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Simulation of a Pressure-ControlledClamping System for ContinuouslyVariable Belt- and Chain TransmissionsBernhard StöcklTechnische Universität München, Garching

Introduction

The introduction of continuously variabletractor drives is meanwhile considered asecure trend on highly developed markets[1, 2]. In addition to Fendt andCase/Steyr, John Deere and Deutz-Fahrintend to offer hydrostatic-powersplittransmissions as of 2001. Chain conver-ters seem interesting, especially becauseof their excellent mechanical efficiency(best values approximately 95%). Cur-rently, their load limits are insufficient forlarge tractors. However, they have grownsteadily [3]. After the series introductionof a chain converter transmission for cars(Audi Multitronic) [4, 5], the increase intransmittable power can be expected tocontinue in the future.

Background

As part of the Special Research Area 365“Environmentally Friendly Drive Tech-nology for Vehicles” financed by theGerman Society for the Advancement ofScientific Research, an autonomous hy-brid vehicle with a continuously variablei2-transmission is being developed by fivecooperating departments at the Techni-

sche Universität München [6, 7]. The coreof the transmission is a chain converterfrom the company P.I.V.-Reimers An-triebstechnik. Power is transmittedthrough friction between the tension chainand the two disc sets, which are installedon the drive- and the output shaft. Thesedisc sets consist of two conical discs each,one of which is firmly connected to theshaft, while the other one is axially mo-vable. The adjustment of the distance ofthe two movable discs causes the chain torun at different radii, i.e. different trans-mission ratios. The movable disc is de-signed as a hydraulic cylinder so that theclamping of the chain and the discs aswell as the adjustment can be realized hy-draulically. Two aspects are decisive forthe level of oil pressure: first, the amountof the torque to be transmitted sets a basiclevel in order to prevent the chain fromslipping and, hence, damage to the con-verter [8]. Second, the adjustment of thetransmission requires the pressure to beincreased. The torque-proportional pres-sure is provided by the P.I.V. torque sen-sors situated in the power train (one eachin the input- and the output shaft). The olddesign of the torque sensors (pressure in-crease through throttling) requires a con-stant oil volume flow, no matter whether

or not the torque rises or an adjustment iscarried out.

The New, Pressure-ControlledSystem

From an energetic viewpoint, throttlecontrol means a big disadvantage. For thisreason, an efficient system controlled ac-cording to the pressure requirements wasdesigned at the Department for Agricultu-ral Machinery [9] in order to improve theoverall efficiency of a chain convertertransmission. It was possible to realize asimple design (figure 1). It consists of avariable displacement pump, one 3-waypressure control valve each, and a noveltorque sensor [9] which is based on theball-ramp principle of the P.I.V. constantflow torque sensor. The advantages of theconstant flow system – its highly dynamiccharacter and the possibility of fast stand-still adjustment – were retained. In orderto guarantee the highest possible degreeof security against chain slipping whilekeeping excess clamping to a minimum,the pump function of the P.I.V. torquesensor was taken over.

Pump FunctionWhen at large positive torque gradientsthe required clamping pressure is built uptoo slowly due to the inertia of the pressu-re control valve and the pump, the torquesensor adjusts the clamping pressure hig-hly dynamically: if the axial force gene-rated from the torque at the ball ramps islarger than the pressure force in the sensorchamber, the movable plate pumps oilvolume into the circuit and thus increasesthe pressure abruptly (figure 2). A con-stant set-pressure increase provides addi-tional safety in the case of fast torque rise.However, since this leads to growingfriction- and leak losses, this factor shouldbe as small as possible.

Electronic Torque MeasurementIn order to determine the set value for thepressure control valve, the torque is mea-sured electronically using the moment-

The transmittable power of continuously variable belt- and chain trans-missions has been steadily increased in recent years so that they can beused on tractors of the lower and medium power classes. In the currentcommon designs, the hydraulic system, which is required for clampingand adjustment, exerts a strong influence on the total losses. In order toincrease the overall efficiency of such a transmission, new, pressure-controlled clamping hydraulics with significantly higher system-relatedefficiency were examined with the aid of computer simulation. These stu-dies focused on the realization of highly dynamic clamping pressuresupply in cases of sudden torque increase, which occur frequently intractors. For the optimization of efficiency, excess clamping must beavoided. For further examinations, a real-time simulation system was setup which, in addition to measurement data collection on the test bench,allows for the speedy and efficient development of control strategies.

