BiotribologyofNaturaland Arti fi cialJoints
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ReducingWearThroughMaterial SelectionandGeometricDesignwith ActualLubricationMode
TeruoMurakami
ProfessorEmeritus,KyushuUniversity,Japan
Elsevier
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5Biotribologyofarti ficialjointswithartificialcartilage209
5.1Effectivenessofcompliantartificialcartilage
5.2Effectivenessofhydrogelarti ficialcartilage
5.3Roleofbiphasiclubricationinhydrogelartifi cialcartilage
5.4Rolesofboundarylubrication
5.5Influenceofhydrogelweardebris
5.6Bionicdesignwithbiomimeticartificialcartilage
6Biotribologyofregeneratedcartilage263
6.1Medicaltreatmentstorepairfocalchondraldefects
6.2Theinfluenceofmechanicalstimulationonregenerated cartilagetissue
6.3Theinfluenceoftribologicalstimulationonregenerated cartilagetissue
7Summarizationandfuturedirectionsofbiotribologyofhuman andarti ficialjoints279
7.1Biotribologyofhumanandartifi cialjoints
7.2Summarizationofbiotribologyofhumanandartificialjoints
7.3Futuredirectionsofbiotribologyofhumanandartificialjoints
Preface
Justahalf-centuryago, “Biotribology” as “thoseaspectsoftribologyconcernedwith biologicalsystems” wasintroducedbyProf.DowsonandProf.WrightattheConferenceontheRheologyofLubricantsheldinNottinghamin1972(Dowson&Wright, 1973).Biotribologyincludesvariousareas/topicsontribologyinbiologicalsystems. Particularly,thebiotribologyofnaturalandartificialjointshasbeenthemostimportant issuesincetheintroductionofbiotribology.Here,tribologyisdefinedas “thescience andtechnologyofinteractingsurfacesinrelativemotionandrelatedsubjectsand practices” anditsthreepillarsarefriction,lubrication,andwear.Inbothnaturaland artifi cialjoints,friction,lubrication,andwearplayimportantrolesinadequateloadcarryingcapacityandsmoothmovementinmusculoskeletalsystems.
Asdescribedinthisbook,theingeniousmultimodelubricationmechanismsin humansynovialjointsarelikelytobringextremelylowfrictionpropertyandlong durabilitywithminimalwearinvariousdailyactivities.However,undersomesevere conditionssuchasatmal-alignmentand/oratedgeloading,theoccurrenceoflocal directcontactsbetweenrubbingcartilagesurfacesmayraisefrictionlevelandcause localwearand/ordeteriorationofsurfaces.Tosustainhealthyfunctionsofhuman synovialjoints,thewell-suitedstrategyfromtheviewpointofbiotribologybecomes important.
Inrecentartificialjointssuchastotalhipreplacementsandtotalkneereplacements withultrahighmolecularweightpolyethyleneinmixedlubricationregime,localdirect contactbetweenrubbingmaterialsininsuf ficient fluid filmlubricationmaycausesome wearproblems.Byapplyingimprovedhighlycross-linkedpolyethyleneandimproved hardmaterials,whichwereoptimizedwithgeometricdesign,wearvolumeswere signi ficantlyreduced.However,weardebris-inducedosteolysisproblemshavenot beencompletelysolved.Furtherimprovementsinwearreductionwithbiotribological viewpointsarerequired,althoughsomesuccessfulcaseshavebeenreported.
Asaneffectivemethodofsolvinggeneraltribologicalproblems,itisrecommended toconsiderfromthethreeviewpointsoflubrication(lubricants),design,andmaterials.
Forartificialjointsinhumanbody,itispredominantlyapplicabletoadopttheimprovementsofmaterialselectionsandgeometric(macro-,micro-,andnanoscopic)designs, becausethereisthelimitationtochangeperiprostheticlubricantsoptionally.Itis consideredthattheimprovementoflubricationmechanismmaybeapplicable.
Instrengthdesigntopreventfailuresofmaterials,thecriteriaas[themaximum stress] [thepermissiblestress]arerecommended,butinmostdesignsforanatomical kneeprostheseswithUHMWPE,theplasticdeformationcanoccuratconcentrated
contactsunderhighloadconditions.Inaddition,incaseofwearphenomenaatdirect contactareas,forexample, W L values(W:load, L:slidingdistance)areapplicableas wearcriteria.Furthermore,thecorrosivesituationshouldbeconsideredinbiological environment.Biotribologicalsurveywithbiomechanicalviewpointforclinicalsituationbecomesimportant.
Thisbookiscomposedofthefollowingchapters:
Chapter1 Importanceofbiotribology
Chapter2 Biomechanicsofhumanandartifi cialjoints
Chapter3 Biotribologyofnaturaljoints
Chapter4 Biotribologyofarti ficialjoints
Chapter5 Biotribologyofarti ficialjointswitharti ficialcartilage
Chapter6 Biotribologyofregeneratedcartilage
Chapter7 Summarizationandfuturedirectionsofbiotribologyofhumanandartifi cialjoints
Eachchaptercontainsfundamentalissuesandprovidesspeci ficexamplestogive usefulinformationonchaptertopics.In Chapter1,theoutlineofbiotribologyis described.Tribologicalbehaviorsofnaturalandartificialjointsshouldbeevaluated withgeneralunderstandingofinfluenceofbiomechanicalconditions,andthe importanceofbiomechanicsforbothjointsisindicatedin Chapter2.Theimportant termsofbiotribologyfornaturalsynovialjointsandarti ficialjointsarediscussedin Chapter3 and Chapter4,respectively.Thesimilarityoftribologicalpropertiesto naturaljointsinartificialjointswithartificialcartilageisindicatedin Chapter5. Thetribologicalbehaviorsofregeneratedcartilagearediscussedin Chapter6.In Chapter7,allcontentsinthisbookaresummarizedandthefuturedirectionsofbiotribologyofhumanandartifi cialjointsarediscussed.
