MODELING HYBRID MULTIBODY SYSTEMS: APPLICATION TO VEHICLE HYDRAULIC...

MULTIBODY DYNAMICS 2005, ECCOMAS Thematic ConferenceJ.M. Goicolea, J. Cuadrado, J.C. Garcıa Orden (eds.)

Madrid, Spain, 21–24 June 2005

MODELING HYBRID MULTIBODY SYSTEMS:APPLICATION TO VEHICLE HYDRAULIC SEMI-ACTIVE

SUSPENSIONS

M. Delannoy?, P. Boon†, B. Vandersmissen† and P. Fisette?

?Department of Mechanical EngineeringCenter for Research in Mechatronics (CEREM)

Universite catholique de Louvain (UCL), Belgiume-mail: [email protected]

† Tenneco Automotive, Monroe European Technical Center (METC)Technology DepartmentSint-Truiden, Belgium

Keywords: Vehicle dynamics, hybrid modeling, semi-active suspensions, hydraulic.

Abstract. The goal of this research project is to analyze the performances of a modern ve-hicle equipped with a novel suspension system linking front, rear, right and left cylinders viaa semi-active hydraulic circuit, developed by Tenneco Automotive. In addition to improvingthe vehicle’s vertical performances (in terms of comfort), the car body roll motion (stiff) andrear/front wheel-axle units’ wrap motions (soft) can be obtained and tuned via the control of 8electro-valves. The proposed system avoids the use of classical anti-roll bars, which would beincompatible with the wrap performance.A major problem of the project is to produce a realistic and efficient 3D multibody dynami-cal model of an Audi A6 coupled with a dynamical hydraulic model of the suspension system,including cylinder, accumulator and pipe dynamics, valve characteristics, oil compressibility,etc. Particular attention is paid to properly assemble “resistive”components without resortingto the use of an artificial volume, as done by some commercial software.According to Tenneco Automotive requirements, this model must be produced in a Matlab-Simulink form, in particular for control purposes. Thanks to the symbolic approach underlyingthe ROBOTRAN program [1] and to the C compilation Matlab interface, the complete modelcan be obtained as a unique plant dynamics block, running nearly real time on a standard PC.Simulation results highlight the advantages of this new suspension system, in particular regard-ing the behavior of the car which can remain stiff in roll (stability in curves) while maintaininga soft wrap behavior.

1

[email protected]

M. Delannoy, P. Boon, B. Vandersmissen and P. Fisette

1 INTRODUCTION

Conventional suspension systems exhibits a significant compromise between ride comfort(bounce and single wheel stiffness), vehicle handling (roll stiffness) and wheel loading duringwrap motion (articulation stiffness). These systems do not allow for decoupled roll and bouncedamping modes, hindering the ability to tune a well balanced, safe and capable suspension sys-tem for all driving conditions both on and off road.Kinetic suspension systems1, developed by Tenneco Automotive, are unique in that they canprovide reduced diagonal articulation stiffness (soft wrap behavior), increased roll stiffness,high levels of comfort and mode decoupled roll and bounce damping. All these parameters areindependently tunable.In the design process of such system, it is essential to evaluate a lot of parameters like the di-mensions of cylinders or the volume of accumulators.Before manufacturing a prototype, a computer model of the system helps in investigating theparameter sensitivity. By means of simulation, the parameters can be adjusted and the perfor-mance of a novel suspension system can be evaluated at low cost.

Suspension design is based on a multidisciplinary approach involving mechanical and hy-draulic phenomena. Nowadays, more and more engineering systems integrate different physicaldomains, e.g. mechatronic systems, that integrate electronic, mechanical and control aspects.The design and optimization of such systems require models including correctly all these phys-ical domains. In [2], the coupling of electrical and mechanical dynamical models is analyzed indepth. Here, a rigorous coupling of hydraulic and mechanical models is proposed.

As far as we are concerned, a multibody model is necessary to deal with the vehicle dynam-ics: the ROBOTRAN software can generate the multibody equations of the system [1]. Abouthydraulic model, the development learns from the nonlinear shock absorber model in [3] and[4], and also from dedicated hydraulic commercial software, as for example [5].

