A Study and Review on Vehicle Suspension System and Introduction of a HighBandwidth Configured Quarter Car Suspension System

Abstract

The suspension system reduces the effect of vibration caused by the road and driving
conditions. Leading automotive companies have started to use intelligent suspensions
in their high-end automobiles’. But much m When travelling, vehicles experience
dynamic excitations of varying magnitudes. Such excitations could lead to induced
vibration or noise, which affect the vehicles’ integrity and occupants. A prominent
method of vibration isolation in vehicular system is the suspension system. The main
objective of a car suspension system is to improve the ride comfort without
compromising the ride handling characteristic. Over recent years, the massive
developments in actuators, sensors and microelectronics technology have made the
intelligent suspension systems more feasible to implement in automobile industry.
These systems are designed and fabricated in such a way that they are able to reduce
the drivers' and passengers’ exposure to harmful vertical acceleration. The quarter-car
suspension model is the best bench-mark to study and analyze the dynamic behavior
of vehicle vertical isolation properties. This paper presents background information
and a description of the quarter-car suspension model which can be used to evaluate
the performance of intelligent suspension system.

Full text

Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
ISSN:1991-8178
Australian Journal of Basic and Applied Sciences
Journal home page: www.ajbasweb.com
Corresponding Author: S.B.A. Kashem, Faculty of Engineering, Swinburne University of Technology Sarawak, Kuching
93500, Sarawak, Malaysia.
A Study and Review on Vehicle Suspension System and Introduction of a High-
Bandwidth Configured Quarter Car Suspension System
1S.B.A. Kashem, 2K.B. Mustapha, 3T. Saravana Kannan, 4Sajib Roy, 5A.A. Safe, 6M.A. Chowdhury, 7T.A. Choudhury, 8M. Ektesabi, 9R.
Nagarajah
1,2,3,6Faculty of Engineering, Swinburne University of Technology Sarawak, Kuching 93500, Sarawak, Malaysia.
4Faculty of Engineering , East West University, Dhaka, Bangladesh.
5Faculty of Engineering , Chittagong University of Engineering and Technology, Chittagong, Bangladesh.
7Faculty of Science and Technology, Federation University Australia, Churchill, VIC 3842, Australia.
8,9Faculty of Science, Swinburne University of Technology, Hawthorn, VIC 3122, Australia.
A RT I CL E I N FO
A B ST RA C T
Article history:
Received 13 November 2013
Accepted 23October 2013
Available online 30November 2011
Keywords:
Vehicle; Semi-active; Suspension;
Damper; Car; Adaptive; Intelligent;
review; comparison.
The suspension system reduces the effect of vibration caused by the road and driving
conditions. Leading automotive companies have started to use intelligent suspensions
in their high-end automobiles’. But much m When travelling, vehicles experience
dynamic excitations of varying magnitudes. Such excitations could lead to induced
vibration or noise, which affect the vehicles’ integrity and occupants. A prominent
method of vibration isolation in vehicular system is the suspension system. The main
objective of a car suspension system is to improve the ride comfort without
compromising the ride handling characteristic. Over recent years, the massive
developments in actuators, sensors and microelectronics technology have made the
intelligent suspension systems more feasible to implement in automobile industry.
These systems are designed and fabricated in such a way that they are able to reduce
the drivers' and passengers’ exposure to harmful vertical acceleration. The quarter-car
suspension model is the best bench-mark to study and analyze the dynamic behavior
of vehicle vertical isolation properties. This paper presents background information
and a description of the quarter-car suspension model which can be used to evaluate
the performance of intelligent suspension system.
© 2015 AENSI Publisher All rights reserved.
To Cite This Article: S.B.A. Kashem, K.B. Mustapha, T. Saravana Kannan, Sajib Roy, A.A. Safe, M.A. Chowdhury, T.A. Choudhury, M.
Ektesabi, R. Nagarajah., A Study and Review on Vehicle Suspension System and Introduction of a High-Bandwidth Configured Quarter Car
Suspension System. Aust. J. Basic & Appl. Sci., 9(30): 59-66, 2015
INTRODUCTION
When travelling, vehicles experience dynamic
excitations of varying magnitudes. Such excitations
could lead to induced vibration or noise, which affect
the vehicles’ integrity and occupants. A prominent
method of vibration isolation in vehicular system is
the suspension system. The main objective of a car
suspension system is to improve the ride comfort
without compromising the ride handling
characteristic. Over recent years, the massive
developments in actuators, sensors and
microelectronics technology have made the
intelligent suspension systems more feasible to
implement in automobile industry. These systems are
designed and fabricated in such a way that they are
able to reduce the drivers' and passengers’ exposure
to harmful vertical acceleration. The quarter-car
suspension model is the best bench-mark to study
and analyze the dynamic behavior of vehicle vertical
isolation properties (Allen, J.A., 2008; Kashem,
S.B.A., 2012). This paper presents background
information and a description of the quarter-car
suspension model which can be used to evaluate the
performance of intelligent suspension system.
Vehicle suspension system:
A suspension system is an essential element of a
vehicle to isolate the frame of the vehicle from road
disturbances. Figure 1 shows a typical car suspension
system. It is required to maintain continuous contact
between a vehicle’s tyres and the road. The most
important element of a suspension system is the
damper. It reduces the consequences of an
unexpected bump on the road by smoothing out the
shock. In most shock absorbers, vibration energy is
converted to heat and dissipates into the
environment. Such as, in the viscous damper, energy
is converted to heat via viscous fluid. In hydraulic
cylinders, the hydraulic fluid is heated up. In air

