A Study of Active Engine Mounts Fredrik Jansson & Oskar Johansson

A Study of Active Engine Mounts Fredrik Jansson & Oskar Johansson
A Study of Active Engine Mounts
Examensarbete utfört i Reglerteknik
vid Tekniska Högskolan i Linköping
Fredrik Jansson & Oskar Johansson
Reg nr: LiTH-ISY-EX-3453-2003
Linköping 2003
A Study of Active Engine Mounts
Examensarbete utfört i Reglerteknik
vid Linköpings tekniska högskola
Fredrik Jansson och Oskar Johansson
Reg nr: LiTH-ISY-EX-3453-2003
Supervisor: Andreas Eidehall
Linköpings Universitet
Claes Olsson
Volvo Car Corporation
Examiner: Professor Fredrik Gustafsson
Linköpings Universitet
Linköping 17th December 2003
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Institutionen för systemteknik
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ISRN LITH-ISY-EX-3453-2003
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Studie av aktiva motorkuddar
A Study of Active Engine Mounts
Fredrik Jansson and Oskar Johansson
Achieving better NVH (noise, vibration, and harshness) comfort necessitates the use of active
technologies when product targets are beyond the scope of traditional passive insulators, absorbers,
and dampers. Therefore, a lot of effort is now being put in order to develop various active solutions
for vibration control, where the development of actuators is one part.
Active hydraulic engine mounts have shown to be a promising actuator for vibration isolation with
the benefits of the commonly used passive hydraulic engine mounts in addition to the active ones.
In this thesis, a benchmark of actuators for active vibration control has been carried out.
Piezoelectric actuators and electromagnetic actuators are studied further and two methods to
estimate parameters for electromagnetic actuators have been developed. A parameterized model of
an active hydraulic engine mount valid for frequencies from zero to about 300 Hz has also been
developed. Good agreement with experimental data has been achieved.
active engine mount, actuator, active vibration control, electromagnetic actuator model, parameter
Achieving better NVH (noise, vibration, and harshness) comfort necessitates the use of
active technologies when product targets are beyond the scope of traditional passive
insulators, absorbers, and dampers. Therefore, a lot of effort is now being put in order to
develop various active solutions for vibration control, where the development of
actuators is one part.
Active hydraulic engine mounts have shown to be a promising actuator for vibration
isolation with the benefits of the commonly used passive hydraulic engine mounts in
addition to the active ones. In this thesis, a benchmark of actuators for active vibration
control has been carried out. A parameterized model of an active hydraulic engine
mount valid for frequencies from zero to about 300 Hz has also been developed. Good
agreement with experimental data has been achieved.
This thesis is the final part of our Master of Science degrees in Applied Physics and
Electrical Engineering at Linköping University. It could not have been completed
without help from a great number of people. We wish to take this opportunity to express
our appreciations for their help throughout this project.
First, our warmest gratitude to two persons in particular, our supervisors Claes Olsson,
Ph.D. student at Department of Chassis and Vehicle Dynamics at Volvo Car
Corporation, Gothenburg, and Andreas Eidehall, Ph.D. student at Division of Automatic
Control in Linköping. Having the opportunity to work with those very ambitious persons
has made this work interesting and enjoyable. In addition to all the splendid guidance
during this project would we like to thank them for their careful reading, correcting and
critiquing of our thesis.
Thanks also to Dr. Ahmed El-Bahrawy at Volvo Car Corporation for taking part in many
fruitful discussions and helping us with many valuable advices.
We would also like to thank other colleagues at Volvo Car Corporation, namely Jochen
Pohl, Lars Janerstål, Lars Rigner and Göran Sjöstrand for their continuing support and
interest in our work.
Finally, we would like to thank our examiner Prof. Fredrik Gustafsson at Department of
Electrical Engineering at Linköping University, for his help during the work.
