, Volume 4, Issue 4, pp 369–379 | Cite as

On the relevance of analytical film thickness EHD equations for isothermal point contacts: Qualitative or quantitative predictions?

  • Jean-David Wheeler
  • Philippe Vergne
  • Nicolas Fillot
  • David Philippon
Open Access
Research Article


Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues. As they rely upon a full separation of the moving surfaces by a thin (or very thin) fluid film, the knowledge of its thickness is of paramount importance, as for instance to developing lubricated mechanisms with long lasting and efficient designs. As a consequence, a large collection of formulae for point contacts have been proposed in the last 40 years. However, their accuracy and validity have rarely been investigated. The purpose of this paper is to offer an evaluation of the most widespread analytical formulae and to define whether they can be used as qualitative or quantitative predictions. The methodology is based on comparisons with a numerical model for two configurations, circular and elliptical, considering both central and minimum film thicknesses.


thin film lubrication elastohydrodynamic lubrication (EHL) film thickness prediction EHD analytical equation central film thickness minimum film thickness circular contacts elliptical contacts 



contact length or dimension in the entrainment direction (m)


contact width or dimension perpendicular to the entrainment direction (m)


ratio of reduced radii of curvature, D = Rx / Ry

E1, E2

Young modulii of solids 1 and 2 (Pa)


reduced modulus of elasticity (Pa) 2/E′=(1+v 1 2 )/E1+(1+v 2 2 )/E2


dimensionless material parameter (Hamrock & Dowson) α * ·E′


central film thickness (m)


minimum film thickness (m)


ellipticity ratio = \(\frac{b}{a}\)


dimensionless material parameter (Moes) = G·(2U)0.25


dimensionless load parameter (Moes) for point contact = W / (2U)0.75


Hertzian pressure (MPa)


reduced radius of curvature in the entrainment direction (m)


reduced radius of curvature perpendicular to the entrainment direction (m)


inlet temperature (K)


mean entrainment velocity (m/s) =(u1 + u2 ) / 2

u1, u2

velocity in the x-direction of surfaces 1 and 2 (m/s)


dimensionless speed parameter (Hamrock & Dowson)=μ·ue /(E′·Rx)


normal load (N)


dimensionless load parameter (Hamrock & Dowson) = w/(E′·Rx2)


reciprocal asymptotic isoviscous pressure, according to Blok [21] (Pa-1)


lubricant dynamic viscosity (Pa·s)


lubricant dynamic viscosity (Pa·s) at the inlet temperature T0


lubricant density (kg·m-3) at the inlet temperature T0


composite roughness of the mating surfaces (m)



This work was partly financed by SKF in the framework of the global program “Advanced Bearing Lubrication”.


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Authors and Affiliations

  • Jean-David Wheeler
    • 1
  • Philippe Vergne
    • 1
  • Nicolas Fillot
    • 1
  • David Philippon
    • 1
  1. 1.Univ Lyon, INSA Lyon, CNRS, LaMCoS-UMR5259VilleurbanneFrance

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