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WL-TR-94-2069

DEVELOPMENTOF AHIGH TEMPERATURE,HIGHSPEED DISCLUBRICANT TESTMACHINE DAVIDM ICOLSON RICHARDS SAYLES

TribologySection,DepartmentofMechanicalEngineering,ImperialCollegeofScience,Technology,andMedicine,London,SW72BX. United ingdom

O'..

June1994Sep87 -Jun94

1QO/JJ S

&MZ

Approved forpub licrelease;distribution unlimited.

1 9 9 4 1 2 0 8 0 1 4A ER O PR OPU LS I ON A ND P O W E RDIRECTORATEW R I G H TA B O R A T O R YA IR F O R C E M A T E R I E L C O M M A N D W RIG HT -PAT T ERSO N A IR F O R C E BASE, OH I O 45433-7251

TTr, rwT k

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NOTICEWhengovernmentdrawings specifications or otherdataareusedforanypurposeotherthanmconnectionwithadefinitelygovernment relatedprocurement heUnitedStatesGovernmentincursnoresponsibilityorrSL t1at; 1 nwhatsoever- ecthatheovernmentayhaveo?w ltinY WtYsuPPliedthesaiddrawings specifications orrarlinfctoberegardedbyimplication rotherwiseinanymanneronstrued sicensingheolderrnytherersonrcorporation orasconveyinganyrightsorpermissiontomanufacturethereto aRYpatentedinventionthatmayinanywayberelatedThistechnicalreporthasbeen reviewedandisapprovedforpublication.x^>: - - - - OTHOMASA.JACKON Ph.D.ActingChiefLubricationBranchFuelsandLubricationDivision

ionDirectorate

Ifyouraddresshaschanged ifyouwishtoberemovedfromourmailinglist orittheaddresseeisnolongeremployedbyyouroraanizationpleasenotifyWL/POSL,Wright-PattersonAFBOH 454337103tohelpSsmaintainacurrentmailinglist.CopiesofthisreportshouldnotbereturnedunlessreturnisrequiredXSZS Cntobligations rnoticeona

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R E P O R TD O C U M E N T A T I O NAG E FormApprovedOMBNo .0704-0188Publicreport ingburdenfo rthiscol lect ionof in formationsest imated to average ho u rpe rresponse,inc ludingthet imefo rreviewinginstruct ions,searchingexist ingdatasourcgatheringan dmaintain ingth e datan e e d e d , an dcomplet ing an dreviewingth ecol lect ion ofin formation .en dco m m e n t sregarding thisb u r de ne s t ima teor an yotheraspectof tcol lect ionof in formation ,inc ludingsuggest ions fo rreduc ingthisb u r de n ,to WashingtonHeadquartersServ ices ,Directoratefo rInformationOperat ionsan dReports ,1215JefferDavisHighway,Suite1204,Arlington ,V A2202-4302,an d to th eOfficeof Man ag e m e n tan dB u dge t ,PaperworkReduct ionProject(0704-0188) ,W as hin g t o n ,D C20S03.1.GENCYSENL YLeaveblank) 2 EPORTAT EJune99 4 3 EPORTYP ENDDATESCO VEREDFinal 9/01/87-6/30/944.I T L EAN DUBTITLEDevelopment faHighTemperature,HighpeedDiscLubricantTestMachine

5 UNDINGNUMBERS CF49620-87-C-0084W L / P OE2203FAFOS R /EOARDE1102FPR048T A6W 1

6 AUTHOR(S)David .NicolsonRichard. ayles7 ERFORMINGRGANIZATIONN A ME( S )AN DADDRESS(ES) TribologySectionDepartmentfMechanicalEngineeringImperialCollegefScience, echnology,ndMedicineL o n d o n ,W 7B XUnited ingdom

8.ERFORMINGO RGANIZATIO NREPORTNUMBER

9.PONSORING/MONITORINGAGENCYNAME(S)A NDADDRESS(ES) AeroPropulsionndowerDirectorateWrightLaboratoryAirForceMaterielommandWright-PattersonFBH 45433-725110.SPONSORING /MONITORING AGENCYEPORTNUMBER

W L-TR -94-2069

11.UPPLEMENTARYNO TES

12a.DISTRIBUTION/AVAILABILITYTATEMENT ApprovedorPublicRelease;Distributionsunlimited.12b.ISTRIBUTIONCODE

13.ABSTRACTMaximum 200words)Scuffingnddhesiveailuremodesareutlinedorovideheontextor moredetailedeviewfearubricationdistinguishing,nparticular,elasthydrodynamandboundaryubricationegimes. Themajorcuffingheories,reonsideredagainstheparticularequirements fubricatingatighemperaturesndentrainmentpeeds. Existingubricantestersareclassifiedndvaluatedwithrespectoheirorrelationwithieldxperience. Theeedor discmachineutilizingmini-discsrivenatighpeedssroposedoatisfybothxistingndfutureestequirements. Detailsfigdesign,ommissioningndevelopmentredetailedogetherwithrototypexperiencewhichdictatedhatimprovedepeat-abilityndeproducibilityverurrentmethodsutweighsncompleteeproductionofheontactycle. Earlyfailures f imilarnatureohosexperiencedinhighpeederospaceapplicationsarebeingusedotudyhemechan ismfighspeedhighemperature)cuffingwithyntheticubricants.

14.UBJECTERMS Lubricants, oadCarrying,Test, urbineEngine,HighTemperature 15.NUMBEROFAGES96 16.RICECODE 17. SECURITYCLASSIFICATION OFEPORTUnclassified

18. SECURITYLASSIFICATION OFHISAG E Unclassified 19. SECURITYLASSIFICATIONOFABSTRACT Unclassified

20.IMITATIONOF ABSTRACUnlimited

NS N540-01-280-5500 Standardor m98Rev.-89)PrescribedyNS Itd .39-18298-102

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F O R W A R DThisreportdescribesheresearchonductedypersonnelfImperialollegeL o n d o n

EnglandnContractNo. 49620-87-C-0084.he o rkwaserformeduringheeriodSeptember98 7oJune994.

Theworkwa sccomplishednderProject048,ask,04806,W o rkUnit0480651,HighTemperatureMini -D iscD evelopm ent,withD r.hillipW .entersa sth eprojectmoni to r .

Acr.;'.ioii Fo rLTl'IC 'l/.':II. -> - .

k 1 1 J;:::. ;,-rBy

nrDie tmAv::J: ..: ' , 0Social

11

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1.4.4.3 Baiteile

1 2 59 9

10

ContentsChapter L u b r i c a n toadarryingca pa c i ty 1.0ackground

1 .1Gearcontactmechanics12Gearlubrication1.3Gearfailuremodes1.3.1ea r

1.3.2cuffing1.3.2.1cuff ingtheories1.3.2.2xperienceo fscuffingin otherfields3

1.4Reviewo fadhesivewearandscuffing testmethods51.4.1H im strength testmachines 6 1.4.2implegeometrytestmachines(TypeI Tests)71.4.3Gear testingmachines(TypeI I Tests) 71.4.3.1he LA.Egearlubricanttestmachine91.4.3.2he RZ.G gearlubricanttesting machine0 1.4.3.3he Rydergeartest machine 11.4.4Disclubricanttestingmachines(TypemTests)5 1.4.4.1FAPL disc tester 81.4.4.2heAmslerdisctestmachine 8

281.4.4.4earingSimulator 81.4.4.5earedrollertester 9 1.4.4.6earrollertester 9 1.4.4.7ig ht e m p e r a t u r e ep tester 9 1.4.4.8ini-disc \1.4.4.9mperial/Mobil3.5" hydrostaticdisc machine01.4.4.10ociety of AutomotiveEngineers'disctestmachine1

1.5heimplications fo rL CCtestingwithdevelopments intransmission lubricantsan dmaterialsChapter2 Mini-disconf igu r at ionn design 2.1Designobjectives 0

2.2yder gearcontactparameters J2.2.1ydersimulation 2 33

m

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2.3earingsimulationusingdiscs 72.4esting costs 32.5eneralarrangement o f mini-disctest rig 9

2.5.1rive-train 22.5.2upportand loadingof discs 3

2.5.2.1asbearings 42.5.2.2ybridtilting pads 52.5.2.3ivotdesign2.5.2.4esthead lubrication 22.5.2.5ncillarylubrication 2

2.5.3ealing 32.5.4Heating g

2.5.4.1nsulation 72.5.5nstrumentation2.5.5.1orque measurement g2.5.5.2emperature measuremen t 92.5.5.3peed measurement 02.5.5.4iscload 0

Chapter3 R esultsn destrogramme3.1ummaryo f commissioningandpreliminarytesting23.2esultsof teststo date 23.3equirementsfor futuretestingand analysis 5References g

rv

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10 19 20

Listfi gu r e s Figure1.1 Rydergeartoothcontactc y c l eus ing measuredflank prof i lesFigure1.2 Lu b r ican tregimesFigure1.3 Coeff icient offriction versusspecif ic film thicknessFigure1 .4 Wear regime Figure1.5 IA E geartest m achineFigure1 .6 F2Ggear testing machineFigure1.7 Crosssection ofRydergeartestm a c h i n e 2 Figure1.8 Effect oftoothhunt ing 3 Figure1 .9 Ryder toothloading 4 Figure1.10 Gearcontacts imulat ionb y discs 6 Figure1.11 Imperial/Mob disc ma ch ine 1Figure1.12 S AE disc machine 2Figure1.13u lk lubricanttemperaturewith projected aircraft speed 3 Figure1.14el icopter maingearboxlubricantdeve lopment4 Figure1.15andidate lubricantf luidsforelevated temperature5 Figure2.1isc sl id ingveloc i tyversusloadfo r constantPV s2 Figure22hermalbehaviourofth eRy dertestaccord ing toOlver'sm od e l3 Figure2 .3hermalbehaviour ofmini-discaccord ing to Olver'sm o d e l4Figure2 .4redictedeffectofspeed upondisc scuf f ingFigure2 .5ractical d Nrating

Figure2 .6in i-discversusRy dertestingcos t sFigure2 .7ini -discspecimen Figure2 .8eneralarrangementofmini-disctestri g 051Figure2 .9chematic ofdrive-train Figure2.10asbearing Figure2.11ydrostatic pad withintegralpiston Figure2 .12ivoted pad journalbearingafterMiche l lan dhybrid version6 Figure2.13ad design optimisation rout ine 8Figure2 .14y br idpad performance Figure2.15ketchofhybrid pad Figure2 .16inalan dprototypehybridpadssec t ionedat middlestation1Figure2.17chematic oflabyrinthsealFigure2.18esign oflabyrinthseal i.4 5 4 7 48 4 9 5 2 5 4 5 5 5 9 6 0

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Figure2.19nduct ionheating ofAM S6 2 6 0an dsi l icon nitridediscs6 Figure2.20chematic oftorquemeasurement 8Figure2.21is c temperaturemeasurementb yinfra-red emiss ion9 F i g u re3.1Conventional 's c u f f 7 F i g u re3.2urface topographyofmini-disc afterrunning-in8F i g u re3.3urface topographyofscuf fedmin i -d isc 9 F i g u re3.4reliminary scuff ing resultswith highspeed mini-disc0 F i g u re3.5o g fi le10/11^3 1F i g u re3 .6i ighspeed's cu f f 2 Figure3.7urfacetopography ofTiighspeed 's cu f f 3Figure3.8xialbandsof*polished m ini -d isc 4 Figure3.9ogfile11/11/93 4 Figure3.10og file16/11/93 5 Figure3.11lternativeapproachesto assessofscuff ingenvelope6

vi

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Listfab lesTable1. 1ubrica ntfi lm strengthtestingmachinescategorisedb y type6 Table2arametersfo r IAE,FZG an d Rydergeartestmachines8Table1.3i sc machine operat ingcondi t ions 7 Table 2.1p ec i m enconf igurations 9 Table 22yder gearcontactparameters 1 Table 2 .3ecessed hydrostat ic ,hydrodynanrican d plainbearing parameters6

vu

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Chapter1L u b r i c a n tL o a dCarrying Capacity

1.0 B a c k g r o u n dAk eyrequirement in th edeve lopmentoftransmiss ionsi s th eneed to increasespeci f icpower ,i .e.torqueand/orangularveloc ity p eruni tmass ,withoutimped ing upon rel iabil i ty .Existingtestmethodsar einadequatein predict ingcertainfailure mechani sms ,such as scuf f ing,andhave resulted in the need to developalternativeload carrying capaci tytests.Load carryingcapaci ty i s on e mea s ureof lubricat ionef f i cacy .Thisreport out l inesth edesignan d construct ionofa mini-disc ri gto evaluatescuff ing,togetherwithtestresul tsundertaken at ImperialCollege,London on behal fofWrightPattersonairforcebase(WPAFB).

