• CN:11-2187/TH
  • ISSN:0577-6686

›› 1983, Vol. 19 ›› Issue (3): 51-60.

• 论文 • 上一篇    下一篇

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等距共轭曲面原理及其应用

高业田;曾韬   

  1. 哈尔滨工业大学;国营五一机械厂
  • 发布日期:1983-06-01

THE PRINCIPLE OF EQUIDISTANT CONJUGATE SURFACE AND ITS APPLICATIONS

Gao Yetian;Zeng Tao   

  1. Harbin Institute of Technology 国营五一机械厂
  • Published:1983-06-01

摘要: 在齿轮啮合原理中,等距共轭曲面原理是很有价值的。当我们研究某一对共轭曲面不方便时,可以应用这一原理转而去研究它们的等距共轭曲面,特别是可以把对在一般点处的啮合研究转化为对节面上点的研究,从而使问题和计算大大简化。应该指出的是,等距曲面(曲线)的初步概念早已应用于凸轮机构和摆线针轮啮合的简单特例中。文献[1]、[2]、[3]中都用了类似的名词。在文献[1]的平面啮合部分曾几次用了等距曲线的概念;文献[2]称之为当量共轭齿面,给出了当量齿面接触线方向角和当量共轭曲率公式,用于弧齿锥齿轮的切齿计算中,阐明了Gleason公司“SGM”计算卡编制原理与方法;文献[3]也采用了等距曲面的方法,并明确指出相互包络曲面的等距曲面也相互包络。本文把它作为一个普遍性的问题提出来,称之为等距共轭曲面原理,加以全面详尽地严格论证。讨论了等距曲面的主方向、主曲率之间的关系,论证了等距曲面的共轭性质,给出了相应的界函数和法曲率的关系式,举例说明了它的应用。在应用举例中,主要以“SGM”为例,说明应用等距共轭曲面原理和威尔德哈泊的研究成果[4],可以导出其他的计算卡。

Abstract: In the theory of conjugate surfaces, the principle of equidistant conjugate surfaces is very important. Applying the principle, the meshing on a conventional point is converted to that on a point on the pitch surface; therefore this problem is greatly simplified. But nobody has discussed this principle before. In this paper the conception of equidistant conjugate surfaces is offered, their conjugate characteristic is proved, and the corresponding formulas are given. The principle of equidistant conjugate surfaces may find many applications. The authors take "SGM" as an example to explain that basing on the research of E. Wildhaber and applying the principle, various sheets for setting computation are given.