PRIUS動(dòng)力系統(tǒng)sinmulink建模

2IntroductionForthisproject,weexaminedthetransmissiondescribedinPatentNo.6837816foruseinahybridToyotaPrius.Specifically,welookedatmodifyingthenumberofgearteeth,theshiftsequence,andtheshifttimeinordertooptimizethetimetoacceleratefrom0to60mphusingthetransmissionshowninFigure2.1.Figure2.1:DiagramofTransmissionThetransmissionisdrivenbyaninternalcombustionengine(20)andan electric motor (30) with shaft 50 as the output. There are twoplanetarygeartrainsandfourclutches(61,62,63,and64).Wearegivensixteendifferentoperatingmodes,whichinvolvevariousclutchconfigurations.Table2.1showsallofthepossibleoperationalmodes.Table2.1:OperationalModesClutchesMotorEngagedOperatingNo.OperationalMode61626364Condition1Motor-OnlyXMotor2Power1XXMotor3Power2XXMotor4Power3XXMotor5EngineCharge1XXGenerator6EngineCharge2XXGenerator7EngineCharge3XXGenerator8ContinuousVariableXGeneratorTransmission/Charging9Engine-Only1XXFreeWheeling10Engine-Only2XXFreeWheeling11Engine-Only3XXFreeWheeling12Engine-Only4XXStationary13RegenerativeBreakingXGenerator014RegenerativeBreakingXXGenerator115RegenerativeBreakingXXGenerator216RegenerativeBreakingXXGenerator33ProblemStatementTheprojectobjectivewastooptimizethetimerequiredforaToyotaPriustoacceleratefrom0to60mphusingthetransmissiondescribed.Therearethreeparametersusedfortheoptimization:thenumberofteethofeachgear,theshiftsequence,andtheshifttiming.Table 3.1 lists the pertinent parameters as assigned by the Rose-HulmanMechanicalEngineeringDepartmentforthisproject.Table3.1:KnownParametersParameterGivenValuesProjectedCross-SectionalS27.7ft2AreaVehicleWeightW3160lbfDragCoefficientcd0.26EngineTorqueRelationshipTengine(0.011nengine25)ftlbf(600to5000rpm)MotorTorqueRelationshipTmotor(0.037nmotor220)ftlbf(0to6000rpm)WheelRadiusrwheel1ftFinalGearReductionGRfinal4.52:1RollingResistanceCoefficientCr0.005AirDensity0.00237slugsft3In order for the transmission to fit the size ofthe Prius, constraintswere imposed on the number of gear teeth to limit the sizes of thegears.Thenumberofteethontheringgearwasnomorethan150teeth.Asaminimum,thenumberofteethoneithertheplanetgearorthe sun gear was noless than 14teeth. Using the guidelines forgeartraindesign,theratiosofgearteethwerenogreaterthan10:1.Forthepurposeofthisproject,wemadeafewadditionalassumptions.Forsimplicity,weassumedtheclutchingchangestobeinstantaneous.Wealsoassumedthatthecarwheelswererollingwithoutslip.4DesignCalculationsIn order toanalyze the problem, we created afree-body diagram ofthe Toyota Prius. We made the assumption that the car could betreatedasapointmass.Thefree-bodydiagramisshowninFigure4.1.N yFDrag

DirectionofmotionfrollFDriveWFigure4.1:Free-BodyDiagramofCarFromthisdiagram,weappliedconservationoflinearmomentum,thatdPis Fy,inthey-directiontoobtain:0 N W (1)where Nisthe normal force inlbf and Wisthe weight inlbf. Whensimplified,theequationbecomesNW.(2)Wealsoappliedconservationoflinearmomentum,thatisdP,inFxdtthex-directiontoobtain:mdvcarFDriveFDragfroll(3)dtwhereFDriveisthedrivingforceofthecarinlbf,FDragisthedragforceinlbf,andfrollistherollingresistanceforceinlbf.Forthisproject,weassumedthatthedragforcecouldbemodeledasfollows:FDrag

