Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula

[+] Author and Article Information
P. Sainsot, P. Velex

Contact and Solid Mechanics Laboratory, UMR CNRS 5514 INSA de Lyon, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cedex, France e-mail: Philippe.Velex@insa-lyon.fr

O. Duverger

Po⁁le Machines et Commandes, CETIM Senlis, France

J. Mech. Des 126(4), 748-752 (Aug 12, 2004) (5 pages) doi:10.1115/1.1758252 History: Received April 01, 2003; Revised November 01, 2003; Online August 12, 2004
Copyright © 2004 by ASME
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Weber, C., 1949, “The Deflection of Loaded Gears and the Effects on their Load Carrying Capacity,” Dept. of Scientific and Industrial Research, Sponsored Research, Germany, Report no 3.
Weber, C., and Banaschek, K., 1953, “Formänderung und Profilrücknahme bei Gerad-und Schrägverzahnten Antriebstechnik,” Heft 11, F. Vieweg und Sohn, Braunschweig, Germany.
O’Donnell,  W. J., 1960, “The Additional Deflection of a Cantilever Due to the Elasticity of the Support,” ASME J. Appl. Mech., 27, September, pp. 461–464.
O’Donnell,  W. J., 1963, “Stresses and Deflections in Built-In Beams,” ASME J. Eng. Ind., 85, August, pp. 265–273.
Attia,  A. Y., 1964, “Deflection of Spur Gear Teeth Cut in Thin Rims,” ASME J. Eng. Ind., 86, November, pp. 333–342.
Cornell,  R. W., 1981, “Compliance and Stress Sensitivity of Spur Gear Teeth,” ASME J. Mech. Des., 103, pp. 447–459.
Lundberg,  G., 1939, “Elastische Berührung zweier Halbraüme,” Forsch. Ing.-Wes., 10(5), pp. 201–211.
ISO/DIS 6336-1.2, 1990, “Calculation of Load Capacity of Spur and Helical Gears-Part I: Basic Principles and Influence Factors,” Draft International Standard, pp. 87–95.
Muskhelishvili, N. L., 1975, Some Basic Problems of the Mathematical Theory of Elasticity, 2nd English Edition, P. Noordhoff Limited, The Netherlands, pp. 230–235.
Seager, D. L., 1967, “Some Elastic Effects in Helical Gear Teeth,” PhD dissertation, University of Cambridge, pp. 180–183.


Grahic Jump Location
(a) Example of finite element model (Z=57,h=4,r̄c=0.2)—Global model (b) Example of finite element model (Z=57,h=4,r̄c=0.2)—Detail on one tooth
Grahic Jump Location
Geometric parameters needed for the expression of θf
Grahic Jump Location
(a) Elastic ring and tooth parameters—Geometrical parameters for gear body (b) Elastic ring and tooth parameters—Geometrical parameters for one tooth
Grahic Jump Location
Geometrical parameters used in Weber-Banaschek’s equations



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