60 S.B.A. Kashem et al, 2015
Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
cylinders, the hot air is emitted into the atmosphere.
But the electromagnetic damper is different; here the
vibration energy is converted into electricity via an
electric motor (induction machine or DC motor or
synchronous machine) and stored in a condenser or
battery for further use (Suda, Y., et al., 2004).
Fig. 1: Vehicle suspension.
Suspension systems are categorized as passive,
active and semi-active considering their level of
controllability. Although all the types of the
suspension systems have different advantages and
disadvantages, all of them utilize the spring and
damper units.
2.1 Passive suspension system:
Fig. 2: Passive suspension system.
Passive suspension systems are composed of
conventional springs and oil dampers with constant
damping properties (Figure 2). .In this model m1 and
m2 represent the un-sprung mass and sprung mass
respectively, k 1 is the tyre stiffness coefficient or
tyre spring constant, k 2 is the suspension stiffness or
suspension spring constant. c0 and ct are the
suspension damping constant and the tyre damping
constant respectively, Fr is friction of suspension, q,
z1 and z2 represents road profile input, displacement
of un-sprung mass and displacement of sprung mass
respectively.
In most instances, passive suspension systems
are less complex, more reliable and less costly
compared to active or semi-active suspension
systems. The constant damping characteristic is the
main disadvantage of passive suspension systems.
For a passive suspension, the use of soft springs and
moderate to low damping rates is needed but the use
of stiff springs and high damping rates is needed to
reduce the effects of dynamic forces. Designers
utilize soft springs and a damper with low damping
rates for applications that need a smooth and
comfortable ride such as in a luxury automobile.
On the other hand, sports cars incorporate stiff
springs and a damper with high damping rates to gain
greater stability and control at the expense of
comfort. Therefore, the performance in each area is
limited for the two opposing goals (Gillespie, T.,
2006). There is always a compensation need to be
made between ride comfort and ride handling in the
passive suspension system as spring and damper
characteristics cannot be changed according to the
road profile.
2.2 Semi-active suspension System:
Fig. 3: Semi-active suspension system.
The semi-active suspension system was first
proposed by Karnopp et al. in 1973. In this model,
Figure 3 is a semi-active suspension model. Here fd
can generate an active actuating force by an
intelligent controller. Since then, semi-active
suspension systems have continued to acquire
popularity in vehicular suspension system
applications, due to their better performance and
advantageous characteristics over passive suspension
systems. In semi-active suspension systems, the
damping properties of the damper can be changed to
some extent. The adjustable damping characteristics
in semi-active dampers are achieved through a
variety of technologies, such as: Electro-Rheological
(ER) and Magneto-Rheological (MR) fluids,
solenoid-valves and piezoelectric actuators. It has
been widely recognized that a semi-active suspension
system provides better performance than a passive
system. As it is safe, economical and does not need a

