車輛外文文獻(xiàn)翻譯-干式雙離合器變速器的離合器扭矩公式和校準(zhǔn)【中文5690字】【PDF+中文WORD】,中文5690字,PDF+中文WORD,車輛,外文,文獻(xiàn),翻譯,干式雙,離合器,變速器,扭矩,公式,校準(zhǔn),中文,5690,PDF,WORD Clutch torque formulation and calibration for dry dual clutch transmissionsYonggang Liua,b,Datong Qina,Hong Jiangc,Charles Liuc,Yi Zhangb,aThe State Key Laboratory of Mechanical Transmission,Chongqing University,Chongqing 400044,ChinabDepartment of Mechanical Engineering,University of Michigan-Dearborn,Dearborn,MI 48128,United StatescTransmission&Driveline Research&Advanced Engineering,Ford Motor Company,Dearborn,MI 48128,United Statesa r t i c l ei n f oa b s t r a c tArticle history:Received 2 March 2010Received in revised form 15 September 2010Accepted 21 September 2010Available online 20 October 2010This paper focuses on the clutch torque formulation and calibration for dry dual clutchtransmissions(DCT).The correlation on the theoretical clutch torque and control parameters isestablished based on constant friction power and clutch actuator kinematics.An algorithmbased on powertrain dynamics is proposed for the calculation of clutch torque during vehiclelaunch and shift operations.This algorithm uses wheel speed sensor data as input and iscapable of determining the clutch torque while both clutches are slipping,thus provides areliable correlation between clutch torque during real time operations and clutch actuatorcontrol variables.The accuracy of the proposed algorithm has been validated by torquemeasurement in prototype testing on prove ground.2010 Elsevier Ltd.All rights reserved.Keywords:Dual clutch transmissionsClutch torqueCalibration1.IntroductionDual clutch transmissions(DCT)feature drivability comparable to conventional automatic transmissions and fuel economyeven better than manual transmissions.Due to these advantages,there is an on-going trend in the automotive industry to developand market DCT vehicles that are fuel efficient but at no expenses of performance and drivability 1,2.It can be predicted thatvehicles equipped with dual clutch transmissions will have a significant market share in the near future.The clutch torque control during launch and shifts is crucial for development of vehicles with DCT drive trains.Kinematically,gear shifting in a dual clutch transmission is similar to clutch-to-clutch shift in a conventional automatic transmission.Manyvaluable researches by both analytical and experimental means have been successfully conducted in transmission dynamics andcontrol areas.Researchers at the Ford Research Laboratory 3,4 were among the first to quantitatively analyze dynamic transientsduring transmission shifts by computer modeling and testing.The synchronization of the oncoming and off-going clutches hadbeen achieved using hydraulic washout valves in automatic transmissions that have clutch-to-clutch shift patterns 5.Systematicstrategies that integrate engine control and clutch torque control had been developed for production vehicles for optimizedvehicle launch and shift quality 6,7.Researches and developments as those cited above have made possible the technologymaturity of conventional automatic transmissions.Despite the similarity in clutch-to-clutch shift characteristics,a dual clutch transmission differs from a conventional automatictransmission in that the later has a torque converter between the engine output and transmission input.The presence of thetorque converter cushions the powertrain dynamic transients and is therefore conducive for smoothness during vehicle launchand shifts.Without the cushion effect of torque converter,clutch torque control requires high precision to achieve launch and shiftquality comparable to automatic transmissions.In a previous paper,the authors proposed a systematic model that analyzes thedynamic behavior of dual clutch transmissions and validated the model simulation based on prototype vehicle testing 8.As afurther study,the work presented in this paper is concentrated on the clutch torque formulation and calibration for dry dual