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Research Papers

An Application of Mean Square Calculus to Sliding Wear

[+] Author and Article Information
Cláudio R. Ávila da Silva

Department of Mechanics (DAMEC), Federal University of Technology-Paraná (UTFPR), Avenida Sete de Setembro, 3165, Curitiba, Paraná 80230-901, Brazil

Giuseppe Pintaude

Department of Mechanics (DAMEC), Federal University of Technology-Paraná (UTFPR), Avenida Sete de Setembro, 3165, Curitiba, Paraná 80230-901, Brazilgiuseppepintaude@gmail.com

Hazim Ali Al-Qureshi, Marcelo Alves Krajnc

Computational Applied Mechanics Group (GMAC), Federal University of Santa Catarina (UFSC), P.O. Box 476, Florianópolis, Santa Catarina 88040-900, Brazil

J. Appl. Mech 77(2), 021013 (Dec 14, 2009) (8 pages) doi:10.1115/1.3173603 History: Received May 23, 2008; Revised April 10, 2009; Published December 14, 2009; Online December 14, 2009

In this paper the Archard model and classical results of mean square calculus are used to derive two Cauchy problems in terms of the expected value and covariance of the worn height stochastic process. The uncertainty is present in the wear and roughness coefficients. In order to model the uncertainty, random variables or stochastic processes are used. In the latter case, the expected value and covariance of the worn height stochastic process are obtained for three combinations of correlation models for the wear and roughness coefficients. Numerical examples for both models are solved. For the model based on a random variable, a larger dispersion in terms of worn height stochastic process was observed.

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Figures

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Figure 2

Graphs of types (a), (b), and (c) covariance functions defined in [−1/2,1/2]

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Figure 6

Graphs of covariance functions of the WHSP for cases (a), (b), and (c)

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Figure 7

Graphs of variance functions of the WHSP for cases (a), (b), and (c)

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Figure 1

Graphs of types (a), (b), and (c) covariance functions defined in [0,1]×[0,1]

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Figure 3

Expected value of the worn height stochastic process

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Figure 4

(a) Covariance function (Eq. 28); (b) Variance function

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Figure 5

Graphs of functions C̃(⋅) for cases (a), (b), and (c)

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