Research Papers: Elastohydrodynamic Lubrication

A Multiscale Study on the Wall Slip Effect in a Ceramic–Steel Contact With Nanometer-Thick Lubricant Film by a Nano-to-Elastohydrodynamic Lubrication Approach

[+] Author and Article Information
D. Savio

Université de Lyon,
CNRS, UMR5259,
INSA-Lyon, LaMCoS,
Villeurbanne F-69621, France
SKF Aeroengine France,
Z. I. no. 2, Rouvignies,
Valenciennes 59309, France

N. Fillot

Université de Lyon,
CNRS, UMR5259,
INSA-Lyon, LaMCoS,
Villeurbanne F-69621, France
e-mail: nicolas.fillot@insa-lyon.fr

P. Vergne

Université de Lyon,
CNRS, UMR5259,
INSA-Lyon, LaMCoS,
Villeurbanne F-69621, France

H. Hetzler, W. Seemann

Institute of Engineering Mechanics (ITM),
Karlsruhe Institute of Technology (KIT),
Karlsruhe 76131, Germany

G. E. Morales Espejel

Université de Lyon,
CNRS, UMR5259,
INSA-Lyon, LaMCoS,
Villeurbanne F-69621, France
SKF Engineering and Research Centre,
Nieuwegein 3430 DT, The Netherlands

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 15, 2014; final manuscript received February 23, 2015; published online April 15, 2015. Assoc. Editor: Zhong Min Jin.

J. Tribol 137(3), 031502 (Jul 01, 2015) (13 pages) Paper No: TRIB-14-1166; doi: 10.1115/1.4029937 History: Received July 15, 2014; Revised February 23, 2015; Online April 15, 2015

