PRIUS动力系统sinmulink建模

1、2IntroductionForthisproject,weexaminedthetransmissiondescribedinPatentNo.6837816foruseinahybridToyotaPrius.Specifically,welookedatmodifyingthenumberofgearteeth,theshiftsequence,andtheshifttimeinordertooptimizethetimetoacceleratefrom0to60mphusingthetransmissionshowninFigure2.1.VFigure2.1:DiagramofTra

2、nsmissionThetransmissionisdrivenbyaninternalcombustionengine(20)andanelectricmotor(30)withshaft50astheoutput.Therearetwoplanetarygeartrainsandfourclutches(61,62,63,and64).Wearegivensixteendifferentoperatingmodes,whichinvolvevariousclutchconfigurations.Table2.1showsallofthepossibleoperationalmodes.Ta

3、ble2.1:OperationalModesClutchesEngagedMotorOperatingNo.OperationalMode61626364Condition1Motor-OnlyXMotor2Power1XXMotor3Power2XXMotor4Power3XXMotor5EngineCharge1XXGenerator6EngineCharge2XXGenerator7EngineCharge3XXGenerator8ContinuousVariableTransmission/ChargingXGenerator9Engine-Only1XXFreeWheeling10

4、Engine-Only2XXFreeWheeling11Engine-Only3XXFreeWheeling12Engine-Only4XXStationary13RegenerativeBreaking0XGenerator14RegenerativeBreaking1XXGenerator15RegenerativeBreaking2XXGenerator16RegenerativeBreaking3XXGenerator3ProblemStatementTheprojectobjectivewastooptimizethetimerequiredforaToyotaPriustoacce

5、leratefrom0to60mphusingthetransmissiondescribed.Therearethreeparametersusedfortheoptimization:thenumberofteethofeachgear,theshiftsequence,andtheshifttiming.Table3.1liststhepertinentparametersasassignedbytheRose-HulmanMechanicalEngineeringDepartmentforthisproject.Table3.1:KnownParametersParameterGive

6、nValuesProjectedCross-SectionalAreaS27.7ft2VehicleWeightW3160lbfDragCoefficientcd0.26EngineTorqueRelationship(600to5000rpm)Tengine(0.011engine25)ftlbfMotorTorqueRelationship(0to6000rpm)Tmotor(0.037nmotor220)ftlbfWheelRadiusrwheel1ftFinalGearReductionGRfinal4.52:1RollingResistanceCoefficientCr0.005Ai

7、rDensityCccccrslugs0.00237一,ft3InorderforthetransmissiontofitthesizeofthePrius,constraintswereimposedonthenumberofgearteethtolimitthesizesofthegears.Thenumberofteethontheringgearwasnomorethan150teeth.Asaminimum,thenumberofteethoneithertheplanetgearorthesungearwasnolessthan14teeth.Usingtheguidelinesf

8、orgeartraindesign,theratiosofgearteethwerenogreaterthan10:1.Forthepurposeofthisproject,wemadeafewadditionalassumptions.Forsimplicity,weassumedtheclutchingchangestobeinstantaneous.Wealsoassumedthatthecarwheelswererollingwithoutslip.4DesignCalculationsInordertoanalyzetheproblem,wecreatedafree-bodydiag

9、ramoftheToyotaPrius.Wemadetheassumptionthatthecarcouldbetreatedasapointmass.Thefree-bodydiagramisshowninFigure4.1.“nyDirectionofomotiont>FDrag4frollFDriveWFigure 4.1: Free-BodyDiagramofCarFromthisdiagram,weappliedconservationoflinearmomentum,that.dPis-Fy,inthey-directiontoobtain:0NW(1)whereNisthe

10、normalforceinlbfandWistheweightinlbf.Whensimplified,theequationbecomesWealsoappliedconservationoflinearmomentum,thatisdPdtFx,inthex-directiontoobtain:FDriveFDragfrollwhereFDriveisthedrivingforceofthecarinlbf,FDragisthedragforceinlbf,andfrollistherollingresistanceforceinlbf.Forthisproject,weassumedth

11、atthedragforcecouldbemodeledasfollows:F12SFDrag2cdvcarSwhere cd is the unitless drag coefficient,is the density inslugs .-ft 3 , vcar isarea in ft2.thevelocityin-ft,andSistheprojectedcross-sectionalsWemodeledtherollingresistancewiththefollowingequation:(5)froll&Wwhere Cr is the unitless coeffici

12、ent of rolling resistanceandW is theis rollingweightofthecarinlbf.Thisassumesthatthevehiclewithoutslip.Tofindthedrivingforce,wecreatedafree-bodydiagramofthewheel.Thefree-bodydiagramofthewheelisshowninFigure4.2.TdFigure 4.2: Free-BodyDiagramofCarWheelWe thenapplied conservation of angularmomentum, th

