Revision 1 - Tribology in Mechanical Engineering - Fall 2010

8/8/2019 Revision 1 - Tribology in Mechanical Engineering - Fall 2010

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Revision1TribologyinMechanicalEngineering(MAE493N/593T)Fall2010KonstantinosA.Sierros([email protected])

Contents1. Introduction

1.1Definitionoftribology1.2Historyoftribology1.3Bearingsandlubricants

2. Surfaces2.1Surfaceparameters2.2Examinationofsurfaces2.3Statisticalnatureofsurfaces2.4Statisticaltreatmentofsurfaces2.5Metallicsurfaces2.6

Tribologyandsurfaceengineering2.7Surfacetreatments

3. Contactbetweensurfaces3.1 Introduction

3.2 Singleasperitydeformationmodel

3.3Multipleasperitycontact

3.4Hertziancontacts

3.5Nonconformingsurfacesincontact

3.6 Surfaceandsubsurfacestresses

3.7Experimentalmeasurementsofcontact

3.8Elastoplasticcontact

4. Furtherreading
mailto:[email protected]:[email protected]


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1. Introduction1.1DefinitionoftribologyOnepossibledefinitionoftribologycanbegivenasfollows;Tribologyisthescienceandtechnology

studyingtheinteractionofsurfaceswhichareincontactandmovingrelativelytoeachother.Tribology

isaveryoldsubject,aswewillseelaterinsection1.2,dealingwithfriction,wearandlubrication.Wear

isthedamagetooneorbothsurfaces,involvedintherelativemotion,involvinginmostcases

progressivelossofmaterial.Frictionistheresistanceencounteredbyonebodyinmovingoverthe

other.Finally,lubricationistheactiontakentoreducethefrictionalforcebetweensurfacesbyusing

lubricants.

However,itwasnotuntil1966whenProf.PeterJostcoinedthewordtribologyinhisfamousJost

report.TribologyistheproductoftheGreekwords and . meansrubbingand

meansstudy.Theconceptcouldbealsocalledtriboscienceandtribotechnology.

1.2HistoryoftribologyTribologicalactivityisalreadyobserved5000yearsagoinMesopotamia(currentlytheregioncovering

Iraq)werewheeledcarriageswereusedoften.Thedevelopmentofsuchcarriagesinvolvedbearing

designanddevelopment.Bearingsareviewedprimaryastribologicalcomponents. Anotherexampleof

earlytribologicalactivityisshowninFigure1.Astonecolossus(AncientEgypt4000yearsago)ismoved

byEgyptianswiththeaidoflubrication.

Figure1:TransportofEgyptianstonecolossus(4000yearsago).(FromWilliamsEngineeringTribology)Earlytribologicalprogresswasmostlyachievedintheareaofbearings.Lubricatedbronzebearings,used

inwarchariots,weredesignedanddeveloped2400yearsagoinChina.Designanddevelopmentof

pivots,bearingsandprototypemechanicaldevicestookplaceinAncientGreece2000yearsago.The

developmentoflathealsotookplacearoundthistime.ARomanengineerandarchitect,Marcus

VitruviusPolio,workedontheballistaaswellasothertribologicalideas.DuringtheMiddleAgesChina

wasleadingthetechnologicalraceandEuropewasfollowing.Theuseofanimalfatsaslubricantswas

explored.

LeonardodaVinci,Figure2,contributedalotofideasanddesignstothefieldoftribology.He

recognizedtheimportanceoflubricationandhewasalsooneofthefirsttocommentonthreebody

abrasivewear.Hisnotebookswerekeptinaprivatecollectionfor200yearsinhibitingtherapid

developmentofthesubjectatthatstage.


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Duringthe15thcentury,bearingsstartedtoemploymetalsratherthanwoodandstone.Largescale

machinerywasalsodevelopedandtheuseofrollingelementbearingswasintroduced.

