1. Lubrication

2. Wear

Tribology

Chapter 4

Tribology

64

Thescienceoffriction,wearandlubricationiscalledtribology.ThewordisderivedfromtheoldGreekword“tribos”,whichmeans“rubbing”.AsdescribedinChapter1,thesealringsofamechanicalshaftsealrubagainsteachotherwithaverythinlubricatingfilm.

Tribologyisaveryoldscience.AnoldEgyptianinscriptionsimilartofig.4.1.showshow172slaveswereabletopullalargestatueonasled.

Fig. 4.1: Assuming the slege is made of wood sliding against wood, it can be calculated that this only is possible when lubricated with water. The man standing on the sledge is pouring water under the sledge to lubricate, and three more slaves are bringing water to the tribologist.

1. LubricationThepressuredistributioninthelubricatingfilmiscomposedofahydrostaticandahydrodynamiccontribution.Thehydrostaticcontributionarisesduetothepressuredifferencebetweenthepumpedmediumsideandtheatmosphericside.Thehydrodynamicpressureisgeneratedasapumpingactionduetotheslidingmotionofthesurfaces.Thedifferentlubricationregimesforhydrodynamicpressureareoftendescribedbymeansofaso-calledStribeckcurve.Seefig.4.2.

Athighvelocitiesandnottoohighloads,thehydrodynamicpressurecompletelyseparatestheslidingparts,allowingtheformationoffull-fluid-filmlubrication.Atlowervelocitiesorhigherloads,thehydrodynamicpressureisnotsufficienttocompletelyseparatetheslidingparts.Inthissituation,amixedlubricationregimeexistswherepartoftheloadissupporteddirectlybythecontactpointsofthesurfaces.Thetopographyofthesurfacesaffectswherethemixedlubricationregimeisreached.Atevenlowervelocitiesorhigherloads,thegeneratedhydrodynamicpressurebecomesinsignificant.Thislubricationregimeiscalledboundarylubrication.Thethicknessofthelubricatingfilmofthemechanicalshaftsealmustbeverysmalltoavoidexcessiveleakage.Consequently,thesealisalwaysinthemixed-orboundarylubricationregime.

65

Coefficient of friction

Boundarylubrication

Mixedlubrication

Full-fluid-filmlubrication

Surface roughness, R

Lubricating film

Load

h 0 h~R h>> R

V

Viscosity x velocityLoad

Solid 1

Solid 2

hhh

h

R = Surface roughness

Fig. 4.2: Stribeck curve showing different lubrication regimes

Tribology

66

Duty parameterThemechanicalshaftseallubricationnumberonthex-axisinfig.4.2iscalledthedutyparameter,G,definedbythisformula:

h: dynamicviscosity w : angularvelocity(2pn[sec-1]) k : balancingratiooftheseal Dp:pressuredifferenceacrossthesealface p

s: pressureinthesealgapcausedbythespring.

Moredetailsaboutdutyparametercanbefoundin[1].

Forsmalldutyparametervalues,theleakageisverylowandthesealoperatesintheboundarylubricationregime.Forlargedutyparametervalues,evenfull-filmlubricationcanbeachieved.

Examples:Thedutyparameter,G,inboilerfeedwateristypically10-8,incolddrinkingwater10-7andincrudeoil10-5.

Thedescriptionofthelubricationregimewiththedutyparameterisnotbasedonthecalculationofaphysicalphenomenon,butmoreonempiricalstudies/methodesbasedoncommonpractice.Thefollowingsectionprovidesfurtherphysically-basedmodeldescriptionsofhydrodynamiclubrication.

Hydrodynamic pressure distributionInthefull-fluid-filmlubricationregime,thefrictionbetweenthesurfaceswiththerelativevelocity,v

0,isdeterminedbythe“internalfriction”inthelubricatingfilm.Theshearresistance

ofafluidiscalled“viscosity”,representedbythesymbol,h,(eta).

