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RESEARCH PAPERS

# Transient Three-Dimensional Solution for Thermoelastic Displacement Due to Surface Heating and Convective Cooling

[+] Author and Article Information
Ashlie Martini

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208a-martini@northwestern.edu

Shuangbiao Liu1

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

Q. Jane Wang

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

1

Currently at: Caterpillar Inc., Peoria, IL.

J. Tribol 127(4), 750-755 (Jan 27, 2005) (6 pages) doi:10.1115/1.1924574 History: Received August 04, 2004; Revised January 27, 2005

## Abstract

In tribological contact, frictional heating may lead to temperature rise, which in turn may result in thermal displacement of the contacting bodies. The quantification of these effects is desirable in order to more accurately predict wear and failure of contacting surfaces. The change in temperature at a contact area may be attributed to the combined effects of frictional heating and convective cooling. This paper presents a transient, three-dimensional solution for the normal surface displacement of an elastic half-space due to an arbitrarily distributed, moving heat source and surface convection.

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## Figures

Figure 1

Description of the physical domain and coordinates

Figure 2

The normal displacement (−u3) at 0.5s shown equivalently in two and three dimensions: (a) three dimensional, (b) two dimensional

Figure 3

The normal surface displacement (−u3) due to frictional heating only (i.e., no convection) shown at t=0.05, t=0.1, t=0.5, t=1, and t=5s

Figure 4

The normal surface displacement (−u3) due to frictional heating and convection (h=1000W∕m2∕°C) shown at t=0.05, t=0.1, t=0.5, t=1, and t=5s

Figure 5

The normal thermal displacements (−u3) with convection (h=1000W∕m2∕°C) at 5 and 10s adjusted to a reference point at the edge of the displacement

Figure 6

Comparison of the normal surface displacement (−u3) after 5s with no convection and convection where h=1, 10, 100, 500, and 1000W∕m2∕°C

Figure 7

Percent that normal displacement at the center of contact is reduced due to convective cooling, %=(∣u3,heatsource∣−∣u3,convection∣)∕(∣u3,heatsource∣)×100, after 5s as a function of the surface heat transfer coefficient

Figure 8

Percent that normal displacement at the center of contact is reduced due to convective cooling, %=(∣u3,heatsource∣−∣u3,convection∣)∕(∣u3,heatsource∣)×100, for h=10, 100, and 1000W∕m2∕°C as time increases from 0.05to5s

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