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1.1 GearContactM e ch a n i c sTooth contactloadsvary duringmeshing an dth erelativemotionbetweenth eteeth comprisesbothsl id ingan d rol l ingat differentpointswithin th emeshing c y c l e .his c y c l eis illustrated in Figure1.1from m a x i m u mnegativesl id ing1tengagement ,throughzeroat th epitch point(i.e.purerol l ing)to m a x i m u mposit ivesl id ingatdisengagement .

Fi gure1. 1v der G e a r ToothCo n tac tCvcle UsingMeasimjd F lan k Profiles(CourtesyofEat on TransmissionsIM\

-% loadsharing

10 15 205Rollangle, 30 351Slidingistame d asthedifferencebetweentherespectiverollingvelocit ieso fmeshingteeth.Fo rslidingto be posit ive,conventiondictatesthatbothrollingan dsliding arei n th esamedirection.

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Staticcontactanalysis datawasemployed to p r o d u c eFigure1.1,he n c en o al lowancewasmadefo rdynamic effects,al ignmentorpitche n o r swhichwi l lsuper imposetransientloads .Intransmitt ingp o w eran d relativemot ionbetweengeared shafts,toothcontacti s non-conformal .or a rectangularcontact2ofwidth/,th emeancontactstresscan b edefined as:aoad - w contactarea 2xbxl '

where:IxWxR'

(2 )b-4xWxR'" V*x lxE*

* ( ) R l& R2 ar eradiiofteethat pointofcontact,Eiand E2,vian d V 2 ar em o d u l ian d Poison 'sratiosrespec t ive ly .Given oy =hardness:w _(hardness)2

H e n c ed ie opt imum materialparameteris oneofhigh(hardness2/E*),whilstth erelativeradius,R' ,varieswith rollangle .Besidesal lowab le contactstress,th egeometry ofth etoothmeansthattherewil lalsob eatensilestressat therootfi l letdu eto bending.fth etoothis model l edas a cantilever then from:

2I n pract icetoothcontactis- elliptical buto fhighaspectratioinspurgears.or simplicitythishasbeenapproximated t o anominalline contactfo rthepurposeso fthisstudy.

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Mxy/ 4)

it can b eshown,AGMA( 19 65)thatW =fn(hardnessgeometry) _wheregeometry embra cestoothshape ,thicknessan d rootfilletT herootbendingstressistensi lean doc c u r sonth esurfacewhilstth em a x i m u m compress ivestressissub-sur facean dthereforeconstrained,oc> typica l ly1 .2 G Pac f.0 .5 GPafo rperformancegears.In practice,th eteethar eheattreatedwhi c hmodif iesth eargumentabove ,insofarasth ematerialis n o longer hom oge n e ou swhilstth econtactis no tsmoothb u toc c u r sovernumerous discreteasperities.Inaddition,toothmeshingis dynamicwhichaffectsbothtoothloadingan dintroducesfatiguewheretoughnessis paramount.Neverthelessth eanalysisd oe sprov ideanins ightintoth erequisitematerialparametersfor gears.

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1 .2 Gearu b r i ca t io nWhils ttractioncanb eimproved b y increas ing th e equ ivalentm od u l u s ,E * ,in orderto reduce th eareaofcontact ,in pract icem u c h more isto b ega inedfrom lubricat ion.hreeregimes ,shownin Figure12ar ebroadlydist inguishable correspond ing to th evariationincontactcond i t ionsillustrated in Figure1.1:o u n d a r yb l) ixed u ll Elastohydrodynamic lubricat ionehl)

Figure1.2ubricantR e g i me s

Contact\/ Mechanics \\A/\ SurfaceN^ A/ F l u i d \hemistry Dynamics] "MIXED" VJ c 0- (Practical GearOperation)

Boundarylubricat ion i sthatwhich"cannotb eattributedtoth e b u l k viscouspropertiesofth elubricant ,b u tarisesfrom aspecif icsolidlubricant interact ion".Boundarylubricat ion l owerstraction.hi sis achievedb y th ecreationoflo wshearstrengthinterfac ia lf i lmsappropriateto th eseverity ofth econtact(temperature,pressurean dsl id ingspeed)reduc ingadhesionan dtraction.T hemechani sm an d interaction offluidan dmaterialparametersis c om p l e xan ddominated b yth ephys i ca land chemical propertiesofth esurfacesin c o n t a c tncreased rotational speed assisted b y better finish,improved geometryor higherl ubr i cantinletviscosity,wil l

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enableafullelastohydrodynamicfilm to developvi aamixed regimeasillustratedin Figure.3.

Figure1.3oefficientofFrictionversmS pecificFilmThfrR r|ff? j f i

Min.fluidfriction0.01

A =

where(6)

h= filmthicknessOi

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/O 7x7 7 07xg"x/'041xE*0* 3h =27xY 3 7 )

whereU=U]+2Ui& 2re peripheralveloc i t i esofbodies1& 2 respec t ive lyFrom Equation(7 )it is ev identthatdie m i n i m u mfi lm thicknessisstrongly inf luencedb y th eentrainmentspeed ,U,th ein let viscosity, 7 ,an dthe pressure viscos i ty coef f i c ient ,aGear geometryan dspeed dictateth eentrainmentspeed.ubricant t h e o l o g ydeterminesth einletviscos i ty and pressurev i scos i ty coeff icient,largely accordingto temperature.The opt imum fi lm th i cknessis mat whi c hjust ,complete lyseparatesth esurfaces .In pract icethe in f luenceoftemperatureupon viscosityis substantial lygreater than u p onth epressure viscosity coeff ic ientan d it is thereforeth ev i scos i ty indexwhich is opt imised.Thebenefitsofoperat ing u n d e rful l e las tohydrodynamkcond i t ionsw o u l d mean complete separation ofth etoothsurfaces .H owe v e r ,in pract ice,l o w rotationalsp eed and/orweight,prec ludethis.Itm ay b ec on c l u d e dthatdis t ingu i shingbetweenregimesdependsu p o n whether shearis predominant lywithinth ef lu id filmor withinth esurfacelayers.ransition betweenregimesdependsu p o nspec i f i c operatingcondit ionss uchas gear typeandarrangement,material,loading,accuracy ,f inish,lubricant ,lubricat ionan dc leanl iness. H e n c eeffective gear design needsto take intoaccount:i . Gear size in relation to load carryingcapacity 3an d resistanceto scuf f ing4ii . Allowablecontactstressand resistanceto pittingi i i . Toothsizeto ensureadequatebendingstrength iv . Cost3Scuf f ingis use d as th ecriterionofL CC whi ls t operatingin th eM ixedR e g i m eofFigureL 2 ,an dis th etransition frommildacceptable wearocatastrophicwear

T h etermsatfingsuse d t hroughoutratherthanth eAmericanusa geofscoring.

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Whereadvancedtransmiss ionsar econcerned(i),(ii)an d(iii)ar eofprimaryconcernin maximis ingspecif ic p owe ran d reliabil ity.h is iss ou ghtb ymaximis ingLoad CarryingCapacityand/orspeed* throughoptimising g eo m et ry ,dynamics ,material,lubricant etc .Thiss tudyis primarily concerned withth enature ofextens iveadhesiveweara saresultofc om b i n e d boundary an d elastohydrodynamic lubricat ion fa i lure.

5 Hsing(1974)import a nceofL CCu p o ntransmiss ionw e i g h tw h e r e50% ofc o m m e r c i a ll ifecyclear eattr ibutable to fue l(weight)an dCocking(19 84)highratiof inalstageconfigurat ion

8

costs

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1.3 Gearai lureModesT heAGMAc lassif ies gear failure m od e sas follows:

ea r lasticflowScuffing ractureInterferencerocessRelatedSurface fatigueompound

Gearfailure is frequentlymulti fariousan d s uchdist inct ionsar eprimarilya meansofcharacterisat ion.orth epurposeofthis report wearandscuffingre rev iewed .Scuff ingoftenmanifestsitself asgrosswear.1.3.1 W e a rIf th elubricant fi lm between meshing teethduringrunning i sinsuff icient to separateth esurfaces ,asperity contactwilllead to wear.Wearcan b ecategorised as :

ol ishing oderate xcessive Pol i shingwear isth em o stfrequentlyobserved wherelo w speedgearsoperat ingin ab ou n daryregimec om b i n easperitycontactwithextreme pressure(ep)action.Moderatewear c ano c c u rat geartipsan d roots,wheregearsar einsuff iciently hardan de pact ioninadequate.revention is poss ib leb yus ingeither amoreviscous or act ivelubr ica ntorb y changing th eoperatingcondit ions,i .e.geometry ,surfacefinish,load,etc.If wearis a l lowedto b e c o m eexcess ivethe reduct ion in tooththicknessand/orcreation o fcrack initiationsiteswilleventual lyimpairtoothbendingstrength.

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T w ofurthertypesofwearar eofnote:abrasion,two or three-body,an d corrosion.Ineffectivelubricantfiltration promotestw ob od y abras ion,whilstcondensat ion,fo rexample ,can causecorrosivewear.Acceptab lelevelsofwearvary.orexample ,whati s considered acceptablefo r automotive gears,is l ikely to b e excess ivefo rasetofprecis ion instrumentgears.Wear during' running- in'is invariablyconsidered benef i c ia l .W e a rregimescan b edepicted in termsofload-speed plotsasshownin Figure1.4.

Figure1.4Wear Reg i m es .Shel lriQfif lBandingfatiguefailure

Impactfracture

Partialhy dro dy n amc Tslow wear inevitable Fu P hydrodynamiclubrication, possibleabrasivewearbycontaminants

Speed

1.3.2 Scuf f ingScuf f ingisdef inedb yth eA G M A(1980)as "grossadhesivewear,characterisedb ytoothasperitycontactsweld ingan dtearing".tis usua l lyth eresul toftoothdamageassociated with defectivelubricat ion.ocal ised scuff ing,fo r example ,can b ecausedasaresultoftoothmisal ignment,form errors,inadequateti pre l ie forexcess ive dynamicloading.ncontrast to othertypesoflubrication-related toothfa i lurewhich taket imeto develop,

10

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scuf f ingo c c u r sprecipi tously6an dis thereforeofprimaryconcern.Unlesscaughtearlyon an d rectif ied,scuff ingwill renderagearse ttotally un-serviceable. Very l ightscuff ing,termed./r0i/,can either healcomplete ly ifcond i t ionschange ,or remainl imited to th erootfal lowedto deve lop ,materia llossa b ov ean d b e l o wth epitch l inewil ldestroyth etooth profile,create noisean dvibrat ion,an dm ay lead eventual ly to toothfracture.1.3.2.1 ScuffingheoriesScuf f ingmechani smscan b esummarisedas acombinat ion ofBlok'scr i t icaltemperaturecriterion an d Dyson'sfa i lureofehl.heremaininghypothesesar eto agreater or lesser extentbased orderivedfrom these,Dyson (1975) .Blok attributesgearfailure to a crit ica ltemperature,compris ing th esu m ofthe b u l k (skin)temperature an dth eflashtemperature rise in th econtact ,0f,whichm ayfo r agiven material/ lubricantcombinat ion b ewritten as:

/' pxiyx(v 11)where:li=coeff icient o ffriction W =loadperunitlengthvi,V2 =sl id ing veloc i tyofbod ies1& 2 B\,Bi=thermalconstant ofb od i e s & 2 b=contacthalf-width,Ref.Equation(2 )

(8)

6'Fatiguescoring'phenomenainvestigated byMacPherson(1972)is oneofsurfacemicro-pittingfatiguecausing scuffing.

1 1

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Asvian dV 2nrp mofpinion

hence e,-xw*x** 10)

whi c h ,ifn is constantm ay b erewritten,2(n)lxW=constant .

whi c his similar to th ePV Scriteria7,namely:n2xW=constant (12)

Dyson'stheory,onth eotherhand,is based onth el ambdaconcept ,namely ,ifth eratiooffilm thickness to compos i tesurfaceroughnessislessthanuni ty ,thenfailure ofehlan dscuf f ingar emorel ikely to occur .Sinceehlis stronglyaffectedb ylubricantinletviscos i ty ,an yreduct ionin v i scos i ty wil lincreaseth elevelo fasperitycontactand,in turn,r e d u c einletviscosity throughthermalf eedback .helocal isedlubr icantf i lmsbetweencontact ingasperities,known as micro-ehlwill col lapsein th eabsenceofhighambient pressurecreatedb y th emacrc-eh lhenceafilm separating th esurfacesnolonger exists.T h u swhi leBlokscriterionis on eofcritical contacttemperature,thatofDyson'sis crit icalinlettemperature.mpiricalevidenceover th evalidity ofeither theory variesaccordingto th esourcean dtestmethodemployed.However ,their u se is widespread in th eabsenceof7PV SafterA l m e n(1942) ,th epr od uctofth emeanHertzianpressure an dth es l id ingve loc i ty ,w hereP * V W an dVs~nhencePV,Wn2 .Grosberg(1977)not esth ee x p o n e n tvariesbe twe e n-1an d2 a ccord ingto th esource.