Inthecaseoftwoflatsurfaces,movingrelativetoeachotheratthevelocityv0andseparated

byafluidwiththeviscosity,h,themoleculesofthefluidnormallyadheretothesurfaces.Consequently,thevelocityofthefluidnearasurfaceisalmostidenticalwiththevelocityofthesurface.Whenthedistancebetweenthesurfacesissmall,thefluidflowislaminar(noturbulence).Inthiscase,thevelocityincreaseslinearlybetweenthetwosurfaces;theforce,F,requiredtokeepthesurfacemovingisproportionaltotheareaofthesurface,A,andtotheshearstrain,v

0/h,whereh,isthedistancebetweenthesurfaces.Seefig.4.3.

hwkDp+p

sG=

Thus,theshearstressF/Aisproportionaltothechangeofshearstrain,v0/h:

F/A=hv0/h

Ormoregenerallywithtasshearstress:

t=h∂v/∂h(Newtonianfluids)

Inthecaseofparallelfacesshowninfig.4.3,thevelocitydistributiondoesnotcauseanypres-sureincrease.Ifoneofthesurfacesistiltedslightly,thefluidwillbeforcedintoasmallercross-sectionandthereforecompressed.Thiswillcausethepressuretoincreaseandcreateapressuredistributionbetweenthesurfaces.Seefig.4.4.

Foragivengeometry,thepressureprofilecanbecalculatedusingtheReynoldsequation:

Thelubricatingfilmcalculateddependsonvelocity,v0

,andload,F

N.However,inallcasesthe

pressuredistributiongeneratedbetweenthesurfaceswillonlybeabletoseparatethesurfacesbyadistancecomparabletothewedgeheight(h

2–h

1).Seefig.4.4.

Moredetailsaboutlubricationtheorycanbefoundin[2].

V = V0

F

V = 0

h

Area A

V0F

N

p (x, y)

∂∂x (h3(x) )+ = 6v . η

h2

h1

∂∂y

∂p∂x

∂h(x)∂x(h3(x) )∂p

∂y

yx

z

h(x)

67

V = V0

F

V = 0

h

Area A

V0F

N

p (x, y)

∂∂x (h3(x) )+ = 6v . η

h2

h1

∂∂y

∂p∂x

∂h(x)∂x(h3(x) )∂p

∂y

yx

z

h(x)

V = V0

F

V = 0

h

Area A

V0F

N

p (x, y)

∂∂x (h3(x) )+ = 6v . η

h2

h1

∂∂y

∂p∂x

∂h(x)∂x(h3(x) )∂p

∂y

yx

z

h(x)

Fig. 4.3: Velocity distribution and shear resistance, F, of a fluid film between two surfaces, h being the distance between the surfaces

Fig. 4.4: Slightly tilted moving surface creating a pressure profile

Waviness of seal ringsTominimiseleakage,thesurfaceofthemechanicalshaftsealringsmustbeflat.Consequently,nohydrodynamicpressureshouldbegeneratedbetweentherelativelyrotatingsealfaces.Flatsealringsarenormallyobtainedbylapping.However,evenveryaccuratelymachinedsurfacesarenotcompletelyflat.Somesurfacewavinessoftheorderof1/10000mmalwayspersist.Whenthereisarelativerotationbetweensealrings,thesmallwavinessgeneratesahydrodynamicpressure.Thispressureincreasesthelubricatingfilmthickness,resultinginahigherleakagerate.Seefig.4.5.

Wavinessalsoappearsasaresultofmechanicalandthermaldistortion,butinmostcasestheresultinghydrodynamicpressureisnotsufficienttocompletelyseparatethesurfaces.Theeffectofwavinessonthehydrodynamicpressuredistributionisfurtherdiscussedin[3].Theconclusionisthatthesafestcompromisebetweenlubricationandleakageisobtainedbylappingthesurfaceasflataspossible.

Hydrodynamic tracksInshaftsealsforverylow-viscosityfluidslikehotwaterandgases,thehydrodynamiclubricationcanbeincreasedbymakingtracksinthesealringorseat.Seefigures4.6and4.7.

Tribology

68

Fig. 4.6: Hydrodynamic tracks in seal rings for hot water

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

00 0.05 0.1 0.15

Roughness, Ra [µm]

Direction of rotationLeakage rate [ml/h]

Waviness [µm]

Leakage rate [ml/h]

0.2

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41.0

Surface

Substrate

Contaminant layer,5 nm

Adsorbed gas layer,0.5 nm

Oxide layer, 10 nm

Asperity

Surfacefilm

Fig. 4.5: Example of measured leakage as a function of waviness

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

00 0.05 0.1 0.15

Roughness, Ra [µm]

Direction of rotationLeakage rate [ml/h]

Waviness [µm]

Leakage rate [ml/h]

