Improved Clutch-To-Clutch Control in a Dual Clutch Transmission

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Improved Clutch-To-Clutch Control in a Dual Clutch Transmission
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english
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Wang, Zhe
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University of Florida
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Master's ( M.S.)
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University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
SCHUELLER,JOHN KENNETH
Committee Co-Chair:
CRANE,CARL D,III

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dct -- transmission
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Mechanical Engineering thesis, M.S.
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Abstract:
A dual clutch transmission (DCT) is a type of automatic transmission featured with a dual-clutch module and two input shafts. A DCT is able to provide a high-quality gear shifting with a gear pre-selection procedure and overlapping of clutch engagement. The gear pre-selection procedure means that the synchronization of the oncoming gear has been completed before the actual gear shifting procedure starts. And due to the overlapping mechanism of the two clutches, torque is transferred from the engine to the driving wheels without interruption during gear shifting. Therefore, it provides a rapid gear shifting without sacrificing fuel efficiency and riding comfort. In addition, with a precisely computed and accurately controlled slippage of the dual-clutch module, the DCT is able to provide a fast and smooth gear shifting. The performance of a DCT during gear shifting relies on a well-designed clutch engagement controller. A good clutch engagement controller should be able to achieve (1) a fast clutch-to-clutch shifting and (2) a smooth gear shifting without noticeable torque disturbance. This research work proposes a newly designed clutch-to-clutch shifting controller that satisfies both objectives mentioned above. The presented control law is implemented in a linear control method that explicitly separates the controlling of the two clutches. The presented control method can be applied to a wide range of applications with easy implementation and a good robustness. Computer simulations in Simulink proved that the control objectives were realized with a robust and relatively simple controller. According to the simulation results, the average magnitudes of the output torques were reduced by 32.5% with the help of the proposed clutch-to-clutch control law. Also, by observing a couple of contrast simulations, we found that the output torque difference grew larger as the clutch actuator time constant became larger. In addition, simulation results showed that smaller clutch pressure changing rate contributed to a smoother gear shifting.
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by Zhe Wang.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
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Adviser: SCHUELLER,JOHN KENNETH.
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Co-adviser: CRANE,CARL D,III.

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ClutchtorqueformulationandcalibrationfordrydualclutchtransmissionsYonggangLiua,b,DatongQina,HongJiangc,CharlesLiuc,YiZhangb,aTheStateKeyLaboratoryofMechanicalTransmission,ChongqingUniversity,Chongqing400044,ChinabDepartmentofMechanicalEngineering,UniversityofMichigan-Dearborn,Dearborn,MI48128,UnitedStatescTransmission&DrivelineResearch&AdvancedEngineering,FordMotorCompany,Dearborn,MI48128,UnitedStatesarticleinfoabstractArticlehistory: Received2March2010 Receivedinrevisedform15September2010 Accepted21September2010 Availableonline20October2010Thispaperfocusesontheclutchtorqueformulationandcalibrationfordrydualclutch transmissions(DCT).Thecorrelationonthetheoreticalclutchtorqueandcontrolparametersis establishedbasedonconstantfrictionpowerandclutchactuatorkinematics.Analgorithm basedonpowertraindynamicsisproposedforthecalculationofclutchtorqueduringvehicle launchandshiftoperations.Thisalgorithmuseswheelspeedsensordataasinputandis capableofdeterminingtheclutchtorquewhilebothclutchesareslipping,thusprovidesa reliablecorrelationbetweenclutchtorqueduringrealtimeoperationsandclutchactuator controlvariables.Theaccuracyoftheproposedalgorithmhasbeenvalidatedbytorque measurementinprototypetestingonproveground. 2010ElsevierLtd.Allrightsreserved.Keywords: Dualclutchtransmissions Clutchtorque Calibration1.Introduction Dualclutchtransmissions(DCT)featuredrivabilitycomparabletoconventionalautomatictransmissionsandfueleconomy evenbetterthanmanualtransmissions.Duetotheseadvantages,thereisanon-goingtrendintheautomotiveindustrytodevelop andmarketDCTvehiclesthatarefuelef cientbutatnoexpensesofperformanceanddrivability [1,2] .Itcanbepredictedthat vehiclesequippedwithdualclutchtransmissionswillhaveasigni cantmarketshareinthenearfuture. TheclutchtorquecontrolduringlaunchandshiftsiscrucialfordevelopmentofvehicleswithDCTdrivetrains.Kinematically, gearshiftinginadualclutchtransmissionissimilartoclutch-to-clutchshiftinaconventionalautomatictransmission.Many valuableresearchesbybothanalyticalandexperimentalmeanshavebeensuccessfullyconductedintransmissiondynamicsand controlareas.ResearchersattheFordResearchLaboratory [3,4] wereamongthe rsttoquantitativelyanalyzedynamictransients duringtransmissionshiftsbycomputermodelingandtesting.Thesynchronizationoftheoncomingandoff-goingclutcheshad beenachievedusinghydraulicwashoutvalvesinautomatictransmissionsthathaveclutch-to-clutchshiftpatterns [5] .Systematic strategiesthatintegrateenginecontrolandclutchtorquecontrolhadbeendevelopedforproductionvehiclesforoptimized vehiclelaunchandshiftquality [6,7] .Researchesanddevelopmentsasthosecitedabovehavemadepossiblethetechnology maturityofconventionalautomatictransmissions. Despitethesimilarityinclutch-to-clutchshiftcharacteristics,adualclutchtransmissiondiffersfromaconventionalautomatic transmissioninthatthelaterhasatorqueconverterbetweentheengineoutputandtransmissioninput.Thepresenceofthe torqueconvertercushionsthepowertraindynamictransientsandisthereforeconduciveforsmoothnessduringvehiclelaunch andshifts.Withoutthecushioneffectoftorqueconverter,clutchtorquecontrolrequireshighprecisiontoachievelaunchandshift qualitycomparabletoautomatictransmissions.Inapreviouspaper,theauthorsproposedasystematicmodelthatanalyzesthe dynamicbehaviorofdualclutchtransmissionsandvalidatedthemodelsimulationbasedonprototypevehicletesting [8] .Asa furtherstudy,theworkpresentedinthispaperisconcentratedontheclutchtorqueformulationandcalibrationfordrydualclutch transmissions.Firstly,thetheoreticalornominalclutchtorqueiscorrelatedtotheclutchdesignparametersbasedonthe MechanismandMachineTheory46(2011)218 … 227 Correspondingauthor. E-mailaddress: anding@umich.edu (Y.Zhang). 0094-114X/$ … seefrontmatter2010ElsevierLtd.Allrightsreserved. doi: 10.1016/j.mechmachtheory.2010.09.005 Contentslistsavailableat ScienceDirectMechanismandMachineTheoryjournalhomepage:www.elsevier.com/locate/mechmt