12

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betteralternatives8.mplic itin thisempiricism isth ediff icul tyin predict ingth e onsetofscuff ing,especial ly whereformulatedlubricantsar econcerned.In pract ice ,b ou n daryf i lmscompl i cate matters an dan y adequatescuf f ingtheorym u s texplain bothth efailure ofe las tohydrodynamican dsubsequent fa i lure ofth ebounda ryf i lm.inalanalysisindicatesthat it is th ewear ofth eboundaryfi lm thatdictatest f w jrtual onsetofscuff ing,orequa l ly ,recoverywhereth e coef f i c i entofbounda ry frict ionis lo w enough to permit d ie ehlfilm to re-form.Itis usual ly poss ib leto ensurescuf f ingisavoided b y refining d ie surface f inish,modi fy ingdie tooth prof i le ,improvinglubr ica ntadditive o rcoo l ing . However,in s om e circumstances it m ayb enecessaryto redesign th egear.orexample ,af inerpitchwillreduce die extentofs l iding,albeit for a reduct ionin toothbendingstrength.ncreasedlubricantviscosity is not necessari ly benef i c ia l ,asviscousshear heatingc anlead to areducedfilm bes idesincreasingtraction.1.3.2.2xperiencefcuffingntherieldsScuf f ingcan o c c u r in eng inesbetween piston-ringand bore,and on occas ionbetween piston-skirt an d bore.xper iencehasl ed to empir i ca ldes ignsfo r b om piston an d ring,subject to:

pplication: rateofpressure rise,bore distortion,r u b b i n gspeed ,an d temperature.aterial: ringan d l inercompatibi l i ty ,and finish.ubricant: addit ives .For example,piston-ring chromium plat ingan d cross-honing ofth ebore c an b ec om b i n e dwithanappropriatelubricantadditive to mitigateagainstscuff ing,Avery(1967)& Neale(1974) .Neale(1971)notesthat piston ringscuff ing is not c o m m o nin serviceasconsiderableeffortis expended during deve lopmentin prevent ion.

8Fo rexample,AGMA(1965)advocatesaflashtemperatureo f145Cfo rAMS6 2 6 0spurgearshardened to 60Rcandlubricatedwithan esterto Mil-L-7808.

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Scuff ingcan alsoo c c u rbetween c a m san dtappets,Dyson(1961) .hedynamicsar emorec om p l e xthanthose ofpiston-ringan dbore,as rotationofth etappettendsto redu ceth eflashtemperaturean dhelprenew th econtactsurface,whilstth econtactgeometry an dfriction vary with c am rotation.n c e againapplicat ion,materialan dlubricantinf luence th el ikel ihood ofscuf f ing.orexample ,historically chi l led cast-iron c a m san d tappetshavebeenusedto resistscuff ing.More recentlyactivelubricantsan d overheadc am des igns ,whichr e d u c evalvetrainloads,haveenabledalternative materialswhichar emoreresistantto pitt ingto b eusedsuccessfu l ly .Assessed underB l o k ' scriterion;typicalflashtemperaturesat 5 0 0 0 rp m ar eofth eordero f180C,b u tcan b eas highas 350Cwithfriction coef f i c ient saround 0 .08.Designsar ealsofrequentlyassessed onP V ,withtypicalvaluesin th eregionof33GPam/s.lash temperaturesfo rpiston-ringan dborear eofth esameorderasbetween c am an dtappe* ,b u tsignif icandy higher a mbienttemperaturemea nsthatasperity contactis particularlyundesirable .Although scuff ing p ers eis n otexperienced with rol l inge lementbearings,a form ofadhesivewear,k n ownassmearing,issomet imesobserved wherethereiss ignif icants l iding.rime l ocat ionsar ebetween:

hec a gean drol l ingelementsth ef lange an d roller contactsin rollerbearingsth einnerracean d elements in highspeedl ightlyloadedbearings

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1 .4 ReviewofAdhesiveWearndcuf f ingestMethodsAt th eturnofth ecenturylubricanttestingwaslargely conf ined to viscos i ty ,specif ic gravity,flashpointan d colour ,H y d e(1922) .An oi l 'ssuitabi l i tyfo rany part icularappl icat ion w o u l db e derivedfrom eitherexperience or journaltesterss u c has th eThurstonorIngram &Stapfer, Hurs t(1911) .Althoughth epropertyofo i l iness was observed it was notunt i lref inedmineraloi ls gainedwideracceptanceas lubricants 9thatattemptswere m a d eto identifyit snature.Earlyfi lm strengthlubricanttestmachinessuchas th eNapier,similarin configurat ionto th eT u n k e n ,were developed asth eadventofhypoid gearing10addedimpetusto th edemand for epand subsequent lyanti-wear additives,Musgrove(1944) .T hecourse oflubricant deve lopmenthas le d to aproliferation oflubricant testersemploy ing n u m e r o u sconf igurations to assess lubricant performance withoutth ecostan dcomplexi ty offield servicetesting.S u c hteststendto ratelubricantsaccording to specif ic operatingcond i t ions ,inc luding:

Film StrengthCorrosionCompatibilitye.g.with elastomericsealsan d gear casematerials) DepositionFoamingOxidationandthermalstabilityWear

9Frequentlyo naccountofotherproperties,suchasbetteroxidation resistance.10Manyearlyfailuresofhypoid gearscouldb etracedto insufficientrigidityo fth eassembly, b u twhenrigidlymounted,satisfactory operation requiredasuitablyactivelubricant even

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1.4.1 FilmtrengthestMachinesEaseofmoni tor ingtestparameters,acceleratedtesting an d reducedtest-costpromotes laboratory overfield testing.However,extremecaution m u s tb etakenin correlating resul tsagainstful l-scaleservice,Macpherson( 1 9 8 6 )an dWolf(1932) .In view thatth eresearchundertakenonbehal f ofW P A F Bis primarilyconcerned with scuf f ing,film strengthtestinemo&i /macnineshavebeen reviewedin isolationwith respectto assess ing lubr ica ntLoadCarryingCapacity .Laboratorytestmethodsusedto assesswear an dscuf f ingperformancecan b ecategorised into threetypesoflubricanttestmachine:

impleGeometry Testing Machines:thoseus ing s imple geometrictestspec imensunderpuresl id ingcond i t ions(referredto as Type ITests).GearTestMachines:thoseus inggearsasth etestspecimen (referredto as T y p eH Tests).Disc TestMachines:thoseus ing discsto s imulate aparticularpointo o th epathofcontact(referred to as T y p e mtests).

Table1 ,1ubricantR im StrengthTesting MachineCatepnri^H r y Typ f t TYPE

m m m

P in&'Vb l o c k (Falex)B l o c k &ringTimken .es t4-Ballm/c(S he l l -S e ta ,Falex)Almen AlphaL F W-1Timken Ry derGearm fc

FZGGearm/cIAEGea rm/c

Am slerdiscmac hin eS AE disc mac hin e

Im pe r ia l /Mobi l Corytondiscmac hin e

F A 1 M I W E rPTTPPI^spe c i f i c wear seizurespe c i f i c wear seizurespecific w ear seizure

seizurespecif ic wear spec i f icareascuffedspecific wearspec i f icareascuffed.in it ia lscuffspecif ic areas c u f fspecif ic wear in it ia lscuffspecif ic wearin it ia lscuffspecif ic wear in i t ialscuff

STANDARDASTMD - 2 6 7 0 ASTMD-3233 IP2 4 0 ASTMD-2509IP2 39 ASTMD-2783 ASTMD-4172ASTM D-2714 ASTMD-1947IP33 4 DIN5135 4

IP16 6

Fed.TestSt d79 1mthd65 01 .1

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1.4.2 SimpleGeometryest ingMachinesTypeests)Convenience an dth erelativeease b y whi c hparameters c anb emonitored accountsfo rth ewidespreadu se o fSimpleGeometry Testing Machines.hel imited correlation withfiddexperience c anb e attributedto inadequatereproduct ion ofservicecond i t ionsin alaboratory environmentan d th ec o m p l ex it y an d diversenatureofpracticalsystems.No attemptis madeto s imulate th egear contactc y c l e oran ypartofithemotion iso n e ofpuresliding an dcontactgeometry varieswithrun-time although th eFakxtestdoes attemptto partly caterfo rth ec h a n g e in contactcondit ions b y spec i fy inga run-in procedure .T helimitationofpuresl id ingis ac o m m o n feature ofType Itestsan d h asbeentackledb y var iousresearchers,such asBrix( 1 9 4 6 )w h o modi f i ed th eTunken conf iguration to osci l late onerotating disc againstaself-al igning plate to introduceroll ing. 1.4.3 GearestingM a c h i n e sT y p eIests)GearTesting Machinesu se spurgearsastestspec imensto determinedie relativeload carryingcapacityoflubricantswithp o w erre-circulating on th efour-square princ iple.Thisal lows torqueto b e"locked" into th esystem,whereby th ep owe rrequiredis merely thatneeded to overcomesystem losses .T heoperating c ondit ionsofGear Test ing ,Machinesar epre^ieterrnincdto ensure thatth em o d eoffailureis invariablyscuff ing with increased torque.Gear testsar eused to compare relativeperformanceofo n e o i lto another, ratherthanan absolute measure ofperformance. Therear ethreekey differencesb e t w eenth evarioustypesofgear machines:

he method ofapply ingth eload,during running orstatichetheror notth eteethhunt

th eextent to whichth elubricant bulktemperatureiscontrolled

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Ta ble1.2 out l inesth egearan doperatingparametersfo rth emajor typesofGearTestingMachines.

Table1 .2ea r an dQperar inpParam et ersfnr T ARFTfiUan dR v d e r Ge a r Tes t Machines

G e area ta ch i ne IA E IA E IA E P Z G . F Z G .R Y D E R Pinionspeed,rpm 2000 4000 60 0 0 2175 2175 10000No .ofteeth,pinion/gear 15/16 15/16 15/16 16/24 16/24 28/28Addendum mod.co e f.xo 0.375 0.375 0.375 0.8635 0 0 Addendum mod.coef.xG 0.494 0.494 0.494 -0.5 0 0 tiprelief,pinJGearu r n 12.7,7. 6 1 1 7 ,7. 6 12.7,7. 6 0 0 5-1012Pressureangle 2 6 3 1 7 2 6 3 1 7 26.317 22J 22.5 22JFacewidth,m 4.77E-3 4.77E-3 4.77E-3 20.1E-3 20.1E-3 635E-3TestOu temperature. C 6 0 70 11 0 9 0 9 0 74 Testoi lflow,mlt/min 28 4 56 8 56 8 Di p Di p 270 InitialLoad,N 12 7 12 7 12 7 90 9 0 93 Load-stressincrement1^ 6 4N 6 4N 6 4N 185MPa 185MPa 93N Runningperiod,min 5 5 5 15 7.5 10 Rest period,m in 5 5 5 A/R A/R 10 Maxsl idingvelocitym /s 3.96 7.92 11.89 3.96 3.6 11.89Pitchl inevelocitym /s 8. 4 16.7 25.1 8. 3 8. 3 46.74

11I n additionto th econdit ionsdetailedin Table1.2 theIAE geartestca nalso b e carriedou tat 200C,ateither2000rp mor 60 0 0rpm.1ZIntriguinglygearswereoriginallyspecified withouttip reliefon thegroundsthatitdi dno timproverepeatability,Ryder(1959).Figure1.9 indicatest h a tth etipreliefnow specifiedis relativelyinsignificant.13IAE&Ryderar epitchlinetoads,FZ Gis crowntoothstress.

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1.4.3.1h enstitutefAutomotiveEngineers'IAE)earestmachineFigure1.5AE Gear TestMachine.MansionM9S21

MOOTHSt**.

ITOOTHTUT

ISTOOTHTOT

TheIA Egearteststipulatesatotalof fourdeterminationsrunningtwo pairsofgears,testingbothforwarda nd reversefaces.hegearsoperatea tanextended centre,giving riseto a highpressureanglea nd consequendyincreased relativesliding.Thetestisinterruptedbetweeneachloadstagefo ra visualinspectionof th eteeth.f lessthan60 %ofthefacearea aboveth epitchlineisscuffed,thetoothloadisincreased by lockingadditionaltorqueinto th esystem whilstth erig isstatic.n th eeventthatonlyonefaceisdam aged thisisdeemedaninitialfailureload.omplete failurerequiresthatboth faceandcounterfacea redamaged .Hence,anaveragefailureloadis derived from eightfailurevalues,initiala ndcomplete.

