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FORAERONAUTICS
TECHNICAL NOTE 3491
EXPERIMENTAL INVESTIGATION OF
FRICTION,
SHORT
-,--
ECCENTRICITY
AND OIL FLOW OF LONG AND
JOURNAL BEARINGS WITH
_uMD -NUMBER CHARXS
By G.B.Du.Bois,F.W. Ocvirk,L,WeheandR.
Cornell
L-
RATIO,
Washington
September1955
., ,
,.-,. . -.’;<d-J~dr...-.,,,,.+’. L.. 0
—
. ..- ----- . . . . . -—
TECHLIBRARYfCAFB.NM
u lIIMll!llllNATIONALADVISORYcoMlmrrEEFORAERONAUTICSDOLL55J
,.
TECHNICALNOTE3491
EXPRIMENTMINVESTIGATIONOFECCENTRICITYRATIO,
FRICTION,ANDOILFLOWOF IONGAND
SHORTJOURNALBEARINGSWITH
ILMD-NUMBER
By G.B.-iS,andR. L.
CHART;
F.W. Ocvirk,Wehe
Theperformancesofplainbebringsundercomparedandsummarizedby single-linecurves
steadycentralloadingcoveringtherangeof
are
length-diameterratiosbothaboveandbelow1. Experimentaldataoneccentrici~ratio,friction,andoilflowforlength-diameterratiosof 1,1.,and2 areshownforcomparisonwithearnerdataforlength-
diameterratiosof1/4,1/2,and1. Thecaibineddataprovidechartsofplain-bearingperformancewhichcoverthepracticalrangeoflength-dismeterratio.
Theloadnumiberl/Cn inisthecapacitynumber,p istheoilviscosi~,N’ isthe
theform p/pN’(c~d)2(d/Z)2,where Cnthecentralunitbearingload,p isjournalspeed,cd isthedismetral
bearingclearance,d isthebesringdiameter,and Z isthebearinglength,isusedasthe.basicvariableonwhicheccentrici~,friction,andoilflowratedepend.Chartsarepresentedto showthatthe.eccentrici~-ratiodatafallnearlyona single13_neforbothlongandshortbearingsifthe (d/Z)2 termintheloadnumberistakenasuni~forbearingsof Z/d greaterthan1;ineffect,theloadnumberforlongbearingsbecomesthereciprocaloftheScmmerfeldnumber1/s.Frictionandoilflowrate,however,areshowntodependontheloadnumberwithoutthismalification,forbothlongandshortbearings.
Plotsoffrictiondataintermsoffrictionratio F/F. arepre-sentedtofecusattentionontheclifferencebetweenjournalfrictionandbearingfriction.Experimentaljournal-frictiondatafromothersourcessreincluded.
.. -—- —.—— .—. — ——. —————— ..—,. ——————.——.— . .— —
2 NACATN3491
Analyticalcurvesby SOmtnerfeld,Cameron,andWoodandtheshort-bearingapproximationareshownforcomparisonwiththeexperimentaldataforeccentrici~ratioandfriction.CurvesresultingfromtheintegrationofSommerfeld’spressure-distributionfunctionforanextentof18ooofthepressurefilmarealsoshown.
INTRODUCTION
TnanearMerreport(ref.1), theanalyticalcurvesoftheshort-bearingapproximationwerefoundtobe inusefulagreementwithexperi-mentaldataoneccentricity,friction,andoilflowforcentrallyloadedplainbearingswithvaluesof Z/d of1/4,1/2,and1. A fewearlyexperimentswithbearingsof Z/d of2 indicated@at itwasnecessary,withregsrdto eccentrici~,to limittheusefulnessofthecurvestobearingsof Z/d notexceeding1. Forthisreason,a conclusionwasdrawnthatfurthertestingonbearingsof 2/d between1 and2 wasnec-essaryto covertherangeofbearingconfigurationsusedinpractice.
.Thenewexperimentaldatainthepresentreportwereobtainedfrom
testsconductedintheMachineI!esignLaboratoriesat CornellUniversity,Ithaca,NewYork,asa partofa bearing-researchinvestigationconducted ~underthesponsorshipandwiththefinancialaidoftheNationalAdvisory ,
CommitteeforAeronautics.Experimentaldataonbesringsof1~-inch
diameterwith Z/d ratiosof3/4,1, 1$ and2 arereportidhereinand
correlatedwithetistingdataforvaluesof Z/d of 1/4,1/2,and1.Ihthelong-bearingtests,loadsup to 1,700poundsor8E poundspersquareinchwereusedat speedsup to 7,0~ rpmwithME 10 oil andwithclearancesramgingfrom0.0018to0.0038inch. Thedataarecoqibinedinchartscoveringtherangeofvaluesof Z/d in commonuse. Theinte-grationsforthe%mnerfeldz casearegivenin theappentiwhichwaspreparedbyProfessorWehe.
AnalyticalI?ackground
Analyticalsolutionsby CsmeronandWo&i(ref.2)gitingpointslocatingcurvesfor Z/d ratiosof1/4,1/2,1,andinfinityareavailable.
)Sommerfeldref.3)providesananalyticalsolutionfor
bearingsofinfiniteZ d. Theshort-bearingapproximationappliesbestto shortbearingsandisusefulintherangeofvaluesof Z/d Up to 1.‘Ihus,no analyticalsolutionsfor Z/d intheneighborhoodof2 areavailable.Thisexperimentalinvestigationwasinitiatedtoprovideexperimentaldata,particularlyoneccentricity,usingbearingsof Z/d= 1,1+,and2. A shortbearingof Z/d= 3/4 wasalsoincludedinorderthat
—. .— ——— —
NACATN3491 -
a parallelinvestigationon(ref.4) couldbe conductidTheequipmentandtechniquethosereportedinreference
3
themisaligningcharacteristicsofbearingsWing thesametestbearingsandjournals.usedintheexperimentationweresimilarto1 fortheshortbearings.
3%hissolutionforbearingsofinfinitelength,SommerfeldshowedthatthebasicnondimensionalgroupingofbearingvariablesonwhicheccentricityandfrictiondependistheSommerfeldnuniber
S_dVd2(d)pc (1)
Forfhit-eshortbe=ings,theshort-bearingappro-tion yieldssingle-linecurvesofeccentricityratioandfrictionusingthecapacitynum-ber ~ asthebasicvariable:
%= %$(U (2)
Itmaybe seenthatthevariablesofequations(1)and(2)areclifferentby thefactor(Z/d)2.
bad NMber
Thereciprocalofthecapaci~nuuiberjorloadnuuiberl/~, isusedinfigures1 to4. Theloadnumber,whichisthereciprocalformofthebasicvariable,is choseninordertoexpandtheinterestinghigh-loadregionandto showthevariationofeccentricity,friction,andoilflowrateindirectproportionto thecentralload.
Theexperimental.dataoneccentricity,friction,andoilflowrate .infigures1 to4 showtheextenttowhichtheSOmmerfeldnuniberandloadnuniherreduceda~ tonearlysingleMne chartsforbearingsof Z/dfrom1/4to 2. Theinfluenceofthe (Z/d)2 terminthisregardisshown. Chartsofexperimentaldatafromreference1 forbearingsofZ/d= 1/4,1/2,and1 axe.reproducedinfiguresl(b),2(b),andA(b)forcomparisonwithchartsofdatareportedhereininfiguresl(a)toA(a)onbearingsof Z/d= 1,% - 2“
FrictionRatio
Jnfigure2,theratioofthefrictiontorquemeasuredonthebearingtotheanalyticalPetrofffrictionatno load,thefriction
— ———..—.-—. _ .—_____ ————_- —— ._. _ —— —-— —-— ..— —
k
ratio F/Fo,isusedasa%e moreconvenienttouse
NACAm 3491
basicvariable(ref.1). Thisisbelievedtothanthecoefficientoffrictionf %asedon
loadd focusesattentiontothequantitiesonwhichfriction&ectlydepends.A similarratio,thepower-lossratio j,isusedbyWilcockandRosenblatt(ref.5). Thefrictionratioisshownanalyticallytodependontheloadnumberby theshort-bearingapproximation.
ItisgeneralJyrecognizedthatthefrictiontorqueonthejournalisgreaterthanthefrictiontorqueonthebearingbytheamountofthecouplecausedby thelatempldisplacementofthejournalinthebeming.The13ne-ofactionoftheloadanditssupportingreactionareseparatedby thisdisplacementtoforma couple.‘Ihedifferenceinfrictionisconsiderableundercertainconditionsaxlcanbe shownona singlecurveinfi~e 3 by plottingthecouplefrictionratioAF/Fo(d/Z)2againsttheIcednuaiber.
OilFlowFactor
Theoilflowratefromthetestbearingisrepresentedinfigure4bya single-linecurveobtainedbytheuseoftheoilflowfactorq,whichistheratiooftheexperimentalflowratetotheanalyticalendleakagerateoftheconvergingwedgeportionoftheoilfilm. Thisisplottedagainsta modificationoftheloadnumbercalledtheinlet-oil-pressurenuniber
I1 $.> inwhichtheinletoilsupplypressureissub-
stitutedfortheunitbearingpressureintheloadnumber.Thismethcdofplottingoilflowrateisthesameas thatusedintheearlderreportcoveringvaluesof Z/d lessthan1 (ref.1)exceptthatthereciprocalformofthenumiberisusedinthisreport.
SYMBOLSI
Dimensionalquantities: ~
cd diametralbearingclearance,in.
+ radialbearingclearance,dc 2, in.
d bear@gdiameter,in.
e eccentiici@forcentralloading,in.
% lateraldisplacementof journal,in.
0
,,
——— .— —
NACATN3491 5
‘v
Fb
Fj
F.
