FORAERONAUTICS

TECHNICAL NOTE 3382

EXFERZMENTSWIT’HA ROTATING-CYLINDER

VLSCOMETERAT HIGHSHEARRATES

By J.A. Cole, R. E. Petersen, sndH. W. Emmons

Harvard University

Washington

June1955

https://ntrs.nasa.gov/search.jsp?R=19930083941 2020-04-15T12:39:27+00:00Z

TECHLIBRARYKAFB,NM

l~lllulllllll’lll[lllNATIONALADVISORYCCMMITTEEFORAERONAUTICS ‘ DDLLM51

TECHNICALNOTE3%2

EXPERIMENTSWITHA RUTATING-CYLINDER

VISC=ER AT HIGHSHEARRATES

By J.A. Cole,R. E. PetersenlandH. W. Emuons

SUMMARY

Twostraightmineraloilsanda polymer-centsiningoilhavebeentestedina rotating-cylinderviscometerathighshearrates(maximumO.= miXLionreciprocalseconds)andtheaccompanyingheateffectshavebeeninvestigated.

Thetorquemeasurementsareoflowaccuracyandfailto establishthemoderatelynon-Newtonimbehaviorofthepolymer-containingoil,butthetemperaturemeasurements,whichareingoodagreementwithathermalanalysis,do indicatethepresenceoftemporaryviscositydecreasem athighshearratesforthisoil.

INTRODUC?ICHIN

Infullfluidfilmorhydrodynamiclubricationtheviscosityisthenestimportantphysicalpropertyofthelubricant,andotherquantitiesinvolved,suchasdensity,thermalexpansioncoefficient,heatcapacity,andthermalconductivity,areofrelativelyminorconcern.Theloadcapacityandfrictiontorqueofa bearingaredirectlydependentontheviscosityofthelubricant,andthusthebearingperformanceiscontrolledby theinfluenceoftheoperatingtemperature,pressure,sadshearrateor stressontheviscosity.

Theeffectoftemperatureonviscosityisconsiderableandwellknow. To indicateordersofmagnitude,a lightmineraloilmayundergoa tenfoldreductioninviscosityfora temperaturerisefrom2’j0C to100°C!.Theeffectofpressureislessstriking;but,indew ofthehighfil.mpressuresgeneratedinheavilyloadedbearings,it is stiUimportantandhasbeenwidelystudied.A lightmineraloil,forexample,mayincreasefifteenfoldinviscosityat no C andfivefoldat 100°Cfora pressurerisefrom1 to 1,000atmospheres.

b Mostlubricatingoils=e Newtonian,at anyrateoverthenormalrangeofoperatingconditions,andviscosityis independentof shear

2 NACATN3382.

rate. Nevertheless,thepossibleeffectof shearratehasbeena matterof interestformanyyearsinasmuchastherehasbeenscxnecontroversyasto whetherstraightmineraloilsshownon-Newtonianbehavioratvery Fhighshearrates;sayover1 millionreciprocalseconds.Withtheincreasinguseofveryhighspeedbearingsthisquestionhasgainedinsignificance,sinceinhigh-speedbearingsthewholeoftheoilfilmissubjectedto a highshearrate,whereasinheavilyloadedlowerspeed .-bearingstheshearrateishighonlyovera smallfilmarcnearthepointofminimumfilmthickness.

It is,however,thequestforlubricantssuitableforuseatextremesoftemperature,highorlow,and/orwithimprovedviscosity.temperaturecharacteristics,thathascausedan increaseof interestinnon-Newtonianeffects.Syntheticadditives(viscosityindeximprovers)formineraloilshavebeendevelopedwhichgivea flatterviscosity-temperaturecharacteristicattributableto thecoilingoflongmolecularchains;thatis,thetemperatureriqecausesuncoilingdueto increasedvolubilityinthebaseoilandthischangeofformpartiallyoffsetstheviscositydropnormallyarisingfroman increaseintemperature.

Theeffectivenessofviscosityindex@rovers increases,ingeneral,withincreaseinmoleculechainlengthbutis inpartvitiatedbytheeffectof shearrate.Undershearconditionstherecanbe a permanent *

viscositylossduetomechanicalbreakdownofthemolecularchainintosmallermolecules,smd.therecanbe temporaryorreversibleviscositylossduetomolecularorientation.

KTheseeffectsbecomemorepronounced

withincreaseinmolecularchainlengthsothata compromisemustbesoughtbetweentheuseof smallq~tities ofhigh-molecular-weightaddi- =tivesonthescoreofeconomyandtheuseoflargeramountsoflowermolecularweightcompoundsonthescoreof stability.

Itmaybe mentionedthattheamountsofthepoQmerizedestersofacrylicandmethacrylicacidsorpolymerizedisobutyleneusedforthisPqose are-, oftheorderof”2or3 percentby weight;and,sincetheirmolecularweightsmaybe 100timesthatofthebaseoil,themolecu-larratioisverysmallindeed.Themechanismoftemporaryviscositylossisthesameasthatexpectedforstraightmineraloils,butthelongermoleculessufferalinementat lowershearstresses.

—

An experimentalstudyofnon-Newtonianeffectsinlubricantsiscomplicatedby thetendencyforhighshearratestobe associatedwithconsiderableheatdissipationduetoviscouslosses,sothatviscositydropsdueto shearrateareovershadowedbyviscositydropsduetotem- .

peraturerise.Thermaleffectsathighshearratescanbeminimizedbya suitablechoiceofvariablesinbothcapillaryandrotating-cylinderviscometers,sincetherateofheatproductionforeitherisapproxi-matelyproportionaltotheproductofviscosity,filmthickness,andshearratesqmed. It isthereforeclearlyadvantageousto obtainthehighshearraterequiredas faraspossibleby useof smallfilmthicknessesor capillarydiameters.

