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Simulation Modelling Practice and Theory 19 (2011) 2131–2150
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory
journal homepage: www.elsevier.com/locate/simpat
Evaluation of antilock braking system with an integrated model of full vehicle system dynamics
T.K. Bera, K. Bhattacharya, A.K. Samantaray ⇑
Department of Mechanical Engineering, Indian Institute of Technology, 721 302 Kharagpur, India
a r t i c l e
i n f o
a b s t r a c t
Antilock braking system (AB

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Evaluation of antilock braking system with an integrated model of fullvehicle system dynamics
T.K. Bera, K. Bhattacharya, A.K. Samantaray
⇑
Department of Mechanical Engineering, Indian Institute of Technology, 721 302 Kharagpur, India
a r t i c l e i n f o
Article history:
Received 12 December 2010Received in revised form 6 July 2011Accepted 8 July 2011Available online 5 August 2011
Keywords:
Bond graphAntilock braking systemVehicle dynamics
a b s t r a c t
Antilock braking system (ABS), traction control system,
etc.
are used in modern automo-biles for enhanced safety and reliability. Autonomous ABS system can take over the trac-tion control of the vehicle either completely or partially. An antilock braking systemusing an on–off control strategy to maintain the wheel slip within a predeﬁned range isstudied here. The controller design needs integration with the vehicle dynamics model.A single wheel or a bicycle vehicle model considers only constant normal loading on thewheels. On the other hand, a four wheel vehicle model that accounts for dynamic normalloading on the wheels and generates correct lateral forces is suitable for reliable brake sys-tem design. This paper describes an integrated vehicle braking system dynamics and con-trol modeling procedure for a four wheel vehicle. The vehicle system comprises severalenergy domains. The interdisciplinary modeling technique called bond graph is used tointegrate models in different energy domains and control systems. The bond graph modelof the integrated vehicle dynamic system is developed in a modular and hierarchical mod-eling environment and is simulated to evaluate the performance of the ABS system undervarious operating conditions.
Ó
2011 Elsevier B.V. All rights reserved.
1. Introduction
The main motivating factor behind this work on vehicle dynamics and antilock braking systems are the conditions thatprevail in Indian roads, especially in sub-urban, semi-urban and rural areas, where road infrastructure is poor and trafﬁc ischaotic. The vehicle performance is severely challenged in these conditions and optimizing the performance of the mecha-tronic systems require controllers to be tuned by trial and error through exhaustive simulations and ﬁeld testing. This is whyIndian automobile industry has been very conservative in adopting modern technology. The ABS is to be designed for diversedriving conditions, especially where frequent braking and acceleration is required. Thus, increasing the life of the brakingsystem in these conditions becomes important.Modeling and simulation of physical phenomena and physical systems plays a very important role in understanding theunderlying science. The necessary steps involved in modeling are writing the equations for each elementary physical system,sorting these equations and implementing them in a solver. This approach becomes time-consuming when the systembecomes complex and multidisciplinary in nature. A common tool enabling a uniﬁed approach to the physical modelingof various disciplines is bond graph[1–4]. Bond graph technique is also well suited for modular modeling of large physicalsystems. A vehicle dynamic system is a multi-energy domain system which involves mechanical, hydraulic, pneumatic, elec-tronic, electrical, chemical (batteries or fuel cells), thermal domains, to name a few. Bond graph modeling is an ideal tool to
1569-190X/$ - see front matter
Ó
2011 Elsevier B.V. All rights reserved.doi:10.1016/j.simpat.2011.07.002
⇑
Corresponding author. Tel.: +91 3222 282998/282999; fax: +91 3222 282277.
E-mail addresses:
samantaray@lycos.com,ak_samantaray@yahoo.com,samantaray@mech.iitkgp.ernet.in(A.K. Samantaray).