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W hilst f lowrateandinitialtemperatureofthetest lubricanta re controlled,no provisionism a d efo rcooling.Howeverth einterruptionsbetweeneachloadstagewillallowth egearsto cool..5litresoftestlubricanta rerequiredfo reach run.

1.4.3.2TheZ GForschungsstellerahnrderndGetriebebau14)g e arubricantestingmachineTheFZ Ggeartest machineshownin Figure1.6issimilartoth eIA E testm ach ine.wo gearprofileshavebeenstandardised,detailedas"A "a ndMCin Table12.Thepinion ofprofile"C "ha salong addendum to increaseth eextentofslidingwhichisnecessaryto testfullyformulated oils.

Figure1.6ZT.geartesting mach ine.IP334/80

ooiv imO TO U..H0t*m)T11 ,1 \.*fMUVMOCA H S

TOROUCMIASUMtMCLUTCH

C3

c

V>* "

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An immersionheateris used toraiseth es umptemperatureto 9 0 C beforeth etestc om m e n c e s .hegearshuntan d ar edip l ubr i catedAteach loadstageth egearsar einspected fo r scuff ing an dweighed fo rwearwhilstth elubr ica nti s coo ledba ckto 90C.T he failure load is thatatwhichth ewearrateincreases dramatical ly ,i.e.it is necessaryto b eable t odist inguish betweenload stagesoflowan d highwear.As withth eIA Etest,bothfacesofth eteethar eu sed fo r rat ing purposes .Discrepancies betweenforwardan dreverse resultsm ay oc c u r when test ingactive lubricants ,an d ratingsar econsidered suspectifthey differ b y morema n o n e loadstagefo ra given machine.T he particular strength ofth eFZ Gtestis attributedb yOlver (1993)to b eth ecoo l ing ofthe testlubricantback to 9 0 Cbetween eachloadstage.h is ensuresthateachstagestartsfrom a c o m m o n bu lk temperature,1.4.33TheRydere arestmachineASTMD1947,or th eRyder testas it is more c o m m o n l y k n own ,i s illustrated in Figure1.7.orqueisintroduced into th e four-square arrangementb yapplying hydraulic pressure duringrunning to producean axialload o n th ehel i ca lslavegears.At the endofeach load stage,th etorqueis released when th etestisinterrupted fo rinspection ofth eteeth.B om d ie Erdco&W A D Dgear testmachinesar esimilar in conf igurationan d operation,an d b om c o m p l ywithASTMD1947-77.heW A D D gear testmachinei s,in essence ,adeve lopmentofth eRyder.mprovements in materialand des ign permitoperation u pto 30,000 rp m an d370C.T hetestheadisarrangedto u se only5 00 m loftestlubricant ,withaseparatelubricantsupplybe ingusedfo rth eremainderofth etest-rigwhi c hismaintainedat 743C.However ,thereisnoprovisionfo r cool ing ofth etestlubr ica ntan d despiterapidrec irculat ionan d exposed pipework it issuggested thatin pract iceit riseswel labove74Cin d ie higherloadstagesan dthishas considerable inf luenceu p o n lubricantperformance.

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Figure1.7rossSectionofR yder GearTestMachine.A S T Mn047)

p D r iveShaf tQ D rivenShaf tR S laveG e a rS SlaveG e a rT TestG e a r(narrow) U TestG e a r(wide)

V Supporto ilin W Supportandloado ilin X Supporta ndloado ilin Y L o a dchamberZ L o a dchamber

ScuffingfrequentlyoccursatafairlylowloadintheRydertestasaconsequenceof thelackof toothhunting.hespreado fdamageismoregradualthanineithertheFZG or IA Egear testmachines,asillustratedin Figure1.8.

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Figure1.8ffectofToothHunting.Benzing(19ftn

IAE.FZQ

Load

R y d e rrecognised thatth efrequentoccurrenceofscuffing undervery lo wloadsremained limited to th etipsandd id n o tdevelopuntilth elaterload stages.n orderto discriminate lubricantperformancehearbitrarily defined th ecriterionfo rfailureas215%of totaltootharea scuffed,whichis equivalentto tw o thirds of th eteem scuffed over onethird of then-workingarea,Ryder (19S9).n practice,itisnecessaryto applyload stagesbeyond thoserequired forRyder's22.5% criterionto identify th efailureload stagewitha nyconfidence. Forcertainactive lubricants thiscan prejudicesubsequenttestingon thereverse side.E a c h pairofgearsa retested onbothflanksa sperth eIA E test.fonlytw odeterm inat ionsa re m a d e ,i.e.asinglepairofgears,repeatabilitystipulatesthatscuffingloadsdo no tdifferby morethan13.8kN/m a t95% confidencelevels. hereas if four determinat ionsa rem a d ethenth eaverage ofeachpairshouldnotdifferby more than 9.75kNAn.R eproducibilitybetweeninstallationsspecifiesthatsingleobservationstakena ttw o posi t ionsmustagreewithin13.8kN/m a t95 %confidencelevels, whilstthe averag esmus tagreewithin 11.6kNAn.

L o a d ratingsa re usuallyquotedrelativeto a standard reference oil,fo r example;Mil-L-7808is rated a t88%ofRef .O ilC which ha sa failure loadof73 kN/mbasedupon fourdeterminations.Thedifficultiesin meetingtheseconditionshavebeen reviewedby variousauthors.Forexample,workbyKelley(1953)showedthata nincreasein surfaceroughnessof0.25

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micronsr .m scan decrease loadc a n y i n g capaci tyb y25% an dmisal ignmentofonly 0.005radianscan decreaseth eload carryingcapaci tyb y3 5 % .Carper( 1 9 7 1 )demonstratedthatti pre l ie fofonly10microns ,whichis withinth eRydergearto lerance,can increased ie load carryingcapac i tyb ys om e5 0 % .More r e c e n d y ,W i l so n(1987)detailed die problemsexper iencedb ySier Bath,asubsidiaryofAlcor ,in matching th eperformance ofth eoriginalPratt& Whitney gears despite c loseattentionto tolerance.Furthermore,analysisofmeasuredtoothprof i leshas revealed prematuree n ga ge m e n tofdie Ryderteethunderl oad ,in advanceofconjugate action.his w o u l d a c c ou n tfo r th elocal ised scuff ing exper iencedat lo w load stagesan dwil l affectrepeatabil ity.(Thisis no tapparent from Figure1 .9 as rol langleis used asth eabscissa).

Figure1.9vderToothLoading.fCourtesv ofEatonT ransmissions T jf l)

G Pa

10 1505R o l langle, 30 3524

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1.4.4 Discu b r i ca ntest ingM a ch ine sT y p eIIests)AlthoughMerritt(1935)is credited15or th efirst u se ofadisctestma ch inein gears imulat ion,th ec on c e p thad been around fo rseveralyearsin th eform ofth eAmslerdisc machine16.nfactMartin(1916) demonstratedan awareness ofth econcept ,throughth eu seofrigid cy l indersto s imulatetoothcontact ,in h is paperonth etheoryofinvolutegearing.W he n e v e rorwhoeverfirst employed discsfo rlub ricant evaluat ionthe approach remains valid todayan d is cogent lysummarised b y Mansion in his discussion ofEvans '(1941) p a p er

itisdesirabletotesteplubricantsundersomethingmoreapproachingservice conditionsthanisofferedby mostof th eso-calledeptestingmachines(yet)itmustbeunderstoodthattheinvolutegearinwhatever form,isrecognisedtobe farfromidealasatestspecimen,since,evenbythe mostaccurate geargrindingmethodsthereproducibyofform fallsfarshortofwhatcanbeachievedonanytypeofcircularspecimen.Thereisalso,ofcourse,thedisadvantageofcost".

Disc lubricanttesting machines(Typemtests)ar ea c om p r om i s ebetweens imple geometry testing machinesan dgeartestingmachines ,partiallys imulat inggear c o n t a c tFigure1.10 over leafillustratesthatapair ofdiscscanb eused t oreproducecontactcondi t ionsat an yparticular posi t ionofa gear'smeshing c y c l e .Thediscsmustb erotatedat th esameangularve loc i tyas th epinion an dgearrespect ively,an dm edisc radiiequa lthose ofth egeartoothprofi leat th epointofsimulatedcontac t Therelativeradiusofcurvatureofth etw o discsis th esameas thatofth epinionan dgear.Gearkinematics imulat ionis incompleteinsofar as contactcondi t ionsvaryduringth emeshingc y c l ewhilst th erelativesurfacemotion ofth ediscsremaincons tantThemain attributesofthe disc lubricanttestingmachinear eth e greatercontrol overoperationalan dsystem p arameters.15Cameron(1966) ,Dowson(1966)&Johnson(1987)16Amslerdisc m/c1922 ref.Machinery(1948)an dAutomobile Engineer(1948)

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Figure1,10Gear ContactSimulat ionhvni^s.MerrinMQ42 , )

VtlodtyDiagram

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Numerousdisctestmachineshavebeen developed fo r researchpu iposes .hemajordiscmachinesandtheirsalientcharacteristicsar ereviewed in T a b l e1.3.

Table1 .3DiscM a c h i n eOperat i ng (Ywvtitjmrc MachineRc L Afasck. S Z R % GP a Elm/s lam/s PVs17GN/ms Geomet ry Lflb. TempIDL'Cxidjhim m AFAPLCaper(1972)A Rao(1981)

1002 0-100 2.8 3.7-17.5 3.7-17.5 31.7 ellipsecrown 472mm

jet 150AmslerO D o n o g h u e(1966)

35 .17.5 (3.175) 0-100 2.4 0-1.8 0-0.9 1.7 line j seetextBatteUe

Orcutt(1962),SiWey(1961)ASchlosser(1963)

76.2 zero unlessdisc red.varied0.8 0-4.8 a sVI ellipsecrown

381mmdry tub A /R 1100

BearingsimulatorB e l l(1970) 18 zero unlessdisendvaried 2.8 0-185 a sVI Asym.

ellipse279mm,10*e m w n ,tapn-j 279

Geared rollertesterBenedict (1961) 45.7.30.5(10.2) 13 1.0 0-19 33V1-1.33V1 24.1 line < * P 204

GearrolltesterJackson(1960)

63.5(6.35)

0-96 1.1 0-33 0.58 13 line j 370 Hightemp,eptesterHopkins(1962)50.8 58-100 (4.0) 125-3.7 0-33 9.9 ellipse crown 381914m m

370 Mini-discNicolson(1988) 19 (635) 0-100 1.2 0-5.5 0-5.5 4.4 line j 15 0I.C.MobilCameron(1971) 82.5(6.35) 0-98 1.0 0.2-21 02-21 14 line splash/iet 150SA EVan derMinne(1937)

48.5.48.5(12.7)

54.SI.91 2.0 5 .0 0.25.0.34.2 6.7 line d n > see text

Theke ydistinctions betweenthesedisctest machinesa nd theirapplicationa re discussed below:

17Conditionsfo rmaximumPV s@arbitrary,notional50 %S/R,definedhereas(V 1-V r2)/(Vi+V 2)

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1.4.4.1F A P L The A ir ForceA ero PropulsionLaboratory( A F A P L )discmachineuses100.2m m diameter discsof 4724 m m crown radius.lthough thisproducesanellipticalcontact,theaspectratioissufficiently highasto approximate to anominalline contacthis rigisversatile,for example,bothdiscsca neitherbedrivenindependently or coupledvia a toothedbelt,Carper et al(1972)andR ao(1981).uetal(1976)andL a ne(1979carried outextensiveparametrictesting ontheA F A P L discmachine whichhas provided considerable data.

1.4.4.2h emsleris cestac h ine TheAmsler disctestmachineha soverhungshaftsa t52.8m m nominalcentresanddriven thougho pposite ends.iscs ca n beof anysizecomm ensurate withthecentredistancebetween theshafts.estlubricantis je tfedat cmVsecand nocontrolovertemperatureisprovided.W hilstthereisnostandard testprocedure itisusualto run-inat minimum speedand load.orqueismeasuredbymeans o f a pendulum deviceandwear rateascertained eitherbyweightloss or reduction intheouterdiameter of thering.iscsm aybere-finishedfo r re-use,O'Donaghue(1966).

