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An Interfacial Friction Law for a Circular EHL Contact Under Free Sliding Oscillating Motion

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Abstract

The friction response of a lubricated interface under free sliding oscillating motion is investigated as a function of the contact pressure and the rheology of the lubricant in terms of viscosity and piezoviscosity. For loaded contacts, both velocity dependent friction, referred to as viscous damping, and friction independent of the instantaneous sliding velocity contribute to the energy dissipation. Viscous damping mainly corresponds to the dissipation in the lubricant meniscus surrounding the contact, while dissipation within the confined lubricated interface is mainly independent of the instantaneous sliding velocity. The friction coefficient independent of the instantaneous sliding velocity falls on a master curve for the wide range of tested operating conditions and lubricant rheological properties. The master curve is a logarithmic function of a dimensionless parameter corresponding to the ratio of the viscosity of the confined lubricant to the product of the pressure and a characteristic time. The physical meaning of this latter and the friction law are discussed considering the confined interface as a viscoelastic fluid or a non-Newtonian Eyring fluid.

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Abbreviations

a :

Radius of the contact area

c 0 :

Viscous damping coefficient without contact

h c :

Central film thickness

k :

Spring stiffness

m :

Moving mass

t c :

Characteristic time

x(t):

Displacement response

x max :

Initial displacement

E′:

Reduced Young’s modulus

E(t):

Energy decay

E i(t):

Energy dissipated by friction independent of the instantaneous sliding velocity

E v(t):

Energy dissipated by viscous friction

F n :

Applied normal force

M :

Dimensionless load parameter

P :

Mean contact pressure

P max :

Maximum contact pressure

R x :

Reduced radius of curvature

S :

Slide to roll ratio

\(\bar{U}\) :

Dimensionless velocity

U e :

Entraining velocity

U s :

Sliding velocity

α :

Piezoviscous coefficient

\(\bar{\alpha }\) :

Dimensionless piezoviscous coefficient

\(\dot{\gamma }\) :

Mean shear rate

\(\dot{\gamma }_{\text{E}}\) :

Effective shear rate

η 0 :

Dynamic viscosity at ambient pressure

η(P):

Dynamic viscosity under contact pressure

\(\bar{\eta }\) :

Dimensionless viscosity

μ :

Overall friction coefficient

\(\bar{\mu }\) :

Dimensionless sliding friction coefficient

μ k :

Friction coefficient independent of the instantaneous sliding velocity

τ :

Interfacial shear stress

τ 0 :

Eyring stress

\(\bar{\tau }_{\text{c}}\) :

Dimensionless shear stress in the centre of the contact

ζ :

Overall equivalent viscous damping coefficient

ζ 0 :

Equivalent viscous damping coefficient without contact

ζ k :

Equivalent viscous damping coefficient

Δ :

Energy decay curve error

Ω :

Circular natural frequency

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Acknowledgments

The authors would like to thank Dr F. Brémond for helpful discussions. They are indebted to the institute Carnot Ingénierie@Lyon (I@L) for its support and funding.

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Authors and Affiliations

  1. Laboratoire de Tribologie et Dynamique des Systèmes, UMR CNRS 5513, Ecole Centrale de Lyon, Université de Lyon, 36, avenue Guy de Collongue, 69134, Ecully Cedex, France

    E. Rigaud, D. Mazuyer & J. Cayer-Barrioz

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  1. E. Rigaud
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  2. D. Mazuyer
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  3. J. Cayer-Barrioz
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Correspondence to E. Rigaud.

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Rigaud, E., Mazuyer, D. & Cayer-Barrioz, J. An Interfacial Friction Law for a Circular EHL Contact Under Free Sliding Oscillating Motion. Tribol Lett 51, 419–430 (2013). https://doi.org/10.1007/s11249-013-0177-z

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