The aim of this project is to build and analyze a multibody model of a complete car equippedwith the hydraulic semi-active suspension system, Kinetic H2 with 8 electro-valves. This sys-tem takes part in the “Kinetic” research of Tenneco Automotive. According to Tenneco Auto-motive requirements, the model must be produced under the form of a Matlab-Simulink plantdynamics block ready for subsequent simulation and parameterization.

In the following section,the suspension system and the intended advantages are presented.Section3 deals with the modeling of hydraulics components which are present in the system. The dy-namical hydraulic model of the suspension system will be formulated and implemented to berigorously coupled with the full car multibody model.Section 4 describes the multibody modelof the car, and section 5 is devoted to the coupling between the dynamical mechanical equationsand the hydraulic equations to produce ahybrid unified modelof the system.Finally, section 6highlights the advantages of this suspension system by means of pertinent results and parameter-ization, which are compared to a car equipped with independent dampers and classical anti-rollbars.

2 THE “KINETIC H2” SYSTEM DESCRIPTION

The Kinetic H2 system, shown in Figure 1, is a suspension system which replaces existingdampers with simple double acting cylinders and a complex hydraulic circuit. This systemavoids the use of classical anti-roll bars whose functions are ensured by the suspension system.

The 8 cylinder chambers and 2 accumulators are interconnected via hydraulic lines (see

1http://www.kinetic.au.com

2

http://www.kinetic.au.com


Figure 1). At the connection of the cylinder chambers, a combination of two check valves andan electro-valve (“CES” valve) can regulate the flow of the fluid.

The H2 replaces the stabilizer bars and the shock absorber

Figure 1: Kinetic H2 System (from Tenneco Automotive).

Each cylinder performs the normal wheel/body damping functions using the most recentdamping technology incorporated within the cylinders, and enable to modify the damper char-acteristic by thesemi-activesetting of the valve.The Kinetic H2 circuit provides extremely high levels of roll stiffness whilepassivelymain-taining low levels of single wheel and diagonal articulation stiffness. The interconnection alsoprovides the opportunity to incorporate roll damping independently of wheel/body damping.The system incorporates two accumulators to compensate for volume variation.

The two upper left chambers are interconnected together and with the two lower right cham-bers, and conversely. So, there are two independent circuits which are linked by the 4-cylindersmovements. In case of roll motion (see Figure 2 a), one of the two circuit will be compressed

Figure 2: Roll and wrap motion (from Tenneco Automotive).

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under a high pressure of fluid. The second circuit will be expanded. The difference of pressurein upper and lower chamber will produce damper force which will oppose the roll motion of thechassis.In case of bounce or wrap motion (see Figure 2 b), the two circuits will exchange fluid betweenleft, right, front and rear side. That will not lead to high pressure levels into the two circuits.

3 HYDRAULIC MODEL

To establish the hydraulic model of the Kinetic H2 system, let us identify its relevant com-ponents that will be use (see Figure 3):

• 4 double acting cylinders (8 chambers);

• 2 accumulators;

• 8 identical groups of valves;

• 12 hydraulic lines.

Figure 3: H2 circuit.

In subsection 3.1, equations are establish for the dynamical behavior of each component,and in subsection 3.2, efficient assembling of components in terms of reliability and computerperformance is proposed.

3.1 Hydraulic components

These developments aim to be general so that they can be applied to a large configuration ofhydraulic suspension systems, as done in commercial hydraulic software like [5]. Although thelatter are capable of modeling the Kinetic H2 circuit as a “hydraulic system”, they could notsatisfy the objective of the present research since it is necessary to:

• couple the model with the multibody dynamics of the car;

• generate the complete model on a unique plant dynamics to be run in Simulink with highcomputer performances.

The hydraulic components can be classified in two family: thevolumesfor which the statevariable is the pressure and theresistancesfor which the state variable is the flow.

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3.1.1 Double acting cylinders

A double acting cylinder is composed of two volumes: the rebound and compression cham-bers, separated by the piston (see Figure 4 a).

(a) description (b) intermediate position (c) fully rebounded

Piston

RodReboundChamber

CompressionChamber

Figure 4: Double acting cylinder.