Figure2:LeonardodaVinci(AnnoDomini14521519)TheMiddlepartof17thcenturymarkedthebeginningoftheAgeofReason.Thescientificmethodwas

developedalongwiththeformationoftheRoyalSociety(England)andtheAcademieRoyaledes

Sciences(France).Itshouldbementionedthatbytheendofthe17thcenturythelawsoffrictionwere

statedandwestillusethem!

MilestonesinthedevelopmentoflubricationtheoryweresetbyIsaacNewtonandClaudeNavier.The

laterdefinedthecoefficientofviscosityinfluidmotionequations.LeonhardEuler(17071783)provided

thefirstmathematicalapproachtotribologybydefiningandcalculatingthestaticanddynamic

coefficientoffriction.

The18thcenturymarkedthestartoftheindustrialrevolution.Bearingsandtribologicalelementsof

machinesbasedonbrass,steelandtinalloysweredevelopedandused.CharlesCoulombwasthe

pioneerfordevelopingtheoreticalinsightsforexplainingfriction.Hestatedthatthemechanical

interlockingofsurfaceasperitiesisthemechanismresponsibleforcausingfrictionbetweensurfacesin

contactandrelativesliding.Theadhesionanddeformationcomponentsoffrictionwerealsoaddressed.Coulombalsoinvestigatedtheeffectofloadandareaonthefrictionalresistanceforarangeofmaterial

combinations.

Furthermore,lubricationissueswereaddressedduringthe18thcenturybyNikolaiPetrovand

BeauchampTower.Frictionathighvelocitieswasinvestigatedandtheconceptofhydrodynamic

lubricationwasborn.TheoreticalanalysesoflubricatedbearingswereconductedbyOsborneReynolds.

Inaddition,greatadvancementsinthefieldofcontactmechanicstookplaceduringthatperiod.Heinrich

Hertzworkedontheanalysisofdrycontactbetweensurfaces.Heanalyzedthecontactstressesandthe

deformationbetweenelasticsolids.

Duringtheearly19thcenturythefieldsofgasandvapourlubricationwereinitiated.Anumberof

researchersworkedinthisareaincludingSommerfield,Michell,KingsburyandLordRayleigh.Thelate

19thcenturymarkedtheevolutionofbearingdesign.Also,theeffectsofstiffnessandstabilityof

bearingsaswellastheintroductionofboundarylubricationtookplaceduringtheearly20thcentury.

BowdenandTabor(CavendishLab,CambridgeUniversity)workedonthefundamentalmechanismsof

frictionduringthe1950sand1960s.1966wastheyearwhenthewordtribologywascoinedbyProf.Jost

inhisreport.


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Currently,researchintribologyismovingtowardssmallerscalesandsingleasperitycontactcases.

Thereisaneedtounderstandindividualtribologicaleventsatthenanoscale.Thedevelopmentofthe

ScanningTunnelingMicroscope(STM)byBinnigandRohrer(IBMResearchZurich)markedanewera

whichledtoconcentratedresearcheffortsforunderstandingsingleasperitytribologicalcontacts.

1.3BearingsandlubricantsAbearingisadevicewhichpermits2componentsinamechanismtomoverelativetooneanotherin

either1dimensionor2dimensionswhileconstrainingtheirmovementintheremainingdimension(s).

Inpracticemosttribosystemsinvolvebearingsofsomesortoranother.Threetypesofimportant

engineeringbearingsareshowninFigure3below.

Figure3:Threetypesofengineeringbearings:(a)linearbearingcarryinganormalload;(b)journalbearingsustainingaradialload;(c)thrustbearingcarryinganaxialload.(FromWilliamsEngineering

Tribology)

Thereisanumberofbearingsystemsusedtosolvetribologicalproblems.Figure4presentsuchsystems.