1
N
N’
‘film
P
PC
PO
P~
P
p@y
Q
r
%4>tg
u
v
e
$
verticaldisplacementQf journal,in.
frictio~forceonstationarybearingsurface,lb
frictionforceonrotatingjournslsurface,lb
Petrofffrictionforceatno loadandzeroeccentricity,ti~N’2d(d/cd)’,lb
bearinglength,in.
journalspeed,rpm
journalspeed,rps
localfluidfilmpressure,lb/sqin.
appliedcentralunitbearingloadonprojectedarea,lb/sqin.
capsulepressureof
inletoilpressure,
pressureat e = 0
load,lb/sqin.
lb/sqin.
and I-Cin Somerfeldsolution,lb/sqin.
appliedcentralbearingload,lb
componentsofcentralloadparallelandnormaltobearingandjournalcenters,lb
experimentaltotalrateofoilflowfrombearing,
bearingradius,in.
temperatureat stations4 and9,respectively,OF
surfacespeedofjournal,in./sec
centipoiseoilviscosity, orreyns6.9x 106
~ -iab~ gitinglocalfilmpressure,deg
lineof
cuin./sec
attitudeangle,anglebetweenloadlineandlineofcentersofbearingandjournal,deg
- — ..——.—— — -—— —
6
Nondimensionalquantities:
NACATN3491
&d
Cn
%0
l/&
l/~.
f
F/F.
‘b/Fo
. Fj/Fo
M/F.
Z/d
n
%
nv
q
s
1/s
XJY
z
clearanceratio
pNt d’~’inlet-pressurecapaciwnumber,p()()o cd d
had muiberforvaluesof 2/d lessthan1
inlet-oil-pressurenumber
coefficientoffriction,F/P
frictionratio
bearingfrictionratio
journalfrictionratio
cou@efrictionratio
length-diameterratio
eccentricityratioorattitudeforcentralloading,e/Cr
horizontalcomponentofeccentrici~ratio,%/+.
verticalcomponentofeccentricityratio,ev/Cr
oilflowfactory*
Sommerfe3dnuuiber,()
@’d’,P cd
loadnumberforvaluesof 2/d greaterthan1
coordinates
viscosity,centipoise
.—. .—— ——— ————-----——
NACATN3491 7
APPARATUS
Thebearing-testingmachineusedintheseexperimentsisillustratedinfigures~ to 8 andisthesameas~t describ~dinreference1. Themannerinwhichthetestelementswere”supportedandlosdedisshowninfigures5 and6. lHgure7 showsthemechanicalsystemformeasuringjournaldisplacements,andfigure8 givesthelocationsofthethermo-couplesWed todeterminebearingtemperatures.
TestBearingandJournals
A singlebronzebearingandfive.steelshaftsof1~-inchnominal
diameterwereusedintheconfigurationshowninfigure~. Eachoftheshaftsrepresenteda givenlength-diameterratioanda givenclear- ,anteas listedbelow:
.
AveragediametralClearance
shaft Z/d clearance, ratio,
%c~d,
in. in./in.
6A 2 0.00252 0.ool&j6B 2 .00376 .oo2~
116C ~ .00196 .oolk26D 1 .00183 .CX)1336E ; .00258 .00187
ThesetestelementswerealsousedinthemisaMnementexmrimentsasreportidinreference4. SAE10 oilwasusedas thetestl-tiricantandwasfedtothetestbearingat a pressureof40 to16opoundspersquareinchthrougha l/8-inch-diameteroilholelocatedoppositethecentralload.Theoilwaspreheatedto140°F nearthepump,butthetemperatureoftheoilwasmeasuredas itenteredthebearingbecauseofsmallheatlossesintheoillines.
Thetestshaftsweredrivenby a high-s~ed,direct-current,variable-speedaircraftmotorhavinga speedrangeof1,000to 10,(NOrpm.
---——— ——— -—— .
NACATN3491
LoadingAppsxatus
As showninfigure6,thecentralloadwasappliedhydraulicallyby a pressurecapsuleandwastransmittedto thehearingthroughanoil-pressurizedsphericalseat.Theoilflowthroughthesphericalseatfloatsthebearinggivingitfreedomtorotateanddisplaceontheapplicationofcentralload.Thelineofactionoftheloadpassesthroughthecenterofthesphericalseat,whichislocatedaccuratelyatthecenterofthebesring.
DisplacementMeasurements
Thecoordinatedisplacementsofthejournalendsrelativetothebearingweremeasuredlythemechanicalarrangementillustratedinfig-ure7 inwhichhorizontal.andverticalmotionsaretransmittedbybronzeridersonleversthroughverticalralstofourO.0001-inchdialindi-cators.Thisisthessmesystemreportedinreference1 exceptthattheleversweremcd.ifiedtogivea 2:1magnificationofthedisplace-mentsto improvetheaccuracyinreadingthedials.A duplicatesetof .rodsisusedfortemperaturecompensation.
l&ictionTorquemeter
Frictiontorquewasmeasuredlythehydraulictorquemetershowninfigure6. Thetorquemeterconsistsoftwol/2-inchpistonswhichareconnectedtothemastextendingfromthetestbearingsothatthepistonforcesopposeeachother.A flowoflightoilisforcedintothespaceattheheadofeachpistonandisdischargedthroughportspartia12ycoveredby thepistons.Thefrictiontorqueofthebearingappliesaforcetothepistonsto causea slightchangeinthedischargeportarea,resultingina pressuredifferentialonthetwopistonstobalancetheappliedforce.Thepistonsarecenteredintheirboresby apressurizi.ngsystemofre~evedareas,thuseliminatingfrictionalcontact.
Thedifferenceinpressureonthetwopistonsis indicatedbyamercurymanometerandisproportionaltothetorqueonthetestbearing.Manometerreadingswereconvertedtofrictiontorqueby direct’caM-brationunderrunningconditimsby app@inglmuwnincrementsofmomenttothebear~ hubby theweightsshowninfigure6 andrecordingthecorrespondingchangesinthemamxneterreadings.
OilFlow~asurements
AS showninfigure6,a drainholeinthebottomofthemachinehousingallowstheoilflowingfromthetestbesringtobe collected
——— .—. .____ — ———. .—. .
umcllTN3491 9
in a panwhichmaybe removedforweighing.&oringsamdbaffleswhichpreventthemidng ofthe
shownaretheslingertest-bearin~oilwith
theoilfromthesupportbearingsandthe-sphericalseat. -
-rature Measurement
tion-constaxtanthermocoupleswereusedtomeasurebearingtemper.aturesat14locationsinthebearinghubwithin1/16inchofthebearingsurfaceas showninfigure8. Thermocouple9 gavethebearing-hubtemperatureata point2 inchesradiallyfromtheoilfilm,andthermo-couple16wasusedtodeterminethetemperatureoftheincomingoilattheoilinlettothetestbearing.
TESTPROCEDURE
Forthefiveshafts,twoseriesofexperiments”wereconductedata nmiberofconstantspeedsandinletoilpressus. Displacemmtexperiments,inwhicheccentricitywasmeasured,weremadeonallshafts.IRrictionandoilflowexperimentsweremadeseparatelyfromthedisplace-menttestsbecauseofthenecessityofdisconnectingthebronzeriderswhichwerea sourceofunwantedfriction.Measurementsoffrictionand
oilflowweremadeonthelongerbearingsof ~ = l;and2.
DisplacementExperiments
Variationsindisplacementwereobtainedby varyingthecentralloadat constantspeed.Itwasfoundthatby operatingunderconstantspeedthevariationsinbearingtemperatureweresmall.A nearly.con-stanttemperatureoftheapparatusatthermalequi~briumassuredaminimumthermaleffectinthemeasurements.Beforethedataweretaken,thetestelementsandthemeasuringapparatuswerebroughttoequilibriumtemperatureby rumningthemat constantspeedandcentralloadforaperiodof20to30minutes.
At theendofthewarmuppericxi,thenetcentralloadandtheinletoilpressurewerereducedto zerosothattheindicatordialscouldbesettoa datumpositionrepresentingzerodisplacementofthejournalrelativeto thebearing.An inletoilpressurewasthenapplledandheldconstant.Displacementdataasreadfromthefourdialswerethenrecordedforvariousincrementsofcentralload.Theloadwasincreasedinfourtoeightincrementsandthendecreasedinthesameincrementstopermitaveragingofdata. Thefollowingdatawererecorded:Journaldisplacements,capsulepressureof centralload,bearingtemperalnmesat
.- .— —-—-—— -- —— —..—— ___ .—_— .— —— .—...._.__ ..—. —..._
10 NACATN3491
criticallocations,inletoilpressure,speed,directionofrotation,inletoiltemperature,roantemperature,andoiltemperatureaftertheheater.Thesameprocedurewasfollowedfortheoppositedirectionofrotationsothatthedatacould%e averagedforthetworotations.AsshownintableI,constant-speedrunsatapproximately500,1,200,2,500,and5,0CK)rpmwereconductedforeachofthefivetestshaftstodeter-minetheeffectsof Z/d andclearanceonthebearingcharacteristics.me ~ app~edcenttiloaciintietestswas1,713poundson s~t 6Candthe~unit loadonprojectedareawas874psionshaft6D.Themaximumbearingtemperaturerecordedwas198°F at 7,000rpmfors~t 6D.
FrictionandOilFlowExperiments
Frictiontorqueandoilflowrateweremeasuredsimultaneously,withthedisplacement-measuringapparatustemporarilydisconnectedinordertoeliminatethefrictionoftheridersandtheoilflowtothem.Theprocedureofwarmingup andapplyingincrementsofloadat constantspeedwasthesameas inthedisplacementexperiments.At eachload,aftertheoilflowstabilized,thefric$iontorquemeterwasread,andtheflowratewasdeterminedbyweighingtheoilcollectedinperiaisof1 to 2 minutes.
