Journal of Friction and Wear

, Volume 34, Issue 1, pp 38–45 | Cite as

Synergetic representation of stick-slip mode of boundary friction



The melting of an ultrathin lubricating film clamped between two atomically smooth solid surfaces that are in relative motion is studied based on the Lorentz model for the approximation of a viscoelastic medium. An equation of motion for the stresses has been derived in the form of a three-order differential equation and analyzed at various friction surface temperatures. In all cases, the phase portraits and the time dependences of the stresses have been plotted. It has been found that, depending on the temperature and the lubricant parameters, either the damped oscillation mode or the stochastic oscillation mode may occur. The stochastic oscillation mode is presented in the phase plane as a strange attractor. It has been shown that initial conditions have a critical effect on the system behavior. Based on the model, the behavior of two types of tribosystems, i.e., with the unidirectional shear of the surfaces and under an alternating external effect, has been described.


boundary friction friction force shear stresses strange attractor Lorentz system 


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  1. 1.
    Persson, B.N.J., Sliding Friction. Physical Principles and Applications, Berlin: Springer-Verlag, 2000.MATHCrossRefGoogle Scholar
  2. 2.
    Yoshizawa, H. and Israelachvili, J., Fundamental Mechanisms of Interfacial Friction. 2. Stick-Slip Friction of Spherical and Chain Molecules, J. Phys. Chem., 1993, vol. 97, pp. 11300–11313.CrossRefGoogle Scholar
  3. 3.
    Berman, A.D., Ducker, W.A., and Israelachvili, J.N., Origin and Characterization of Different Stick-Slip Friction Mechanisms, Langmuir, 1996, vol. 12, pp. 4559–4563.CrossRefGoogle Scholar
  4. 4.
    Yamada, S., Nanotribology of Ethers: Effects of Molecular Asymmetry and Fluoroalkyl Chains, Langmuir, 2005, vol. 21, pp. 8724–8732.CrossRefGoogle Scholar
  5. 5.
    Israelachvili, J., Adhesion Forces between Surfaces in Liquids and Condensable Vapors, Surf. Sci. Rep., 1992, vol. 14, pp. 109–159.ADSCrossRefGoogle Scholar
  6. 6.
    Popov, V.L., Thermodynamics and Kinetics of Shear-Induced Melting of a Thin Layer of Lubricant Confined between Solids, Tech. Phys., 2001, vol. 46, pp. 605–615.CrossRefGoogle Scholar
  7. 7.
    Filippov, A.E., Klafter, J., and Urbakh, M., Friction through Dynamical Formation and Rupture of Molecular Bonds, Phys. Rev. Lett., 2004, vol. 92, p. 135503.Google Scholar
  8. 8.
    Yang, C.-R., Chiou, Y.-C., and Lee, R.-T., Tribological Behavior of Reciprocating Friction Drive System under Lubricated Contact, Tribol. Int., 1999, vol. 32, pp. 443–453.CrossRefGoogle Scholar
  9. 9.
    Ciraci, S. and Buldum, A., Atomic-Scale Study of Friction and Energy Dissipation, Wear, 2003, vol. 254, pp. 911–916.CrossRefGoogle Scholar
  10. 10.
    Braun, O.M. and Manini, N., Dependence of Boundary Lubrication on the Misfit Angle between the Sliding Surfaces, Phys. Rev. E, 2011, vol. 83, p. 021601.Google Scholar
  11. 11.
    Volokitin, A.I. and Persson, B.N.J., Quantum Friction, Phys. Rev. Lett., 2011, vol. 106, p. 094502.ADSCrossRefGoogle Scholar
  12. 12.
