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Research Papers: Friction and Wear

# Assessment of the Tribological Contact Between Sliding Surfaces Via an Entropy Approach

[+] Author and Article Information
Vera Deeva

School of Earth Sciences and Engineering,
Tomsk Polytechnic University,
Lenina pr. 30,
Tomsk 634050, Russia

Stepan Slobodyan

Transport, Oil and Gas Faculty,
Omsk State Technical University,
Mira pr. 11
Omsk, 644050, Russia;
Material Engineering
and Metal Technology Department,
Tver State Technical University,
Komsomolsky pr. 5,
Tver, 170026, Russia
e-mail: sms_46@ngs.ru

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 25, 2018; final manuscript received September 29, 2018; published online November 1, 2018. Assoc. Editor: Sinan Muftu.

J. Tribol 141(3), 031602 (Nov 01, 2018) (6 pages) Paper No: TRIB-18-1205; doi: 10.1115/1.4041644 History: Received May 25, 2018; Revised September 29, 2018

## Abstract

The interaction observed between two surfaces in contact with one another is part of a number of physical processes, such as wear. In this paper, we present a numerical study of the asperities between two surfaces in contact with each other. The real contact area between two surfaces varies due to the multiple roughness scales caused by the stochastic nature of asperities. In our research, we employ a tribological system comprising two partitions: C1 is the contact set (CS), where the two surfaces are in direct contact with each other, and C2 is the noncontact set, where the two surfaces are not in contact with each other. Here, we have developed a new numerical model to describe the CS using ε-entropy to prove the existence of a minimum value for entropy in sliding contact scenarios. In this system, the lower and upper bounds of entropy are determined through the Kolmogorov approach using the aforementioned model. Using this model, we conclude that the ε-entropy value is bound between ln 2 and 2·ln 2 for a tribological system comprising two partitions. Additionally, we conclude that a correlation between the stochastic tribological contact behavior and the rate of entropy change is the key parameter in thermal nonequilibrium scenarios.

