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,
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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Tonn, W., 1937, “Beitrag zur Kenntnis des Verschleissvorganges beim Kurzversuck,” Z. Meta Ukd., 29, pp. 196–198.
Khruschov, M. M., and Babichev, M. A., 1956, “An Investigation of the Wear of Metals and Alloys by Rubbing on an Abrasive Surface,” ASME Friction Wear Mach., 11, pp. 1–12.
Bahadur, S., 1978, “Wear Research and Development,” ASME J. Lubr. Technol., 100(4), pp. 449–454. [CrossRef]
Rabinowicz, E., Dunn, L. A., and Russell, P. G., 1961, “A Study of Abrasive Wear Under Three-Body Conditions,” Wear, 4, pp. 345–355. [CrossRef]
Khruschov, M. M., 1974, “Principles of Abrasive Wear,” Wear, 28, pp. 69–88. [CrossRef]
Pintaude, G., Tanaka, D., and Sinatora, A., 2003, “The Effects of Abrasive Particle Size on the Sliding Friction Coefficient of Steel Using a Spiral Pin-on-Disk Apparatus,” Wear, 255(1-6), pp. 55–59. [CrossRef]
Factor, M., and Roman, I., 2002, “Use of Microhardness as a Simple Means of Estimating Relative Wear Resistance of Carbide Thermal Spray Coatings: Part 1. Characterization of Cemented Carbide Coatings,” J. Therm. Spray Techn., 11(4), pp. 468–481. [CrossRef]
Factor, M., and Roman, I., 2002, “Use of Microhardness as a Simple Means of Estimating Relative Wear Resistance of Carbide Thermal Spray Coatings: Part 2. Wear Resistance of Cemented Carbide Coatings,” J. Therm. Spray Techn., 11(4), pp. 482–495. [CrossRef]
Rabinowicz, E., 1983, “The Wear of Hard Surfaces by Soft Abrasives,” Wear of Materials: International Conference on Wear of Materials, K. C.Ludema, ed., ASME, New York, pp. 12–18.
Schneider, J.-M., Bigerelle, M., and Iost, A., 1999, “Statistical Analysis of the Vickers Hardness,” Mater. Sci. Eng. A, 262, pp. 256–263. [CrossRef]
Wang, J., Zhai, C.-S., Yang, Y., and Sun, B.-D., 2006, “Vickers Microindentation and Statistical Analysis of Microhardness of Detonation Sprayed Nanocomposite Al2O3-TiO2 Coatings,” J. Compos. Mater., 40, pp. 943–953. [CrossRef]
Cataldo, E., Soize, C., and Sampaio, R., 2013, “Uncertainty Quantification of Voice Signal Production Mechanical Model and Experimental Updating,” Mech. Syst. Signal Process., 40, pp. 718–726. [CrossRef]
Dorini, F. A., and Sampaio, R., 2012, “Some Results on the Random Wear Coefficient of the Archard Model,” ASME J. Appl. Mech., 79(5), p. 051008. [CrossRef]
Bryant, M. D., Khonsari, M. M., and Ling, F. F., 2008, “On the Thermodynamics of Degradation,” Proc. R. Soc. London A, 464, pp. 2001–2014. [CrossRef]
Nosonovsky, M., 2010, “Entropy in Tribology: In the Search for Applications,” Entropy, 12, pp. 1345–1390. [CrossRef]
Doelling, K. L., Ling, F. F., Bryant, M. D., and Heilman, B. P., 2000, “An Experimental Study of the Correlation Between Wear and Entropy Flow in Machinery Components,” J. Appl. Phys., 88, pp. 2999–3003. [CrossRef]
Naderi, M., Amiri, M., and Khonsari, M. M., 2010, “On the Thermodynamic Entropy of Fatigue Fracture,” Proc. R. Soc. London A, 466, pp. 423–438. [CrossRef]
Amiri, M., Khonsari, M. M., and Brahmeshwarkar, S., 2012, “An Application of Dimensional Analysis to Entropy-Wear Relationship,” ASME J. Tribol., 134(1), p. 011604. [CrossRef]
Shannon, C. E., and Weaver, W., 1949, The Mathematical Theory of Communication, University of Illinois, Urbana, IL.
Conrad, K., 2013, “Probability Distributions and Maximum Entropy,” retrieved November 14, 2013. Available at: http://www.math.uconn.edu/~kconrad/blurbs/analysis/entropypost.pdf
Jaynes, E., 1957, “Information Theory and Statistical Mechanics,” Phys. Rev., 106(4), pp. 620–630. [CrossRef]
Jaynes, E. T., 1957, “Information Theory and Statistical Mechanics II,” Phys. Rev., 108(2), pp. 171–190. [CrossRef]
Papoulis, A., 1984, Probability, Random Variables, and Stochastic Processes, 2nd ed., McGraw-Hill, New York.
Kapur, J. N., and Kesavan, H. K., 1992, Entropy Optimization Principle With Applications, Academic, San Diego, CA.
Soize, C., 2001, “Maximum Entropy Approach for Modelling Random Uncertainties in Transient Elastodynamics,” J. Acoust. Soc. Am., 109(5), pp. 1979–1996. [CrossRef] [PubMed]
Chevalier, L., Cloupet, S., and Soize, C., 2005, “Probabilistic Model for Random Uncertainties in Steady State Rolling Contact,” Wear, 258, pp. 1543–1554. [CrossRef]
Udwadia, F. E., 1989, “Some Results on Maximum Entropy Distributions for Parameters Known to Lie in Finite Intervals,” Siam Rev., 31(1), pp. 103–109. [CrossRef]
Bozzi, A. C., and Mello, J. D. B., 1999, “Wear Resistance and Wear Mechanisms of WC-12/100Co Thermal Sprayed Coatings in Three-Body Abrasion,” Wear, 233-235, pp. 575–587. [CrossRef]


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. 1

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

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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In