HIL Simulation of the Hydraulics and Mechanics of an Automatic

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Schlegel C., Bross M., Beater P. HIL−Simulation of the Hydraulics and Mechanics of an Automatic ...

The Modelica Association 67 Modelica 2002, March 18−19, 2002

HIL-Simulation of the Hydraulics andMechanics of an Automatic Gearbox

Clemens [email protected] Simulation GmbH

Munich, Germany

Marco [email protected]

BMW AGMunich, Germany

Peter [email protected]

Universität -GH PaderbornSoest, Germany

Abstract

In this article, hardware-in-the-loop (HIL) simula-tion of a passenger car automatic gearbox is dis-cussed. The simulation includes detailed models ofthe mechanics and hydraulics and less detailed mod-els of the other parts of the car’s drive train like itsengine, torque converter, differential gearbox, chas-sis and driving resistances. After a short descriptionof the components to be modeled, special issues ofsimulating variable-structure mechanical systems(coupled frictional elements), simulating hydraulicsand simulating in real time with the gearbox controlelectronics hardware in the loop are discussed. Asimulation based, detailed assessment of the dynam-ics of the gearbox hydraulics show that it might bemodeled (under certain assumptions) with fixedcausality without major loss of accuracy. Thereforenonlinear systems of equations in the hydraulic partsof the model can be avoided. This enables the usageof a model based on hydraulic component submod-els, rather than on overall global dynamics to beused for real time simulations with standard HIL-simulation hardware. The article ends with a shortdiscussion of HIL-simulation results and an outlookon future work.

1. Introduction

The motivation to realize tests in a HIL-environmentis manifold, but two main reasons are:

Shorter development time. The time available forthe development of new components and cars isbecoming shorter and shorter. Thus, a lot of time hasto be saved during the development phase. HIL-

simulation and testing is a possibility to achieve this,as

• There is no need to wait for prototype produc-tion, if the data of these are available for model-ing,

• No driver and test circuit is needed,• Test conditions can be reproduced precisely,• Tests can even be automated.

Rising complexity due to interacting electroniccontrol systems. Cars have always been aggrega-tions of several subsystems like engine, gearbox,brakes and so forth, and thus showed a certain com-plexity. But in former times those systems workedrather independently and could therefore be devel-oped and tested separately. Nowadays the subsys-tems of passenger cars are strongly interdependent:

• Different control systems act on the same dy-namics (e.g. both motor management (DME)and gearbox controller (EGS) influence the lon-gitudinal dynamics (fig. 1).

• Different control systems share sensor informa-tion that is exchanged via CAN bus for controlpurposes, but also for self-diagnosis.

• Functions are spread over several controllers.

As a consequence systems can no longer be testedseparately and the number of different error casesthat have to be tested increases drastically. The testenvironment has to include all essential parts orfunctionalities of all interacting systems. Optimaltesting should be automated in order to handle thenumber of error cases. Both requirements lead toautomated HIL simulation and testing.

This article describes the test environment that wasinstalled at BMW in order to test the control system

HIL−Simulation of the Hydraulics and Mechanics of an Automatic ... Schlegel C., Bross M., Beater P.

Modelica 2002, March 18−19, 2002 68 The Modelica Association

Figure 1: System overall view

(EGS) of the automatic gearbox. For the above men-tioned reasons, it was not sufficient to model onlythe gearbox itself that is controlled by the EGS, butalso the remainder of the powertrain and parts of itscontrollers and communication structures. Figure 1gives an overview of the components, physical inter-actions and information flow:

• The EGS represents the hardware in the loopand is the item under test. All other parts aresimulated.

• Gearbox mechanics, hydraulics and actuatorshave been modeled in detail. This was necessary,as one of the goals of this setup was the possibil-ity to simulate the effects of failure of one of theactuators or the hydraulic valves.

• The less detailed models contain only thosefunctionalities that are necessary for the simula-tion, e.g. the model of the DME does not controla full model of the engine, but is necessary totransmit the required signals via CAN bus to theEGS.