61 S.B.A. Kashem et al, 2015
Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
large power supply, semi-active suspension has
recently been commercialized for use in high-
performance automobiles (Irmscher, S. and E. Hees,
1966; Konik, D., et al., 1996; Nakayama, T., et al.,
1966; Yi, K. and B.S. Song, 1999;
Sankaranarayanan, V., et al., 2008). However, there
still exist many challenges that have to be overcome
for these technologies to achieve their full potential.
MR degradation with time, sealing problems and
temperature sensitivity are some crucial issues of the
MR dampers that need development.
2.3 Active suspension system:
Fig. 4: Active suspension system.
The active suspension system (Figure 4) actuates
the suspension system links by extending or
contracting them through an active power source as
required. Conventionally, automotive suspension
designs have been a compromise between the three
contradictory criteria of road handling, suspension
travel and passengers comfort. In recent years the
use of active suspension systems has allowed car
manufacturers to achieve all three desired criteria
independently. A similar approach has also been
used in train bogies to improve the curving behaviour
of the trains and decrease the acceleration perceived
by passengers. But this makes the system expensive
and increases the design complexity and energy
demands.
From the above discussion, it is apparent that a
semi-active suspension system is more appropriate
for implementing and evaluating the performance of
various control strategies.
Quarter-car suspension model:
Quarter car suspension system is wide used to
investigate the performance of intelligent suspension
system. In this paper, a two degree of freedom
quarter-car model has been described. A quarter-car
model imitates the heave or the vertical motion of the
vehicle alone. As the design goal of most semi-active
suspension system is to reduce the vertical
acceleration, the quarter-car model is sufficient for
evaluating the performance of control strategies
(Hrovat, D., 1997). The sprung mass, suspension
components, un-sprung mass and a wheel are the
basic components of a quarter-car model. For a
quarter-car model, sprung mass means the body or
chassis of the car and it represents almost one fourth
of the weight of the whole body of the car. The
suspension system bridges the connection between
the wheel and body of the car and consists of many
parts, and varies according to the type of the
suspension system such as passive, semi-active or
active suspension (described in the previous section).
Un-sprung mass includes the weight of everything
geometrically below the suspension system, such as
axle, wheel and rim. The wheel denotes the tyre,
which incorporates the spring and damping
characteristics.
A two degree of freedom quarter-car model as
shown in Figure 5 (a) is known as an ideal model and
used by some researchers (Zhang, H., 2009; Abdalla,
M.O., 2009; Fateh, M.M. and S.S. Alavi, 2009).
Faheem et al., (2006) presented an insight on the
suspension dynamics of the quarter car model with a
complete state space realisation. In the ideal case the
sprung mass and un-sprung mass is free only to
bounce vertically. In this model m1 and m2 represent
the un-sprung mass and sprung mass respectively, k 1
is the tyre stiffness coefficient or tyre spring
constant, k 2 is the suspension stiffness or suspension
spring constant. fd can generate an active actuating
force by an intelligent controller. c0 and ct are the
suspension damping constant and the tyre damping
constant respectively, Fr is friction of suspension, q,
z1, z2 represents road profile input, displacement of
un-sprung mass and displacement of sprung mass
respectively.
Fig. 5: (a) Ideal quarter-car model, (b) simplified
quarter-car model.
The ideal dynamic equations of motion of un-
sprung and sprung masses which satisfy Newton’s
second law of motion are given by the equation 1.
g
m
F
f
zz
k
zz
c
z
m
g
m
F
f
q
z
k
q
z
c
zz
k
zz
c
z
m
r
d
r
d
t






































































