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A Film Thickness Correction Formula for Double-Newtonian Shear-Thinning in Rolling EHL Circular Contacts

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Abstract

Lubricants which contain a polymeric thickener will often display a second Newtonian plateau in measured flow curves. Like other manifestations of shear-dependent viscosity, this shear response will lead to an inaccurate prediction when the classical film-thickness formulas are employed. A correction formula has been developed from numerical experiments for a range of parameters of the double-Newtonian modified Carreau equation. The parameters of this shear-thinning model were selected from measurements for real lubricants obtained in Couette viscometers and a capillary viscometer. In addition, a full EHL film thickness formula has been derived from the same numerical experiments. The correction formula and the full formula were successfully validated using published film thickness data and published viscosity data for an EHL reference liquid, a polymer solution. Clearly, viscometer measurements of shear-dependent viscosity which contain the inflection leading to the second Newtonian are essential for a film-thickness calculation when a high-molecular-weight component of the lubricant is present.

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Abbreviations

a, b, A, B, C :

Parameters for correction formulas

c :

Weight fraction of polymer

E :

Combined elastic modulus of the rollers

F :

Load

G :

Effective liquid shear modulus associated with rotational relaxation time

h :

Film thickness

\( h_{\text{cNewt}} \) :

Newtonian solution for central film thickness

h 0 :

Rigid body separation

H, M, L :

Blok dimensionless parameters

n :

Power-law exponent

\( M_{\text{W}} \) :

Molecular weight of polymer

p :

Pressure

R g :

Universal gas constant

T :

Temperature

U :

Surface velocity

α :

Reciprocal asymptotic isoviscous pressure coefficient

\( \dot{\gamma } \) :

Shear rate

δ :

Equivalent elastic deformation

Γ :

Inlet Weissenberg number

η :

Generalized (non-Newtonian) viscosity

μ :

Low shear (first Newtonian) viscosity

μ 0 :

Ambient pressure, low shear viscosity

μ 2 :

Second Newtonian viscosity

ρ :

Mass density

τ :

Shear stress

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Acknowledgments

This work was partially supported by the Lubrizol Corporation and by the Center for Compact and Efficient Fluid Power, a National Science Foundation Engineering Research Center funded under cooperative agreement number EEC-0540834. The first author wishes to thank the Council for International Exchange of Scholars (CIES) and the Fullbright commission for funding his visiting scholar program at the Georgia Institute of Technology.

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Authors and Affiliations

  1. Department of Industrial & Mechanical Engineering, Lebanese American University, Byblos, Lebanon

    W. Habchi

  2. G.W. Woodruff School of Mechanical Engineering, Center for High Pressure Rheology, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    W. Habchi & S. Bair

  3. The Lubrizol Corporation, Wickliffe, OH, 44092, USA

    F. Qureshi & M. Covitch

Authors
  1. W. Habchi
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  2. S. Bair
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  3. F. Qureshi
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  4. M. Covitch
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Correspondence to S. Bair.

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At the time this work was done, the first author was holding a visiting scholar position at Georgia Institute of Technology.

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Habchi, W., Bair, S., Qureshi, F. et al. A Film Thickness Correction Formula for Double-Newtonian Shear-Thinning in Rolling EHL Circular Contacts. Tribol Lett 50, 59–66 (2013). https://doi.org/10.1007/s11249-012-0078-6

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