2. Modeling driveline and gearboxmechanics

An automatic gearbox can be simulated only if theinput and output torques or speeds are known.Therefore, at least the engine and the longitudinaldynamics of the vehicle also have to be modeled.Figure 2 shows a corresponding model: Engine(controlled by a control unit and a driver model),torque converter, gearbox, final drive, brake wheels,vehicle inertia and driving resistances. The engine ismodeled by a torque map, the torque converter bystatic characteristics, and all other components, apartfrom the gearbox, by the well known physical rela-tions.

Figure 3 shows an outlined sketch of the 5 speedgearbox ZF 5HP24 [1] which was investigated.Apart from the hydrodynamic torque converter itconsists of three planetary wheel sets and sevenswitching elements: Three clutches (A, B, C), threebrakes (D, E, F), and a freewheel (FF). The gearshiftpattern (fig. 4 ) indicates which switching elementshave to be active to engage a certain gear.

If appropriate component models are given, theobject-orientation of Modelica allows to derive thecomplete simulation model (fig. 5) easily from thegearbox scheme of figure 3. For the componentmodels the standard Modelica library “Mechan-ics.Rotational” [2] and the Modelica powertrainlibrary [3] have been used. For more details of mod-eling automatic gearbox mechanics see [4].

Clutches, brakes and freewheels in a simulationmodel result in a variable structure system, this isbecause two shafts can stick or slip relative to each

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Chassis

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Gearboxmechanics

andhydraulics

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Figure 2: Drive train simulation model

Figure 3: Outlined sketch of 5 speed automaticgearbox ZF 5HP24

Figure 5: Gearbox mechanics simulation model

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R x xN x1 x x2 x x3 x x4 x x5 x x

Figure 4: Gearshift pattern

R1

ratio=r1

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Shaf t6

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other. The number of states is changing during atransition from stick to slip and vice versa. Neglect-ing some “fast” dynamics in order to reduce simula-tion time results in a typical idealized frictioncharacteristic shown in figure 6. The friction torqueis a discontinuous and in part non-unique function ofthe relative speed of the clutch disks. Thereforeadditional equations have to be set up for a completesystem description.

Figure 6: Idealized friction characteristic

In the Modelica libraries used, friction is modeled ina parameterized form (in contrast to [4]) with acurve parameter included plus a state machine de-scribing the transitions between the unique and non-unique parts of the idealized friction characteristic.Because the relative speed in the clutch is an outputof the integration algorithm and computed with alimited precision only, finding the transition betweenthe unique and non-unique parts of the friction char-acteristic is not trivial. This holds especially forsystems with several interacting clutches, like thesystem treated here.

Modeling a clutch by a parameterized friction de-scription in connection with a state machine resultsin a mixed system of discrete and continuous equa-tions, which cannot be solved by standard methodslike Gaussian elimination. There are a few methodsto solve such mixed systems [5], all of them neediteration at an event instance (transition from stuckto sliding mode and vice versa). Using Dymola [6]for processing of the Modelica models, these itera-tions proved to converge quite quickly. Therefore thereal-time condition was met in the HIL setup withonly a few exceptions.

3. Modeling gearbox hydraulics

The hydraulic system of an automatic gearbox con-sists of different elements with the following func-tions:

• Electro-hydraulic elements provide a hydraulicpressure as a function of the electrical currentflowing through the element.

• Switching valves open or close canals.• Proportional valves amplify pressures and / or

transform hydraulic impedances.• Cylinders generate a normal force on a clutch

pack if a hydraulic pressure is applied on them.

Figure. 7 gives an overview over the elements andtheir interactions. In the following section a shortoutline of modeling techniques for hydraulic sys-tems is given.