KeywordsContinuously variable transmission, belt- and chain transmission, tractors, hydraulics, simulation

Agrartechnische Forschung 7 (2001) Heft 2, S. E 52-E 56 E 53

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Simulation ModelsThe simulation software used was MAT-LAB/Simulink with the hydraulics exten-sion Hydraulic Blockset. Since the dyna-mic behaviour of the pressure control val-ve is decisive for the total function of theclamping pressure control system, a mo-del was developed which was accurate inevery detail (figure 3). The valve was di-vided into three individual functions:main control valve, flow control valve,and valve cone. This division was re-tained in the simulation model. Thesesubsystems are interactively connected toeach other and consist of basic elementssuch as cylinders, springs, proportionalvalves, etc. The physical function of thetorque sensor was also modelled usingsuch basic elements (figure 4). In the mo-del, pressure is generated by a simpleconstant pressure pump.

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gure 1: New concept of a pressure-controlled clamping system with modified torque sensors Test BenchIn order to prove the simulation quality of

oportional twisting angle at the torquensor. This angle is deduced from thease shift of two measuring gearwheels

hose sides are scanned by an inductivensor. A good measuring signal requirese precise setting of the distance betweenth sensors and the gearwheel. In additi-, the eccentricity of the two gearwheels relation to each other must be kept to ainimum (< 0.05 mm): if the air gap bet-een the gearwheel and the sensor chan-s during one revolution, the frequency the rpm superimposes the signal course the phase shift. Since the latter equalse temporal difference of both sensor si-als, this effect influences the measure-ent result significantly.

mulation of the Clampingydraulics

ne basic requirement that simulationust fulfill is the precisest possible repre-

sentation of reality with its dynamics.When a complex model is developed, theindividual components are first modelledand verified through measurements. Af-terwards, the models are put together toform the entire system. The modularstructure allows single elements to be ex-changed easily for the examination of dif-ferent concept variants and further opti-mization. A big advantage of simulationresides in the avoidance of expensive testbench set-ups and of damage to the com-ponents.

the model, calculated values were compa-red with those measured on the test bench.For this purpose, one half of the newclamping system was installed on a com-ponent test bench which, in addition to avariable displacement pump, a pressurecontrol valve, and a torque sensor, con-tains a torque measurement shaft for mea-surement data acquisition and a disc brake(figure 5). In addition to providing a con-stant braking moment, the brake allowsfor abrupt moment increase. Thus, espe-cially cases of very steep torque rise(danger of chain slipping) [8], which arecritical for the life span of the chain con-verter, can be realized.

Simulation ResultsAn important criterion for valve beha-viour is the response to a set-value step(figure 6). In the case of torque rise, thebehaviour during the first milliseconds isdecisive because the fast supply of the re-quired pressure is necessary for the da-mage-free operation of the chain conver-ter. If the course of the simulated sensorpressure is considered, it proves to be al-most identical as compared with the mea-sured oil pressure until the secondovershoot. Only the height of the peaks

Figure 2: Structure ofthe new torque sensorafter axial space opti-mization

Figure 3: Structure of the pilot-operated control valve: hydraulic diagram

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of the torque sensor. The pressure controlvalve now – falsely – tries to reduce thepressure to the set value and causes oil toflow into the tank. As long as the torquesensor pumps, pressure remains at a highlevel (figure 7). After the movable platehas reached the limit stop, however, pres-sure diminishes quickly because the pres-sure control valve continues to reducepressure by maintaining an oil flow intothe tank. In the end, the valve resets thepre-set value. The experiment shows thatonly in the first 40 ms is a torque-proportional pressure reached because thevalve has a certain inertia. By this mo-ment, the calculation of the set pressurefrom the measured torque must be com-pleted in order to prevent the valve fromreducing the pressure.The next step consists of the integrationof the torque measurement at the new tor-que sensor and the outputting of this valueto the pressure control valve. On the basisof earlier experiments [9], torque measu-rement was reprogrammed on a more ef-ficient microprocessor with which theoutput of the calculated torque value oc-curs approximately 20 times faster. In theexperiment, the pressure is readjusted bythe pressure control valve depending onthe torque, which is applied abruptly. Inthe simulation, the required pressure iscalculated from the axial shift of the ballramps of the torque sensor, which resultsfrom the conversion of the moment intoan axial force. Figure 8 shows the simul-taneous increase in torque and pressurecaused by the pump function. Due to the

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igure 4: MATLAB/Simulink model of the new torque sensor

igure 5: Layout of the component test bench

aries. This behaviour must be attributedo the measured pump pressure, which isot shown here. Due to the pump con-roller, it also increases briefly while itemains constant in the simulation. further fundamental characteristic is the

ffect and duration of the pump functionecause the maximum stroke of the mo-able plate (figure 2) is limited by the de-ign. This means that pressure supply by

the pressure control valve and the pumpmust be completed in any case by the timethe pumping effect ceases. For the exami-nation of the time characteristics, the loadmoment is increased abruptly while theset pressure at the pressure control valveremains the same (figure 7). The set pres-sure at this moment is smaller than thetorque-proportional pressure in the sensor,which is increased by the pump function

fast calculation of the new set pressure,the pressure control valve no longer triesto reduce the pressure. 50 ms later, thepressure control valve reacts to the requi-red higher pressure level and increases thepressure further. On the one hand, thestrong pressure overshoots result from thecharacteristics of the pressure control val-ve (cf. figure 6). On the other hand, apumping effect due to the axial movementof the movable plate (figure 2) causes a