1.4.4.3atte l le Th eBattellediscmachinemploys adjustableclearancetiltingpa d journalbearingsfo rradialsupportand springloaded singleballthrustbearingsfo raxialpositioning,W ilson(1959),Sibley(1961),Orcutt(1962)andSchlosser(1963).hediscshaftsaregeared togetherviaatiming beltand motivepowerisprovidedbyana irturbine.nebearing housing isrestrainedsolelyby astraingauged cantilever fo rtractionmeasurements.ilm thicknessmeasurements aremadewitha coUimatedx-rayfromeitherside or en delevations.he discenclosureisheatedbyradian t heatinglampsupto1100Cnequart of testlubricant,separatefrom themain oi lsupply,isrequired.lternativelyasolidlubricantm aybetestedusing eithera irorinert ga sasasupplystream.

1.4.4.4earingimulatorBell(1970)devisedasmalldiscmachinewithindependentlydrivenshaftsto simulatehighspeedballbearing kinematics.ncommonwithmanydiscmachines,ring discsare

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shrunkontoshaftsandloadedtogetherby meansof acantileverbeam arrangement.varietyo fheatingmethods,including inductionheating of the discs,are combined to reachtemperaturesof 315C,Parker(1971)and Kannel(1974).

1.4.4.5earedol lerester B enedict (1961)and Leach(1965) investigatedgearfatigueandscuffing using ring discspressedonto parallelshaftsa t threeinch centresandlinked by eccentricphasing gears.The lower discbeingdiplubricated supplies thecontacthediscsare loadedpneumatically.

1.4.4.6earolleresterTheGear Rollertester,patternedafterm atdesignedby Zandtand Kelley(1953),wasused byJackson etal(1960)to investigategearscuffing a televated temperaturesusing2.5 inch diameter discs,whereonedisc rotated a ta fixedspeed of175rpm and theothera ta variablespeed upto10,000 rpm.lectrical heatingof thediscenclosure andpre-heating of dietestlubricantenablingindependent control over discandlubricanttemperature upto 370C Jackson used a variation o fKelley's(1953)noveloperating procedurewhereby afterrun-in ,a load nearthescuffinglimitwa sapplied beforethespeedwasthen increaseduntilfailure.

1.4.4.7 ig hemperature.P .esterHopkins'(1962)HighTemperatureeptester requireda mere60m lsampleo f testlubricant byimmersingthediscs in aclosefittingheated reservoir.he discswereoverhung onvertically arrangedshafts,one discbeingrestrained to around100rpm and theotherdrivenupto1400rpm.oading wa sachievedbydisplacingoneof thedriveshaftsso thatitinclined relativeto theother.heheavily crowneddiscswouldreducethe effect of thismisalignment.

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1.4.4.8ini-DiscNicolson(1988)usedamini-disctestmachine,a precursorIDthiswork,tosimulate gearscuffing.herod-likespecimensha dathicker centralsectionwhichcompriseda0.75"discandatangonthebottom facematedwiththedriveshaftvia anOldham coupling.Thesimplicity o f thespecimendesign permittedclosecontrol overtheir manufacture.

1.4.4.9mperialMobil.5 ydrostat iciscm a c h i n eThe Imperial/Mobildiscmachinewa sdesignedby Cam eron&Macpherson(1971) to tacklethe perennialproblem of ensuringnominallinecontactbetweendiscs.2.5m m diameterbearinginner races wereused astestspecim ens.heseweresupped over rigid fixedmandrilswithhydrostatic pocketstobothlocate and load therings tog ether,asshownin Figure1.11.Torque,inclusiveo fbearinglosses,hydrostaticload,shaftspeeds,andtemperature wereinstrumented. typicaloperating procedurecomprisesarun-inundernominalloadfo r15minutes,incrementedby445Neveryfive minutesthereafter untilscuffing isindicated.Six litresoftestlubrican tarerequired fo roperation.LaterversionsoftheImperial/Mobilhydrostatic DiscMachinecombined on eof thehydrostatic padswitha pistontoincreasediscload to overlkNAnand replaced splashlubricationof thecontact withanoil jet

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Figure1.11mper ial/MobilD isc Machine.Cam eronAMa cPhcrsnnMQ71)..HPOIL 4-STRAINA U G E FIXEDO DY D R I V I N GLADES TRACK S H E A R PINS

STABIL IS INGETS H .P H Y D R O S T A T I COCKETS

1.4.4.10heocietyfAutomotiveEngineersSAE)iscestmachineTheS A E disctestmachine,illustratedin Figure1.12,is baseduponan earlierdesign used by theUni tedStatesBureauof S tandards accoid ing to Neely(1936).hetest isexceptionalin having beenassigneda standard.Tw o TimkenT48651externally re-groundouter-racewaysemployedastestpieces a rcstraddle-mountedbetweentaperrollerbearingsonparallel horizon talshafts.ftera30 second run-in,load isappliedautomatically untileitherscuffing is detected orth emaximum load of 2.7kNreached.o th' endurance'weartestinga ndshock load ing at35 0N persecond ca nbe evaluated,W es t(1946).

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1 .5 T hemplicat ionsorCCest ingwitheve lopmentsn transmiss ionu b r i ca nt sndmater ia lsPrev ioussect ionshaveoutl ined th enaturean d bas i su p o nwhichlubricantload carryingcapac i tyis current lyassessed.Although net L CCperformance is determinedb y bothmateria lan d lubricantin combinat ionit is conven ientto cons idereachseparately.Transmission lubricantscan broadly b edist inguished betweenthose fo rwhichL CC is ofprima ryconcern,s uchascertainhel icopter maingear b o x es ,an d thosefo r which L CC is secondary to ,say,thermalcapac i ty ,fo r example turb inep owe rtake-offs.Figure1.13illustratesthatturbinelubricant deve lopment hasbeendrivenb y the risein ambientoperat ingtemperaturesfo r increased turbineef f i c iency .Althoughtheselubricants havebeen formulated to inc ludeboth ep an danti-wear additives it is theirthermalperformance thath asbeen optimised.

Figure1.13u lk lubricantTemperaturewith Projecte d AircraftSneeriJ O O O r io n

HO 0 0 UJ -

200 0

-200 2ARCRAFTSPEED,M A C H N O .At presentth eapproachis to providethermalbarriersbetweenth eturbinean d adjacent transmiss ioncomponentsas wel lasextensivecoo l ing .heseincuraweight penaltywhi c hwil lincrease ifth erisein b u l koperat ingtemperaturescont inues .orexample,it

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c a nb es eenfrom F i g u r e1.13thatasflightspeedsexceedm a c h2.5th eram air t e m pe r a t ur eexceedsth eb u l k oilt e m pe r a t ur ewhichwillrestr i ctcooling capacityto f u e lut i l i sa t i on .h is isofpart i cular relevancein viewofd ie r e n e w e d interest in th e SupersonicT r a nspo r t(SST)p r o g r a m .C o m p a r e dwithtu r b in el ubr i c ant development,l ubr i ca ntdevelopmentpr i m ar i l y with r e s p e c tt o L C C ism o r e rec en t ,indeedth efirstd ed i c ated hel i c o p ter m a i n gear-boxl u b r i c a n tspecificationisstillundergoingqualificationasPhaseIIshownin F i g u r e1.14 .Previously,s u c hconsiderationshavebeensecondaryto s u p p l y logisticsan d economicswhichledtoth ewidespreaduseoft u r b i n el u b r i c an ts ,e.g.PhaseI,despiteexcesst h e r m a lc a p a c i t yatth ecostofL C C .

Fi gure1,14Helicopterm ai ng e a r b o xl ubr i ca ntr i evr in p men t d.M.01 A . Oyiwi* roc

LCC1 0 2 % I cS \\\\\\\/\\Rash point246*C

Mibk22S2S .g.ETO50 0

pourpoint-54C

Rathpoint24 6 * C

pour \f,\ointB ,54-C D-ENG-2497 ,U.K DOO-L-585734 ,U.S .g.ET O2 5 ,ASTO5 5 5 ? see textEhasaJI.g.CastrolA N 15 7 EhaaaJ ( - )

Phasemin Fi gure1.14isasyetonlyc o n j e c t u r eb u tit iss u r m i s e dthatit willbea commonl ubr i ca ntto bot h t ur b i neandt ran s mis s io n ,combiningLCCwitht h e r m a lperform anc e .it hth i sin m i n d hig ht e m pe r a t ur ec and i dat esw h i c hare reviewedwith L CCin m i n d :

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Figure1.15Candidatelubr ica ntf luidsfo relevatedtemperature.Loomis f1982^

|YMTWKH Y M M X A W aa" wBuatsns

WriOKlStUCOKSC-OMPS

inoncim,tnmmnyaTwom.trocHUOUKIOnunes

FUMMRMUfiM2IIMJm m m VMKMNK.%

Hindered polyolester, range-51Cto 240C,a formulated version ofthisbased uponpentaerythritol a imedat meet ingspec .Mil-1^27502exhibitsgood lubricat ion abi l i tyan d fairfireresistancehowever it requiresa foamingdepressantan d the poss ib i l i t yofextendingit sthermaloperating rangestill furtheris quest ionable .Compared withth edibasicesterofPhasen,l o w e rV I) Polyphenylthers,range-4Cto 288C a five ringed p o l y p he n y letherbased f lu id,formulat ioninc ludestr icresylphosphatefo ranti-wear.Despi t e bothhightempstability an dauto-ignition temperature,it shighpourpointrequiresth eu se ofa di luentssuchas trichloroethyleneb u tit has beenused successful ly in amilitary gasturbine.Fluorinatedpotyethers, range-34C to 360C,again dem onstrateexce l l enttemperaturestabilityalthoughthisi smarredb ytoxici tyabove260 Cas wel l as th enatureof" s o m ehighlyhalogenated m aterialsto react violently witha luminiuman dmagnes ium al loysat highshearstresses" D u p on t(1988),m os taerospacegearboxesinc ludesuchalloys.Fluoroethertriazines,range-30Cto 343C,exhibi texcel lentstability,non-f lammable an dar egood boundarylubricants .h ey exhibi timproved lo w temperaturepropert iescompared to th ePolyphenyl ethersan dar enot corrosiveathightemperatures .roblemsofhighvolati l ityan d poorf luidi tyat l o wtemperaturesar ebe ingso lved b u tevenin quantity product ionthese f lu idswil lb eso expensiveas t ol imittheir appl icabi l i tyan d failto justify theird e v e l op m e n tcosts .

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Othercandidatesinc lude;improved sUicones,range-6 1 Cto 240C,which despiteouts tandingV I,temperaturecoeff ic ient ofviscos i ty ,have l imitedfireresistance an dboundarylubricat ingabil ityan dC-ethersinc lud ingthoseblendedwiththiophenyldisiloxanesoenhanceth epourpoint)whichwere def i c ientin lubricat ing abi l i tya swel lass ludg ing dur ing enginetests.Although synthetic hydrocarbonsar ecomparatively w id e ly usedan dhaveexce l l entb ou n daryan d rheo log ica lpropert iesthey have poor fireresistance an dar eoxidativelystable onlyto 2 0 0 Cso theirpotentialis l imited unlessused in an inertsystem.Alternativemethodsof lubricat ionat elevated temperaturealsoinc ludes o l i da n d/ o rdrylubricat ionan dtw o phasel ubr i ca t ion.hese ar eouts ideth es c o p e ofthisw o r k .Although transmission temperatureshaven otrisenin unisonwithturbinetemperaturesthisis largely d u eto extensivecoo l ing in th ea b sen c eoftransmission niateriak whichar eab leto withstand extended operationabove120Ch is approachi ssteadily b e c om i n glesstenable as th e weightpenaltyincurredb y c o o l i n g wil lonly increaseas p owe rratingsrise.herear ealsospecif ic requirements ,s u c has thatfo rhel icopter maingearboxesto b eab le to withstandonce-offexcurs ion*to 300C in th eeventoflubricanttoss.helack ofsu i tab lematerials ha spreviously mea ntproviding aback-uplubricantsupply in combinat ion withsecondary reservoirsinstead.T henature ofgear toothcontactreviewed in 1.1whereby an intrinsically toughmaterialisheat-treatedt oprovide th erequis itesurfacehardnessm u s tthereforeb ereconci led with operationatelevatedtemperature.nth ecaseofhel icopter maingearboxesth erisein geartemperatureisenvisaged toaround150 Cb u tfo rtransmiss iontake-offsth eai m mu stb etakenas th ebu lklubricanttemperatureinsofarasthiswou l d el iminateth eneedfo r thermalbarriersan d extens ivecool ing.L o w an dmedium al loy carburis inggearsteelssuchasS 82 or AISI9310startto temperabove140Cwhichha sbeenapproached in two ways;(i )alloying to redu cedecompos i t ion ofmartensitefo rexampleCB S6 00 an d(ii)alloying to promotesecondary hardeningthroughth eprecipitat ionofal loy carbides ,fo r exampleCB S1000.Unfortunately,althoughsecondaryhardeningincreasesto amaximum around5 0 0Cthisc o i n c i de swithm i n i m u mtoughness.Davies(1989)reviewstw oalternativeswhichshow promise ,nitridingan dbinary hardening.Nitridingal loysar ctemper-resistant b u ttendto exhibi tlower corestrength an dshal lower casedepththancarburis ing a l loysb u tacombinat ionofth etwo,henceth e

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term'b inary'achievesadequatecase depth,temperresistance,hardnessan d res idualstressdistribut ion.Gearperformancei salsobe ingimproved b ysmelt ing ref inementss u c hasv a c u u m ar cremelt(VAR)an dmanufactur ingref inementss uchasshot-peening.nevitably thesewillaffectL CC althoughscuf f ing resistance is l ikelyto benef i tmost from increased hothardness.Coatingsar ealready extensively u s e d to promote mnning- inan d c o m b a tscuf f ingin gears,W c o d l ey ( 19 77)an d Nicho lson(1981) .At present thesear eeither sacrif ic ial ormodi fy th esurface,y etpotentialexistsfo r hard coat ingssuchast itanium nitride,provided prob lemsregardingf inishan d adhes ion 18can b eovercome.T h e patternofal loysteel d ev e l o p m en tfo r transmiss ionshas fo l lowed thatpioneeredfirhightemperaturebearingsteels .Alternative transmission matm^to a rel ikely to fol low thispathas temperaturescont inueto rise,whilstemphasis ing th eneedfo rtoughnessan dth eparticularrequirementsofL CCin resistancetoscuff ing.

