Abstract-- Significant improvements in automobile suspension
performance are achieved by active systems. However, current
active suspension systems are too expensive and complex.
Developments occurred in power electronics, permanent
magnet materials and microelectronic systems justifies
analysis of the possibility of implementing electromagnetic
actuators in order to improve the performance of automobile
suspension systems without excessively increasing complexity
and cost. In this paper, the layouts of hydraulic and
electromagnetic active suspensions are compared. The
actuator requirements are calculated, and some experimental
results proving that electromagnetic suspension could become
a reality in the future are shown.
Index Terms-- Active suspension, automobile suspension,
linear actuator, permanent magnet.
I. INTRODUCTION
he use of electromagnetic linear actuators in
automobile suspensions has already been proposed by
other authors. The reliability of electrical drives and
unconstrained integration with electronic control systems
are very important factors that justify the generalized use of
electromagnetic actuators in automobile suspensions.
Earlier attempts at using electromagnets in
electromagnetic automobile suspension were made by Tall
in 1961 and Lyman in 1966 [1], [2]. Lately, several authors
have proposed other kinds of electromagnetic systems for
automobile suspensions based on rotational actuator [3]-[8].
However, the use of rotational actuators requires a gearbox
to convert the rotational into linear movement, and to
increase the force value.
Linear actuators do not require any kind of gearbox. The
first automobile suspension systems using linear actuators
were proposed in [9]-[16].
Other works describing the advantages of electrical
Manuscript received November 13, 2001. This work was supported by
the project PRAXIS/P/EEEI-14270/1998, named "Electromagnetic
Vehicle Suspensions" funded by the PRAXIS Program and Portuguese
FCT.
I. Martins is at Escola Superior de Tecnologia, University of Algarve,
Campus da Penha, 8000 Faro, Portugal (e-mail: imartins@ualg.pt). J.
Esteves, G. D. Marques and F. Pina da Silva are at Instituto Superior
Técnico - Technical University of Lisbon, Av. Rovisco Pais, 1049-001
Lisbon, Portugal.
suspensions and linear permanent magnets actuators have
also been published [17]-[19].
The main objective of ground vehicle suspension systems
is to isolate the vehicle body from road irregularities in
order to maximize passenger ride comfort and to produce
continuous road-wheel contact, improving the vehicle
handling quality [20].
Currently, three types of vehicle suspensions are used:
passive, semi-active and active. All systems implemented in
automobiles today are based on hydraulic or pneumatic
operation. However, it is found that these solutions do not
satisfactorily solve the vehicle oscillation problem, or they
are very expensive and increase the vehicle’s energy
consumption [14], [18].
Significant improvement of suspension performance is
achieved by active systems. However, these are only used
in a small number of automobile models because they are
expensive and complex.
In Fig.1 a block diagram of a single-wheel hydraulic
automobile active suspension is presented. The vehicle
engine drives a hydraulic pump to power the suspension
based on hydraulic actuators that create oscillation-damping
forces between the vehicle body and the wheel assembly. A
hydraulic valve is driven by a low-power electromagnetic
actuator in order to handle the actuator forces. The control
system, together with a power electronics converter, drives
the low-power electromagnetic actuator.
Other Wheels
Suspension
Systems
Hydraulic Single-Wheel Active Suspension System
Sensors and
Instrumentation
Power
Electronics
Control System
Low-Power
Electromagnetic
Actuator
Hydraulic
Valve
Hydraulic
Actuator
Single-Wheel
Suspension
Vehicle
Engine
Hydraulic Pump
and
Power supply
Fig. 1. Block diagram of a hydraulic single-wheel active suspension.
In the last ten years, developments in power electronics,
Permanent-Magnets Linear Actuators
Applicability in Automobile Active Suspensions
Ismenio Martins, Member, IEEE, Jorge Esteves, Member, IEEE, G. D. Marques, Member, IEEE, and
Fernando Pina da Silva
T
permanent magnet materials and microelectronic sys
tems
have brought significant improvements in the electrical
drive domain. Increases in dynamic and steady state
performances, reductions in volume and weight,
unconstrained integration with electronic control systems,
reliability, and cost reduction are i
mportant factors that
justify the generalized use of electrical drives.
