Modeling and simulation of an automated manual ...MODELING AND SIMULATION OF AN AUTOMATED MANUAL TRANSMISSION SYSTEM Hua Huang, Sebastian Nowoisky, René Knoblich, Clemens Gühmann

MODELING AND SIMULATION OFAN AUTOMATED MANUAL TRANSMISSION SYSTEM

Hua Huang, Sebastian Nowoisky, René Knoblich, Clemens Gühmann

Technische Universität BerlinDepartment of Energy and Automation Technology

Chair of Electronic Measurement and Diagnostic TechnologyBerlin 10587, Germany

{hua.huang@campus., sebastian.nowoisky@, r.knoblich@, clemens.guehmann@}tu-berlin.de

ABSTRACTWith the continuous growth in the emissionrequirements and higher riding comfort demand, theshift quality takes more and more an important role inautomated transmission control algorithms. In order toeffectively optimize the corresponding controlparameters and functions in the transmission controlunits (TCU), the model-based calibration is a suitablemethod. For this purpose a detailed dynamic modelwhich can provide a virtual platform for shift qualityoptimization is imperative and necessary. In this paper a5-speed automated manual transmission (AMT) is usedas a research object and a detailed Modelica® basedhydro-mechanical dynamic model is presented. Finally,model simulations are compared with the measurementsfrom a test bench. Testing results show the dynamicmodel can describe detailed gear shifting phenomena.

Keywords: automated transmission, hydraulic, dynamicmodeling

1. INTRODUCTIONWith the continuous growth in the stricter emissionrequirements and higher riding comfort demand, theshift quality takes more and more an important role inautomated transmission control algorithms. With thetraditional software development process, theserequirements rapidly increase the manpower andfinance resources, especially the optimization periodduring real vehicle calibration. In order to effectivelyoptimize the corresponding control parameters andfunctions in the transmission control units (TCU), themodel-based calibration is a suitable method. Thegeneral process is shown in figure 1. Firstly, a formulaexpression based transmission model is built. By meansof measurements from a test bench or a real vehicle, thedraft model is detailed and improved till it reachescorresponding requirements. Afterwards, this model istaken as a virtual platform to optimize the shift quality.Finally, the optimized control parameters are verified onthe test bench or in the real vehicle, the operation mapsare generated and stored into the TCU.

Figure 1: Model-based Optimization Process

Traditionally the shift quality is assessedsubjectively by the driver's feeling. For the model-baseddevelopment the shift quality objective evaluation is acritical step. This requires that the automatedtransmission model has a detailed performance such asspeed oscillation and the longitudinal accelerationvariations during a gear shifting. Only the detaileddynamic transmission model can reproduce thesebehaviors. Moreover, an AMT is designed andimproved on the basis of a manual transmission (MT), itinherits the MT features such as lower weight, highefficiency and convenient maintenance. With the helpof improved electronic technology and optimizedcontrol algorithms, AMT also offers its own advantages,such as improved driving convenience, reduction oflife-cycle costs and enabled low fuel consumption.

In this paper a 5-speed AMT with dry clutch ischosen as the research object (see Figure 2). AModelica® based nonlinear dynamic hydro-mechanicalAMT model for the future model-based shift qualitydevelopment is presented. The model is relativelysimple, yet it visually describes AMT system detailedstructures as “what you see is what you get” andpredicts the important dynamic gear shifting behaviorsquite well, such as 5 stages synchronization (pre-sync,locking, unlocking, turning hub and engagement),magnetic valve fluid pressure fluctuation under differentcurrents and the driveline oscillation during transmittedtorque changes.

Proceedings of the Int. Conf. on Integrated Modeling and Analysis in Applied Control and Automation, 2013 ISBN 978-88-97999-25-6; Bruzzone, Dauphin-Tanguy, Junco and Merkuryev Eds.

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mailto:[email protected]




Figure 2: Schematic Diagram of the 5-speed AMT

The structure of this paper is: Section 2 gives anintroduction of the hydro-mechanical components anddetailed description of the corresponding workingprinciples. Section 3 presents the simulation results andthe results are also compared with measurements froman AMT equipped test bench. Finally, a summary andfurther research outlook is concluded.