18Inadequate adhesion ca noftenb etracedto excessivemismatching o f themoduli ian dPoissons'ratiosfo rth ecoatingan dsubstrate.

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Chapter2 Mini-DiscMachineConf igurat ion es ign

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2 .1 DesignObject ivesThreespec imen configurat ions:mini-disc,spherical roller an d bal lwereconsidered againstd ie fol lowing criteriaprior to design

ontactshapeearingsize&speedontact pressureubricantflowemperaturenvironment

Th eadvantagesan d disadvantagesofeach conf igurationar eshown inTable 2 .1

Table2.1pec imenConfigurationsC O N F I G U R A T I O N A D V A N T A G E S D I S A D V A N T A G E S

(a) mini-diac

-H-h -m -L inecontactca n beachieved.

Crowning allowse l l ipt ical contactDrivealignment avoidshigh

speedinstability.Non-standard specimen

geometry.R elat ivelyhighcontactloadsand ri g power reauired.(b )sphericalroller1 EllipticalcontactInherentd yn a m icstability. Standard specimengeometry( thoughnotyetforsilicon nitride). Alignmentof drivefor highspeed operat ion.D ifficulttoproduceaccurately.

(c)ballt Inherentd yn a m icstability.Standard cheap and accuratespecimens. L o w contactloadsa nd powerrequired.Couplingforhighspeeds-easierthan either(a) or(b). Only 'point'contactCont ac tgeometry changes during running,(extendedtests).39

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W h s tth ebaUarrangementwould have beenth eleastdiff icult approachitwas considered inappropriate becauseth eresult ing'point*contactchangessubstantial lywith runningan d is unrepresentat iveofspurtoothc on t a c tThisalsoappl iesto th espherica lrollerdespiteth ehighaspectratioofth econtactnormalto th erol l ingm ot i on .Consequently th edisc is cons idered th em os tappropriatebeca us eofnomina ll ine contat tyetifrequired,th ediscscan b ecrownedto produceanellipticalcontac t T heaspectratioofth econtactb e c o m e sprogressivelyl o w erwith increasedtoad,hence rel iance u p o n contactstressesto achieve scuff ing,often c lo s etoth ematerialyie ld pointis a p oor solution.oad carrying capacityneedsto b eassessed at speeds(andtemperatures)thatobviateth eneed fo rs uchunrealist iccontactstresses.Inseek ing t om e e tthesecriteriatogetherwithth eobject ivescwtl inedin Chapter1it wasc on c l u d e dthatin th einterests ofbothf lexibi l i tyan dcost ,ah ighspeed an dhightemperaturemini-disc machineshouldb econstructedwhich w o u l dal lowtestingas c lose lyasposs ib le to anidealoperat ingce iKngof15x106d N a nd400GThesedes ign object iveswere onerousin thattheyrepresenteda four-fold increase in temperaturerangean dtwenty-foldincrease in speed overp rev i o u sdesigns.urthermore,priorworkb yNicolson (1988)underU.S.A.F contract F4 96 2 0 - 8 6 - C - 0 0 5 9 ,revealedth ediff icultyin achiev ingcorrelation withth eRyder testwhichi t se l fexhibitspoorrepeatabil ity .Thischapter outl inesth econfiguration an ddesignofth einini-discmachineto correlatewithth eRydermeshingcyc lean dencompassfuturerequirementsfo r loadcarryingcapaci ty testing.

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2 .2RyderGearContactarameters Using af ini tee l e m e n tc o n t a c tmodeltosimulateth eR y d e rgear c ont ac t cycle, m e a s u r e d tooth p ro f i l esu n d e rreal i st i c bendinghavebeenc o m p a r e dwith ' ideal 'involutet ee thinTable2.2.No allowanceh asbeenmadeforeithertooth b e n d i n g or p ro f i l edeviationan d contactstressesar eb a s e du p o nsmoothequivalentcylinderswith noregard fort ipeffects.

Table2.2RvderParam et ersLE GI m a H l L P C i d e a l 2123b.IkkaL LESIC L P S T morfeTPITCH HPSTC P STC 2 1 2 % .'ideal' H EC'jfrwl' HEC'model'*'' E Q M T 'ideal' irjoderollarade0 13.69 14.90 16.51 18.99 20.90 22.50 25.83 26.50 31.80 3239 33.38rl,nun 10 1 1 12 14 15 16 19 19 23 23 24 r2,mm 24 23 22 20 19 1 8 16 15 1 1 1 1 10reLnd. 7.0 7.3 7.7 8.2 8.4 8.5 8.4 8.4 7.5 73 7.1 S /R -42% -37% -30% -20% 12% -5% 9% 12% 34% 37% 41% Vs m/s) -15.08 -13.26 -10.84 -7.12 -4.25 -1.85 3.15 4.15 12.11 1329 14.48Load \N 381 1202 1424 3000 3000 3000 3000 3000 1348 1202 381Hem G P a 0.44 0.76 0.81 1.14 1.12 1.12 1.12 1.12 0.79 0.76 0.44P VS.GN/ms 6.62 10.08 8.74 8.10 4.78 2.07 3.52 4.66 9.62 10.11 6J0

notes (0P C -Lowestpointof contact,H P S T C -Highest pointof singletoothcontactetc.'model 'refers to loaded tooth profile,' ideal 'neglects bothtooth bending and profilevariationfrom idealinvolute,( i i) R ao(1981) quotesmaximum averageHertzian stressfo r Ryder of1.0 GPa.(iii)Thereis,strictly,zeroloada ttheHighestorLowest Po in t o f Contact,the figureusedfo rtheloaded,measured profileisthatnodenearest,in orderto providea valuefor P V,Table2.2hig hl ig htsth edifficultyin r e p r o d u c i n g th eR y d e r c ont ac tc o n d i t i o n s .orexampleasl ideAol lratio(S/R)of37% wasusedin th e pre l i m i nary w o r kbyNicolson(1988)asrepresent ing th epositionofmaximumPVS(LP C& H P C'ideal')whereth e discsweredr i v enat fixedspeeds.However,asTable2.2i l lustrates,thisvarieswhenac t ua ll o ad ed gear profi lesare considered,an dm a k e sth echoiceofas ing le setofcontactconditionsu p o n w h i c hto b a s esimulationsomewhatarbitrary.qua l l y ,Ryder'sf a i l u re cri ter ion of2 2 . 5 % toothareascuffeddoesnotp ro v id eap rec i s ean dthereforeconvenientmeshingp o i n t19.

19Bothth eHPSTCa n d theHPC,ar ecommonly used asdatumsfor simulation.he actuallocationofscuffingonset is affectedbyprofilemod ification,tiprelief, toothsection a n d pressureangle.

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2.2.1 R y d e rimula t ion Itis apparentfrom th ediscussion ofRyderparametersthatthesear el ess tightly defined thanm i ghtb efirstconstruedOlver(1991) demonstrated thatscuf f ingperformanceis strongly in f luencedb y disc geometry ,speed an dload.heseaspects ar econsidered insofarthey m i ghtbestb earranged to achievesimilarscuff ing performance t othatexper iencedwithth eRy dertestFigure11illustratesthatifP V ,fo r a19mm (3/4") diameterdiscmachineis matched againstth e lastpartofth etoothto b escuf fed ,namely 8.74 GN/msheload requireddiminisheswithsl id ingspeed.

Figure2.1iseSl id ingVeloc i ty versusLoad fo r ConstantPV ^3530 25

V m/ss01510

-0

5

Q

4

v O.

[ P Vs=8.74GN/ms 2 .38mm(3/32 )trackwidth

4 .76mm(3/16 )trackwidtho 9 .52mm(3/8 )trackwidth

- .o o"*.."O - .' i

< > --t'". t-*U-.L1H.?. . : . .

500 1000 1500 Load,N

2000 2500 3000

20Thelocat ionofth e' ta i ls 'ofth e2 25%s c u f fwere ca lcu la te dtheoret ical ly b y a ssuming thatscuff ingprogressedat u n equ alratesfrom rootan dti ptherebyr e ach ingth ep i tc hl ines imul t a neous ly .Howe ve r ,th e analysisha sp ro du c edtw o differentva luesofP V fcorrespond ingto uppe ran dl owerscuf f ingboundaries .

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T heappl ied load,an din turnload capac i tyneededfo rth esupportingbearings ,variesaccordingto th etrackwidth chosen.ti s evident,however,thataload capacity in excessof200Nisrequiredwhi c hw o u l d entai lspeedsin excess of40 ,000 rpm ifth edisc entrainmentvelocity is matchedto thatofth eRyderc o n t a c ttshould also b enoted thatdie u se of3/4" diameterdiscs do e snotmatchth eprecise relative radiiat an y pointofth eRyder tooth c o n t a c th is r e d u c e sth e theoreticalsmooth contactwidthb y approximately2 5 % ,b u tas a roughness in th eorderoflu m rms ,at typi ca lscuf f ingloads,w o u l d increase d ie contactwidth b y a b o u t2 5 % ,it i sn otthoughtto b es ign i f icantP V Sis onlyon emethod ofcompari son ,scuff ing severity i sfrequently assessed us ingcriticaltemperature criterionwhi c hsuggests thattotalcontacttemperature shouldb econtr ived to b eth esamefo r bothd i scan d Ryder to enhance correlat ion.TheRydergearswere assessed us ing am od e lwritten b y Olver(1993) .Ob/er ' sm od e lis an extensionofth eprinciples he reported in1991to explainscuf f ingin differentsizeddisc machines.nessence ,it isa thermalf eedbackm od e lwhereth eheatcapaci ty an dheattransfercharacteristics ofaparticular system and it sgeometry can he accn m m n dnt f f d alongwith th emoreconventional lubricant properties an d contact parameters needed to determine steady-state fi lm properties.

Figure 2 .2herma lBehaviourofth eRyderTestaccordingto CHver'sModelH O O T )2 0 0 16 012 080 4 0 -

T-r-r-r-iTF, C

. 7e ,C o /ZX1000* .X100

lr~Ti1~

f.,,,1 .500

-7-:7*t-

JIII' I10 0 0 1500Load,N

I ' ' ' | ' ' '4.:.,:fi:4.::

A7>45CJ

slope11.4C/380N -( re fe rtotext)

J-i_L2000 2500 3000

4 3

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Hieresu l t si l lustratedin figure2.2mustb equalifieda sth ethermalcoefficientsan d s u rf ac e areaofth etesthead wereestimatednep r e d i c t e d1 1 . 4 Crisep er380Nl o ad stagef o rtu i to u s lyagreeswith thatmeasuredb yBenedict(1968)of 12Cfigure22i l lustrates thatfo r aref eren c e oilf a i l u reloadof2200l b / in ,c o r r e s p o n d i n gtoa loadof2260N,th emodelpred i c t saflasht e m p e r a t u r e ,7>of45C an db u l kt em perat ure ,T of1 2 5 Cwhere

w h e r e T jTpre gear an dp in io nt em perat ure respectivelyItisthispart i cular c o n d i t i o n forwhichsimulationhasbeens o u g h t ,u s i n g1 9 m m (3/4")discsrotat ing atspeedsvx&V 2equivalentto th eRyderHPSTC

F i g u r e2 .3h e r m alPrhavioiirofMin i -rH s ra c c o r d i n gm mMnr i dnoo oc\r\1 3 )

20018016 0140120100

Boundary 80conditionsfixedat74*C (-Ryder)Q

O og * J 5 T O _

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ant i c i pa t ead i f ferento p t i m u m trackwi dt h .q u a l l y ,it m ay b epur po r t e dthatth ec ont ac t points imu lated s h o u l dn o tbeth eHPSTCb u tth e'tail*ofth e22 . 5% scuffedareaa su s e d in rep l i c a t i ngl o ad i n t ens i t y .Theeffectofincreasedspeedu p o n scuffing,asp red i c ted byOlver'smodelisshownin Figure2.4.T h eonset,asdeterminedb y th ecoefficientoffric t ion,occursear l i erat hig h speedb u tth erate ,dp/dN,islower.