This evolution justifies an analysis of implementing
suspension systems using electromagnetic actuators in order
to improve the performance without increasing energy
consumption or costs.
In Fig. 2 a block diagram of an automobile suspension
using an electromagnetic linear actuator is shown. An
electrical generator feeding a battery now replaces the
complex and expensive hydraulic power supply. The
hydraulic valve and actuator have been removed from the
system. An electromagnetic actuator driven by the control
system through a power electronics converter is the main
component of the wheel suspension system.
The actuator and power electronics must be larger in this
case. However, the system is simpler since it has fewer
devices and mechanical parts. Because it has no hydraulic
devices, this is an oil-free system.
This paper shows that it is now possible to build an
electromagnetic actuator producing the required forces, and
with suitable power and dimensions for this application.
Other Wheels
Suspension
Systems
Electromagnetic Single-Wheel Active Suspension System
Sensors and
Instrumentation
Power
Electronics
Control System
Electromagnetic
Actuator
One-Wheel
Suspension
Vehicle Engine/
Generator
Battery
Fig. 2. Block diagram of an electromagnetic single-wheel automobile
active suspension.
II. ACTUATOR REQUIREMENTS
A. Active Suspension Models
1) Hydraulic Suspension
Figure 3 presents a model for vehicles with independent
suspensions, where
s
m represents a quarter of the 'sprung'
mass of a vehicle,
u
m the 'unsprung' mass of one wheel
with the suspension and brake equipment,
s
k the spring
stiffness,
t
k the tire stiffness and
s
b the damper
coefficient. The variable
f
F represents the friction force
[21].
The dynamic behavior of a single-wheel suspension
system may be expressed by differential equations (1) and
(2).
Afussussss
FFzzbzzkzm
+=
)()(
&&&&
(1)
Afrutussussuu
FFzzkzzbzzkzm
++=
)()()(
&&&&
(2)
The force of the hydraulic actuator is represented by
A
F .
The actuator force law (3) is defined as in [21] and [22] and
is given by:
sA
zCF
&
=
(3)
where
C is a constant coefficient.
z
s
z
u
z
r
m
u
m
s
k
s
k
t
b
s
F
A
Fig. 3. Model of a hydraulic single-wheel active suspension.
2) Electromagnetic Suspension
The electromagnetic actuator replaces the damper and the
hydraulic actuator, forming with the spring an oil-free
suspension. Fig. 4 presents a model of an electromagnetic
suspension [16].
Fig. 4. Model of an electromagnetic single-wheel active suspension.
The friction force of an electromagnetic actuator can be
neglected. So, the dynamical equations of the suspension
system become,
Aussss
Fzzkzm
+=
)(
&&
(4)
Arutussuu
Fzzkzzkzm
=
)()(
&&
, (5)
and the electromagnetic actuator force law, to obtain the
same dynamics as the hydraulic suspension, results
sussA
zCzzbF
&&&
=
)( . (6)
3) Control System
The control system must ensure the calculation of an
actuator reference force F
Aref
, in conformity with expression
(3) in the case of a hydraulic suspension, or with (6) in the
case of an electromagnetic active suspension. The actuator,
power electronics converter, mechanical components and
instrumentation feedback are also parts of the closed loop
automatic control electromagnetic suspension system. The
suspension dynamics is governed mostly by the actuator
force and by the suspension mechanics, in accordance with
(4) and (5).
In figure 5 the electromagnetic active suspension control
system diagram is shown. The force reference is obtained
from the sprung and unsprung speeds, related to a zero
vertical speed point fixed on the sky (skyhook speeds) [21].
A coefficient K=1/K
, related to the actuator construction
parameters and to the magnetic field, enables the reference
current to be calculated, correspondingly to the required
force. The current value is controlled by a sliding mode
controller [23].
Sliding Mode
Current
Controller
Power
Electronics
Electromagnetic
Actuator
One-Wheel
Suspension
K
b
s
C
Sensors and
Instrumentation
F
A
i
F
Aref
i
ref
+
+
+
+
_
_
z
s
z
u
Control System
Fig. 5. Electromagnetic active suspension control system.