clutchtransmissions.Firstly,the theoretical or nominal clutch torque is correlated to the clutch design parameters based on theMechanism and Machine Theory 46(2011)218227 Corresponding author.E-mail address:andingumich.edu(Y.Zhang).0094-114X/$see front matter 2010 Elsevier Ltd.All rights reserved.doi:10.1016/j.mechmachtheory.2010.09.005Contents lists available at ScienceDirectMechanism and Machine Theoryjournal homepage: that the friction power is constant over the friction disk face.This formulation provides the basis for the design ofclutch and its actuator.Secondly,an algorithm based on powertrain dynamics is established for the calculation of clutch torque inthe launching clutch during launch and in both clutches during shift.This algorithm uses wheel speed sensor data as the input andiscapableofaccuratelycalculatingtheclutchtorquewhilebothclutchesare slippingona realtimebasis.Thealgorithmhasseveraladvantages:a)it enables the determination of clutch torque without using the friction coefficient of the friction disk that varies asa function of temperature;b)it provides an effective way to calibrate the clutch torque against the design and control variables ofthe clutch and its actuator;c)it provides a reliable correlation between clutch torque and clutch control variable during real timeoperation for adaptive transmission control.Thirdly,the analytical formulation and algorithm for clutch torque calculation arevalidated against prove ground test data and laudable agreements are achieved between analytical and test data.2.Analytical clutch torque formulation2.1.Actuator kinematics and clutch torqueThe structure of one of the clutches and its actuator in a dry clutch DCT 9 is illustrated in Fig.1.The other clutch and actuatorassembly has similar design.Normally open clutch design is applied in DCT for safety considerations.As shown in the figure,theclutch actuator(or controller)consists of motor,spring,screw and roller.When the motor turns,the roller is displaced a distance xalong the screw,creating the leverage for the generationof an axial force on the release bearing.This force is then magnified by thepressure plate level,resulting in the pressure force that clamps the friction disk.For a given clutch actuator design,the clutchtorque is a function of motor rotation angle that is related to the roller displacement x by the screw parameter.In this paper,the concept of constant friction power(i.e.the conversion rate from kinetic energy to friction work during clutchslippage)is used for the formulation of the nominal clutch torque 10.Based on this assumption,the energy conversion rate isexpressed as follows:fpv=Ct1where,f is the friction coefficient of friction disk,p is the pressure,v is the relative velocity at a point,and Ctis the energyconversion rate per unitary area on the friction face.Based on this assumption,the pressure at any point over the disk face isexpressed as,p=Ctfv=Ctfr=Cr2where is the angular velocity and r is the radius at the point.The quantityCtfis a constantover the disk face andis designatedasC.Apparently,the pressureover the disk face varies reverselyproportional to the radius.The maximumpressure pmaxoccurs at theFig.1.Sketch of dual clutch controller structure.219Y.Liu et al./Mechanism and Machine Theory 46(2011)218227inner radius of the friction disk and the constant C can be expressed as C=d2pmax,with d as the inner diameter of the friction disk.Plugging C back into Eq.