F i g u r e2.4red i c ted EffectofSpeedrmonDiscScuffing

Increasingspyd

Load

T he traction m o d e lusedb y Olverisbased uponthatofBair(1982)21here/iis proportionaltotemperaturesubjec tto l imit ingshear stress.Withinth emodel: 7,need n otnecessari ly risewithincreasingspeed.H owe v e r ,th eheatgenerated: Q/ixv (15)henceQcould stillb erising.Meanwhi le th em od e lheattransfercoeff icient,uponwhichheatdissipation depends ,wil lalso risewithspeed: 21Surfaceroughnessan dlubricantstronglyinfluence themodel,theroughnessusedw asthato fRydergearswhilstth elubricantwas an estercorresponding to thereferenceoil. r u n - i n

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A 1 6 )Itshould b enotedthatth eentrainmentveloc it ies ar ehigh,6m /sris ingto 90m/s .helessrapids c u f fat h igherspeedsm ay b eexplainedb y conventional ehl theory;iftherei ssuff icientfi lm toseparateth esurfacesthen it wil lb edu eto th espeed rather thanviscosity whi c hwil lb e extremelyl ow.An yfurtherincreasein temperaturewithincreasingload wil lhaverelativelylittle effectuponviscosityan dhencefeedba ckin reducedfi lm th i ckness .Superf ic ial lyeither th eload intensity orcrit icaltemperaturecriteriaar eappl icableb u tin pract iceth eonsetofscuff ing is affected b yadditional parameters.Additiveresponse,fo rexample ,is notincorporated intoth ecriticaltemperaturehypothesis .N oattempthas beenma deto repl icateth erelativecontact wherebygrossconformity mightb e c o m es ignif icant,Sayleset al (1981)an d Archard(1973) .urthermoren oattempt has been ma detos imulatedie transientnatureofth econtactc y c l ebut ,"thedesirefo r correlation withth eRyder mus tb ese tagainstth einherently poor repeatabil ityofth egeartest".

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2.3 Bearingimulat ionUsingDiscsThe primaryobject iveofs imulat ing gearscuff inghas alreadybeen discussed althoughthisis n otto disregard poss ib lebea r ings imulat ion.hed Nrating illustratedin Figure US,despite wide usage ,fails to takepropera c c ou n tofsizean d centr i fugaleffects. Nonethelessit providesan indicat ionofbothth epresentenvelope an d futuretestrequirements .

10

E e -S 10> 0) Q.(0

Figure2 .5ract ica ld NRat ing.Hamrock(198nafter Bamberger(197D6

10

1000

1 nr

*

f 'TTTresentimit.5 milliondN i

i

i i Nii i10 10 0

bearingbore,mm At highspeedth ecentrifugalforceexperiencedb y the rol l ingelements leadsto outerracecontrol.nessenceth einneran doutercontactanglesar en o longer equalan dsignificant slipoccursat th einnerrace.twil lb eapparentthatas the innerracecontact is elliptical it wou l d b enecessaryto crown th ediscsto achieveacontactofsimilaraspectratio,an dc o n eth ediscsfo rasymmetry.ro m Bel l(1970)these parametersar eenvisagedto b e: 10 "(250 mm)crown,10 c o n etaperan d 220 0 1bf( lOkN)appl iedload at10,000rpm.h e ri gshouldcater fo r axialload caused b y th edisctaper.

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2 .4 Test ingCostsT hesimplici tyan dsize ofth espec imenm i n i m i sessample costsand enhancespotentialfo rmanufacture inawidevarietyrfmaterials an d f inishes.hesefactorsar el ike ly to b e c o m e evenmores ignif icantin future,however ,amajorc om p on e n tofload carrying capaci tytest ingcostsar erelatedto ma npower an dth eextentoft e s t b g ijecessary to achieveacceptablerepeatability.igure 2 .6 is an estimate ofth etestmg>stsincurred fo r eightR y d e ran d mini-disc detenmnations .R ao(1981)postulateddisc repeatabilityw o u l d b esuchasto reduceth en u m b e rofdetenmnat ionsfo rqualification testingto jus tthree,instead ofrightas requiredb y th eRyder.fso ,an dthiscan only b eborneou tb y exper ience ,thenth ec o s tbenef i tsofth emini-d iscwou l d b esubstantial.Whereexoticor nove lmaterialsar econcerned,assuming suchmaterialscan b eprocured in aform sui tablefo rgearmanufacture,cost benef i t sar el ikely to b eevennxmarked.

$6000

$4000

$2000-

Fjgurc2 .6 Mini-discv ,^ veT ^ Ryder

$5828Rydercostsbasedupon980AFestimatesoreterminationsrebased1994

Spec imencostOperatortime

No a l lowancefo rspec imen recycl ingha sbeeninc luded because ofth edisadvantageincurredb yreduceddisc diameter,howeverrecyc l ing m ayb e c o m e viable fo rexot ic materialssuchassi l icon nitridewhichat present,under l imitedorderquantity,costaround$400.

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2 .5 Genera lA r r a ng e m e ntofMini-DiscestR ig Precedingsectionsconf irm bothth efeasibility an dattractionsofus ingmoderate ly narrow track,smal ldiameterdi s c sdrivenat highspeed.hissect ionpresentsan overview ofdie mini-disc an dgeneralarrangement,fo l lowed b y adetailed descript ionofth e princ ipal elements .i gure2 .7i l lustratesth emini-disc specimen.

Figure2 .7Mini-Disc Spec imen

c u ftoe+.000

1'"'-.0O2

1.400

07Snn+-0000/oo-.00050.7000.

I M P E R I A L C O L L E G E O F SCIENCE,TECHNOLOGY AND MEDICINIDAI Nk oUocTi i b o l ocSBct i aj ,xhtrionRoad.anden,SW72BX^^7J**%( 0 71) 2Z58968da:9294 84 IM PC O L G Fax:(071)823-8*45v4wTteReviled mini -d i s c sp ec i men detai lDnwingN o: * Itaie: 3Sole: Ful lsize De 29A/WM M m . AMS6260.M50 *" i'm i". flhf*"]lendradius

nottoexceed1/32" 1.ayno tbe n ecessar ytogrindtang alterheat-teatment provided that

tolerances aremet .2.ater ialAM S6260or as required,M50 Si Mete3.ea tt r eat men tAM S6 2 6 0 :Case25--.040",81-84R .core

chamfer toleave5-40R3/16"track 4-***diamet er sto18-25micro- inchesrm saxial,5-8radial ,1centresleftIn eithernd acceptablebu tshouldn'texceed.125"da.

t_ 5.nlessotherwisenoted roundedgesto.005"-.0t5"

+.002 Dim.A/2{1 -.0020U1 DjnmminnA;AMS6260.85off@3/8"AMS6260,85off@ 3/16" AMS6260,30off@ 3/32" M50,40off@3/8" M50,40off@3/16"M50,20off3/32"

Foran ygivenpair ofspec imens ,on ehas awider trackto reduce end effects .hedisc spec imensar edrivenvia opposi t eendswhilstsupported b yhybridbearingsasshown in Figure2.8an d Figure2 .9 overleaf .hesear emountedin ahinged'nut-cracker*whichenablesth etw o d i sc sto b el oadedan dprovidesreadyaccessto replace th espec imens .Heatedtestfluidis fe dto th ehybrid bearing padsand th econtactb yaprecis ion gearpum pwhichis located direct lybeneathth etest enc losure.hetest enc losureformingth e sump.

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Figure2 .8fa )GeneralArrangementofMini-Disc TestR ig

iIff

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Figure2.8(b )eneralA r ran g emen tofMini-D iscTestR ig

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2.5.1 Drive-train T helayoutofth e drive-trainisshownin Figure2.9,withthatofth eb o b b i nhou s i n gin Figure2.18in82.5 .3 .

F i g u r e2.9chematicofDrive-train 3.375:1 flatbelt

layshaftBlayshaftA

Ratio'si l lustratedare thosefor37% S / R ,alternative.48:36gearingfor1 9% S / R .

Fo r s imp l ic i tyasingle, variablespeeddrive m ot orhas beenused in afour-squarearrangementsothatth epower requiredi s mere lythatabsorbed in th edisc contactan dbearings.ayshaft'A*isdrivenvi aipofy-velt an d layshaft,'B\coupledto'A 'vi aapair ofunequa lhel i ca lgearsto reverseth erelative rotation22 .Asrotationalspeedsu pto100,000 rpm wereenvisaged,ahighfinaldrive ratiohas been used in combinat ion withaminimaldrivenpul l ey diameter us ingflat belts.hesetransmitadequate p o w er at moreconventional speeds together withth eabilityto c op e withth ehigh speedandsmal lbend radius.hebeltsspecif ied comprisew o v en polyester impregnatedwithneoprene .heflatbeltsdriveth eb o b b i nsp ind leswhi c har emountedbetweenpre-l oaded deep-groovebearings pre-tested to 90,000rpm.22Iti srecognised thatvibrationca naffect scuffing&fatigue performance.Smith& Macpherson(1978),b utmeshingfrequencies ofthelayshaft gearsare outside thoseconsidered critical.

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Dist inct ionneedsto b edrawnb e t w een th eonsetofcatastrophicscuff ingand partialse izure fol lowedb yrecovery.his is d on eb ydenoting al imiting co ef f ic ientoffriction in th edisc contactat whichdie transmission is rated,\i=0.2 ,an daccept ingsignif icant slip thereafter.he extentofslipismoni tored via spec imen speeds as detai ledin \2.5.5.Tension is critical withflatbelts .h eentire layshaft assembly isk ey edperpendicular to th e driveline axesan dlayshaft'B 'c an b erotated around'A'whichenab leseach be l tto b etensioned individually .ens ionis appl ied b y astrain gaugedcantilever afterit wasdiscovered thatmeasuring lateral def lec t ionof the beltswasinadequate.The bobb inspindleendshave b e e n machined to provide a tangtodriveeachspec imenvi a an Oldham coupl ing .nitialattemptsto avoid d ie need fo ra'f loating'coupl ing b y drivingth especimen direcdy,us ing tw o shearpins ,d id n otmeetwith success an dc a u sedexcess ivelabyrinth wear descr ibed in 52.5.3.With d ie aim ofensuring each drivespindle remainedconcentricwith it srespective disc axis,th ebobb in hous ingswere init ia l ly attached to each jaw ofdie'nut-cracker'.However ,in pract ice thisw asn otf o u n d to b esuf f i c i endyrig id.nstead th edi s c swere loaded staticallyin th e'nut-cracker'which w asshimmed appropriately to allow fo r running c learance,an d th e drive c om p on e n t sal igned withd ie disc axesbeforebe ing rigidlyc lamped.

2.5.2 Supportn doad ingfDiscsMounting th espec imensin an ov e r hu n garrangement,as used b yBel l(1970)amongstothers,w ascons idered inappropriateb e c a u s e d ie spec imensneeded to b eground ontheirrespect ivedriveshaftsto ensureconcentr i c i ty .h is would largely nul l i fy th eadvantagesofth emini-discs impl ic i tyan d prove less condus ive to even loading ofd ie c o n t a c thero dshapean dindependents upportofth emini-disc is designed to avoidthisproblem.Whilstthisgeometrywou l d b emaintained it w asproposedthatgasb eused asth e mea nsofsupportinstead ofhydrostat icjournalbear ingsused previously.