2202
11201
12122
1121211
(1)
The simplified model as shown in Figure 5 (b)
has been used in most recent studies (Gupta, A., et
al., 2006; Guo, D., 2004; Nguyen, L.H., et al., 2009;
Priyandoko, G., 2009; Scheibe, F. and M.C. Smith,
2009; Bin Abul Kashem, S., 2014; Kashem, S.B.A.,
2008; Bakar, S.A.A., et al., 2008; Yan, B., 2012;

62 S.B.A. Kashem et al, 2015
Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
Zhu, X., 2012; Hu, H., et al., 2012; Jiang, X., 2012;
Chen, S.Z., et al., 2012; Wang, W.R., et al., 2012;
Soliman, A.M.A., et al., 2012; Shisheie, R., et al.,
2012; Shiri, A., 2012; Zhang, J.J., 2012; Choudhury,
S.F. and D.M.A.R. Sarkar, 2012; Kruczek, A., et al.,
2011; Kruczek, A., et al., 2011; Mourad, L., 2011;
Roqueiro, N., 2011; Edelmann, J., 2011; Pellegrini,
E., et al., 2011; Collette, C. and A. Preumont, 2010;
Du, F., et al., 2010) as the effect of the tyre damping
coefficient ct is negligible compared to the tyre
stiffness coefficient. So omitting the tyre damping
force ct (
 qz2
), the equation (1) becomes equation
(2).
g
m
F
f
zz
k
zz
c
z
m
g
m
F
f
q
z
k
zz
k
zz
c
z
m
r
d
r
d



























































2202
11201
12122
121211
(2)
Explanation of motion equations of quarter-car:
To understand the motion equations for the
quarter-car suspension, it is better to start from ideal
mass-spring-damper motion equations, which are
well known. First one considers horizontal motion as
shown in the Figure 6.
Fig. 6: Mass spring characteristics.
In this figure, x is the position of the square
block in meters, m is the mass of the block in
kilograms, k is the spring stiffness in Newton’s per
meter and Fspring is the spring Force in Newton’s.
When a spring is stretched from its equilibrium
position due to an external force, the spring itself acts
as a force proportional to the length it is stretched
and this force acts in the opposite direction to the
stretch.
Fspring ∞ − stretch
Or
Fspring = −k × stretch
If x = 0 at the position where the spring is in
equilibrium, then x is equal to the stretch of the
spring. So the force of the spring becomes
Fspring = − k x
In addition, there is a force that opposes the motion
of the mass as shown in the Figure 7.
Fig. 7: Mass-spring-damper configuration.
In this figure, c is the damping constant in
Newton-second per meter and v is the velocity of the
block in meters per second. This force is the damping
force and it is proportional to the mass velocity
which also opposes the mass velocity, such as
Fdamping ∞ − v
Or
Fdamping = −c v
So the total force acting on spring-mass-damping
system is
F = Fspring + Fdamping = − k x − c v (3)
According to Newton's law of motion F = m a.
From the definition of acceleration, the first
derivative of position x is equal to the velocity v and
the acceleration a is equal to the second derivative of
position x.
x
a


And
x
v


Now the differential equation becomes,
x
k
x
c
x
m


(4)
The simple mass-spring-damper model
described above is the foundation of vibration
analysis. This is defined as the single degree of
freedom (SDOF) model, since it has been assumed
that the mass only moves up and down in the same
axis. The Figure 8 is a more complex system
involving more mass which is free to move in more
than one direction adding degrees of freedom.
Fig. 8: Two degree of freedom horizontal multiple
mass spring damper.