Gothenburg, December 2003
Fredrik Jansson and Oskar Johansson
1.1 Engine Mounts ...............................................................................................2
1.2 Objective ........................................................................................................3
1.3 Limitations .....................................................................................................3
1.4 Approach .......................................................................................................3
Actuator Technologies and Principles
2.1 Promising Actuator Technologies and Principles .........................................6
2.1.1 Electrorheological and Magnetorheological ..............................................6
2.1.2 Electrostatic .............................................................................................7
2.1.3 Electrostrictive .........................................................................................7
2.1.4 Hybrid......................................................................................................8
2.1.5 Hydraulic and Pneumatic..........................................................................8
2.1.6 Magnetostrictive.......................................................................................9
2.2 Selected Actuator Technologies and Principles........................................... 10
2.2.1 Electromagnetic ..................................................................................... 10
2.2.2 Piezoelectric........................................................................................... 11
2.3 Other Actuator Technologies....................................................................... 12
2.3.1 Electrochemical...................................................................................... 12
2.3.2 Phase change.......................................................................................... 12
2.3.3 Pyrotechnical ......................................................................................... 13
2.3.4 Shape Memory....................................................................................... 13
2.3.5 Thermomechanical ................................................................................. 14
Sensor Types
3.1 Piezoelectric sensors.....................................................................................16
3.1.1 Piezoelectric accelerometers ...................................................................17
Axtuator and Sensor Selection
4.1 Actuator Selection ........................................................................................19
4.1.1 Comparison between Actuator Technologies and Principles.....................20
4.2 Relationship between Actuators and Sensors Parameters ..........................23
4.3 Estimate the Effectiveness for Control ........................................................24
4.3.1 Open Loop Controllability and Observability ..........................................24
4.3.2 Closed Loop Stability .............................................................................25
4.4 Placement .....................................................................................................26
Study of Electromagnetc and Piezoelectric Actuators
5.1 Electromagnetic Actuators...........................................................................27
5.1.1 Model of a Typical Voice Coil ................................................................27
5.1.2 Parameter Identification ..........................................................................30 Method 1: The Heuristic Method .....................................................31 Method 2: The Least Square Method ...............................................33
5.1.3 Validity of the Model..............................................................................34
5.1.4 Examples of parameter identification ......................................................35 Example A: Voice Coil Reaction Mass Actuator ..............................35 Example B: Voice Coil Reaction Mass Actuator ..............................40
5.1.5 Specification-dependent Design ..............................................................42
5.2. Piezoelectric Actuators................................................................................44
5.2.1 Piezoelectric Model ................................................................................44
5.2.2 Piezo Stack Actuator...............................................................................48
5.2.3 Amplified Piezo Actuators ......................................................................50
5.2.4 Simulation of Piezoelectric Stack Actuator Model ...................................50
5.2.5 Validity of the Model..............................................................................53
Modelling of an Active Hydraulic Engine Mount
6.1 Passive part ..................................................................................................56
6.1.1 Inertia Track...........................................................................................57
6.1.2 Decoupler...............................................................................................58
6.1.3 Transmitted Force...................................................................................59
6.1.4 Complete Passive Mount Model..............................................................60
6.1.5 Validity of the Passive Engine Mount Model...........................................61 Superimposed inputs .......................................................................62
6.1.6 Experimentally Validation of the Passive Engine Mount Model...............62
6.2 Complete active engine mount .....................................................................68
6.2.1 Validity of the complete active engine mount model................................71
6.2.2 Validation of complete active engine mount ............................................71
6.2.3 Linearization of the Complete Active Engine Mount Model.....................72
Conclusions and Recommendations
Recommendations ................................................................................76
Appendix A Actuator Technologies and Principles
Appendix B Sensors – Types and Designs
Appendix C Max Energy Density
Appendix D Technology – Principle – Supplier
Chapter 1
To achieve better NVH (Noise, Vibration and Harshness) comfort, the development and
use of ANVC (Active Noise and Vibration Control) systems is necessary, when goals
and visions are beyond the scope of traditional passive insulators, absorbers and
Consumers demand better ride-comfort in their cars, but use of passive solutions would
increase the weight. At the same time, higher safety demands, greener cars and lower
fuel consumption demands lower weight of the car. Introducing ANVC systems in
automobiles will to some extent solve these contradicting demands. This thesis suggests
solutions to this contradiction, and discusses actuators, sensors and active engine
mounts. The purpose is to construct a complete model of an active engine mount. In the
way to accomplish that a benchmark of the today existing actuator technologies suitable
for use in ANVC has been carried out and is presented in Chapter 2. Chapter 3 is short
overview of the sensors used today in active vibration control with the intention to
introduce the area and should not be seen as a complete benchmark.