A novel nano-to-elastohydrodynamic lubrication (EHL) multiscale approach, developed to integrate molecular-scale phenomena into macroscopic lubrication models based on the continuum hypothesis, is applied to a lubricated contact problem with a ceramic–steel interface and a nanometric film thickness. Molecular dynamics (MD) simulations are used to quantify wall slip occurring under severe confinement. Its dependence on the sliding velocity, film thickness, pressure, and different wall materials is described through representative analytical laws. These are then coupled to a modified Reynolds equation, where a no-slip condition applies to the ceramic surface and slip occurring on the steel wall is described through a Navier-type boundary condition. The results of this nano-to-EHL approach can contradict the well-established lubrication theory for thin films. In fact, slip can occur over the whole contact length, leading to a significant modification of the lubricant flow and consequently of the film thickness. If both walls move at the same velocity, the flow is reduced at the contact inlet and the film thickness decreases. If the nonslipping wall entrains the fluid, this one is accelerated resulting in a larger mass flow; nevertheless, the surface separation is reduced as the lubricant flows even faster in the contact center. The opposite effect occurs if the slipping surface entrains the fluid, causing a lower mass flow but higher film thickness. Finally, friction is generally smaller compared to the classical no-slip case and becomes independent of the sliding velocity as total slip is approached.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Habchi, W., Vergne, P., Eyheramendy, D., and Morales-Espejel, G., 2011, “Numerical Investigation of the Use of Machinery Low-Viscosity Working Fluids as Lubricants in Elastohydrodynamic Lubricated Point Contacts,” Proc. Inst. Mech. Eng., Part J, 225(6), pp. 465–477. [CrossRef]
Horn, R., and Israelachvili, J., 1981, “Direct Measurement of Structural Forces Between Two Surfaces in a Nonpolar Liquid,” J. Chem. Phys., 75(3), pp. 1400–1411. [CrossRef]
Israelachvili, J., 1991, Intermolecular and Surface Forces, 2nd revised ed., Colloid Science Academic Press, pp. 245–247.
Allen, M., and Tildesley, D., 1987, Computer Simulations of Liquids, Clarendon Press, Oxford.
Chan, D., and Horn, R., 1985, “The Drainage of Thin Liquid Films Between Solid Surfaces,” J. Chem. Phys., 83(10), pp. 5311–5324. [CrossRef]
Christenson, H., Gruen, D., Horn, R., and Israelachvili, J., 1987, “Structuring in Liquid Alkanes Between Solid Surfaces: Force Measurements and Mean-Field Theory,” J. Chem. Phys., 87(3), pp. 1834–1841. [CrossRef]
Gao, J., Luedtke, W., and Landman, U., 1997, “Layering Transitions and Dynamics of Confined Liquid Films,” Phys. Rev. Lett., 79(4), pp. 705–708. [CrossRef]
Jabbarzadeh, A., Harrowel, P., and Tanner, R., 2006, “Crystal Bridge Formation Marks the Transition to Rigidity in a Thin Lubrication Film,” Phys. Rev. Lett., 96(20), p. 206102. [CrossRef] [PubMed]
Gee, M., McGuiggan, P., Israelachvili, J., and Homola, A., 1990, “Liquid to Solidlike Transitions of Molecularly Thin Films Under Shear,” J. Chem. Phys., 93(3), pp. 1895–1906. [CrossRef]
Granick, S., 1991, “Motions and Relaxations of Confined Liquids,” Science, 253(5026), pp. 1374–1379. [CrossRef] [PubMed]
Fillot, N., Berro, H., and Vergne, P., 2011, “From Continuous to Molecular Scale in Modelling Elastohydrodynamic Lubrication: Nanoscale Surface Slip Effects on Film Thickness and Friction,” Tribol. Lett., 43(3), pp. 257–266. [CrossRef]
Jabbarzadeh, A., Atkinson, J., and Tanner, R., 2002, “The Effect of Branching on Slip and Rheological Properties of Lubricants in Molecular Dynamics Simulation of Couette Shear Flow,” Tribol. Int., 35(1), pp. 35–46. [CrossRef]
Jabbarzadeh, A., and Tanner, R., 2011, “Thin Lubricant Films Confined Between Crystalline Surfaces: Gold Versus Mica,” Tribol. Int., 44(6), pp. 711–719. [CrossRef]
Martini, A., Roxin, A., Snurr, R., Wang, Q., and Lichter, S., 2008, “Molecular Mechanisms of Liquid Slip,” J. Fluid Mech., 600, pp. 257–269. [CrossRef]
Priezjev, N., and Troian, S., 2004, “Molecular Origin and Dynamic Behavior of Slip in Sheared Polymer Films,” Phys. Rev. Lett., 92(1), p. 018302. [CrossRef] [PubMed]
Savio, D., Fillot, N., Vergne, P., and Zaccheddu, M., 2012, “A Model for Wall Slip Prediction of Confined n-Alkanes: Effect of Wall–Fluid Interaction Versus Fluid Resistance,” Tribol. Lett., 46(1), pp. 11–22. [CrossRef]
Thompson, P., and Robbins, M., 1990, “Shear Flow Near Solids: Epitaxial Order and Flow Boundary Conditions,” Phys. Rev. A, 41(12), pp. 6830–6837. [CrossRef] [PubMed]
Thompson, P., and Troian, S., 1997, “A General Boundary Condition for Liquid Flow at Solid Surfaces,” Nature, 389, pp. 360–362. [CrossRef]
Kato, T., and Matsuoka, H., 1999, “Molecular Layering in Thin-Film Elastohydrodynamics,” Proc. Inst. Mech. Eng., Part J, 213(5), pp. 363–369. [CrossRef]
Teodorescu, M., Balakrishnan, S., and Rahnejat, H., 2006, “Physics of Ultra-Thin Surface Films on Molecularly Smooth Surfaces,” Proc. Inst. Mech. Eng., Part N, 220(1), pp. 7–18. [CrossRef]
Martini, A., Liu, Y., Snurr, R., and Wang, Q., 2006, “Molecular Dynamics Characterization of Thin Film Viscosity for EHL Simulation,” Tribol. Lett., 21(3), pp. 217–225. [CrossRef]
Chen, D., and Bogy, D., 2010, “Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Hard Disk Drives,” Tribol. Lett., 37(2), pp. 191–201. [CrossRef]
