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TECHNICAL BRIEFS

Approximate Analytical Model for Hertzian Elliptical Contact Problems

[+] Author and Article Information
J-F. Antoine1

LGIPM-CEMA, IUT de Thionville-Yutz, 1 Impasse Kastler, 57970 Yutz, Francejf.antoine@enim.fr

C. Visa

LGIPM-CEMA, IUT de Thionville-Yutz, 1 Impasse Kastler, 57970 Yutz, Francevisa@agip.science.univ-metz.fr

C. Sauvey

LGIPM-CEMA, IUT de Thionville-Yutz, 1 Impasse Kastler, 57970 Yutz, Francesauvey@iut.univ-metz.fr

G. Abba

LGIPM-CEMA, Ecole Nationale d'Ingénieurs de Metz, Île du Saulcy, 57045 METZ Cedex, Franceabba@enim.fr

1

Corresponding author.

J. Tribol 128(3), 660-664 (Mar 13, 2006) (5 pages) doi:10.1115/1.2197850 History: Received March 23, 2005; Revised March 13, 2006

In rolling bearing analysis Hertzian contact theory is used to compute local contact stiffness. This theory does not have a closed form analytical solution and requires numerical calculations to obtain results. Using approximations of elliptical functions and with a mathematical study of Hertzian results, an empirical explicit formulation is proposed in this paper and allows us to obtain the dimensions, the displacement, and the contact stress with at least 0.003% precision and it can be applied to a large range of ellipticity of the contact surface.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Contact problem definition: bodies I and II in contact, planes of principal curvatures, geometrical parameters, and applied force Q (7)

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Figure 2

Variations of the ellipticity parameter κ=(B∕A)γ and of the exponent γ in terms of B∕A ratio

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Figure 3

Error on ellipticity parameter κ in terms of B∕A made by using 18

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Figure 4

Error on ellipticity parameter κ in terms of B∕A for different models

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Figure 5

Errors on Hertzian theory results in terms of B∕A

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