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## References

Lorenz, B. , Oh, Y. R. , Nam, S. K. , Jeon, S. H. , and Persson, B. N. J. , 2015, “ Rubber Friction on Road Surfaces: Experiment and Theory for Low Sliding Speeds,” J. Chem. Phys., 142(19), p. 194701. [PubMed]
Rowe, K. G. , Bennet, A. I. , Krick, B. A. , and Sawyer, W. G. , 2013, “ In Situ Thermal Measurements of Sliding Contacts,” Tribol. Int., 62, pp. 208–214.
Ciavarella, M. , “ A Comment on “Meeting the Contact-Mechanics Challenge” by Muser et al. [1],” Tribol. Lett., 66, pp. 37–39.
Shannon, С. E. , 1948, “ A Mathematical Theory of Communication,” Bell Syst. Tech. J., 27(4), pp. 379–423; 623–656.
You, Y. , 2017, “ Random Dynamics of Stochastic Reaction-Diffusion Systems With Additive Noise,” J. Dyn. Differ. Eq., 29(1), pp. 83–90.
Weedbrook, C. , Pirandola, S. , García-Patrón, R. , Cerf, N. J. , Ralph, T. , Shapiro, J. , and Lloyd, S. , 2012, “ Gaussian Quantum Information,” Rev. Mod. Phys., 84(2), pp. 621–627.
Anisimov, M. A. , 2004, “ Thermodynamics at the Meso- and Nanoscale,” Dekker Encyclopedia of Nanoscience and Nanotechnology, J. A. Schwarz, C. Contescu, and K. Putyera, eds., Marcel Dekker, New York, pp. 3893–3904.
Bol'shanin, A. A. , Slobodyan, S. M. , Yakovlev, A. R. , and Vasil'eva, L. A. , 1987, “ Two-Channel Optical Transducer for an Industrial Inspection System,” Meas. Tech., 30(10), pp. 954–956.
Qi, G. , 2017, “ Energy Cycle of Brushless DC Motor Chaotic System,” Appl. Math. Mod., 51, pp. 686–688.
Deeva, V. S. , Slobodyan, S. M. , and Teterin, V. S. , 2016, “ Optimization of Oil Particles Separation Disperser Parameters,” Mater. Sci. Forum, 870, pp. 677–682.
Mo, F. , Shen, C. , Zhou, J. , and Khonsari, M. , 2017, “ Statistical Analysis of Surface Texture Performance With Provisions With Uncertainty in Texture Dimensions,” IEEE Access, 5, pp. 5388–5398.
Zhou, Y. , Bosman, R. , and Lugt, P. M. , 2018, “ A Model for Shear Degradation of Lithium Soap Grease at Ambient Temperature,” Tribol. Trans., 61(1), pp. 61–70.
Slobodyan, M. S. , 2011, “ The Probability Factor of Contact Measurements,” Meas. Tech., 54(1), pp. 68–73.
Su, J. , Ke, L. , Wang, Y. , and Xiang, Y. , 2017, “ Axisymmetric Torsional Fretting Contact Between a Spherical Punch and an FGPM Coating,” Appl. Math. Modell., 52, pp. 576–581.
Gallavotti, G. , 2004, “ Entropy Production and Thermodynamics of Nonequilibrium Stationary States: A Point of View,” Chaos, 14(3), pp. 680–690. [PubMed]
Feng, Z. , 2017, “ Magnetic Entropy Change of Layered Perovskites La2 − 2xSr1 + 2xMn2O7,” J. Appl. Phys., 97(10), p. 103906.
Ciavarella, M. , and Papangelo, A. , 2018, “ The “Sport” of Rough Contacts and the Fractal Paradox in Wear Laws,” Facta Univ.: Mech. Eng., 16(1), pp. 65–75.
Deeva, V. , Slobodyan, S. , and Martikyan, M. , 2016, “ Physical Model of the Sliding Contact of Conductors of the Alloy Cu-Zr and Cu-Re Under High Current Density,” Mater. Today: Proc., 3(9), pp. 3114–3120.
Zhang, Y. , Kovalev, A. , Hayashi, N. , Nishiura, K. , and Meng, Y. , 2018, “ Numerical Prediction of Surface Wear and Roughness Parameters During Running-In for Line Contacts Under Mixed Lubrication,” ASME J. Tribol., 140(6), p. 061501.
Imanian, A. , and Modarres, M. , 2016, “ Development of a Generalized Entropic Framework for Damage Assessment,” Fracture, Fatigue, Failure and Damage Evolution (Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 8), A. Beese , A. Zehnder , and S. Xia , eds., Springer, Cham, Switzerland, pp. 73–78.
Bryant, M. D. , 2009, “ Entropy and Dissipative Processes of Friction and Wear,” FME Trans., 37, pp. 55–59.
Aghdam, A. B. , and Khonsari, M. M. , 2011, “ On the Correlation Between Wear and Entropy in Dry Sliding Contact,” Wear, 270(11–12), pp. 781–783.
Kumar, N. , Singh, T. , Rajoria, R. S. , and Patnaik, A. , 2016, “ Optimum Design of Brake Friction Material Using Hybrid Entropy-GRA Approach,” MATEC Web Conf., 57, p. 03002.