Itisexpectedforthisbooktocontributetosustainingofhealthysituationinhuman joints,repairingofdiseased/damagedjoints,andimprovingofartifi cialjointsin interdisciplinarybiomedicalcollaborationswithadvancedtechnologiesthrough mutualunderstandingofbiotribology.
Iwouldliketoexpressmyappreciationtoallresearchers/authorsinreferenced worksincludingmycolleaguesandcollaborators.Iamgratefultoallpublishersfor theirkindpermissiontoreusepreviouslypublishedmaterial.Iwouldliketothank Elsevierforthepublicationofthisbookwithprofessionalsupports.
Reference
TeruoMurakami ProfessorEmeritus KyushuUniversity,Japan
June2022
Dowson,D.,&Wright,V.(1973).Bio-tribology.InT.C.Davenport(Ed.), Therheologyof lubricants (pp.81 88).AppliedSciencePublishersLtd,InstituteofPetroleum. viii Preface
Importanceofbiotribology 1
1.1Introductiontobiotribology
Priortoappearanceoftheterm biotribology, tribology as “thescienceandtechnology ofinteractingsurfacesinrelativemotionandrelatedsubjectsandpractices” wasproposedinareport “Lubrication(tribology) educationandresearch” (TheJostReport) in1966(DepartmentofEducationandScience,1966).Thisreportquanti fiedthe impactoftribologyontheeconomyandsocietyingeneral.Theterm “tribology” derivesfromGreek “sribu,tribos” tomean “rubbing,” andtribologyincludesfriction, lubrication,wear,bearingdesign,andsoon.Therefore,tribologyisaninterdisciplinaryscienceandtechnologyencompassingphysics,chemistry,materialscience,geology,biology,mathematics,andrelatedengineering.
Withworldwideawarenessoftribology,thenewterm biotribology wasintroduced as “thoseaspectsoftribologyconcernedwithbiologicalsystems” byDowsonand WrightattheConferenceontheRheologyofLubricants(organizedbytheInstitute ofPetroleum,theInstitutionofMechanicalEngineersandtheBritishSocietyof Rheology)heldinNottinghamin1972(Dowson & Wright,1973).
Themainareasinthisproposalareasfollows:
1. Theinfluenceofmicroorganismsonlubricantsemployedinmachinery.
2. Theabrasivewearcharacteristicsofhumandentaltissues.
3. Theuseoflowfrictionprotectivecoatingsonrazorblades.
4. Fluidtransportinthebody(e.g.,(a) fluidmechanicsofureter,(b)themovementofsputum, and(c)the flowofblood).
5. Themotionandlubricationbyplasmaofredbloodcellsinnarrowcapillaries.
6. Levitationbymeansof “aerostaticbearings” forthetreatmentofburns.
7. Theactionofsaliva.
8. Tribologicalstudiesofperformanceofnaturalsynovialjoints.
9. Tribologicalaspectsofendoprostheses.
First,forareas1to7intheabovelist,shortcommentsincludingcurrentviewpoints areremarked.
1. Thebiodegradationoflubricantswithanaqueousphase,suchascutting fluidsbyproliferationofmicroorganismssuchasbacteria,yeasts,andfungi,isamostseriousproblem. Infectionbymicroorganismsdeterioratesthelubricants,andlowersthepHanddepresses therust-inhibitingandlubricatingproperties,accompaniedwithbadsmells.Appropriate qualitycontrolandmaintenanceforlubricantsisrequired.
2. Resistancetoabrasivewearofmaterialsisrelatedtotheindentationhardness.Theenamelas thetoplayerofteethisthehardesttissueinhumanbody,andithashighwearresistancebut canbewornbyabrasivewearduetotrappedhardparticlesinfoodsatocclusalloadduring
2BiotribologyofNaturalandArtificialJoints
masticationorduetosuspendedhardparticlesduringtoothbrushing(Zhou & Jin,2015). Dentaltribologyisanimportantsubjectinoraltribology.
3. Coatingsonrazorblades(carbonsteelorhardenedstainlesssteel)shouldhavelowfrictionand protectivepropertiestopreventdamageandcorrosionoftheblades.Forexample,metallic hardcoatingistreatedtoimprovetheresistancetowearandcorrosionoftheacutecutting edgeofblade.Furthermore, fluoroethyleneresiniscoatedonmetalliccoatinglayertoenable thebladetoglidesmoothlyovertheskinsurface.Variouscoatingmethodshavebeenapplied.
4. Inthe fieldsofbiofluidtransportandbiofluidmechanics,varioustribologicalphenomenaare found.(a)Inuretertheurineistransportedbyperistalticactionfromthekidneytothe bladder.Tribologicalviewpointsarerequiredtoestablishappropriatetransportbyperistaltic action.(b)Sputumismattercoughedupandexpectoratedfromthemouth,composedof salivaanddischargesfromtherespiratorypassagessuchasmucus,phlegm,orpus.Themovingbehaviorofdropletscontainingsputumwithvirusfromhumanmouthtosurroundingatmosphereshouldbeappropriatelyestimatedtopreventthevirusinfectionbyconsideringthe influenceoforalandmaskfrictionandair flowresistance.(c)Thebloodismainlycomposed ofbloodcells(redbloodcells,whitebloodcells,platelets)andplasma.Thenon-Newtonian viscouspropertyofbloodchangesdependingonconcentrationandstateofaggregateof bloodcells.Aplasmaticlubricatinglayeralongthecapillarywalliseffectiveinreduction offriction.Theelucidationofmechanismoftheformationofthrombiwithconsideration forinfluencesofblood flowandmutualinteractionofconstituentsisanimportantsubject.