Figure 7: Interaction of hydraulic subsystems

The early simulation languages were block-oriented[7] and emulated analog computers. They were verywell suited for the simulation of control systemswhere the output signal of a control block doesn’tinfluence the input. Hydraulic systems, however,work differently: The state at the input port of acomponent is dependent on the state of the outputport. A hydraulic line illustrates this: If the line isclosed at the end the pressure at the entrance willrise according to the input flow rate. If the line isopen at the end the pressure at the input will fallalmost to atmospheric pressure. These dependenciescan be modeled with block-oriented software butlead to awkward models because of the necessaryfeedback loops. It is very difficult to build modularmodels with this approach.

Modelica enables acausal modeling, i.e. it is possi-ble to describe the behaviour of a component with-out defining which variables are input and which areoutput variables. As a consequence it is possible touse the same library model for a hydraulic pump(input is the mechanical power, output the flow rate)and a hydraulic motor (input is the hydraulic power,

TStick

TFriction

TCoulomb

Electro-hydraulicactors

p,qHydraulicvalves

p,q Cylindersi



output the torque at the shaft). This object orientedmodeling approach thus resembles the design strate-gies of component manufacturers: They use (to agreat extent) the same parts for pumps and motors.[8].

Hydraulic systems can be described by differential-algebraic equations (DAE). The differential equa-tions are usually non-linear first-order equations thatmodel the pressure build up in lumped volumes.Only special cases require partial-differential equa-tions (PDE) to describe the behaviour of long lines.Usually these PDEs are discretized to arrive at asystem of first order ODEs.

Figure 8: Modeling approach using lumped volumes.

Figure 9: Library models; the lumped volumes at theports are included but not shown in the icons.

Figure 10: Diagram layer of library valve modelwith included volumes at the ports shows moredetails.

For standard applications it has proven very helpfulto place a lumped volume at each port of a compo-nent to model the behaviour of the compressible oil(fig. 8). This leads to a simple structure of the result-ing DAE-system. However to be able to solve thisDAE with standard solvers it is necessary to reducethe index. In former times this was done by handfrom the modeling engineer by adding the amount ofoil of all components connected at a particular node,nowadays it can be done automatically by the tool.

To avoid the manual placement of volumes and theresulting cluttering of the diagram layer librarymodels are available that have already included thelumped volumes at the ports but don’t show them inthe icons. The resulting diagram layer is almostidentical to a standard hydraulic circuit diagram (fig.9 + 10). It can therefore be read also by engineerswith training in hydraulics but no deeper experiencein modeling and simulation [9].

When modeling hydraulic systems it makes sense tofollow the path of the oil: The source is the pump,the sink is the tank, the cylinders, motors and valvesare in between. Using an appropriate library evencomplex circuits can be modeled in a short period oftime if the required parameters of the componentsare known [10].

The advantages of the outlined concept are obvious.Hydraulic components can be modeled in a trulymodular way. They can be arranged in an arbitrarystructure – parallel or in series. The resulting nonlin-ear DAE system can be solved for the derivatives ofthe state variables thus avoiding the numerical solu-tion of systems of nonlinear equations. There arehowever also some drawbacks. The lumped volumesbetween components can become very small, theymay contain less than a thimble full of oil. As aconsequence the pressure builds up very rapidly. Inmathematical terms this means a stiff system that haseigenvalues near the origin and almost at minusinfinity. Using advanced integration algorithms withautomatic step size control these DAEs can besolved successfully but the required computing timewill usually be greater than the simulated time. Con-siderations of the numerical stability will restrict thepermissible step size for fixed step-size algorithmsthat are used for HIL simulations.

One way to reduce the required computing time isthe observation that not all pressure states (lumpedvolumes) are significant for the overall behaviour ofthe model. In that case it is possible to eliminate a

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state. As an example figure 11 shows two orifices inseries.

If the pressure dynamics of the lumped volumebetween the two orifices is not significant one canneglect it and assume that the flow rate through bothorifices is identical. It is then possible to calculatethe flow rate through both orifices as a function ofthe pressure differential across both orifices. Thisapproach is identical to the assumption of a zerovolume.

Figure 11: Two orifices in series.