13、at isM center I,to the system above to getFDrive rwheelTDriveI(6)where F Driveis the driving force in lbf ,rwheelistheradius of the carwheel in ft, and TDrive is the drive torqueinftlbf .In thiscase, weassumed that I was negligible sincethemassof thewheel issignificantlylessthanthemassoftheentirecar

14、.Thus,wesimplifiedtheequationtoFDriverwheelTDrive.FurthersimplificationleadstotheequationF DriveTDriverwheel(8)The driving torque is governed bythe torque of the motorand thegearreductionsaccordingtothefollowingequation:TDrive(TengineGRengineTmotorGRmotor)GRfinalwhereGRengine is the gear reduction o

15、f the engine, GRmotoristhe gearreduction.FDrive(Tengine GRengineTmotorGRmotor ) GRfinalrwheel(10)reductionofthemotor,andGRfinalisthefinalgearSubstitutingequation(9)intoequation(8)wegetInordertofindTout,weappliedconservationofenergyandsimplifiedtoget:PinPoutTininToutoutTmotormotorTengineengineToutout

16、ToutTmotormotorTengineengineoutToutTmotorGRmotorTengineGRengine.(11)Using all of theseequations,wederivedasingleequationforthemotionofthecar:dvcarmdt(T motorGRmotorT engine GRengine) GRfinalrwheel12 GdVcar2 S CrW. (12)In order tolimit the possible clutch configurations, wechose toanalyzethefirstfour

17、modesonly.Motor-only,Power1,Power2,andPower3arethemodeswherethetorqueofthemotorisaddedtotheacts as atorqueoftheengine.Forothermodes,thetransmissiongeneratororbrakingmechanismorremainsstationary.Thesemodesdonotprovideoptimalaccelerationcapabilities,sowechosetoneglectthem.Forthefourmodesweanalyzed,wec

18、alculatedtheplanetarygearratiosusingthetablesshowninAppendixA.TheresultingratiosareshowninTable4.1.Table4.1:PlanetaryGearAnalysisModesMotorSpeedEngineSpeed1:MotorOnlyin,motorN202outN201in,engine0outin,motor/N202in,engine/N2021”乙2:Power111MoutN201MoutIN201NN101N101N202in,motor/N202in,engineN102N102N2

19、013:Power21MMoutN201out1N101N102in,motor,in,engine)4:Power311outout5FinalDesignTheequationsderivedinthecalculationssectionweremodeledusingMATLABandSimulink(seeAppendixB)inordertonumericallyevaluatetheperformanceofthetransmission.Thisenabledustovaryeachoftheinputstotestdifferentstatesandconfiguration

20、softhetransmission.Bygraphicallyexaminingeachoutput,wewereabletoarriveatcertainconclusionsbasedontheresultingoutcome.Thismethodofguessandcheckinfacthelpedusrealizecertainfundamentalpropertiesoftheengine,whichwemaynothaveotherwiseobserved.ForinstancewhenPowerMode2wasengaged,itwasobservedthatforwhatev

21、ershiftperioditwasengagedfor,weweregettinglessperformancethanwithPowerMode3.ThisledustotryusingagearshiftsequencethatactuallyomittedPowerMode2fromthesequence.Intheend,wewereabletogetdesirableresultsforour0to60mphtime.Afteranalyzingmanydifferentconfigurations,wearrivedatoneparticularsetup,whichseemed

22、tobeourbestoption.Althoughtherewasnowaytotesteverypossiblecombinationbythemethodsweused,theconfigurationbelowseemedtobebestwecouldachievebasedonourjudgments.Table5.1:GearTeethandClutchSequenceN10165teethN102125teethN10330teethN201120teethN202150teethN20315teethMotor-OnlyTime0.30secPower1Time2.68secP

23、ower2Time0.00secPower3Time5.20sec6ResultsByimplementingthevaluesinTable5.1intheSimulinkmodel,theoptimal0to60mphtimewas8.18seconds.AgraphicalrepresentationfortheperformanceofourcarduringthisaccelerationperiodcanbeseeninFigure6.1.Table6.1liststheinitialandfinalvelocitiesofthecarforeachclutchsequence.0

24、-60MPHFigure6.1:CarVelocityasaFunctionofTimeTable6.1:ClutchSequenceCarVelocityModeInitialVelocityFinalVelocityMotor-Only0mph4.38mphPower14.38mph35.13mphPower335.13mph60.02mph7 Conclusions&RecommendationsOurresultofan8.18second0to60mphisanimprovementfromthecurrenttransmissionmodelusedintheToyotaP

25、rius.Thereareafewreasonsthatourtimediffersfromthecurrentmodel.Ourestimatefortherollingresistancewaslenientandassumedthecarrolledwithoutslip.Inactuality,therewouldbesomeslipcausingadifferentapproximationfortherollingresistance.Anotherreasonourvaluediffersisthatwetreatedtheshifttimeasinstantaneous.Tog