5. Redbloodcellisabiconcavediscofabout8 mmouterdiameterinanormalsituation (Fig.1.1a).Whenaredbloodcellmovesinnarrowcapillariesof5 10 mminnerdiameter, itasassumesalowfrictionalshapeandgoesthrough(Fig.1.1b),wheretheelastohydrodynamiclubrication filmthicknessisestimatedas0.2 mmandconstituentsinbloodplasma appeartoplayaboundarylubricatingrole.Inaddition,theimportantroleoftheendothelial surfacelayerliningthevesselwallswhilepassingthroughsmallerborecapillaryisindicated (Secombetal.,2006).
6. Levitationofburn-injuredpatientisappliedbyaerostaticbearingsduringthetreatmentof severeburnstocontrolinfection,toprotectagainstcontamination,andtoprovidesuitable environmentfortheregenerationoftissues.
7. Salivaactsasstarchdigesterandasolvent,andaidsincleaningaction,moistening,andlubrication.Itplaysaprotectiveandfriction-reducingroleofboundarylubricantbetweenteeth andoralsofttissuesandmakesswallowingeasier.Inaddition,salivaisasourceofinorganic ions(calciumandphosphateions)necessaryforremineralizationduringrepairingoferosive damageofteeth(Zhou & Jin,2015).
Figure1.1Geometryofredbloodcellandits flowinnarrowcapillarybloodvessel. Red bloodcellasabiconcavedisccanassumealessfrictionalforminanarrowcapillary.
Inthepoints8and9, “tribologyofnaturalandartificialjoints” wasthemostactive researchtopicatthattime,asdemonstratedinProceedingsoftheSymposiumon LubricationandWearinLivingandArti ficialJointsheldinLondonin1967.Innatural andartifi cialjoints,friction,lubrication,andwearplayimportantrolestomaintainand/ orcontroltheirfunctionandlongdurability.
Here,themutualrelationshipbetweennaturalandarti ficialjointsisshortly describedforthetypicalcasesofhumanhipjoints(Fig.1.2).Inthehealthynaturalsynovialjointscomposedofboneendscoveredwithcompliantbiphasicarticularcartilagelayerslubricatedwithsynovial fluid,theirsuperiorlubricatingabilityand excellentloadcarryingcapacitywithappropriaterangeofmotionbringtheextremely lowfrictionandminimalwearinvariousdailyactivitiesforawholelife(Fig.1.2a).In somejointsundersevereloading/rubbingordiseasedconditions,however,evenarticularcartilagecanbewornanddeteriorated.Forexample,inthecaseofosteoarthritis withworseningofwearanddeterioration,pathognomonicchangessuchasosteophyte, bonehardening,andscarinjointcapsuletakeplace(Fig.1.2b).Theadvancedosteoarthritislowerstheabilityofwalkingandproducesseverepain.Forpatientswhoare deficientinabilitytomoveandsufferseverepain,itisrecommendedtoapplytotalhip arthroplasty,inwhichdamagedjointisreplacedbyartifi cialhipjointusually composedofultrahighmolecularweightpolyethylene(UHMWPE)acetabulumand metallicorceramicfemoralheadwithstem(Fig.1.2c).Successfultotaljointarthroplastybringssigni ficantbenefitsofrecoveryofactivityandrelieffrompaintopatients. Inbothnaturalandartificialjoints,tribologicalpropertiesplayveryimportantroles. Theimportantmattersoftribologyinnaturalandartificialjointsweredescribedby Dumbletonin1981(Dumbleton,1981).Inthisbook, “biotribologyofnaturalandartificialjoints” isdescribedasthemainthemeincludingthecurrentviewpoints.
Figure1.2Naturalandartificialhipjoints. Totaljointarthroplastybyartificialjointfor diseasedjointcanbringtherecoveryofactivityandrelieffrompain. ModifiedwithpermissionfromOka,M.(Ed.).(1990).Arti ficialJointsandBiomaterials. MedicalViewCo.,Ltd.
4BiotribologyofNaturalandArti
AfterproposalofbiotribologybyDowsonetal.,varioustopicsonbiotribology havebeenadded.Forexample,in1988,Sasadaetal.(1988)gaveadditionaltopics ofbiotribologyasshownbelow.
As fi eldsofclinicalmedicine:
1. Frictionofcontactlensandeye.
2. Skinfriction,particularlyevaluationofgrippingforceby finger.
3. Frictionandlubricationbetweentendonandtendonsheath.
4. Frictionbetweengenitalsandcondom.
5. Roleoffrictioninmechanicalbalancinginlivingbody.
6. Frictioninartificialorgans.
7. Surfacedeteriorationofimplantmaterialsduetofriction.
8. Frictioninmedicaltreatmentsuchasfrictionbetweenscalpelandbiologicaltissue.
As fi eldsofbasicmedicineandbiology:
1. Roleoffrictionalstimulusasphysicaland/orchemicalformsongeneration,growth,metabolism,pathologicalchanges,andmedicaltreatmentinvariousorgans.