Figure4:(a)Dryrubbingbearing;(b)hydrodynamicfluidfilmbearing;(c)hydrostaticfluidfilmbearing;(d)rollingelementbearing;(e)Magnetic/electrostaticbearingand(f)elastomericbasedoscillation

bearing.(FromWilliamsEngineeringTribology)


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Untilthemiddleofthe19thcenturyanimalfatswereusedasthelubricatingmediumbetweenhigh

frictionsurfaces.Then,duetothegrowthofoildrilling,mineraloilsbecameavailableaslubricants.They

aremostlymadefromhydrocarbons(CandHcompounds).Hydrocarbonscanbeparaffinic,naphthenic

andaromatic.Paraffinichydrocarbonscontainnoringstructureswhereasnaphthenicandaromatic

hydrocarbonshaveringstructures.Thedifferencebetweennaphthenicandaromatichydrocarbonsis

thatthelatercontainssingleanddoublebondsbetweenthecarbonandhydrogenatoms.Also,the

aromaticoilscanbefoundinmuchsmallerquantitiesthantheothertwotypes.

Finally,theviscosityofafluidisaveryimportantparameterinlubricationscienceandtechnology.The

dynamicorabsoluteviscosity(n)ofafluidisameasureoftheresistanceitofferstorelativeshearing

motion.

.

=n

(Equation1)

Theshearingforceorabsoluteviscosity(n)isequaltotheratiooftheshearstress()overthevelocitygradient( dot).Thekinematicviscosityisequaltotheratiooftheabsoluteviscocityoverthedensityof

thefluidandisapropertydescribingtheflowduetoselfweightorgravity.

2. Surfaces2.1SurfaceparametersItisknownthatnorealsurfacecanpocessperfectgeometry.Allsurfacesexhibitsurfaceroughnessand

waviness.Surfaceroughnessisdescribedbysurfacevariationswithveryshortwavelengthswereaswavinessisdescribedbyundulationswithrelativelylongwavelengthsinthemmscale.Theroughness

parameterisimportantwhendefiningcontactbetweensurfacessincewhentwosurfacescontacteach

other,thesurfaceasperities(tipsofthesurfaceroughness)mustfirstcarrytheloadasshowninFigure5

below.

Figure5:Twosurfacesincontact.Some

surfaceasperitiesarefirstcarryingtheload.


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2.2ExaminationofsurfacesMicroscopicalmethodsatdifferentscalesareusedinordertoexaminetribologicalsurfaces.Optical

sed.

e

.3StatisticalnatureofsurfacesThereis asinglenumericalparameterthatcanadequatelydescribethegeometryofasurface.The

microscopy(upto1000timesmagnification),scanningelectronmicroscopy(upto300000times

magnification)andtransmissionelectronmicroscopy(upto750000timesmagnification)areallu

Additionally,atomicforcemicroscopyandsurfaceprofilometryareusedextensivelytocharacterizeth

topographyofvarioussurfaces.

2

not

simplestparametersthatdescribesurfacegeometryarecentrelineaverageroughness(Ra)andtheroot

meansquareroughness(Rq).

dxyLR

L1

= 0

(Equation2a) (Equation2b)

quations2andbareshowingtheexpressionsforRaandRq.Listhelengthofthesurfaceprofileandyis

owever,thereisanissuewhenquantifyingsurfacesusingthesurfaceroughnessRa.Theissueisthat

Figure6:(a)RavalueofasurfaceoverasamplinglengthL.Theshadedareasareequal.Bothprofiles(b)

=

L

q dxLR y0

21

E

theheightofthesurfacemeasuredabovethemeanlevel.