The differential equation of a volume, from [5], is

dp

dt=

Q

V β(1)

wherep is the pressure in the volumeV , Q is the flow into the volume andβ is the fluidcompressibility coefficient.

So, a cylinder has two state variables of pressure,preb andpcomp. The input of the system isthe two flowsQreb andQcomp in each chambers , the strokeZ and the piston velocityZ (seeFigure 4 a). The output is the forceFdamp developed by the cylinder.The geometrical change of volume in the chambers due to motion of piston leads to the twofollowing relations for the volume of chambersVreb andVcomp:

Vreb = (lreb 0 + (Zmax − Z)) Areb (2)

Vcomp = (lcomp 0 − (Zmax − Z)) Acomp (3)

whereAreb andAcomp are respectively the section of rebound and compression chambers,Zmax,lreb 0 andlcomp 0 are respectively the stroke, the length of the rebound and compression chamberswhen the cylinder is fully rebounded (see Figure 4 b and c).

Due to the piston motion, additional flows must be added:

Qreb+ = Z Areb (4)

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Qcomp+ = −Z Acomp (5)

This leads to a set of two differential equations that predict, according to eq. (1), the evolutionof the pressures in the cylinder.

dpreb

dt=

Z Areb + Qreb

Vreb β(6)

dpcomp

dt=−Z Acomp + Qcomp

Vcomp β(7)

The force developed by the cylinder is straightforwardly obtained from both rebound and com-pression chambers.

Fdamp = Acomp pcomp − Areb preb (8)

3.1.2 Accumulators

In the accumulator, a large volume of gas (Vgas) is present and is compressed and expandedunder adiabatic conditions. The volume of gas compensates the addition or subtraction of fluidin the hydraulic line (see Figure 3). The oil compressibility is negligible compared to that ofthe gas.

In [3], for the model of a double tube shock absorber, the pressure of the fluid in the accumu-lator is computed by the use of an algebraic equation derived from the adiabatic law,p V γ = cst.Here, the accumulator is considered separately, as an independent hydraulic component, that isa volume with a pressure state variable.

The input of the system is the flow in the accumulatorQacc and the state variable is thepressurepacc. At any time, the pressure of gas is equal to the pressure of fluid in the accumulator,pgas = pacc. The total volumeVacc is equal to the sum of the volume of gasVgas and the volumeof fluid Voil and is constant at any time.

dVacc

dt=

dVgas

dt+

dVoil

dt= 0 (9)

On the other hand, the variation of fluid volume is equal to the input flowQacc:

dVoil

dt= Qacc (10)

Hence, the variation of gas volume is obtained by

dVgas

dt= −Qacc (11)

From an initial volume (V0) and pressure (Vgas0), the adiabatic law (γ = 1.4) is

pgas (Vgas)γ = p0 gas (V0 gas)

γ = cst (12)

The derivation of the adiabatic law leads to

d (pgas (Vgas)γ)

dt=

dpgas

dt(Vgas)

γ + γ pgas (Vgas)γ−1 dVgas

dt= 0 (13)

Finally, the differential equation of the pressure in the accumulator is

dpacc

dt=

p1+ 1

γacc

(p0 gas (V0 gas)γ)

1γ

γ Qacc (14)

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3.1.3 Valves and hydraulic lines

Valves and hydraulic lines are both resistive components. They regulate the flow betweentwo volumes.

The valve characteristics can be described by a law between the drop of pressure∆p and theflow Q:

Q = f(∆p). (15)

These curves were obtained experimentally.The hydraulic line model uses a dynamical equation in which the state variable is the flowQ

and the input are the pressuresp1 andp2 at the connections.

dQ

dt=

1

Lh

(p1 − p2 −∆ptube(Q)) (16)

The pressure drop∆ptube is obtained via the characteristic of the tube as a function of theinstantaneous flow.Lh is the hydraulic length defined as follow:

Lh4=

V ρ

A2=

l ρ

A(17)

3.2 Assembling of resistive components

To connect two volumes together, it is necessary to insert a resistive component betweenthem to determine the flow between the two volumes.Several resistive components between two volumes or more leads to unknow pressure at theconnections between the resistances.