2. Roleoffrictiononvitalfunctions.
3. Tribologicalapproachonfunctionalchangesinbiologicalevolution.
4. Frictionalbehaviorsbetweencells.
Asadditional field:
1. Feedbackofconceptionandknowledgeonfrictionalphenomenainbiologicalsystemstoscienceandengineeringsuchasbiomimeticsandbio-inspiredtechnology.
Furthermore,manytopicsinbiotribologyarefamiliartoallinoureverydaylives,as discussedin “Atribologicalday” byDowson(2009).Someexamplesinthemorning activitiesareshownbelow.
1. Well-functioningsynovialjointsormorningstiffnessonrisingfromourbeds:effectiveness oflubricationmechanismofsynovialjoint.
2. Easinesstoremoveclothingpriortotakingamorningshoweranddifficultytopullonsocks andundergarmentsaftersoakingtheskininwaterandthendryingwithatowel:effectiveness ofskinhydration.
3. Slipatenteringorleavingabath:dangeroflowfrictionsuchaseffectofunguentupon friction.
4. Careforcombing,brushing,andwashinghair-keratinous fibers:differentialfrictioneffect duetosurfacepropertyofhaircuticle.
5. Comfortableshavingwithlowfrictionandprotection:lowfrictionPTFEcoatingsonthecutting flanksofthebuilt-inbladesindisposablerazors.
6. Satisfactorytransportoffoodsatbreakfastwhichareprocessedbyteeth,andthentransported acrosstongueintothedietarytract:adequatecuttingandgrindingactionofteethfacilitated byversatilemandibularjointsandtransportbytonguewhichareassistedinlubrication, moistening,andbringingoutdelicioustastebysalivary fluids.
7. Maintenanceoforalhygieneandavoidingseriouserosionofthenaturaldentaltissuesor restorativedentalmaterials:controlofwearofteethbyappropriateselectionoftoothbrush anddentifrice.
Ifalltopicsareextendedtofulldayactivities,othervariousbiotribologicalphenomenawillbefound.Anexampleisknownaswell-functioninglungs,hearts, ocularsurfaces,andgutinmovement:lowfrictionandeffectiveprotectionfor softtissuesbylayersofsurface-activephospholipidinpleura,pericardium,ocular surfaces,andgutsinsynergisticmultimodelubricationof fl uid- fi lmlubrication andboundarylubrication.
Intheextensive fieldsofbiotribologyasdescribedpreviously,researchandtechnologiesofthejoint,skin,andoraltribologyhavemadefurtherprogressascurrent fundamental fields,butotherbiomedicalandbiological-relatedtribologyhasbeen developed.Inaddition,theimportanceofbiotribologyinfurthernew fieldsincluding biomimetics(Dowson & Neville,2006)andbio-inspiredtribology(Shiddaiah & Menezes,2016)hasbeenexplored.Thedevelopmentoffurtheradvancedartificial jointsbasedonbio-inspiredtribologyisexpected.
1.2Friction
Frictionisdefi nedas “theresistingforcetangentialtothecommonboundarybetween twobodieswhen,undertheactionofanexternalforce,onebodymovesortendsto moverelativetothesurfaceoftheother” (OrganisationforEconomicCo-operation andDevelopment(OECD),1969).Andcoef ficientoffrictionorfrictioncoef ficient isdefinedastheratioobtainedbydividingthefrictionforcebynormalforcepressing thesebodiestogether.
Frictionforrubbingsurfacesshowsdifferentbehaviorsdependingonenvironment suchasdry,boundarylubricated,or fluid filmlubricatedcondition.First,frictionunder dryandunlubricatedconditionsisdescribed.
1.2.1Frictionunderdryandunlubricatedconditions
ItiswellknownthatAmontons’ laws(1699)orAmontons-Coulomblaws(1785) shownbelowarebroadlyapplicabletoslidingfrictionunderdryandunlubricated conditions.
1. Frictionforce F isproportionaltonormalforce(appliedload) W
2. Frictionforce F isindependentofthesizeoftheapparentcontactarea.
Asshownin Fig.1.3,whenpullingforce Fp isappliedtoablockishbodyunder normalload W,ablockslideswhileitsbottomsurfaceisappliedwithfrictionforce F inreversedirection.Whenpushingforceisappliedontheleft,frictionforceacts inreversedirectiontopushingforce.Formanycasesfrictionforceisproportional tonormalforce.Theratiooffrictionforcetonormalforceisdefinedasfrictioncoefficientorcoef ficientoffriction: m.
6BiotribologyofNaturalandArtificialJoints
Figure1.3Frictionforceforablockmatteronplate. Frictionforce F occurswhenpulling force Fp isappliedtoblockmatterundernormalload W.
Frictioncoef fi cientchangeswidelyaccordingtomaterialcombinationand environment.
Here,inassociationwiththe fi rstlaw,Coulomb’sfrictionindicatesthatfriction forceisproportionaltonormalload.
Next,importantcommentisgiveninrelationtothesecondlaw.Usualrubbingsurfacesarenotperfectlysmoothbuthavevarioussurfaceroughnesseswithdifferent irregularitywithvalleysandpeaks.Therefore,whentwobodiescontact,theactual loadingareasarenotapparentcontactareasbutdiscretelydistributedinrealcontact areasasshownin Fig.1.4.Atthesecontactpoints,theroughnessesorasperitiestouch theother,andthustherealareaofcontactisverynarrowthantheapparentcontact area.Iftheload,thecontactpressure,andtheareaof i-thcontactpointareassumed as Wi, pi and Ai,respectively,thepressureatcontactpointisshownas
Inusualcasesformetal-metalcontacts,thecontactpressure pi islargeandequalto theyieldpressureofsoftermetal pm inducingtheplasticdeformationatthelocalcontactpoints.