    Lyashenko, I.A., Khomenko, A.V., and Metlov, L.S., Thermodynamics and Kinetics of Boundary Friction, Tribol. Int., 2011, vol. 44, pp. 476–482.CrossRefGoogle Scholar
  13. 13.
    Boiko, V.I., Valyaev, A.N., and Pogrebnyak, A.D., Metal Modification by High-Power Pulsed Particle Beams, Phys.-Usp., 1999, vol. 42, pp. 1139–1166.ADSCrossRefGoogle Scholar
  14. 14.
    Pogrebnyak, A.D., Ponomarev, A.G., Shpak, A.P., and Kunitskii, Yu.A., Application of Micro- and Nanoprobes to the Analysis of Small-Sized 3D Materials, Nanosystems, and Nanoobjects, Phys.-Usp., 2012, vol. 55, pp. 270–300.ADSCrossRefGoogle Scholar
  15. 15.
    Khomenko, A.V. and Lyashenko, I.A., Phase Dynamics of a Thin Lubricant Film between Solid Surfaces at the Deformation Defect of Shear Modulus, J. Phys. Studies, 2007, vol. 11, pp. 268–278.ADSGoogle Scholar
  16. 16.
    Khomenko, A.V., Lyashenko, I.A., and Borisyuk, V.M., Self-Similar Phase Dynamics of Boundary Friction, Ukr. J. Phys., 2009, vol. 54, pp. 1139–1148.Google Scholar
  17. 17.
    Khomenko, A.V. and Lyashenko, I.A., A Stochastic Model of Stick-Slip Boundary Friction with Account for the Deformation Effect of the Shear Modulus of the Lubricant, J. Friction Wear, 2010, vol. 31, pp. 308–316.CrossRefGoogle Scholar
  18. 18.
    Khomenko, A.V. and Lyashenko, I.A., Statistical Theory of the Boundary Friction of Atomically Flat Solid Surfaces in the Presence of a Lubricant Layer, Phys.-Usp., 2012, vol. 55 (10), (in press).Google Scholar
  19. 19.
    Luengo, G., Israelachvili, J., and Granick, S., Generalized Effects in Confined Fluids: New Friction Map for Boundary Lubrication, Wear, 1996, vol. 200, pp. 328–335.CrossRefGoogle Scholar
  20. 20.
    Popov, V.L., A Theory of the Transition from Static to Kinetic Friction in Boundary Lubrication Layers, Solid State Comm., 2000, vol. 115, pp. 369–373.ADSCrossRefGoogle Scholar
  21. 21.
    Khomenko, A.V. and Lyashenko, Ya.A., Periodic Intermittent Regime of a Boundary Flow, Tech. Phys., 2010, vol. 55, pp. 26–32.CrossRefGoogle Scholar
  22. 22.
    Ruelle, D. and Takens, F., On the Nature of Turbulence, Comm. Math. Phys., 1971, vol. 20, no. 3, pp. 167–192.MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    Loskutov, A.Yu. and Mikhailov, A.S., Osnovy teorii slozhnykh system (Foundations of Complex System Theory), Moscow: 2007.Google Scholar
  24. 24.
    Lyashenko, I.A., Khomenko, A.V., and Metlov, L.S., Phenomenological Theory for the Melting of a Thin Lubricant Film between Two Atomically Smooth Solid Surfaces, Tech. Phys., 2010, vol. 55, pp. 1193–1199.CrossRefGoogle Scholar
  25. 25.
    Lyashenko, I.A., Tribological System in the Boundary Friction Mode under a Periodic External Action, Tech. Phys., 2011, vol. 56, pp. 869–876.CrossRefGoogle Scholar
  26. 26.
    Lyashenko, I.A., First-Order Phase Transition between the Liquidlike and Solidlike Structures of a Boundary Lubricant, Tech. Phys., 2012, vol. 57, pp. 17–26.CrossRefGoogle Scholar
  27. 27.
    Lorenz, E., Deterministic Nonperiodic Flow, J. Atmos. Sci., 1963, vol. 20, pp. 130–141.ADSCrossRefGoogle Scholar

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© Allerton Press, Inc. 2013

Authors and Affiliations

  1. 1.Sumy State UniversitySumyUkraine
  2. 2.Peter Grünberg Institut-1Forschungszentrum JülichJülichGermany

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