Linear Electromagnetic Actuators For A V
Linear Electromagnetic Actuators For A V
Linear Electromagnetic Actuators For A V
Suspension System
Group 2: Adalberto Lazo Castro (250480019), Shubham Yadav (251117553) and
Parampreet Singh (251077118)
Abstract
This paper focuses on actuators used in an automobile suspension system. There are three main types of suspensions: passive,
semi-active (or adaptive) and active. Due to the unpredictability of various road and driving conditions that a vehicle can
face, suspension systems and the types of actuators used are a very important topic. In this paper, active suspension systems
are investigated, specifically, electromagnetic suspensions. Electromagnetic suspension systems are fully active suspension
systems that eliminate sensations felt from road irregularities by performing active roll and pitch control. These systems use
electromagnetic actuators which have fast response capabilities. Therefore, it can provide a higher ride quality than the more
conventional suspensions. In this paper, linear electromagnetic actuators are analysed, known as Tubular Permanent Magnet
Actuators (TPMA). This paper exemplifies the modelling and design of such electromagnetic actuators. The application to a
BMW530i car suspension has shown effective results in terms of size, weight and performance.
Keywords: Electromagnetic suspension system, active suspension system, Tubular Permanent Magnet Actuator (TPMA),
BMW 530i, Halbach magnet array.
1
the vehicle. An onboard computer system (Electrical Control suspensions). As shown in figure 1 (B and C), There are two
Unit (ECU)) is installed within the vehicle which helps to different types of linear electromagnetic actuators. The first
automatically sense the road conditions and adjust this is an active interior-magnet Tubular Permanent Magnet
movement of the suspension and height of the chassis. It is Actuator (TPMA) where the coils are stationary, and the
capable of fully controlling all critical parameters such as the magnets are movable. The second is called an active exterior-
thrust force, damping force and stroke length of the piston. magnet TPMA. The latter type will be investigated.
Therefore, they can eliminate the vibrations felt on a vehicle
body, as opposed to a conventional passive suspension
system. The actuator of the active suspension system can be
of four main types: hydraulic, pneumatic, electromagnetic or
hybrid.
2
An electromagnetic actuator has been designed, shown in
figure 4, to be able to produce a force for suspension control
Measurements performed on the MacPherson suspension [7]. This actuator has been retrofitted for the BMW 530i
strut are shown in figure 3 [4]. It is observed that the rebound MacPherson front suspension strut. Measurements were
spring has an effect at an approximate -0.015 metre stroke. calculated on a test track in Germany and performance
Damper force achieves irregular value in bump and rebound specifications were able to be derived. It was found that a
region. Minor damping potential is required while in peak and root mean square (RMS) force of 4000 N and 2000
compression, so that vehicle is capable of riveting bumps. N, respectively, was required to eliminate the vehicle roll
Suspension travel is limited because of kinematic limitations angle. However, it has been stated that these driving
and need an explicit quantity of damping. Usually for conditions are quite rare and therefore, a duty cycle of 50% is
preventing “abruptness” additional rebound damping is chosen resulting in an RMS force of 1000 N [8].
employed within the suspension [5].
3
Since the circumference of coil in the design is relatively
smaller, it helps in reducing copper losses. Additionally, (3.4)
positioning it on the sprung mass, it ensues the lack of
moving wire. Angular coils are arranged in a way which is in
(3.5)
accordance to Lorentz’s equation (3.1) and an axial force is
generated. where, z =zs−zu is the displacement of the actuator
(suspension travel), τp the pole pitch, î the amplitude of the
(3.1) current and φ, the speed dependent commutation. The EMF
No constant power is required to raise the vehicle, since the Ei is defined as,
spring placed in parallel with the actuator counterbalances its (3.6)
weight. where kEi is the EMF gain and v = v s −vu is the speed of the
actuator. With the assumption that î and v are independent,
the force provided by the actuator is defined as,
(3.7)
where ki is the force gain and d is the damping coefficient.
The calculated force as a function of current is shown in
figure 7. In the same figure is a linear estimate of this
measured force given by
Figure 5 - Electromagnetic Actuator - Detailed view of three
phases. (3.8) [8]
(3.2)
where the subscript i represents phases a, b or c. Also, R i
represents the resistance per phase and Li is the inductance.
The current in each phase is given by Figure 7 - Actuator Force vs Current Graph (Ki = 115 N/A)
[8]
(3.3)
4
3.2 Sensors Selection vehicle mass. As previously mentioned, against the cylinder
walls is a sliding bearing. This bearing allows the piston to
As shown in figure 4, the electromagnetic actuator has three move linearly up and down. Its tubular structure gives the
sensors installed on it [10]. First is the piezoelectric sensor actuator the ability to deliver large direct drive forces in a
located on the sprung mass, which provides the acceleration small volume. To improve comfort and handling, its
value of the vehicle body. Its location is important since it bandwidth is very high (hundreds of hertz),
provides the measurement for the ride smoothness and also
determines and controls the ride quality. The second sensor is The strong magnetic field due to the Halbach array is
a laser sensor located on the unsprung mass, which measures concentrated within the cylinder walls of the actuator, over
the travel distance between the sprung and unsprung mass. the three-phase winding arrangement. The sensors are used
This is important as the commutation of the actuator is a to determine the intensity of the current required according to
direct measure of the suspension travel, thus it is crucial that the condition and location of the sprung and unsprung mass.
the measure of the distance is precise. It provides a real-time The input from the sensors are computed with the help of a
measure for the suspension position and checks for its limit. microcomputer onboard, which processes the command for
Corrective actions are processed if the suspension reaches current required inside the winding. Due to the current, a
close to its limits. Lastly, there is a 50 g acceleration sensor magnetic field is generated around the coils, which reacts
that measures the acceleration of the unsprung mass. Since it with the Halbach magnetization inside the actuator. Since a
is impossible to measure the absolute compression of a tire three-phase current is provided, each coil has alternate poles,
over a road surface, which tends to be unpredictable in which responds with alternating Halbach magnets and
nature, this measurement is the most convenient way to produces a force proportional to the current induced. This in
determine the state of the tire. turn allows for the elimination of the vibrations felt on the
vehicle body from road irregularities.
