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On the generation of conjugate flanks for arbitrary gear geometries
Author(s) -
Johann A.,
Scheurle J.
Publication year - 2009
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.200910005
Subject(s) - involute , action (physics) , generalization , parametric statistics , flank , conjugate , kinematics , representation (politics) , mathematics , surface (topology) , calculus (dental) , geometry , mathematical analysis , classical mechanics , physics , medicine , statistics , dentistry , quantum mechanics , sociology , politics , anthropology , political science , law
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)