1cd2

vcar

2

S

(4)where

cd

istheunitlessdragcoefficient,

isthedensityin

slugsft3

,

vcar

isthe

velocity

in

ft

,and

Sisthe

projected

cross-sectional

area

in

ft2

.sWemodeledtherollingresistancewiththefollowingequation:froll

Cr

W

(5)where Cris theweight of thewithoutslip.

unitlesscarin

lbf

coefficient. This

ofrollingresistanceandassumesthatthevehicle

Wistheis rollingTofindthedrivingforce,wecreatedafree-bodydiagramofthewheel.Thefree-bodydiagramofthewheelisshowninFigure4.2.TDriveWFDriveNFigure4.2:Free-BodyDiagramofCarWheelWethenappliedconservationofangularmomentum,thatisMcenterI,tothesystemabovetogetFDriverwheelTDriveI(6)whereFDriveisthedrivingforceinlbf,rwheelistheradiusofthecarwheelinft,andTDriveisthedrivetorqueinftlbf.Inthiscase,weassumedthatIwasnegligiblesincethemassofthewheelissignificantlylessthanthemassoftheentirecar.Thus,wesimplifiedtheequationtoFDriverwheelTDrive.(7)FurthersimplificationleadstotheequationFDriveTDrive.(8)rwheelThedrivingtorqueisgovernedbythetorqueofthemotorandthegearreductionsaccordingtothefollowingequation:TDrive(TengineGRengineTmotorGRmotor)GRfinal(9)whereGRengineisthegearreductionoftheengine,GRmotoristhegearreductionofthemotor,andGRfinalisthefinalgearreduction.Substitutingequation(9)intoequation(8)wegetFDrive(TengineGRengineTmotorGRmotor)GRfinal.(10)rwheelInordertofindTout,weappliedconservationofenergyandsimplifiedtoget:PinPoutTininToutoutTmotormotorTengineengineToutout(11)ToutTmotormotorTengineengineoutToutTmotorGRmotorTengineGRengine.Usingalloftheseequations,wederivedasingleequationforthemotionofthecar:dvcar(TmotorGRmotorTengineGRengine)GRfinal12W.(12)mrwheelcdvcarSCrdt2In order to limit the possible clutch configurations, weanalyzethefirstfourmodesonly.Motor-only,Power1,Power2,andPower3arethemodeswherethetorqueofthemotorisaddedtothetorque of the engine. For other modes, the transmission

chose toacts as ageneratororbrakingmechanismorremainsstationary.Thesemodesdonotprovideoptimalaccelerationcapabilities,sowechosetoneglectthem.Forthefourmodesweanalyzed,wecalculatedtheplanetarygearratiosusingthetablesshowninAppendixA.TheresultingratiosareshowninTable4.1.Table4.1:PlanetaryGearAnalysisModesMotorSpeedEngineSpeed1:MotorOnlyin,motor1N202in,engine0outN201outin,motor2:Power1outin,motor3:Power2out

N202in,engine1N201outN202in,engine1N201out

N2021N201N101N101N202N102 N102N201N101N102in,motor4:Power3out5FinalDesign

1

in,engineout

1TheequationsderivedinthecalculationssectionweremodeledusingMATLABandSimulink(seeAppendixB)inordertonumericallyevaluatetheperformanceofthetransmission.Thisenabledustovaryeachoftheinputstotestdifferentstatesandconfigurationsofthetransmission.Bygraphicallyexaminingeachoutput,wewereabletoarriveatcertainconclusionsbasedontheresultingoutcome.Thismethodofguessandcheckinfacthelpedusrealizecertainfundamentalpropertiesoftheengine,whichwemaynothaveotherwiseobserved.ForinstancewhenPowerMode2wasengaged,itwasobservedthatforwhatevershiftperioditwasengagedfor,weweregettinglessperformancethanwithPowerMode3.ThisledustotryusingagearshiftsequencethatactuallyomittedPowerMode2fromthesequence.Intheend,wewereabletogetdesirableresultsforour0to60mphtime.After analyzing many different configurations, we arrived at oneparticularsetup,whichseemedtobeourbestoption.Althoughtherewas no way to test every possible combination by the methods weused, the configuration

below

seemed

to

be

best

we could

achievebasedonourjudgments.Table 5.1: GearSequenceN101N102N103N201N202N203Motor-OnlyTimePower1TimePower2TimePower3Time