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igure 6: Step response of the pressure control valve Figure 7: Time characteristics of the pumping effect of the new torquesensor

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Use of Rapid Control Prototyping

hase shift which simulates a torquehich is too high. Thus, pressure is setigher than actually required. However,is guarantees that the movable plate is

ressed back into its initial position. Sin-e, in the case of set-value steps, pressurence again falls below the set pressure (cf.gure 6), the above-described effect is re-eated by means of renewed, weakerumping. Even in the critical moments ofst torque rise, there is no damage to the

onverter due to chain slipping. These ex-eriments were carried out at a slight ex-ess clamping pressure of ca. 2 bar in or-er to avoid small torque- and pressureuctuations immediately causing a pum-ing effect. For energetic reasons, howe-er, further reduction of this safety mar-in is appropriate.s the comparison with the measurement

hows, the dynamic behaviour of theressure control valve and the torque sen-or was well simulated within the periodetween 0.15 and 0.25 s (figure 8). Espe-ially in the range of high dynamics, theourses of the measured and the simulatedressure were approximately congruent. the future, later deviations (between

.25 and 0.7 s) will be reduced throughe optimization of the simulation model.

eal-Time Simulation

addition to classic simulation, there ise possibility of interactive real-time data

xchange between the computer and theal environment (e.g. the test bench)0]. This means that the calculations ine simulation program must be carried

ut in the same time domain as the realrocesses. The basic prerequisite for thesealculations is an efficient computerhich can administer a sufficient numberf entries and outlets within an appro-riate scanning time. During simulation,e program parameters can be changed,

nd all data can be checked and analyzed.

For a simulation model prepared withMATLAB/Simulink to be reliably proces-sed in real time over the entire simulationperiod, a special program code suitablefor real-time application must be develo-ped [11]. This function is included in thereal-time packages.The real-time code can be processed onthe same PC where MATLAB/Simulinkis installed. It is also possible to integratean additional computer – a PC, an indu-strial PC, a single-board computer, or aspecially adapted version (e.g. from thedSpace company). This second computercontains the I/O cards and is used exclu-sively for the execution of the real-timecode. Since no standard operating systemis employed, the achievable performanceis far higher. In addition, several compu-ters can be interlinked in order to increasetheir performance.

Rapid Control PrototypingRapid Control Prototyping (RCP) meansthat the controller is simulated on the PC,which communicates with a real testbench. This approach allows control stra-tegies to be examined without the time-consuming programming of a control unitand accelerates the goal-oriented, efficientdevelopment of new controllers and con-trol units.

Hardware-in-the-LoopIf one speaks of Hardware-in-the-Loop(HIL), this means that a real control unitis connected to the simulated environment[12]. The controlled system is generallyknown from the preceding simulationphase. Hardware-in-the-Loop no longerfocuses on the control strategy, but on theexamination of its implementation intothe source code adapted to the control unitand on the test of the hardware. This en-ables a controller realized in hardware tobe commissioned without the danger ofthe controlled system being damaged.Even examinations in limit ranges can becarried out without any danger.

At the Department for Agricultural Ma-chinery, the simulation program MAT-LAB/Simulink is used for a real-time si-mulation with the extensions Real-TimeWorkshop and Real-Time Windows Tar-get.The control of the clamping pressure atthe chain converter is divided into thecontrol circuit of the pressure control val-ve and the calculation of the set pressurefrom the applied torque. For the develop-ment of the torque measurement at thetorque sensor, a Rapid Control Prototy-ping System was realized. The TTL si-gnals of the two inductive sensors wereused to calculate the phase shift, which isproportional to the torque and results fromthe force balance at the ball ramps. Therelation between clamping pressure andtorque is 1 bar : 10 Nm. This relation isdetermined by the geometry of the ballramps. The pressure-equivalent tension,which constitutes the set signal for thevalve, was calculated by entering the ten-sion-pressure performance data of the pi-lot-operated pressure control valve. Thisvalue was finally generated by the D/Aconverter card and output to the pressurecontrol valve. This approach allowed datato be processed without time-consumingprogramming of a control unit. At the sa-me time, the integration of the pressurecontrol valve into the development of tor-que measurement enabled the behaviourof the control circuit to be observed.The gained insights were used to programa control unit which now calculates thephase shift (angle difference). The con-version into the set pressure has not yetbeen implemented because this results ina series of advantages for test operation. Itis possible, for example, to adjust the zeropoint of the phase shift by altering a con-stant in the software. At present, differentpressure control valves are also being ex-amined on the test bench. The differentcharacteristic lines of the valves canquickly be determined and exchanged inthe Simulink model without the code ofthe control unit having to be altered andloaded anew every time. Figure 9 showsthe connection between the individualelements.The next step will be the designing of acontrol strategy for the clamping- and ra-tio control of the entire hydraulic circuit.Hence, a draft design is being developedthrough simulation which then will be va-lidated on the test bench using the above-presented Rapid Control Prototyping Sy-stem. For this purpose, a second testbench is available which allows a com-plete chain converter transmission to beexamined in the drive train.

