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Research Papers: Friction & Wear

Maximum Entropy Approach for Modeling Hardness Uncertainties in Rabinowicz's Abrasive Wear Equation

[+] Author and Article Information
Fabio Antonio Dorini

Department of Mathematics,
Federal University of Technology – PR,
Av. Sete de Setembro, 3165,
Curitiba PR 80230-901, Brazil
e-mail: fabio.dorini@gmail.com

Giuseppe Pintaude

Department of Mechanics,
Federal University of Technology – PR,
Av. Sete de Setembro, 3165,
Curitiba PR 80230-901, Brazil
e-mail: giuseppepintaude@gmail.com

Rubens Sampaio

Department of Mechanical Engineering,
PUC-Rio,
Rua Marquês de São Vicente, 225, Gávea,
Rio de JaneiroRJ 22453-900, Brazil
e-mail: rsampaio@puc-rio.br

1Address all correspondence related to ASME style format and figures to this author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 3, 2013; final manuscript received December 17, 2013; published online February 5, 2014. Assoc. Editor: George K. Nikas.

J. Tribol 136(2), 021607 (Feb 05, 2014) (6 pages) Paper No: TRIB-13-1206; doi: 10.1115/1.4026421 History: Received October 03, 2013; Revised December 17, 2013

A very useful model for predicting abrasive wear is the linear wear law based on the Rabinowicz's equation. This equation assumes that the removed volume of the abraded material is inversely proportional to its hardness. This paper focuses on the stochastic modeling of the abrasive wear process, taking into account the experimental uncertainties in the identification process of the worn material hardness. The description of hardness is performed by means of the maximum entropy principle (MEP) using only the information available. Propagation of the uncertainties from the data to the volume of wear produced is analyzed. Moreover, comparisons and discussions with other probabilistic models for worn material hardness usually proposed in the literature are done.

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Figures

Grahic Jump Location
Fig. 1

Illustration of the coefficient of variation δW as a function of δH

Grahic Jump Location
Fig. 2

Illustration of the pdf of W; mH = 768Nm-2; δH = 0.07; Lθ = 10N

Grahic Jump Location
Fig. 3

Illustration of the pdf of W; mH = 401Nm-2; δH = 0.24; Lθ = 10N

Grahic Jump Location
Fig. 4

Illustration of the pdf of W; mH = 937Nm-2; δH = 0.40; Lθ = 10N

Grahic Jump Location
Fig. 5

Illustration of the pdf of W; mH = 937Nm-2; δH = 0.50; Lθ = 10N

Grahic Jump Location
Fig. 6

Illustration of the behavior of the relative errors (||fW-fW[i]|| ∞)/mH, i ∈ {G,TG,Ln,We}, in function of δH, 0.1 < δH< 0.7; Lθ = 10 N. This plot corresponds to an envelope of relative errors for several values of mH,mH = 1,2,...,1001.

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