(2),the pressure on the disk face is then expressed as,p=12pmaxdr:3The pressure force on the pressure plate can then be calculated as follows:F=2D=2d=2prdr=2D=2d=212dpmaxrrdr=pmaxdDd24where,D and d are the outer and inner diameters of the friction disk respectively.The clutch torque of one contact surface iscalculated by the following,TCL=2D=2d=2fpr2dr=2fD=2d=212dpmaxrr2dr=fpmaxdD2d2?8=pmaxdDd2D+d4=fFD+d4:5The number of contact surfaces is two for each clutch,so the nominal clutch torque TCLis calculated byTCL=fFD+d2:62.2.Correlation on clutch torque and control parameterThepressureforceonthepressureplateis relatedtotheforceonthereleasebearingthroughthepressureplatelever.However,due to the deformation of the pressure plate lever that has a design similar to a diaphragm spring and the existence of backlashes,there exist non-linear characteristics between the clutch torque and the actuator control parameter.To account for this non-linearity,testshave been performedtomeasure therelease bearingforce(i.e.theengagementload).Basedontest data,thereleasebearing force is correlated to the engagement travel as shown in Fig.2.As shownin Fig.2,there are substantial forces(denoted asF0)on therelease bearingof both clutches whenengagement travelsare zero due to high rigidity for the pressure plate lever.Because of this,two separate functions must be used to correlate therelease bearing force Fbwith the roller displacement.Theengagementloadbeforereleasebearingtravelsis illustratedin Fig.3.As shownin Fig.3,thereleasebearingforceFbandthespring force Fsis related as follows before Fbreaches F0,Fb=xrollerLxrollerFs7Fig.2.Relationship between travel and load of bearing.220Y.Liu et al./Mechanism and Machine Theory 46(2011)218227where,xrollerindicates the position of the roller,L is the total effective length of lever,and Fsis the spring force with an initial valueFs0.The spring displacement is very small when FbbF0since release bearing displacement is near zero and the spring force remainsalmost constant,i.e.,Fs=Fs0if FbbF0.At the threshold when Fb=F0,the displacement of roller xpcan be solved from Eq.(7)asfollows,xp=F0Fs0+F0L:8Fig.3.Engagement load before release bearing travels.Fig.4.Engagement load after release bearing travels.221Y.Liu et al./Mechanism and Machine Theory 46(2011)218227Therefore,when xrollerxp,the release bearing force is represented in terms of roller displacement by Eq.(7).After the bearing begins to travel,a separate function is required to correlate the release bearing force and the rollerdisplacement since the spring compression is affected by the bearing travel.The engagement load after release bearing travels is illustrated in Fig.4.As shown in Fig.4,the amount of spring compressionchanged by the bearing travel is determined as follows,xs=xbLxrollerxroller9where xsis the increment of spring length and xbis the engagementtravel of bearing.Due to this increment,the spring force afterbearing moving is expressed as follows:Fs=Fs0kxrollerLxrollerxb10where k is the spring stiffness.The equilibrium of the actuator lever requires the following equation to be satisfiedFsxroller=FbLxroller:11Combining Eqs.(10)and(11),the release bearing force Fbcan be represented in term of the roller displacement asfollows:Fb=xrollerLxrollerFsxroller xp=F0Fs0+F0LFs0kxrollerLxrollerxb?xrollerLxrollerxrollerN xp=F0Fs0+F0L:8:122.3.Clutches torque and control parameter correlationAs indicated in Eq.(6),the clutch torque is a function of the pressure force on the pressure plate,friction coefficient and clutchdimensions.The main parameters of the two clutches used in the prototype are shown in Table 1.Table 1Main parameters of clutch.ParametersClutch 1Clutch 2Clutch outer diameterD1=232.5 mmD2=225 mmClutch inner diameterd1=157 mmd2=157 mmLever ratioiratio1=3.6iratio2=4.2Friction coefficientf1=0.35f2=0.35Fig.5.Relationship between clutch torque and displacement of roller.222Y.Liu et al./Mechanism and Machine Theory 46(2011)218227According to Eq.(6),the nominal clutch torque in both clutch 1 and clutch 2 can be calculated as follows,TCL1=f1Fb1iratio1 D1+d1=2=1000=0:35 3:6Fb1 232:5+157=2=1000=0:2454Fb1TCL2=f2Fb2iratio2 D2+d2=2=1000=0:35 4:2Fb2 225+157=2=1000=0:2808Fb2?13where,Fb1and Fb2are the release bearing forces for clutch 1 and clutch 2 respectively.The spring constants are selected to be150 N/mm for both actuators and the length of the actuator lever is L=100 mm.The roller displacements at which release bearingbegin to move are xp1=25 mm and xp2=30 mm respectively.The initial spring forces are determined by Eq.