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RESEARCH PAPERS

# Thermal Analysis of the Transient Temperatures Arising at the Contact Spots of Two Sliding Surfaces

[+] Author and Article Information
Jen Fin Lin1

Department of Mechanical Engineering,  National Cheng Kung University, Tainan City, 701, Taiwan, ROCjflin@mail.ncku.edu.tw

Jung Ching Chung, Jeng Wei Chen

Department of Mechanical Engineering,  National Cheng Kung University, Tainan City, 701, Taiwan, ROC

Ta Chuan Liu

Engine Engineering Department, Industry Research Laboratories, Industrial Technology Research Institute, Hsinchu, 1040, Taiwan, ROC

1

Corresponding author. Telephone: +886-6-2757575; Fax: +886-6-2352973.

J. Tribol 127(4), 694-704 (May 26, 2005) (11 pages) doi:10.1115/1.2000983 History: Received July 22, 2004; Revised May 26, 2005

## Abstract

The three-dimensional hyperbolic heat conduction equation is solved to obtain the analytical solution of the temperature rise at the contact area between an asperity and a moving smooth flat. The present analyses can provide an efficient method to avoid the problem of being difficult to give the correct boundary conditions for the frictional heat conduction at an asperity. The mean contact area of an asperity which is needed in the heat transfer analysis is here obtained by a new fractal model. This fractal model is established from the findings of the size distribution functions developed for surface asperities operating at the elastic, elastoplastic and fully plastic regimes. The expression of the temperature rise parameter $T∕f$ ($T$: Temperature rise, $f$: friction coefficient) is thus derived without specifying the deformation style of a contact load. It can be applied to predict the $T∕f$ variations due to the continuous generations of the frictional heat flow rate in a period of time. The combination of a small fractal dimension and a large topothesy of a surface is apt to raise the contact load, and thus resulting in a large $T∕f$ value. A significant difference in the behavior exhibited in the parameters of temperature rise and temperature rise gradient is present between the Fourier and hyperbolic heat conductions; Fluctuations in the thermal parameters are exhibited only when the specimen material has a large value of the relaxation time parameter.

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## Figures

Figure 1

Schematic diagram for the contact of rough surfaces

Figure 2

Schematic diagram of three time parameters

Figure 3

Variations of T∕f with time for (a) the diamond and steel materials having the surface asperities with two topothesies, (b) the steel material having the surface asperities with three fractal dimensions

Figure 4

Variations of the dimensionless total loads evaluated at different D and G values with the dimensionless separation. The specimen material is diamond

Figure 5

Variations of T∕f with the dimensionless total load. They are evaluated at different D and G values for diamond and steel

Figure 6

The effect of sliding velocity on T∕f

Figure 7

Variations of (a) T∕f, (b) −∇T∕f with time for the hyperbolic and Fourier heat conductions, and (c) −K∇T∕f with time for the hyperbolic heat conduction in the diamond and steel materials

Figure 8

Variations of (a) T∕f, (b) −∇T∕f, and (c) −K∇T∕f with time for the hyperbolic and Fourier heat conductions in the glass material

Figure 9

Variations of T∕f with time for the diamond material evaluated at three dimensionless separations. The constant values of T∕f are obtained from Archard’s model developed for the steady heat transfer

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