Chu, L., Lin, J., Li, W., and Lu, J., 2012, “A Model for Line-Contact EHL Problems—Consideration of Effects of Navier-Slip and Lubricant Rheology,” ASME J. Tribol., 134(3), p. 031502. [CrossRef]
Fukui, S., and Kaneko, R., 1988, “Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow,” ASME J. Tribol., 110(2), pp. 253–261. [CrossRef]
Sham, T., and Tichy, J., 1997, “A Scheme for Hybrid Molecular-Dynamics Finite-Element Analysis of Thin-Film Lubrication,” Wear, 207(1–2), pp. 100–106. [CrossRef]
Ching, W.-Y., Xu, Y.-N., Gale, J., and Rühle, M., 1998, “Ab-Initio Total Energy Calculation of Alpha- and Beta-Silicon Nitride and the Derivation of Effective Pair Potentials With Application to Lattice Dynamics,” J. Am. Ceram. Soc., 81(12), pp. 3189–3196. [CrossRef]
Rogal, L., Dutkiewicz, J., Czeppe, T., Bonarski, J., and Olszowska-Sobieraj, B., 2010, “Characteristics of 100Cr6 Bearing Steel After Thixoforming Process Performed With Prototype Device,” Trans. Nonferrous Metals Soc. China, 20(Suppl. 3), pp. 1033–1036. [CrossRef]
Berro, H., 2010, “A Molecular Dynamics Approach to Nano-Scale Lubrication,” Ph.D. thesis, MEGA, INSA de Lyon, 2010ISAL0084, http://theses.insa-lyon.fr/publication/2010ISAL0084/these.pdf
Borgen, O., and Seip, H. M., 1961, “The Crystal Structure of Beta-Si3N4,” Acta Chem. Scand., 15(8), p. 1789. [CrossRef]
Lide, D., 2004–2005, Handbook of Chemistry and Physics, 85th ed., CRC Press, Boca Raton, pp. 4–161.
Rollmann, G., Rohrbach, A., Entel, P., and Hafner, J., 2004, “First-Principles Calculation of the Structure and Magnetic Phases of Hematite,” Phys. Rev. B, 69(16), p. 165107. [CrossRef]
Cornell, W., Cieplak, P., Bayly, C., Gould, I., Merz, K., Ferguson, D., Spellmeyer, D., Fox, T., Caldwell, J., and Kollman, P., 1995, “A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids and Organic Molecules,” J. Am. Chem. Soc., 117(19), pp. 5179–5197. [CrossRef]
Jorgensen, W., and Tirado-Rives, J., 1988, “The OPLS Force Field for Proteins. Energy Minimizations for Crystals of Cyclic Peptides and Crambin,” J. Am. Chem. Soc., 110(6), pp. 1657–1723. [CrossRef]
Minfray, C., Mogne, T. L., Martin, J.-M., Onodera, T., Nara, S., Takahashi, S., Tsuboi, H., Koyama, M., Endou, A., Takaba, H., Kubo, M., Carpio, C. D., and Miyamoto, A., 2008, “Experimental and Molecular Dynamics Simulations of Tribochemical Reactions With ZDDP: Zinc Phosphate–Iron Oxide Reaction,” Tribol. Trans., 51(5), pp. 589–601. [CrossRef]
Zhang, L., Balasundaram, R., Gehrke, S., and Jiang, S., 2001, “Nonequilibrium Molecular Dynamics Simulations of Confined Fluids in Contact With the Bulk,” J. Chem. Phys., 114(15), pp. 6869–6877. [CrossRef]
Xia, T., Ouyang, J., Ribarsky, M., and Landman, U., 1992, “Interfacial Alkane Films,” Phys. Rev. Lett., 69(13), pp. 1967–1970. [CrossRef] [PubMed]
Schneider, T., and Stoll, E., 1978, “Molecular-Dynamics Study of a Three-Dimensional One-Component Model for Distortive Phase Transitions,” Phys. Rev. B, 17(3), pp. 1302–1322. [CrossRef]
Gupta, S., Cochran, H., and Cummings, P., 1997, “Shear Behavior of Squalane and Tetracosane Under Extreme Confinement. III. Effect of Confinement on Viscosity,” J. Chem. Phys., 107(23), pp. 10335–10343. [CrossRef]
Jabbarzadeh, A., Atkinson, J., and Tanner, R., 1999, “Wall Slip in the Molecular Dynamics Simulation of Thin Films of Hexadecane,” J. Chem. Phys., 110(5), pp. 2612–2620. [CrossRef]
Bocquet, L., and Barrat, J.-L., 2007, “Flow Boundary Conditions From Nano- to Micro-Scales,” Soft Matter, 3(6), pp. 685–693. [CrossRef]
Martini, A., Hsu, H., Patankar, N., and Lichter, S., 2008, “Slip at High Shear Rates,” Phys. Rev. Lett., 100(20), p. 206001. [CrossRef] [PubMed]
Priezjev, N., 2007, “Rate-Dependent Slip Boundary Conditions for Simple Fluids,” Phys. Rev. E, 75(5), p. 051605. [CrossRef]
Bridgman, P., 1926, “The Effect of Pressure on the Viscosity of Forty-Three Pure Liquids,” Proc. Am. Acad. Art Sci., 61(3), pp. 57–99. [CrossRef]
Cauldwell, D., Trusler, J., Vesovic, V., and Wakeham, W., 2009, “Viscosity and Density of Five Hydrocarbon Liquids at Pressures up to 200 MPa and Temperatures up to 473 K,” J. Chem. Eng. Data, 54(2), pp. 359–366. [CrossRef]
Berro, H., Fillot, N., and Vergne, P., 2010, “Hybrid Diffusion: An Efficient Method for Kinetic Temperature Calculation in Molecular Dynamics Simulations of Confined Lubricant Films,” Tribol. Lett., 37(1), pp. 1–13. [CrossRef]
Cento, P., and Dareing, D., 1999, “Ceramic Materials in Hybrid Ball Bearings,” Tribol. Trans., 42(4), pp. 707–714. [CrossRef]
Habchi, W., Eyheramendy, D., Vergne, P., and Morales-Espejel, G., 2012, “Stabilized Fully-Coupled Finite Elements for Elastohydrodynamic Lubrication Problems,” Adv. Eng. Softw., 46(1), pp. 4–18. [CrossRef]
Reynolds, O., 1886, “On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, 177, pp. 157–234. [CrossRef]
Habchi, W., Eyheramendy, D., Vergne, P., and Morales-Espejel, G., 2008, “A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem,” ASME J. Tribol., 130(2), p. 021501. [CrossRef]
Dowson, D., and Higginson, G., 1966, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication, Pergamon Press, Oxford, p. 80.
Roelands, C., 1966, “Correlational Aspects of the Viscosity–Temperature–Pressure Relationship of Lubricating Oil,” Ph.D. thesis, Techische Hogeschool Delft, Delft, The Netherlands. Available at: http://repository.tudelft.nl/view/ir/uuid%3A1fb56839-9589-4ffb-98aa-4a20968d1f90/
Szeri, A., 2005, Fluid Film Lubrication: Theory and Design, Cambridge University Press, Cambridge, pp. 73–80.