(8)as Fs1=1689 Nand Fs2=1860 N.Before the release bearings start to move,the clutch torque and roller position can be expressed as following,TCL1=0:2454Fb1=0:2454 xroller1Lxroller1Fs=414:48 xroller1100 xrolle1xrolle1xp1=25TCL2=0:2808Fb2=0:2808 xroller2Lxrolle2Fs=522:29 xroller2100 xroller2xrolle2 xp2=30:8:14After the bearings start to move,the relationship between engagement travel xband the bearing load Fbcan be obtained fromFig.2,which means that Fbis a function of xb,i.e.,Fb=f(xb).When the engagement travel is smaller than 4 mm,it is accurateenough to fit the function f(xb)by the following linear functionFb1=99:5xb1+563xb1 4mm:15Fig.6.Dual clutch transmission dynamic model.Table 2Main parameters of test vehicle.ParametersValueVehicle massM=1400 kgTransmission gear ratiosi1=3.917i2=2.429i3=1.436i4=1.021i5=0.848i6=0.667Final drive gear ratioia1=3.762ia2=4.158Tire radiusr=0.2975 mAir resistance coefficientCD=0.328Frontal areaA=2.12 m2223Y.Liu et al./Mechanism and Machine Theory 46(2011)218227So Eqs.(12)and(15)can be combined together(with =xrollerLxroller)to correlate the clutch torque in clutch 1 as follows,TCL1=0:2454 1689 99:51+150 5632199:5+15021!=412411+207242199:5+15021xroller1N xp1=25:16Similarly,the clutch torque in clutch 2 can be represented as a function of xroller2as,TCL2=0:2808 1860 38:252+150 7972238:25+15022!=199782+335702238:25+15022xroller2N xp2=30:17The clutch torques represented by Eqs.(16)and(17)can also be represented graphically by Fig.5.3.Algorithm for clutch torque calculationEqs.(14),(16)and(17)provide the analytical calculation for the clutch torque in terms of roller position.However,thiscalculation must be calibrated for real world applications since the clutch friction coefficient is temperature dependent.In thissection,an algorithm based on powertrain dynamics is proposed for the accurate calculation of the clutch torque as described inthe following.3.1.DCT powertrain dynamicsIn a previous paper 8,the DCT powertrain dynamics during launch and shifts has been investigated in detail.The dynamicmodel for the dual clutch transmission used in the research is shown in Fig.6.In this model,gear shafts are modeled as lumpedmasses and the four synchronizers are modeled as power switches.As indicated in Fig.6,the mass moments of inertia of thelumped masses are denoted as following:engine output assembly including clutch input side(Ie),clutch 1 driven plate(I1),clutch2 driven plate(I2),solid shaft(I3),hollow shaft(I4),transfershaft 1(I5),transfer shaft 2(I6),output shaft(I7).In similar fashion,e,1,2,3,4,5,6,and 7denote the respective angular velocities.The wheel angular velocity is denoted by w.T1,T2and Torepresent output torques of clutch 1,clutch 2 and output shaft respectively.The vehicle equivalent mass moment of inertia on theoutput shaft is denoted by I.The stiffness and damping coefficient of the powertrain system are not considered since they do notaffect the clutch torque calculations.3.2.Calculation algorithm for clutch torqueThe calculation for cutch torque is based on the powertrain system dynamics.The equations of motion for vehicle launch and12 upshift are presented in the following text.For other operation modes,similar equations can be derived according to thepower flow path,as detailed in 8.Fig.7.Clutch torque comparison during launch.224Y.Liu et al./Mechanism and Machine Theory 46(2011)2182273.2.1.LaunchIn the launchmode,theclutch torquein clutch1 is graduallyincreased untilit is fully engaged,whiletheclutch torquein clutch2 is equal to zero.The torque of clutch 1 is directly used to drive the vehicle.The system of equations of motion is presented asfollows.TeTCL1=Ie e18TCL1T1=I1 119T1Taia1i1=I1eq 320TaTo=I7 721ToTLoad=I w22where,i1is first gear ratio,ia1is final drive ratio which is shared by the 1st,2nd,5th and 6th gears.Teis the engine output torque.TCL1is the clutch torque in clutch 1.Tais the final drive output torque.Ieq1is the equivalent mass moment of inertia in the first gearFig.8.Clutch torque comparison during 12 upshift.Fig.9.Clutch torque comparison during operation in the 4th gear.225Y.Liu et al./Mechanism and Machine Theory 46(2011)218227for the lumped masses including the transfer shaft 1,assembly of the solid shaft and all other components rotating accordingly inthe first gear.wis the angular velocity of the wheel.The road load torque TLoadis expressed by the following equation:TLoad=fW+RA+RGr23where,f is rolling resistance coefficient,W is vehicle mass,r is tire radius,RAand RGare the air and grade resistances respectively.As can be seen from Eqs.