=Ai ¼ pm
Figure1.4Apparentcontactareaandrealcontactarea. Incontactbetweenactualbodies withsurfaceroughness,theactualloadingareasarediscretelydistributedinrealcontactarea.
Therefore,totalrealcontactarea AR atload W isestimatedasshownbelowfor loadingareawithnumerouscontactpoints.
Thus,therealcontactareaisdeterminedbytheloadandyieldpressure,andindependentofthesizeoftheapparentcontactarea.
Althoughtheproportionalrelationshipbetweenrealcontactareaandloadisderived forplasticcontactatasperities,itispointedoutbyGreenwood Williamsonthatthe realcontactareaisproportionaltotheload,evenforcontactingsurfaceswithsurface roughnessatelasticcontact(Greenwood & Williamson,1966).Therefore,formany contactstatesoftwosolidbodies,therealcontactareaisproportionaltotheload.
Coulombaddedthethirdlaw:
3. kineticfrictionforce F isindependentofslidingspeed V.
Thethirdlawisnotalwaysapplicableforveryloworveryhighspeed. Itshouldbenotedthatfrictionforslidingpairincludesomepolymericmaterial changeswithslidingspeeddependingonviscoelasticbehavior(Myshkin & Kovalev, 2009).Furthermore,thefrictionforce-slidingspeedrelationshipdependsontesttemperature.Inslidingtestconductedneartheglass-transitiontemperaturethesliding speedhasaremarkableeffectonfriction.
Ingeneralrecognition,frictionalresistanceiscausedbytwomainfactors:adhesion anddeformation(orplowing).
Adhesiveforce isdefinedastheattractiveforcebetweentheadjacentsurfacesin frictionalcontacts.Whenasolidbodyismovedalongtheinterface,theforcerequired tosheartheadhesivejunctionformedbetweentherubbingsurfaces(Fig.1.5a)actsas thefrictionforce.Thefrictionforce Fa asthemolecularcomponentduetotheadhesive termisshowninthefollowingformula,whentheshearingstressatjunctionandtotal normalloadisassumedas s and W,respectively.
8BiotribologyofNaturalandArtificialJoints
Asseenin Eq.(1.5),thefrictionforceduetoadhesivetermisproportionaltothe load.Formanyslidingcaseswithinfinitesimalfrictionduetodeformationterm,this formulacorrespondstothe firstandsecondAmontons-Coulomblaws.
Inthemeanwhile, plowing isdefi nedastheformationofgroovesbyplasticdeformationofthesofteroftwosurfacesinrelativemotion(Fig.1.5b)wheretheuppercylindricalorsphericalsolidbodyishardmaterial(indenter)andlowersolidissofter metal.Thesoftmetalisplasticallydeformedathighcontactpressure,andtheresistant frictionforceofthesoftermaterialtotheplowingbyasperitiesoftheharderoneis showninthefollowingformula.
here A0 isthefrontalprojectedcontactareaand p0 istheyieldpressureforsofter material(p0 ¼ pm).
Inanotherexample,whenapolymerwithviscoelasticpropertyslidesagainstahard surface,theenergydissipationasdeformationfrictiontermiscausedbythehysteresis lossforpolymericmaterial.
Forvariousrubbingpairs,thefrictionforce F iscomposedofadhesiveanddeformation(orplowing)termsasshownbelow.
Formostrubbingsurfacesofmachineelementsandrelatedpartswithsmallroughness,theadhesiontermisextremelylargerthanthedeformationone.Therefore,frictionforceisapproximatedasbelow.
(1.8)
Asdescribedabove,frictionforceformanyrubbingsurfacesisproportionaltothe normalload.Frictioncoef ficient m definedby Eq.(1.1) indicatestheleveloffriction. Someexamplesinslidingpairsatdryconditioninairareshownin Fig.1.6 (Tribonet: FrictionCoefficientTablesinAirandVacuum,2020).
1.2.2Staticfrictionandkineticfriction
In Fig.1.3,ifthepullingforceissmallerthanfrictionalresistance,theblockstaysstationary.But,whenthepullingforceexceedsthefrictionalresistantforce,theblockbeginstomove.Inmanycases,frictionwhenabodystartsmovingislargerthanfriction whenthebodyissliding.Todiscriminatethesefrictiontypes,thefrictiontoactona stationarybodyandfrictiontoactonamovingbodyarecalledthe staticfriction and the kineticfriction,respectively.Frictioncoef ficientwhenabodystartsmovingis calledthemaximumstaticfrictioncoef ficient.
Thestaticfrictionalbehaviorcanbeconfirmedbyobservingthemovingofabody onaninclinedsurfacewithchangingtheinclination.Whenabodyofweight W putson
Fp ¼ A ' p '
F ¼ Fa þ Fp
F yFa
Figure1.6Examplesoffrictioncoefficientbetweenvariousmaterialsinair. Experimental dataforfrictioncoefficientsarecitedfromTribonet. DatafromTribonet:Frictioncoefficienttablesinairandvacuum.(2020). https://www.tribonet. org/wiki/friction-coef ficients-in-atomosphere-and-vacuum/
aninclinedsurfacewithtiltangle q, W isdissolvedtotheforcenormaltoinclinedsurface Fn andtheforceparalleltothesurface Fp,whichtendstocausethesliding.Both forcesareshownbelow.