In the Kinetic H2 circuit, there are combination of resistances (see Figure 3):

• two serial resistances: the pressure in between is not known;

• connections between three hydraulic lines in one point: the pressure at the connectionpoint is not known.

Some commercial tools, as [5], solve these problem by inserting a “virtual” volume at eachinterconnection between resistive components. This volume leads to add a pressure state vari-able and above all, this requires to fix a value for this volume, whose physical mean is not easyto interpret. If the volume is too large, the pressure of the volume will act as buffer. If thevolume is too small, this will induce numerical instabilities during the integration process.So, here is proposed to solve this assembling problem by the use of a global characteristicsand/or by computing the pressure at the resistance connection by means ofconstraintson theflows.The “virtual volume” technique can solve all combination of resistive components as the ex-pense of “artificial” value and numerical stiffness, and the proposed approach is far more robustbut has to be developed for each particular combination.

3.2.1 Two valves in series

In this case the constraints consists in equally the flowQ trough the two resistances.The total drop pressure∆p can be separated into a sum of two pressure drops:

∆p = (p1 − pn) + (pn − p2) = ∆p1 + ∆p2 (18)

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If Q = f1(∆p1) andQ = f2(∆p2) are the characteristics of the valves, by inverting if possiblethese characteristics, eq. 18 can be written as follow:

∆p=f−11 (Q) + f−1

2 (Q) = g−1(Q) (19)

Hence, it is possible to build the global characteristic of the two valves:

Q = g(p1 − p2) (20)

For instance, Figure 5 illustrates the global characteristic resulting from the addition – along thepressure drop axis – of the two characteristics of the valves in series.

Dp

Dp - Dp

Dp2

1

2 1

Dp

f f gQ

Q

1 2

Figure 5: Two valves in series: Global characteristic.

3.2.2 One valve and one hydraulic line in series

Here, the flowQ is a state variable and is equal through the valve and the hydraulic line. Ifpn is the pressure at the connection, the characteristic of the valve is

Q = fvalve(p1 − pn) (21)

and the differential equation of the hydraulic line is

dQ

dt=

1

Lh

(pn − p2 −∆ptube(Q)) (22)

By inverting eq. (21) and insertingpn into eq. (22), the following differential equation forthe two components is obtained:

dQ

dt=

1

Lh

(p1 − p2 −∆ptube(Q)−∆pvalve(Q)) (23)

where∆pvalve4= f−1

valve(Q).

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3.2.3 Connection between three hydraulic lines

The three differential equations of the hydraulic lines are:

dQi

dt=

1

Lh i

(pn − pi −∆ptube i(Qi)) , for i = 1 : 3 (24)

wherepn is the pressure at the interconnection andpi is the pressure at the other connection ofthe hydraulic linei.At the connection, similar to the Kirchoff law for current, the sum of flow must be equal to zero,leading to the following constraints:

hQ(Q) = Q1 + Q2 + Q3 = 0 (25)

So the three differential equations (24) are not independent. But the pressure at the interconnec-tion pn is not known. By means of the derivative of the constraints (25),hQ(Q) = 0, it makespossible to compute the pressure at the connection:

pn =(

p1 + ∆ptube 1

Lh 1

+p2 + ∆ptube 2

Lh 2

+p3 + ∆ptube 3

Lh 3

) 11

Lh 1+ 1

Lh 2+ 1

Lh 3

(26)

3.3 Kinetic H2 model

From Figure 3, it is possible to separate the circuit into 4 identical assembling of valves andhydraulic lines, as depicted in Figure 6. Each assembling is composed of 3 hydraulic lines anda set of check-valves and electro-valves.

A global characteristic is found for the group of valves (in the dotted rectangle in Figure 6).Firstly, a unique characteristic for the check-valve in series with the electro-valve is computedaccording to section 3.2.1. Then, the two check-valves being mounted “head-to-tail” allows usto use the global characteristic resulting from the positive or the negative flows.

For the 3 hydraulic lines, a set of 3 differential equation is used in which the global charac-teristic of the group of valve is used.

Figure 6: Kinetic H2: assembling of resistances.