Taking a brick and carton of milk is a great example for
explaining the unpredictable nature of the tire stiffness. The 5. Actuator Design
sensor will treat both of them as solids, but the carton of milk
will be compressed easily by the tire while the brick might A quarter car model, which represents one corner of the
cause damage. Measurements done by the use of sensors are vehicle, will be analyzed. The quarter car model has been
affected by the noise level during measurement. When using proven to most accurately predict comfort and handling of
only acceleration sensors, the measurement of suspension the vehicle. Thus, it will be considered for the actuator
travel can be done by integration, but considering the design and only the vertical dynamics will be examined.
posssible sensor drift and accuracy required for the
commutation, the suspension travel is measured directly.
5
(5.8)
(5.1)
The wheel hop frequency refers to when the tire starts to
(5.2) wobble and become unstable. By relating the suspension
travel to the sprung motion, equation 5.6 can be rewritten as:
, , and are displacement, speed and acceleration
of the sprung mass, ms, respectively. Tire and spring stiffness
(5.9)
are given by kt and ks , respectively. Damping is ds and the
actuator force in the model is Fact. Displacement, speed and
From this equation, the rattle space frequency, which cannot
acceleration for the unpsrung mass, which consists of tire,
change due to the actuator force, can be defined as:
rim, brake and suspension are defined as , and
, respectively. The degrees of freedom, in this case is two,
which comes from the displacement of the sprung and (5.10)
unsprung masses. The vertical acceleration, , will be
used for estimating car comfort and hence the weighting
criterion, ISO 2631-I, will be used [11]. For handling, the tire
compression, , will be considered.
(5.3)
(5.4)
While designing the controller, the RMS force will have the
following constraint (equation 5.5):
(5.5)
6
In this section, important parameters, limits and constraints With the derived constraints, values and limits of the system,
of the suspension were defined, which has need be taken into the linear quadratic and robust controls were used to develop
consideration when designing the controller of the system. controllers with varying comfort and handling level. In
comfort focused controller, the acceleration of sprung mass
5.2 Linear Quadratic control was minimized by means of the tire compression while in
handling focused controller, tire compression was controlled.
In this control method, only constant parameters are to be Both control approaches were used to simulate varying
used with no deviation. Estimation will be made for the comfort and handling settings.
spring mass, as a load of two average passengers with half a
tank of gas, distributed evenly over the four tires. Other
6.1 Linear Quadratic Control
parameters are shown in table 3 below.
Among the various control settings, it was found that the
comfort can be increased by 35% as opposed to the passive
system, while handling can be improved by 48.5% at the cost
of 23% comfort[8].
(5.11)
7
Meanwhile, controller 11 achieved the most optimal handling
improvement of 25.5%, sacrificing comfort levels by 6%.
Weighting filters are used for designing all 11 controllers
with distinct settings for handling and comfort. In controller
1, comfort is maximum priority. Furthermore, comfort
decreases by 10%, while handling increases by 10% as
controller 11 is approached.
7. Conclusion
8
capability of offering the highest force density, among other [5] D. Bastow, G. Howard, and J. Whitehead, Car Suspension and
aspects. A traditional MacPherson strut is used as the base. Handling. Professional Engineering Publishing, 2004.
The actuator is in parallel with a passive spring to support the [6] Blom RE, Vissers JP, Merkx LL, Pinxteren M. Flat plank tyre
tester, user’s manual. Technical report, Eindhoven University of
vehicle weight. Furthermore, as a passive fail-safe, aluminum
Technology; 2009 Oct.
rings are fitted to eddy current damping. [7] Gysen BL, Janssen JL, Paulides JJ, Lomonova EA. Design
aspects of an active electromagnetic suspension system for
Simulation results show how the actuator performs on a automotive applications. IEEE transactions on industry
generic terrain with the parameters given in this paper. A applications. 2009 Jul 14;45(5):1589-97.
quarter-car model was used to evaluate the improvements in [8] Van der Sande TP. Control of an automotive electromagnetic
suspension. suspension system. Master's thesis, Eindhoven University of
Technology. 2011
The two approaches used for designing a controller was [9] Gysen BLJ, Paulides JJH, Encica L, Lomonova E. Slotted
tested on a quarter car model and it has been found that the tubular permanent magnet actuator for active suspension
robust control approach outperforms the linear quadratic systems. In Proc. 7th International Symposium on Linear Drives
control (LQR) approach. In robust control, there was an for Industry Applications (LDIA), Incheon, South Korea.
improvement in comfort by 60.7 %, which means that sprung Incheon: LDIA. 2009. p. 1-2
mass experienced 60.7% less acceleration than the passive [10] Van De Wal M, Philips P, De Jager B. Actuator and
system. This comfort setting deteriorates the dynamic tire sensor selection for an active vehicle suspension aimed at
compression by 125.7%. Similarly, for handling focused robust performance. International Journal of Control.
controller, improvement of 21.2% in handling is achieved by 1998 Jan 1;70(5):703-20.
comprimising 41.8% of comfort. Improvements in the [11] Okunribido OO, Magnusson M, Pope MH. The role of
simulation results are limited by suspension travel and whole body vibration, posture and manual materials
actuator force, in comfort and handling-focused controllers, handling as risk factors for low back pain in occupational
respectively. drivers. Ergonomics. 2008 Mar 1;51(3):308-29.
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