Abodystaysatoriginallocationunderlowinclinedconditionwhen Fp issmaller thanthestaticfrictionalforce Ff (Fig.1.7a),butatsomeangle q,itwillbegintoslide whentheforce Fp isgreaterthanthestaticfrictionalforce Ff (Fig.1.7b).Attheonsetof sliding,theseforcesareequal.Thestaticfrictioncoef ficientisestimatedasshown below.
Inthecaseof Fig.1.7b (q ¼ 30 ), ms isabout0.577. Inmanyfrictionexperiments,thefrictionalforcecanbedirectlymeasuredbythe loadcell.
1.2.3Frictionunderlubricatedconditions
Frictionunderlubricatingconditionsiswidelychangeddependingonthecorrespondinglubricationmodes.InStribeckcurve,therelationshipbetweenfrictioncoef ficient andthelubricationparameter[viscosity speed/load]asasimilarparametertoHersey numberisshownforboundary,mixed,and fluid fi lmlubricationregimes(Fig.1.8).
10BiotribologyofNaturalandArtificialJoints
Figure1.7Slidingofabodyoninclinedsurface. Ablockwillbegintoslideoninclined surfacewhentheforce Fp isgreaterthanthestaticfrictionalforce.
Figure1.8Stribeckcurve. Fluid filmthicknessincreaseswithanincreaseinlubrication parameter:Viscosity Speed/Load.Dependingontherelativeratioof fluid filmthicknessto surfaceroughness,thelubricationmodesandcorrespondingfrictionlevelschange.
Ingeneral,the fl uid filmthicknessoflubricantincreaseswithanincreaseinthelubricationparameter.Thedetailedmechanismsfortypicallubricationmodesaredescribed laterinSection1.3,RolesofLubrication.Intheregionatlowlubricationparameter, highfrictionisobservedasaconsequenceofseverecontactbetweensolidsurfaces coveredwithadsorbed fi lmsunderthin fi lmconditioninboundarylubrication.In contrast,intheregionathighlubricationparameter,lowfrictionismaintaineddue tolowshearingforceofthethicker fluid film,whichpreventsthedirectcontactbetweenrubbingsurfaces,in fluid filmlubrication.Inthismode,frictiongraduallyincreaseswithanincreaseinthevalueofthelubricationparameter.Inmediumregion atmixingofboundaryand fluid fi lmlubricationmodes,frictionchangesfromhigh tolowlevelswiththelubricationparameter.Thisregioniscalled mixedlubrication
1.2.4Rollingfriction
Asmentionedpreviously,thefrictionforcegivesresistancetorelativemotionin slidingcontactandthismodeiscalled slidingfriction.Incontrast,therollingfriction showsresistancetorollingmotionasobservedinrollingbearings.Someexamplesof rollingfrictionforregularpolygonsareshownin Fig.1.9,wherethreecasesinrolling motionofregularhexagonalcylinder,regulardodecagonalcylinderandcircularcylinderaredemonstrated.Here, G iscenterofgravity, h isitsheight, C1 and C2 arevertexesandedgesofcontactzone, O iscenterof C1 C2 zone, x isthedistanceofOC1, q isangleforGC1 andcentroidalline, W isweightofcylinder,and FR isdrivingforce whichisequilibriumtorollingfrictionforce.
Torollthecylinders,therollingmomentby FR atcontactedge(vertex) C1 is requiredtobeinequilibriumtothemomentproducedbytheweight.Therefore,the followingequationsareobtained.
Thus,rollingfrictioncoef ficientsareestimatedas0.58and0.26forhexagonaland dodecagonalcylinders,respectively.Forpolygonalcylinders,frictioncoeffi cientbecomeslowerwithanincreaseinnumberofsides.Forcombinationofrigidcircularcylinderandrigid fl atplaneasultimatepolygon,itbecomeszero.However,friction coef ficientforusualcircularcylinderbecomesinfinitesimalas0.001orsobyvery smallrollingresistance,becauseusuallynarrow fl attenedcontactareaisformedfor elasticbodiesbyelasticdeformationduetonormalload W.
Figure1.9Rollingofpolygoncylinders. Rollingfrictioncoefficientforpolygoncylinderon planebecomeslowwithanincreaseinnumberofsides.
12BiotribologyofNaturalandArtificialJoints
Asdescribedpreviously,therollingfrictionforrollerorballisverylow,andthereforetherollingbearingssuchasrollerandballbearingshavebeenwidelyappliedin variousindustrialuses.
Inhumanhistoryontechnology,theuseofroundwoodsasrollerstomovebigand heavystonestatueinAssyriainabout700BCEandtheinventionofballbearingin Ca.50CEinItalyisreportedasoldprecedents(Dowson,1979).
Ontheotherhand,inanimalhistory,theadvantageoflowfrictioninrollingmotion hasbeentakentomovebiggerballofdungbydungbeetles(Scarabaeussacer) (Fig.1.10 (Wikipedia:Scrab(Artifact),2020)).Inhumankneejoints,thecombination ofslidingandrollingcontactenablessmoothandstable flexion-extensionmotionin widerangeofmotion.
1.2.5Lowfrictionandhighfrictioninbiosystems
Therangeoffrictioninbiosystemsisverylarge.Inthissectionsomeexamplesare described.
Asanexampleoflowfriction,theextremelylowfrictionfrom0.002to0.03is observedfornaturalsynovialjointsevenundersevereoperatingconditionswith highload,lowviscosity,andslowvelocityconditionasseeninStribeckcurve (Fig.1.8).Thislowfrictionislikelytobeattainedbysuperiorlubricationmechanism withsynergisticperformanceasrubbingapairofcompliantbiphasicarticularcartilageswithlubricioussurfaceslubricatedwithsynovial fluidcontainingusefulconstituents(Fig.1.11).Underoperatingconditionswithdifferentseveritiesfornaturaljoints invariousdailyactivities,itisrequiredforminimizingfrictionandwearthatvarious
Figure1.10Dungbeetlesrollingaballofdung. Dungbeetlesmovethebiggerballofdung usingrollingmotion.