In general, using these techniques, one has to find acompromise between placing a lumped volume ateach connector and not using them at all. The firstapproach avoids nonlinear systems of equations, butgenerates a stiff system. The second approach doesnot generate a stiff system, but the resulting systemof nonlinear algebraic equations has to be solvednumerically. Thus, both approaches will lead to longsimulation times (compared to simulated time), theoptimum is a combination of both.

Unfortunately, using this method simulation timesare still far from real-time using a standard HILsimulation processor (we used a Motorola PowerPC750 processor running at 480MHz). Thus, anothersimplification has to be made. Detailed analysis ofthe hydraulic system shows that it is possible to usea causal approach for some elements: For the major-ity of the valves, the generated pressure of one valvecan be considered to be independent of the valve thatis driven by that pressure, as the volume flow of oilis usually small. Thus, a model can be derived froman acausal model where the majority of the elementsis modeled in a causal way, which speeds up simula-tion times to an extent that real-time simulationbecomes possible.

4. Gearbox electronics & HIL

After having combined all necessary simulationmodels (all subsystems shown in fig. 1 apart fromthe gearbox controller EGS), they have to be imple-mented on an appropriate real-time processor to-gether with all interfaces needed. For the Modelicaimplementation of the gearbox mechanics model, weused Dymola and exported the processed model as aSimulink S-function [11]. The fixed causalityhydraulics model and the software interfaces to thehardware have been implemented in Simulink too.Since the gearbox controller provides no triggersignal the simulated plant model has to be sampledmuch faster than the controller. The EGS under testoperates at 100 Hz, requiring a sampling rate of 1kHz for the simulation model. For the real-timesimulation hardware we used boards by dSPACE[12].

Setting up a HIL simulation often non-standardinterfaces are needed due to I/O reversal: Sensorsand actuators are simulated, but they interface in partdirectly to the power-electronics part of the controlunit which needs the respective electric loads forproper operation. In contrast, standard real-time I/Ointerfaces provide TTL-level signals only.

The EGS senses the speed of the gearbox input- andoutput shafts and oil temperature. Based on thesesignals (interfaced directly) and other signals likevehicle speed, throttle position, and estimated enginetorque (interfaced indirectly via CAN bus), the ac-tual gearshift is performed according to a shift mapand a set of parameters adjusting the slope of thehydraulic forces acting on the respective clutchpacks to the actual driveline and vehicle state. Dur-ing a gearshift the EGS may require via CAN busthe engine controller to reduce engine torque for asmooth transition.

On the output side the EGS interfaces directly toelectro-hydraulic components of the gearbox. Therespective original parts are included in the HILsetup to provide proper electrical loads. That partsare combined in a load box which may be exchangedfor simulation of another automatic gearbox type.Without proper electric loads at the power-electron-ics interfaces the EGS would operate in emergencymode only (4th gear, no gear shift) due to imple-mented watchdog functions. For the same reasonhealth monitoring signals of other controllers have tobe provided via CAN bus, too.

Orifice1 Orifice2

OilVolume



Figure 12: HIL simulation control main panel

For the operator interface to the simulation we usedthe board vendors software ControlDesk [12]. Figure12 shows the main panel with standard passenger carinstrumentation, gearshift control, simulation con-trol, and simulation output of the actual state and thepressure history of all six clutches of the gearbox.

With the HIL setup described the effects of partial ortotal failure of one or more mechanic, electric, orhydraulic components of the gearbox can be studiedin detail. For interfacing to the EGS software, e.g.for changing parameters, disabling certain parameteradaptation functionalities, etc. an additional deviceis needed. We used INCA [13] for that task.

5. Simulation Results

The following simulation results show the hydraulicpressure (in [N/mm2]) for two cylinders as a result of

two gear shifts. Until t = 1s, the neutral gear is en-gaged. Then, the first gear is engaged, and the gear-box switches to the second gear at t = 3s. Figure 13shows the simulation results for the acausal model,simulated with Dymola. Figure 14 shows the same,but the results are based on a causal model with thesame parameters.