H

differenttopographiesmayhavethesameRavalueassowninFigures6band6c.UsingRqcanleadto

quantifyingthesurfacevariationwithgreatersignificance.

and(c)havethesameRavalueof0.64a.(FromWilliamsEngineeringTribology)


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2.4Statisticaltreatmentofsurfaces(z)ofthezaxis.Forrealsurfacesabellshapedcurveis

observedandtheprobabilitydistributionfunctionisdescribedbyaGaussiandistributionwhichdenotes

ineif

ertoattemptto

quantifytheshapeofthedistributioncurve.Momentsinstatisticsareasetofnumbersthatdescribe

(Equation3)

sing s(Sk)ofthesurface.WhenSk=0,thedistributionis

symmetrical.Ifasurfacemodificationprocessstartsremovingthepeaks,thenS


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Takingintoaccountthehorizontaldimension,oneshouldconsiderthenumberofpeaksperunitlength

ofthesurfaceprofileandthenumberofcrossingsperunitlengthwiththemeanmeasurementlevel.

However,boththepeakdensityandthezerocrossingdensityarehighlydependentonthesampling

(Equation4)

Figure7:Someexamplesof theirautocorrelationfunctions.

2.5MetallicsurfacesWhenmetalsurfacesareexposedtoairtheyabsorbO2andH2Ovaporandtheyconsequentlyform

oblemetalssuchasPd,Auandothersarenotveryreactiveandtheyform

monolayerswhichare12atomsthick.Therateofgrowthofmetaloxidefilmsdependsonthe

to

e

interval.Theuseofautocorrelationfunctions, (t),isaimingtowardsincludinginformationonthe

spatialvariationsofsurfaces.

+L

dxxzxL

0

2)()

= L

zt (1

lim1

)(

surfaceprofilestheirdistributionfunctionsand

metaloxidelayer(s).N

crystallographicorientationoftheunderlyingsubstrateandthetemperature.Hightemperatureslead

increasedgrowthratesandroughersurfaces.Someexamplesofmetaloxideformationincludeth


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formationofvariousironoxidesonironsurfacesinatmosphereandtheformationof2ormore

differentlayersofcopperoxidesonacoppersurfaceuponexposuretoair.

Acriticalquestionarisesatthisstage.Ismetaloxideformationbeneficial?Theanswerisyesandno.In

somecasestheyarebeneficialsincetheunderlyingmetalsurfacesbecomepassivatedandfurther

.6Tribologyandsurfaceengineeringomemechanicallyabraded,polishedandmachined.The

formationofaBeilbylayerisobserved.ABeilbylayerisalayerofparentmaterialthatisheavily

ide,

Figure8:Crosssectionofa EngineeringTribology)

technologiesinordertoproduceacompositematerialunattainableineitherthebaseorsurface

icationof

ting

.7Surfacetreatmentsandcoatingsentsandthecoatingdepositionmethodsavailabletothesurface

engineer.

chemicalactivity,suchascorrosion,ininhibited.SuchexamplesincludeAlandTisurfaces.However,insomeothercasesmetaloxidesontopofmetalsurfacesisnotbeneficialbecausetheoxide

microstructureisopenanddoesnotprotecttheunderlyingmetal.Ironoxidesareaprimeexample.

2

Duringsurfaceengineeringsurfacesbec

deformedasaresultofsurfaceengineering.Itmayconsistofasmearedlayerofmetal,ametalox

polishingpowderandotherresidues.

typicalpolishedmetalsurface.(FromWilliams

Surfaceengineeringisdealingwiththeapplicationofbothtraditionalandinnovativesurface

materialsindividually.Surfaceengineeringisdividedintwomainbranches.Thesurfacemodif

anexistingsurfaceandthedepositionofadditionalmaterialintheformofathinlayerontheexis

surface.

2

Table1summarizesthesurfacetreatm


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Table1:Surfacetr neeringTribology)

. Contactbetweensurfaces

sthatareplaneandparalleltoeachotherarebroughttocontacteachother,contact

willinitiallyoccuratonlyfewasperities.Iftheloadisincreased,moreasperitieswillcomeintocontact

p)contactonaflatrigidsurfaceisanidealcasesinceitprovides

asimplegeometricalproblemtoworkon.Itistruethatrealsurfaceasperitieshavebluntsurface

planesurfaceunderaload

w.Theradiusofthecontactcirclewillbeequalto .

eatmentsandoverlaycoatingtechniques.(FromWilliamsEngi

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3.1 IntroductionWhentwosurface

(seeFigure5).Itisnecessarytounderstandthecontactconditionsbetweenasperitiesand

macroscopicallyforunderstandingwearandfrictionmechanisms.