4“

wcA m 3382 & 3

*Inregardtothechoiceof equipmentforthistypeof investigation,

therotating-cylinderinstrumentisgenerallypreferredto thecapillary1 instrumentwhenallfactorsaretakenintoaccount.Thelatterisproba-

blysimplerandhastheadvantagesofa staticpieceofequipment,but,ontheotherhand,thepumpingnecessaryintroducesthefurthercomplica-tionofpressure-viscosityeffectsandpossibleexternalpermanentvis-cosityloss.Theshearstressandshearratevaryacrossthecapillarycrosssection,whereasintherotating-cylinderinstrumentshearstressisconstantacrossthefilmandshearratevariesonlywhenvelocitiesandfilmthicknessesarelarge.Withthecapi31arytube,thetimeofflowpassageathighshearratesmaybe sosmallthatmolecularorienta-tionmaynothavetimetobecomefullyestablished,whereasintherotating-cylinderviscometerthessmefluidsamplecanbe continuouslysheared.

Thedesirabilityofusinga smallfilmthicknessintherotating-cylinderviscometerissubjectto thelimitationsimposedby difficultyandcostof construction.Witha smallclearancesuchmattersasround-ness,alinement,surfacefinish,andthermalexpansionbecaneincreasinglyimportant,andas smallclearancesaredifficultto measureaccuratelytheinstrumentmustbe calibratedintermsofviscosityinsteadofbeingusedabsolutely.Ultimately,whenthefihnthicknessis comparablewiththesmplitudeofthesurfaceroughness,thereisdangerthatanomalousresultsmaybe obtainedwhenhydrodynamiceffectsaremeasuredon amicroscopicscale.4

Thisinvestigation,whichwasbeguniu1948,coversthedesign,construction,andmodificationofan apparatusfordetermininghydrody-namicbearingperformanceandthetestsmadeusingthisapparatus(refs.to 4 andpresentreport).Thelubricantstestedwerekerosene(ref.2),frcmnwhichanomalousviscosityresultswereobtained,n-butylsebacate,siliconeGE 200,andEtnaOilLight(ref.3), allofwhichprovedto beNewtonianwhentestedat shearratesupto 0.224,0.067,and0.2C6mil-lionreciprocalseconds,respectively.Inthepresentreport,whichisthelastphaseofthisinvestigation,thermalconditionsintheviscome-terareinvestigatedathighshearrateswhenusingbothNewtonianandnon-Newtonianoilsofknownproperties.As isevidentfromthecompara-tivefiguresintableI, inwhichtheworkof otherinvestigators(refs.to 20)is summarized,thepresentviscometeris inefficientinthesensethattheshear-raterangeisnotverygreatwhiletheheatdissipationislarge.Thisdifficultycanbe overcomeby furthermodification,butasitstandstheequipmentisverywe’llsuitedto an eqloratoryexaminationofthethermalconditionswhichwillariseatveryhighshearratesoftheorderof severalmillionreciprocalsecondswhenrecourseto smallclearancesas intheviscometersofNeeds(ref.19)andBarber,Muenger,andVillforth(ref.20)willno longerpreventthecomplicationofther-

* maleffects.

.

,

Thebasictheoryfordiscussedinreference21

NACATN3382#

thermaleffectsfirstdevelopedbyBrattasandextendedby I&g (ref.15)isusedfor

thisstudy.Blok,ina paperpresentedattheSixthInternational v.

CongressforAppliedMechanics,hasgivena veryusefulgeneralizationofthistheory,andtheresultsaregiveninappendixA. Theanalysis,whichisbasedontheexistenceoflaminarconditionsina Newtonianfluidandontheassumptionofan exponentialviscosity-temperaturerelation(validfora notgreaterthanfourfoldvariationoflubricantviscosityacrossthefilm),expressesrotor-statortemperaturedifferenceM’,apparent:iscosityqar,andshearstressS (allexpressednon-

—

dimensions.11~)intermsoftwonondimensionalvariablesP and Ngivenby thefollowingformulas: -.

Heat-partitionfactor,

P= HeatconductedfromfilinviastatorHeatgeneratedinfilm

Heat-dissipationfactor,

~= ~%@k

where

P viscosity-temperaturecoefficient

7s viscosityat statortemperature

u surfacespeed

k thermalconductivity

Thetheoryshowsthatthe

oflubricant

relativeviscosity(theratiooftheapparentviscosityqar deducedfromthemeasuredtorquetothevis-cosityqs atthestatorsurfacetemperatureTs)decreasesfromtheisothemalvalueofunityas P and N increase.

Ithasbeennecessaryto extendtheanalysisforthepresentresearch,andthesenewresultsappearinappendixB. Expressionsaregivenforthefilmtemperaturegradient,a quantitymeasuredinthepresentreportinsteadofrotor-statortemperaturedifference,andforthetemperaturecorrectiontothestatorsurfacetemperaturetobring ~itintolinewiththeapparentviscosity.Thelatterisa moreexactformofthe“parabolic*’constant-viscositycorrectionusedearlierin

—

8

k.,

NACATN 3382 5

.

thisinvestigation(ref.3),anditiscomparedwitha generalizedformofthisparaboliccorrection.Sincetherotating-cylinderviscometeris

9 a constantshear-stressinstrument,theanalysiscanbe extendedto non-Newtonianfluidsprovidedthattheratioofthehigh-shearto zero-shearviscosityisa functionoftheshearstressonly.An examinationofexistinginformationonnon-Newtonianlubricantssuggeststhatthisisnotanunreasonableassumption.Thesenewresultspermittheeffectsoftemperatureandshearstressonviscositytobe separated.

Themeasurementofviscositybyflowandpressuredropthroughtheannulusnecessitatesan extensionofthetheoryto accountfortheeffectofthedecreaseinviscosityontheaxialvelocity.Thepressuredropsusedwereso smallthattheaxialshearstressandtheflowenergydis-sipatedarebothnegligiblecomparedwiththecorrespondingrotationalquantities.Theresultsofthistialysisareagainexpressedas a rela-tiveviscosity(theratiooftheapparentviscosity~a deducedfromtheflowandpressuredroptotheviscosityI’ISattheStatorsmfacet~erat~e Ts)=

Thisworkwasdoneat EarvardUniversityunderthesponsorshipandwiththefinancialassistanceoftheNational.AdvisoryCommitteefor

. Aeronautics.