2. MODELINGThis section mainly introduces the AMT modelingprocess and implementation method. Each partseparately presents its hydro-mechanical elementsworking principles. Then the dynamic processes areexpressed through Bernoulli's theory and Newton's laws.The corresponding Modelica® modules are alsodescribed. Finally, in order to compose a nonlinearAMT system, the dynamic shafts are used to flexiblyconnect with the engine, clutch and gearbox.

2.1. Gearbox ModelA gearbox is used to transmit power from the engine tothe driving wheels, satisfy the rotate speed and torquerequirement to the vehicle driving condition. Thegearbox is divided into two parts: hydraulic part(magnetic valves and cylinders) and mechanical part

(synchronization system).As figure 3 shows, the hydraulic fluid is first

pumped by a bang-bang controller from the tank to thepressure accumulator where it is stored under highpressure. Then the fluid is transmitted through magneticvalves to different branches.

2.1.1. Hydraulic ComponentsIn order to realize a shift actuation, there are mainly twotypes of magnetic valves: Pressure control valves(PCV1 and PCV2 in figure 3) and switch valves (SV1and SV2 in figure 3). The two pressure control valvesare used to control the rotation of a piston rocker, whichis connected with a gear shifting lever. The other twoswitch valves are connected to another piston rocker,which is used to select the gate position (VolkswagenAG 1999). Since the process of gate selection has a tinyinfluence on the gear shift quality, only the gearselection and the pressure control valves modeling aredescribed.

The pressure control valve shown in figure 4 hasthree ports: supply port, release port and output port.The output port is connected with an integrated sensingchamber, which gives a feedback force to the plunger.The magnitude of this force depends on the output portpressure and the effective area of the sensing chamber.

Figure 4: Schematic Diagram of the Pressure ControlValve

Figure 3: Hydraulic System Plan


45

The hydraulic fluid follows through the supply port,generates a force and moves the plunger to the left tillthe spring force is equal to the supply pressure. Thisstable state is called middle position. The steady-stateequation is expressed in equation 1, where As, Ar are theeffective areas of supply port and release port chambers,Ps, Pr are the supply port and release port hydraulicpressures, Fspring0 denotes the initial spring preload force.

rrssspring APAPF 0 (1)

When this magnetic valve is actuated by a current i,the coil induces an electromagnetic force Fmagnetic (seeequation 2), which gives the plunger an impulse tomove to the left side. During the plunger movementprocess, the orifice area of the supply port to output portincreases and output pressure grows. Since the outputport is connected with the sensing chamber, a pressuredfluid is accumulated and reacts against the plunger.Besides the reaction of pressure force, the plunger isalso affected by the spring force and friction. Theseforces take the plunger a back and forth spring-dampingmovement till it stops at the middle position again.Equation 2 describes the transient response,

cidx

dLiF

FF

FvsignF

FF

FAPAP

APAPFvm

vx

plungermagnetic

stribeckprop

coulombplungerfriction

frictionspring

springsliderrr

ssmagneticplungerplunger

plungerplunger

2

0

0

00

21

)

)((

(2)

where xplunger, vplunger and mplunger is plunger position,speed and mass, Aslider is the effective area of sensingchamber, Fmagnetic is the magnetic force induced bycurrent i, coil inductance L and converter constant c(depends on the structure parameters such as fluxdensity and wire length) (Modelon 2009), Ffriction is theresistance friction including constant coulomb frictionFcoulomb, speed proportional friction force Fprop andstribeck friction Fstribeck, Fspring is spring force bystiffness k. If a dither signal is added into the magneticvalve control, Fstribeck can be taken as zero.

The final steady-state is given by equation 3. Inthis state the plunger stops at the middle position, itsvelocity and acceleration are zero. The spring returns tothe initial position and takes a force as large as thepreload force Fspring0.