Simulation Modelling Practice and Theory 19 (2011) 2131–2150
Contents lists available atScienceDirect
Simulation Modelling Practice and Theory
journal homepage:www.elsevier.com/locate/simpat
Nomenclature
a
distance of front axle from the vehicle cg
A
area
b
distance of rear axle from vehicle cg
B
stiffness factor
c
half of track width
C
shape factor
C
1
maximum value of friction curve
C
2
friction curve shape
C
3
friction coefﬁcient difference between the maximum value and value at
r
x
= 1
C
4
wetness characteristic value
D
peak value
E
curvature factor
F
force
h
height of vehicle cg from suspension reference point
J
polar moment of inertia
K
stiffness
k
g
discontinuous controller gain
l
length
m
mass
M
moment
r
effective radius
R
damping
V
volume
v
,
V
velocity, velocity vector
x, y, z
displacements in three directions
_
x
;
_
y
;
_
z
velocities in three directions
€
x
;
€
y
;
€
z
accelerations in three directions
x
0
output variable
y
i
input variable
a
lateral slip angle
c
camber angle
d
steering angle
_
h
;
€
h
angular velocity, acceleration
s
torque
r
slip ratio
l
coefﬁcient of friction
l
m
motor torque constant
Subscripts
a armb brakingbc brake cylinderbd brake drumc vehicle bodycfr, crr front and rear cornering forceca cablecx, cy, cz
x
,
y
,
z
direction of vehicle bodye equivalentE enginefr frontl leftlm mechanical lossm motornfr, nrr normal for front and rear wheelr rightre returnrr rearstx, sty, stz
x
,
y
,
z
direction of structurest steering (front axle)
2132
T.K. Bera et al./Simulation Modelling Practice and Theory 19 (2011) 2131–2150
develop an integratedmodel of such a systemwith couplingof several energydomains.Multibond graphis suitable for com-pact representation of complex multibody system models[5,6]. Moreover, efﬁcient control algorithms can be derived fromanalysis of the bond graph structure[7–10]. For the above reasons, bond graph models have been extensively used for designof mechatronic systems[1,11,12]. Although this article concerns only a few energy domains, bond graph modeling has beenused here to keep open the possibilities for addition of further dynamical component models (
e.g.
, IC engine, electric motordrive, fuel cell, transmission system,
etc.
).Bond graph modeling has been extensively used in vehicle dynamics studies[13,14]. A four-wheel, non-linear vehicle dy-namic model with electrically controlled brakes and steering was developed by Margolis and Shim[15]. Three dimensionaldynamics of coupled bodies and the multiple transformations required to model multibody systems were developed byPacejka[16]. The engine modelalong withdrive trainand vehicledynamicsmodelswithcomplexitywasdeveloped byLoucaet al.[17]. In this paper, initially,a bicycle model withsteering is consideredfor basicbrakesystemdesign. Thena full vehiclemodel which has 6-DOF for the vehicle chassis and also 6-DOF for each wheel and includes tyre forces[18]is used to studythe vertical, longitudinal and lateral vehicle dynamics. The bond graph model for the braking system is then integrated withthe vehicle model for dynamic analysis.Antilock braking system (ABS) is an electronically controlled braking system that maintains control over the directionalstability of the vehicle during emergency braking or braking on slippery roads by preventing wheel lock-up. Another advan-tage of using ABS is reduction in the stopping distance during emergency braking or braking on slippery roads. This isachieved by utilizing the maximum brake power available for which the wheel does not get locked[19]. However soft sur-faces or surfaces made up of gravels can enhance stopping distances. Conventional ABS has some limitations in control andperformance. One main drawback of conventional ABS is the slip control strategy where the slip is maintained in an accept-able range[20]rather than at the optimal value. Friction forces generated during vehicle acceleration or braking are propor-tional to the normal load on the wheels of the vehicle. Studies show thatthe frictioncoefﬁcientis a non-linear function of thewheel slip[21]. ABS controller is developed to keep the vehicle slip in a particular range for which the road wheel frictioncoefﬁcient is highest, to achieve optimal performance. Obtaining an accurate mathematical model of ABS is very difﬁcult asthe controller operates in an unstable equilibrium point. It is also very difﬁcult to identify the actual road surface by usingany available sensor. Therefore, road condition information cannot be used in optimization of the ABS controller perfor-mance. Various control algorithms such as sliding mode control[22], fuzzy logic[23], and neural networks are reported
in literature to optimize the ABS performance.One ﬁnds several articles in literature dealing with quarter car ABS models. However, the quarter car model is unsuitableto evaluate ABS performance during a curve negotiation. This necessitates the use of a bicycle model of the vehicle wheresteering or handling model is included. Although the bicycle model offers improved response characteristics than the singlewheel model, it does not represent the true dynamics of the ABS equipped vehicle. When a vehicle brakes, the vehicle tiltsforward and the load shifts from the rear wheels to the front wheels. The reverse happens when the vehicle accelerates. Like-wise, during a turn, the vehicle load is transferred from the inner wheels to the outer wheels. The peak ABS braking forcedepends on the value of the coefﬁcient of friction between the tire and the ground, which in turn depends on the normalload on the tire and other factors. Thus, proper accounting of the load transfer is required to accurately predict the ABS sys-tem performance. The load transfer mechanism during braking and turning cannot be represented in the bicycle model.Therefore, a four wheel vehicle model should be used for ﬁnal performance evaluation, although the single wheel and bicyclemodels may be used in the initial design stage.The structure of this paper is as follows: First, models of various subsystems of the full vehicle model are explained alongwith the control algorithms for ABS. Then the detailed bond graphs of bi-cycle model and full vehicle model are constructedbased on the various kinematic relations. Finally, simulation results of vehicle dynamics along with antilock braking systemare provided and compared.