So, the full hydraulic model has 10 pressure state variables (4×2 cylinder chambers and 2accumulators) and 12 flow state variables (4×3 hydraulic lines). The input are the 4 strokes andvelocities of the cylinders and the 8 currents of the electro-valves. The output are the 4 forces

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developed by the cylinders which are functions of the pressures, according to relation (8).The model can be written as a set of 22 differential equations (ODE):{

p = fp(p, Q, Z, Z)

Q = fQ(p, Q, I)(27)

wherep is the 10 pressures andQ is the 12 flows, subjected to the following constraints:{hQ(Q) = 0

hQ(Q) = 0(28)

4 MULTIBODY MODEL

The car used in the study is an Audi A6. The four suspensions could be modeled via the sametopology (five bars suspensions) (see Figure 7) and thus lead to similar sub-structures in themodels. Two types of wheel ground model are implemented. For 4-poster test rig simulation, avertical model of contact was used including the possibility to impose the height of the groundunder each wheel. For road simulation, a lateral model is introduced, to take into account the3D motion of the wheel, and the precisious computation of the geometric contact point.

Figure 7: Rear-left suspension multibody structure.

The 3D multibody model of the car includes:

• 55 generalized coordinatesq (67 for the car equipped with anti-roll bars);

• 16 3D-body loop leading to 40 independent non-linear algebraic constraintsh(q) = 0 (52for the car equipped with anti-roll bars);

• 4 wheel/ground models.

The equations of motion of the system can be written as a set of mixed differential-algebraicequations (DAE) [6]:

M(q)q + c(q, q, Fext(q, q)) = φ(q, q) + JT λ

h(q) = 0

h(q, q) = J(q)q = 0

h(q, q, q) = J(q)q + J q(q, q) = 0

(29)

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whereM is the symmetric generalized mass matrix,c is the non linear dynamical vector whichcontains the gyroscopic, centrifugal and gravity terms and the contribution of the external re-sultant forces and torquesFext, φ represents the generalized joint forces,J = ∂h

∂qT denotes theconstraints Jacobian matrix,λ is the Lagrange multipliers associated with the constraints.

By means of the coordinate partitioning (u, v) of the generalized variable (q), the system canbe reduced to a purely differential form (ODE), in terms of the independent variablesu:

M(u, v(u))u + F(u, u, v(u)) = 0 (30)

This system can be easily solved with respect to the generalized accelerationu by usingCholesky decomposition of the mass matrix and then by solving the linear system:

u = fu(u, u, v(u)) (31)

The functionfu is computed by ROBOTRAN in a fully symbolic way ([1] and [7]).In the case of poster simulation, 3 d.o.f. are allowed to the chassis (bounce, pitch and roll).

So, there are 7 independent coordinatesu. In the case of road simulation, 6 d.o.f. are allowedto the chassis, leading to 10 independent coordinatesu.

5 COUPLING MECHANICAL AND HYDRAULIC MODELS

At previous sections, we obtained a set of ODE for the hydraulic (eq. (27)) and the multibody(eq. (31)) models. At the same time step, the coupling between the equations is done via thedamper forces (Fdamp) which are function of the pressure for the mechanical equation and withthe damper lengths and velocities (Z,Z) which are function of the generalized coordinates forthe hydraulic equations. The global system of equation (ODE) is:

dudt

= fu(u, u, v(u), Fdamp(p))dudt

= udpdt

= fp(p, Q, Z, Z)dQdt

= fQ(p, Q, I)

(32)

u0, u0, p0, Q0

-

-

-

Fdamp = Fdamp(p)-

v = v(u)v = v(u, q)

?

- -

Z = Z(q)

Z = Z(q, q)-

Fext(q, q, p)φ(q, q)

- M(u)u + F(u, u, p) = 0

p = fp(p, Q, u, u)

Q = fQ(p, Q, I)

u = fu(u, u, p) �

�u, u, p, Q�∫

��

�u, u, p, Q

6

at timet

Figure 8: Integration step.

11


The flowchart of the numerical integration scheme is shown in the Figure 8. Let us point outthat the whole ODE model is properly evaluated at a given time step (i.e. dashed rectangle) andnot via a co-simulation process which would couple the sub-model by means of a numericaltechnique.