26、etabettermodeloftheactualcar,weshouldhaveaddedthetimestoshiftbetweenclutchconfigurations.Wealsoassumedthecarcouldbetreatedasapointmass.Themodelcouldbeimprovedbyredoingtheconservationoflinearmomentumcalculationsforarearwheeldrivecar.Themodelcouldalsobeimprovedbyincorporatingconservationofangularmomen

27、tum.Despitealloftheseapparentshortcomings,webelievethistransmissiondesignisareliableandworthwhilerepresentationoftheactualhybridtransmission.8 ReferencesMotor Integrated Parallel HybridTsai,Lung-Wen.;Schultz,GregoryA.,Transmission.US6,837,816.(4January2005).Tsai,L.,Schultz,G.andHiguchi,N.,“ANovelPar

28、allelHybridTransmission,”ProceedingsofASMEDesignEngineeringTechnicalConferences,2000.AppendixA:PlanetaryGearAnalysisModeNo.1:MotorOnlyGeargeararmgear/armRatioSun201inoutN202outK1N201N201N203Planet203outN202outzN203N203N202Ring2020outoutRatiO：-Jn-1N02,Whereinmotorandengine0outN201ModeNo.2:Power1Gearg

29、eararmgear/armRatioSun201inoutN202outK1N201N201N203Planet203outN202outN203N203N202Ring2020outoutRatio:31N02here.1,whereinmotorengineoutN201ModeNo.3:Power2Geargeararmgear/armRatioSun201inoutN202outK1N201N201N203Planet203outN202outN203N203N202Ring2020outoutRatio:m01N02outN201Geargeararmgear/armRatioSu

30、n101outinoutinN101N103Planet103inN101outinN103N103N102Ring102outinN101outinN1021N101N101N202Ratio:in,engineN102N102N201,N101out1101N102ModeNo.4:Power3Geargeararmgear/armRatioSun101inin0nioiN103Planet103in0N103N102Ring102outin0Ratio:-n-1,whereoutinmotorengineAppendixB:SimulinkModelsMotorOnlyModenwo净即

31、闻3HTd.|.ii=，in/rrilHu*C*3HollfeA1IV1rrH»F!M-k£i.mi|-r#ihaUMidi-1.GA|hM'*rp".mr门0LI占Fdptard1里="*Iri|ai门。昌»百福Qu_3国营1勒叶*%ProgramDescription:%Thefollowingprogramcalculatesthetimeittakesforacartoaccelerate%from0to60MPH.Theprogramalsooutputstheinitialandfinal%velocitiesduringe

32、achoperationalmodeforthetransmission.%Input:N_101-numberofteethonsungear101%N_102-numberofteethonringgear102%N_103-numberofteethonplanetgear103%N_201-numberofteethonsungear201%N_202-numberofteethonringgear202%N_203-numberofteethonplanetgear203%t_final_mo-lengthoftimespentinmotor-onlymodes%t_final_p1

33、-lengthoftimespentinpower1modes%t_final_p2-lengthoftimespentinpower2modes%t_final_p3-lengthoftimespentinpower3modes%Output:zeroSixtyTime-timeforcartoacceleratefrom0to60mphs%velocity_final_mo-velocityatendofmotoronlyintervalmph%velocity_final_p1-velocityatendofpower1intervalmph%velocity_final_p2-velo

34、cityatendofpower2intervalmph%velocity_final_p3-velocityatendofpower3intervalmph%*%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(varie

35、dinput)v_0_mo=0;%velocityatstartofmotoronlymodemph%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('Times')%ylabel('Carveloci

36、tyinMPH')%title('MotorOnlyMode')%velocityatbeginningofintervalmphvelocity_initial_mo=velocity_mo(1)%velocityatendofintervalmphvelocity_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

37、_final_mo*5280/3600;%velocityatstartofpower1modemph%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('Times')%ylabel('CarvelocityinMP

38、H')%title('PowerOneMode')%velocityatbeginningofintervalmphvelocity_initial_p1=velocity_p1(1)%velocityatendofintervalmphvelocity_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*

39、5280/3600;%velocityatstartofpower2modemph%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('Times')%ylabel('CarvelocityinMPH')%ti

40、tle('PowerTwoMode')%velocityatbeginningofintervalmphvelocity_initial_p2=velocity_p2(1)%velocityatendofintervalmphvelocity_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*5280/360

41、0;%velocityatstartofpower3modemph%runsSimulinkmodelforpower3modesim('power_three',t_initial_p3,t_final_p3)t_p3=time;velocity_p3=velocity_out;%plotsthepower3modeoverprescribedlengthoftime%figure(4)%plot(t_p3,velocity_p3)%grid%xlabel('Times')%ylabel('CarvelocityinMPH')%title('PowerThreeMode')%velocityatbeginningofintervalmphvelocity_initial_p3=velocity_p3(1)%velocityatendofi