Thefollowingdatawererecordedforeachloadcondition:l&lctiontorqueas indicatedby themanometer,weightof oilflowfromthetestbearing,timeofoilflow,capsulepressure,bearingtemperatureatcriticallocations,inletoilpressure,speed,directionofrotation,inletoiltemperature, roomtemperature,andoiltemperatureaftertheheater.Thesamedataweretakenfortheoppositedirectionofshaftrotationsothatdatacouldbe averagedforthetworotations.AsshownintableII,constant-speedreinsat approximately5~, l,2~jand5,0~ rpmwereconductedonthelongj~ruals6A,6B,and6c. The c.msximumappliedcentralloadwas1,688poiihdswitha maximumunitloadonprojectedareaof59 poundspersqusreinchonshaft6c. me maxi-mumbearingtemperaturerecordedwas181°F at5,OOOrpn.
REsuErs
Theexperimentaldataoneccentricityratio,friction,andoilflowrateareshowninfigures1 to4 ina formintendedtobe tiefulinthedesignofplainbesringswithvaluesof Z/d ashighas 2. Thenondimensionalcoordinatesshownarethosedeterminedfromtheanalyt-icalsolutionofreference1. ‘I!&coorctha.tepointvaluesshownweredeterminedfromthefollowingexpressionsby usingtheWmwn quantitiesfromtheexperimen<ests.
NACATN3491
IOadnuniber:
Eccentricityratio:
n = e/~ =
nv= +cr
&v)2+(%)2
nh= e~Cr
Bearingfrictionratio:
‘b~=
Couplefrictionratio:
L@()()
Oilflowfactor:
Qq=
YCd2C@’@)Il
Ihlet-oil-pressurenuniber:
/1 %0 = (l/@(pO/p)
.’
(4)
(5)
(6)
(7)
. ..— .. .. . ..— —.-—. .—_._. ._. .————. ._ _ ____ _——
12 ‘TtACATN3491
.LoadNunber
Theexperimentalquantitiesintheloadnuuiher(eq.(3)) aretheload,viscosi~,speed,diametralclearance,andbearingdiameterandlength.Theunitload p ona projectedareawasdeterminedfromP P/td andthetotalnetload P appliedby thepistonwascalcu-la=tidfrom P = 5.0(pc- 12.5) where pc isthecapsulepressureactingonthepistonareaof5.0squareinches.Thetareweightofthebearingandattachedappsratusisrepresentedinthesetestsby a pressureof12.5poundspersquareinch.
Viscosi@valuesfortheSAIZ10 oilweretakenfromthecurveof .figure9 andconvertedtoreynsby divl~ thecentipoisevaluesby6.9x 106. Oilfilmviscosityp wasdeterminedfromthetemperatureofthermocouplek located1/16inchfromthebearingsurface.
Dismetralclearanceatroomtemperaturewasdeterminedfrommeasure-mentsofbearingandjournalwithelectrolhitgages.Forrunningcon-ditions,clearancewasdeterminedby subtractingthechangein clearance .giveninfigure10fromroom-temperatureclearance.Theclearanceinfigure10representsthecalculatedclearancechsmgecausedby differ-entialthermalexpansionofbearingandjourna1 asa functionofthetemperaturegradientinthebearinghousing.Thermocouplesk and9 were1/16inchand2 iJ2Chf33, respectively,fromthebearingsurfaces,givingtemperaturedifferences(* - @) inMcativeofthegradient.Theslopeofthecurveinfigure10isappro-tely one-thirdoftheslopeofthatusedinreference1. Additionalstudyindicatedthattheear~erslopeshouldbe smaller.Thedifferentialexpansionproblemwasreevalu-atedanalyticallyby themethodofmshenko (ref.6).
Eccentiici@Ratio
Calctitionsofexperimentalvaluesofeccentricityratio n infigurel(a)weredeterminedfromthecoordinateverticalandhorizontidisplacementsoftheshaftmeasuredat theriderslocatedbeyondthe
endsofthebearingl= inchfromthecenterMne ofthebearing(cf.16
fig.5). Eightobservatimaofa coordinatedisplacementwereaveragedtodeterminethemeanvalueata givenload.Readingsoftwodials,oneateachend,astheloadingwasbeingincreasedandthendecreased,gave.fourobservations.Fourmoreobservationswereavailablefortheoppositedirectionofrotation.
Ihorderto correctthevaluesoftheeccentricityratio,theslightdisplacementsat zeroloadandzeroinletoilpressure,atwhichitwasassumedthatthejournalandbearingaxeswerecoincident,were
NACATN3491 13
averagedandsubtractedfromtheaveragedvaluesofdisplacementunderload. Ml displacementswerehalvedbecauseofthe2:1multiplicationofthemeasuringsystem.
Anothercorrectionwasmadeto accountfortheeffectofshaftdeflectionondisplacementmeasurements.Calculationsofshaftbendi&deflectionsweremadeassmninga uniformlydistributedloadoverthelengthofthebearingandvar@ngmmen%sofinertiaM-the sMghtlysteppedshaft:Mflectioncorrectionsweremade,onmeasuredverticaldisplacementsonly.,Becausethejournalwithinthebearinglengthisdeflectedtoa fourth-degreeparabola,thecorrectionsweremadetosimulatetheverticaldisplacementofan ideaUystraightjournallocatedone-fifthoftheheightoftheparabolabelow~“ a~x. Theverticalandhorizontalcomponentsofeccentrici~ratio + and ~ werecal-culatedby dividingthecorrectedcoordinatedisplacementsby %heradial.clearance(eqs.(4)),andtheeccentricityratio n wascalculate&asthesqme rootofthesumofthesquaresoftheccmiponents.
Theexperimentaldataofeccentricityratioshowninfigurel(b)forshortbearingsarefromreference1 andsreshownforcomparisonwithfigurel(a)forlongbearings.
BearingIZrictionRatio
ExperimentalvaluesofbearingfrictionratiO l?b/l?oin figure2(a)werecalculatedfromeqwtion(5)inwhichthefrictionforce Fb wasdeterminedfromthemercurymanometerreadingsofthetorquemeter.Multiplicationofthemanometervaluesby thecalibrationfactorFcgavethefrictiontorque.Theaverqgevalueof Fc was0.475pound-inchoftorqueperinchdifferenceofmercury.Dividingthefrictiontorqueby thebearingr@ius gavethefrictionforce ~.
Theexperimentalfrictiondatdforshortbearingsfromreference1areshowninfigure2(b)forcomparisonwiththelong-bearingdatainfigure2(a).
‘lhefriction-ratio
Couplel?rictionRatio
datashuwninfigure2 representmeasuredvaluesoffrictionactingonthebearingofthejournal-bearingcombination.As discussedinanothersection.ofthisreport,thefrictionratioofthejournalFj/Fomaybe obtainedanalyticallyby addingthecouplefrictionratioAF/Fo tothebearingfrictionratio Fb/Fo. Thecouplefrictionratiois ofinterest,sincewhenmultipliedby (d/Z)2 it is
14 NACATN3491
a single-linefunctionoftheloadnumberas showninfigure3. Thepartofthefrictionontherotatingmeniberwhichisduetothecoupleformedby thecentralloadandthelateraldisplacementoftherotatingmemberrelativetothestationerymeniberisrepresentednondimensionally,by @F..
Theexperimentaldatashowninfigure3 werereducedfromdatagivenby McKeeandMcKee(ref.7)andPE&u13mhandBlair(ref.8).Bothinvestigatorspresentfrictiondatafromtestsinthefour-bearingmachinewhichmeasuresjournalfriction.McKeeandMcKeepresentdatainexperimentalcurvesof f againstZN/p with cd/d and Z/d ratiosgiven,andPalmlichandBlairgivetabularexperimentaldataof f(d/cd)
2 withthe Z/d ratioagaitit@/p(d/cd)vertedto Fj/Fo and l/~ valuesby the
f = f#P
given.Thesedataarecon-followingexpressions:
(9)
F.= 2&lN’zd(d/Cd)(Petrofffriction)“
TheMcKeesmdMcKeeconversionsare
6.9x 106x 60
i = (~/p)(d/Cd)*(Z/d)2
fp
2x2pNf2d(d/cd)
f(P/Zd)
21-c2pN’(d/Cd)
P-(]cd (%/d)(2/d)2a @’ F (c#d)(Z/d)*
(12)
.
(lo)
(n)
— ——. — ———— .—
NACATN3491 15
ThePalsulichandBbir conversionswe
Fj (fd/cd)z 2 1—=F. (!()21f2-~
(13)
(14)
Valuesof M/Fo(d/Z)2 showninfigure3 weredeterminedfromequation(6)usingtheexperimentalvaluesof Fj/Fo andtheanalyticalvaluesof Fb/Fo fromtheanalyticalcurveoffigure2.
OilFlowFactor
Theoilflowfactorq infigure4(a)wascalcu&ed fromequation(7)as inreference1. Theoilflowrate Q in cubicinchespersecondwasconvertedfromthemeasuredflowinpoundsperminuteusingthespecificgravi~oftheoilatbearingtemperature.Becausedisplacementmeasurementswerenotsimultaneouswithmeasurementsofoilflow,valuesofeccentricityratio n inequation(7)weretakenfromtheexperimentaldataoffigurel(a)forcorrespondingtestcon-ditions. Theinlet-oil-pressurenumber I1 Cpoj~fist which q iS
plottedinfigure4,wasdeterminedfromtheloadnumberandtheratioofinletoilpressurep. tounitbearingpressurep asinequation(8).
Exper-ntaloilflowfactorsfortheshortbearingsofreference1areshowninfigure4(b)forcomparisonwiththelo~-bearingdatainfigure4(a).
ExperimentaldatafromMcKee(ref.9)forabearingwlthasingleoilholearealsoshowninfigures4(a)and4(b)andcomparewellwiththeexperimentaldataofthisinvestigation.AdditionalMcKeedatafromreference9 enablea curvetobe drawnfora bearinghavinganaxialoil~oovewhichis somewhatshorterthanthelengthofthebearing.