The results for both models are fairly similar, prov-ing the assumption to be correct for most of the time.This is not the case for the pressure in cylinder Aaround t=3.5 s (red circle). In the acausal, precisemodel, the pressure in A falls slightly, because cylin-der E gets filled by a considerable volume flow.Thus, the working pressure drops, which is alsoreflected in the pressure in cylinder A. As it can beexpected, the causal model does not show this effect.

Figure 15 shows the influence of a EGS parametermodification (application parameter). The resultrepresents an uncomfortable gear shift, as the pres-



sure in cylinder E shows a peak (blue circle). Thefact that changes in these parameters are reflected inthe pressure buildup opens the possibility to usethese models for application purposes, too.

Figure 13: Simulation results: Acausal model

Figure 14: Simulation results: Fixed causality model

Figure 15: Simulation results: Effects of poorapplication parameters.

6. Conclusion & Outlook

Using the available component models of Modelica,quite detailed models of gearbox hydraulics andmechanics have been developed. Further investiga-tion showed the possibility to model the gearboxhydraulics in part with fixed causality, which al-lowed real-time simulation of both hydraulics andmechanics. This model was implemented on a HILenvironment together with the gearbox controller.For fully automated component failure tests of theEGS the respective models have to be enhanced byfailure injection inputs.

The fixed causality hydraulics model may also beimplemented in Modelica. This would enable to splitup the combined mechanics and hydraulics model in“slow” and “fast” parts and thus using the potentialadvantage of Dymola’s inline integration scheme[14]. A limitation may be that the presumable “slow”mechanic parts of the model need “fast” samplingtoo, in order to meet the real-time condition if itera-tions occur at an event instance in the clutch models.

An other area of future investigation might be theuse of simulation models for application purposes.This creates the need for further improvement of themodels without loss of simulation speed. Since onlya limited set of signals are available for measure-ment with reasonable effort, setting up proceduresfor identification and validation of those refinedmodels needs to be addressed.

References

[1] Funktionsbeschreibung Automatikgetriebe5HP24. ZF Getriebe GmbH, Saarbrücken

[2] Modelica Association.Modelica.Mechanics.Rotational,http://www.modelica.org/library/library.html

[3] PowerTrain library, http://www.dynasim.se

[4] M. Otter, C. Schlegel, H. Elmqvist, Modelingand Realtime Simulation of an AutomaticGearbox using Modelica, 9th EuropeanSimulation Symposium ESS’97, Passau,Germany, Oct. 19.-22., pp. 115-121, 1997.

[5] M. Otter, H. Elmqvist, S.E. Mattsson, HybridModeling in Modelica based on the



Synchronous Data Flow Principle. IEEEInternational Symposium on Computer AidedControl System Design, Hawaii, August 22-27, USA, Proceedings of CACSD'99, S. 151-157, 1999.

[6] Dymola, http://www.dynasim.se

[7] J.C. Strauss, D.C. Augustine, B.B. Johnson,R.N. Linebarger, F.J. Sanson,. (1967) The SCIContinuous System Simulation Language(CSSL). Simulation, IX(6)281-303, 1967.

[8] P. Beater, Entwurf hydraulischer Maschinen –Modellbildung, Stabilitätsanalyse und Simula-tion hydrostatischer Antriebe und Steuerun-gen. Berlin, Heidelberg, New York, SpringerVerlag. 1999.

[9] P. Beater, Modeling and Digital Simulation ofHydraulic Systems in Design and EngineeringEducation using Modelica and HyLib. Lund,Modelica Workshop 2000, pp 33 – 40, 2000.

[10] HyLib. Library of Hydraulic Componentshttp://www.hylib.com

[11] Simulink, http://www.mathworks.com

[12] http://www.dspace.de

[13] http://www.etas.de

[14] A. Schiela, H. Olsson, Mixed-mode Integra-tion for Real-time Simulation. Lund, ModelicaWorkshop 2000, pp 33 – 40, 2000

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HIL Simulation of the Hydraulics and Mechanics of an Automatic