Elliptic Elastic Contact Between High Order Symmetrical Surfaces

[+] Author and Article Information
Emanuel N. Diaconescu

Department of Mechanical Engineering, University of Suceava, 1 University Street, Suceava, 720225, Romaniaemdi@fim.usv.ro

J. Tribol 128(4), 908-914 (Apr 13, 2006) (7 pages) doi:10.1115/1.2345420 History: Received May 04, 2004; Revised April 13, 2006

This paper proves that a generalized Hertz pressure (the product of Hertz square root and an even polynomial of degree 2n with respect to coordinates) applied over elastic half-space boundary generates a polynomial normal displacement of degree 2n+2. Polynomial surface coefficients are combinations of elliptical integrals. The equation of rigid punch surface generating this pressure is derived, as well as the conditions in which an elliptical contact occurs. For second order surfaces, n=0, these results yield all Hertz formulas, whereas new formulas are derived for contact parameters between fourth, sixth, and eight order surfaces.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Elliptic contact domain

Grahic Jump Location
Figure 2

Dimensionless pressure distribution between fourth order surfaces

Grahic Jump Location
Figure 3

Dimensionless axial pressure profiles: p1—fourth order surface, dashed line; p2—sixth order surface, solid line; p3—eighth order surface, dotted line



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