Tribology Letters

, 64:44 | Cite as

Transition Between Mixed Lubrication and Elastohydrodynamic Lubrication with Randomly Rough Surfaces

  • Julien Bonaventure
  • Juliette Cayer-Barrioz
  • Denis Mazuyer
Original Paper
First Online:
Received:
Accepted:

Abstract

We are interested in understanding the effect of roughness on friction in mixed lubrication (ML) and elastohydrodynamic lubrication (EHL), notably in the case of realistic surfaces. Rolling–sliding experiments in piezoviscous base oil are conducted between rough steels obtained with different machining, polishing and coating processes in order to represent realistic surface conditions found typically in a car engine. The Reynolds number based on the maximum lubricant film thickness in our experiments is below \(R_{e}=4\cdot 10^{-3}\). Our experiments at moderate pressure (\({<}1\) GPa) and speeds (mm/s \(\rightarrow\) m/s) allow to reach EHL for all surface roughnesses which range from the nanometre up to the micron. These surfaces have a complex and multi-scale texture and require a statistical description. Using the most raw and simple filter on large topographic measurements, we correlate the most probable standard deviation of surfaces to friction during Stribeck experiments occuring both in ML and EHL without measurable wear. In order to predict the conditions leading to high friction in ML, we propose a friction-based definition of ML and describe the role played by pressure and roughness on the onset of ML.

Keywords

Friction Lubrication regimes Random roughness Stribeck Transition 

Abbreviations

\(a_H\)

Hertz contact radius (m)

BL

Boundary lubrication

\({\mathrm{d}}x\)

Interferometer sampling interval (x and y) (m)

\(E_{1,\,2}\)

Elastic moduli of the solid bodies (Pa)

EHD, L

Elastohydrodynamic, ‘-’ lubrication

\(F_f\)

Friction force (N)

\(F_{f\,{\mathrm{Couette}}}\)

Couette friction force (N)

\(F_n\)

Load (N)

h

Film thickness spatial distribution (m)

\(h_c\)

Central film thickness (m)

\(K_{l}\)

Lub. thermal conductivity (W/(m.K))

lub.

Lubricant

\(L_w\), L

Moving window size, cut-off length (m)

ML

Mixed lubrication

p

Pressure spatial distribution (Pa)

\(\bar{P}\)

Mean contact pressure (Pa)

\(R_e\)

Reynolds number \(U_{\mathrm{e}}\, h \, \rho /\eta\)

\(R_{x}\)

Reduced curvature in the rolling direction (m)

t

Time (s)

\(S_q\)

Standard deviation (3D) (m)

\(S_q^{L_w}(x,y)\)

Local standard deviation (m)

\(S_{q\;(L_w)}\)

The most probable value of \(S_q^{L_w}\) (m)

SRR

Slide-to-roll ratio \(u_s/u_{\mathrm{e}}\)

T

Room temperature (\(^{\circ }\) C)

\(u_{b,\,d}\)

Surface speeds (ball and disc) (m/s)

\(u_{\mathrm{e}}\)

Entrainment speed \((u_b+u_d)/2\) (m/s)

\(u_s\)

Sliding speed \(u_b-u_d\) (m/s)

x, y, z

Spatial coordinates (m)

\(\alpha\)

Pressure viscosity coefficient (\({\mathrm {Pa^{-1}}}\))

\(\eta\)

Viscosity inside the contact (Pa.s)

\(\eta _0\)

Inlet viscosity (Pa.s)

\(\dot{\gamma }\)

Shear rate (\({\mathrm {s^{-1}}}\))

\(\nu _{1,\,2}\)

Poisson ratios of the solid bodies

\(\rho\)

Lub. gravity (\({\mathrm {kg.m^{-3}}}\))

\(\sigma _{1,\; 2}\)

Generic standard deviation of surface \(1,\; 2\) (m)

\(\sigma _c\)

Composite standard deviation (m)

\(\tau\)

Mean Couette shear stress \(F_{f\,{\mathrm{Couette}}}/\pi a_H^2\) (Pa)

\(\tau _{\mathrm{visq}}\)

Lub. viscous shear stress (Pa)

\(\varDelta T\)

Temperature increase (\(^{\circ }\)C)

\(\nabla _{xy}\)

2D gradient operator \(\left[ \frac{\partial \;}{\partial x} \; \frac{\partial \;}{\partial y} \right]\)

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Notes

Acknowledgments

This work benefits from financial funding of DGCIS via the project GMPDLC\(^2\) and from the Région Auvergne Rhône-Alpes. The authors thank Dr. Anthony Chavanne (IREIS) for providing surfaces used in this work.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Laboratoire de Tribologie et Dynamique des SystèmesÉcully CedexFrance

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