Laboratory testing of contact phenomena can be prohibitively expensive if the interacting bodies are geometrically complicated. This work demonstrates means to mitigate such problems by exploiting the established observation that two geometrically dissimilar contact pairs may exhibit the same contact mechanics. Specific formulas are derived that allow a complicated Hertzian contact pair to be replaced with an inexpensively manufactured and more easily fixtured surrogate pair, consisting of a plane and a spheroid, which has the same (to second-order accuracy) contact area and pressure distribution as the original complicated geometry. This observation is elucidated by using direct tensor notation to review a key assertion in Hertzian theory; namely, geometrically complicated contacting surfaces can be described to second-order accuracy as contacting ellipsoids. The surrogate spheroid geometry is found via spectral decomposition of the original pair’s combined Hessian tensor. Some numerical examples using free-form surfaces illustrate the theory, and a laboratory test validates the theory under a common scenario of normally compressed convex surfaces. This theory for a Hertzian contact substitution may be useful in simplifying the contact, wear, or impact testing of complicated components or of their constituent materials.
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April 2011
Technical Briefs
Determining a Surrogate Contact Pair in a Hertzian Contact Problem
Rebecca M. Brannon
Rebecca M. Brannon
Department of Mechanical Engineering,
e-mail: brannon@mech.utah.edu
University of Utah
, 50 S. Central Campus Dr., 2134 Merrill Engineering Bldg., Salt Lake City, UT 84112
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Anthony P. Sanders
Rebecca M. Brannon
Department of Mechanical Engineering,
University of Utah
, 50 S. Central Campus Dr., 2134 Merrill Engineering Bldg., Salt Lake City, UT 84112e-mail: brannon@mech.utah.edu
J. Tribol. Apr 2011, 133(2): 024502 (6 pages)
Published Online: March 17, 2011
Article history
Received:
March 21, 2010
Revised:
January 12, 2011
Online:
March 17, 2011
Published:
March 17, 2011
Citation
Sanders, A. P., and Brannon, R. M. (March 17, 2011). "Determining a Surrogate Contact Pair in a Hertzian Contact Problem." ASME. J. Tribol. April 2011; 133(2): 024502. https://doi.org/10.1115/1.4003492
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