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assumptionthatthefrictionpowerisconstantoverthefrictiondiskface.Thisformulationprovidesthebasisforthedesignof clutchanditsactuator.Secondly,analgorithmbasedonpowertraindynamicsisestablishedforthecalculationofclutchtorquein thelaunchingclutchduringlaunchandinbothclutchesduringshift.Thisalgorithmuseswheelspeedsensordataastheinputand iscapableofaccuratelycalculatingtheclutchtorquewhilebothclutchesareslippingonarealtimebasis.Thealgorithmhasseveral advantages:a)itenablesthedeterminationofclutchtorquewithoutusingthefrictioncoef cientofthefrictiondiskthatvariesas afunctionoftemperature;b)itprovidesaneffectivewaytocalibratetheclutchtorqueagainstthedesignandcontrolvariablesof theclutchanditsactuator;c)itprovidesareliablecorrelationbetweenclutchtorqueandclutchcontrolvariableduringrealtime operationforadaptivetransmissioncontrol.Thirdly,theanalyticalformulationandalgorithmforclutchtorquecalculationare validatedagainstprovegroundtestdataandlaudableagreementsareachievedbetweenanalyticalandtestdata. 2.Analyticalclutchtorqueformulation 2.1.Actuatorkinematicsandclutchtorque ThestructureofoneoftheclutchesanditsactuatorinadryclutchDCT [9] isillustratedin Fig.1 .Theotherclutchandactuator assemblyhassimilardesign.NormallyopenclutchdesignisappliedinDCTforsafetyconsiderations.Asshowninthe gure,the clutchactuator(orcontroller)consistsofmotor,spring,screwandroller.Whenthemotorturns,therollerisdisplacedadistance x alongthescrew,creatingtheleverageforthegenerationofanaxialforceonthereleasebearing.Thisforceisthenmagni edbythe pressureplatelevel,resultinginthepressureforcethatclampsthefrictiondisk.Foragivenclutchactuatordesign,theclutch torqueisafunctionofmotorrotationanglethatisrelatedtotherollerdisplacement x bythescrewparameter. Inthispaper,theconceptofconstantfrictionpower(i.e.theconversionratefromkineticenergytofrictionworkduringclutch slippage)isusedfortheformulationofthenominalclutchtorque [10] .Basedonthisassumption,theenergyconversionrateis expressedasfollows: f p v = Ct 1 where, f isthefrictioncoef cientoffrictiondisk, p isthepressure, v istherelativevelocityatapoint,and Ctistheenergy conversionrateperunitaryareaonthefrictionface.Basedonthisassumption,thepressureatanypointoverthediskfaceis expressedas, p = Ctf v = Ctf r = C r 2 where istheangularvelocityand r istheradiusatthepoint.Thequantity Ctf isaconstantoverthediskfaceandisdesignatedas C .Apparently,thepressureoverthediskfacevariesreverselyproportionaltotheradius.Themaximumpressure pmaxoccursatthe Fig.1. Sketchofdualclutchcontrollerstructure. 219 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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innerradiusofthefrictiondiskandtheconstant C canbeexpressedas C = d 2pmax,with d astheinnerdiameterofthefrictiondisk. Plugging C backintoEq. (2) ,thepressureonthediskfaceisthenexpressedas, p = 1 2 pmax d r : 3 Thepressureforceonthepressureplatecanthenbecalculatedasfollows: F =2 D = 2 d = 2p r dr =2 D = 2 d = 2 1 2 d pmaxr r dr = pmax d D Š d 2 4 where, D and d aretheouterandinnerdiametersofthefrictiondiskrespectively.Theclutchtorqueofonecontactsurfaceis calculatedbythefollowing, TCL=2 D = 2 d = 2f p r2 dr =2 f D = 2 d = 2 1 2 d pmaxr r2 dr = f pmax d D2Š d2 8 = pmax d D Š d 2 D + d 4 = f F D + d 4 : 5 Thenumberofcontactsurfacesistwoforeachclutch,sothenominalclutchtorque TCLiscalculatedby TCL= f F D + d 2 : 6 2.2.Correlationonclutchtorqueandcontrolparameter Thepressureforceonthepressureplateisrelatedtotheforceonthereleasebearingthroughthepressureplatelever.However, duetothedeformationofthepressureplateleverthathasadesignsimilartoadiaphragmspringandtheexistenceofbacklashes, thereexistnon-linearcharacteristicsbetweentheclutchtorqueandtheactuatorcontrolparameter.Toaccountforthisnonlinearity,testshavebeenperformedtomeasurethereleasebearingforce(i.e.theengagementload).Basedontestdata,therelease bearingforceiscorrelatedtotheengagementtravelasshownin Fig.2 Asshownin Fig.2 ,therearesubstantialforces(denotedas F0)onthereleasebearingofbothclutcheswhenengagementtravels arezeroduetohighrigidityforthepressureplatelever.Becauseofthis,twoseparatefunctionsmustbeusedtocorrelatethe releasebearingforce Fbwiththerollerdisplacement. Theengagementloadbeforereleasebearingtravelsisillustratedin Fig.3 .Asshownin Fig.3 ,thereleasebearingforce Fbandthe springforce Fsisrelatedasfollowsbefore Fbreaches F0, Fb= xrollerL Š xrollerFs 7 Fig.2. Relationshipbetweentravelandloadofbearing. 220 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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where, xrollerindicatesthepositionoftheroller, L isthetotaleffectivelengthoflever,and Fsisthespringforcewithaninitialvalue Fs 0. Thespringdisplacementisverysmallwhen Fbb F0sincereleasebearingdisplacementisnearzeroandthespringforceremains almostconstant,i.e., Fs= Fs 0if Fbb F0.Atthethresholdwhen Fb= F0,thedisplacementofroller xpcanbesolvedfromEq. (7) as follows, xp= F0Fs 0+ F0L : 8 Fig.3. Engagementloadbeforereleasebearingtravels. Fig.4. Engagementloadafterreleasebearingtravels. 221 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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Therefore,when xroller xp,thereleasebearingforceisrepresentedintermsofrollerdisplacementbyEq. (7) Afterthebearingbeginstotravel,aseparatefunctionisrequiredtocorrelatethereleasebearingforceandtheroller displacementsincethespringcompressionisaffectedbythebearingtravel. Theengagementloadafterreleasebearingtravelsisillustratedin Fig.4 .Asshownin Fig.4 ,theamountofspringcompression changedbythebearingtravelisdeterminedasfollows, xs= xbL Š xrollerxroller 9 where xsistheincrementofspringlengthand xbistheengagementtravelofbearing.Duetothisincrement,thespringforceafter bearingmovingisexpressedasfollows: Fs= Fs 0Š k xrollerL Š xrollerxb 10 where k isthespringstiffness.Theequilibriumoftheactuatorleverrequiresthefollowingequationtobesatis ed Fsxroller= FbL Š xroller : 11 CombiningEqs. (10)and(11) ,thereleasebearingforce Fbcanberepresentedintermoftherollerdisplacementas follows: Fb= xrollerL Š xrollerFsxroller xp= F0Fs 0+ F0L Fs 0Š k xrollerL Š xrollerxb xrollerL Š xrollerxrollerN xp= F0Fs 0+ F0L : 8 > > > < > > > : 12 2.3.Clutchestorqueandcontrolparametercorrelation AsindicatedinEq. (6) ,theclutchtorqueisafunctionofthepressureforceonthepressureplate,frictioncoef cientandclutch dimensions.Themainparametersofthetwoclutchesusedintheprototypeareshownin Table1 Table1 Mainparametersofclutch. ParametersClutch1Clutch2 Clutchouterdiameter D1=232.5mm D2=225mm Clutchinnerdiameter d1=157mm d2=157mm Leverratio iratio 1=3.6 iratio 2=4.2 Frictioncoef cient f1=0.35 f2=0.35 Fig.5. Relationshipbetweenclutchtorqueanddisplacementofroller. 222 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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AccordingtoEq. (6) ,thenominalclutchtorqueinbothclutch1andclutch2canbecalculatedasfollows, TCL 1= f1Fb 1iratio 1 D1+ d1 = 2 = 1000=0 : 35 3 : 6 Fb 1 232 : 5+157 = 2 = 1000=0 : 2454 Fb 1TCL 2= f2Fb 2iratio 2 D2+ d2 = 2 = 1000=0 : 35 4 : 2 Fb 2 225+157 = 2 = 1000=0 : 2808 Fb 2 13 where, Fb 1and Fb 2arethereleasebearingforcesforclutch1andclutch2respectively.Thespringconstantsareselectedtobe 150N/mmforbothactuatorsandthelengthoftheactuatorleveris L =100mm.Therollerdisplacementsatwhichreleasebearing begintomoveare xp 1=25mmand xp 2=30mmrespectively.TheinitialspringforcesaredeterminedbyEq. (8) as Fs 1=1689N and Fs 2=1860N. Beforethereleasebearingsstarttomove,theclutchtorqueandrollerpositioncanbeexpressedasfollowing, TCL 1=0 : 2454 Fb 1=0 : 2454 xroller 1L Š xroller 1Fs=414 : 48 xroller 1100 Š xrolle 1xrolle 1 xp 1=25 TCL 2=0 : 2808 Fb 2=0 : 2808 xroller 2L Š xrolle 2Fs=522 : 29 xroller 2100 Š xroller 2xrolle 2 xp 2=30 : 8 > > < > > : 14 Afterthebearingsstarttomove,therelationshipbetweenengagementtravel xbandthebearingload Fbcanbeobtainedfrom Fig.2 ,whichmeansthat Fbisafunctionof xb,i.e., Fb= f ( xb).Whentheengagementtravelissmallerthan4mm,itisaccurate enoughto tthefunction f ( xb)bythefollowinglinearfunction Fb 1=99 : 5 xb 1+563 xb 1 4mm : 15 Fig.6. Dualclutchtransmissiondynamicmodel. Table2 Mainparametersoftestvehicle. ParametersValue Vehiclemass M =1400kg Transmissiongearratios i1= 3.917 i2= 2.429 i3= 1.436 i4= 1.021 i5= 0.848 i6= 0.667 Finaldrivegearratio ia1=3.762 ia2=4.158 Tireradius r =0.2975m Airresistancecoef cient CD=0.328 Frontalarea A =2.12m2223 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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SoEqs. (12)and(15) canbecombinedtogether(with = xrollerL Š xroller)tocorrelatetheclutchtorqueinclutch1asfollows, TCL 1=0 : 2454 168999 : 5 1+150563 2 199 : 5+150 2 1 = 41241 1+20724 2 199 : 5+150 2 1xroller 1N xp 1=25 : 16 Similarly,theclutchtorqueinclutch2canberepresentedasafunctionof xroller 2as, TCL 2=0 : 2808 186038 : 25 2+150797 2 238 : 25+150 2 2 = 19978 2+33570 2 238 : 25+150 2 2xroller 2N xp 2=30 : 17 TheclutchtorquesrepresentedbyEqs. (16)and(17) canalsoberepresentedgraphicallyby Fig.5 3.Algorithmforclutchtorquecalculation Eqs. (14),(16)and(17) providetheanalyticalcalculationfortheclutchtorqueintermsofrollerposition.However,this calculationmustbecalibratedforrealworldapplicationssincetheclutchfrictioncoef cientistemperaturedependent.Inthis section,analgorithmbasedonpowertraindynamicsisproposedfortheaccuratecalculationoftheclutchtorqueasdescribedin thefollowing. 3.1.DCTpowertraindynamics Inapreviouspaper [8] ,theDCTpowertraindynamicsduringlaunchandshiftshasbeeninvestigatedindetail.Thedynamic modelforthedualclutchtransmissionusedintheresearchisshownin Fig.6 .Inthismodel,gearshaftsaremodeledaslumped massesandthefoursynchronizersaremodeledaspowerswitches.Asindicatedin Fig.6 ,themassmomentsofinertiaofthe lumpedmassesaredenotedasfollowing:engineoutputassemblyincludingclutchinputside( Ie),clutch1drivenplate( I1),clutch 2drivenplate( I2),solidshaft( I3),hollowshaft( I4),transfershaft1( I5),transfershaft2( I6),outputshaft( I7).Insimilarfashion, e, 1, 2, 3, 4, 5, 6,and 7denotetherespectiveangularvelocities.Thewheelangularvelocityisdenotedby w. T1, T2and Torepresentoutputtorquesofclutch1,clutch2andoutputshaftrespectively.Thevehicleequivalentmassmomentofinertiaonthe outputshaftisdenotedby I .Thestiffnessanddampingcoef cientofthepowertrainsystemarenotconsideredsincetheydonot affecttheclutchtorquecalculations. 3.2.Calculationalgorithmforclutchtorque Thecalculationforcutchtorqueisbasedonthepowertrainsystemdynamics.Theequationsofmotionforvehiclelaunchand 1 … 2upshiftarepresentedinthefollowingtext.Forotheroperationmodes,similarequationscanbederivedaccordingtothe power owpath,asdetailedin [8] Fig.7. Clutchtorquecomparisonduringlaunch. 224 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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3.2.1.Launch Inthelaunchmode,theclutchtorqueinclutch1isgraduallyincreaseduntilitisfullyengaged,whiletheclutchtorqueinclutch 2isequaltozero.Thetorqueofclutch1isdirectlyusedtodrivethevehicle.Thesystemofequationsofmotionispresentedas follows. TeŠ TCL 1= Ie e 18 TCL 1Š T1= I1 1 19 T1Š Taia 1i1= I1 eq 3 20 TaŠ To= I7 7 21 ToŠ TLoad= I w 22 where, i1is rstgearratio, ia 1is naldriveratiowhichissharedbythe1st,2nd,5thand6thgears. Teistheengineoutputtorque. TCL 1istheclutchtorqueinclutch1. Taisthe naldriveoutputtorque. Ieq 1istheequivalentmassmomentofinertiainthe rstgear Fig.8. Clutchtorquecomparisonduring1 … 2upshift. Fig.9. Clutchtorquecomparisonduringoperationinthe4thgear. 225 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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forthelumpedmassesincludingthetransfershaft1,assemblyofthesolidshaftandallothercomponentsrotatingaccordinglyin the rstgear. wistheangularvelocityofthewheel.Theroadloadtorque TLoadisexpressedbythefollowingequation: TLoad= f W + RA+ RG r 23 where, f isrollingresistancecoef cient, W isvehiclemass, r istireradius, RAand RGaretheairandgraderesistancesrespectively. AscanbeseenfromEqs. (18) … (22) ,clutchtorque TCL 1canbecalculatedusingEq. (18) orEqs. (19) … (22) respectively.Ifthe enginetorqueandenginespeedcanbemeasuredaccuratelyduringvehiclelaunchtorque TCL 1canthenbedirectlyfoundfrom Eq. (18) .However,theenginetorqueandspeedduringtransientoperationsareveryhardtomeasureaccuratelyresulting unacceptableinaccuracyforclutchtorquecalculation.Ontheotherhand,thewheelspeedofvehicleismorestableincomparison withenginespeedandcanbemeasuredwithhighaccuracy.Therefore,theclutchtorque TCL 1canbecalculatedwithhighaccuracy usingEqs. (19) … (22) InEqs. (19) … (22) ,theangularvelocitiesarerelatedasfollows: 1= 3, 7= wand 3= 7 ia 1 i1.Thustheequationscanbe combinedtopresent TCL 1intermsof wasfollows: TCL 1= I7+ I ia 1i1+ I1+ I1 eqia 1i1 w+ TLoadia 1i1: 24 Accordingtotheaboveequation,theclutchtorque TCL 1canbecalculatedduringlaunch,andtheaccuracyonlydependsonthe wheelaccelerationthatisthederivativeofthewheelspeedfromthespeedsensor. 3.2.2.Shifts Theshiftprocessisdividedintotwostages,whicharetorquephaseandinertiaphase.Thesystemequationsfora1 … 2shiftare presentedinthefollowing,whichcanbeeasilyextendedtoothershifts. TeŠ TCL 1Š TCL 2= Ie e 25 TCL 1 i1+ TCL 2 i2ŠTa=ia 1= I3+ I1 i2 1+ I2+ I4 i2 2+ I5hi 5 26 TaŠ To= I7 7 27 ToŠ TLoad= I w 28 where, i2issecondgearratio, ia 2is naldriveratiowhichissharedbythe3rdand4thgears. TCL 2istheclutchtorqueinclutch2. Since 5= 7ia 1= wia 1,Eqs. (26)to(28) canbecombinedintoonesingleequation: TCL 1i1ia 1+ TCL 2i2ia 1Š TLoad= I3+ I1 i2 a 1i2 1+ I2+ I4 i2 a 1i2 2+ I5i2 a 1+ I7+ I hi w: 29 Whenclutchtorque TCL 1or TCL 2equalszero,theotherclutchtorquecanbecalculatedfromEq. (29) intermsof w.However, duringthegearshiftprocess,therearefrictiontorquesinbothclutchesandtheycannotbesolvedusingEq. (29) alone.Forthe samereasonmentionedpreviously,Eq. (25) doesnotprovidehelpsinceenginetorqueisnotknown. AsrepresentedinEqs. (13) … (17) ,theclutchtorqueisafunctionofclutchdesignparameters,frictioncoef cientandcontrol parameters.Theproportionoftheclutchtorquesinthetwoclutchesshouldbeindependentofthefrictioncoef cientsincethe temperatureeffectisthesameforbothclutches.Therefore,clutchtorquesinclutch1andclutch2areproportionedbythe followingratio: K = TCL 1TCL 2= K1K2 30 where, K istheclutchtorqueproportion. K1and K2arethefactorsdependingonclutchdimension,actuatorparametersandroller positionasdetailedin Section2 .CombiningEqs. (29)and(30) leadstothedeterminationofthetwoclutchtorques TCL 1and TCL 2in termsof w: TCL 2= I3+ I1 i2 a 1i2 1+ I2+ I4 i2 a 1i2 2+ I5i2 a 1+ I7+ I hi w+ TLoadK i1ia 1+ i2ia 1TCL 1= KTCL 2: 8 > > < > > : 31 226 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227

