On the generation of conjugate flanks for arbitrary gear geometries
On the generation of conjugate flanks for arbitrary gear geometries
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关于任意齿轮几何形状的共轭齿面的生成
DOI：
10.1002/gamm.200910005
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Scheurle
中科院分区：
文献类型：
--
作者：
A. Johann;J. Scheurle
在本文中，我们提出了一种新的三维数学齿轮理论的方法。我们从所谓的齿轮运动学基本定律的一般表述开始。在此基础上，我们推导出了共轭齿面生成的解析闭合解，给出了任意指定齿面轮廓的(局部)参数表示。此外，我们还研究了构造产生指定作用面的齿面对的问题。作用面将以隐式全局而不是参数的方式表示。为了说明一般理论，我们考虑了一些具体的例子，包括直齿圆柱齿轮的标准渐开线齿廓以及它的更复杂的三维推广(©2009 Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
In this paper, we present a novel approach to three‐dimensional mathematical gearing theory. We start from a general formulation of the so called basic law of gear kinematics. Based on that we derive an analytic closed form solution for the generation of conjugate tooth flanks, given a (local) parametric representation for any prescribed flank profile. Also, we study the problem of constructing pairs of tooth flanks that give rise to a prescribed surface of action. Surfaces of action will be represented in an implicit global rather than in a parametric way. To illustrate the general theory, we consider a number of specific examples including the standard involute profile for spur gears as well as a more sophisticated three‐dimensional generalization of that (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)