Tribology Letters

, Volume 49, Issue 1, pp 227–238

An Advanced Rough Surface Continuum-Based Contact and Sliding Model in the Presence of Molecularly Thin Lubricant

Original Paper

Abstract

A model of molecularly thin lubricant layer behavior for rough, sliding contact is presented in this work as a function of lubricant layer morphology. Building on previous work by the authors where the lubricant layer was assumed to be uniform in thickness and morphology, lubricant contributions to contact are presently treated at the asperity level and the effects of lubricant bonding ratio and coverage are accounted for. Effective stiffnesses for lubricated asperities are used to calculate the bearing and shear forces, while variable surface energy is modeled at the asperity level and used within an improved continuum adhesive formulation. Contributions from asperities in lubricant and solid contact for partial coverage are determined within the context of a statistical mechanics model. The proposed model can be used to study the mixed nanolubrication regime expected during light contact or “surfing” recording in magnetic storage, where sustained nanolubricant contact would partially deplete mobile molecules from the contact interface.

Keywords

Nanotribology Magnetic data storage Roughness effects Adhesion Boundary lubrication friction 

List of Symbols

An

Nominal area of contact

BR

Bonding ratio

C

Coverage ratio

c1,2,3

Surface energy fitting coefficients

d

Mean plane separation (asperity heights)

d0

Liquid gap = h0 − κ

E, E1,2

Young’s modulus of solid substrates

Fs

Total adhesive force

Fs,lube

Adhesive force in lubricant

Fs,nc

Non-contact adhesive force

H

Hardness

h

Mean plane separation (surface heights)

h0

Solid–solid gap

K

Maximum contact pressure factor

kc

Solid contact stiffness

kfr

Solid frictional stiffness

klateral

Total lateral (frictional) stiffness

knormal

Total normal (contact) stiffness

kP

Bearing (normal) stiffness

kQ

Shear stiffness

m0,2,4

Spectral moments

mP

Bearing force curve-fitting coefficient

N

Number of asperities

nQ

Shear force curve-fitting coefficient

P

Total contact force

P0

Maximum experimental bearing force

Plube

Bearing force

Q

Total frictional force

Q0

Maximum experimental shear force

Qlube

Lubricant shear force

R, R1,2

Mean radius of asperity

SL

Logistic function switch

t

Total average lubricant thickness

tm

Mobile lubricant thickness

U

Shearing (sliding) velocity

x

Lateral direction (along slider motion)

z

Asperity height

\( \dot{\gamma } \)

Shear rate

Δγ

Surface free energy

ε

Equilibrium spacing

η, η1,2

Areal density of asperities

κ

Minimum liquid gap

λ

Coverage cutoff distance factor

ν, ν1,2

Poisson ratio

Π

Disjoining pressure

σ, σ1,2

RMS roughness of asperity heights

σs

RMS roughness of surface heights

φ

Gaussian distribution PDF

φL

PDF of lubricant-contacting asperities

φNC

PDF of non-contacting asperities

ω

Interference = zdε

ωc

Critical interference

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of CyprusNicosiaCyprus
  2. 2.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of Mechanical EngineeringKhalifa University of Science Technology and ResearchAbu DhabiUAE

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