2. Brake system model
The wheels are modeled by their mass, rotary inertia, radius and tyre stiffness. The tyre is the most important amongwheel components because tyre forces and moments play an important role in vehicle dynamics. Tyre forces are necessaryto control the vehicle. As the tyres are the only means of contact between the road and the vehicle, they are the key factors
stw steering wheelsx, sy, sz
x
,
y
,
z
direction of suspensiont tyretfr, trr tangential (front and rear)v vehiclew wheelwx, wy, wz
x
,
y
,
z
direction of wheel1 left suspension reference point
T.K. Bera et al./Simulation Modelling Practice and Theory 19 (2011) 2131–2150
2133
determining the vehicle handling performance. Tyre models are broadly classiﬁed as physical models, analytical models, andempirical models. The physical models are constructed to predict tyre elastic deformation and tyre forces[25]. In such mod-els, complex numerical methods are required to solve the equations of motion. Analytical models are not useful at large slipand at combined slip. Empirical models based on experimental correlations are generally more accurate[26]. Pacejka’s
magic formula
[18]is a widely used empirical model with which one can compute the longitudinal and cornering forces and self-aligning moment.
2.1. Tyre slip forces and moments
The tyre forces and moments from the road surface act on the tyre as shown inFig. 1. The forces acting along
x
,
y
and
z
axes are longitudinal force
F
x
, lateral force
F
y
and normal force
F
z
, respectively. Similarly the moments acting along
x
,
y
and
z
axes are overturning moment
M
x
, rolling resistance moment
M
y
and the self-aligning moment
M
z
, respectively[27].In actual case, the wheel speed and linear acceleration[28]are measured and used to compute the longitudinal slip. Thelongitudinal slip ratio is deﬁned as the normalized difference between the circumferential velocity and the translationalvelocity of the wheel[29]. It is expressed as
r
x
¼
_
h
wy
r
w
À
_
x
w
_
h
wy
r
w
ð
during traction
;
assuming
_
h
wy
>
0
Þ
_
x
w
À
_
h
wy
r
w
_
x
w
ð
during braking
;
assuming
_
x
w
>
0
Þ
8<:
ð
1
Þ
Lateral wheel slip is the ratio of lateral velocity to the forward velocity of wheel[18]. It is given as
r
y
¼
tan
a
¼
_
y
w
_
x
w
ð
2
Þ
For small slip ratios, the longitudinal force
F
x
and lateral force
F
y
can be approximated as
F
x
=
r
x
C
x
and
F
y
=
r
y
C
y
where,
C
x
and
C
y
are longitudinal tyre stiffness (coefﬁcient) and cornering coefﬁcient, respectively, and
r
x
and
r
y
are the longitudinalslip ratio and lateral slip ratio, respectively[30]. However, these linear relations are invalid for large slip ratios.The empirical magic formula based on experimental data is adopted for the development of a tyre-road friction model.The magic formula gives more accurate results for larger slip angles and is also applicable to wide range of operating con-ditions. Longitudinal slip velocity (
i.e.
,
_
h
wy
r
w
À
_
x
w
during traction and
_
x
w
À
_
h
wy
r
w
during braking) develops longitudinal force
F
x
whereas lateral or side slip velocity
_
y
w
and camber angle
c
generate side force
F
y
and self-aligning moment
M
z
. Pacejka’s
magic formula
states that longitudinal force, side force and the self-aligning moment are functions of longitudinal slip andside slip, respectively. It is given as
y
o
¼
D
sin
C
tan
À
1
Bx
i
À
E Bx
i
À
tan
À
1
ð
Bx
i
Þ
À ÁÈ ÉÂ Ã
ð
3
Þ
where output variable,
y
o
:
F
x
,
F
y
or
M
z
and input variable,
x
i
:
r
x
or
r
y
.Ply-steer, rolling resistance, conicity effects may cause slight variation in the function in Eq.(3), but these variations maybe neglected. The constant parameters (
B
,
C
,
D
,
E
) can be determined by measuring the tyre forces and moments by sophis-ticated equipments.Pacejka’s
magic formula
is unsuitablewhen snow andice start signiﬁcantlyaffecting the vehicle performance. Moreover,itdoes not consider the velocity dependence of friction, which is critical while designing brake systems. Therefore, anotherformula developed by Burckhardt[21]is usually used in research on brake system design. Details of the Burckhardtformulaeare given in the next section.
Fig. 1.
Tyre forces and moments.2134
T.K. Bera et al./Simulation Modelling Practice and Theory 19 (2011) 2131–2150

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