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4.Casestudy Theclutchtorquecalculationalgorithmdescribedin Section3 hasbeenimplementedbasedonMatlab/Simulinkplatform.A prototypevehiclewithparametersshownin Table2 istestedonprovegroundwith attrack.Vehicleacceleration,wheelspeed, dualclutchrollerpositionandtransmissiongearpositionsarerecordedduringthetest.Atorquesensorismountedonthehalf shafttomeasurethedrivetrainoutputtorque. Themeasuredhalfshafttorqueisconvertedbyrelatedgearratiostobetheequivalenttorquevalueontheinputshaft.This equivalenttorqueiscomparedwiththeclutchtorquecalculatedbytheproposedalgorithmasdescribedinthefollowing. 4.1.Launch Inthelaunchoperation,gearpositionis1standtheclutchtorquecanbecalculateddirectlybyEq. (24) .Thevehicleacceleration orwheelspeedfromtestistheonlymodelinput.Thecomparisononclutchtorqueisshownin Fig.7 .Theclutchtorquecalculated fromthetorquealgorithmhighlyagreeswiththeclutchtorqueobtainedfrommeasurement. 4.2.1 – 2upshift Duringashift,themeasuredhalfshafttorquecannotbeconvertedtobetheequivalenttorquevaluesontheinputshaftsince theproportionofthemeasuredclutchtorquesisnotknown.Therefore,theresultanthalfshafttorque,thatisthesumofthetwo clutchtorquesmultipliedbytherespectivegearratios,iscomparedwiththemeasuredhalfshafttorque.Asshownin Fig.8 ,the outputtorqueduring1 … 2upshiftishighlyagreeabletothetestdata,indicatingtheeffectivenessandaccuracyofthetorque calculationalgorithm. 4.3.Operationatagearposition Theclutchtorquewhenvehicleoperatesinonegearcanalsobecalculatedbythealgorithmproposedinthepaper.Theresults in4thgearoperationareshownin Fig.9 .Thetorqueinclutch1equalszerobecauseonlyclutch2isnowtransferringtheengine torquetodrivevehicle.Asshowninthe gure,thetorqueinclutch2isalmostthesameasthetestresults,whichrecon rmsthe accuracyoftheproposedalgorithm. 5.Conclusion Thispaperisfocusedonthedualclutchtorqueformulationandcalibration.Theclutchtorqueformulationisproposedbasedon constantenergyconversionrateoverthefrictiondiskface.Thecorrelationonclutchtorqueandtheparametersoftheclutch actuatorhasbeenestablishedintermsofrollerposition,andtherelateddesignparameters.Forcalibrationpurposes,aclutch torquecalculationalgorithmhasbeenproposedbasedonDCTpowertraindynamics.Thisalgorithmusesvehiclewheelspeed obtainedfromspeedsensorastheinputandisimplementedusingMatlab/Simulinkplatform.Theeffectivenessofthealgorithm hasbeencon rmedbytestdataobtainedbyprovegroundtestingoftheprototypevehicle.Theapproachproposedinthepaper providesananalyticaltoolfordualclutchsystemdesignandtheaccuratecontrolofclutchtorquesthatiscrucialforthelaunchand shiftsofDCTvehicles. Acknowledgement The nancialsupportfromtheFordInnovationAllianceProgramfortheworkpresentedinthispaperisgreatlyappreciated. References[1]B.Matthes,Dualclutchtransmissions „ lesionslearnedandfuturepotential,ProceedingofTransmissionandDrivelingSystemsSymposium-4WD/AWD,SAE PaperNo.2005-01-1021,2005. [2]J.Wheals,A.Turner,K.Ramasy,A.O'Neil,DoubleClutchTransmission(DCT)UsingMultiplexedLinearActuationTechnologyandDryClutchesforH igh Ef ciencyandLowCost,,2007SAEPaperNo.2007-01-1096. [3]T.W.Megli,M.Haghgooie,D.S.Colvin,ShiftCharacteristicsofa4-SpeedAutomaticTransmission,,1999SAEPaperNo.1999-01-1060. [4]E.Fujii,W.E.Tobler,E.M.Clausing,T.W.Megli,M.Haghgooie,Applicationofdynamicbandbrakemodelforenhanceddrivetrainsimulation,Jour nalof AutomobileEngineering216(11)(2002)873 … 881. [5]S.Bai,R.Moses,T.Schanz,M.Gorman,Developmentofanewclutch-to-clutchshiftcontroltechnology,ProceedingofTransmissionandDriveling Systems Symposium2002,SAEPaperNo.2002-01-1252,2002. [6]M.Livshiz,M.Kao,A.Will,ValidationandCalibrationProcessofPowertrainModelforEngineTorqueControlDevelopment,,2004SAEPaperNo.200 4-010902. [7]H.Walamatsu,T.Ohasho,S.Asatsuke,Y.Saitiou,Honda's5speedallclutchtoclutchautomatictransmission,ProceedingofTransmissionandDri veling SystemsSymposium2002,SAEPaperNo.2002-01-0932,2002. [8]Y.Liu,D.Qin,H.Jiang,Y.Zhang,Asystematicmodelfordynamicsandcontrolofdualclutchtransmissions,JournalofMechanicalDesign,ASMETra nsaction 131(2009)061012. [9]U.Wagner,A.Wagner,ElectricalShiftGearbox(ESG) „ ConsistentDevelopmentoftheDualClutchTransmissiontoaMildHybridSystem,,2005SAEPaper No.2005-01-4182. [10]T.Reye,ZurTheoriederZapfenreibung,DerCivilingenieur4(1860)235 … 255. 227 Y.Liuetal./MechanismandMachineTheory46(2011)218 – 227



