雙立柱堆垛機設(shè)計【三維SW模型】【全套含12張CAD圖紙】
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AileronDesignChapter12DesignofControlSurfacesFrom:AircraftDesign:ASystemsEngineeringApproachMohammadSadraey792pagesSeptember2012,HardcoverWileyPublications12.4.1.IntroductionTheprimaryfunctionofanaileronisthelateral(i.e.roll)controlofanaircraft;however,italsoaffectsthedirectionalcontrol.Duetothisreason,theaileronandtherudderareusuallydesignedconcurrently.Lateralcontrolisgovernedprimarilythrougharollrate(P).Aileronisstructurallypartofthewing,andhastwopieces;eachlocatedonthetrailingedgeoftheouterportionofthewingleftandrightsections.Bothaileronsareoftenusedsymmetrically,hencetheirgeometriesareidentical.Aileroneffectivenessisameasureofhowgoodthedeflectedaileronisproducingthedesiredrollingmoment.Thegeneratedrollingmomentisafunctionofaileronsize,ailerondeflection,anditsdistancefromtheaircraftfuselagecenterline.Unlikerudderandelevatorwhicharedisplacementcontrol,theaileronisaratecontrol.Anychangeintheailerongeometryordeflectionwillchangetherollrate;whichsubsequentlyvariesconstantlytherollangle.Thedeflectionofanycontrolsurfaceincludingtheaileroninvolvesahingemoment.Thehingemomentsaretheaerodynamicmomentsthatmustbeovercometodeflectthecontrolsurfaces.Thehingemomentgovernsthemagnitudeofaugmentedpilotforcerequiredtomovethecorrespondingactuatortodeflectthecontrolsurface.Tominimizethesizeandthusthecostoftheactuationsystem,theaileronsshouldbedesignedsothatthecontrolforcesareaslowaspossible.Inthedesignprocessofanaileron,fourparametersneedtobedetermined.Theyare:1.aileronplanformarea(Sa);2.aileronchord/span(Ca/ba);3.maximumupanddownailerondeflection(dAmax);and4.locationofinneredgeoftheaileronalongthewingspan(bai).Figure12.10showstheailerongeometry.Asageneralguidance,thetypicalvaluesfortheseparametersareasfollows:Sa/S=0.05to0.1,ba/b=0.2-0.3,Ca/C=0.15-0.25,bai/b=0.6-0.8,anddAmax=30degrees.Basedonthisstatistics,about5to10percentofthewingareaisdevotedtotheaileron,theaileron-to-wing-chordratioisabout15to25percent,aileron-to-wing-spanratioisabout20-30percent,andtheinboardaileronspanisabout60to80percentofthewingspan.Table12.17illustratesthecharacteristicsofaileronofseveralaircraft.1bAba/2CaSa/2bai/2Aa.Top-viewofthewingandailerondAupdAdownb.Side-viewofthewingandaileron(SectionAA)Figure12.1.GeometryofaileronFactorsaffectingthedesignoftheaileronare:1.therequiredhingemoment,2.theaileroneffectiveness,3.aerodynamicandmassbalancing,4.flapgeometry,5.theaircraftstructure,and6.cost.Aileroneffectivenessisameasureofhoweffectivetheailerondeflectionisinproducingthedesiredrollingmoment.Aileroneffectivenessisafunctionofitssizeanditsdistancetoaircraftcenterofgravity.Hingemomentsarealsoimportantbecausetheyaretheaerodynamicmomentsthatmustbeovercometorotatetheaileron.Thehingemomentsgovernsthemagnitudeofforcerequiredofthepilottomovetheaileron.Therefore,greatcaremustbeusedindesigningtheaileronsothatthecontrolforcesarewithinacceptablelimitsforthepilots.Finally,aerodynamicandmassbalancingdealswithtechniquestovarythehingemomentssothatthestickforcestayswithinanacceptablerange.Handlingqualitiesdiscussedintheprevioussectiongovernthesefactors.Inthissection,principalsofailerondesign,designprocedure,governingequations,constraints,anddesignstepsaswellasafullysolvedexamplearepresented.12.4.2.PrinciplesofAileronDesignAbasiciteminthelistofaircraftperformancerequirementsisthemaneuverability.Aircraftmaneuverabilityisafunctionofenginethrust,aircraftmassmomentofinertia,andcontrolpower.Oneoftheprimarycontrolsurfaceswhichcausetheaircrafttobesteeredalongitsthree-dimensionalflightpath(i.e.maneuver)toitsspecifieddestinationisaileron.Aileronsarelikeplainflapsplacedatoutboardofthetrailingedgeofthewing.Rightaileronandleftaileronaredeflecteddifferentiallyandsimultaneouslytoproducea2NoAircraftTypemTO(kg)b(m)CA/CSpanratiodAmax(deg)bi/b/2bo/b/2updown1Cessna182LightGA1,406110.20.460.9520142CessnaCitationIIIBusinessjet9,97916.310.30.560.8912.512.53AirTractorAT-802Agriculture7,257180.360.40.9517134Gulfstream200Businessjet16,08017.70.220.60.8615155Fokker100AAirliner44,45028.080.240.60.9425206Boeing777-200Airliner247,20060.90.220.3210.76230107Airbus340-600Airliner368,00063.450.30.640.9225208AirbusA340-600Airliner368,00063.450.250.670.922525rollingmomentaboutx-axis.Therefore,themainroleofaileronistherollcontrol;howeveritwillaffectyawcontrolaswell.Rollcontrolisthefundamentalbasisforthedesignofaileron.Table12.1.CharacteristicsofaileronforseveralaircraftTable12.12(lateraldirectionalhandlingqualitiesrequirements)providessignificantcriteriatodesigntheaileron.Thistablespecifiesrequiredtimetobankanaircraftataspecifiedbankangle.Sincetheeffectivenessofcontrolsurfacesarethelowestintheslowerspeed,therollcontrolinatake-offorlandingoperationsistheflightphaseatwhichtheaileronissized.Thus,indesigningtheailerononemustconsideronlylevel1andmostcriticalphasesofflightthatisusuallyphaseB.BasedontheNewtonssecondlawforarotationalmotion,thesummationofallappliedmomentsisequaltothetimerateofchangeofangularmomentum.Ifthemassandthegeometryoftheobjet(i.e.vehicle)arefixed,thelawisreducedtoasimplerversion:Thesummationofallmomentsisequaltothemassmomentofinertiatimeoftheobjectabouttheaxisorrotationmultipliedbytherateofchangeofangularvelocity.Inthecaseofarollingmotion,thesummationofallrollingmoments(includingtheaircraftaerodynamicmoment)isequaltotheaircraftmassmomentofinertiaaboutx-axismultipliedbythetimerateofchange(/t)ofrollrate(P).Inboardaileron1Outboardaileron23Lcg=IxxPt(12.7)orP=LIxxcg(12.8)Generallyspeaking,therearetwoforcesinvolvedingeneratingtherollingmoment:1.Anincrementalchangeinwingliftduetoachangeinaileronangle,2.Aircraftrollingdragforceintheyzplane.Figure12.11illustratesthefront-viewofanaircraftwhereincrementalchangeintheliftduetoailerondeflection(DL)andincrementaldragduetotherollingspeedareshown.TheaircraftinFigure12.11isplanningtohaveapositiveroll,sotherightaileronisdeflectedupandleftailerondown(i.e.