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Thermal Elastohydrodynamic Lubrication of Point Contacts Using a Newtonian/Generalized Newtonian Lubricant

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Abstract

The classical ElastoHydroDynamic (EHD) theory assumes a Newtonian lubricant and an isothermal operating regime. In reality, lubricating oils do not behave as perfect Newtonian fluids. Moreover, in most operating conditions of an engineering system, especially at high speeds, thermal effects are important and temperature can no longer be considered as constant throughout the system. This is one reason why there has always been a gap between numerical results and experimental data. This paper aims to show that this gap can be reduced by taking into consideration the heat generation that takes place in the contact and using appropriate rheological models. For this, a unique thermal ElastoHydrodynamic lubrication model is developed for both Newtonian and non-Newtonian lubricants. Pressure, film thickness and traction results are then compared to their equivalent isothermal results and experimental data. The agreement between thermal calculations and experiments reveals the necessity of considering thermal effects in EHD models.

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Abbreviations

ρ :

Lubricant’s density

η :

Generalized Newtonian viscosity

μ :

Newtonian viscosity

H :

Film thickness

p :

Pressure

p h :

Hertzian contact pressure

a :

Hertzian contact radius

x,y,z :

Space coordinates

U m :

Mean entrainment velocity

U :

Elastic displacement vector (U = {u, v, w})

L :

Load

u i :

Surface velocity of body i

u f, v f :

Fluid flow velocity components in the x- and y-directions, respectively

h 0 :

Film thickness equation constant

R :

Ball’s radius

σ:

Stress tensor

ɛ:

Strain tensor

C :

Compliance matrix

T :

Temperature

T 0 :

Ambient temperature

T R :

Reference temperature

c i :

Heat capacity of body i

ρ i :

Density of body i

k i :

Thermal conductivity of body i

E i :

Young’s modulus of body i

υ i :

Poisson’s ratio of body i

x in :

Inlet abscissa of the contact

p + :

Positive part of the pressure distribution

μ 0 :

Lubricant’s zero pressure Newtonian viscosity

ρ 0 :

Lubricant’s zero pressure density

SRR:

Slide-to-roll ratio = 2(u s  − u p )/(u s  + u p ) 

H c :

Central film thickness

H min :

Minimum film thickness

\(H_{c_{\rm min}}\) :

Minimum film thickness on the central line of the contact in the x-direction

K 0,K ′0 ,B,R 0 :

Tait-Doolittle model constants

G c,n c :

Carreau equation constants

μ1,μ2 :

Low-shear and high-shear limiting viscosities, respectively

β K ,ɛ c ,a V :

Tait-Doolittle model constants

DT :

Temperature variation = T−T 0

M, L :

Dimensionless Moes–Venner parameters \( \begin{array}{l} P=\frac{p}{p_{\rm h}}\quad \bar{{\rho}}=\frac{\rho}{\rho_0} \quad \bar{{\mu}}=\frac{\mu }{\mu _0 }\quad H=\frac{hR}{a^{2}}\\ X=\frac{x}{a}\quad Y=\frac{y}{a}\quad Z=\left\{ {\begin{array}{l} \frac{z}{a}\hbox{:Solids p and s}\\ \frac{z}{h}\hbox{:Lubricant}\\ \end{array}} \right.\\ \end{array} \)

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Acknowledgements

The authors thank Prof. E. Ioannides (SKF Group Technical Director) for his kind permission to publish this work. They also wish to express their gratitude to the French Ministry of National Education and Scientific Research for partially financing this study.

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Authors and Affiliations

  1. LaMCoS, INSA-Lyon, CNRS UMR5259, Lyon, 69621, France

    W. Habchi, D. Eyheramendy & P. Vergne

  2. Ecole Centrale Marseille, Laboratoire de Mécanique et d’Acoustique, 13451, Marseille Cedex 20, France

    D. Eyheramendy

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

    S. Bair

  4. SKF Engineering and Research Center, Nieuwegein, The Netherlands

    G. Morales-Espejel

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  1. W. Habchi
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  2. D. Eyheramendy
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  4. P. Vergne
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Correspondence to W. Habchi.

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Habchi, W., Eyheramendy, D., Bair, S. et al. Thermal Elastohydrodynamic Lubrication of Point Contacts Using a Newtonian/Generalized Newtonian Lubricant. Tribol Lett 30, 41–52 (2008). https://doi.org/10.1007/s11249-008-9310-9

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