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IMPROVED CLUTCH TO CLUTCH CONTROL IN A DUAL CLUTCH TRANSMISSION By ZHE WANG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2014

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2014 Zhe Wang

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3 ACKNOWLEDGMENTS I can never express enough thanks to my committee for their continued support and encouragement during the research work: Dr. John Schueller, my committee chair; Dr. C arl Crane. I express my most sincere gratitude for the learning opportunity and guidance provided by my committee. My research work could not be completed without the support of my parents: Miss. Yaxian Liu and Mr. Minqiang Wang. Thank you for your gener ous support for my study.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 3 LIST OF TABLES ................................ ................................ ................................ ............ 6 LIST OF FIGURES ................................ ................................ ................................ .......... 7 ABSTRACT ................................ ................................ ................................ ..................... 8 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 10 Research Overview ................................ ................................ ................................ 10 Problem Formula tion ................................ ................................ ............................... 11 Analysis Method ................................ ................................ ................................ ..... 12 2 LITERATURE REVIEW ................................ ................................ .......................... 14 Approach of In vestigation ................................ ................................ ....................... 14 Clutch Torque Formulation and Calibration ................................ ............................ 15 Study of Engine Clutch Control ................................ ................................ ............... 15 Study of Impact of Clutch Applying Time to Gear Shift Quality ............................... 16 Clutch Engagement Control Strategies ................................ ................................ ... 16 Summary ................................ ................................ ................................ ................ 17 3 DUAL CLUTCH TRANSMISSION WORKING PRINCIPLE ................................ .... 19 4 POWERTRAIN MODEL ................................ ................................ .......................... 24 Engine Model ................................ ................................ ................................ .......... 24 Clutch Model ................................ ................................ ................................ ........... 25 Gearbox Model ................................ ................................ ................................ ....... 26 Output Shaft Model ................................ ................................ ................................ 27 Final Drive Model ................................ ................................ ................................ .... 27 Vehicle Body Model ................................ ................................ ................................ 27 5 CLUTCH TO CLUTCH SHIFT CONTROLLER DESIGN ................................ ........ 34 Background Materials ................................ ................................ ............................. 34 Vehicle Launch ................................ ................................ ................................ ....... 34 Power On Upshift ................................ ................................ ................................ ... 35 Power On Downshift ................................ ................................ ............................... 35 Clutch to Clutch Shift ................................ ................................ .............................. 36 Supervisory Gear Shifting Controller ................................ ................................ ...... 36

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5 Clutch to Clutch Shifting Controller ................................ ................................ ......... 37 6 NUMERICA L SIMULATION ................................ ................................ .................... 45 7 DISCUSSION ................................ ................................ ................................ ......... 56 Validation of the Proposed Clutch to Clutch Shift Control Law ............................... 56 Discussion of Influence of Clutch Actuator Time Constant ................................ ..... 56 Discussion of Influence of Clutch Pressure Profile on Gear Shift Quality ............... 57 8 CONCLUSION ................................ ................................ ................................ ........ 60 REFERENCES ................................ ................................ ................................ .............. 62 BIOGRAPH ICAL SKETCH ................................ ................................ ............................ 63

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6 LIST OF TABLES Table page 4 1 Gearbox Parameters ................................ ................................ .......................... 28 4 2 Dual Clutch Module Parameters ................................ ................................ ......... 29 4 3 Engine Parameters ................................ ................................ ............................. 29 4 4 Input shaft Parameters ................................ ................................ ....................... 29 4 5 Output Shaft Parameters ................................ ................................ .................... 29 4 6 Final Drive Parameters ................................ ................................ ....................... 30 4 7 Vehicle Body Parameters ................................ ................................ ................... 30 6 1 Simul ation Results ................................ ................................ .............................. 47 7 1 Peak Output Torques A ................................ ................................ ...................... 58 7 2 Peak Output Torques B ................................ ................................ ...................... 59 7 3 Peak Output Torques C ................................ ................................ ...................... 59

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7 LIST OF FIGURES Figure page 3 1 Dual Clutch Transmission Schematic Diagram. ................................ .................. 22 3 2 Dual Clutch Transmission Stick Diagram. ................................ .......................... 23 4 1 Vehicle Model with DCT. From: Matlab(version: R2011b (7.13.0.564)) ........... 31 4 2 Simplified Diagram of DCT Model ................................ ................................ ...... 32 4 3 Model of Output Shaft. ................................ ................................ ........................ 33 5 1 Clutch Lock ................................ ................................ ................................ ......... 39 5 2 Control Logic of Supervisory Gear Shifting Controller ................................ ........ 40 5 3 Clutch to Clutch Shifting Control Law ................................ ................................ 41 5 4 Clutch to Clutch Shifting Control Law ................................ ................................ 42 5 5 Lock Clutch 1 ................................ ................................ ................................ ...... 43 5 6 Lock Clutch 2 ................................ ................................ ................................ ...... 44 6 1 Original Output Torque Dynamics ................................ ................................ ...... 48 6 2 Optimized Output Torque Dynamics (actuator time constant 0.02s) .................. 49 6 3 Optimized Output Torque Dynamics (Actuator Time Constant 0.04s) ................ 50 6 4 Optimized Output Torque Dynamics (Actuator Time Constant 0.01s) ................ 51 6 5 Optimized Output Torque Dynamics (Actuator Time Constant 0.001s) .............. 52 6 6 Optimized Output Torque Dynamics (Actuator Time Constant 0.1s) .................. 53 6 7 Optimized Output Torque Dynamics ................................ ................................ ... 54 6 8 Optimized Output Dynamics ................................ ................................ ............... 55

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8 Abstract of Thesi s Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science IMPROVED CLUTCH TO CLUTCH CONTROL IN A DUAL CLUTCH TRANSMISSION By Zhe Wang May 2014 Chair: Jo hn K. Schueller Major : Mechanical Engineering A dual clutch t ransmission (DCT) is a type of automatic transmission featured with a dual clutch module and two input shafts. A DCT is able to provide a high quality gear shifting with a gear pre selection pro cedure and overlapping of clutch engagement. The gear pre selection procedure means that the synchronization of the oncoming gear has been completed before the actual gear shifting procedure starts. And due to the overlapping mechanism of the two clutches, torque is transferred from the engine to the driving wheels without interruption during gear shifting. Therefore, it provides a rapid gear shifting without sacrificing fuel efficiency and riding comfort. In addition, with a precisely computed and accurate ly controlled slippage of the dual clutch module, the DCT is able to provide a fast and smooth gear shifting. The performance of a DCT during gear shifting relies on a well designed clutch engagement controller. A good clutch engagement controller should b e able to achieve (1) a fast clutch to clutch shifting and (2) a smooth gear shifting without noticeable torque disturbance. This research work proposes a newly designed clutch to clutch shifting controller that satisfies both objectives mentioned above. T he presented control law is implemented in a linear

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9 control method that explicitly separates the controlling of the two clutches. The presented control method can be applied to a wide range of applications with easy implementation and a good robustness. Co mputer simulations in Simulink proved that the control objectives were realized with a robust and relatively simple controller. According to the simulation results, the average magnitudes of the output torques were reduced by 32.5% with the help of the pro posed clutch to clutch control law. Also, by observing a couple of contrast simulations, we found that the output torque difference grew larger as the clutch actuator time constant became larger. In addition, simulation results showed that smaller clutch p ressure changing rate contributed to a smoother gear shifting.

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10 CHAPTER 1 INTRODUCTION Research Overview A utomatic transmission s that provide automatic gear selection and automatic gear shifting have become increasingly popular for passenger vehicles. T here are currently four common kinds of automatic transmissions : classical automated transmission, automated manual transmission, dual clutch t ransmission (DCT), and continuously variable t ransmission (CVT). The increasing demand for improved automotive fu el economy and riding comfort has led to the development of new control technologies for automatic transmission s Each type of automatic transmission works in a different way, but the dual clutch t ransmission may be an optimal solution for achieving best f uel efficiency and superior riding performance because of its unique structure. The unique structure of the dual clutch t ransmission, featured by a dual clutch module, enables the DCT to work as two independent manual transmissions under a precise control of the dual clutch module. It is widely thought that DCT has a simple structure and a good fuel economy like manual transmission. At the same time, a DCT is able to achieve dynamic performance as good as a classic automatic transmission and realize gear sh ifting almost as smooth as a CVT. However, the unique structure of DCT, the dual clutch module, also produces control problem s during gear shifting. An improper clutch applying time may cause undesired torque disturbance to the vehicle and unsatisfactor y fuel economy. An effective control logic for gear shifting decision s is required to regulate gear shifting operation, and a precisely computed and accurate implemented gear shifting controller, including the clutch to clutch shifting controller, is the k ey to achieve a fast and smooth

