DesignofaLandingGear
forDHC-2Beaver
MECH360,FALL2015,DR.MOHAMMADALEMI
BY:AKSHIVBANSALANDIANTHOMPSON
TableofContents
STATEMENTOFPROBLEM:
3
ASSUMPTIONS:
3
MATERIALPROPERTIES:ALUMINUM6061-T6
4
SUMMARYOFAPPROACH
4
ANALYSIS
5
MATLABSCRIPT
SOLIDWORKSDRAWINGS
ANSYSANALYSIS
5
6
7
RESULTS
10
CIRCULARLANDINGGEARDESIGN
ELLIPTICALLANDINGGEARDESIGN
11
12
CONCLUSION
13
2
StatementofProblem:
TheDHC-2BeaverisaplanemanufacturedbyDeHavilland.Weweretaskedwith
designingalandinggearforthisplane.Thedesignissubjecttosomegivenconstraintsandhas
tobeabletowithstanditsnormalloadingduringlanding.Becauseoftheaviationapplication,
weareusinganaircraftgradealuminum6061-T6.Thismaterialallowsustoweldthelanding
gearontotheplane;thiswillbethemeansofattachment.Wewereconstrainedtoalengthof
1.5mandafactorofsafetyof1.8.Thetypicalloadingconditionthatwewereaskedtoconsider
wasaplanewithagrossweightof22.7kN,withaverticalapproachof5m/sandahorizontal
approachspeedof35m/s.Subjecttotheseconstraintsweanalysedtwodifferentcross-sections
withtheaimofminimizingtheweightofthelandinggear.
Assumptions:
•
Transmissionoftheforcethroughthelandinggearisslowenoughsothattheimpact
loadingwillbedistributedoverbothlandinggears,evenwithslightasymmetriesin
landing.
•
Factorofsafetyisappliedtotheallowablestressesinouranalysis.
•
Forcesthroughthewheelareexertedasnetforcesatthecentroidofthelandinggear
crosssectionwithnotorsionalmomentbecauseofthewheelaxle’sattachment.
•
Strainenergyduetotransverseshearissmallandthereforenegligible.
•
Therunwayisaflathorizontalsurface,leadingtoapurelyverticalimpactload.
•
Duringlanding,theweightoftheplaneistakenbyliftinthewings,sothelossof
potentialenergydoesnotneedtobeconsideredinimpactloading.
•
Brakingwillbeappliedaftertheimpactloadoflandinghasdissipated.
•
Afterlanding,theplanewilldecelerateataconstantratewithafrictional,horizontal
brakingforceappliedtothewheels.
•
Allkineticenergyoftheplaneistransferreddirectlytostrainenergyinthelandinggear
•
Attachmentofthelandingismuchstrongerthanthelandinggear
3
MaterialProperties:Aluminum6061-T6
Property
3
Value
2710kg/m 310MPa
165MPa
276MPa
160MPa
70GPa
26GPa
Density(ρ)
UltimateTensileStrength(Sut)
UltimateShearStrength(Ssut)
TensileYieldStrength(Sy)
ShearYieldStrength(Ssy)
ModulusofElasticity(E)
ShearModulus(G)
SummaryofApproach
Westartedbychoosingtwodifferentshapestoanalyse.Wechosetouseahollow
cylinderandahollowellipse.Theseshapessimplifiedthemomentofinertiaanalysisand
allowedustotaperthecross-sectionalongthelandinggear’slength.Havingnosharpanglesin
thecrosssectionalsoavoidscreationofstressconcentrations.Whenexaminingexistinglanding
geardesigns,wenoticedthatthevastmajorityofthemhadataperedcrosssectionofthis
shape.Inordertoanalyseloadingonlesssymmetriccrosssections,wewouldneedtocalculate
thestressesinvariousplanes.Weavoidedthisissuebyusingshapeswithadegreeofradial
symmetry.
Toincreasethestabilityoftheplaneduringlandingandwhilestationary,wechoseto
angleourlandinggearsoutwardfromtheplanetogiveitawider,morestablebase.Wealso
consideredthatwemayangleourlandinggearsslightlyforwardtoincreasestabilityduring
landingatadownwardangle.Theseangleconsiderationsarealsopresentinpre-existing
landinggeardesigns.