Romanishina, T. , Romanishina, S. , Deeva, V. , and Slobodyan, S. , 2017, “ Numerical Modeling of Synovial Fluid Layer,” IEEE International Young Scientists Forum on Applied Physics and Engineering (YSF), Lviv, Ukraine, Oct. 17–20, pp. 143–146.
Tufano, D. , and Sotoudeh, Z. , 2017, “ Exploring the Entropy Concept for Coupled Oscillators,” Int. J. Eng. Sci., 112, pp. 18–31.
Banjac, M. , Vencl, A. , and Otović, S. , 2014, “ Friction and Wear Processes–Thermodynamic Approach,” Tribol. Ind., 36(4), pp. 341–343.
Volkov, V. F. , Peshel', A. K. , Slobodyan, S. M. , and Tyryshkin, I. S. , 1981, “ Registration of a Pulsed Laser Beam by a Matrix of Charge-Coupled Devices,” Instrum. Exp. Tech., 24(6 pt. 2), pp. 1522–1524.
Carpick, L. R. W. , 2018, “ The Contact Sport of Rough Surfaces,” Science, 359(6371), pp. 38–38. [PubMed]
Deeva, V. , and Slobodyan, S. , 2017, “ Influence of Gravity and Thermodynamics on the Sliding Electrical Contact,” Tribol. Int., 105, pp. 299–303.
Machado, J. A. , 2010, “ Entropy Analysis of Integer and Fractional Dynamical Systems,” Nonlinear Dyn., 62(1–2), pp. 371–378.
Majcherczak, D. , Dufrenoy, P. , Berthier, Y. , and Nait-Abdelaziz, M. , 2006, “ Experimental Thermal Study of Contact With Third Body,” Wear, 261(5–6), pp. 467–470.
Collet, P. , and Eckmann, J. , 2006, Concepts and Results in Chaotic Dynamics: A Short Course, Heidelberg, Berlin.
Wright, S. , Scott, D. , Haddow, J. , and Rosen, M. , 2001, “ On the Entropy of Radiative Heat Transfer in Engineering Thermodynamics,” Int. J. Eng. Sci., 39(15), pp. 1691–1693.
Kanazawa, Y. , Sayles, R. , and Kadiric, A. , 2017, “ Film Formation and Friction in Grease Lubricated Rolling-Sliding Non-Conformal Contacts,” Tribol. Int., 109, pp. 505–510.
Lieb, E. H. , and Yngvason, J. , 2014, “ Entropy Meters and the Entropy of Non-Extensive Systems,” Proc. R. Soc. A, 470(2167), p. 0192.
Kolmogorov, A. N. , 1958, “ On the Entropy per Unit of Time as the Metric Invariant of the Automorphism,” Dokl. Akad. Nauk SSSR, 124, pp. 754–755 (in Russian).
Sinai, Y. G. , 1959, “ On the Concept of the Entropy for a Dynamic System,” Dokl. Akad. Nauk SSSR, 125, pp. 768–771 (in Russian).
Sinai, Y. G. , 1988, “ About A.N. Kolmogorov's Work on the Entropy of Dynamical Systems,” Ergodic Theory Dyn. Syst., 8, pp. 501–505 (in Russian).
Deeva, V. S. , and Slobodyan, S. M. , 2017, Entropy Estimation of a Dynamical System Via a Contact Interaction, CRC Press/Safety and Reliability–Theory and Application: ESREL/Taylor & Francis, Portoroz, Slovenia, p. 373.
Carcaterra, A. , 2014, “ Thermodynamic Temperature in Linear and Nonlinear Hamiltonian Systems,” Int. J. Eng. Sci., 80, pp. 189–195.
Frigg, R. , 2006, “ Chaos and Randomness: An Equivalence Proof of a Generalized Version of the Shannon Entropy and the Kolmogorov–Sinai Entropy for Hamiltonian Dynamical Systems,” Chaos Solitons Fractals, 28(1), pp. 26–34.
Keller, K. , Mangold, T. , Stolz, I. , and Werner, J. , 2017, “ Permutation Entropy: New Ideas and Challenges,” Entropy, 19(3), pp. 134–150.
Ahmed, M. U. , and Mandic, D. P. , 2012, “ Multivariate Multiscale Entropy Analysis,” IEEE Signal Proc. Lett., 19(2), pp. 91–96.
Ford, I. , 2013, Statistical Physics: An Entropic Approach, Wiley, New York.
La, H. P. , Sarkar, S. , and Gupta, S. , 2017, “ Stochastic Model Order Reduction in Randomly Parametered Linear Dynamical Systems,” Appl. Math. Mod., 51, pp. 744–763.
Prajapati, D. K. , and Tiwari, M. , 2017, “ Topography Analysis of Random Anisotropic Gaussian Rough Surfaces,” ASME J. Tribol., 139(4), p. 041402.
Deng, C. Y. , Zhang, H. B. , Yin, J. , Xiong, X. , Wang, P. , and Sun, M. , 2017, “ Carbon Fiber/Copper Mesh Reinforced Carbon Composite for Sliding Contact Material,” Mater. Res. Express, 4(2), p. 025602.
Morris, N. , Mohammadpour, M. , Rahmani, R. , Johns-Rahnejat, P. M. , Rahnejat, H. , and Dowson, D. , 2018, “ Effect of Cylinder Deactivation on Tribological Performance of Piston Compression Ring and Connecting Rod Bearing,” Tribol. Int., 120, pp. 243–254.