ANALYSISANDDISCUSSION
Thedependenceofeccentrici~ratio,friction,andoilflowontheloadnumberl/~ isshowninfigures1 to4. The (Z/d)2term
———— — . .
16 NACATN3491
intheloadnumberservestoreduceexperimentaldataforvariousvalues.
of 2/d tonearlya singlecurve.A singleexceptionisthecurveforeccentricityratioinfigurel(a)inwhichtheexperimentaldataclusterneara singleHne onlyifthe (2/d)2termintheloadnunberistaken
&
asunityforthelongbearingsforwhich Z/d is weaterthan1. Forthebearingfrictionr“atioinfigure”2,thecouplefrictionratioinfigure3, andtheoilflowfactorinfigurek, the (Z/d)2termappearstobebasica22yapplicableforbesringswithvaluesof Z/d from1/4to 2.
Figures1 to4 areintendedto serveasdesignchartsforbearingshavingloadnumbersup to 100coveredby theexperimentaldatafromthesetests.As showninfigurel(a),eccentricityratiosaveragingn= 0.93 wereattainedexperimentallyat loadnumbersofapproximately90.Abovethis,thevalueofeccentiici~ratioapparentlybecomesasymptoticto n= 1.00 astheloadnmiberbecomesWinite.
EccentricityRatio.
Twosetsofexperimentaldataoneccentricityratioappearinfig-urel(a)andaxeshownseparatelyinfiguresl(b)andl(c). Thoseinfigurel(b)areforthelongbearingsof Z/d= 3
fto 2 fromthe
experimentsusingshafts6Ato 6E. tifigwe l(c aredatafromrefer-ence1 forshortbearingsof Z/d= 1/4to 1. Itmaybe seenthatthedeviceofassumingvaluesof Z/d ofunityforthelongbesringsmakesthelong-sadshort-beartieccentricityd&tanearlycoincident.Theunitbearingpressureonprojectedarea p appearsintheloadnmiber,ratherthanthe.totalload,andtheabovedevicecanbe interpretedtomeanthattheafiowableunitbearingloadispracticallyindependentofZ/d forvaluesof Z/d abovelbut thatforvaluesof Z/d lessthan1theallowableunitbearingloadf~ asthesquareof Z/d.
Theexperimr@xaltitsoffiguresl(b)andl(c)arealsoshowninfiguresn(a) andn(b) usingthecapacitynumber& astheabscissaratherthanitsreciprocal,theloadnumiberl/~. Infigure11,theusefulloadregionis compressedintherangeofabscissasfromO to0.1,whereasinfiguresl(b)andl(c),whichusetheloadnuniberl/b, thisregionextendsfrom10to infinityinproportiontotheunit.load.Theload-nunibermethcdofplottingavoidsdevoting90percentof thegraphtotheL@ht-loadregionbelowa loadnumberof10.
Theexperimentalvaluesofeccentrici~ratioaremateriallylargerthanthoseindicatedbytheanalyticalcurveoftheshort-bearingapproxi-mation.Someofthedifferencebetweenthecurvesmaypossiblybe duetothesensitivityoftheexperimentaldatato smallerrorsindetermina- :tionofeitherthecoldclearanceortheclearanceatrunningtemperature.
uNACATN3491 17
Usualmeasurementsofthebearingclearancetendtogivereadingsatthetopofthewavinessofthesurfaces,ratherthantheeffectivedisrm+r.An analyticalcorrectionforthechangeofclearanceat‘runningtemperaturewasusedin calculatingtheexperimentaldataandshouldbe includedinmakinguseofthecurves.An appreciationofthemagnitudeofthechangeineccentrici~correspondingtoa differencein n valueof 0.90to 0.95isgivenby consideringthatthisrepresentsa changeindisplacementofaboutO.~O@O inchinthesetests.
Perhapsthemostimportantfactorrelatedto thedifferencebetweentheanalyticalcurvegivenby theshort-bearingapproximationandthee~rimentaldataistheomissionintheanalyticalsolutionoftheeffectofthecircumferentialpressureclifferentialontheleakageinthecircumferentialdirectionoftheoilfilm. Theanalyticalsolutionincludesthesideleakageandthecircumferentialflowduetorotation,buttheomissionofpartofthecircumferentialleakagementionedwouldtheoreticallycausetheexperimentalvalueof n tobe abovetheanalyt-icalcurveby a small.unknownamount.Itisalsopossiblethatthedifferencebetweentheanalyticalandexperimentalcurvesisrelatedtotheuseofa temperaturenearthebearingsurfaceto obtaintiscosity,ratherthanthetemperatureoftheoilfilm.A constantviscositywasalsoused,ratherthanone&angingfrompointtopointwiththeoilfilmtemperatureandpressure.
Allofthesefactorsarerepresentativeofmethodsthatwouldcommonlybe usedinpredictingbearingperformancefromthecurves.Theexperimentalcurveisthusrepresentative“oftheeffecttobee~ectedwhenthesemethodsareused.
Consideringthesefactors,a singleexperimentalMe is showninfigurel(a)whichistheaverageofau ofthedatainbothcurvesl(b)andl(c).Whilefiguresl(b)andl(c)differslightlyinthelight-loadregion,thesingleexperimentallineoffigure1(a)is consideredtobea practicalinterpretationofthedata. Forpracticaluseandtobe ontheconservativeside,itisrecommendedthattheexperimentalcurveinfigurel(a)be used,ratherthantheanalyticalcurve.
b figurel(a)theexperimentalvaluesareabout15percentgreaterthantheanalyticalonesforloadnunibersbetween10and100. Forloadnunbersaboveabout60 itisanadvantagetohavean approximationthatbecomesasymptotictoa valueof n oflinthesam waythat,theanalyticalcurvedoes. Forvaluesoftheloadnur&r greaterthan100theexperimentalvalueevidentlyliesbetweentheanalyticalvalueLargerthan0.93as itbecomesasymptoticand1. Thiseffectcanbeobtainedby adding0.5(1- n) totheanalyticalvalueof n.
Blendingof (1/d)2transition.- Thedeviceof consideringthe
(Z/d)2 termintheloadnuniberashavinga valueof1 forvaluesof Z/d
—
18 NACATM3491
greaterthan1 canbe expressedmathematicallyby consideringthe*
Z/d termtohaveanunlmownexponentof x. Thevalueoftheexponentxchangesfrom2 forvalues of Z/d lessthan1 to zerofor .Z/dgreaterthBxl1.
\.,Thetransitionoftheexponentfroma valueof2 to zerocan
thenbe consideredto occurina smoothmanner,andtheshapeofthetransitioncurveandtherangeof Z/d inwhichthetransition OCCllrSremaintobe determinedexperimentally.
Thedifferencebetweena smoothblendingofthechangeintheexponentx andanabruptchangeisminimizedby thefactthatthetransitionoccursintheneighborhoodofa valueof Z/d of1,wherethevalueof (Z/d)xis1 regardlessofthevalueof x. Theabruptchangemaybe sufficientlyaccurateforpracticalpurposes,as indicatedby thefollowingarbitraryexsmple.Assumethatthevalueof x shouldbe 2 at Z/d= 1 andthendecreases~early to zeroatwhere (1.2)0=1. Themaximum
Z/d= 1.2changeoccursata valueof Z/d of
about1.1where (Z/d)x= (1.1)1,withtheeffectdecreasingineitherdirectionfrom1.1. Thusthemaximumeffectofthismethcilofblendingisa changein loadnumberofabout10percentatmidrange,iftherangeinwhichthetransitionoccursis 0.2pointsof Z/d. .
An~ical curves.-Analy-ticalJy,informationoneccentricityratioagainstloadnuniberforshortbearingsisavailablefromthesolutionsby theshort-bearingapproxhnation(ref.1)andby themethodofCameronandWood(ref.2). Theseareshownas theuppergroupofcurvesinfigures12and13. Thecurvefromtheshort-bearingapproximationisa singlecurvetheoreticallyapplicableto shortbearings.TheCsmeronandWoodexactsolutionofReynolds’equationgivespointsindicatingseparatecurvesfor Z/d= 1/4,1/2,and1. A comparisonoftheseuppercurveswiththeexperimentalcurvewhichisrepeatedinfigure13showsthattheplottingofthedataasa functionoftheloadnumberusingthe (Z/d)2termfor Z/d< 1 is justifiable.Theuseoftheloadnuniberinthismannerpermitsdirectcomparisonofanalyticalandexperimentaldataforau valuesof Z/d ononecurve.ThelocationsoftheCsmeronandWocxipointsarealsofoundtobe inrelativelycloseagreementwiththeexperimentalcurvesadsubstantiatetheuseofthecurveinfigurel(a)forpracticalpurposeswhenusingtheloadnuniberaa a parameter.
Ihfigmes 12and13,thelowergroupme analyticalcurvesforinfinitevaluesof Z/d fromtwosolutionsby Scmmerfeld(ref.3) andonefromCsmeronandWood(ref.2). ThesecurvesforinfinitevaluesofZ/d ofnecessityrefertotheabscissascalelabeled1/S sincenofinitevaluesof Z/d areavailable.Itcanalsobe saidthatthecurvesareplottedinaccordancewiththedevicetiatinfinitelylongbearingsareconsideredtobe of Z/d= 1, suchthattheSommerfeldnumberappliesratherthanthecapaci~number.Itis interestingthattheinfinite-hearingcurvesagreewiththeshort-bearingcurvesatthe
——— . —.——— ——— .--—–
,
NACATN3491
highloadnumbersalthoughtheyaregreatlydivergentatItisperhapsforthisreasonthatuseoftheSomnerfeld
19
lowloadnumbers.solutionfor
bearingswith Z/d= 1 hasbeensuccessful.However,forbearingsshorterthan Z/d= 1,useoftheSommerfeldsolutionwouldbe lesscon-servativeas Z/d decreasesfrcxn1.