B. Suspension Forces
1) Critical Working Points
Resonance frequencies are the most critical working
points not only from the standpoint of comfort and safety,
but also for the design of the actuator power and force
values. These frequencies, given by expressions (7) and (8),
are the natural frequency values of the two suspension
subsystems: the 'suspension spring stiffness/sprung mass'
and the 'tire stiffness/unsprung mass' [20].
s
s
S
m
k
f
2
1
0
=
(7)
u
t
U
m
k
f
2
1
0
=
. (8)
2) Actuator Stroke, Velocity and Force Values
The parameters needed for the actuator design were
obtained by systematic use of numerical simulations. These
include stroke and velocity values, peak and r.m.s. force
and power values.
The numerical simulation of equations (4) and (5), using
the control law (6), was conducted with parameters from
[21] and [22]. These parameters are presented in Table I.
TABLE I
S
USPENSION SIMULATION PARAMETERS
Symbol Quantity Value
s
m
sprung mass 290 Kg
u
m
unsprung mass 59 Kg
s
k
spring stiffness 16,812 N/m
t
k
tire stiffness 190,000 N/m
s
b
damper coefficient 1000 N/m/s
C active force coefficient 3000 N/m/s
In the first stage, the actuator forces were investigated in
simulation, using a 1.2 Hz frequency and 1-inch amplitude
sinusoidal wave as road input disturbance. This amplitude
is normally used in published works on this subject [22] and
others. The frequency chosen is approximately the sprung
mass resonance frequency, also normally used to verify
suspension operation.
The actuator parameters for the analyzed case are
presented in Table II. Simulation results of the
instantaneous force are presented in Fig. 6.
TABLE II
S
IMULATION RESULTS FOR A 1.2 HZ FREQUENCY
AND 1-INCH AMPLITUDE INPUT DISTURBANCE
Quantity Value
Max. Stroke 50 mm
Max. Velocity 0.28 m/s
Peak Force 450 N
R:M.S. Force 295 N
Peak Power 65 W
R.M.S. Power 37 W
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-500
-400
-300
-200
-100
0
100
200
300
400
500
Time (seconds)
Force (Newton)
Fig. 6. Active suspension actuator instantaneous force, using a
sinusoidal road perturbation of 1.2 Hz frequency and 2.54 cm amplitude.
Although in most situations, the suspension input-
disturbance
r
z is smooth, suspensions must operate in a
large spectrum of input disturbance frequency values due to
road irregularities, which creates a set of frequencies of
distinct amplitudes. The most significant of these
frequencies are the resonance frequencies of the sprung and
unsprung masses.
ISO 2631 standard gives the acceptable time period
exposure of a car passenger to a set of vertical acceleration
levels. These vibration levels are set in terms of r.m.s.
acceleration values which produce equal 'fatigue-decreased
proficiency'. In most situations, exceeding the specified
exposure causes noticeable fatigue and may be a cause of a
large number of automobile crashes. In the above standard,
the r.m.s. acceleration upper bound is taken to be twice the
'fatigue-decreased proficiency' levels. The 'reduced comfort
boundary' is assumed to be about one third of standard
levels [24].
Automobile drivers automatically avoid the set of
'reduced comfort boundary' frequencies values, simply
because they feel uncomfortable, by decreasing or
increasing the vehicle’s speed. Consequently, the sprung
mass acceleration levels are normally below the levels
defined as the 'reduced comfort boundary'. These
considerations were used to define the actuator steady state
power.
For calculation of the actuator steady state operation
upper limits, a numerical simulation of the suspension
model was conducted. As model disturbance, a combined
signal was used composed of the sum of two sinusoidal
waves with different amplitudes and frequencies. These are
respectively the sprung and unsprung mass resonance
frequencies. The numerical simulation results, conducted
for three amplitude sets, are presented in table III. For each
frequency-amplitude set the 'reduced comfort boundary'
time was found, as shown in table III.
In Fig. 7 the instantaneous force simulation result is
presented.
TABLE III
S
IMULATION RESULTS FOR THE
REDUCED COMFORT BOUNDARY
Quantity
1.2 Hz /
1.5 cm.
9 Hz/
0.05 cm.
1.2 Hz /
3.5 cm.
9 Hz/
0.15 cm.
1.2 Hz /
8.5 cm.
9 Hz/
0.25 cm.
Reduced comfort
time boundary
4 hours 1hour 1 min.