00

000

springsliderrr

ssmagnetic

FAPAP

APAPF

(3)

With equation 1 and equation 3 the relationshipbetween magnetic force and sensing chamber reactionforce can be expressed in equation 4. For a detailedmagnetic valve the physical geometrical parameters arefixed, so the conclusion that pressure control valvecommand current has a linear relationship with outputpressure can be accepted. This relation is described inequation 5, where m is the slope, n is the offset and i0

denotes the initial current which is used to overcome thefriction from static condition (Nowoisky 2012a).

)( 00000 AAPAPAPF sliderslidermagnetic (4)

00

00 )(

0

iiniim

iiP (5)

Fluid flow q during this process can be expressedby Bernoulli's equation (see equation 6), α is thedischarge coefficient and ρ is the density of fluid. Whenthe plunger moves from the middle to the left position,the output port is connected to the supply port, fluidflow and its pressure level increase. When the plungermoves to the right side from the middle position, theoutput port is connected to the release port. This causesfluid flows to the tank. When the plunger is in themiddle position, there is no flow rate except leakage,the output port pressure keeps a stable value (Merritt1967).

rightxAPP

middle

leftxAPP

q

plungersr

plungerss

)()(2

0

)()(2

0

0

(6)

Based on the above description, a Modelica® basedmodule can be built as figure 5 shows. Its componentsare modeled based on the Modelica Standard Library(MSL) and hydraulic library HyLib® (ModelciaAssociation 2008, Modelon 2009). The geometricalparameters are identified through measurements, theothers are fixed through experiments and calculationfrom theoretical and physical laws.


46

Figure 5: Dynamic Module of Pressure Control Valve

2.1.2. Mechanical ComponentsSynchronizers are important components in thetransmission. It uses friction and locking elements tosynchronize the occurring speed difference during gearshifting. As shown in figure 6, the gear shifting processcan be divided into 5 stages according to the gearshiftposition and the difference speeds (Kiencke 2005). Thisdivision is defined under the assumption that thegearshift sleeve is at the beginning in the neutralposition:

Stage 1: Gearshift force FS causes an axialmovement of the gearshift sleeve and triggers the gearshifting process. The movement stops when thesynchronizer ring blocks the gearshift sleeve.

Stage 2: The axial force is transmitted from thegearshift sleeve to the synchronizer ring, resulting in afriction torque TR, which is much larger than the gearingtorque TZ. At this stage the speed difference between the idler gear and transmission shaft is reducedto zero.

Stage 3: When the speed difference is close tozero, the friction torque TR vanishes. At this moment thesynchronizer ring turns back to release the gearshiftsleeve.

Stage 4: The gearshift sleeve begins to move until itencounters the synchronizer hub external gearing. Thespeed difference increases again as thesynchronizing torque diminishes.

Stage 5: The whole synchronization process iscompleted as soon as the gearshift sleeve toothingengages the synchronizer hub gearing. The power flow

is transmitted from the transmission shaft to the gear.

The torque detailed values are changed accordingto the synchronization stages: The friction torque TR

given by equation 7 (applied to stages 1 and 2) iscalculated through the gearshift force FS, the number offriction surfaces j and some other geometric values. Thegearing torque TZ expressed as equation 8 (used instages 2 and 3) is calculated by gearshift force FS,clutch diameter dKS, teeth angle β and friction µ lt

between gearshift sleeve and synchronization ring (INA2007, Kirchner 2007). The Modelica® basedsynchronizer module is shown in figure 7. It is modeledbased on MSL library and some new created Modelica®

based blocks (such as SynStatusCheck block andRingandHub block). Detailed description and modelingprocess are in Huang (Huang 2012).

sin2ftms

SR

djFT (7)

2cos

2sin

2sin

2cos

2

lt

ltksS

Z

dFT (8)

Figure 7: Dynamic Module of Synchronizer

In order to improve the dynamic behavior duringgear shifting, the simplified dynamic shaft with viscousand elastic effect is necessary. The transmission shafts(crankshaft, main shaft and secondary shaft) areconsidered as spring-damper elements connected withinertias. The whole driveline schematic diagram isexpressed in figure 8. The necessary friction losses arealso added. They are modeled with lookup-tables basedon experiment data.