Thedifferencesinthethreecurvesshownforinfinitevaluesof Z/d area resultofdifferentassmnptionsasto thecircuml?erentialextentofpressurizedoilfilm. TheSommerfeldsolutionbasedona %tor360°etientofthefilmassumesthatnegativepressurescontributetotheloadcapaci~ofa bearing.IhtheCameronandWoodsolution,thefilmextentissomewhatgreaterthan1800jdependinguponassumptionsregardingboundaryconditionsofthecircumferentialpressuregradient.ThethirdcurveshownisbasedonSommerfeld’spressure-distributionfunctionforsm infinitebearing,buttheintegrationstodetermineloadcapaci~asa functionof n arebasedona pressurizedfilmof m or180°extent,thuseliminatingtheeffectofnegativepressures.Equations(15)and(16)belowshowthedifferenceintheanalyticalfunctionsoftheSommerfeldtypeonthebasisofextentoftheoilfilm.Forthe % film
() ‘1/2
s=PN’ d 2=(2 +n2)(l-n2)——p cd X%2n
Forthe m film
pN’fd\2 ( )(2+n21-n2S.yy = -#-
(15)
(16)
Theintegrationsforthe’determinationtheappendix.
- n2)+ kn~~”
ofequation(16)areshownin
Comparingthelowergroupof curvesinfigure13whichrefertobearingsofinfinitevaluesof Z/d withexperimentaldataof Z/dof2 orlessseemsto indicatethattheassumptionof Z/d ofinfini~givestoolowa valueofeccentricityratioat lightloads.The “assumptionofinfinitevaluesof Z/d el.imina$esthkeffectofendleakageonthepressuredistributionintheoilfilm. ThespreadoftheGta infiguretotheuppergroupinfinitkvaluesof
l(b)forbearingsof Z/d of1.5and2 is closerof curvesat ldghtloadsthantothecurvesforZ/a.
.—. —..——.—- .—
20 NACATN3491
.I!earingFriction
Curvesofbearingfrictionratio ~/F. forlongbearingsandshortbearingsareshown,respectimly,infigures2(a)and2(b).Bothcurvesshowtheexperimentaldataplottedasa functionoftheloadnuniberl/~ inwhichthe (Z/d)2termisincluded.Itmaybe seenthattheshort-andlong-bearingexperimentaldata,whencompsredwiththeanalyticalcurve,arenearlycoincidentwithoutdistinguishingbetweenshortorlongbesringsintheloadnuniberas isdoneinthecurvesofeccentricityratio.Thecurveobtainedby meansofthedeviceofusing 1/S forthelongbearingsinwhich Z/d istakenasunitvis shownh figure14(a)forthesameexperimentaldataoffigure2(a).Itmaybe seenthatthesamedatasxeinbetteragreementwiththeshort-bearinganalyticalcurveinfigure2(a)thaninfigure14(a).Itisinteresting,however,thattheexperimentaldataforlongbearingsinfigure14(a)areinfairlyreasonableagreementwiththeanalyticalcurvesforinfinitevaluesof Z/d by CameronandWood(ref.2)andby theSommerfeldsolutionfor1800filmextentofthisreport.
Anal#sicalcurvesforbearingfrictionratiofromthesolutionsof u
CameronandWod (ref.2)andtheshort-besringapproximation(ref.1)agreewellwhenplotteda@nst loadnumberl/Cn forshortbearings.Theseareshowninfigure14(b)for Z/d= 1/4,1/2,and1. Originally,theCsmeronandWoodcurvesforfrictionwereplottedon coordinatesof f(r/cr)againsttheSommerfeldnwiber.A repottingoftheircurvesofbearingfrictionas infigure14(b)showstheinfluenceof (Z/d)2indrawingthecurvesfor Z/d= 1/4,1/2,and1 together.
Journall?riction
TheCameronandWoodcurvesof joun&lfrictionratio F3/Fo againstloadnumberinfigurel~(a)showa greaterdivergencewith 2/d thanthebearingfrictioncurves.infigure14(b).Theyalsoshowthatthediffer-encebetweenjournalfrictionandbearingfrictionmaybe greatforhighleadnunibersandlargevaluesof t/d. Thessmecurvesplottedon coor-dinatesof f(r/c&)againstS alsoshowa differencebetweenjournalandbearingfriction,butthisdifferenceisdifficulttodistinguishsincethehighloadvaluesplotneartheorigin.By plottingfrictionratioagainstloadnuniber,thedifferencebetweenjournalandbearingfrictionisshownmoreclearly.
Analytically,theshort-bearingapproximationdoesnotindicateadifferencebetweenjournalandbearingfrictionbecauseoftheassump-tionttitthecircumferentialveloci~profileintheoilfilmislinear.Ihthisrespect,theagreementoftheCameronandWoodandshort-bearingcurvesforbearingfrictionis of considerableinterest.Fromequilibrium
‘d
——
NACATN 3491 21
.
conditions,thebearingfrictiontorqueistheoreticallylessthanthejournalfrictiontorqueby thecouplePe sin~. Curvesforjournalfrictioncanbedeterminedfromrelationshipsoftheshort-bearingapproximationby addingthiscoupletothefrictiontorqueofthebearing.!lhecurvesofjournalfrictioninfigure15(a),labeledshort-bearingapproximation,arebasedonthisadditioninaccordancewiththefollowinganalysis.
ThedifferencebetweenjournalandbearingfrictiontorqueAF(d/2)isequalto thecoupleoftheload P andthelateraldisplacementofthejournal~=esin~:
A+= Pe sin@ (17)
lhtermsoffrictionratio:
g= %&-E) (18)
Substitutionof P = ~N’(d/cd)2(t/d)2(l/~)Zd,e = n(cd/2),andthePetrofffrictionF.= 2#pN’Zd(d/cd)gives
& _ n sin@ (Z/d)2F. 2f12 Cn
(19)
(rAFd .nsin@l—-F. 1
(20)2fi2~..-
Since sin@ andtheloadnumberl/Cn arefunctionsof n asgiveninreference1,thecurveof (Al?/Fo)(d/t)2 againstloadnumberfromequation(20)isa singlelineas showninfigure3.
TheratioAl?/Foisthecouplefrictionratiowhichisaddedtothebearingfrictionratioto obtainthe~ournalfrictionratio
(21)
— .— —-——— ——. .——.——.—.. — ._ —
..— — .- —.. — .
22 NACATN3491
Asshowninfigure15(a),theplotof journalfrictionratioagainstloadnumbergivesa familyofcurveswhichtiein closeagree-mentwiththecurvesfromtheCameronandWoodsolution.
~rimental dataonjournalfriction.- Sinceexperimentaldataofjournalfrictionaxenotavaila%lefromthisinvestigation,datafromMcKeeandMcKee(ref.7)andPalsulichandBlair(ref.8)areshownin
[figures15b) to l~(f)forcomparisonwiththeanalyticalcurvesfromequations19)and(21). Bat-afromtheseinvestigatorswereobtainedfromthefour-bearingmachinewhichmeasuresthefrictiontorqueofthejournal.
McKeeandMcKeepresentdatafora 1# -inch-diameter%earingwith
a rangeof clearanceratiosfromO.00~ t; O.O&O for Z/d= 1/4,1/2,3/4,1,ad 2.8. Comparativelylightloadswereused,buthighloadnunibersoftheorderof5~ wereobtainedat lowrotativespeeds.Thesedataareshowninreference7 asexperimentalcurves,ratherthanpoints,plottedoncoordinatesof f (frictioncoefficient= F/P)againstZN/p.Sincethe Z/d andcd/d informationaregivenwiththecurves,con-versionofthedatato Fj/Fo and l/Cn coordinatesispossibleasshowninfigures15(b)to 15(e).
.
Figures15(b)andla(c)comparetheMcKeeandMcKeedatawithequation(21)fortheshortbearingsof Z/d= 1/4and1/2 andfig-ures15(d)and15(e)comperethemfor Z/d= 1 and2.8. Thesecurvesshowthatagreementoftheanalyticalandexperimentalcurvesisbette(rfor Z/d= 1/2,1,and2.8 thanfortheveryshortbearingof 2/d= 1/4wheretheloadswereverysmall.-Sinceonesetofdatafor 2/d= 1 isgivenintabularforminreference7,itispossibleto showpointdatainfigures15(d)and15(e)forthefrictionrisebeyondthehookpointintheregionofboundarylubrication.Thesequenceofdatapointsaroundthehookis shownby the ZN/p curveinsetinfigure15(d).Thepointsabovethehookrapidlyleavethescaleofthe Fj~Fo curve.Thehookpointisindicatedonthe Fj/Fo curveby an increaseofslope 0ofthelinewhichtendstorisealmostverticallytopointsofftheverticalscale.Themoreroundedthehookonthe ZN/p curve,themoregradualthechangeof slopeinthe Fj/Fo c~e.
Highloadnumbersareshownintheexperimentalcurvesoffig-ures15(b)and15(c)for Z/d= 1/4and1/2 becauseoftheinfluenceofthe (t/d)2termintheloadntier,andthenwdmumloadnunibersfor Z/d= 1 and2.8 sremuchsmaller.
PalstichandBlairpresentexperimentaldatafroma four-bearingmachinesimilarinprincipletotheMcKeeandMcKkemachinebutmodified “to operateathigherloadsandgreaterspeeds.Dataarepresentedfor
b
———.
NACATN3491 23
a bearingapproximately2 inchesin diameterand11incheslongwithaF
diametralclearanceof0.004inch. Speedsashighas 5,000rpmandunitloadsto4,000poundspersquareinchwereused. Theexperimentaldatasrepresentedinreference8.usingcoordinatesof f(r/c)and S,wherec is theradialbearingclearance.
