special problems of space meshing. In the range of plane meshing, compared with the three existing methods both at home and abroad, one obvious feature of this method is that there is no need to apply complex formulas and is intuitive. Compared with the kinematic method and the envelope method, the method has the same function, but involves fewer concepts and fewer operation steps. Compared with the normal method of the tooth profile, which has a strong function that can be applied to a gear ratio, it is easier to understand and use. Especially easy to remember. An example is given in the article, which shows that this method is a better way to solve the problem of plane meshing.