Hydrodynamic Lubrication of Rough Surfaces

87 Pages·2005·1.36 MB·English

by  Fredrik Sahlin

2005:83
LICENTIATE T H E S I S
Hydrodynamic Lubrication
of Rough Surfaces
Fredrik Sahlin
Luleå University of Technology
Department of Applied Physics and Mechanical Engineering
Division of Machine Elements
2005:83|: 02-757|: -c -- 05⁄83 -- 
2005:83
HYDRODYNAMIC LUBRICATION OF
ROUGH SURFACES
FREDRIK SAHLIN
LuleåUniversityofTechnology
DepartmentofAppliedPhysicsandMechanicalEngineering,DivisionofMachineElements
2005:83|ISSN:1402−1757|ISRN:LTU-LIC--05/83--SE
HYDRODYNAMIC LUBRICATION OF ROUGH SURFACES
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ISSN: 1402-1757
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Abstract
Interactingsurfacesarefrequentlyfoundinmechanicalsystemsandcomponents.Alubri-
cantisoftenaddedbetweenthesurfacestoseparatethemfrommechanicalcontactinorder
toincreaselifeandperformanceofthecontactingsurfaces.Inthisworkvariousaspectsof
hydrodynamiclubricationareinvestigatedtheoretically.Thisiswhereinteractingsurfaces
arecompletelyseparatedbyafluidfilmwhichisoftenthedesiredoperatingconditionof
machinecomponentswhenwearandfrictionistobereduced.Differentflowregimescan
beidentifiedwithinthescopeofhydrodynamiclubrication.
Ifthesurfacesareseparatedbyathickfluidfilmtheinfluencefromsurfaceasperitiesis
smallandthesurfacescanbetreatedassmooth.Iftherateofchangeinfilmthicknesswith
respecttothespatialdirectionsissignificantlylargeandiftheflowvelocityorReynolds
numberislarge,theordinaryfluidmechanicalapproachtreatingviscousflowwithCom-
putational Fluid Dynamics (CFD) has to be used. CFD is used to investigate influence
fromtheuseofanartificialmicroscopicsurfacepatternononeofthetwointeractingsur-
faces. Theinfluencefromthepatternisisolatedfromanyotherpressuregeneratingeffects
bykeepingtheinteractingsurfacesparallel. Resultsareshownfordifferentshapesofthe
micro-pattern.IftheReynoldsnumberdecreases,thesystementersaregimecalledStokes
flowwheretheinertiaeffectsareneglected. ThefullCFDapproachiscomparedwiththe
Stokesforvariousphysicalandgeometricalcases.
Ifthechangeinfilmthicknessissmallinthespatialdirections,thethinfilmapproxi-
mationisapplicableandthefullmomentumequationsdescribingfluidflowtogetherwith
the mass continuity equation can be reduced to the Reynolds equation. Depending on
boundaryconditions,lowpressurescanoccuratlocationofexpandingfluidgapleadingto
tensilestressappliedtothelubricant.However,arealliquidlubricantcanonlyresistsmall
tensilestressesuntilitcavitatesintoamixtureofgasandliquid. Thisoftenhappensclose
to atmospheric pressure due to contamination and dissolved air into the liquid and oc-
cursathigherpressuresthantheactualvaporization. Toavoidpressuresreachingtoolow
levels, a general cavitation algorithm applied to the Reynolds equation is presented that
accommodatesforanarbitrarydensity-pressurerelation. Itis nowpossibleto modelthe
compressibilityofthelubricantinsuchawaythatthedensity-pressurerelationisrealistic
throughoutthecontact. Thealgorithmpreservesmasscontinuitywhichisofimportance
wheninter-asperitycavitationofroughsurfacesisconsidered.
For small film thicknesses the surface roughness becomes important in the perfor-
manceofthelubricatedcontact. Eventhesmoothestofrealsurfacesisroughatamicro-
scopiclevelandwillinfluencethecontactcondition. TheReynoldsequationstillapplies
since the heights of the surface asperities are small compared to the spatial elongation.
Treatmentoftheroughnessofarealsurfaceinadeterministicfashionishoweverbeyond
i
the scope of today’scomputers. Thereforeotherapproachesneedto be employedin or-
dertotakethesurfaceroughnessintoaccount. Inthisworkahomogenizationmethodis
