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Research Papers: Contact Mechanics

# Estimation of the Real Area of Contact in Sliding Systems Using Thermal Measurements

[+] Author and Article Information
Brian Vick

Mechanical Engineering Department, Virginia Tech, Blacksburg, VA 24061bvick@vt.edu

William C. Schneck

Mechanical Engineering Department, Virginia Tech, Blacksburg, VA 24061wschneck@vt.edu

J. Tribol 133(3), 031407 (Jul 28, 2011) (12 pages) doi:10.1115/1.4004302 History: Received June 11, 2010; Revised May 05, 2011; Accepted May 24, 2011; Published July 28, 2011; Online July 28, 2011

## Abstract

The objectives of this paper are to develop a means to estimate the real area of contact in sliding systems using thermal measurements and to provide experimental design guidance for optimal sensor locations. The methods used are a modified cellular automata technique for the direct model and a Levenberg–Marquardt parameter estimation technique to stabilize inverse solutions. The modified cellular automata technique enables each piece of physics to be solved independently over a short time step, thus reducing a complicated model to a sequence of simpler problems. Overall, the method proved successful. The major results indicate that appropriately selected measurement locations can determine the contact distribution accurately. The best measurement location is found to be just downstream of the nominal contact zone in the moving body. This is significant since direct access to the contact zone is usually impossible. Results show that it is best to locate a sensor in the moving body. However, placing the sensor in the static body can also provide a reasonable image of the contact distribution. This is useful because the static body is easier to instrument than a moving body. Finally, the estimation method worked well for the most complex model utilized, even in a suboptimal measurement location

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## Figures

Figure 15

Contact distribution RMS residual plot for two bodies with geometry shown. Uniform distribution with St/Lx+=0.5 and err +=±0.02.

Figure 1

Analytical result of temperature rise over real contact area [1]. The temperature rise is expressed as the change in temperature divided by the friction coefficient.

Figure 5

Schematic portrayal of the physical system. Three contacts of varying intensity are depicted.

Figure 6

Sample contact distributions

Figure 7

Formulation summarized by physical location

Figure 10

Estimated dimensionless contact distributions for various input distributions. The actual distribution is the solid line, and the estimated distribution is the dashed line. Lx+=10, StLy+=0.1, err +  = 0.02.

Figure 11

Contact distribution RMS residuals, with varying contact distributions

Figure 12

Contact distribution RMS residual for varied error case. Uniform contact distribution with Lx+=10, StLy+=0.1.

Figure 13

Contact distribution log10(ΔfdRMS+) density plot. StLy+=1,err+=0.

Figure 14

log⁡10(ΔfdRMS+) plot for one sensor in two dimensions. Uniform distribution with Lx+=10,Ly+=1,St/Lx+=0.1 and err +=±0.02. 100 grid points were used in both the x +  and y +  directions.

Figure 2

The parameter estimation process

Figure 3

Depiction of the physical system. The inset is a detailed view of the interface.

Figure 4

Schematic representation of the (a) direct problem (b) inverse problem and (c) parameter estimation problem

Figure 8

Arbitrary contact distribution discretized for estimation

Figure 9

Sample dimensionless temperature data taken at a normalized location of xs +   = 1.1 and 6.1. Err +   = ±0.02, Lx+=10, St/Lx+=0.1, and Δx+=0.1,Δt +=0.5.

## Errata

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