Figure 6: Synchronizing Process


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Figure 8: Schematic Diagram of Driveline

2.2. Clutch ModelFigure 9 depicts the push-type single-plate dry clutchused in the researched AMT system.

Figure 9: Schematic Diagram of Clutch

The release fork and the disk spring are used to gainan axial pressure to the release bearing and the pressureplate. The release force Frelease causes an increasednormal force on the clutch plate (consists of drive disk,torsion spring, hub and etc.), the engine and the gearboxare then separated. When the force Frelease releases, thepressure plate comes close to the clutch plate, and theengine torque can be transmitted from flywheel to thegearbox through drive disk and torsion spring. Diskspring and the torsion spring are two importantelements in clutch components for the gearshift qualityresearch.

2.2.1. Hydraulic ComponentsA proportional valve (PV1 in figure 3) is used to controlthe clutch cylinder movement. This dynamic process isdescribed in equation 9. The movement depends on themass of the cylinder piston mpiston, acceleration apiston,piston area Apiston, pressure P, the friction force Ffriction

(mentioned in equation 2) and the counterforce F(s)from the mechanical clutch component.

)(sFFPAam frictionpistonpistonpiston (9)

The derivation of piston pressure is calculatedthrough equation 10, where K is compressibilitymodulus and V0 is the offset volume due to hydraulicfeed line.

)(0

pistonpistonpistonpiston

vAqxAV

KP

(10)

The proportional valve has the feature that theopening area APV has a linear response to the inputcurrent i. The causing volume flow q expression issimilar to equation 6 (the valve opening area iscontrolled by the electric current i rather than plungerposition xplunger).

2.2.2. Mechanical ComponentsThe clutch capacity describes the characteristic of thetorque transmitted over the clutch while the slidingstage. It is expressed in equation 11,

)(3

)(222

0

330

i

iaxc rr

rrzFT

(11)

with axial force Fax on the friction lining, speeddepended friction coefficient µ , friction surfaces platesnumber z, outer and inner friction surface radius r0 andri. It is worth noting that during the clutch slippingphase, the clutch transmitted torque equals to the clutchcapacity. When the clutch engages (becomes a couplingsystem), the torque equals to the engine torque minusengine friction loses. For simplification, the releasebearing axial displacement is used as module input forthe calculation of clutch capacity, and the relationshipbetween clutch transmitted torque and release bearingaxial displacement is depicted by a lookup-tablegenerated through experiment (Nowoisky 2013). Therelease bearing axial counterforce Fcounter is a resultantforce of disk and coat springs. It can be obtained fromaxial force Fax under the assumption that the disk springis a stiff lever. But actually the disk spring has avariable stiffness depends on the compressed clutchposition. A lookup-table, which avoids the stiff levertransformation problem, is used to describe this counterforce when releasing bearing has an axial displacement.

The clutch torsion damping system is used toreduce rotational irregularities induced by internalcombustion engines (Luk 2012). This element issignificant for the dynamic model in the purpose of shiftcomfort calibration. The clutch torsion damping systemis modeled with a spring-damping system (multiplecompression springs and a damper). Figure 10 depictsthe torsion spring characteristic. When the relative angle

begins from zero, the smaller spring with stiffnessk1 is firstly compressed (this process is used for vehicle

idle operations), after the relative angle reaches 1 ,

the smaller spring is fully compressed, and the stiffer


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spring with stiffness k2 starts to be compressed (thisprocess is used for vehicle driving operations). When

2 reaches, springs are stopped to be compressed and

comes to a mechanical stop (Naunheimer 2011, Drexl1997). The Modelica® based clutch module is shown infigure 11. Its mechanical components are modeled withMSL library and hydraulic components are modeledwith HyLib® library. The corresponding parameters arefixed through measurements and test bench experiments.

Figure 10: Torsion Spring Characteristic

Figure 11: Dynamic Module of Clutch System

3. MODEL SIMULATIONIn order to verify the rationality and effectiveness ofthis dynamic model, some tests are carried out. Thesesimulations are carried out with Dymola® DASSL(differential-algebraic system solver) integrationAlgorithm, tolerance setting is 0.0001 (Dynasim AB2010). Detailed testing results of synchronizers can befound in Huang (Huang 2012).