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11 gear shifting. The supervisory gear shifting controller monitors the current engine state (including engine torque, engine speed, throttle opening, fuel/air mixing rate, etc.), vehicle speed, and current gear to make a decis ion for gear shifting operation, including upshift, downshift and hold. The dedicated gear shifting controller, including clutch to clutch shift controller, controls the clutch slippage in different phases by applying different clutch pressure s During th e clutch to clutch shift procedure, with a precisely computed and accurately implemented control law, the clutch to clutch shifting controller provides a clutch to clutch control that ensures a rapid and smooth operation without sacrificing much of fuel ef ficiency and performance. The research objective here is to study a simple and robust clutch to clutch shifting controller. The designed clutch to clutch shifting controller provides a linear control method based on measurements of clutch slippage, clutc h capacity, and transmission output torque. The dedicated gear shifting controller is validated by simulation results in Matlab/Simulink platform. Problem Formulation A d ual clutch t ransmission (DCT) shows an advantage over the other kinds of transmissi on s b y allow ing the torque transferred from the engine to the driving wheels without interruption. From a kinematic point of view, a clutch to clutch shift of a d ual clutch t ransmission is similar to that of a clutch to clutch shift in a conventional aut omatic transmission (AT). But, due to the absence of torque converter that dampens shift transient s a DCT shows different dynamic characteristics from an AT. The absence of torque converter makes a dual clutch t ransmission more sensitive to input torque

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12 i n difference Therefore, an advanced control law for the dual clutch module during clutch to clutch shift controller is needed to minimize gear shifting time and reduce the output torque difference of a DCT. Output torque in this thesis is defined as the to rque measured at the output shaft of a DCT. Torque difference is defined as the difference between the desired output torque and the actual output torque. In a DCT, the two clutches are engaged alternatively in different gears. A typical gear shifting pr ocess involves a clutch to clutch shift, that is, the engagement of the oncoming clutch and the disengagement of the off going clutch. An electrohydraulic unit actuates the operation of the two clutches. The clutch to clutch shifting enables a DCT to perfo rm a fast gear shifting without power interruption between the engine and the driving wheels. But a precise and reliable control of the clutch to clutch shifting is difficult to achieve due to the complexity of the characteristics of the frictional clutch, hydroelectric elements, measurement noise and unpredictable disturbance s An unreliable and poorly designed clutch to clutch controller may cause clutch tie up, engine flare, undesired performance, and even safety problem s The objective of the research i s to design a reliable, simple, and tunable clutch to clutch controller with an easy implementation. Analysis Method To analyze the behavior of DCT during gear shifting transient and validate the effectiveness of the designed controller, a vehicle mod el that is equipped with a 5 speed DCT is adopted from Matlab/Simulink. The adopted model consists of engine, powertrain, vehicle body, and other necessary factors such as wind velocity and road incline. In the research work, a newly designed and optimized clutch to clutch shift controller is added to the adopted model to test the performance of the clutch to clutch

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13 controller and verify its effectiveness. The simulation is performed in the Matlab/Simulink platform. The control law proposed in this paper aims to achieve the following goals: (1) to reduce the output torque disturbance due to manufacturing in difference undesired input from the environment, inherent design offset, and other possible disturbances, and (2) to minimize the gear shifting operation time Previous research has proved that there is a trade off between the rapidness and the smoothness of gear shifting. The presented research work will focus more on improving the smoothness. Since the presented controller is a tunable design with a few pa rameters, it is possible to tune the controller for a specific requirement.

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14 CHAPTER 2 LITERATURE REVIEW Approach of Investigation It is a common practice in the automotive industry to analyze, simulate, and predict powertrain dynamic performance b y computer simulation. A great deal of research efforts has been focused mainly on modeling, control and optimization of automotive powertrain, both in system level and component level. Various formulation methods and techniques have been used in modeling automotive powertrain dynamics and simulating powertrain dynamic performance. Mostly, researchers first derive equations of motion to model components of the powertrain system. After that, the researchers build the whole system by integrating all the relev ant components. The computer models are implemented in different platforms, including generically developed codes and object oriented programming tools, to do simulation and tests. The most commonly used simulation platform is Matlab/Simulink. DCT Kinema tics E. Galvagno [1] investigated the transmission kinematic s and dynamics of a dual clutch t ransmission at the system level. The research took into consideration of all possible transmission configurations that may occur corresponding to various power f low paths. A mathematical analysis of the dual clutch t ransmission with different degree of freedom was proposed to describe kinematic and dynamic behavior of DCTs with various layouts. Consequently, several sets of equations of motion were written in an i ndexed form that could be integrated in a vehicle model to allow the description of both the gear shifting transient performance and operation with in a specific gear.

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15 Clutch Torque Formulation and Calibration Yonggang Liu [2] developed a method for the t orque formulation and calibration of dual clutch module with dry frictional plates. His research correlated the theoretical clutch torque and control parameters based on constant friction power and clutch actuator dynamics. In addition, an algorithm based on powertrain dynamics was proposed for calibration of clutch torque during vehicle launch and gear shifting operations. The effectiveness and accuracy of the proposed algorithm were validated by prototype testing. Xinyong Song [3] worked on a systematic approach for the pressure based clutch fill and engagement control of wet friction clutches. The major challenges in the controller design is the complicated dynamic behavior of the frictional clutch system, the ON/OFF characteristics during the clutch fi ll phase, the pressure chattering effect introduced by inappropriate control gain design, and the precise pressure tracking requirement during clutch to clutch shifting transient. To address these problems, a wet clutch model that was able to precisely sim ulate pressure torque dynamics in a relatively wide range was created and validated. Then, a sliding mode controller that could deal with the chattering phenomenon was designed to achieve robust pressure control. In addition, an observer was designed to es timate the clutch piston motion. The proposed pressure based clutch control method was verified as an effective and robust approach by experimental results. Study of Engine Clutch Control Paul D. Walker [4] proposed a method of combining engine and clutc h control to achieve the best possible gear shifting quality. The powertrain was modeled as a simplified four degree of freedom system with reduction gears and two clutches. Numerical simulations were conducted to justify the capability of the proposed met hod to

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16 reduce shift transient developed in dual clutch transmissions. According to the simulation results, it was shown that the adoption of torque based control techniques for both the dual clutch unit and engine, which made use of the estimated target cl utch torque, significantly improved the powertrain response as a result of reduction of output torque in difference in the gear shift transient. The simulation results indicated that by using the ideal torque parameters it was possible to minimizes the torq ue output in difference Study of Impact of Clutch Applying Time to Gear Shift Quality Manish Kulkarni [5] studied the shift dynamics of a DCT with clutch applying timing. A n engine powertrain model was created using Matlab/Simulink as the simulation pla tform for the simulation, analysis and control of shifting dynamics for DCT vehicles. The model had been used to analyze the variation in output torque in response to different clutch applying timing by applying three different clutch pressure profiles dur ing shifts. Vehicle launch and gear shift process were both simulated to ass ess transmission shift quality and validate the effectiveness of the shift control. Clutch Engagement Control Strategies The design of the clutch engagement controller has also b een paid great attention by researchers. As a result, there are several approaches for achieving a fast and smooth clutch engagement. Magnus Pettersson [6] introduced a novel strategy for controlling the engine to a state where neutral gear could be eng aged, implemented with standard sensors. The proposed method is developed from the idea that gear shifting control can be obtained by controlling the torque transmitted by the drive shaft to zero. The presented control method has two advantages: (1) gear e ngagement can be completed fast with small speed oscillations, (2) the observers in the controller can be constructed in a simple

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17 manner. The research work showed promising simulation and experimental results with easy implementation. Koos van Berkel [7 ] presented a simple and robust controller to achieve a fast and smooth clutch engagement for a dual clutch t ransmission with a consistent performance under different initial conditions and uncertainties. The research work proposed a controller design that explicitly separated the control laws for a fast clutch engagement and a smooth clutch engagement by introducing clutch engagement phases. The control objectives were achieved with a simple and robust controller in related simulation and experiments. Va n der Heijden [8] compared two optimal control strategies for clutch engagement based on hybrid control principles. The conclusion was that piecewise linear quadratic optimal control (PWLQ) was a better control method compared with the model predictive con trol (MPC) that le d to large computation cost. A novel controller was constructed with piecewise linear optimal quadratic control techniques. This technique suggested searching for piecewise quadratic Lyapunov functions using convex optimization. The key i dea was to make the piece Lyapunov function continuous across the regional boundaries. The advantages of PWLQ techniques was validated by simulation, and the results showed that it performed as well as the PI based controller, but needed less tuning work. Summary Although a great deal of research work have been carried out to achieve a fast and smooth clutch to clutch control, there is still a lack of an explicit and easy control law to control the oncoming clutch and the off going clutch simultaneously.

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18 In this paper, a linear clutch to clutch controller is proposed to achieve a fast and smooth gear shifting. The presented controller for a clutch to clutch shift is designed with feedback loops based on the actual torque transmitted through each clutch. To analyze the dynamic behavior of DCT powertrain during gear shifting performance, a DCT powertrain model was adopted fro m Matlab/Simulink. The goal of the clutch to clutch controller is to realize a fast and smooth gear shifting with the standard automo tive sensors. The effectiveness of the proposed controller was validated by related simulation results of the modified DCT powertrain model with the proposed clutch to clutch controller.