Figure 8: Rise in oilpressure caused by thepressure control valveand the torque sensor inthe case of abrupt tor-que increase

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easurement Data Collectionased on MATLAB/Simulink

ased on this real-time simulation, a mea-urement data collection system has beeneveloped. This means that, via the A/Donverter card, all measured values areansferred to the PC, where they are vi-ualized and recorded. For real-time re-resentation, different possibilities arevailable, for example in the form of aontinuous graph over time, round in-truments, a LED bar display, etc. Thisllows realistic display masks for the in-ividual applications (such as the instru-ent panel of a tractor) to be developed. addition to mere data acquisition, this

pproach provides access to all measure-ent data during an experiment andakes them available for control purpo-

es. This great flexibility enables differentontrol strategies to be implemented andxamined without time-consuming con-ersion measures.

eferences

ooks are indicated by •.] Brunotte, D. u. J. Seeger: Stufenlose Ge-

triebe für den Serieneinsatz. O+P Ölhy-draulik und Pneumatik 44 (2000) Heft 6,S. 394–397.

] • Renius, K. Th.: Trends in tractor deve-lopment, West European view. ICAMESeoul 13.–16.11.2000. Proceedings BandI, S. 31–52.

] • Faust, H. u A. Linnenbrügger: CVT-Entwicklung bei LuK. 6. LuK-Kolloquium,19./20. März 1998. Deutscher Tagungs-band S. 159–181. Herausgeber LuKGmbH & Co., Bühl/Baden, 1998.

[4] Nowatschin, K. et al.: multitronic – Dasneue Automatikgetriebe von Audi (Teil 1).ATZ Automobiltechnische Zeitschrift 102(2000) Heft 7/8, S. 548–553.

[5] Nowatschin, K. et al.: multitronic – Dasneue Automatikgetriebe von Audi (Teil 2).ATZ Automobiltechnische Zeitschrift 102(2000) Heft 9, S. 746–753.

[6] • Höhn, B.-R. (Hrsg.): Arbeits- und Er-gebnisbericht Juli 1993 - Juni 1996 Son-derforschungsbereich 365: Umwelt-freundliche Antriebstechnik für Fahrzeu-ge. Technische Universität München,1995.

[7] • Höhn, B.-R. (Hrsg.): Arbeits- und Er-gebnisbericht Juli 1996 - Dezember 1999Sonderforschungsbereich 365: Umwelt-freundliche Antriebstechnik für Fahrzeu-ge. Technische Universität München,1999.

[8] •Sauer, G.: Grundlagen und Betriebsver-halten eines Zugketten-Umschlingungsgetriebes. DissertationTechnische Universität München. Fort-schritt-Berichte VDI, Reihe 12, Nr. 293,VDI-Verlag, Düsseldorf, 1996.

[9] • Westenthanner, U.: Hydrostatische An-press- und Übersetzungsregelung fürstufenlose Kettenwandlergetriebe. Dis-sertation Technische Universität Mün-chen. Fortschritt-Berichte VDI, Reihe 12,Nr. 442, VDI-Verlag, Düsseldorf, 2000.

[10] Stüwing, M. u. S. Dronka: Elektrohydrau-lische Antriebe zur Hardware-in-the-loop-Simulation mechanischer Systeme. O+PÖlhydraulik und Pneumatik 44 (2000)Heft 1, S. 20–22.

[11] Lang, Th: Schnelle Reglerauslegung inder Hydraulik durch Einsatz einer ganz-heitlichen Entwicklungsumgebung.Agrartechnische Forschung 5 (1999) Heft1, S.46–53.

[12] Kessler, F. u. J. Gebert: Testautomatisie-rung und Antriebsstrangmodellierung anHIL-Steuergeräteprüfständen in der BMWGetriebeentwicklung. ATZ Automobil-technische Zeitschrift 102 (2000) Heft 5,S. 312–323.

Author

Dipl.-Ing. Bernhard StöcklTechnische Universität MünchenBoltzmannstraße 1585748 GarchingTel.: +49/(0)89/289-15898Fax: +49/(0)89/289-15871E-mail: stoeckl@ltm.mw.tum.de

Figure 9: Data flow bet-ween the simulation com-puter, the control unit, andthe test bench