SURVEYcm’LmmATum

A numberofwritershavespeculatedthatthepossiblereductionofliquidviscosityundershearingflowconditionsiscausedby orientationofrod-shapedmolecules.Bondi(ref.22)hascalculatedthatforthemolecular-weightrangeappropriateto ordinarylubricatingoils,a mini-mumshearstressoftheorderof500,000dynes/sqcmwouldbe necessaryto producea perceptibletemporaryviscositydecrease.Formuchlargermolecules,suchastheviscosityindeximproversalreadymentioned,smallershearstresseswouldbe required.

It isinstructiveto examineearlierexperimentalworkonfloworientationwiththisvalue in mind,amplifyinga similarreviewpre-sentedbyBlokattheSixthInternationalCongressforAppliedMechanics.Table.Isummarizesinvestigationscarriedoutduringthepast20years,theearlierworkdealingonlywithordinarylubricantsandthelaterwork,withpolymer-containingoilsalso. It seemsthatinno casewasBondi’scriticalshearstressreached,and,inthefivecaseswherenon-l?ewtonianeffectswereclaimedforordinarylubricants,therewerealsolargether-maleffects.Thema~orityoftheevidenceindicatesthatstraightmineraloilsbehaveinpracticeasNewtonianfluids;evenat shearratesashigh.as 2 millionreciprocalseconds,thestressisunlikelyto a~roachBondi’scriticalvaluebecauseofheatdissipationandconsequentviscosity

.

6 NACATN3382

“

reduction.Theonlyrecentinvestigatorsto claimnon-NewtonianeffectsareWard,Neale,andBilton(ref.17),inwhoseapparatuscarewastakentomeasurethelargethermaleffects.Therearetwopossiblesourcesof werrorintheirwork:Heatlossviatherotor,saidtobe “virtuaKlythermallyinsulated,”wouldpermita temperaturemaximumto occurinside _thefilminsteadofattherotorasassumedandtheir“criticaltest”for

—

anomalousviscositythenbreaksdown;and,further,itseemslikelythatinsufficienttimewasallowedfortheestablishmentofthemalequilibrium.

Thedefinitivepapersonpolymer-containingoilsarethoseof,Fenske,Klaus,andDannenbrink(ref.18),Needs(ref.19), andBarber,Muenger,ad Villforth(ref.20)inwhichagreementontheextentofviscositydropfora givenoiliswithinabout~ percent.

SYMBOIS

h

k

N

N’

n

P

P

s

T

u

u

w

w

Y

filmthickness

thermalconductivity

heat-dissipationfactor,1+ ~2

B? ‘modifiedheat-dissipationfactor,+$

maximumrotationalspeed

heat-partitionfactor, HeatlostviastatorHeatgeneratedinfilm

pressure

circumferentialshearstress

temperature

rotorsuxfacevelocity

radialvelocity

axialvelocity

axialflowper

film-thickness

unitcircumference

coordinatemeasuredfromrotorradiallyoutward

.—“

K

3382

viscosity-temperature

i

Pnondimensionalshearstress,Sh—qsk

temperaturedifferencebetweenTstemperature

absoluteviscosity

measuredorapparentviscosityfrc?n

measuredorapparentviscosityfrommeasurements

andeffectivefilm

torquemeasurements

flowandpressure-drop

viscosityat statortemperatureunderzero-shearconditions

viscosityat statortemperatureunderprevailingshearconditions

kinematicviscosity

Subscripts:

r rotor

s stator

APPARATUS

TheHarvardrotating-cylinderviscometerhasbeendescribedinpre-viousreportsofthisinvestigation(refs.1 to 3). Briefly,itconsistsofa 2-inch-diameterhardenedNitra120ysteelrotorsupportedverticallyattheupperendby twoangularcontactprecisionballbearingsandrotatinginsidea bearingor statorofthesamematerial,4 incheslongwith0.003-inchradialclearance.Thisstatoriscarriedona dog-legspringmounting,whoseeffectivetorsionalstiffnessisapproximately0.032poundperthousandthofan inchasmeasuredatthestatoroutsidediameterof6 inches.

. TherotorIsdrivenby an electronicallyspeed-controlled15horse-powerdirect-currentmotorthrougha gearboxandfinalbeltdrive.

-.i

8 NACATN 3382

Interchangeablegearsandtwosupplyvoltagesgivea controlledspeedrangeof12to 1.2,500rpmanda maximumpossiblespeedof25,000rpm.Motorandrotorspeedsareelectricallyindicated. ?-

ThestatortemperaturefieldisdeducedfromthereadingsofH thermocouplessytmnetricallydisposedthroughoutthestatorandswitchedto a manuallybalancedprecisionpotentiometer.A single

——

thermocouplerecordsoilinlettemperatureandothersrecordoilout-lettemperatures.

Torquecanbe deducedfromtheangulardeflectionofthestatoronitsmounting,whichmaybe indicatedonanextendedscaleusingan elec-tronicpickupdescribedindetailinpreviousreports(refs.1 to 3) ofthisinvestigation.Sincethecompletionofreference4,torquemeas-urementhasbeendirectlymadeby a nullmethod,thetorsionmountingbeingusedmerelyasa springpivot.Torqueisappliedby a deadloadingsystato restorethestatorto thezeropositionas indicatedby an ‘X75microscope.As describedina subseqwntsection,torquemeasure-mentisnotveryprecise.Thisisascribedtotheimperfectelasticpropertiesofthestatorthemnocoupleleadscontributingaboutone-thirdofthetorsion-mounthg-stiffnessvaluequoted.

Thetestlubricantissuppliedviaa tqbepassingdownthecenter m

ofthehollowrotor.A stationarydiskattheendofthetubeinsures—

thatthestatormeasuredtorquedoesnotincludethatdueto theendoftheshaft.As notedinthepreviousreport(ref.k),thePresentlarge

,w.

clearancetendsto emptyandgivean incompletefilmunlessa continuoussupplyofoilundera smallheadisarranged.In orderto kep theaxialflowto a minimum,an alternativeoilsupplysystemmaybe used,oildrippingintoa constant-headsightglassattachedtothestator.Thisdoesnotinvolvea forceonthestatorwhichwouldaffectthetorque

—

reading..

A fewtestsweremadeat severaldifferentheads.Theoilflowwasmeasuredby collectingtheoilina calibratedcylinderfora measuredperiodoftime. An independentmeasureofviscositywasthusobtained.