3.2SingleasperitydeformationmodelModelingasingleasperity(roughnessti

profilesandtheirslopesdonotexceed10o.Itisthereforeconvenienttomodelasperitiesasperfectly

smoothsurfaceprotuberanceswithspherical,conicalorpyramidalshape.

Thesimplestscenarioistopressatotallyelasticsphereofradiusronarigid

Figure9:Elasticdeformationofaspherepressedagainstarigidplane.(FromI.HutchingsTribologyofEngineeringMaterials)


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Theareaofcontactbetweentheelasticsphereandtherigidflatisequalto 2.Themeancontact

pressureornormalstressisgivenbyequation5below.

2

wPmean =

(Equation5)

Figure10:Thedistributionofcontactpressureforapurelyelasticsphereloadedagainstarigidflatsurface.

AsshowninFigure10,thedistributionofcontactpressureiszeroattheedgeofthecontactandis

observedtobeamaximumatthecenterofthecontact.

Asthenormalloadincreases,eitherthesphereortheplanewillstartdeformingplastically.Therefore,

therearetwodistinctcases.Thefirstcaseisthatthesphereisrigidandthustheplanewilldeform

plasticallyandthesecondcaseisthattheplaneisrigidandplasticflowwillthereforebeconfinedinthe

sphere.Bothcasesprovidedthattheextentofdeformationisnottoolarge,yieldsimilarresults.Plastic

flowwillstartoccurringatadeptharound0.47 andastheloadincreasesthemeanpressureoverthe

contactareawillbeabout3Y.Yistheuniaxialtensileyieldstressofthesoftmaterial.

3.3MultipleasperitycontactForrealsurfacestheGreenwoodWilliamsontheory(1966)isusedasthebasetheoretical

considerationformultipleasperitycontact.Itassumesthatallcontactingasperitieshavesphericaltips

ofthesameradiusr.Italsoassumesthattheasperitiesdeformelasticallyuponapplicationofaload,

followingHertzianrelations.

Figure11:Contactmodelforaroughsurfaceonasmoothrigidplane(FromI.HutchingsTribologyofEngineeringMaterials)

(Equation6)dzzdzNErWd

)()(3

4 2/32/1

=


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Equation6givestheloadWaccordingtoGreenwoodWilliamsontheory.Nisthetotalnumberof

asperities,EistheYoungsmodulusofthetwomaterials,ristheasperitytipradius,zistheheightofan

individualasperityabovethereferenceplane(seeFigure11),disthedistancebetweenthesmooth

surfaceandthereferenceplaneand (z)isthedistributionfunction(discussedinchapter2).

GreenwoodandWilliamsonderivedthetheoryforpurelyelasticcontactbutalsoincludedcalculationstoallowforpredictingtheonsetofplasticflowatthecontactingasperities.Theproportionofasperity

contactsatwhichplasticflowoccursdependsontheplasticityindex .For 1mostasperitiesaredeformingplasticallyunderlight

loading.

3.4HertziancontactsInHertziancontacts,deformationtakingplaceintheelasticregimeandthereforesmallstrains

dominate.IfviewedfromthemacroscaletheradiiofcurvatureofbodiesinHertziancontactismuch

largerthanthecontactarea.Thesurfacesarenonconformingandtheyarecontinuous.Frictional

effectsarenotconsideredduringHertziancontacts.