23Ref.ctrct ip tFY1455-87-03006/D1,1styr 'Dev.ofhighspeed,hightemperaturemini-discm/c'

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2.5.2.1asearingsThebenef i tofgaslubricat ionis thatbearingperformance is largelyindependent oftemperature 24,testlubricantan d speed.Us eofgasw o u l d a lso permi tmoreeffectivecontroloverlubricantfeed to th econtact,inc lud ingth eextent oflubricantstarvationwhichis ofparticularinteresturthermore,th egas m ayb eus e d to controlth eenvironment surroundingd ie discs, providingan atmosphericb l a n k e tDespitea lo w specif icload capaci ty,whichinvariablymeansthatc learancesar e s igni f icandy lessthan l iquidlubricated bearings25fric t ional losses ar eextremelyl o w .h is isdesirablewhen measuring tractioncoeff icients.Considerableeffortwasexpended in attemptingto achievesuf f i c ientload capacityusing hybridgas bearings .O neversionis illustrated in F igure2 .10 .Despite th eattractions ofus inggas it did notprovepossible to achieveadequateload capac i tywithoutresortingto excess ive flowrates.twasconc luded thatalthoughthisapproachwastheoret ica l lyfeasibleusinga hybridtilt ing pad arrangementan d givensuff ic ient ly stringenttolerances,th emargin w asinadequatewhen differentialexpans ion b e t w een th ed i sc san d pads,transientloadsan d debriswereinc luded .Consequently th etestf lu id wou l d haveto b eusedfo r disc su p p o r t

F i g u r e2.10GasBearing

24 I n contrastto l iquids,a i r or nitrogenincrease i n viscosityofth eorderof200% between20-400C25Journalbearingfriction < * ? /c,(laminarSo wfor agivengeometry .speed)whereasloadcapacityH /c2hencefor similarspec.load,i fn -10 0*r/.thenc 10 *c c=clearance,jj=viscosity.

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2.5.2.2HybridiltingadsFigure2.11illustratesth ehydrostaticpa d developed by Olver(1991)from Macpheison's(1972)original design.Mini-discssupportedin thisw a y havebeen runsuccessfully a tPV,f13.3G N / m stesting formulatedlubricantsa t125Cbisar rangementprovides easeof loading vi a controlof th esupplypressure,Ptogether with discself-alignmenL Furthermore,if a fixeddisplacementpumpisused inconjunction withapressure reliefvalve,thepa d film thicknessis largelyi ndependentof th eappliedload,given m a tth epumpdelivery issufficienta nd boththermala nd dynamiceffects areignored.

Figure.2.11 ydrostat icPadwithIntegralPiston.

pistonarea

clearance&

P rpa deffective areas

orifice dia.stiffness(neglecting thermaleffects)

floating'bearingpad discs

However,th eperformanceof a prototypebased uponthis design w asnotsatisfactory,confirmingthepreviousmini-discexperiencewhenrunningfluidsof low viscosity.Moreover,a thighspeedsrecessed hydrostaticpadsbecomemarkedlylesseffective,Mohsin(1981),a nd significanteccentricityoccursbetweenth edrivea nd discaxesdue to dynamics .nordertosatisfythewiderangeof fluidviscosity,discspeeda nd temperature,hybridtiltingpadswereproposed.Theplaintilting pa d invented by Michellin(1905)becamesynonymouswiththrustapplicationsbutherecognised their equalpotentiala s journalbearings proposingth esegmented multi-pad a rrangementillustrated inFigure2.12(a).o rthe wideoperat ing

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rangeenvisagedahybridvariantofMiche lTstilt ing pad bearingwou l db enecessary a sillustrated in Figure2.12 (b).

Fig,2 .12fa )Pivotednad hvdrodvnamicjournalhearinfafterMirhH)(19371and(h \hvbndrmm-disccnnfigumtinfi

load

lubricantfeedthroughpivotcentres(a ) (b )

Design optimisation ofhybridbear ingsisnotstraight forward,fo r example , optimising static load capacityat m i n i m u m p o w errequiresthatth eratiooffr ict ionallosses to pumping power,Ktshou ld l iebetween1an d 3whilstth eop t i m u m recesslocation is at quarterstation 2 .imul taneous ly ,asload capaci tyisa funct ionofth e recessarea,thisshould bemaximised commensurate withmaintaining/V-g^atrsi l lwidthto preventexcess ive flow.heseobjec t ivesmust ,however,b ereconc i l edwithdynamic optimisation for whichn o recessesar epreferredan dth eopt imum va lueof A Tiesbetween 3an d12 ,Koshal(1981) .ab le2 .3 highl ightsthisquandary.

Table2 .3ecessed Hydrostat ic .Hvdrodvnamic an dPlainH ybr idhearinfpar^rpftmParame te r Re ce sse d hvrtmaaric

t f f i f l r i n y Pressure-fedhvdrodvnamic beariny Pla inhvbridhearinf

suKKestedland-width ratio 0.25 OorOJ 0.1 suggested powerrat io,K27min.m a x .1.03.0 40.0 3.012.0

feed geometry 4-6recesses axialercircumferentialgrooveplain,doubleentry

26a/L= 0.25 a sshown in Figure2.16K=3- 6wherem axtemperatureriseisimportant,3-12fo rmaximumtoleranceb a n d .

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In designinga hybridbearing it isusualto specify dynamicloadand diam eter,assumea lengthto diameter ratio a nd powerratio,K in ordertodetermine th esupplypressure28.Afterconfirmationthatthis issufficienttosupportth estaticload,a numericalsolution is used to(tetermine the operating clearanceaccordingtoth efluid viscosity before verifyingth eflowratea ndstiffness.n theeventthatoneof theseparametersis inappropriate eitherformanufactureorperformance, then firstth eclearance a ndsubsequently th esupplypressure mus tbe altered a nd th eprocessrepeated.qually,adifferent viscosity m a y be considered.However,thism a y affectth etemperatureriseexperiencedbylubricantpassing throughth ebearing a nd inturnaffectstiffnesswhereorificesare used,R o w e(1983).In ordertoassessperformancea nd optimisedie hybridbearing designa program w aswritten,based uponthatof Spikes(1983)incorporat ingbothtilta ndhydrostatic jacking.A finitedifferencemethodoutlinedin Figure2.13overleafwa sused to solveReynolds 'equationforth epa d pressurefield.his providedth edesignillustrated in Figure2.15,th eperformanceofwhichis presentedin Figure2 .14 .ttentionis drawnto both th elargel/D swella stheshallowrecesses.heunusually largerecessesa re due to th e pivotredesign,wherebyth e projected pivotareamustbelessm a n thatof th erecesses to ensureth epa d functionscorrectly at start-up.xpediencydictated anisoviscous approachwithoutal lowancefo rlocalvariation in viscosity, hencethereis an over-estim ateofbearingperformancea thighspeedswherethereisth eapparentmargin in load capacity.Theprogram w asalso used toassesstheeffectofmanufacturing inaccuracyupon performancesucha sthatof incorrectrecess location.

28O p t i m u mloadcapacity i sachieved fo r0 . 4 < P I/P S

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Figure2 .13ad DesignOptimisat ionRontjpxspecify//D,radialclearance,pad ar c an deccentricity

specifylocationof pivotIZ pecifylocation/

speefyralaxatbn constantan dconvarganoa Iapportionrid ovarhalofpad,(symatryaboutcantrastation),normaBaspa dar e tounity

calculateclaarancabatwaanshaftand pa d ZTZcalculata d h MIcalculatain fk jancacoafficiantsfo raachnodaIcalculataprassuraat aachn odausinginf luencecoafficiants&boundary conditionsset ,&maintain ,recesses to hydrostaticpra ssura

ka ra teusingover-relaxationmethoduntilressurefieldconvergeasum pressuresovergridusingSimpson'sruleto determinecentreof pressurevarytiltangle

scaleoutput,according to vscosity,jbad,Nnd

width,0

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Figure2.14HybridPadPerformance.PredictedIsoviscousPressureProfiles

PIBOUE15000000-1350000012000000-

1650000165000015000001350000

000s 010500000- 12000000

5 E7500006

0-0-0-

105000037S

000| ^ B 45 0- 6000000B 3 0- 4500000

IPi 1500000- 3000000 BELOW L500000

Sta t ionary .Load320N

FIBOUES500000.076500000680000005950000051000000425000003400000025500000170000008500000

BELOW

9350000935000085000007B500005800000595000?51000004250000340000025500001700000850000

1000rpm.Load748N

R ad i a lclearance=0.001*shaft radiusViscosity=0.02P a S ,seetextPadwith =0.47* pa dlengthEccentricity=0.7Recesspressure=17.5B ar

cf .2.7KN@ 5000rpm&12.6KN@ 25000rpm59

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Figure2.15 ketchofHvhririP ad

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2.5.2.3 Pivot design

The pivotdes ign wasreassessed afterth etungsten carbide pivot sshattered duringoperation.Figure2 .16inal(i)an d Prototype(b )Hybr idPad

Sect ioned at MiddleStation

t / -m i"J.J-L-.GII II c " 00II11 LI

99_1U

BiAII I JL Deva(Ni/Graphite)3/8'da.440Cpivot

0.701300.7000

S316

>IUJ4I

/m m d a.yungstenAarbide YJivot

(a ) (b )

Inm o d i f y i n gth e design,se e Figure2 . 16 ,th etungstencarbidebal lswere replaced with440C'mushrooms'an dth epad materialaltered to Deva,a proprietary,sinteredmaterialc o m p o sed ofnicke lan dgraphite.his softerp ad materialw asnecessaryto ensure die counter -borein th epa dwould stillyield to provideaconformalsealwithth epivot despiteth eincreased ba l ldiameter.Devals o offeredmarkedlysuperiordry s l idingproperties

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fo rth e journalfaceinth eeventofover-loadHowever,inconsequenceofthismodificat ion,thepadscouldno longerbeheldonto their pivotsina mannerakinto iDzusfastener.nstead,finegaugewirelinksth epadstogether, providingacradleto retainthepadswhenchanging specimens.tissuggested thata method of individuallyattachingthepadsloosely totheir pivotsisincorporated intoth edesign.

2.5.2.4esteadubricationThedesireto usega sfo rsupportingth ediscswithoutresortingto useof th etestfluidw a sattemptedpartlybecause ofanticipated limited fluid availability a nd difficultyinspecifying asuitablepump.ne-shotlubrication w a simpracticalwhilst a nypumpwouldhaveto copewith the rang e of temperature,exoticnatureof th eproposedfluidsa nd delivery. Entrapped gasesanddebrisbodeil lforrapid recirculation im plicitwithth esmal ltestfluid volume.A fterdue consideration a compactchemicalgearpumpwasspecified.Manufacturedout ofstainlesssteel andrated to copewithth erangeofviscositya nd temperature.hepump'sperformance wa sreliantupontightclearancesso thermalgradientsha d to be avoided.hepumpwas modifiedwith cross-drillingsto acceptcartridgeheatersa nd th ebearingsreplaced withplaincarbonbushes.Testlubricantis fedto a nozzle directedinto th ediscentrainment,althoughalternativelocationsca nbe readilyimplemented.

2.5.2.5AncillaryubricationThe drive-bobbinspindlesandlayshaftgearsa relubricatedseparatelyfrom th etest-head byan oilmisthisisfedto nozzles,locatedadjacenttothebearing andlayshaftgearentrainment,whichforcethemistto coalescea ndlubricate.tisnecessaryto ensurethatth emistisprevented from encroachingth etestenclosureandcontamina t ingthetestlubricantonsumptionisregulatedbythea ir flowandthemixturebyaneedle-valve.

29 Theaddit ionalcos t&com ple x i tyofman u fac tu r in gbot hth ep u m pan dteste nc losur e outofHastel loy was n ot warrantedas corros ivefluid candidatesw o u l d b eofl imited interest

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2.5.3 Sea l ingThe design of th esealschanged duringth e c ou r s eoftestrig de v e l o p me n tnitialu se ofgas hybrid bearingsentailed th eu se ofalabyrinthseal ingarrangement .T helabyrinthsealinterposesa' tortuous f low pathbetween high an d lo w pressureregionsb y m e a n sofaseriesofnon-contact ing restrictorsan dseparating chambers ' .he funct ionofth erestrictorsisto conver td ie pressure head intokinet icenergy w h i c his thendiss ipatedthroughoutth echambers .hey ar eparticularlysui table fo rhightemperature service although b y comparison with face seals,l eakageratesar egeneral lygreater.Labyrinth design i s a compromisebetweenmaximis ingth en u m b e rofthrottlings per unitlengthan d minimising th ekinet iccarry-overwithan adequatepitch.N o al lowance is necessary fo rrotational effectsat th espeedsenvisaged. T he mostwidespread method ofanalysisfo l lowsthatofMartin(1908)whichcalculatesth e leakage b y considering the restrictorsasaseries ofannularorif ices,fo