Therotor-statorfilmresistanceandcapacitymaybe recordedduringa testrun.

A detailedcriticalexaminationofthedesignandconstructionoftheapparatusispresentedinreference4. Itwasconsideredthatthelocatedrotor,a funcbnentalfeatureofthedesign,wasonthewholelesssatisfactorythanthemoreusualself-centeredrotoremployedinotherdesignsandunsuitableforuseasa preset-eccentricityjournal-bearingmachine.A numberoflesssweepingchangesweresuggested,butttmehasnotpe?mittedtheiradoption.Theseincludedtheuseofa coaxialflexi- -blecouplingforthefinalrotordriveinplaceofthepresentbeltdrive,

-,#

NACATN3382 9

theuseofa sma~errotorclearance,a stiffeningofframework,andtheprovisionofrotorthermocouples.--

An unexpectedlimitationonthemaximumspeedat

theviscometer

whichtheviscom-etercouldbe operatedarosefromoverheatingofthemainbearingsandimpendingseizureofthefiberretainers.Thisdifficultyincreasedduringthecourseoftheinvestigation,permittingspeedsupto only>,000rpm,andreplacementbesxingswerenotreceivedintimeto estab-lishwhetherthiseffectwasinherentinthedesign,becauseoftheinevitablehightemperaturesathighshearratesandabsenceof continu-ouslubricationofthemainbearings,orwhetheritwasmerelya resultofbearingdeteriorationovertheseveralyearsthe-chinehasbeeninuse. Thebearingsarenotprotectedagainsttheingressof dustfromtheatmosphere.

EXPERIMENTAL

Thebasicrequirementfortheusethermalconditionsnowpresentathigh

MEmKm

oftheinstrumentunderthesevereshearratesisthattemperature

equilibriumshallbe established,inasmuchasthethermaltheoryused.postulatesthermalequilibrium.

Torqueandtemperaturereadingsduringa wazming-uprunhaveshown\ thattheratesoftemperatureriseandtorquedecreasebecomesmallafter2 to 3 hours,bute~rience hasindicatedthatit isdesirableto oper-ateatthetestspeedforabout6 hoursbeforemakingthefinaltempera-turerecord,andthisrestrictsteststo oneperday. Onceconditionsaresufficientlysteady,thereadingsfrcmthen statorthermocouplesandothertemperaturesaresuccessivelyrecordedanddividedforcon-venienceintothreegroups.At thebeginningandendofeachgroupacontroltemperatureisreadasa checkonthetemperatureequilibrium,thepotentiometeris checked,andreadingsaretakenofspeed,torque,andoiloutflow.Theccsnpletesetofreadingstakesabout1 hour.

Statortemperaturesareplottedona largescaleagainsttheloga-rithmoftheradiusandarefoundto followcloselytheeqectedlinearrelation.Thegraphicalmethodhelpsto eliminaterandomerrorsandisusedto givethebestapproximationto theextrapolatedstatorinsidesurfacetemperatureandradialtemperaturegradient.Thestatortempera-tureandthegradientvarysomewhatbothaxiallyandcircumferentia12y,especiallytheformer,andthearithmeticmeansaretaken.Torqueandspeedareaveragedoverthewholerun.

Fora givenoil,thesurfacetemperature,temperaturegradient,and% torqueshouldgivea smoothcurvewhenplottedagainstspeed,witha

smallscatterdueto day-to-dayvariationofroomtemperature.Thishas

-i

10 NACATN3382

beenfoundtobe a usefulcheckontheconsistencyofreadings,particu-larlyWhenthereisanydoubtabouttemperatureequilibriumor oilfilmcampleteness.

●

PRECISION

Thermocouplevoltagesareactuallyreadto 0.1microvoltandareprobablyrepeatableto *1microvolt.TheInternational.CriticalTablescalibrationforthecopper-constantanthermocouplesisused;the100°Cfixedpointisoccasionallycheckedand,asmentioned,thepotenticaneterisveryfrequentlychecked.Themaximumprobableerrorsintheextrapo-latedstatorsurfacetemperatureandthestatorgradientareestimatedto be 0.05°C (maximumvalue,lx0 C)andO.@” C perinch(maximumvalue,~“C perinch).

LowshearviscositiesaremeasuredinA.S.T.M.U-tubeviscometers;temperaturesaremeasuredwiththetest-rigthermocoupleequipment.Densitiesaremeasuredina rektive-densitybottle.Thefind centi-poiseviscosityisestimatedtobe within1/2percentofthetruevalue.

Therotorspeedvaries1 percentduringa testrun;theaccuracy.

ofmeasurementof speedisabout1 percent.

Ifthenullmethodfortorquemeasurementisused,thereappearsto*.

be a variationin zeropositionduetotemperatureandotherfactorsofabout60,000dyne-cmandthe’microscopepermitsadjustmentundertestingconditionsto about20,000dyne-cm.Thus,thetorqueerrorcanbe ashighas80,000dyne-cm,andfortheusualtorquevaluesofapproximately~ milliondyne-cm,thisrepresentsa precisionof3 percent.

Themanufacturingandmeasuringtolermcesfortherotorandstatorare*0.OCXllinchsothattheradialclearancemaybe atworst0.0001inchor 3.3percentdifferentfromthenamindvalue of 0.003. Themaximumpossibleerrorduetomisalinementanddifferentialthermalexpansionisabout1 percent.Thus,theclearanceprecisionisabout4.3 percenttowhichshouldbe addedtheerrordueto surfacecurvatureintroducedby

—

useoftheformula

Apparentviscosity= (Stress)(l@dialclea~ce)Surfacevelocity

whichisabout0.3percentmaximum.

.

NACATN 3382 u

.

