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RESEARCH PAPERS: Power Transmission and Gearing Papers

Analytical Reconstruction of the Running Surfaces of Gear Teeth Using Standard Profile and Lead Measurements

[+] Author and Article Information
W. D. Mark

Bolt Beranek and Newman Inc., Cambridge, Mass. 02238

J. Mech., Trans., and Automation 105(4), 725-735 (Dec 01, 1983) (11 pages) doi:10.1115/1.3258543 History: Received May 31, 1983; Online November 19, 2009

Abstract

A method is developed for analytically reconstructing the geometric deviations of the running surface of a gear tooth from a perfect involute surface. The method uses standard profile and lead deviation measurements and is applicable to both helical and spur gears. The reconstruction is carried out by using normalized Legendre polynomials. For this class of functions, it is shown that the optimum locations of the profile and lead deviation measurements are the locations of the zeros of the Legendre polynomial of degree equal to the number of profile or lead deviation measurements taken–after appropriate normalization of the tooth width or depth, as appropriate. A least squares fit procedure for establishing a common origin of ordinates for sets of profile and lead deviation measurements is formulated, and its solution is carried out in closed form. Account is taken of the noninsignificant errors that typically arise in profile and lead deviation measurements so that the final analytically reconstructed tooth surface is free of inconsistencies.

Copyright © 1983 by ASME
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