‘se ‘y be Convertidb %/Foand l/Cn valuesasshowninfigure15(f).An exactvalueof Z/d isnotgiven,buta inspectionof thetabulardataindicatesthatthebearing
was2* by Ii inchestith Z/d= 0.607.Figure15(f)showsthecomparison
of experhentaldatawithequation(21).Wad numbersinexcessof 1,OCOwereobtainedas shown.Theexper~entaldataagreewellwiththeana-lyticalcurvebelowa loadnumberof 1~ butarebetweentheanalyticalcurvesof I/d= 0.607and1 at thehighloadnumbers.Inreference8,thep“lotof thefrictiondataon f(r/c)and S coordinatesdidnotexhibita hookpointevenat theveryhighloadnumbers.
An importantfeatureoftheanalyticalcurvesinfigure15(f)isthatonthecoordinatesshowntheyindicateJournalfrictiontobeseveralhundredpercentofthebearingfrictionathighloadnumbersandhighvaluesof Z/d.
BoththeMcKeeandMcKeeandPalsuMch-BlairdatawereusedtodeterminethecouplefrictionratioAF/Fo forplottingAl?/Fo(d/t)2as infigure3. Experimentaldataof couplefrictionratioweredeter-minedby subtractingtheshort-bearinganalyticalvalueofbearingfrictionratiofromtheexperimentaljournalfrictionratio.As showninfigure3,mostoftheexperimentaldataareabovetheanalfiicalcurve.TheMcKeeandMcKeecurveswhichdidnotcontinuebeyondthehookareinrelativelygoodagreementwiththeanalyticalline,exceptforthedataat 2/d= 1/4,whichareoffthescale.Themethodofplottingthedifferenceof journalandbearingfrictionas infigure3magnifiesthedifferencesshowninfigures15(b)to 15(e)andisworthyofwideracceptanceas a tooltomagnifythespreadoffrictiondataathighloadswhicharehiddenneartheoriginofthe ZN/p curves.
Analyticalcurves:infinitevaluesof 2/d.-Analyticalcurvesofbearingandjournalfrictionforbearingsof infinitelengthareshowninfigure16 on coordinatesoffrictionratioand 1/S. Thethreesetsof curvesshownarederivedfromtheanalyticalsolutionsof CameronandWood(ref.2)andSommerfeld.Twosetsoftheanalyt-icalcurvesarebasedontheSommerfeldpressure-distributionfunction,onesetas givenby Sommerfeld(ref.3) fora ~ or360°pressurizedfilmandonesetfora m or1800pressurizedfilmas determinedintheanalysisoftheappendix.Inallthreesolutions,thefrictionforce F isdeterminedfromintegrationsoffilmshearingstressesover360°.However,theeffectoffilmpressureontheshearingstressesdependsupontheangularextentofthepressurizedfilm. As shownin
...—
24 NACATN3491
theappendix,thefriction-ratiocurvesfortheSomerfeldm casemaybe determinedfromthesumoftwointegrations,onefromtheSommerfeldshearingstressfunctionforthepressurizedfilmof m extent,andonefromtheshort-%earingapproximationfunctionforthenonpressurizedfilmof n extentwherea linearcircumferentialvelocityprofileisasswmd.Equations(22)and(23)belowshowthedifferenceinformofthefriction-ratiofunctionsofthe 2JCand m casesoftheSomnerfeldsolution.Forthe 2YCfilm
Forthe z film
Fb 21- ~2)—=F.
(2+ n2)(l- n2)1/2
9= 21+2n2F. 2 1/2
(2-1-n2)(l- n )
Fb 1 (4- n2)—=-F. 2
( )(2+n21-n )2 1/2
(22)
(23)
.
AEshowninfigure16jtheSOmmerfeldm curveandtheCameronandWoticurveforbearingfrictionarealmostidenticalintheload-numberrangeshownandareinfairagreementwiththeexperimentaldataforlongbearingsinfigure14(a).Theanalyticalcurvesforjournalfrictionaresomewhatdivergent,theScmmerfeld% curvegivingthelargestfrictionvalues.
TheSommerfeld% solutionshowsthegreatestdifferencebetweenbearingandJournalfrictionas showninfigure16. ‘lhisisa directresultoftheassumptioninthe ~ solutionthatnegativepressureqcontributetotheload-carryingcapacityofa bearingandcausedis-placementsalwaysnormaltotheloadlineas shownintheclearancecirclediagramoffigure17. Themomentarmofthefrictioncoupleisalwaysgreatirthereforeinthe % solutionthanthemomentarmsofthe x solutionortheCameronandWocdsolutionforthesamevalueof n.
.—-— ——.
:U
.
25NACATN3491
IfinfiniteZ/d analyticalsolutionsaretobe usedinlong-finite-be@ngappl.icat~ons,itwouldseemthattheCameronandWocilandSommerfeldx solutionsarethemostrealisticsincemostexperi-mentershavereporteddisplacementcurvesofthesemicircularformshowninfigure17.
.,ThedisplacementcurvefortheSommerfeldz caseshowninfig-
ure17 isbasedonequation(24)delierminedfromtheanalysisintheappendix:
(24)
oilFlow
Theexperimentaldataforoilflowfactorq shown.infigure4(b)arefromreference1 butarereplottedinorderto showoilflowrateasa reciprocalfunction.Theinlet-oil-pressurenumberl/~. con-tainstheloadnumberl/en andtheratioof oilsupplypressurep.totheunitbearingpressure.Thecurvepresentedinreference1 isshownforcomparisoninfigure18. Bothcurvesshowtheexperimentaldataforshortbearingshavinga singleoilfeedholelocatedoppositetheload.Alsoshownaredatafromtestsby McKee(ref.9)for%earingswitha singleoilholeandforbesringswithanaxialoilgroove.Thecurvesoffigure4(b)applytobearingsof Z/d up to 2,althoughonlytheshort-bearingdataareshownbecausethelong-bearingdataplotsoneartheorigin.An enlargedplotwithscalesfivetimessizeis shown
separatelyinfigure4(a)withdatafor ~ = 1,1A and2.d *Y Thesolid
linedrawnthroughtheexperimentaldataforlongbearingswitha singleoilholeinfigure4(a)isthesamelineshowninfigure4(b).
As in~catedinreference1,theoilfluwfactorq (eq.(7))istheratiooftotaloilflowrate Q issuingfromtheendsofthebearingtotheanal@icaUydeterminedflowrate fidZcd(N~/2)ndiscMgh.g frOIII
thepressurized180°ofthebearing.Theanalyticalflowrate,basedontheshort-bearingapproximation,maybe viewedas a volumetricdis-placementratein cubicinchespersecond.Itisequaltothedifferencebetweentheflowrateenteringatthepointofmaximumfilmthiclalessandthatleavingthebearingat thepointofminimumfilmthiclmess,undertheeffectsofrotitionandviscosity,at zerocircumferentialpressuregradient.Thetotalflowrate Q wasdeterminedlyexperi-ment.almeasurement.By empiricalmethodsofplottingtheexperimentaldata,itwasfoundthattheoilflowfactorq appearstobe a functionoftheinlet-pressurecapacitynumberho:
—.— — —— ——- ——.——z— —.—...
.—.——.
26 NACATN3491
However,thereciprocalformo? thecur&soffiguresk(a)andk(b)seemstogive--evenbettercorrelationasa functionof theinlet-oil-“I
I~resswe‘mber 1 %0 ‘ (l/cn)(Po/P)as giveninequation(8).
IE@uresk(a)andk(b)areintended”toserveas a meansforthedeterminationofoilflowrate Q fromknownconditionsinvolvingthevariablesintheloadnuniberandthelumwnoilfeedpressurepo. Itshouldbe noticedthatthedeticeoftakingZ/d as 1 forvaluesofZ/d greaterthan1 isnotusedfortheoilflowcurves,exceptindirectlywhenthevalueof n so obtainedentersintothecalculationoftheanalyticalpartoftheoilflowrate.
Figure4 isnotintendedtobe usedasa devicetopredictthe ‘.
oilsupplypressurep-o.No criterion,otherthanoperatingtemperature,isavailablewhichspecifiestheminimumvalueofoilflowfactorq oroilflowrate Q. Casesofbearingsperformingsuccessfullyonthickfilmsunderstarvedconditionsofoilflowareknown,butthedegreetowhichstarvationcanbe toleratedisnotkn6wn.lHgurek(a)indicatesthatbearingshatig Z/d greaterthsn1 areapttohavean oilflowfactorq lessthan1,whichmaybe an indicationthatoilgroovesaredesirableforlongbe~gs toficreaseoil fluwandloweroperating“-rature as Wcatedby figure37 inreference1.
USEOF CURVES
l?Lgures1 to4 maybe usedtopredicteccentricity,minimumfilmthiclmess,bearingandjournalfriction,journalpowerloss,andoilflowrateforbearingsto I/d= 2. However,thevariablescontainedintheloadnumberandinlet-oil-pressurenumbermustbe known,includingtherunningtemperatureofthebearingwhichdeterminesfilmviscosity.Inletoilpressuremustalsobe lumrn.Forbearingsof I/d of1 orless,theloadnumbermaybe calculatedincludingtie (l/d)*termtodeterminetheabove-namedperformancecharacteristics.However,forbearingsof Zjd ~eaterthan1,twoloadnumbersarerequired.Theloadnumber1/S withoutthe (z/d)*termisusedto determinetheeccentric@ratio n fromfigurel(a)whichisusedinthecalculationofoilflowrate Q fromfigure4. Ioadnumberl/Cn including(Z/d)2 ‘-
.
-. _— -
NACATN3491 27
isrequiredinthedetermination-ofbesringandjournalkriction,couplefrictionratio,andinlet-oil-pressurenuniber.
A methcdofapproximatingmaximumbearingtemperatureby theuseofa heatbalancediagramisdescribedinreference1. lRtgures2 and3canbe usedto estimatebearingfrictionandtheincrementofcouplefrictionto obtainthefrictionoftherotatingelementwhichgives.thepowerlosssndheatgenerated.Mgure4 givesoilflowd.ataforuseinestimatingtheheatcarriedawayby theoilflow.
CONCLUSIONS .