.-

Thus,usedabsolutelytheviscometermayindicateapparentviscosi-tieswitherrorsas largeas 9 percentatworst,andusedrelativelywitha standardviscosityfluid,abouthalfthisemount.

msuims

Duringthepresentinvestigationthreelubricantshavebeentestedintheshearraterange0.001to 0.25millionreciprocalsecond.TheseareEtnaOilLight(Socony-VacuumOilCo.),an SAE10 straightmineraloildenotedby EOL;Flowrex300(Socony-VacuumOilCo.),an SAE30straightmineraloildenotedbyF300;API103(AtlanticRefiningCo.),a mineraloilcontaininga relativelylowmolecularweightpolymeras aviscosityindeximprover.DatafortheAPI103non-Newtonianlubricanthavealreadybeenobtainedby otherinvestigators(refs.18to 20).

Figures1, 2,and3 showthemeasuredviscositiesforeachoftheoilsplottedonA.S.T.M.chartsagainsteffectivefilntemperature,withtheparaboliccorrectionforthestatortemperaturebeingused. Thelow-shear-viscosityvaluesobtainedwithU-tubeviscmetersandtherangesofshearrateandstressareshown.

Figures4, 5,and6 showtherelativeviscositiesandindicatemoreclearlytheetientofdeviationsfromtheexpectedvalues.

Figures7,8, and9 showthefilbntemperaturegradients;a steel-oilconductivityratioof 320isassumed,asusedpreviously.Thether-malconductivityofau threeoilshasbeentakenas 0.00033cal/°Cunits.Theviscosity-temperaturecoefficientistakenfroma graphofviscosityagainsttemperaturededucedforeachoilfromitslowshearviscosity-temperaturecurve,sincethecoefficientvariesconsiderablyoverthetemperaturerangeoftheseexperimentseventhoughitis sufficientlyconstantfortherangeoftemperaturesoccurringinthefilminanyonetestto satisfytherequirementsoftheanalysis.CalculationoftheReynoldsnuaibershowsthatthemaximumvalueinthepresenttestsisabo~two-thirdsoftheTaylor-criticalvalue.

Measurementshavebeenmadeoftilmdielectricconstantandfilmelectricalresistivity(thelatterundera gradientof 0.6kilovoltsdirect-currentpercenttiter).ForboththeNewtonianandthenon-Newtonianoilstherewasno significantdecreaseof eitherquantitywithshearrate.Resistivityshowedsomedecreasedueto temperaturerise.Themeasurementswereoflimitedpreci.sionbecauseofelectricalnoiseattherotorgroundingbrush.

In allthetestsreportedhereina smallaxialflowoflubricantwasmaintainedto insurecompletefillingoftheclearancespace;however,

—

u mcA TN 3382

.theconvectiveheatdissipationby thisflowwassmallandshouldnataffecttheapplicationofthethermalanalysisofappendixA. A smallPUKPi%actionathighspeeds,attribtiedto centrifugalaction,has PbeenobservedandhasbeenUscussedinreference4.

Inthefewtestsmadewithvaryinghead,inwhichthe“axial”vis-cositywasobtained,thedissipationremainednegligible.

DISCUSSION

IntheA.S.T.M.viscosity-temperaturechartsoffigures1,2,and3,therandomdeviationsofthemeasuredviscositiesfromthemeanstraightlinesdrawnandthedisplacementsoftheselinesfromthelow-shearlinesareingeneralagreementwiththeestimateofprecisiongivenpreviously.

Thedisparitybetweentheobservedandlow-shearviscositiesforEOLislargerthanthatpreviouslyreportedbyllmnonsandSoo(ref.3)usingthesameapparatus.Theirlow-shearviscositiesappeartobeincorrecthowever;thisisprobablyattributabletotheiruseofaSayboltviscometer.

Thelowaccuracyofviscositymeasurementisemphasized therelative-viscosity-heat-dissipation-factorcurvesoffigures$ 5,and6inwhicharealsoindicatedtheexpecteddeviationsfromthelo~-shearviscosityratioofunitydueto filmtemperatureriseand,inthecaseofAPI103,dueto non-Newtonianbehavior.ThelattervaluesarebasedonresultsbyNeeds(ref.19) forthisoil,andfigure5 bringsouttheconstant-stresscharacteristicoftheviscometer.Fora givenoil,thereisa comparativelysmallchangein shearstressovera rangeofshearrate,andthenon-NetionianviscositydecreaseforAPI103isfairlyconstantat only5 or6 percentovermostoftheshear-raterangecovered.Thisoilcontainsa low-molecular-weightpoQmerandisnotmcrkedlynon-Newtonian.Thepresentequipmentfailsto establishanynon-Newtonianbehavioraccordingto figure5.

Figure6(b)showsthethreetestpointsobtainedfromaxial-flowmeasurements.Thedataaccuracyis insufficientto establishthecor-rectnessoftheanalysis.

Figures7,8,and9 showthefilmtemperaturegradientatthestatorintermsoftheheat-dissipationfactor.InthecaseofAPI103(fig.9),thefactoristhemodifiedvariableN’ basedontheviscosityatthestatortemperatureandtheprevailingshearstress,Needs’resultsagainbeingused,sothatthetheorystillappliesas showninappendixB.

NACATN 3382 13

.Valuesoftheheat-partitionfactorP areindicated(fig.9)and

theagreementwiththepredictionsofthethermaltheoryisgood. In“7 thecaseofAPI103,thismaybe takenas confirmingthevaluesobtained

by Needsfortheextentofthenon-Newtonianbehavioroftheoil,althoughitwouldbemoreconvincingiftheoriginallycalibratedheat-partitionfactorP, eqpalto A, stillapplied.HoweverjcontinueddeteriorationofthemainbearingshasalteredP, thereasonbeingthattheincreasedfrictionalheatdissipationatthesebearingsatthetopoftherotorreducesthetemperaturegradientfrombottcmtotopandthusmoreoftheheatdissipatedinthefilmmustescapeviathestator.Thetwoanoma-louspointsmarkd A infigure9 correspondtothosesimilarlymarkedirifigure3. Excessiveheatdissipationatthemainbearingsoccurredduringthesetests.

