An Extension of Hertz’s Theory in Contact Mechanics

[+] Author and Article Information
Guanghui Fu

 Lam Research Corporation, 4540 Cushing Parkway, Fremont, CA 94538guanghui.fu@lamrc.com

J. Appl. Mech 74(2), 373-374 (Jan 20, 2006) (2 pages) doi:10.1115/1.2188017 History: Received November 08, 2005; Revised January 20, 2006

Hertz’s theory, developed in 1881, remains the foundation for the analysis of most contact problems. In this paper, we consider the axisymmetric normal contact of two elastic bodies, and the body profiles are described by polynomial functions of integer and noninteger positive powers. It is an extension of Hertz’s solution, which concerns the contact of two elastic spheres. A general procedure on how to solve this kind of problem is presented. As an example, we consider the contact between a cone and a sphere. The relations among the radius of the contact area, the depth of the indentation, the total load, and the contact pressure distribution are derived.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Cone-sphere contact under zero load

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Figure 2

Indentation of an elastic half-space with a rigid second-order polynomial punch

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Figure 3

Contact pressure distributions: solid line is for the cone-sphere contact, dotted line is for the cone–half-space contact, and dashed line is for the sphere–half-space contact



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