Figure 12 shows the pressure control valve outputpressure responses under different step currentsbeginning at 0.05.s. The output pressure firstly has anovershoot which is generated by current, and then the

plunger takes a back and forth spring-dampingmovement till it stops at middle position (see figure 4),so the output pressure takes an oscillation at thebeginning and then keeps a stable value at the end.When the input command current value is less than600.mA, the valve output pressure is zero since theimpulse cannot overcome the fluid viscosity and someother friction.

0 0.05 0.10

5

10

15

20

25

30

35

pres

sure

[ba

r]time [s]

400mA600mA800mA1000mA1200mA1400mA

0.15

Figure 12: Simulation Result of Pressure Control Valve

Finally, the model is compared with measurementdata from an AMT equipped test bench (Knoblich 2011,Nowoisky 2012b). Two three-phase asynchronousmotors are used as drive and load engine. In this testingthe drive engine and load engine were set in constanttorque mode, 10.Nm and -20.Nm. After the system hasreached the steady-state, the clutch was totally openedand gear was shifted from neutral position to 1st gear,then the clutch was closed in a ramp mode. For thesimulation model the magnetic valves were triggeredwith the same signals as those of the test bench. Theshafts of the model input and output are connected withthe constant torque values of 10.Nm and -20.Nm. Thecomparison results are shown in figure 13. If the drivemotor has a positive torque, the engine speed andgearbox input speed at the beginning have a positivevalue (figure 13 (a) and (b)). For the same reason thegearbox output rotates with a negative value (figure 13(c)). At 1.s the clutch begins to open (figure 13 (e)) andsubsequently the gear shifts (figure 13 (d)), the gearboxinput speed decreases and synchronizes with the outputspeed. Afterwards, at 2.s the clutch closes in a rampmode (figure 13 (e)), engine speed and gearbox inputspeed begin to engage (at 4.s). Since the torquetransferred from the drive engine is larger than the onefrom the load torque, the input speed increases to apositive value again (figure 13 (b)). From thecomparison it can be seen the model can accuratelyreproduce the gear shifting process and the normalizedroot mean square errors (NRMSE, see equation12) arebelow 10.%. Moreover, this model describes theimportant shifting behavior for the shift qualityevaluation (e.g. the speed oscillation during the clutchengagement) and expresses the influences with differentcontrol variants (e.g. the change trend of the clutch


49

cylinder pressure), these shifting phenomena are notpossible to be represented through a very simple model.The CPU-time costs 0.88 seconds for this simulation (7seconds) under a quad-core processor.

2

1 )min()max(

1

N

i measmeas

simmeasNRMS yy

yy

Ne (12)

4. SUMMARY AND OUTLOOKThis paper gives a detailed introduction to AMT systemworking principles, presents a relative simple buteffective Modelica® based dynamic model. The shiftbehaviors are also successfully verified throughexperimental data. This model has following features:

1. Represents a detailed AMT gear shift process,describes synchronization process with 5stages.

2. Describes detailed hydro-mechanical actuators,represents the pressure control valve dynamicresponse.

3. Models torsion damping system in clutch andspring-damping system in driveline, whichmakes speed oscillation during torque changespossible. This improves dynamic model closerto a real one.

4. Detailed expresses the relationships betweenthe control parameters and the shift process,this makes the model-based calibrationpossible.

5. Develops a multi-domain model, dynamicallyintegrates hydraulic and mechanical systemstogether.

6. The model is developed based on Modelica®, it

describes the system in a physical perspective.This makes other co-developer or user moreeasily to understand the physical meaning.

7. The tested AMT modules have a goodmodularity for other similar systems setupsonly through parameters changes.

8. Supplies a complete virtual AMT systemplatform for future mode-based shift qualitycalibration.

Based on the above description and comparison,this dynamic nonlinear model makes model-based shiftquality calibration on automated transmissions possible.

REFERENCESVolkswagen AG, 1999. Self-study Programme 221:

Electronic Manual Gearbox, Design and Function.Volkswagen AG.