+dA).Thetotalaerodynamicrollingmomentinarollingmotionis:Mcgx=2DLyA-DDyD(12.9)Thefactor2hasbeenintroducedinthemomentduetolifttoaccountforbothleftandrightailerons.Thefactor2isnotconsideredfortherollingmomentduetorollingdragcalculation,sincetheaveragerollingdragwillbecomputedlater.TheparameteryListheaveragedistancebetweeneachaileronandthex-axis(i.e.aircraftcenterofgravity).TheparameteryDistheaveragedistancebetweenrollingdragcenterandthex-axis(i.e.aircraftcenterofgravity).Atypicallocationforthisdistanceisabout40%ofthewingsemispanfromrootchord.+dADDrightDLleftDLrightdyyyoyicgDDleftzyDyA+dAFrontviewFigure12.2.Incrementalchangeinliftanddragingeneratingarollingmotion4Inanaircraftwithshortwingspanandlargeaileron(e.g.fightersuchasGeneralDynamicsF-16FightingFalcon(Figure3.12)thedragdoesnotconsiderablyinfluenceontherollingspeed.However,inanaircraftwithalongwingspanandsmallaileron;suchasbomberBoeingB-52(Figures8.20and9.4);therollinginduceddragforcehasasignificanteffectontherollingspeed.Forinstance,theB-52takesabout10secondstohaveabankangleof45degreesatlowspeeds,whileforthecaseofafightersuchasF-16;ittakesonlyafractionofasecondforsuchroll.Owingtothefactthataileronsarelocatedatsomedistancefromthecenterofgravityoftheaircraft,incrementalliftforcegeneratedbyaileronsdeflectedup/down,createsarollingmoment.LA=2DLyA(12.10)However,theaerodynamicrollingmomentisgenerallymodeledasafunctionofwingarea(S),wingspan(b),dynamicpressure(q)as:LA=qSClbwhereClistherollingmomentcoefficientandthedynamicpressureis:(12.11)q=12rVT2(12.12)whereristheairdensityandVTistheaircrafttrueairspeed.TheparameterClisafunctionofaircraftconfiguration,sideslipangle,rudderdeflectionandailerondeflection.Inasymmetricaircraftwithnosideslipandnorudderdeflection,thiscoefficientislinearlymodeledas:Cl=CldAdA(12.13)TheparameterCldAisreferredtoastheaircraftrollingmoment-coefficient-due-to-aileron-deflectionderivativeandisalsocalledtheaileronrollcontrolpower.Theaircraftrollingdraginducedbytherollingspeedmaybemodeledas:DR=DDleft+DDright=12rVR2StotCDR(12.14)whereaircraftaverageCDRistheaircraftdragcoefficientinrollingmotion.Thiscoefficientisabout0.71.2whichincludesthedragcontributionofthefuselage.TheparameterStotisthesummationofwingplanformarea,horizontaltailplanformarea,andverticaltailplanformarea.Stot=Sw+Sht+Svt5(12.15)TheparameterVRistherollinglinearspeedinarollingmotionandisequaltorollrate(P)multipliedbyaveragedistancebetweenrollingdragcenter(SeeFigure12.11)alongy-axisandtheaircraftcenterofgravity:VR=PyD(12.16)Sinceallthreeliftingsurfaces(wing,horizontaltail,andverticaltail)arecontributingtotherollingdrag,theyDisinfact,theaverageofthreeaveragedistances.Thenon-dimensionalcontrolderivativeCldAisameasureoftherollcontrolpoweroftheaileron;itrepresentsthechangeinrollingmomentperunitchangeofailerondeflection.ThelargertheCldA,themoreeffectivetheaileronisatcreatingarollingmoment.Thiscontrolderivativemaybecalculatedusingmethodintroducedin19.However,anestimateoftherollcontrolpowerforanaileronispresentedinthisSectionbasedonasimplestripintegrationmethod.Theaerodynamicrollingmomentduetotheliftdistributionmaybewrittenincoefficientformas:DCl=DLAqSb=qCLACayAdyqSb=CLACayAdySb(12.17)ThesectionliftcoefficientCLAonthesectionscontainingtheaileronmaybewrittenasCLA=CLaa=CLadaddAdA=CLatadA(12.18)wheretaistheaileroneffectivenessparameterandisobtainedfromFigure12.12,giventheratiobetweenaileron-chordandwing-chord.Figure12.12isageneralrepresentativeofthecontrolsurfaceeffectiveness;itmaybeappliedtoaileron(ta),elevator(te),andrudder(tr).Thus,inFigure12.12,thesubscriptofparametertisdroppedtoindicatethegenerality.yCydy2CLawtdAyoIntegratingovertheregioncontainingtheaileronyieldsCl=Sbi(12.19)whereCLawhasbeencorrectedforthree-dimensionalflowandthefactor2isaddedtoaccountforthetwoailerons.Forthecalculationinthistechnique,thewingsectionalliftcurveslopeisassumedtobeconstantoverthewingspan.Therefore,theaileronsectionalliftcurveslopeisequaledtothewingsectionalliftcurveslope.Theparameteryirepresentstheinboardpositionofaileronwithrespecttothefuselagecenterline,andyotheoutboardpositionofaileronwithrespecttothefuselagecenterline(SeeFigure12.11).6TheaileronrollcontrolderivativecanbeobtainedbytakingthederivativewithrespecttoyCydydA:CldA=2CLawtyoSbi(12.20)t0.80.60.40.20.10.20.30.40.50.60.7Control-surface-to-lifting-surface-chordratioFigure12.3.ControlsurfaceangleofattackeffectivenessparameterThewingchord(C)asafunctionofy(alongspan)forataperedwingcanbeexpressedbythefollowingrelationship:C=Cr1+2yl-1b(12.21)whereCrdenotesthewingrootchord,andlisthewingtaperratio.SubstitutingthisrelationshipbackintotheexpressionforCldA(Equ.12.20)yields:1+2byydyCldA=2CLawtSbyoCyirl-1(12.22)or22l-13CldA=2CLawtCry2Sb+y3byiyo(12.23)ThisequationcanbeemployedtoestimaterollcontrolderivativeCldAusingtheailerongeometryandestimatingtfromFigure12.12.Gettingbacktoequation12.12,therearetwopiecesofailerons;eachatoneleftandrightsectionsofthewing.Thesetwopiecesmayhaveasimilarmagnitudeofdeflectionsorslightlydifferentdeflections,duetotheadverseyaw.Atanyrate,onlyonevaluewillentertothecalculationofrollingmoment.Thus,anaveragevalueofailerondeflectionwillbecalculatedasfollows:7dA=dAleft+dAright1(12.24)2ThesignofthisdAwilllaterbedeterminedbasedontheconventionintroducedearlier;apositivedAwillgenerateapositiverollingmoment.Substitutingequation12.9intoequation12.7yields:LA+DDyD=IxxPAsthenameimplies,Pisthetimerateofchangeofrollrate:(12.25)P=ddtP(12.26)Ontheotherhand,theangularvelocityaboutx-axis(P)isdefinedasthetimerateofchangeofbankangle:P=ddtF(12.27)Combiningequations12.26and12.27andremovingdtfrombothsides,resultsin:PdF=PdP(12.28)Assumingthattheaircraftisinitiallyatalevelcruisingflight(i.e.Po=0,fo=0),bothsidesmaybeintegratedas:fPdF=0PssPdP0(12.29)Thus,thebankangleduetoarollingmotionisobtainedas:F=dPPPwherePisobtainedfromequation12.25.Thus:(12.30)PssF=0IxxPLA+DDyDdP(12.31)Bothaerodynamicrollingmomentandaircraftdragduetorollingmotionarefunctionsofrollrate.Pluggingthesetwomomentsintoequation12.31yields:r(PyD)(Sw