CONCLUiIINGREMARKS

Theresultshaveconfirmedthefactthattheviscometerusedcom-parativelyindicatesapparentviscositywithratherlowprecision,about*5percent, andthusfailsto &l.fferentiatebetweenstraightmineraloils,ahnostcertainlyNewtonianoverthepresentrangeoftestcondi-

. tions,anda polymer-containingoilofbown smallnon-Newtoniancharac-teristics.Thetemperaturemeasurementsdobe made.,-,

Thethermalconditions eAsting intheexaminedandaresubstantiallyaspredictedsivedeteriorationinthemainbearingshaspartitioncalibrationoftheviscometer,asshear-ratersageavailable.

permitthisdistinctionto

apparatushavebeenthoroughlyby thetheory,buta progres-causeda changeintheheat-wellasfurtherlimitingthe

As itstsds,thevisccmeterisrelativelyinefficient:Thelargeclearancenecessitateshighspeedsand,conseqwntly,bothlargethermalcorrectionsanda low-shear-stressrangeforan onlymoderateshear-raterange.Torqueaccuracyislowbecauseofthethermocoupleconnectionstothestator.Axialflowisnecessarytomaintaina completefiUnand,consequently,a fairlykrge tests~~e oflubri~t isneeded.

Withoutchange,otherthanimprovedmainbearings,theapparatuswillbe usefulforan investigationofmoreviscouslubricantsatmoder-atelyhighshearrates,sincelargertorquescanbe measuredmoreaccu-rately.Thegoodtemperatureinstrumentation,improvedearlierinthisinvestigationbytheadditionofrotorthermocouples,makestheequipaentusefulforan investigationofheateffectsinoilfilmsalongthelinesnowstarted.Twoproblemsmeritingattentionaretheeffectoflarger

. axialflowsandconsequentheatconvection,andtheheateffectsundertheturbulentconditionsoftheTaylorvortexmtiion,withandwithoutaxialflow.

14 NM!ATN3382

Witha changeto a smallerclearance,thelocated-rotorfeatureof.

thedesignwillbeccmemoreobjectionable,buttheshearstressandraterangestillbe increased.Thevisccnneterusedinthisinvestigation Pwouldstillbe inferiortotheinstrumentsofNeedsandofBarber,Muenger}andVillforthbecauseoflowtorqueaccuracyexceptatveryhighshearrateswherethereappeem.nceoflargethermaleffectsdespitetheuseofa smallclearancewouldJustifythethermocouplesystem.

HarvardUniversity,Cambridge,Mass.,June12,1953.

NACATN 3382 15

APPENDIXA

TBERMALEFFECTSINABEAKENGOILFIIM

Theresultsaregivenhereinofa generalizationby BlokpresentedattheSixthInternationalCongressforAppliedMechanicsofHagg1sanalysisofthermalconditionsina concentricbearing,theanalysisbeingbasedonthefollowingassumptionsandbasicequations:

(1)Thebearingisinfinitelylong,andthesmallrelativetothediameter

(2)ThelubricantisNewtonianandthe flow

filmthicknessh iS

laminar

(3) Lubricantequilibriumexists

(4)Lubricant

(5)Theshear

thermalconductivityk isconstant,andthermal

viscosityq variesexponentiallywithtemperatureT

stressandenergydissipationresultingfromtheaxialflowofoilarenegligiblecomparedwiththecorrespondingrotationaleffects

(Newtonianflow) (1)

(Thermalequilibrium) (2)

-13Tn = qse (Viscosityis qs at stator, (3)

wheretemperaturedatumistaken)

Intheanalysisa parameterP, theheat-partitionfactor,anda non-dimensionalvariableN,theheat-dissipationfactor,areintroducedas

P= HeatconductedfromfilmviabearingstatorHeatgeneratedinfilm

f% $N=—k

16 NACATN 3%2

.

where

u rotorsurfacevelocity

Theresultsareexpressednondimensionall.yas

~(Tr- ‘s)= 10ge[l+(p -:)Nl(4)

(5)

(6)

whichrepresentrotor-statortemperaturedifference,shearstress,andrelativeviscosity,respectively.Relativeviscosityistheratioofthemeasuredorapparentviscositytothestatortemperatureviscosityandisunityintheabsenceofthermaleffects.

.

*

L

.NACATN3382 17

7

APPENDIXB

EXTENSIONOFANALYSISFORPRESENT

Thefil.mtemperaturegradientatthestator

RESEARCH

ismeasuredinthepresentapparatusinsteadofthatgiveninequation(4)anditcanbeshowntobe

(7)

Thus,oncetheapparatushasbeencalibratedto determineP,ideally,nofurthertorquemeasurementsareneededto findtherelativeviscosityinasmuchas itcanbe deducedfromtemperature-gradietimeasurements.

TO obtaintheeffectivefilmtemperaturea correctionAT mustbeaddedtothemeasuredstatortemperatureTs inorderto correspondto

. themeasuredviscosityTIm andmaybe derivedas

plsr (r=loge~ %+2Ncoth)

r .,% P,.1 P?N+2N (8)PN+2

()13~

dy/dhs

Fora valueof P notexceedingunityanda valueof N whichissmallcmnparedwithunity,equations(4)to (8)canbe representedapproximateelyby

,(Tr- Ts) =(P - *)N

r=N

%r—=1 .-*PN%

(9)

(lo)

(U)

)%%iEs= PN (12)

18 NACATN3382.

pm .*PN (13) -

Itfollowsfromequation(9)thatforverysmallvaluesof N (andthereforeconstantviscosity)thetemperaturedistributionacrossthefilmisparabolic.Onthis-assumptio~,thetemperatureTs canbe showntobe

withthetemperaturegradientpositivefromtherotor.

()3P-2 d!l— —6(P- 1)’dy/dh~

inthedirection

Thecase P = 1/2 isequivalentto thecorrectionence4,buta highervalue P = 3/4 hasnowbeenshown

correctionto

(14)

of y increasing

usedinrefer-to applyto the

apparq~us.The~araboliccorrectionisthenadequateforallpracticalpurposesupto N = 0.1.

Theanalysismaybe extendedto non-Newtonianfluids.Thereistheoreticalande~rimerrtalevidencethatthehigh-shearviscosityof .a polymer-containinglubricantisa functionofmaybe e~ressedas

~highshear- f(s)

~zeroshear

where f(S) isa nondimensionalfunctiontobe

form e-yS(7constant)).

If N is stilldefinedas ~U2, where

zero-shearviscosityatthestatortemperature,

N? = ~vs’U2 c~be introduced,where qs’ isk

tfieshearstressS and

-.