Thefollowingconclusionsmaybe drawnfromtheresultsoftheexperimentalinvestigationofeccentricityratio,friction,andoilflowoflongandshortjournalbearingswithloadnumbercharts:
1.The-performanceofplainbearingsundersteadyloadisreducedto single-klnechartscoveringtheusualrangeoflength-to-dismeterratiosZ/d from1/4to 2 by theuseoftheloadnumberin&mannerdescribed.
2. Inclusionofthe (Z/d)2termintheloadnumbercollectstheexperimentaldataina singlelineinallcasesexceptoneofeccen-tricityratiowhere Z/d valuesgreaterthan1 ne takenasuni-&yincomputingtheloadnumber.
3. The (t/d)2termis.includedintheloadnunibertodeterminethefriction-ratioandtheoilflowfactorfrcnnthefigures.
4. Theadditionoftheincrementoffrictiontorqueformedbythesidewarddisplacementoftheloadto thefrictiontorqueonthestationaryelementtopredictthefrictiontorqueoftherotattigelement,heatgenerated,andpowerlossis supportedby analyticalcurvesandexperi-mentaldataof otherinvestigatorswhohavemeasuredjournalfriction.
5.Themethodofplottingfrictionintwoparts,thebearingfric-tionratio ~/F. andtheincrementoftheloadcoupleAF/Fo,permitshydrodynamicfrictiontobe determinedfromsingle-linecurveswhichhavebeenshowntoapplyto theusualrangesofclearanceandlength-to-diameterratio.ThepredictionoffrictionfromratiosrelatedtothePetrofffrictionatno loadismorerationalthantheuseofafrictioncoefficientbasedonload.
6.Thereciprocalformoftheloadnumberl/Cn ispreferableto~ as a parameter.Theloadnumberincreasesindirectproportionto
28 NACATN3491
unitloadandisproperlyweightedtohavemeaningas a quantitativemeasureofrelativeloading.Theareaonthegraphdevotedtothe13.ght-loadregionisminhized,andtheeffectofhighloadnunibersis shqn moreclearly.
CornellUniversi@,Ithaca,N.Y.,August20,l-.
———.
NACATN3491’ 29
APPENDIX
INI!Q3RATIONSFORSOMMERI!ELDY( CASE
Thefo120wingintegrationsgivingeccentxici~ratio,attitudeangle,andfrictionratioarebasedontheSomerfeldpressure-distributionfunction(ref.3)fora bearingwithoutendleakage.How-ever,a basicchsmgeinassumptionsismadeconcerningthecircumferen-tialextentofthepressurizedfilm. Sommerfeld’sintegrationtodeter-minetheresultantforceorload P includes-thenegativepressureregionofthedivergingwedgeoftheoilfilmaswe= asthepositivepressureregionoftheconvergingwedge.Tneffect,a workingfilmof & or360°isassumedsuchthatthenegativepressureregioncon-tributesto thesupportoftheload.Thefollowin$analysisisbasedontheassumptionthatsupportoftheloadby negativepressuresisnegligibleandthattheworkingfilmis intheconvergingwedgeandisof YC or180°in circumferentialextent.Thesameassumptionismadeintheshort-bearingapproximation(ref.1).
Eccentrici@-RatioFunction
Thefollowingequationisthepressure-distributionfuhctiongivenby Sommerfeldinwhich PS representsthedatumfilmpressureat theleadingandtrailingendsoftheconvergingwedgeoftheoilfilm:
[ 16VUr nsine(2+ncos e) +PPfilm‘~
( )(2+n21+ncose2 )
s (27)
IhthefollowingstepSPs isassumedtobe zerogagepressuresuchthatequation(27)givesfilmgagepressures.Thean- variableeismeasuredfromthelocationofmaximumfilmthickness.
The X and Y coordinatesarechosenparallelandperpendicular,respectively,tothelinejoiningthejournalandbearingcenterswhichareatan eccentricitye. TbeorthogonalcomponentsoftheresultantPare Px and py. T& followinginte~ationsover m radianstherelationshipoftheload P asa functionofeccentrici~
determineratio n:
..—..-—— — —.————— .——
30
P~=zJ
r cose de~filme=o
d 2
()=@12—
cd
.~2
)(2+n2 l-n2
. .
=
Substituting
z“Jl--.:!.
*filmlro‘sine de
n sin2e(2+ n cose) de
(2+ 112)(1+ n .0se)2
d2-() “&m~@L ~
( )( )2 1/22+n2 l-n
,.
i PX2+.PY2
NACATN3491
P= pld>.
and U = I-KIN’
(2 + n2)(l- n2)
&M[Yt2(l-n2)+ 4n~1/2
(29)
(31)
.
.- -.
NACATN3491 31
Equation(31)isthesameasequation(16)inthebodyofthisreport.TheanalyticalcurvesofeccentricityratioagainstSommerfeldnumberrepresentingequation(31)areshowninfigures12and13.
AttitudeAngle I
TheangularlocationoftheresultantP withrespecttotheX-tis,orattitudeangle #, isdeterminedfromthefollowingexpression:
‘Ytan@=—Px
‘=&&!!2n (32)
Theattitudeanglealsogivesthean*-po8itionJoftheminimumfilmthiclmessrelativetotheloadlhe as showninfigure17. Equation(32),whichisthessmeas equation(29),showsthedisplacementpathinfig-ure17tobe nearlysemicircularratherthans~aightas intheSOmmerfelil% solution.
l?rictionRatio
Equationsforfrictionforceson thebearingandjournal’aregivenby%mnerfeld(ref.3)forthe Zh radiansor360°extentof thepressurizedfilm. Todeterminethefriction.forces~’ and Fj’ Orlbearing and -journal,respectively,forthe%mmxrfeld,x case,witha pressurizedfilmextending1800or 1/2of thearc,haH of thevaluesgivenby Samerfeldmay“beusedtorepresenttheeffectof thepressurizedonfriction:
()d ( 2)Fb‘ 23cl-n= pu2~
1/2(2+ n2)(l. n2)
halfof the oilfilm
(33)
(*)
Toequations(33)~d (%) mustbe tidedthefrictionofthenon-pressurizedfilminwhichthevelocityprofileisMnear. Halfofthevaluesgivenby theequationsoftheshort-bearingapproximationmaytieusedtorepresentthisfrictionF’:
—.—. _ ——..—. —_ — .— —.— —.
32 NACATN3491
ThetotalfrictionforcesFb and FI erethesumsofequa-tions(33)and(35)andequations-(~)and”(35):
Fb‘+F’
Fj’+F’
241 + 2n2)‘%)[(2 + n2)(l- ~2)’/2+ (,. :2)’/:
( ti(k+ 5n2)@J2~
cd‘(2-1-n2)(l-“n2)1’2
(37)
IMvidingFb and Fj by theload P inequations(36)and(37)resultsinequs.tiunsinSLibstitutingu = Y’Cdl?‘,
termsofcoefficientoffrictionf~ and fj.P =pZd, and S= (@’/P)(d/cd)2,
fb(d/Cd)= S (~24-n2 )
‘(2+ n2)(l- n2)1/2
*2(4+ ~n2)f3(d/cd)= S
(2+ n2)(1- n2)1/2.
——. —
NACATN3491
To obtainfrictionintermsoffrictionratio,equations(36)(37)aredividedby thePetroffvalueoffrictionFo:
Fb—=F.
=
Equations(40)
I.LUt(d/Cd) I-r(4- n2J2 1/2
(2+ n2)(l- n )
1 (4- n2)z( )( )2+n2 l-n2i’2
q=~ (4+ ~n2)TO 2
(2 + n2)(l- n~l’2
33
and
,(40)
and(41)arethesameasequations(23)andareshownplottedinfigure16forcomparisonwiththeSomnerfeld21solution.
(41)
-. . -. ..———..—. —.. ~-— .-. —.— _ — .— —.— — —
34 NACATN3491
REFERENCES
1.
‘2.
3.
‘4.
5.
6.
7-
8.
9.
D@ois, GeorgeB.,andOcvirk,l&edW.: AnalyticalDerivationandExperimentalEvaluationofShort-EearingApproximationforIiUJournalBear@S. NACARep.11.57,1953. (SupersedesNACATN’S2808~d 2809.)
Cmeron,A.,andWoml,W. L.: TheFullJournalBearing.Proc.InstitutionWch. Eng.(Icmdon),vol.161,W.E.P.Nos,.47-54,1949,pp.59-72.
Sommerfeld,A.: TheHydrodynamicTheoryofLubricationFriction.Zs.Math.und”phys.,vol.-5O,nos.1 and2, 19&, pp.97-155.
DuBois,G.B.,Ocvirk,F.W.,andWehe,R. L.: Experimental~vesti-gationofMisallyingCouplesandEccentiici@at theHs ofMis-alinedPlainBearings.NACATN3352,l=.
Wilcock,D. F.,andRosenld.att,Murray:OilFlow,KeyIbctorinSleeve-BearingPerformance.Trans.A.S.M.E.,vol.74,no.5,JtiY1952,PP,W9-866.
.
!l?imoshenko,S.: StrengthofMaterials.PartII - AdvancedTheoryandproblems.Secondcd.,D. VanI?ostrandCo.,Ihc.,1941,pp.258-264.
McKee,S.A.,andMcKEe,T.R.”:Fcictionof JournalBearingsasInfluencedbyClearanceandLength.Trans.A.s.M.E.,u-51-15-161,vol.51,Aug.1929,PP.593-595.
Palsulich,J.,andBlair,R.W.: TestingofHighlyIoadedSleeveBearings.SAEJour.,vol.~, no.9, Sept.1946,pp.481-490.
McKee,S.A.: OilFlowinPhin JournalBearings.Trans.A.S.M.E.,vol.74,no.5, J- 1952,pp.841-848.
.