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19 CHAPTER 3 D UAL CLUTCH TRANSMISSION WORKING PRINCIPLE A dual clut ch t ransmission (DCT) is shown schematically in Figure 3 1. The dual clutch transmission is adopted from Matlab(version: R2011b (7.13.0.564)) It has five forward speeds and the reverse speed is neglected for simplicity. The dual clutch transmission is mou nted between the engine to the final drive, and the dual clutch transmission transfers power from the engine to the driving wheel while providing desired gear ratios. As shown in Figure 3 1, there are two power transfer path formed by two clutches and corr esponding shafts, synchronizers and gears. When the dual clutch transmission is working in a specific gear, only one of the clutches and corresponding synchronizers are engaged Therefore only one power path transfers power in that working condition. While in gear shifting transients, the oncoming clutch starts to engage and the off going clutch begins to disengage. So before the gear shifting is completed, the power paths both transferring power at the same time. As a unique feature of a dual clutch transm ission, the next gear is preselected and the corresponding synchronizers are engaged before the actual gear shifting starts. In this way dual clutch transmission is able to perform a fast gear shifting. Figure 3 2 shows a dual clutch transmission as typic ally implemented on an automobile. The dual clutch module, that gives name to the transmission, is mounted between the engine flywheel and the two coaxial input shafts of the transmission, one for odd gears and one for even gears. Therefore, the dual clutc h module in the DCT provides the powertrain with two routes from the engine to the driving wheels. The dual clutch module can be single disk or multi disk, dry or wet type, de pending mainly on the amount of power needed to be transfer red and the available room. The coaxial input

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20 shafts consist of a solid shaft and a hollow shaft. The solid shaft carries the 2 nd gear, the 4 th gear and the reverse gear. The hollow shaft carries the 1 st gear, the 3 rd gear and the 5 th gear. Synchronizers are located in a way si milar to a traditional manual transmission. In Figure 2 the synchronizers are located on the two intermediate shafts. The synchronization is completed before gear shifting starts, and this leads to a faster gear shifting operation. When in a specific g ear, the corresponding clutch and synchronizer are engaged and torque is transferred from the engine to the driving wheels through a particular path. Meanwhile, the other clutch is disengaged and the remaining gears freewheel. In the gear shifting process, there is a period that both clutches are transferring torque from the engine to the gearbox. This clutch overlapping process involves the engagement of the oncoming clutch and the disengagement of the off going clutch. The clutch overlapping mechanism ens ures no interruption of the power transmission occurs between the engine and the driving wheels during gear shifting procedure. To achieve a fast and smooth clutch to clutch shifting, a sophisticated control of clutch slippage is performed. The clutch to c lutch control of gear shifting between two consecutive gears is described as following. Take the gear shifting from first gear to second gear as an example. The clutch to clutch shift is automatically controlled by the Electrical Control Unit (ECU) and imp lemented by the relevant actuators. Before the slippage of the two clutches starts to change, the clutch pressures in the two clutches are changed to meet the pressure threshold when the torque capacity of the oncoming clutch starts to be positive and the torque capacity of the off going clutch decreases to the critical level that the off going clutch begins to slip. This procedure eliminates the time delay that could bring an

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21 undesirable impact to the clutch to clutch shift quality. After that, the torque capacity of the oncoming clutch continuous to increases in a pre programmed manner and the torque capacity of the off going clutch is controlled to decrease at a rate that ensures the output torque of the transmission track s the demanded level. The torque c apacity is controlled by the clutch pressure applied by the related actuators. This concurrent process eliminates the power transmission interruption that happens in manual transmission s automated manual transmission s and classic automatic transmission s d uring gear shifting. Therefore, the clutch to clutch control process allows both rapid gear shifting accomplishment and continuous torque transfer to the driving wheels. A similar process is repeated when ever gear shifting between another two consecutive g ears occurs.

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22 Figure 3 1 Dual Clutch Transmission Schematic Diagram Base on : Matlab(version: R2011b (7.13.0.564))

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23 Figure 3 2 Dual Clutch Transmission Stick Diagram From E. Galvagno, M.Velardocchia, A. Vigliani, Dynamic and kinematic mod el of a dual clutch transmissio n, Mechanism and Machine Theory, 46 (2011) 794 805

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24 CHAPTER 4 POWERTRAIN M ODEL The vehicle model with dual clutch transmission which is adopted from Matlab(version: R2011b (7.13.0.564)) describes the longitude dynamic mo del of a DCT based powertrain. The model is built to simulate the dynamic behavior of the powertrain during gear shifting transient. The modeled components in the powertrain are engine, dual clutch module, gearbox, drive shaft and vehicle body. The powertr ain parameters used throughout this paper are listed in Table s 4 1, 4 2, 4 3, 4 4, 4 5, 4 6, and 4 7. Gear ratios are defined as the rotational speed on the engine side divided by the rotational speed on the vehicle side. Engine M odel Since the simulati on is focused on the performance of DCT, the powertrain model uses a single cylinder diesel internal combustion engine f or simplicity. The maximum power of the engine is 100 kW and the maximum speed is 7000 rpm. The engine is the only power source of the p owertrain, and generates power by means of a sequence of physical and chemical processes. The Engine Control Unit monitors and manipulates these processes to control the engine torque, ranging from the possible maximum torque to the minimum torque. The engine torque is influenced by many factors, such as throttle opening, engine speed, air/fuel mix ratio, temperature, air compression ratio, etc. Even the most complicated simulation model could probably result in some offset. Since the research work is f ocused on the control law of clutch to clutch shift, the engine torque is simplified to be a function of only engine speed by linear regression. The neglected dynamics of

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25 the engine can be regarded as the modeling uncertainties, and the robustness of the c lutch to clutch shift controller against these modeling uncertainties will be discussed later. The engine model parameters include engine inertia, initial velocity, engine time constant and initial normalized throttle opening. The demanded engine torque usually equals the nominal engine torque that can be determined by the acceleration pedal position (or the throttle opening) and the manufacturer specific look up table. The engine speed dynamics are modeled by a first order linear differential equatio n as below: where is the torque generated by the engine, and is the torque transmitted through the dual clutch module. Clutch Model The dual clutch module is built as a wet type multi plate system integr ated with the gearbox. The wet type friction clutch is widely used due to its compactness and easiness of controlling. The slippage of the wet type friction clutch plate is determined by the clutch pressure which is supplied by a hydrodynamic actuator. For simplicity, the clutch is modeled as a wet four plate fixed kinetic friction coefficient system. The clutch starts to engage as the clutch pressure exceeds the preset engagement threshold pressure. For the clutch to lock, the relative rotational speed bet ween the driving plate and driven plate should be smaller than a pre selected value.

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26 Gearbox Model Figure 4 2 shows the layout of the 5 speed d ual clutch t ransmission model, which is adopted from Matlab/Simulink. For simplicity, only components that are related to clutch to clutch shifting dynamics such as clutches, gears and shafts are included. And power path s and gear ratio s are presented in a more explicit way. The DCT can present different configurations during normal operation corresponding to diffe rent power paths between the input shaft and output shaft. As shown in Figure 4 2 the input shaft is split into two power paths. One power path can be connected to the final drive via the odd gear shaft S1 if the frictional clutch CL1 is applied. Anoth er power path can be connected to the final driving via the even gear shaft S2 if the frictional clutch CL2 is applied. The pinions, which are labeled as O1 and O2, mesh with the final drive all the time. The gear ratio can be selected by controlling corre sponding synchronizers before the engagement and disengagement of corresponding clutches. (Synchronizers are not included in the figure, because the synchronization procedure is completed before clutch to clutch control is applied.) The speed ratio of the transmission is determined by the selected gears and remains constant during clutch engagement. For example, 1st gear is achieved by engaging 1st gear synchronizer and applying the odd clutch CL1. Other speed ratios are achieved in similar manne r When pow er on gear shifting occurs, the engagement of the oncoming clutch and disengagement of the off going clutch occur at the same time. The power transmission from engine to driving wheels remains continuous thanks to the overlapping of two power paths during the gear shifting transient. The dynamics of the gearbox are modeled as lumped inertias on the primary shafts, and secondary shafts. The transmission loss due to friction is lumped in the

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27 meshing loss coefficient. Gear ratios are listed in Table 2. Gear inertia of each gear is 3* Output Shaft Model The output shaft that connects the gearbox with the final drive is modeled as a linear spring damper system with inertia. The equation of motion can be described by the following function, where and are the stiffness and damping coefficient of the output shaft, and are the rotational speed of the output shaft and final drive, and is the torque transmitted by the output shaft. Figure 4 3 shows the diagram of out put shaft model. The input which is labeled as R is connected with the DCT and the output which is labeled as F is connected to the final drive. Final Drive Model Th e final drive is modeled as a fixed ratio gearbox without compliance or inertia. The transmission loss is lumped in the meshing loss. Vehicle Body Model Since the work mainly focuses on the clutch control, wheel slip is neglected. The vehicle body mass, wheel inertia, side shaft inertia and relevant vehicle geometry parameters are included in the model. To simulate different working conditions, the road incline, wind velocity, vehicle frontal area, and drag coefficient are also included in the model.

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28 Ta ble 4 1 Gearbox Parameters Odd Gears Even Gears Gear Ratio 1st 3.78 3rd 1.43 5th 0.84 2nd 2.18 4th 1.03

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29 Table 4 2 Dual Clutch Module Parameters Each Clutch Effective Torque Radius (mm) 130 Number of Friction Surfaces 4 Engagement Piston Area ( ) 1000 Kinetic Friction Coefficient 0.3 Static Kinetic Friction Coefficient 0.31 De rating Factor 1 Clutch Velocity Tolerance (rad/sec) 0.001 Engagement Threshold Pressure (pa) 1000 Time Constant (sec) 0.02 Table 4 3 Engine Parameters Inertia (kg* ) 0.2 Time Constant (sec) 0.2 Max. Power (kW) 100 Spd. at Max. Power (rpm) 5500 Max. Output Torque (Nm) 380 Min. Output Torque (Nm) 80 Max. Engine Speed (rpm) 7000 Min. Engine Speed (rpm) 500 Table 4 4 Input shaft Parameters Inertia (kg* ) 0.003 Damping Coefficient (N*m/(rad/sec)) 10 Stiffness (N*m/rad) 3000 Table 4 5 Output Shaft Parameters Inertia (kg* ) 0.0002 Damping Coefficient (N*m/(rad/sec)) 20 Stiffness (N*m/rad) 10000

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30 Table 4 6 Final Drive Parameters Gear Ratio 3. 7 Efficiency 0.86 Table 4 7 Vehicle Body Parameters Side Shaft Inertia (kg* ) 0.01 Tire Inertia (kg* ) 0.5 Tire Rolling Radius R (m) 0.312 Number of Wheels per Axle 2 Vehicle Mass (kg) 1600 Horizon tal Distance from CG to Front Axle (m) 1.7 Horizontal Distance from CG to R ear Axle (m) 2 CG Height above Ground (m) 0.5 Frontal Area ( ) 3 Drag Coefficient 0.4