0.2

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41.0

Surface

Substrate

Contaminant layer,5 nm

Adsorbed gas layer,0.5 nm

Oxide layer, 10 nm

Asperity

Surfacefilm

Lubricatingfilm

Thermallycreatedwedge

Hydrodynamictrack

Fig. 4.7: Hydrodynamic wedges in gas seal face

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

00 0.05 0.1 0.15

Roughness, Ra [µm]

Direction of rotationLeakage rate [ml/h]

Waviness [µm]

Leakage rate [ml/h]

0.2

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41.0

Surface

Substrate

Contaminant layer,5 nm

Adsorbed gas layer,0.5 nm

Oxide layer, 10 nm

Asperity

Surfacefilm

Lubricatingfilm

Hydrodynamicwedge

Bythermaldistortion,awedgeiscreatedonthesealfacenearthetracks.Seefig.4.6.Thistypeoftracksinthesealfacepushestheevaporationzoneclosertotheatmosphericsideoftheseal[4].Followingeachtrack,anareawithincreasedpressureiscreated.Thisdesignallowsthepumpedmediumtoenterthesealgapveryeasily;asealingzonestillremainsattheatmosphericsideoftheseal.

Amoreefficientwayofincreasinghydrodynamicpressureistomachinesmallgroovesinthesealface,makingawedgeintothesealgap.Thisdesigniscommoningassealswhereahydrodynamicpressureisdesiredevenwithanextremelylowviscosity.Seefig.4.7.

Roughness of seal ringsFrictionandweardependontheactualareaofcontactandthereforeonthesurfacetopography.RoughnessparameterssuchasR

avalues,indicatetheaveragesizeofthe

roughnessbutnottheshapeofthetopography.Todescribethefriction,wearandlubrication(tribological)propertiesofsurfaces,the“bearingareacurve”(BAC)ismoresuitable.TheBACdescribesthecontactareawithanimaginaryplaneasafunctionofthedistance.Thisplaneispulleddowninthesurface,seefig.4.8.Thedesiredareainacertaindepthiscalledthe“relativematerialratio”(Rmr)valueintherelevantdepth.

Fig.4.8showsabearingsurfaceRmrof5%,40%and80%fordifferentdepths.Thepercentagesarecalculatedasthethicklineinpercentagesofthetotallength.

DifferentmachiningprocessesnormallyprovidedifferentBACs.Seefig.4.9.

69

5 %

40 %80 %

0.00.0 0.8

0.5

1.0

Depth [µm]

Distance [mm]

Fig. 4.8: Cross-section of surface showing how a BAC is obtained

Fig. 4.9: Examples of BACs for a grinded and a lapped surface

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100

Bearing area [%]

Depth [µm]

Grinded

Lapped

Thelappedsurfacehasaplateauwithsomevalleys.Consequently,thebearingarearapidlyincreaseswiththedepthuntilalargeareahasbeenreached.Asopposedtothelappedsurface,theareaofthegrindedsurfaceisslowlyincreasingwithdepthsindicatingamoreevendistributionofvalleysandpeaks.

Fig.4.10showshowtheleakageratediffersaccordingtothedirectionofthescratchesonthesurface.Thearrowsindicatethedirectionofrotationofthesealring.Accordingtofig.4.10,thelubricatingfilmcanbepumpedtothepumpedmediumsideortotheatmosphericside,dependingonthedirectionofthescratchesonthesurface.

Thetypicalsurfacetopographyofsealringsisastatisticdistributionofscratchesinalldirectionsobtainedbymeansofalappingprocess.Ashinysurfacewithasmallroughnesscanbeproducedbylapping.However,wherebothsealringsaremadeofhardmaterials,oneofthesealringsshouldhaveadullfinishtopreventthesealringsfromstickingtogetherduringstandstill.ForadullsurfacefinishlappedtoanRavalueof0.2therunning-inperiodmaylastseveraldays.

