revision 1 - tribology in mechanical engineering - fall 2010
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Revision1TribologyinMechanicalEngineering(MAE493N/593T)Fall2010KonstantinosA.Sierros(kostas.sierros@mail.wvu.edu)
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:kostas.sierros@mail.wvu.edumailto:kostas.sierros@mail.wvu.edu -
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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
3
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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