(15)

(determinedprobablyof

% is stillthestandard

a modifiedvariable

theviscosityatthepre-

vailingshearstressandthestatortemperature.

Analysisthenshowsthat

‘(*) = ~- tanh-ls

NACATN3382 19

Tar—=78‘

Fora fluidof

* ‘“-1JkQcfLa (17)PN’+2

unknownshearproperties,measurementofthetempera-gradierrtenablesN! tobe &du~edfrc&equation(16)andhenc~

T=canbe foundfromequation(17).Theratio— isknownfrc$nthe

7s—measurementssothatthevalueof f(S) appropriateto theshearstressprevailingduringthemeasurementscan-bededu~ed

Theseresults,viscositydecreases

believedtobe new,shouldbeduetothermaleffectsandto

asfolJows:

(18)

of servicein separatingshear-stresseffects

duringtestsonnon-Newtonianfluidsat highshearandthemalconditions.

In orderto determineaxialflow,theassumptionsas statedin.appendfxA areaccepted.However,thefollowingadditionalbasiceqw-tionsarereqyired:

dp+ddz T’-%=*

(axialmomentumequation) (19)

J’hw= Wdy (continuity) (20)o

Theintegrationofeq~tion(19)andtheirdnmductionof q =+gives .

s

whereA istheconstantofto u frcmtherotor(u= U,

dw dp—=-zy+Adu

integration.Now,integratewithw E ()) to theStator (U = (), w

du/dy

(21)

respect=0):

(22)

20 NACATN 3382

.

Substitutionofeq@ ion(22)intoequation(20)resultsinthefollowingrelationbetweentheflowperunitofcircumferenceW andthepressuregradient:

Noticethatthisrelationbetweentheaxialflowandthepressuxedrop—

is independentoftheviscosityanditsvariation(withrate of shear)withintheoriginalassumptions.

Forviscosityas givenby eqpation(3),Blokgivesbetweentangentialvelocityu andthepositiony as

temperatureand

therelationfollows:

By expansionof u asa powerseriesin y,theintegralsinequa-tion(23)canbe evaluated,~d a f-l res~t~Y be obtainedaS

(24)

w [(dph31+N. ~=-x 1276 5

+gP-3P2)-

(J&’z+—

p3)117P,-UP2+T +.. * (25)60 u 420

Inthisformulatheexpressionwithinbracketsistobe ijientifiedwith7#1~” Thefollowingapproximateformulaisthenobtained:

~aa~ (

=l-N-l+7

Thisresultisplottedinfigure6(b).

7~P - 3P2) (26)

.

.

..

NACATN3382 21.

REFERENCES

w

1.Emmons,HowardW.,Head,VernonH.,Batteau,DwightW.,andHammond,JohnM.: A HighRateof ShearViscosimeter.contractNIiv-5630,NACAandHarvardUniv.,Aug.I-2,1949.

2. Emnons,HowardW.,andHead,VernonH.: PreliminaryTestsofaRotatingViscosimeter.ContractNAw-5799,NACAandHarvardUniv.,Nov.1%0.

3. Eutmons,HowardW.,andSoo,Shao-Lee:DevelopmentandPreliminaryTestsofa RotatingViscosimeter.ContractIaIw-6&3,NACAandHarvardUniv.,May1552.

4. Cole,J.A.: NACALubricationProjectResearchReport.ContractNAw-6043,NACAandHarvmdUniv.,Mar.1553.

5. Iqmpoulos,s.: ViscosityofLubricatingOilsWithHighVelocityGradientsintheFilm. Forsch.Geb.Ing.-Wes.,vol.3, no. 6,Nov./Dee.1932,pp.1932,PP.287-2%.

. 6.~ngsbury,Albert:HeatEffectsinLubricatingFilms.Mech.Eng.,vol.55,no.I-1,Nov.1933,pp.685-688.

. 7. Hersey,M. D.,andZhmer,J. C.: HeatEffectsinCapillaryFlowatHighRatesofShear.Jour.Appl.Phys.,vol.8,no.5,May1937,PP.359-363.

8. Bradford,L.J.,andVil.Horth,F. J.,Jr.: RelationshipofViscositytoRateof Shear.Trans.A.S.M.E.,vol.63,no.4, wy@l,PP.359-362.

9.Philippoff,W.: OnCapillaryFlowatExtremelyHighShearRates.Phys.Zs.,vol.43,no.19/20,Nov.1942,pp.373-389.

10.Fr&sel,W.: VerhaltenderSchmier61z~QkeitenbeihohenSchergeschwindigkeiten(TheBehavioroftheViscositiesofLubricati~OilsatHighShearRates).Forsch.Geb.Ing.-Wes.,Bd.14,Nr.3, May/June1943,W. 82-84.

12.Neale,S.M.: AncmdousViscosityShowninOilFlowThroughEngineBearings.Phil.Msg.,vol.34, no.236,Sept.1943,pp. 577.588.

12.Weltmann,R. N.: TMxotropicBehaviorofOils. Ind.andEng.Chem.AnalyticalEd.,vol.15,no.7,July-15,1943,PP.424-429.

22

13.

14.

15●

16.

17.

18.

19.

20●

“21.

22.’

Fritz,W.,andHennenh8fer,J.: CapillaryFlowatHighz.v.D.I.,vol.88,no.5/6,Feb.5,1944,PP.77-78.

Morgan,F.,andMM&, M.: EffectofRateofShearon

NAC!ATN3382

ShearStresses.w

theViscosityofoils.-Phys.Rev.;vol.65,nos.7 and8, Apr. 1 and15, w44,p. 255.

Hagg,A. C.: HeatEffectsinLubricatingFilms.Jour.Appl.Mech.,vol.11,no.2,June19, pp.A-72-A-76.

Morris,W. J.,andSchnurman,R.: A JetViscometerWithVariableRateofShear.Rev.Sci.Instr.,vol.17,no.1,Jm. 1946pp.17-22.(Seealsoletterto Ed.,Nature,vol.167,no.4243,Feb.24,1951,p. 317.)

