Identification of the Heat Flux in a Quasi-Static Thermoelastic System

[+] Author and Article Information
Ilya Kolmanovsky1

 Ford Motor Company, Dearborn, MI 48124ikolmano@ford.com

Michael P. Polis

Department of Electrical and Systems Engineering, Oakland University, Rochester, MI 48309

Irina F. Sivergina

Department of Science and Mathematics, Kettering University, Flint, MI 48504-4898

Here, and in the sequel, ω denotes the derivative of ω.


Corresponding author.

J. Dyn. Sys., Meas., Control 128(3), 608-616 (Nov 28, 2005) (9 pages) doi:10.1115/1.2232685 History: Received July 11, 2004; Revised November 28, 2005

This paper treats the problem of estimating the heat flux through the free end of a thermoelastic rod, which is allowed to come into contact with a rigid obstacle. This problem is motivated by the need to develop techniques for indirect measurement of heating in applications, such as, brake systems and machine tools. Under a quasi-static approximation, the problem becomes that of characterizing thermal processes in the rod. Assuming that direct and exact measurements at the contacting end of the rod cannot be taken, the problem is to determine if there is contact with the obstacle; and if there is contact, to characterize the conductivity processes at the contacting end. We study the case of weighted-average temperature measurements throughout the rod. Identifiability results and on-line recursive estimation procedures are developed.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 4

The true boundary function u(t) (solid line) and the estimate from the input observer û(t) (dashed line)

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Figure 3

The measurement data

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Figure 2

The temperature distribution through the rod as a function of rod length and time (relative to a nominal temperature)

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Figure 1

The thermoelastic rod with two temperature sensors that measure average temperature over parts of the rod. The thermoelastic rod captures many issues common to a number of practical applications where thermoelastic effects are important (4), including disk brakes.




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