63 S.B.A. Kashem et al, 2015
Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
In this model, the two springs act independently,
so it is easy to figure out the forces acting on the two
blocks. It is assumed that the connection of the
spring and damper to the wall is the origin of this
suspended system. Here x1, x2 are the position (left
edge) of the blocks, m1, m2 are the mass of blocks
and k1, k2 are the spring constants. So the motion
equations would be
xk
xx
k
x
c
xx
c
x
m112121 211211 




















(5)





















xx
k
xx
c
x
m12122 222
Fig. 9: Vertical multiple mass spring damper
configuration.
Now the vertical linear motion has been
considered as shown in the above figure. Here a new
force strikes due to gravitation g (m/s2) which acts in
the same direction (downward) as the mass velocity
and equals the product of mass and gravity, so the
differential equation becomes
Now, considering a two degree of freedom
quarter-car suspension model having an actuator
which delivers a force fd as shown in the Figure 9 and
the corresponding motion equation is the equation
(6).
g
mxk
xx
k
x
c
xx
c
x
m1112121 211211 





















2 2 1 2 1
2 2 2 2g
m c k m
x x x x x
  
   
   
   
   

  

(6)
Fig. 10: Forces acting at a point.
If one considers the forces acting on the un-
sprung mass m1 then the forces acting downward is
the m1g force due to gravitation and actuating force
fd. According to Figure 10, force due to the
acceleration of the un-sprung mass
z
m1
1

is acting in
the upward direction. If the displacement z1>q is
positive then the spring force k1(z1-q) and the
damping force c1(z1-q) is negative in the downward
direction according to Figure (10). This is same for a
damping force of co and a spring force of k2 if z1>z2
is positive. The friction force Fr is acting negatively
in the downward direction.
Again for sprung mass m2, the forces acting
downward is the m1g force due to gravity and friction
force Fr. The force due to the acceleration of the
sprung mass
z
m2
2

is acting in the upward direction.
The actuating force fd is acting negatively downward.
Damping force of co and spring force of k2 is
negative in the downward direction under the
condition that displacement z2>z1.
High vs. low-bandwidth suspension system:
A semi-active suspension system has two
sections: semi-active and passive. The semi-active
part usually gets damping force from an external
energy source to control the suspension system (in
regenerative type system, it may differ). The passive
part has a spring and a damper or similar devices. In
some systems this part is rigid but it can be omitted
as well. This can be distinguished as low-bandwidth
and high-bandwidth suspension systems (Kruczek,
A. and A. Stribrsky, 2004).
Low-bandwidth configuration (LBC) represents
the series connection between the active and passive
components of the suspension system (Figure 11 (a)).
In the mathematical modeling, the differential motion
equations are as follows,
g
m
F
z
z
k
z
z
c
z
m
g
m
F
q
z
k
z
z
k
z
z
c
z
m
r
lblb
r
lblb
















































2
2
2
2
0
2
2
1
1
1
2
2
2
0
1
1
1
(7)
where c(dzlb – dz1) = fd is the actuating force.
Through LBC configuration, the active suspension
system can control the car body (sprung mass)
height. But the actuator cannot be omitted or turned
off as it carries the static load. Another disadvantage
of this system is that it is good only in the low
frequency range.
On the other hand, in a high-bandwidth
configuration (HBC), it is possible to control at
higher frequencies than for LBC and also the passive
part can work alone in case of failure of the active
part. The only drawback of HBC is that practically it
can’t control the vehicle height. In a HBC
configuration, active and passive components are
linked in parallel (Figure 11 (b)). The motion
equations of HBC are almost similar to that of LBC
but an extra term is added which is an actuator force
fd.
For the research of intelligent suspension
system, a two degree of freedom HBC semi-active
suspension system should be used, mainly because
there is no requirement of a static load force.

64 S.B.A. Kashem et al, 2015
Australian Journal of Basic and Applied Sciences, 9(30) Special 2015, Pages: 59-66
(a) (b)
Fig. 11: (a) Low-bandwidth suspension model, (b)
high-bandwidth suspension model.
Conclusions:
In this paper, the vehicle suspension system has
been categorised and discussed briefly. It has been
explained that the semi-active suspension system is
the most suitable for road vehicles. A brief
description of the quarter-car model has been given
as well as an explanation of the motion equations
used in the model. High and low bandwidth
suspension systems have also been discussed. As
there is no requirement of a static load force in this
research of a quarter car suspension system, a two
degree of freedom HBC semi-active suspension
system would be the best bench mark to investigate
different semi-active or active suspension systems’
control algorithms.
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