used where the governingequation of the flow condition is formulatedwith a two-scale
expansion, the global geometry and the roughness. Solutions are achieved for the limit
oftheroughnesswavelength,ε→0andthemethodrendersapossibilitytotreatthetwo
scalesseparately. Amethodtogeneratedimensionlessflowfactorscompensatingforthe
surfaceroughnessisdeveloped.Theflowfactors,oncesolvedforaparticularsurface,can
be used to compensate for the surface roughness in any smooth global problem for any
filmthickness.
Acknowledgments
ForthesupportandencouragementintheworkincludedinthisthesisIthankmysupervi-
sors,AssociateProfessorSergeiGlavatskihandProfessorRolandLarssonattheDivision
ofMachineElement.Theyprovidegreatknowledgeandexperienceinthefieldwhichhas
beenofgreatvaluefortheresultspresentedhere.Ialsosendmygratitudetoallthepeople
attheDivisionofMachineElementforprovidingastimulatingresearchenvironment,and
totherestofthepeopleatLuleåUniversityofTechnologywhoinvariouswayshelped.
SpecialthanksgoestomyformerroommateDr.TorbjörnAlmqvistforhisenthusiastic
helpinthe firstperiodofmyPh.D.studies. A secondspecialthanksgoesto mypresent
roommateTech. Lic. AndreasAlmqvistfortheinvaluablescientific discussionsandall
collaborativeresearchwork. Iamtrulygratefulforhisinspiringideasandhispositivity.
A third special thanks goes to Mr. Pär Marklund for all constructive discussions and
collaborationincourses.
Finally I wantto thankmy family and friendswho supportme in upsand downson
theroad.
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Appended Papers
[A] F. Sahlin, S. B. Glavatskih, T. Almqvist, and R. Larsson. Two-dimensional cfd-
analysisof micro-patternedsurfacesin hydrodynamiclubrication. JournalofTri-
bology,127(1):96–102,Jan2005.
[B] F.Sahlin,A.Almqvist,R.Larsson,andS.B.Glavatskih. Acavitationalgorithmfor
arbitrarylubricantcompressibility. SubmittedforpublicationinTribologyInterna-
tional,2005.
[C] F. Sahlin, A. Almqvist, R. Larsson, and S. B. Glavatskih. Rough Surface Flow
FactorsinFullFilmLubricationbasedonaHomogenizationTechnique. Submitted
forpublicationinTribologyInternational,2005.
Additional Papers
[1] A. Almqvist, F. Sahlin, R. Larsson, and S. Glavatskih. On the dry elasto-plastic
contactof nominallyflat surfaces. In Nordtrib 2004, volume11, pages753–762,
Tromso,Harstad,Hurtigruten,Norway,Jun2004.
[2] A. Almqvist, F. Sahlin, and R. Larsson. An abbot curve based surface contact
mechanics approach. In World Tribology Congress III, Washington, D.C., USA,
Sep2005.

Contents
1 Introduction 1
2 HydrodynamicLubrication 5
3 ResearchObjectives 9
4 SummaryofAppendedPapers 11
5 Conclusions 13
6 FutureWork 15
Appendix 17
A FluidFlowEquations 17
A.1 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
A.2 ConservationofMomentum . . . . . . . . . . . . . . . . . . . . . . . . 18
A.3 Navier-StokesEquations . . . . . . . . . . . . . . . . . . . . . . . . . . 18
A.4 StokesEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
A.5 ReynoldsEquation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Papers 23
A 23
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
A.2 CFD-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.3 ResultsandDiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
A.3.1 AdvectiveInfluence . . . . . . . . . . . . . . . . . . . . . . . . 28
A.3.2 PressureDistribution . . . . . . . . . . . . . . . . . . . . . . . . 30
A.3.3 Streamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
A.3.4 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
A.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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