Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

[+] Author and Article Information
M. Leung, C. K. Hsieh, D. Y. Goswami

Department of Mechanical Engineering, University of Florida, Gainesville, FL 32611

J. Tribol 119(4), 846-850 (Oct 01, 1997) (5 pages) doi:10.1115/1.2833895 History: Received May 20, 1996; Revised November 12, 1996; Online January 24, 2008


In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Copyright © 1997 by The American Society of Mechanical Engineers
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