1
TA31EI.- EWHUWRTAL COIiDITIONSIN DI??PMCEMENTExPERIMmm
[& -in.-dam. steeljcmmal and bronzebemingj8SAE10 Ofl SU@id thrcq@ a 1./8-in.diem.Ofl hole qqx)aitiC@ti= Icai]
cd> ~-d, kamm UIllt WxLm!Jmbearing oil inlet
Shal?t l/d N, MdJm.unlcaa, lad, p,in.
mP, lb *$, q) presmme,
lb/6qin. Po) w4 ~.
6A 2 0.-52 0.00183 5m, 1,007 m 80l,m 1,293 %“ 9 M2,50il 1,438 &g5,m 1,538 g 1~ R5,CCI0 1,653 170 1.20
63 2 0.cH3376 o.oo.?~ yo 1%3 223 w1,mo 1,q 266 132 25,(YW 1,4T8 yil 156 2-40.3,030 1,438 3&l @ 140
&62 z 0.00M o.oo142 1,2W 938 329 134 80
1,200 31?a 137 1.28 801,2CN 938 32$) 132 802,500 1,438 508 151 805,030 1,713 601 179 80
6D 1 o.m183 o.cxl133 1,203 988 523 1332,5~ 1,538 814 fig 25,m 1,610 80Y,Coo 1,660 ,% ;$ m
6E 3/4 O.o@8 o.(xl18’7 1,(X20 489 343 1282,500 838 g 139 ::5,CW m. 158 40
TABLE II.- ExPERIMmmL CONDI!IICONBIN FRICTIONM?O OIL FU)W EXP~S
[fl-in.-diem. steel JournalW br~ze bearing; ME 10 oil mrpp~ed8
1+bX@il8@-iL-&WOfi hole OppOBi& COdHd bad
cd) ‘sped,k ~, WsLimsmlad, =yM3dmurnbearing a,l inlet oil flow,
ihaftl/& ~&
t~.> T4>w P, lb
pressure, Q,. lb/aq in. OF Po) w.w ~. lb/ndn
6A 2 0.OCE-52o.00IEFJ1,203 1,283 338 1361,2(XI l,2a!3
o.M338 135 R .(2$8
1,2(XI 1,288 g; 133 120500
.155938 130 80 .m+
500 938 248 132 MO .1485,000 1,663 458 tig .285
6B 2 o.oc576o.w~ 5(XI 836 220 w 80 6.3321,138 136 .4M?
;$% 1,663 ~8 160 : .6485,0co 1,663 @8 158 120 .7%
6C 1$o.ool~o.cQ1421,200 938 329 132 40 O.*5
1,200 938 529 1-33 .do1,203 936 529 134 1% .W5,m 1,689 Ml .1325,m 1,688 ;% 1~ 1% .175
/.0
>9
,$
.7
,6
5
.4(
,3
.Zc
.1 ?! t I I I I I I I I
.’j I 1 1 I I I I I I I 1/0
Loa D
(a) Data for both long
FOR
frmu data in figures l(b) and l(c). ‘
Figure l.- Eccentricity ratio aga~ load number.
aM 2. Data are cambined
!2
u
(b) Data for long bearings with Z/d .1, ~, and 2 ti .gh@ bearlnga with Z/d = 3/4. se,
table I for experherrtal conditions.
Figure 1.- Continued.
,
c
?’h
“o /0 w 90 40 50 60 ?0’80 %
(c) Dataforshort bearinga with Z/d = 1/4, 1/2, and 1. Experimental data are taken fromreference 1.
Figure 1.- Concluded.ww
(a) Data for long bearinge with l/d = l% ‘9Jld2. See table II for exprimerrtal condltione. E*
Figure 2.- Bearing friction ratio againd load number.5
~F
I
I
I
E #
, 1
I
I
,
?
Figure 2.- Concluded.
-Fm
u
~ O/4D ~UM-~y % ‘ /~N) (.)2 (-)’
Figure 3.- Couple friction ratio agaimt load number.F4
,
, a
[/v LITr- t7/L-p/?E5JoicG h’UMB6E&, y~, ‘ ycn g
(a) Data for long bearinga. See table II for experimmt.al conditlona of SHE 6A, 6B,and6C.
Figure 4.-
GOil flow factor againat inlet-oil-pressure number.
!,-
Q\.. ,$ J---J-1 I
IW#
3IT
(NL~T. olk - PRESSUR G NfJM&!ER ,%%
(b) Data for short bearinga.
Figure 4.- Concluded.
70
.gn$ “0 s
o
I
1
, ,
G
7
Figure 5.-Configuration of temt bearing and aheft showing location of oil hole, thermocouples,and dieplacemmt-mamring riders.
o
Figure 6.-Schemat~ctiagramofappsratwforapplytngcentral1-, formeaauringfrictiontorque on teat bearing, and for rceaauringoil flow through test bearing.
1
, I
I(
1
1I
>
1
-%z/M3 Suff=twr
-qq:;-::’” aFigure7.-Mechanlcal system for maasuri~ displacement of Journal rehtive. to bearing.
.
’51 m /’-45’ r-h
q}
+—-—.*, ----
OIL 70 /BEARING
7/4
.
k7%-#-&’AR’--l=F=lFigure 8.- Diagrem of thermocouple locations. All thermocouples
I/16Inch frm bearing surface.except 9 and16arelocated
g
Q
y-
> ,
‘7UNACAIIN3491 49
P 100 /520 ax? 300
TEMPZEX?TURE, ‘F
.Figure9.-Viscosity-temperaturecharacteristicsofS.AE10oilusedin
experiments.“Measumentsofviscosityweremadeina standardSayboltviscosimeter.‘.
—. _ .-__ ———. —.— ..—. —.—
Uo
20
/$
16
M’
/.?
Jo
a
6
4
2
00 /234,5 67 @910// IZ~S/+&
CU4NG& IN DMII+KTKRL f=Lg~K R~C~ ~d.
Figure 10.- Changes in diemetral.clemce as a function of temperature difference of two Epoints in teat-bearing wall. tk and tg are bearing temperatures at l/16 inch and b
2 inches, res~ctively, from bearing surface. Running clearances of test bearing are ‘adetermMed by subtracting change in clearance frcnnrmm-temperatwe clearance.
gP
1 .
* ,
(a) Lcng bearing,’with Z/d = 1, 1~, and 2 and short bar- with Z/d m 3/4. ~e~ti~dataare sue aq In figure l(b); for exprimmtd conditions, see table I.
Figure11.- Eccentricity ratio against Smmerfeld number and capacity number. UP
vlm
,“
,6
,7
,6
I
. .
Short beaings with Z/d = 1/4, 1/2, and 1. _tientaland are from reference 1.
Figure Il.- Concluded.
a!%ta are same as In figure l(c)
E1-
Figure K!.- Analytical curves of eccentricity ratio against lmd number.
wl-!=
,9 — 5’HOR T. J9E14 R /NG,A PP~OXIIWa TION
.8 + — c.4M6.eoM &.VD WOOD
.9 –- –— SOMM6RFELD
.G
5 \
\ ‘,
Nl
4 \ \ \
>,3
b$ \ x.&
‘%’(y . \,2
\\
\ ‘. —/ .*,C mca D
FigureI-3.- AnEJ@Aml curvesof eccedmicity ratio against Ekmnerfeld number andCapaclty number.
I
‘
,)
I
(a) Coiuparimn if’ long-bearing data with analytical curves.
Figure 14,- Bearing friction ratio a@.mt load number.
.
Um
LOa D NUMBER] ‘~ “%(592($)’
(b) Analytical cwveE for short bea@ngs.
Figure 14.- Concluded.
‘ ,
I
,,
,
I
it (a) Analytical curves for long and short bearinga; Camron and Wood
reference 2.
Figure 15.- Curvesof Jcmrnalfrictionratio ag*13t load
cum-m tdmn frm
number.
I
58 NACATN3491
.
(b)ComparisonofexperimentalcurvesofMcKeeandMcK&e(ref.7)with-icdcmes ofequatio~(19)and(21);Z/d.1/4.
0 100 zoo 3C70 +%7 500
LORD NUMB ERA Y&O
(c)ComparisonofexperimentalcurvesofMc~e andMcKee(ref.7)withanalyticalcurvesofequations(19)and(21.);Z/d= 1/2.
.
.
—
Figure15.- Continued.
NACATN3491 59
.
“o /00 208 3da 4.90 5U0
~ 0.4D ~tiM8ER ~ ~tn
(d)ComparisonofexperimentalcurvesofMcKeeandMcKke(ref.7)withanalyticalcurvesofequations(19)and(21);Z/d= 1.
qli’
(e) Comparisonof experimental curves of McKee and McKEe (ref. 7) withanalytical curves of e~tions (19) and(21);Z/d= 2.8.
Figure15.- Continued.
——. — —-—.. ...—z —.. __ . .. —.-——— _ ——
mo
(f) Comparison of expdmmtal data of Palsulich and Blair (ref. 8)with analytical curves of~
equations (19)and(21); 10KW and short bearlnga. ki
Figure U.- Concluded. gP
.
Figure 16.- Analytical curves of journal emd beax
7
friction ratio against 1/S for Imfinltevalues of 1 d.
62 NACATN 3491
SffORT 6E4R ING 4PPzO%IM4710RV
— — CA ME ROAJ &UD WOOD
—-.\ .-~o MM ERFKLD
GCCEAJTJZICITY KG T~O, n
,/
.2
.3
.4
,5
.6/ Y2ii (4
#“,7
&
.9
Figure17. - Clearancecircle diagram showing paths of journalment relative to bearing under central loa~ in terms ofcity ratio against altitude ar@e; analytical curves.
&kplace-eccentri-
.
.
—— .— . .
+—
PP /?-8 Lo-
.20 ,25 30 .35 ,40, ,, $-
Figure 18.- Oil flow factor against inlet-pressure capacity number for short bearings with .z/d = 1/4,1/2, 0.62, and 1. Exprhental data are from references 1 and 9 andare also
shown in figure l(b).
top related