+Sht+Svt)CDRyDF1=Pss0qSClb+12IxxP2dP(12.32)Theaircraftrateofrollrateresponsetotheailerondeflectionhastwodistinctstates:1.Atransientstate,2.Asteadystate(SeeFigure12.13).Theintegrallimitfortherollrate(P)inequation12.32isfromaninitialtrimpointofnorollrate(i.e.winglevelandPo=0)toasteady-statevalueofrollrate(Pss).Sincetheaileronisfeaturedasaratecontrol,thedeflectionofaileronwilleventuallyresultinasteady-staterollrate(Figure12.13).Thus,unlesstheaileronsarereturnedtotheinitialzerodeflection,theaircraftwillnotstopataspecificbankangle.Table12.12definestherollraterequirementsintermsofthedesired8bankangle(F2)forthedurationoftseconds.Theequation12.32hasaclosed-formsolutionandcanbesolvedtodeterminethebankangle(F1)whentherollratereachesitssteady-statevalue.Rollrate(deg/sec)Psstsst2Time(sec)Figure12.4.AircraftrollrateresponsetoanailerondeflectionBankangle(deg)F2F1t1t2Time(sec)Figure12.5.AircraftbankangleresponsetoanailerondeflectionWhentheaircrafthasasteady-state(Pss)rollrate,thenewbankangle(Figure12.14)afterDtseconds(i.e.t2-tss)isreadilyobtainedbythefollowinglinearrelationship:F2=Pss(t2-tss)+F1(12.33)Duetothefactthattheaircraftdragduetorollrateisnotconstantandisincreasedwithanincreasetotherollrate;therollingmotionisnotlinear.Thisimplies9thatthevariationoftherollrateisnotlinear;andthereisanangularrotationaboutx-axis.However,untiltheresistingmomentagainsttherollingmotionisequaltotheailerongeneratedaerodynamicrollingmoment;theaircraftwillexperienceanangularaccelerationaboutx-axis.Soonafterthetworollingmomentsareequal,theaircraftwillcontinuetorollwithaconstantrollrate(Pss).Thesteady-statevalueforrollrate(Pss)isobtainedbyconsideringthatthefactthatwhentheaircraftisrollingwithaconstantrollrate,theailerongeneratedaerodynamicrollingmomentisequaltothemomentofaircraftdragintherollingmotion.LA=DDRyD(12.34)Combiningequations12.14,12.15,and12.16,theaircraftdragduetotherollingmotionisobtainedas:DR=12r(PyD)2(Sw+Sht+Svt)CDR(12.35)Insertingtheequation12.35intoequation12.34yields:LA=12r(PyD)2(Sw+Sht+Svt)CDRyD(12.36)Solvingforthesteady-staterollrate(Pss)resultsin:Pss=2LAr(Sw+Sht+Svt)CDRyD3(12.37)Ontheotherhand,theequation12.32issimplyadefinitemathematicalintegration.Thisintegrationmaybemodeledasthefollowinggeneralintegrationproblem:y=k2xdxx+a2Accordingto20,thereisaclosedformsolutiontosuchintegrationasfollows:(12.38)y=k12ln(x2+a2)(12.39)Theparameterskandaareobtainedbycomparingequation12.38withequation12.32.ry(Sw+Sht+Svt)CDRk=3D2Ixx(12.40)a2=(12.41)(Sw+Sht+Svt)CDyDV2SClb3RHence,thesolutiontotheintegrationinequation12.32isdeterminedas:11lnP2+3F1=IxxryD3(Sw+Sht+Svt)CDRPssV2SClb(Sw+Sht+Svt)CDRyD0(12.42)Applyingthelimits(from0toPss)tothesolutionresultsin:ry(Sw+Sht+Svt)CDRF1=3DIxx2ln(Pss)(12.43)Recallthatwearelookingtodetermineaileronrollcontrolpower.Inanotherword,itisdesiredtoobtainhowlongittakes(t2)tobanktoadesiredbankanglewhenaileronsaredeflected.Thisdurationtendstohavetwoparts:1.Theduration(tss
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