Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

William P. Baker, PhD.


This research develops a mathematical formulation and an analytical solution to frictional heat partitioning in a high speed sliding system. Frictional heating at the interface of sliding materials impacts temperature and the wear mechanisms. The heat partition fraction for a sliding system is an important parameter in calculating the distribution of frictional heat flux between the contacting surfaces. The solution presented in this dissertation considers the characteristics of the slipper's frictional heat partition values along with the experimental loading data. With a physics based, rather than a phenomenological approach, this solution improves the estimate for the slipper's heat partition function. Moreover, this analytical solution is practical in calculating the average surface temperature and estimating the total melt wear volume. The heat partition function compares favorably with existing experimental and analytical data. Using the Strang's Splitting and ADI methods, a numerical method for surface temperature and corresponding wear percentage under dynamic bounce conditions was extensively developed.

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DTIC Accession Number