ModifiedfromWikipedia:Scrab(Artifact).(2020). https://en.wikipedia.org/wiki/Scrab_ (artifact)
Figure1.11Simplifiedmodelofnaturalsynovialjoint. Matingarticularcartilagesurfacesare smoothlyrubbedandlubricatedwithsynovial fluid.
lubricationmodesofnotonly fluid filmlubricationbutboundarylubricationandother modescanplayeffectiveroles(Dowson,1966-67; Murakami,1990; Murakamietal., 2017).Thedetailedmechanismofthemultimodelubricationisdiscussedinthe Chapter3 ofthisbook.
Next,anexampleofhighfrictionisintroducedon fingerskintoeasilyandsubstantiallyholdvariousmaterialsindailylife.Itisexpectedthatthewettingsituationof fingerskinsurfaceplaysanimportantroletocontrolfrictionlevelbecausetheopeningsofeccrinesweatglandsareplacedintheepidermalridgeofthe finger.
Infrictiontesterwherethe fi ngerwasmovedtowardbodyandthewettingcontactsituationswereevaluatedbyobservingthewettedareasonprismsurfaceby totalre fl ectionasshownin Fig.1.12 ( Murakamietal.,1995),themaximumand minimumfrictionvaluesof fi ngerskinonglassprismwereexaminedateach
Figure1.12Frictionalbehaviorof fingerskinonglassplate. Maximumfrictionfor fingeris observedatoptimumwet(sweated)conditionandshowssignificantload-dependancy.In contrast,minimumfrictionwithload-independancyisobservedunderdrycondition. Importanceofbiotribology13
14BiotribologyofNaturalandArtificialJoints
load.Itisnoticedthatveryhighfrictioncoef fi cientsasmaximumvalues( 2.0) withload-dependencywereobservedundertheoptimumwetcondition,while lowfrictionasminimumones( j 0.4)withload-independencywereconfi rmedunderdryconditionwhichwasmonit oredaslittlewettingareaintotalre fl ectionimages.Theconstantfrictioncoef fi cientunderdryconditionisconsideredassolidor boundarylubricationmode.Incontrastwiththisload-independency,frictioncoeffi cientunderoptimumwetconditionishighatlowloadandtendstodecreasewith increasingload.Thisload-dependencyisconsideredfromtwo-termlawoffriction asfollows:
F:Frictionforceforskinonglass.
A:Load-independentadhesiveterm.
P:Normalload
m:Coulomb’sfrictioncoef ficient
f:Frictioncoef ficientforskinonglass.
AdhesivetermAisattributabletosurfaceforcesuchassurfacetension,viscous forceofinterveningliquid(Bowden & Tabor,1954),andothers.Atlowload, A/P ishighand f becomeshigh.Highestfrictionasoptimumvalueateachloadisattained bymaximizingadhesivesurfaceforce,andexcessivewettingreducesfrictionby fluid fi lmeffect.
Next,theinfl uenceofexcessivewettingonfrictionwasexaminedinsimilartester underdifferentwettingconditionsat6Nat1mm/s.Atconditionwithsweating,the rubbingtestwasstartedafterstaticloadingaccompaniedwithspontaneoussweating for1min.Atconditionofwatersupplied,thetestwasstartedafterdistilledwater wassuppliedtobringonsignificantwetting.Itisconfirmedthathigherfrictionis observedon fingerwettedwithsweatingthanthe fingersuppliedwithdistilledwater asshownin Fig.1.13 (Murakamietal.,1995),wheretheimagesoftotalreflectionat 6saregivenasdarkareaforwettedzone.Forwatersuppliedconditionacertainlevel of fluid filmeffectappearstoreducefrictionbutmaintainshigherfrictionexceptlocal dropthandrycondition.Thisfactindicatesthat fingerseemstohaveexcellenthigh frictionmechanismevenunderexcessivewettedcondition.Theskinwithdermalridge includingpalmandsolehashighfrictionpropertyandcalledfrictionskinorsensing skin,wheresweatingappearstoplayanimportantroleincontrollingfriction.By contrast,theotherskinswithoutridgessuchasforeheadandforearmshowlowfriction andsmoothfeelcomparedwithfrictionskins.Althoughskinfrictionvarieswith anatomicalsites,formostofskinsdrierskinhasaloweredfrictionandhydrated skinhashighfrictionincaseswithout fluid filmeffect.Thehydrationincreasesfriction duetoanincreaseofadhesiveforceandanincrementofcontactareawithskinsoftening(Sivamani & Maibach,2006).
Figure1.13Influenceofwettingonfrictionfor fingeronglass. Atconditionwithsweating, highfrictionfor fingerskinissustained.Atconditionwithwatersupply,frictiondecreasesbut maintainshigherfrictionthandrycondition. Importanceofbiotribology15
1.3Rolesoflubrication
1.3.1Lubricationmodes
Lubrication isdefi nedas “thereductionoffrictionalresistanceandwear,orother formsofsurfacedeterioration,betweentwoload-bearingsurfacesbytheapplication ofalubricant” (OrganisationforEconomicCo-operationandDevelopment (OECD),1969).