Ward,A.F. H.,Neale,S.M.,andBilton,N.F.: ViscosityofLubricatingOilsatHighRatesof Shear.&it. Jour.Appl.phys.,SUpp.1, 1951,pp.)2-18.

Fenske,M. R.,Klaus,E.E.,andDamenbrink,R. W.: Viscosity-ShearBehaviorofTwoNon-NewtonianPolymer-BlendedOils. SpecialTech.Pub.No.Ill,A.S.T.M.,June1~1, pp. 3.23.

Needs,S.J.: ThelChgsburyTapered-PlugViscon&erforDeterminhgViscosityVariationsWithTemperatureandRateofShear.SpecialTech.Pub.No.ill,A.S.T.M.,June1~1, pp.24-44.

Barber,E.M.,Muenger,J.R.,andVlllforth,F. J.: A HighRateofShearRotationalViscometer.Paperpresentedto SocietyofRheologyAnnualMeeting,Chicago,1951.

DuncanjJamesA.: HeatEffectsinLubricatingFilms.Mech.Eng.,vol.56,no.2,Feb.1934$pp.120-121.(Ietterto ed.)

Bondi,A.: FlowOrientationinIsotropicFluids.Jour.Appl.Phys.,VOI..16,no.9,~pt. 1945,pp.539-544.

.

.

t s

Tapered rotating cylinder

Tap3r13d rotating oyllznlar

caplrlayFIDbating Cylinflar andtqerd rotatingCyli?lkir

capillaryRotwtinscyllndarRotatingcy13dmrMating CylimkrCapl.ual’yR0t8tlngcylindRr?Wmutatiw w~

E

O.mc$

:%,m33

.W

.ml

.Wb.~—.—-----.m50.00!

.Oo1

:W%w.Ixlolz.m3

l,ym

k,m

l,CCO3,5007W

6,500

5,CKXI

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*,

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“S dEPW@Scm Vismslty @ &s matneoeasarily occur atmdmm dmnr rate ~%estimabla Palua.

-.07--------.2.6C.6d.tj

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Large

LargeIarg9

bu!ga

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Yes

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Bcmdi’B (ref. 22) UriticalValJEb .5.

8

I_

75

50

20

5

3

NACATN3382

Ao 0 ElecfrcmictOrquemeasurement

❑ Electronictorquemeasurementwithzeroctieck

0 NulI opticolmethod

%o

5

❑$ .

❑

oOQo

or

n75 I00 I50 200

I T,‘F250

I.001 .05 .15 .25

Sheerrate,millionreciprocalsec550 7,200 6,400 5,700

Shearstress,dynes/sqcm

300

.

.

.—.

.

.

.

Figurel.-Hnematic-viscosity-temperatureresultsforEtnaOilLight.Continuouslinerepresentsstandardlow-shearvalues.Subsidiaryscalesindicateapproximatelyshearrateandshearstress.Shear-stressscalehasa maximum.

NACATN 3382 25

.

.

.

150

I00

50

$xog 20a)us

o

10 - u

“75 I00 150 200~ ‘F

I I.01

Shear rate, million t’eciprocalsec ml

6,800 Shear stress,dynes/sq cm 8,600

Figure 2.- K%nematic-viscosity-tenrperature results for Flowrex 300.Continuouslinerepresentsstandsrdlow-shearvalues.Subsidiaryscalesindicateapproximatelyshearrateandshearstress.

50

0 Electronictorquemeasurement .❑ Electronic torque measurement

20

~

.81(-JE

“n I00 150 ~T 200 250 300

I I,

I I.01 .05

Sheer rate,millii reciprocal sec.15 .25

34330 7500 Shear stress, dynes/sq cm8,200 13@

Figure3.- Kinemtic-tisco6 Lty-tmnperature results for AP1 103. Contlnuausline represents standard law-shear values. Subsidimy scales i@j.cateapproximately shear rate W shear stress. Points labeled A indicatemlolna.lousvalues.

. , , , r ,

27

.

.1.2

I.0

Q

O Electronic torquemeasurementu Electronictorque measurement

& with zerocheck“

(

%

O NulI opticsI method.--P =0.74

0/

A1 I A/ I I

~u

o .05 .10

% “2N=y

Figurek.- RelativeviscosityresultsforE&aHne (P= O.74)basedontheoryin

.

.

I.4

1.2

Fi&Pre5.-

OilLight. ContinuousappendixA.

O Electronic torquemeasuremento

❑ Electronictorquemeasurementu with zero checko I

. I oI I I

u3 0 0 J *,”P=0.74

--- /- u--—— - ——— 1 -——. .

\

“Weeds(ref.19)

.05fl~

N’= ( U2

.10

RelativeviscosityresultsforAPI103. Continuousline (P= 0.74)basedontheoryin.appendixA.

1.2

()~ ,~.‘s rot.

.8

1.2

Figure6.-

-o c1

(a)o•1

o

Rotationalflow

,8P‘ 0.74-

0 n

Measurementsmade during combinedrotational-axial-flow tests J

o

, “-P=0.74 Rot.—— / ——

0 Ii.\

‘“‘-P=0,74 Ax,(b)

Q n

.05#!ku2

k

.Uo .[0

(a]Rotational-axial-flowresults.

(b)Axial-flowresults.

RelativeviscosityresultsforFlowrexbasedontheoryinappendix

300. ContinuouslineA.

, b

.10

.08

,06

(dP$-KS

,04-

.02

o

0 Electronic torque measurement

❑ Electronic torque meosu rementwith zero check

O Null oDtical method

.05

Figure7.-Temperature-graclientresultslines based on theory in appendixB.n.7L.

7

#

—

/

—

for IMna OilIilght.Continuousll?anvalueof P during tests,

‘1

,Ic

c .Ua , Iu

F@u’e 8.- Temperature-grsdientresultsbaaed on theory lm appendixB. Mean

forFlowrex 300. COntimmua linesvalue of P dllxingtests, 0.74.

,,

o

c

Lo

AA

1.4 I’?2

.7

1,1

1.5

.9

n= It

Figure 9.- Temperature-gradient results for API 103. Conttioufi linesbaaed on theory in appendixB. Ind.itidualvalues of P indicatedfor each test. Points labeled A indicate anomalousvalues.

. Id