Modelon, 2009. HyLib (2009), version 2.7. Product help,Modelon, 2009.

Nowoisky, S., Knoblich, R., and Gühmann, C., 2012a.Comparison of Different Model Types based on aSynchronization of an Automated ManualTransmission. Proceedings of Simulation und Testfür die Automobilelektronik IV, 38-47. 2012,Berlin.

Merritt, H. E., 1967. Hydraulic Control Systems. USA:John Wiley & Sons, Inc.

Modelcia Association, 2008. Modelica StandardLibrary (2008), version 3.1. Product help,Modelica Association.

Kiencke, U., Nielsen, L., 2005. Automotive ControlSystems: For Engine, Driveline, and Vehicle, 2ndedition. Germany: Springer.

INA, 2007. Intermediate Rings for Multi-ConeSynchronizer Systems. Schaeffler Technologies

Figure 13: Comparison of Shifting Process with Measurements

0 1 2 3 4 5 6 7500

1000

1500

2000

(a)

engine rotate speed [rpm]

nesim

, 1.8 %

nemeasure

0 1 2 3 4 5 6 720

40

60

(d)

gear shift position [mm]

sgearsim

, 1.5 %

sgearmeasure

0 1 2 3 4 5 6 7-1000

0

1000

2000

(b)

gearbox input rotate speed [rpm]

n1sim

, 3.9 %

n1measure

0 1 2 3 4 5 6 70

10

20

30

(e)

clutch position [mm]

sclutchsim

, 3.7 %

sclutchmeasure

0 1 2 3 4 5 6 7-200

0

200

time [s]

(c)

gearbox output rotate speed [rpm]

n2sim

, 3.0 %

n2measure

0 1 2 3 4 5 6 70

2

4x 10

6

time [s]

(f)

clutch cylinder pressure [Pa]

Pclutchsim

, 2.9 %

Pclutchmeasure


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AG & Co. KG.Kirchner, E., 2007. Leistungsübertragung in

Fahrzeuggetrieben: Grundlagen der Auslegung,Entwicklung und Validierung vonFahrzeuggetrieben und deren Komponenten (inGerman). Germany: Springer.

Huang, H., Nowoisky, S., Knoblich, R., and Gühmann,C., 2012. Modeling and Testing of the Hydro-mechanical Synchronization System for a DoubleClutch Transmission. Proceedings of the 9thInternational Modelica Conference, 284-294.2012, Germany.

Nowoisky, S., Gühmann, C., 2013. AutomatedParameter Identification for a Dry Clutch.Proceeding of 10th International Multi-Conference on Systems, Signals & Devices(SSD),18-21. 2013, Tunisia.

Luk, 2012. Luk Clutch Course: An Introduction toClutch Technology for Passenger Cars. SchaefflerAutomotive Aftermarket GmbH & Co. KG.

Naunheimer, H., Bertsche, B., Ryborz, J., Novak, W.,2011. Automotive Transmissions: Fundamentals,Selection, Designand Application, 2nd edition.Germany: Springer.

Drexl, H.-J., 1997. Kraftfahrzeugkupplungen: Functionund Auslegung (in German). Germany: ModerneIndustrie.

Dynasim AB, 2010. Dymola (2010), version 7.4.Product help, Dynasim AB.

Knoblich, R., Beilharz, J., and Gühmann, C., 2011.Modellbasierte Steuergeräteentwicklung für Kfz-Getriebesysteme am Prüfstand (in German). InTagungsband Mechatronik, 191-196. 2011,Dresden.

Nowoisky, S., Knoblich, R., and Gühmann, C., 2012b.Püfstand für die Identifikation und denFunktionstest an automatisierten Schaltgetrieben(in German). In Virtuelle Instrumente in derPraxis, 150-156. 2012, Germany.


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Documents

Modeling and simulation of an automated manual ...MODELING AND SIMULATION OF AN AUTOMATED MANUAL TRANSMISSION SYSTEM Hua Huang, Sebastian Nowoisky, René Knoblich, Clemens Gühmann