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31 Figure 4 1 Vehicle Model with DCT From: Matlab(version: R2011b (7.13.0 .564))

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32 Figure 4 2 Simplified Diagram of DCT Model

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33 Figure 4 3 Model of Output Shaft From: Matlab(version: R2011b (7.13.0.564))

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34 CHAPTER 5 CLUTCH TO CLUTCH SHIFT CONTROLLER DESIGN Background Materials The function of clutch to clutch controller is: (1) to track the demanded output torque, (2) to achieve a fast and smooth clutch to clutch shift that reduces friction losses and ensures high riding comfort with a limited torque disturbance, (3) to make a trade off between fast and smooth c lutch to clutch shift that is tunable with calibration parameters that are as few as possible, and (4) to have stability and robustness against uncertainties and disturbances such as errors in the models, measurement noise and unpredicted disturbances. B efore the clutch to clutch shift controller design is introduced, it is necessary to analyze the most common working condition of DCT. The most common working conditions are: (1) Vehicle launch: The vehicle accelerates from standstill until the clutch engageme nt is completed. (2) Power on upshift: The DCT shifts one gear upwards with torque transmitted continuously from the engine to the wheels (3) Power on downshift: The DCT shifts one gear downwards with torque transmitted continuously from the engine to the wheels There are also other less studied gear shifting operations such as power off upshift, power off downshift, and so on. Since they are not related to clutch to clutch shift, they are not included in the research. Vehicle Launch Vehicle launch is the proc ess of accelerating the vehicle from standstill until the clutch is engaged. It is a relatively simple process compared to power on upshift and power on downshift because it usually only requires the operation of one clutch. Before the vehicle launch, the engine is running at idle speed. A fast and smooth clutch

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35 engagement is required to match the speed of the engine and DCT transmission with a trade off between minimal friction loss and high riding comfort. During vehicle launch, there are three phases of clutch engagement defined by clutch slip speed. The clutch slip speed is quantified by the difference between the rotational speed of the driving plates and the rotational speed of the driven plates. The clutch slip speed and clutch torque during the clutch lock transient are shown in Figure 5 1. I n the first phase, the clutch actuator activates the oncoming clutch until the driving plate and the driven plate start to engage but still transmit no torque. In the second phase, the clutch pressure contin uous to increase to reduce the clutch slip speed until the clutch slip speed reaches the locking threshold. In the third phase, the clutch locks and the clutch engagement process is completed. Power On Upshift Power on upshift is requested to improve fu el economy by decreasing the engine speed. Before the power on upshift begins, the next gear has been selected. The power on upshift starts with a clutch to clutch shift phase that means the disengagement of the off going clutch and the engagement of the o ncoming clutch. A good clutch to clutch shift phase is required to be fast and smooth without introducing power transmission interruption and noticeable output torque fluctuation. The clutch to clutch shift will be discussed in later section. After clutch to clutch shift, the oncoming clutch continues engagement procedure until the slip rate reaches the locking threshold. After that, the clutch locks and the power on upshift process is completed. Power On Downshift Power on down shift is requested to incr ease torque by increasing both engine speed and engine torque or to decrease vehicle speed Before the power on downshift

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36 begins, the next gear has been selected. The power on downshift starts with a clutch to clutch shift phase that means the disengagemen t of the off going clutch and the engagement of the oncoming clutch. A good clutch to clutch shift phase is required to be fast and smooth without introducing power transmission interruption and noticeable output torque fluctuation. After clutch to clutch shift, the oncoming clutch continues the engagement procedure until the slip rate reaches the locking threshold. After that, the clutch locks and the power on down shift process is completed. Clutch to Clutch Shift During clutch to clutch shift, the torqu e from the engine transfers from the off going clutch to the oncoming clutch by means of simultaneously engaging the oncoming clutch and disengaging the off going clutch. In order to ensure a fast response, the clutch pressure of the off going clutch is re duced to the locking threshold and the oncoming clutch is pre filled to be prepared for engagement. After that, as the on coming clutch starts to engage, the off going clutch reduces the torque capacity by reducing clutch pressure. To track the demanded ou tput torque of the transmission, the torque transmitted by the off going clutch is computed in real time and implemented to fill the gap between the demanded output torque and actual output torque. Supervisory Gear Shifting Controller The control logic of a supervisory gear shifting contr oller is illustrated in Figure 5 2 Typically, a gear shifting controller makes decision based on various inputs, such as current gear position, current vehicle speed, engine speed, throttle opening, interpretation of dr gear shifting controller makes a decision such as upshift, downsh ift, or gear position holding. Gear position holding is defined as keeping the gear ratio unchanged.

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37 To implement control logic of a gear shifting controller, the following three criteria need to be addressed: (1) to detect the time the shift is initiated, (2) to create a specific rate of engagement and disengagement of the clutches, and (3) to determine the completion of the shift. Clutch to Clutch Shift ing Controller The clutch to clutch shift control algorithm for the clutch pressure regulation during gear shifting for upshifting, downshifting, lock clutch 1, and lock clutch 2 is shown in Figure 5 3, Figure 5 4, Figure 5 5 and Figure 5 6 respectively. During the gear shifting transient, there is a period of time that both clutches are applied. The disengagement of off going clutch and engagement of ongoing clutch are overlapping each other. This process fills the torq ue hole during gear shifting, but on the other hand may bring difficulty to the control of the total output. In order to reduce output torque difference during this period, a new control algorithm is adopted. When the oncoming clutch is being applied in a prefixed manner, the off going clutch torque capacity is controlled to fill the gap between the ideal output torque and the part of total output torque which is contributed by the oncoming clutch. Two electrohydraulic valves that are used to route pressure oil to the clutch actuate the entire procedure. The oncoming clut ch pressure is applied in a preprogrammed manner that allows a firm and fast engagement of the oncoming clutch. Meanwhile, the desired output torque of the off going clutch is calculated based on the difference between the desired total output torque of the transmission and the portion of the total output torque contributed by the oncoming clutch. An inverse clutch unit then determines the desired off going clutch

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38 pressure. After that, the off going clutch is controlled to transfer desired torqu e and the total output torque difference is reduced.

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39 Figure 5 1 Clutch Lock

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40 Figure 5 2 Control Logic of Supervisory Gear Shifting Controller

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41 Fig ure 5 3 Clutch to Clutch Shifting Con trol Law CL1 (Off G oing) to CL2 (Oncoming)

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42 Figure 5 4 Clutch to Clutch Shifting Control Law CL2 (Off G oing) to CL1 (Oncoming)

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43 Figure 5 5 Lock Clutch 1 From: Matlab(version: R2011b (7.13.0.564))

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44 Figure 5 6 Lock Clutch 2 F rom: Matlab(version: R2011b (7.13.0.564))

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45 CHAPTER 6 NUMERICAL SIMULATION The vehicle model with dual clutch transmission which is adopted from Matlab(version: R2011b (7.13.0.564)) describes the longitude dynamic model of a DCT based powertrain. The a dopted vehicle model wa s used to simulate dual clutch t ransmission output torque during gear shifting transient s of a small passenger car. The mass of the vehicle is 1500 kg, and the maximum engine power is 100 kW. All the necessary parameters of the dual clutch transmission are listed in Table 4 1 through Table 4 7. The simulation s were run for power on upshifts from gear 1 to gear 5 with a full throttle opening. The vehicle accelerated from standstill on a horizontal ground. The simulation s were run fo r 50 sec for each time. First, to validate the effectiveness of the proposed clutch to clutch shift control law, a pair of contrast simulation s were run. To compare gear shifting quality, output torque difference wa s chosen as the parameter. The output torque of the dual clutch t ransmission without the proposed clutch to clutch control law was plot in Figure 6 1 And the output torque of the dual clutch transmission improved by the proposed clutch to clutch control law was plot in Figure 6 2 As shown in the figures, the horizontal axes were labeled as time with unit sec and the vertical axes were labeled as output torque with unit N m. After that, to study the impact of clutch actuator time constant on gear shifting quality, a set of contrast simulati on s were performed. The output torque during gear shift with different clutch actuator constants were show n in Figure 6 2 through Figure 6 6 The axes of the figures were labeled in the following way: the X axes were labeled as time

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46 with unit sec and the Y axes were labeled as output torque with unit N m. Figures 6 2 showed the output torque during gear shifting with clutch actuator time constant set as 0.02 sec. Figures 6 3 showed the output torque during gear shifting with clutch actuator time constant set as 0.01 sec. Figures 6 4 showed the output to rque during gear shifting with clutch actuator time constant set as 0.04 sec. Figures 6 5 showed the output torque during gear shifting with clutch actuator time constant set as 0.001 sec. Figures 6 6 showed the output torque during gear shifting with clut ch actuator time constant set as 0.1 sec. Finally, to analyze the influence of clutch pressure profile of gear shifting quality, a set of contrast simulations were conducted. The output torque disturbances during gear shifting with different clutch pressur e changing rate were showed Figure 6 2, Figure 6 7, and Figure 6 8 In Figure 6 2, the output torque was generated with a moderate clutch pressure changing rate. In Figure 6 7, the output torque was produced with a larger clutch pressure changing rate and in Figure 6 8 the corresponding clutch pressure changing rate is smaller than that of Figure 6 2. To analyze the simulation results numerically, peak torque s during gear shifting in each simulation were listed in Table 6 1.

