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公法线是齿轮检测的重要参数。本文从一般着手,先从空间任意二曲面间的公法线出发,通过螺旋齿轮齿面通式,列出一组四元非线性方程组,在解该方程组的基础上,求得螺旋齿轮公法线的通式。本文求得的螺旋齿轮的通式具有普遍意义,不仅适用于现有的各种齿轮,例如渐开线、摆线、元弧等,而且也适用将来新发明的型线齿轮。作为如何应用通式来求解公法线的实例,本文选择元弧(点啮合)齿轮,文中推得的公式和张希康、李华敏求得的公式一致。以上情况说明通式的正确性和普遍性,也从另一方面证明张李61年求得的公法线是数学正确表达式。公法线是检测齿轮制造精度的重要参数。随着技术的日益发展,各种不同型线的齿轮不断出现,因此推求公法线长度计算式是十分必须。众所周知当齿面方程简单时,推求公法线表达式是容易的;然而当齿面方程复杂时,要推求公法线表达式是十分困难的。例如至今还有一些齿轮的公法线计算式还未解决。鉴于以上情况,本文试以一般着手,推导螺旋齿轮公法线的通式。所求得的通式表明:当今后有什么新的型线的螺旋齿轮,只要将它的齿面方程代入到通式,就可马上求得公法线的计算式,因此通式是有普遍意义。作为通式应用实例,选择元孤齿轮说明之。
The common normal is an important parameter for gear detection. Starting from the common normal between any two surfaces in space, this paper presents a set of quaternion nonlinear equations through the general form of the helical gear tooth surfaces. Based on the solution of the equations, Line of the general. The general formula of the helical gear obtained in this paper is of universal significance. It can be applied not only to various existing gears such as involute, cycloid, and arc, but also to newly-invented profile gears in the future. As an example of how to apply general formula to solve common law line, this paper selects the element arc (point meshing) gear. The formulas deduced in this paper are consistent with those obtained by Zhang Xikang and Li Huamin. The above shows the correctness and universality of the general formula, and on the other hand proves that the common normal obtained by Zhang Li in 61 years is the mathematical correct expression. The common normal line is an important parameter to test the precision of gear manufacturing. With the development of technology, gears of different types of gears are emerging continuously. Therefore, it is very necessary to calculate the length of the common law line. It is well known that when the tooth surface equation is simple, it is easy to infer the common normal expression; however, when the tooth surface equation is complex, it is very difficult to deduce the common normal expression. For example, there are still some common normal equations for gears that have not been solved yet. In view of the above, this article tries to generalize, derive the general formula of the common normal helical gear. The general formula obtained shows that: Now what new type of helical gear, as long as its tooth surface equation into the general formula, you can immediately calculate the formula of the common normal, so the general formula is universal . As a general application example, the choice of yuan lonely gear instructions.