3.5NonconformingsurfacesincontactAlongdeformablecylinderincontactwithaflatrigidsurfacecanbeviewedfromthemacroscaleasa

nonconformingcontactgeometry.Theanalysisofsuchasystemcanbeextendedtocaseswhereboth

surfacesarecurvedanddeformablebutstilllonginthe3rddimension.Therearesomeequationsthat

describethistypeofcontact.

Figure12:Adeformablecylinderispressedagainstarigidplane(FromWilliamsEngineeringTribology)AsshowninFigure12,aloadperunitlengthW/Lisappliedandthecenterofthecylindermovesaverticaldistance towardstherigidsurface.Thesizeofthecontactpatch2 needstoberelatedwith

thenormalloadW/Landthegeometryandmaterialpropertiesofthecylinder.Thegaphbetweenthe

twosurfacesisgivenbythefollowingequation7.

(Equation7)

+= zwR

xh

2

2


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Where;wzistheverticaldisplacementofthecylindersurfaceandRistheradiusofthecylinder.

The3dimensionalcaseisthecontactbetweentwodeformablespheresandthecontactpatchisnow

circularinshapeanditsradiusisequalto .

Theverticaldisplacementofeachspherewz1andwz2(Figure13)isgivenbyequations8aand8bforthe

contactregionandforoutsidethecontactregionrespectively.

Figure13:Twopurelyelasticspheresarepressedagainsteachother(FromWilliamsEngineeringTribology)

(Equation8a) (Equation8b)

R

rww zz

2

2

21=+

R

rww zz

2

2

21>+

Where; isthetotalrelativedistanceofapproachofthecentersofthetwospheres,Risequalto

(1/R1+1/R2)andr2isequaltox2+y2.

3.6Surfaceandsubsurfacestresses

Figure14:Lineloadingofanelastichalfspace(FromK.L.JohnsonContactMechanics)


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Asshowninfigure14,thelineloadingofanelasticplaneproducesstressesonthesurfaceandthe

subsurface.Theusualproceduretosolvesuchproblemsistofirstfindthestressesandstrainsinorder

tosatisfytheequilibriumequationsandthecompatibilitycondition.Thenwecanusetheboundary

conditionsandwecanarriveatanalyticalsolutionsbyusingthefiniteelementmethodortheboundary

elementmethod.StressescanbeexpressedinCartesianorPolarcoordinates.

3.7Experimentalmeasurementsofcontact

Figure15:2dimensionalphotoelasticfringepatternsforvariousloadings(FromWilliamsEngineeringTribology)

AsshowninFigure15photoelasticityisagreatexperimentaltoolforvisualizingcontactstressesunder

staticordynamicloading.Contoursofconstantmaximumshearstressareclearlyvisible.

3.8ElastoplasticcontactLoadingbeyondtheelasticlimitbetweenarigidindenterincontactwithadeformingsurfaceisshownin

Figure16.Thesizeandshapeoftheelasticplasticboundaryisnotknownapriori.Withinthecorethe

materialisunderpurehydrostaticcompression.Theelastoplasticzonecanbelocatedfurtheroutfrom

theincompressiblecore.

Figure16:Elasticplasticcontactbetweenarigidindenterpressingagainstadeformingflatsurface(FromWilliamsEngineeringTribology)


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4. FurtherreadingJ.Williams,EngineeringTribology,CambridgeUniversityPress,2005

B.Bhushan&B.K.Gupta,HandbookofTribology,McGrawHill,NewYork,1991

D.Dowson,HistoryofTribology,Longman,London,1979

F.P.Bowden&D.Tabor,TheFrictionandLubricationofSolids,OxfordUniversityPress,PartI,1950and

PartII,1964

I.M.Hutchings,Tribology,EdwardArnold,London,1992

K.L.Johnson,ContactMechanics,CambridgeUniversityPress,1985

TribologyInternational(Journal)

Wear(Journal)

NOTE:NextRevision(no2)willcoverfrictionandwearandtheirrelation

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Revision 1 - Tribology in Mechanical Engineering - Fall 2010