Figure 9: Simulink model.

The unified complete model is implemented in C and compiled for a Simulink S-functionwhose block is depicted in Figure 9.

6 EXPERIMENTS AND RESULTS

Several simulation were realized, like 4-poster test rig, entry curving and sleeping policemanclearing. In order to objectively analyze the performance of the Kinetic H2 system, a model ofa “reference” car was implemented in order to evaluate the performance of the car equippedwith the Kinetic H2 system. The reference car is the same car, but equipped with independenthydraulic dampers and with anti-roll bars.

The simulation aims at:

• comparing for a large range of excitation the real 4-poster test rig measurements and thesimulation of these experiments (i.e. model identification).

• showing and quantify the expected aptitude of the Kinetic H2 system (roll stiffness andsoft wrap behavior) (i.e. behavior analysis);

4-poster test rig can reproduce and simulate road patterns to reproduce several driving con-dition. In [8], Tenneco Automotive developed a standard test procedure to characterize vehicleon 4-poster test rig. The measured displacement, acceleration, force and noise signals enablea view on vehicle dynamics and driving comfort for the full frequency range between 0 and1000 Hz.

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Here, the identification problem that were performed is to fine tune the parameters of the modelto obtain a good correlation up to 15-20 Hz. This will not be discussed in this paper.

The model efficiency, in terms of CPU time, allows us to realize a large amount of simula-tions and parameterization of the model, to explore the possibility of the car equipped with theKinetic H2 system.Only results which highlight the soft wrap behavior, the roll stiffness and the normal dampingadjustment possibility via the control of the valves are presented, here, respectively by meansof the following simulations: wrap excitation on 4-poster test rig, entry curving and sleepingpoliceman clearing.

The figures compare the simulations of the car equipped with the Kinetic H2 system fordifferent setting of the current applied to the valves (0.3, 0.6, 1.0 and 1.6 A at all electro-valves)and also of the reference car with the classical ant-roll bars. By increasing the valve current, thevalve section is reduced. So for the same drop of pressure, the flow is lower, making the systemstiffer.Of course, one needs to develop a controller which will adjust the current of the semi-activesystem for different kind of road excitation. The Simulink format of our model is well suitedfor tuning a controller but will not be considered here, the valve current being constant.

6.1 Wrap excitation

The model used for these simulations has 3 d.o.f. for the car body (bounce, pitch roll). Theinput of the Simulink block are the 4 heights of the ground under each wheel and the current ofthe valves. The output are the generalized coordinates, the pressures and the flows and also theradial forces on the wheels, the cylinder stroke, etc.

The wrap excitation is a specific test in 4-poster test rig. The two diagonally opposite wheels(FL-RR or FR-RL) are excited in phase while the other are excited in anti-phase. It simulatesthe diagonal articulation behavior of the vehicle: the ability of the car to stay in horizontalposition on a very rough track. Simulation are realized for sinusoid excitation of 1, 5, 10 and20 Hz.

Analyzing the car body roll angle, Figure 10 highlights and quantifies the soft wrap behaviorof the Kinetic H2 system. The car body roll angle is higher for the car equipped with classicalanti-roll bars which connects left and right suspensions. Thus, it leads to a stiffer single wheelmotion.

0 1 2 3 4 5−0.015

−0.01

−0.005

0

0.005

0.01

0.015Wrap excitation: Frequency 1Hz − Amplitude 0.02m

Time [sec]

Rol

l ang

le [r

ad]

0.3 A0.6 A1.0 A1.6 ARef Car with ARB

Figure 10: Wrap excitation: car body roll angle.

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6.2 Entry curving

The vehicle starts right at a constant speed. The steering is put progressively to a constantrotation angle. The simulation was realized for several speed and angle.

Figure 11 compares the car body roll angle. The car equipped with the Kinetic H2 systemrolls less than the one with the classical anti-roll bars. The figure shows also the roll angle ofa car equipped with classical independent dampers and without anti-roll bars, which takes asignificant greater roll angle.