Max. Stroke 32 mm 80 mm 160 mm
Peak Force 350 N 900 N 2000 N
R.M.S. Force 186 N 451 N 1041 N
R.M.S. Power 21 W 139 W 615 W
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
Time (seconds)
Force (Newton)
Fig. 7. Active suspension actuator instantaneous force, using a set of
two sinusoidal road perturbation waves of 1.2 Hz, 3.5 cm amplitude and 9
Hz, 0.15 cm amplitude.
III. ACTUATOR DESIGN CONSIDERATIONS
From Tables II and III, and for the suspension
parameters presented in Table I, one can define the actuator
operation limits for an electromagnetic active suspension.
The actuator should be able to produce an r.m.s. force value
of 1050 Newton in the steady state. Its stroke should be 160
mm, and the peak velocity is about 1.2 m/s.
A. Maximum dimensions and shape
The actuator must fit in a reasonable space, near the
wheel. The available room for the actuator depends on the
car design. So it cannot be defined exactly, except for a
specific model.
At present, a cylindrical shape seems the most suitable
because cars are designed to use hydraulic or pneumatic
actuators, and these have a cylindrical shape. Moreover,
this shape allows the use of helical sprigs around the
actuator, and it can be an advantage for the suspension
design.
The design parameters for an experimental
electromagnetic actuator are presented in Table IV.
TABLE IV
A
CTUATOR DESIGN PARAMETERS
Quantity Value
Stroke 160 mm
Steady State Force 1000 N
Peak Velocity 1.2 m/s
R.M.S. Power 615 W
Max. Diameter 150 mm
Max. Length 600 mm
B. Actuator lay-out
A cylindrical permanent-magnet linear actuator can be
built in two possible configurations: moving magnets or
moving coils [19]. However, in an automobile suspension,
to define precisely a non-moving part is not possible. In
fact, both parts of the actuator are in movement, because
one is connected to the sprung mass, and the other to the
unsprung mass. However, a moving part can be taken to be
the part connected to the unsprung mass.
It is better to put the coils on the sprung mass side
because this is the vehicle body side. On the other hand, it
is advantageous for suspension performance to have less
actuator weight on the unsprung mass side. Developments
in high-energy NdFeB magnets allow the construction of
reasonable magnetic excitation arrangements [19].
The moving-magnet cylindrical linear actuator can be
constructed using radial or axially magnetized permanent
magnets.
In the first case, as shown in Fig. 8 a), the magnetic poles
are obtained by assembling radial magnetized NdFeB rings
on a magnetic-steel rod. In the second case, Fig. 8 b), two
opposite-field NdFeB axially magnetized cylinders are
assembled sandwiching a magnetic-steel cylinder. The
magnetic field crosses the cylinder tops, and then the
cylindrical surface.
Fig. 8. Actuator configurations: a) radial magnetization; b) axial
magnetization
In both configurations, copper windings are assembled
inside a longitudinally laminated silicon-magnetic-steel
slotless armature. The airgap is thus the distance between
the poles and the armature, with the copper windings and
their electrical insulation almost filling it.
Radially magnetized NdFeB magnets are very expensive
compared to axially magnetized magnets. Both
configurations were analyzed, using a Finite Elements
Analysis (FEA) program.
C. Actuator design analysis
A prototype of a linear permanent magnets cylindrical
actuator, using axial magnets configuration was designed.
The design analysis of this actuator was made using the
magnetic circuit configuration shown in the Fig. 9. All
calculations were made neglecting the magnetic flux
leakage. Subsequently, all calculations were confirmed
using a FEA program and experimental verification.
h
p
h
m
d
1
d
2
d
3
Slotless
Armature
Permanent
Magnet
Ferromagnetic
Cylinder
Airgap
Fig. 9. Linear actuator magnetic circuit configuration.
The magnetic flux through the permanent magnet top:
4
2
1
dB
SB
m
mm
==
(9)
The magnetic flux density on the ferromagnetic cylinder
wall:
p
m
p
m
p
h
dB
dh
dB
S
B
44
1
1
2
1
1
=
=
=
(10)
where B
m
is the permanent magnet working magnetic flux
density medium value.
Chosen the adequate dimensions for it, one can consider
equal medium magnetic flux densities on the ferromagnetic
cylinder wall, on the top of the ferromagnetic cylinder, and
on the top of the permanent magnet. Therefore,