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47 Table 6 1 Simulation R esults Gear 1 2 3 4 5 Original (Nm) 560 545 540 580 440 Improved (Nm) (Time Constant=0.02sec) 560 540 580 415 310 Improved (Nm) (Time Constant=0.01sec) 550 530 580 415 305 Improved (Nm) (Time Constant=0.04sec) 560 540 580 410 300 Improved (Nm) (T ime Constant=0.1sec) 570 560 565 405 295 Improved (Nm) (TimeConstant=0.001sec) 560 580 580 405 305 Improved (Nm) (Larger Clutch Pressure Increasing Rate) 560 530 580 410 310 Improved (Nm) (Smaller Clutch Pressure Increasing Rate) 550 530 580 405 305

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48 Figure 6 1 Original Output Torque Dynamics Time (sec) Torque (N m)

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49 Figure 6 2 Optimized Output Torque Dynamics (actuator time constant 0.02s) Time (sec) Torque (N m)

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50 Figure 6 3 Optimized Output Torque Dynamics (Actuator Time C onstant 0.04 s) Time (sec) Torque (N m)

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51 Figure 6 4 Optimized Output Torque Dynamics (Actuator Time C onstant 0.01 s) Torque (N m) Time (sec) Torque (N m)

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52 Figure 6 5 Optimized Output Torque Dynamics (Actuator Time C onstant 0. 001 s) Time (sec) Torque (N m)

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53 Figure 6 6 Optimized Output Torque Dynamics (Actuator Time C onstant 0. 1 s) Time (sec) Torque (N m)

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54 Figure 6 7 Optimized Output Torque Dynamics (With A Larger Clutch Pressure Increasing Rate) Time (sec) Torque (N m )

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55 Figure 6 8 Optimized Output Dynamics (With A Smaller Clutch Pressure Increasing Rate) Time (sec) Torque (N m)

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56 CHAPTER 7 DISCUSSION Validation of the Proposed Clutch to Clutch Shift Control Law Comparing the simulation results plot in Figure 6 1 and Figure 6 2 we can see that the output torque difference mainly occurred during gear shifting transient and the torque difference s during gear shifting transients were reduced significantly The magnitudes of the peak output torques during gear shifting transients were chosen to measure the gear shifting smoothness. From Table 7 1, we can see clearly the peak output torques and the differences between the peak output torque and the demanded output torque (160 N m ). Comparing the torque output difference magnitud e, we can see that the output torque difference magnitude was reduced significantly with the adopted clutch to clutch control law that controlled torque capacity to achieve the ideal total output torque. By calculating, we find that the average peak output torques were reduced by 32.5%. Therefore, the clutch to clutch control is effective to reduce output torque difference From the figures in Table 7 1, we find that the effectiveness of the proposed control method is more obvious on gear 4 and gear 5. Therefore, we can further conclude that the control method is more useful when the clutch rotation speed is higher. Discussion of Influence of Clutch Actuator Time Constant By comparin g the output torque difference s in Figure 6 2 through Figure 6 6 we analyzed the relationship between the time const ant of clutch actuators and torque disturbances during gear shifting transient s To measure the output torque difference s, the peak output torques during gear shifting transients were listed in Table 7 2.

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57 By calculating, the differences between the peak output torques and the demanded torques (160 N m ) tended to increase as the clutch actuator time constants grew. The differences were shown in the parenthesis in Table 7 2. Therefore, we conclude that th e faster the clutch actuator responses, the smoother the gear shifting transients are. In addition, by simulation we find that too large clutch actuator time constant may lead to control problems of the engine. For example, engine may exceed its maximum sp eed if the clutch actuator time constant is too large. Discussion of Influence of Clutch Pressure Profile on Gear Shift Quality By comparin g the output torque in Figure 6 2, Figure 6 7, and Figure 6 8 we studied the relation between the gear shifting smoothness and clutch pressure profile. To analyze the relation between the gear shifting smoothness and clutch pressure profile, we listed the peak output torques during gear shifting transients in Table 7 3. By calculating the average differences be tween the peak output torques and the demanded torques (160 N m ) were 314 N m when the clutch pressure changing rate was smaller, 321 N m when the clutch pressure changing rate was moderate, and 322 N m the clutch pressure changing rate was larger. Therefo re, we find that the larger clutch pressure changing rate the severer the torque disturbances during gear shifting transients

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58 Table 7 1 Peak Output Torqu es A Gear 1 2 3 4 5 Original Output Torque (N m ) Difference Between Demanded Output Torque (N m ) 560 (400) 545 (385) 540 (380) 580 (400) 440 (280) Improved Output Torque (N m ) (Time Constant=0.02sec) Difference Between Demanded Output Torque (N m ) 560 (400) 540 (380) 580 (420) 415 (255) 310 (150)

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59 Table 7 2 Peak Out put Torque s B Gear 1 2 3 4 5 Improved Output Torque (N m ) (Time Constant=0. 00 1sec) Difference Between Demanded Output Torque (N m ) 570 (410) 545 (385) 565 (405) 410 (250) 295 (135) Improved Output Torque (N m ) (Time Constant=0.01sec) Difference Betw een Demanded Output Torque (N m ) 560 (400) 540 (380) 580 (420) 410 (250) 300 (140) Improved Output Torque (N m ) (Time Constant=0.02sec) Difference Between Demanded Output Torque (N m ) 560 (400) 540 (380) 580 (420) 415 (255) 310 (150) Improved O utput Torque (N m ) (Time Constant=0.04sec) Difference Between Demanded Output Torque (N m ) 560 (400) 530 (370) 580 (420) 415 (255) 310 (150) Improved Output Torque (N m ) (Time Constant=0.1sec) Difference Between Demanded Output Torque (N m ) 560 (400 ) 580 (420) 580 (420) 415 (255) 310 (150) Table 7 3 Peak Output Torque s C Gear 1 2 3 4 5 Improved Output Torque (N m ) ( With Smaller Clutch Pressure Changing Rate ) Difference Between Demanded Output Torque (N m ) 550 (390) 530 (370) 580 (420 ) 405 (245) 305 (145) Improved Output Torque (N m ) ( With Moderate Clutch Pressure Changing Rate ) Difference Between Demanded Output Torque (N m ) 560 (400) 540 (380) 580 (420) 415 (255) 310 (150) Improved Output Torque (N m ) ( With Larger Clu tch Pressure Changing Rate ) Difference Between Demanded Output Torque (N m ) 560 (400) 540 (380) 580 (420) 420 (260) 310 (150)

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60 CHAPTER 8 CONCLUSION This thesis aims at studying the main factor that causes output torque difference of DCT duri ng gear shifting transient and reducing output torque transient. A model including a dual clutch t ransmission model a simplified vehi cle model equipped with a DCT was adopted from Matlab/Simulink. The importance of clutch to clutch shift control during ge ar shifting transient in reducing the output torque difference was proved by computer simulation in Matlab/Simulink. T he validation of the proposed clutch to clutch control algorithm was justified by comparing output torque difference between the original clutch to clutch law and the proposed one. By analyzing the simulation results, the average differences between the peak output torques and the demanded output torques were reduced by 32.5% with the help of the proposed clutch to clutch shifting control la w. By analyzing the output torque curves in Figures 6 2 through 6 8, we found t he effectiveness of the proposed control method is more obvious when the clutch rotation speed was higher. In addition, clutch actuator time constant ha s influence on gear shi fting smoothness. As showed in Table 7 2, the smaller the clutch actuator time constant is, the smoother the gear shifting transients tend to be. In addition, too larger clutch actuator time constant may result in control problems of engine. In simulatio ns that were reflected in Figure s 6 2 6 7 and 6 8, the smaller clutch pressure increasing rate s leaded to rougher gear shift ing transients. In the future research, t he correlation between clutch pressure increasing rate and the r apidness of gear shifting remains to be studied.

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61 Future work should go further on how to set the clutch pressure profile to achieve the best tradeoff between the rapidness and the smoothness of gear shifting. Also, further studies should extend to other types of vehicles to make the proposed clutch to clutch shifting control law more general.

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62 REFERENCES [1] E. Galvagno, M.Velardocchia, A. Vigliani, Dynamic and kinematic model of a dual clutch transmissio n, Mechanism and Machine Theory 46 (2011) 794 805 [2] Yonggang Liu, Datong Qin, Hong Jian g, Charles Liu, Yi Zhang, Clutch torque formulation and calibrat ion for dry clutch transmission, Mechanism and Machine Theory 46 (2011) 218 227 [3] Xinyong Song, Zongxuan Sun, Pressure Based Clutch Control for Automotive Transmission Using a Sliding Mode Controller, IEEE/ASME transactions on Mechatronics Vol. 17, No. 3, June 2012 [4] Paul D. Walker, Nong Zhang, Richard Tamba, Control of gear shifts in dual clutch transmission powertrain Mechanical Systems and Signal Processing 25 ( 2011 ) 19 23 1936 [5] Manish Kul karni, Taehyun Shim, Yi Zhang, Shift dynamics and control of dual clutch transmissions, Mechanism and Machine Theory 42 (2007) 168 182 [6] Ma gnus Pettersson, Lars Nielsen, Gear Shif ting by Engine Control, IEEE/ASM transaction on Co ntrol System Technology Vol. 8, ISSN: 1063 6536, 2000 [7] Koos vab Berkel, Theo Hofman, Alex Serrarens, Maarten Steinbuch, Fast and Smooth Clutch Engagement Contro l for Dual Clutch Transmissions, Control Engineering Practice 22 (2014) 57 68 [8] A. C. van der Heijden, A. F. A. Serrarens, M. K. Camlibel, and H. Nijmeijer, Hybrid Optimal Co ntrol of Dry Clutch Engagement, International Journal of Control 80:11 (2007) 1717 1728 [9] Shushan Bai, Joel Maguire, Huei Peng, Dynamic Analysis and Control System Des i gn of Automatic Transmissions SAE International 2012 [10 ] Matlab R2011b (7.13.0.564)

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63 BIOGRAPH ICAL SKETCH Zhe Wang was born in Harbin, China. After attending local schools, he entered Jilin Universit y in Changchun, China, where a b achelor s degree in a utomot ive e ngineering was awarded to him in 2012. Shortly there after he went to University of Florida to study for Master of Science in mechanical engineering.