Mainlubricationmodesorregimesoflubricatedrubbingsurfacesaregenerally categorizedasboundary,mixed,and fluid filmlubricationasshowninStribeckcurve (Fig.1.8).Inaddition,solidlubricationorsolid filmlubricationisanotherlubrication modewhichiswidelyemployedbyapplyingpowderorthin filmsolidlubricantsas layerorlamellarstructuressuchasgraphiteandmolybdenumdisulfide.Fundamental featuresformainlubricationmodesaredescribedasbelow.
1.3.2Fluid filmlubrication
Indesignofvariousbearingsandmachineelementswithrubbingsurfaces,itisrecommendedasthe fi rstchoiceforprotectingsurfacesandcontrollingfrictionandwearthat thefull fluid fi lmshouldbeformedandactas fluid filmlubricationtopreventthedirect contactbetweenslidingand/orrollingmatingsurfaces.Itisrequiredfor fl uid filmto supporttheoperatingloadswithpressurized fluid.Thepressurizationof fl uidisestablishedbyhydrostaticorhydrodynamicaction.Theformeriscalledhydrostaticlubricationinwhichpressurized fluidissuppliedbyexternalpumpingsystem.Thelatteris calledhydrodynamiclubricationinwhichrelativemotionofmatingsurfacesbringsin thepressurizationof fluid.Fundamentalfeaturesofhydrodynamiclubricationare mentionedbelow.
16BiotribologyofNaturalandArtificialJoints
The fluidpressurizationinslidingbearingwithrelativemotionofbearingsurface andshaftlubricatedwithoilinlocomotivetrainwasfoundasmeasurementofhigh pressurebyTowerin1883(Tower,1883).ReynoldsappliedNavier-Stokesequation forviscous fluidtothe fluid flowinsmallclearanceandproposedthemechanismof hydrodynamicpressurizationasReynoldsequation(Reynolds,1886).Forsimplified caseofrubbingbodieswithsmallclearance(fluid fi lmthickness) h lubricatedwith fl uidasshownin Fig.1.14 wherethevelocityofloweranduppersurfacesin x-directionare u1 and u2,respectively,andthevelocityofuppersurfacein z-directionis w,the Reynoldsequationareshownbelow.
where p ispressure, r is fluiddensity,and t istime.
Fromthisformula,mainfeaturessuchaspressuredistribution,velocitydistribution, fl uid fi lmthickness,load-carryingcapacity,andfrictioncoef ficientareobtainedunder correspondingboundaryconditions.
Next,theload-carryingmechanismwithhydrodynamiclubricationbasedon fluid pressurizationbyrelativemotionbetweenrubbingsurfacesisdescribed.Togenerate fl uidpressurization,itisrequiredtosatisfythefollowingsituation.
Therefore,iftherighthandvalueof Eq.(1.17) isnegative,itisexpectedthatthe fl uidpressurizationisgeneratedtocarrytheload.
Figure1.14Simplifiedmodelofmatingsurfaceswithvelocityboundarycondition. In subjecton fluid filmlubrication,the fluid filmthickness h isverythin.
The fluidpressurizationmechanismsderivedfromthesethreetermsareidentifiedas thewedgeaction,thestretchaction,andthesqueezeaction,respectively.Thestretch actioncausedbynegativesecondtermisobservedinonlyrareeventualitysuchasthe hydroplaningphenomenonfordeceleratingtireonwetroad;therefore,thedetailed descriptionisfocusedonthewedgeandsqueezeactions.
1.3.2.1Thewedgeaction
The fluidpressurizationisproducedbythewedgeactionfor v(rh)/vx < 0.Forincompressible fluid,thehydrodynamicpressureisgeneratedwhenthereisaconverging wedge.Thecorrespondingsimplifiedexampleat u1 ¼ u and u2 ¼ 0isshownin Fig.1.15a,wherethehydrodynamicpressureand fluid flowdistributionsaredepicted. Iftherubbingsurfacesareparallel,the fluidpressurizationforincompressible fluidby wedgeactionisnotsubstantialized.Inadivergingwedge,thenegativepressureis generatedanditisdiffi culttocarryloadby fluid film.
1.3.2.2Thesqueezeaction
Asanothermechanism,the fluidpressurizationisproducedbythesqueezeactionas v(rh)/vt < 0evenforparallelmatingplanes.Anexampleforparallelplaneswhich closedistancewithapproachingvelocityof vh/vt forincompressible fluidisshown in Fig.1.15b.Intheloadingprocessorincaseswhichthe fluctuatingloadactsto therubbingsurfaces,thesqueezeactionplaysapredominantroletogeneratethehydrodynamicpressure.
Inappropriatedesignofhydrodynamicslidingbearingsforindustrialuses,the speci ficationsarearrangedsothatthefull fluid filmcanbeformedbythewedge and/orsqueezeactionsandthedirectcontactbetweenrubbingsurfacescanbeprevented.Inthesecasesat fluid filmlubricationmode,frictionislowasshowninStribeckcurve(Fig.1.8),becausethefrictionalresistanceiscausedbylowshearing resistanceoflubricating fluid.Furthermore,thewearisinfi nitesimalduetonodirect interactionbetweenrubbingsurfacesandtheirlongerdurabilityisexpected.Toestablishthe fl uid filmlubrication,itisrequiredthattheminimum fluid filmthicknessis largerthanthesurfaceroughnessofrubbingsurfaces.
Figure1.15Wedgeandsqueezeactionsforhydrodynamicpressurization. For incompressible fluid,thehydrodynamicpressureaswedgeactionisgeneratedforconverging wedge.Thehydrodynamicpressureassqueezeactionisgeneratedforapproachingprocess. Importanceofbiotribology17