Gaspard, P. , and Wang, X. , 1993, “ Noise, Chaos, and (ε, τ)-Entropy per Unit Time,” Phys. Rep., 235(6), pp. 291–343.
Amiri, M. , and Khonsari, M. M. , 2010, “ On the Thermodynamics of Friction and Wear,” Entropy, 12(5), pp. 1021–1049.
Nosonovsky, M. , 2010, “ Entropy in Tribology: In the Search for Applications,” Entropy, 12(6), pp. 1345–1390.
Bershadski, L. I. , 1992, “ On the Self-Organization and Concepts of Wear-Resistance in Tribosystems,” Trenie I Iznos (Russian Friction and Wear), 13, pp. 1077–1094.
Nosonovsky, M. , and Mortazavi, V. , 2018, Friction-Induced Vibrations and Self-Organization: Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact, CRC Press, Boca Raton, FL.
Gershman, I. S. , Mironov, A. , Fox-Rabinovich, G. S. , and Veldhuis, S. C. , 2015, “ Self-Organization During Friction of Slide Bearing Antifriction Materials,” Entropy, 17(12), pp. 7967–7978.
Fleurquin, P. , Fort, H. , Kornbluth, M. , Sandler, R. , Segall, M. , and Zypman, F. , 2010, “ Negentropy Generation and Fractality in Dry Friction of Polished Surfaces,” Entropy, 12(3), pp. 480–489.
Kheifets, M. L. , 2016, “ Self-Organization of Structure Formation Processes in Intense Treatment and Operation of Materials,” Adv. Mater. Technol., 3, pp. 14–20.
Creeger, P. , and Zypman, F. , 2014, “ Entropy Content During Nanometric Stick-Slip Motion,” Entropy, 16(6), pp. 3062–3073.
Barszcz, M. , Paszeczko, M. , and Lenik, K. , 2015, “ Self-Organization of Friction Surface of Fe-Mn-C-B Coating With Increased Resistance to Abrasion,” Arch. Metall. Mater., 60(4), pp. 2651–2656.
Klameski, B. E. , 1984, “ An Entropy Based Model of Plastic Deformation Energy Dissipation in Sliding,” Wear, 96, pp. 319–329.
Obozov, A. A. , Serpik, I. N. , Mihalchenko, G. S. , and Fedyaeva, G. A. , 2017, “ Theoretical Aspects of the Patterns Recognition Statistical Theory Used for Developing the Diagnosis Algorithms for Complicated Technical Systems,” J. Phys.: Conf. Ser., 803, p. 012109.
Myshkin, N. , 1991, “ Tribological Problems in Electrical Contacts,” Tribol. Int., 24(1), pp. 45–49.
Leighton, M. , Morris, N. , Core, M. , Rahmani, R. , Rahnejat, H. , and King, P. D. , 2016, “ Boundary Interactions of Rough Non-Gaussian Surfaces,” Proc. Inst. Mech. Eng., Part J, 230, pp. 1359–1370.
Maciąg, M. , 2015, “ Specific Heat of Tribological Wear Debris Material,” ASME J. Tribol., 137(3), p. 031601.
Klimontovich, Y. L. , 2007, “ Entropy and Information of Open Systems,” Phys.-Usp., 42(4), pp. 375–399 (in Russian).
Slobodyan, S. M. , 2006, “ Optimizing Phase-Space Scanning for a Dynamic System Monitoring Chaotic Media,” Meas. Tech., 49(1), pp. 1–6.
Van Trees, H. L. , 1968, Detection, Estimation and Modulation Theory: Part I, II, and III, Wiley, New York.
Posner, E. C. , Rodemish, E. R. , and Rumsey, H. G. , 1967, “ ε-Entropy of Stochastic Processes,” Ann. Math. Statist., 38(4), pp. 1000–1020.

## Figures

Fig. 1

Illustration of the tribological process changes in steps (а) before the contact interaction, (b) start of the sliding interaction and the wear particles appearance, and (c) the flow of the process in the presence of wear particle

Fig. 2

Schematic of the probabilistic sets of the tribological surface contact. С1 is the set of states where the two surfaces are in contact and С2 is the set of states where the two surfaces are not in contact.

Fig. 3

Structural model of the possible states between the boundary lines of ε-entropy: {11} is the state of contact, {12} is the transition state from contact to noncontact, {21} is the transition state from noncontact to contact, {22} is the state of noncontact

Fig. 4

Consistent patterns in the behavior of the probability of correct identification of tribocontact state D (Hξ − H0ξ) in the space of equiprobable entropy thermodynamic states Hξ according to expressions (8) at changes in threshold values H0ξ that correspond to the values of identification error probability F = 5 × 10−1; F = 5 × 10−2; F = 5 × 10−3; and F = 5 × 10−4

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