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

00 0.05 0.1 0.15

Roughness, Ra [µm]

Direction of rotationLeakage rate [ml/h]

Waviness [µm]

Leakage rate [ml/h]

0.2

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41.0

Surface

Substrate

Contaminant layer,5 nm

Adsorbed gas layer,0.5 nm

Oxide layer, 10 nm

Asperity

Surfacefilm

Tribology

70

Fig. 4.10: Measured leakage rate as a function of the roughness value, Ra

and the direction of the scratches on the surface

71

Surface texturingSurfacetexturingisonewayofincreasingthelubricatingfilminasealrunningabovetheboilingpointoftheliquid(forexamplewaterabove100°C).Nosignificantincreaseofleakagewilltakeplacewhenthesealrunsbelowtheboilingpoint,[7].Pocketsinthesealfacesarefilledwiththepumpedmediumandthereforeactasanextrareservoir,preventingthelubricatingfilmfromevaporatingcompletely.Surfacetexturingcanbeachievedbylasermachiningoretching.Ifthesealringsaremadeofamaterialwithclosedpores,thesealfacesappearasatexturedsurface.Theadvantageofporoussealringsisthatthesurfaceremainstexturedevenwhenthesealringsareworn.

Hydrostatic lubricationAsdescribedinChapter1,seethefiguresonpage14,hydrostaticpressurehasalineardecreasethroughthesealgapwithparallelfaces,whereasthedecreaseisnon-linearwithadivergingorconvergingsealgap.Seefigures1.21and1.22,page19.Evaporationoftheliquidinthesealgapalsoaffectsthepressuredistribution.Vapourhasamuchlowerviscositythanliquid,andthereforetheevaporatedliquidquicklyescapesfromthesealgap.Ontheotherhand,thedensityoftheevaporatedliquidismuchlowerthanthedensityoftheliquid,whichmeansthatthevolumeincreasesbyvaporisation.Thusvaporisationcanincreasethehydrostaticpressureabovethelineardecreaseandpushtheevaporationzoneclosertotheatmosphericside.Seefig.4.11.Calculationsofthehydrostaticpressuredistributioninsealgapswithevaporationcanbeseenin[5].

Fig 4.11: Evaporation in the seal gap can increase the pressure in the gap because the pumped medium expands when it evaporates.

Start of evaporation

Start of evaporation

Pumppressure

Vapourpressure

Atmosphericpressure

Pumppressure

Atmosphericpressure

Entry into seal

Entry into seal

Exit toatmosphere

Pum

p p

ress

ure

Pum

p p

ress

ure

Stationaryseat

Rotating seal ring

Stationaryseat

Rotating seal ring

Exit toatmosphere

Dry runningMechanicalshaftsealsforliquidsmustbelubricatedandcooledbyaliquid.Theshaftsealwillbedamagedifitisallowedtorunwithoutaliquid.Intheabsenceofalubricatingfilminthesealgap,frictionalheatisdissipatedinthesealrings.ThefrictionalheatcausesthetemperatureofthesealringstoincreaseuptoseveralhundreddegreesCelsiusafterfewminutesofdryrunning.Thehightemperaturedamagestheelastomericsecondaryseals.Thetemperaturereachedandthetimeittakestoreachthistemperaturedependtoalargeextentofthematerialsofthesealringsandthedesignoftheseal.Shaftsealswithonecarbonsealringmightbecapableofrunningdryforseveralhourswithoutseveredamagetothesealcomponents.

2. WearWearisanundesiredremovalofmaterialfromasurface.Anumberofprocessesmayleadtowearofasurface.Theseprocessesarecategorisedintofourcommontypesofwear[6]:

• Adhesivewear• Abrasivewear• Corrosivewear• Fatiguewear.

Adhesive wearEvenmacroscopicsmoothsurfacesareroughonanatomicscale.Whensuchtwosurfacesarebroughttogether,contactismadeatrelativelyfewisolatedasperities.Whenanormalloadisapplied,thelocalpressureattheasperitiesbecomesextremelyhigh.Intheabsenceoflubricatingfilmsonthesurface,thesurfacesadheretoeachother.However,verysmallamountsofcontaminantspreventadhesion.Seefig.4.12.Tangentialmotionofonesurfacerelativetoanothermightcausethesurfacefilmtodisperseatthepointofcontact;coldweldingofthejunctioncantakeplace.

Continuedslidingcausesthejunctionstobeshearedandnewjunctionstobeformed.Thisistheadhesivewearprocess.Thesurfacetopographyisveryimportanttopreventadhesivewearasitdeterminesthecontactstressinasperities.Thematerialschosenforsealringsshouldnotbeeasilyweldedtogethertopreventadhesivewear.