(18)(22),clutch torque TCL1can be calculated using Eq.(18)or Eqs.(19)(22)respectively.If theengine torque and engine speed can be measured accurately during vehicle launch torque TCL1can then be directly found fromEq.(18).However,the engine torque and speed during transient operations are very hard to measure accurately resultingunacceptable inaccuracy for clutch torque calculation.On the other hand,the wheel speed of vehicle is more stable in comparisonwith engine speed and can be measured with high accuracy.Therefore,the clutch torque TCL1can be calculated with high accuracyusing Eqs.(19)(22).In Eqs.(19)(22),the angular velocities are related as follows:1=3,7=wand 3=7ia1i1.Thus the equations can becombined to present TCL1in terms of was follows:TCL1=I7+Iia1i1+I1+I1eqia1i1?w+TLoadia1i1:24According to the above equation,the clutch torque TCL1can be calculated during launch,and the accuracy only depends on thewheel acceleration that is the derivative of the wheel speed from the speed sensor.3.2.2.ShiftsThe shift process is divided into two stages,which are torque phase and inertia phase.The system equations for a 12 shift arepresented in the following,which can be easily extended to other shifts.TeTCL1TCL2=Ie e25TCL1i1+TCL2i2Ta=ia1=I3+I1i21+I2+I4i22+I5hi 526TaTo=I7 727ToTLoad=I w28where,i2is second gear ratio,ia2is final drive ratio which is shared by the 3rd and 4th gears.TCL2is the clutch torque in clutch 2.Since 5=7ia1=wia1,Eqs.(26)to(28)can be combined into one single equation:TCL1i1ia1+TCL2i2ia1TLoad=I3+I1i2a1i21+I2+I4i2a1i22+I5i2a1+I7+Ihi w:29When clutch torque TCL1or TCL2equals zero,the other clutch torque can be calculated from Eq.(29)in terms of w.However,during the gear shift process,there are friction torques in both clutches and they cannot be solved using Eq.(29)alone.For thesame reason mentioned previously,Eq.(25)does not provide help since engine torque is not known.As represented in Eqs.(13)(17),the clutch torque is a function of clutch design parameters,friction coefficient and controlparameters.The proportion of the clutch torques in the two clutches should be independent of the friction coefficient since thetemperature effect is the same for both clutches.Therefore,clutch torques in clutch 1 and clutch 2 are proportioned by thefollowing ratio:K=TCL1TCL2=K1K230where,K is the clutch torque proportion.K1and K2are the factors depending on clutch dimension,actuator parameters and rollerposition as detailed in Section 2.Combining Eqs.(29)and(30)leads to the determination of the two clutch torques TCL1and TCL2interms of w:TCL2=I3+I1i2a1i21+I2+I4i2a1i22+I5i2a1+I7+Ihi w+TLoadKi1ia1+i2ia1TCL1=KTCL2:8:31226Y.Liu et al./Mechanism and Machine Theory 46(2011)2182274.Case studyThe clutch torque calculation algorithm described in Section 3 has been implemented based on Matlab/Simulink platform.Aprototype vehicle with parameters shown in Table 2 is tested on prove ground with flat track.Vehicle acceleration,wheel speed,dual clutch roller position and transmission gear positions are recorded during the test.A torque sensor is mounted on the halfshaft to measure the drive train output torque.The measured half shaft torque is converted by related gear ratios to be the equivalent torque value on the input shaft.Thisequivalent torque is compared with the clutch torque calculated by the proposed algorithm as described in the following.4.1.LaunchIn thelaunchoperation,gearpositionis 1st andtheclutchtorquecan be calculated directlyby Eq.(24).The vehicleacc