Grahic Jump Location
Fig. 1

Snapshot of a MD system featuring a hybrid interface. In this reference configuration, n-octane is confined between ferrite and silicon nitride walls under typical EHD operating conditions (u2 = −u1 = 1 m/s, P = 1 GPa).

Grahic Jump Location
Fig. 2

Velocity profile across a n-octane film confined between an upper Si3N4 and a lower Fe surfaces under typical EHD operating conditions. The imposed wall speeds u1 = −1 m/s and u2 = 1 m/s along the x-direction are represented by the blue arrows, whereas the fluid velocity is shown by the gray dots. P = 1 GPa, h = 5 nm, and Twall = 303 K.

Grahic Jump Location
Fig. 3

Dependence of the dimensionless slip length Ls/Ls,ref with the wall speeds difference Δu. α-Fe [110] and Si3N4 [001] surfaces, n-octane, P = 1 GPa, h = 5 nm, and Twall = 303 K.

Grahic Jump Location
Fig. 5

Dependence of the dimensionless slip parameter s (a) and slip length Ls/Ls,ref, and (b) with pressure P. α-Fe [110] and Si3N4 [001] surfaces, n-octane, Δu = 2 m/s, h = 5 nm, and Twall = 303 K.

Grahic Jump Location
Fig. 4

Dependence of the dimensionless slip parameter s (a) and slip length Ls/Ls,ref, and (b) with the inverse of the film thickness 1/h. α-Fe [110] and Si3N4 [001] surfaces, n-octane, Δu = 2 m/s, P = 1 GPa, and Twall = 303 K.

Grahic Jump Location
Fig. 7

Viscosity increase with the film thickness for confined n-octane in comparison with the bulk viscosity value. α-Fe [110] and Si3N4 [001] surfaces, Δu = 2 m/s, P = 1 GPa, and Twall = 303 K.

Grahic Jump Location
Fig. 6

Combined dependence of the dimensionless slip length Ls/Ls,ref with the operating conditions. (a) Wall velocity difference Δu and inverse of film thickness (1/h). (b) Wall velocity difference Δu and pressure P. (c) Inverse of film thickness (1/h) and pressure P.

Grahic Jump Location
Fig. 8

Schematic representation of the EHD contact geometry. (a) Line contact between a plane and a cylinder. (b) Equivalent formulation for the numerical resolution.

Grahic Jump Location
Fig. 9

Flow chart of the multiscale approach for the coupling of nanoscale and macroscopic models

Grahic Jump Location
Fig. 10

Film thickness (a) and pressure (b) distributions from the nano-to-EHL approach compared to the classical no-slip solution, for the hybrid contact in a pure rolling configuration

Grahic Jump Location
Fig. 11

Velocity profiles at the contact inlet (a) and center (b) for the steel–ceramic hybrid contact at SRR = 0: nano-to-EHL model with slip on the lower wall (solid curves) compared to the classical no-slip solution (dashed curves)

Grahic Jump Location
Fig. 12

Film thickness dependence on the SRR for the hybrid contact. Variations in h are observed for the nano-to-EHL model with slip, in contrast with the standard no-slip Reynolds solution where the film thickness is independent on SRR.

Grahic Jump Location
Fig. 13

Velocity profiles at the inlet and center of the hybrid contact for the nano-to-EHL model with slip compared to the classical no-slip solution. (a) and (b) SRR = 2: the lower (slipping) wall is stationary. (c) and (d) SRR = −2: the upper (nonslipping) wall is immobile.

Grahic Jump Location
Fig. 14

Mass flow of the lubricant as a function of the SRR in an hybrid contact. Comparison between the nano-to-EHL model with slip on the lower wall with the standard no-slip Reynolds solution.

Grahic Jump Location
Fig. 15

Friction coefficient as a function of the SRR in an hybrid contact. Comparison between the nano-to-EHL model with slip on the lower wall and standard no-slip Reynolds solution.



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