Teeth and65teeth125teeth30teeth120teeth150teeth15teeth0.30sec2.68sec0.00sec5.20sec

Clutch6ResultsByimplementingthevaluesinTable5.1intheSimulinkmodel,theoptimal0to60mphtimewas8.18seconds.AgraphicalrepresentationfortheperformanceofourcarduringthisaccelerationperiodcanbeseeninFigure6.1.Table6.1liststheinitialandfinalvelocitiesofthecarforeachclutchsequence.700-60MPH6050HPM40nytcoev30raC20100123456789100Time[s]Figure6.1:CarVelocityasaFunctionofTimeTable6.1:ClutchSequenceCarVelocityModeInitialVelocityFinalVelocityMotor-Only0mph4.38mphPower14.38mph35.13mphPower335.13mph60.02mph7Conclusions&RecommendationsOurresultofan8.18second0to60mphisanimprovementfromthecurrenttransmissionmodelusedintheToyotaPrius.Thereareafewreasonsthatourtimediffersfromthecurrentmodel.Ourestimatefortherollingresistancewaslenientandassumedthecarrolledwithoutslip.Inactuality,therewouldbesomeslipcausingadifferentapproximationfortherollingresistance.Anotherreasonourvaluediffersisthatwetreatedtheshifttimeasinstantaneous.Togetabettermodeloftheactualcar,weshouldhaveaddedthetimestoshiftbetweenclutchconfigurations.Wealsoassumedthecarcouldbetreatedasapointmass.Themodelcouldbeimprovedbyredoingtheconservationoflinearmomentumcalculationsforarearwheeldrivecar.Themodelcouldalsobeimprovedbyincorporatingconservationofangularmomentum.Despitealloftheseapparentshortcomings,webelievethistransmissiondesignisareliableandworthwhilerepresentationoftheactualhybridtransmission.8ReferencesTsai,Lung-Wen.;Schultz,GregoryA., MotorIntegratedParallelHybridTransmission .US6,837,816.(4January2005).Tsai,

L.,

Schultz,

G. and

Higuchi,

N.,

“ANovel

Parallel

HybridTransmission,

”Proceedings

of

ASME

Design

Engineering

TechnicalConferences

,2000.AppendixA:PlanetaryGearAnalysisModeNo.1:MotorOnlyGeargeararmgear/armSun201N202inoutoutN201Planet203N202outoutN203Ring2020outoutRatio:in1N202,whereinmotorandengine0outN201ModeNo.2:Power1Geargeararmgear/armSun201N202inoutoutN201Planet203N202outoutN203Ring2020outoutRatio:in1N202,whereinmotorengineoutN201ModeNo.3:Power2Geargeararmgear/armSun201N202inoutoutN201Planet203N202outoutN203Ring2020outout

RatioN201N203N203N202RatioN201N203N203N202RatioN201N203N203N202in,motorRatio:outGearSun101Planet 103Ring 102

N202N201gearoutout

armininin

gear/armRatiooutinN101N101N103outinN103N103N101outinN102N102in,engineRatio:out

1

N101N1021

N101 N202N102 N201NN102ModeNo.4:Power3GeargeararmSun101ininPlanet103inRing102outinRatio:in1,whereinmotorengineout