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

00 0.05 0.1 0.15

Roughness, Ra [µm]

Direction of rotationLeakage rate [ml/h]

Waviness [µm]

Leakage rate [ml/h]

0.2

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41.0

Surface

Substrate

Contaminant layer,5 nm

Adsorbed gas layer,0.5 nm

Oxide layer, 10 nm

Asperity

Surfacefilm

72

Tribology

Fig. 4.12: Surface of a material with contaminants

Abrasive wearAbrasivewearorabrasionistheploughingofatipfromonematerialinanothermaterial.Whenasperitiesinonesurfaceremovematerialinanothersurface,itisatwo-bodyabrasion.Theresultofthiswearisasurfacewithregulargrooves.Theabrasionprocessiscallederosion,whenaparticleimpingesthesurfaceandthekineticenergyoftheparticleisusedtoremovematerialfromthesurface.Inthiscase,amorerandomsurfacesimilartoagritblastingcanbeobserved.Hardparticlestrappedbetweentwoslidingsurfacesmaycauseseveredamage.Thisiscalledthree-bodyabrasion.Seefig.4.13.

Three-bodyabrasionalsoappearsasregulargroovesinthesurface.Seefig.5.12,page84.

Theresistanceagainstabrasiondependsontheductilityofthesurfaceaswellasthehardnessofthesurfacecomparedtothehardnessofthetipcausingtheabrasionon.Themoreductilethesurface,themoretendencytoplasticdeformationinsteadofdebrisremoval,thisresultsinlesswear.

Corrosive wearWhensurfacesrubagainsteachotherincorrosiveenvironments,reactionproductsmaybeformedonthesurface.Theseproductsoftenhavealowadherencetothesurfaceandcanberemovedbytherubbingandeventuallycauseabrasivedamage.Corrosivewearcanbeobservedonshaftsealswithhardsealfacesinacorrosivemedium.Thiscanbeduetocorrosionofabinderphasereleasinghardgrainsfromthematerial.

Fatigue wearSurfacesrepeatedlysubjectedtolargestressesmightwearonaccountoffatigue.Stressescanbecausedbythemechanicalloadwhichistypicalforrollerbearings.Thelargeststressestosealringsarecausedbythermalgradientsproducedbyfrictionalheatandevaporation.WearonSiCfacesmayoccurinhotwater.ItmaylooklikeabrasivewearbecauseSiCgrainsarepulledoutduetothermalfatigueofSiC.Thegrainspulledoutcauseabrasionofthesealfaces,leavingtheimpressionthatabrasivewearisthecauseofthewear.Thistypeofwearisonlyseenabovethepressureandtemperaturelimitforstablefriction.ThethermalfatigueofSiCmaybeacomplexprocessinvolvingevaporation,cavitationsandcorrosion.

1.8

1.6

1.4

1.2

10.8

0.6

0.4

0.20

0 0.2 0.4 0.6 0.8 1.2 1.41

DebrisHard particle

Velocity

73

Fig. 4.13: Three-body abrasion

Tribology

SummaryThissectiondescribeshowpressurecanbeestablishedinthelubricatingfilmandhowdifferentmechanismscanleadtowear.Pressureinthelubricatingfilmisincreasedwhenthereisawedgeinthesealfaceinthedirectionofthemovingfacesorifevaporationoccursbetweenthesealfaces.Awedgewillappearwithsealringwaviness,hydrodynamictracksorwithsurfacetexture.Themostcommontypesofwearare:adhesivewearwithsealfacesstickingtogether,abrasivewearduetoploughing,corrosiveorfatiguewear,oracombinationoftheseweartypes.

[1] B.S.Nau:“HydrodynamicLubricationinFaceSeals”,3thInt.Conf.onFluidSealing(1967).

[2] BernardJ.Hamrock:“FundamentalsofFluidFilmLubrication”.

[3] A.O.Lebeck:“FaceSealwaviness,prediction,measurement,causesandeffects”,10thInt. Conf.onFluidSealing(1984).

[4] L.E.Hershey:“ExtendingMechanicalSealServiceLifewhenoperatinginhotWater”,7th Int.Conf.onFluidSealing(1975).

[5] P.Waidner:“Evaporationinthegapoffaceseals–Theoreticalcalculationsandresults forhotwaterapplications”,12thInt.Conf.onFluidSealing(1989).

[6] J.T.Burwell:“Surveyofpossiblewearmechanisms”,Wear1(1957),p119–141.

[7] I.Etsion:“AModelforMechanicalSealwithRegularMicrosurfaceStructure”, TribologyTransactions,vol.39(1996),p677-683.

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