Afterchoosingprovisionalcross-sections,weexaminedtheloadingconditionsforour
landinggear.Wechosetoseparateouranalysisintothreedifferentfailuremodes:impact,yield
duringbraking,andbuckling.
Westartedwiththeimpactloading.Thisfailuremodepresumesthatthestrainenergy
inthelandinggearsisequaltothedecreaseinkineticenergyoftheplaneasitsverticalvelocity
suddenlybecomeszero.Wecanthenreplacethegroundimpactwithanequivalentvertical
forcewhichcausesthissameincreaseofstrainenergyinthelandinggears.Thismeansthatwe
4
needtocreatealandinggearthatdoesnotfailinyieldunderthisequivalentverticalforce.
Afterdeterminingtheequivalentforce,thestresswascalculatedthroughcombinationofaxial
andbendingstresses.WealsoappliedCastigliano’sTheoremtofindtheverticaldeflection
duringimpactloadingtocheckthatitiswithinanacceptablerange.
Yieldinganalysisdealswiththeplanedeceleratingtoafullstopafterithaslandedon
theground.Duringdecelerationalongthelengthoftherunway,weconsidertheonlybraking
forcetobefrictionbetweenthebrakesandthewheel.Inthisanalysis,wewantedtoensure
thatthestressfromtheweightoftheplaneandtheforceduetothedecelerationdonotyield
thelandinggear.
Lastly,wecheckedtomakesuretherewillbenobucklingcausinguncontrolled
deflectioninthestructure.Thesystemoftheplane,landinggear,andgroundcanbemodeled
asafree-fixedcolumn,withaneffectivelengthof2L.Wefoundthecriticalbucklingloadfor
theseloadingandendconditions,andcheckedagainsttherealforcebeingapplied.
Analysis
Toperformourcalculations,wecreatedMATLABscriptstocheckourthreemodesof
failureforavarietyoflandinggeargeometries.Oncewefoundacceptabledimensionswhich
gaveappropriatesafetyfactors,wetransferredourdesignsintoSolidworksandANSYSfor
furtheranalysis.
MATLABScript
TheMATLABscriptstartsbyanalysingthegeometrybasedontheangleofattachment
andattack.Itthensolvesfortheequivalentloadintheshear(V)andaxial(P)directions.The
followingequationswereused,alongwithconservationoftotalenergy,todetermineour
impactloadPm.
5
Wetheninputourshapeparameters.Thisisaccomplishedbystartingwithabaseshape
andenlargingvariousdimensionsalongaspecifiedcurve.Westorethecross-sectionalareasas
elementsinavectorinMATLAB.Wecanspecifyahollowcross-sectionbyremovingascaled
versionofthecrosssectionateverypointbasedonaspecifiedwallthickness.Wefollowa
similarprocedureforthemomentsofinertia.
Wethengothroughandusetheforceandmomentinformationandfindthestressat
everypoint.Westorethisisinanewvector,forbothbendingandaxialstresses.Wesum
stressesandcomparethemaximumvaluesagainsttheyieldstrengthofthematerialto
computeafactorofsafety.
Wefoundthatreducingtheangleofattachmenthelpedlowerthestresses.Wetried
multiplecross-sectionsandeventuallysettledonalineartaperedcross-section.Ourstresses
werelowestat0˚butthiscreatedaveryunstableplane.Wesettledonanglesof5˚and10˚,to
givesomesemblanceofreality.Amorecomplextapermayreducestresses,howeveramore
complicatedshapepresentsmorechallengesinmanufacturing.
WecreatedtwootherMATLABscripts1tocheckforbuckling,andyieldduringbraking.
WealsousedCastigliano’stheoremtoexaminethemaximumdeflectionofthelandinggear.
Thesecalculationsconfirmedthatthelimitingfactorforourlandinggeardesignswasimpact
loading.