0 2 4 6 8 10−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03Entry curving: 10m/s − 5°

Time [sec]

Rol

l ang

le [r

ad]

0.3 A0.6 A1.0 A1.6 ARef Car with ARBRef Car without ARB

Figure 11: Entry curving: Car body roll angle.

The 4 different settings of valve current give a slightly different response only in the transi-tory phase. In the established condition, the system actspassivelyagainst the roll motion.

The model allows us to easily analyze other car behavior like over and under-steering forexample. Figure 12 shows the difference between mean front and rear slip angle under the timeand highlights the under-steering behavior, which is noticeably reduced with the Kinetic H2system.

0 2 4 6 8 10−0.01

0

0.01

0.02

0.03

0.04

0.05Entry curving: 10m/s − 15°

Time [sec]

|αF| −

|αR

| [ra

d]


Figure 12: Entry curving: Under-steering.

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6.3 Sleeping policeman

The sleeping policeman is taken as example to highlight the semi-active capacity to tune thevertical damping of the suspension. By means of adjusting the valve currents, the flows of fluidin the circuit is modified. So, the suspension can be softer (low current value) or stiffer (hightcurrent value). As said in the introduction of this section, the system is stiffer with a highercurrent.

0 0.5 1 1.5 2 2.5 3−0.1

−0.05

0

0.05

0.1

0.15Sleeping policeman: 10m/s − height 0.1m − lenght 3m − slopes 1m

Temps [sec]

Car

bod

y ve

rtic

al d

ispl

acem

ent [

m]


Figure 13: Sleeping policeman: Car body vertical displacement.

Figure 13 shows the car body vertical displacement. With a low current, the response os-cillation are higher and the car take more time to come back to the equilibrium position. Thesuspension is soft.

But in Figure 14 which shows the car body vertical acceleration, with a high current, thevertical acceleration of the car is higher.

So, a fine tuning of the current, via a controller, is needed to lead to a compromise betweencomfort (vertical acceleration), duration and amplitude of the excitation.

0 0.5 1 1.5 2 2.5 3−10

−5

0

5

10Sleeping policeman: 10m/s − height 0.1m − lenght 3m − slopes 1m

Time [sec]

Car

bod

y ve

rtic

al a

ccel

erat

ion

[m/s

2 ]


Figure 14: Sleeping policeman: Car body vertical acceleration.

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7 CONCLUSIONS

The formalism proposed in this paper allows us to establish an efficient model of a moderncar equipped with a hydraulic suspension systems which represents a hybrid hydro-mechanicalsystem, without resorting to co-simulation techniques which require specific numerical syn-chronization process.The modeling of the hydraulic components is implemented in order to be applied to other con-figurations of suspension systems.A key point of our modeling approach is to ensure a rigorous coupling between the hydraulicand multibody dynamical models at the same integration time step. This has been implementedin an input/output Simulink block producing an user-friendly interface ready for simulation,parameterization or control purposes, as required by the industrial partner.

By means of simulation, the expected performances of theKinetic H2 systemare highlightedin comparison with a car equipped with classical suspensions and anti-roll bars.

A fine parameterization of the whole model, and the efficiency of the model obtained fromthe symbolic multibody software, enable to compare the results to experimental measurementsin the view of model identification on 4-poster test rig.

Using as input, the car body corner vertical accelerations and the damper velocities, a con-troller can be straightforwardly designed in Simulink using the present model, as it was re-cently done by Tenneco Automotive for the same car with 4 independent semi-active dampersequipped with the same electro-valves. The goal is to obtain a good compromise between com-fort (human body accelerations) and handling (roll, curve entry, over/under-steering, etc),and atlonger term, to try to perform, viareliable model, the subjective evaluation of a given suspensionsystem, with respect to the above-mentioned criteria .

ACKNOWLEDGEMENTS

This research has been sponsored by the Belgian Program on Interuniversity AttractionPoles,Advanced Mechatronic Systems - AMS(IUAP5/06), initiated by the Belgian State —Prime Minister’s Office — Science Policy Programming (IUAP V/6). The scientific responsi-bility is assumed by its authors.

REFERENCES

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[2] L. Sass.Symbolic modeling of electromechanical multibody system. Ph.D. Thesis, Univer-site Catholique de Louvain, Belgium, January 2004.

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