gear/armRatio0N101N1030N1030 N102AppendixB:SimulinkModelsMotorOnlyModePower1ModePower2ModePower3ModeAppendixC:MatlabCode%**************************************************************************%ProgramDescription:%Thefollowingprogramcalculatesthetimeittakesforacartoaccelerate%from0to60MPH.Theprogramalsooutputstheinitialandfinal%velocitiesduringeachoperationalmodeforthetransmission.%%Input: N_101-numberofteethonsungear101N_102-numberofteethonringgear102N_103-numberofteethonplanetgear103N_201-numberofteethonsungear201N_202-numberofteethonringgear202N_203-numberofteethonplanetgear203t_final_mo-lengthoftimespentinmotor-onlymode[s]t_final_p1-lengthoftimespentinpower1mode[s]t_final_p2-lengthoftimespentinpower2mode[s]t_final_p3-lengthoftimespentinpower3mode[s]%Output:zeroSixtyTime-timeforcartoacceleratefrom0to60mph[s]velocity_final_mo-velocityatendofmotoronlyinterval[mph]velocity_final_p1-velocityatendofpower1interval[mph]velocity_final_p2-velocityatendofpower2interval[mph]velocity_final_p3-velocityatendofpower3interval[mph]%%**************************************************************************%numberofteethoneachgearinthetransmission(variedinputs)N_101=65;N_102=125;N_103=(N_102-N_101)/2;N_201=122;N_202=150;N_203=(N_202-N_201)/2;%**************************************************************************%MOTORONLYMODEt_initial_mo=0;t_final_mo=0.3;%lengthoftimeinmotor-onlymode(variedinput)v_0_mo=0;%velocityatstartofmotoronlymode[mph]%runsSimulinkmodelformotoronlymodesim('motor_only',[t_initial_mo,t_final_mo])t_mo=time;velocity_mo=velocity_out;%plotsthemotoronlymodeoverprescribedlengthoftime%figure(1)%plot(t_mo,velocity_mo)%grid%xlabel('Time[s]')%ylabel('CarvelocityinMPH')%title('MotorOnlyMode')%velocityatbeginningofinterval[mph]velocity_initial_mo=velocity_mo(1)%velocityatendofinterval[mph]velocity_final_mo=velocity_mo((t_final_mo-t_initial_mo)*100+1)%**************************************************************************%**************************************************************************%POWERONEMODEt_initial_p1=0;t_final_p1=2.72;%lengthoftimeinpower1mode(variedinput)v_0_p1=velocity_final_mo*5280/3600;%velocityatstartofpower1mode[mph]%runsSimulinkmodelforpower1modesim('power_one',[t_initial_p1,t_final_p1])t_p1=time;velocity_p1=velocity_out;%plotsthepower1modeoverprescribedlengthoftime%figure(2)%plot(t_p1,velocity_p1)%grid%xlabel('Time[s]')%ylabel('CarvelocityinMPH')%title('PowerOneMode')%velocityatbeginningofinterval[mph]velocity_initial_p1=velocity_p1(1)%velocityatendofinterval[mph]velocity_final_p1=velocity_p1((t_final_p1-t_initial_p1)*100+1)%**************************************************************************%**************************************************************************%%POWERTWOMODEt_initial_p2=0;t_final_p2=0;%lengthoftimeinpower2mode(variedinput)v_0_p2=velocity_final_p1*5280/3600;%velocityatstartofpower2mode[mph]%runsSimulinkmodelforpower2modesim('power_two',[t_initial_p2,t_final_p2])t_p2=time;velocity_p2=velocity_out;%plotsthepower2modeoverprescribedlengthoftime%figure(3)%plot(t_p2,velocity_p2)%grid%xlabel('Time[s]')%ylabel('CarvelocityinMPH')%title('PowerTwoMode')%velocityatbeginningofinterval[mph]velocity_initial_p2=velocity_p2(1)%velocityatendofinterval[mph]velocity_final_p2=velocity_p2((t_final_p2-t_initial_p2)*100+1)%**************************************************************************%**************************************************************************%POWERTHREEMODEt_initial_p3=0;t_final_p3=6;%lengthoftimeinpower3mode(variedinput)v_0_p3=velocity_final_p2*5280/3600;%velocityatstartofpower3mode[mph]%runsSimulinkmodelforpower3modesim('power_three',[t_initial_p3,t_final_p3])t_p3=time;velocity_p3=velocity_out;%plotsthepower3modeoverprescribed