SolidworksDrawings
Toperformavisualinspectionofourprospectivedesignsandensurethatthe
geometrieslookreasonable,weconstructedmodelsofourlandinggearsinSolidworks.We
1
AllthreedescribedMATLABfilesareattachedtothereport
6
usedapre-existingCADmodeloftheDHC-2Beaverasabaseforourmodel.Imagesofour
designsareincludedbelow:
ANSYSAnalysis
WeusedabasicFEAsimulationtocheckthatourMATLABcodewasproducingrealistic
valuesforourimpactloadingcases.WeimportedourSolidworksmodelsintoANSYSthen
modeledourloadingbyapplyingouraxialandshearforcestooneendofthelandinggear.We
fixedtheotherend,asifitwererigidlyattachedtotheplane.
Whileourstresssimulationsdidprovidemaximamuchlargerthanexpected,these
maximaonlyoccurredatpointsofstressconcentrationthatwerecausedbytheboundary
conditions.Asaresultwelookedthemaximumstress,notattheartificialstressconcentrations.
Wecheckthedeflectionsbyaveragingthedeflectionsatthebottomofeachlandinggear.This
bestmatchesourmodelsinceweconsiderthedeformationofthecrosssectionasawhole.
ThevalueswefoundusingANSYSaretabulatedinourresultssection.Imagesshowing
oursimulationoutcomesforbothlandinggeardesignsarebelow.
7
ANSYSDeflectioninCircularLandingGear
ANSYSStressinCircularLandingGear
8
ANSYSDeflectioninEllipticalLandingGear
ANSYSStressinEllipticalLandingGear
9
Results
MaximumCombinedStress2
LocationofMaximumStress
MaximumVerticalDeflection
CriticalBucklingLoad
MATLABCalculationResults
CircularCrossSection
151MPa
685mm
2.44mm
179MN
EllipticalCrossSection
153MPa
460mm
2.28mm
170MN
MaximumCombinedStress2
LocationofMaximumStress
MaximumVerticalDeflection
ANSYSSimulationResults
CircularCrossSection
152MPa
~720mm
2.32mm
EllipticalCrossSection
157MPa
~430mm
2.42mm
YieldfromImpact
Buckling
YieldfromBraking
SafetyFactors
CircularCrossSection
1.829
15.15
398.1
EllipticalCrossSection
1.804
13.65
503.3
LandingGearDesignInfo
CircularCrossSection
467kg
5°
EllipticalCrossSection
577kg
10°
MassofSingleLandingGear
AngleofAttachment
2
NeglectingStressConcentrations
10
CircularLandingGearDesign
11
EllipticalLandingGearDesign
12
Conclusion
Usingouranalysismethods,wewereabletoproducetwodifferentlandinggears
capableofwithstandingthespecifiedloading.Weranafiniteelementanalysisalongsideour
MATLABsimulation,toincreaseconfidenceinourresults.Ourchoiceofhollowellipticaland
circularcrosssectionsprovedtobeeffectiveinresistingyieldandbucklingwhensized
appropriately.
However,thedimensionswefounddonotrepresentonesthatcouldbeimplementedin
afunctionaldesign.Ourmodelsareconsiderablylargerthanexistinglandinggeardesigns,
posingproblemsinaerodynamics,mounting,andmassmanufacturability.Wealsofoundthat
theangulationofourlandinggearsissmallandcouldleadtoplaneinstability.Inpractice,a
moreangledandsmallerlandinggearwouldbeimplementedonanaircraftofthissize.
Weassertthatthisdiscrepancybetweenourdesignedlandinggearsandengineering
expectation,isaresultofconservativesimplificationsinourmodel.Allenergydissipation
duringlandinghasbeenneglected.Inpractice,heat,vibration,anddeflection/rebound
contributesignificantlytoenergydissipation.Ifweweretoconsidertheseeffects,thelanding
gearcouldbedesignedwithamorereasonablesizeandangle.Unfortunately,thiskindof
analysisisoutsidethescopeofthiscourse.
Ifwewantedtofurtherthisdesign,wewouldaddseveralmoreconsiderations.Firstly,
wewouldlooktomodeltheenergydissipation.Wecouldthenexaminetheattachmentofthe
landinggearandtherolethisplaysinloadingandaerodynamics.Thismayleadtomore
complexcross-sectionsbeingdesirable.Lastly,wewouldlooktoexaminingotherfailuremodes
suchasfatiguefromrepeatedlandingsandthermalstressesfromchangingaltitudeand
environment.
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