This Master of Science thesis work has been carried out at Volvo Car Corporation in
cooperation with the Division of Control and Communication, Department of Electrical
Engineering, Linköping University.
1.1 Engine Mounts
The first and most obvious role of the engine mount is to support the engine and
transmission. Another important role of the engine mount is vibration isolation, to reduce
the dynamic force, vibrations, transmitted from the engine to the frame.
The vibrations that the mount has to handle come from two different sources. The engine
vibrations that are to be isolated are typically in the region of 30-200 Hz, with
amplitudes generally less then 0.3 mm. The other source is the frame that is affected by
road surface irregularities via the suspension system. These frequencies are typically in
the region of 1 to 30 Hz and have an amplitude greater then 0.3 mm [58].
The ideal dynamic stiffness for an engine mount is viewed in Figure 1.1 [47]. For low
frequencies, high damping for shock excitation is needed to prevent engine bounce and
give driving stability. For example it is desirable that the engine follows the frame when
the car is going over a bump. At higher frequencies, low damping is desirable to isolate
low-amplitude engine vibrations caused by engine disturbances.
Figure 1.1 Dynamic stiffness of an ideal engine mount
The use of hard rubber would give high stiffness and would be good for providing firm
support for the engine and give good driving stability. However, the use of hard rubber
enables engine vibrations to be easily transmitted to the chassis. To in a further extend
isolate vibrations from the chassis the use of soft rubber is better. Resolving these
contradictory needs of driving stability and vibration isolation different solutions have
been tried out. Today most manufacturers use passive hydraulic engine mounts that can
give a frequency dependent dynamic stiffness. But the increasing demands on the engine
mounts are now becoming out of scope for the passive solutions. This makes it
interesting to investigate the possibilities with use of active engine mounts.
The difference between a passive and an active mount is that an active mount makes it
possible to provide controlled energy to the system. The use of active engine mounts has
many benefits. For instance, they can adapt to manufacturing differences and changes
during the lifetime of the mount. Structures can be made lighter and parts can be
eliminated. It would be interesting to study the effects of removing the engine balance
shaft by the use of active parts. Even though there are a number of benefits with an
active hydraulic engine mount the main advantage is improved performance in vibration
1.2 Objective
The engine suspension system is a promising area for application of AVNC. Therefore,
control systems have been developed but in many cases actuators, sensors and active
engine mounts have been assumed ideal. In reality, the characteristics and also the
working principle of the actuators, sensors and the complete active engine mounts have a
great impact on control algorithm design and the system performance. The questions that
this thesis work aims to answer are:
Which actuator and sensor technologies and principles can be used in AVNC, for
example in active engine mounts and what characterises them?
Which are the characteristics of an active engine mount?
Is it possible to crate a model of an active engine mount that are valid for both lower
(<30 Hz) and higher frequencies (30 Hz to ~300 Hz)?
1.3 Limitations
The work is limited to actuators dealing with single axes isolation. The focus is on
actuators and complete active engine mounts and we will only briefly discuss sensors
and their impact on the complete system.
1.4 Approach
To fulfil the objectives the project was divided in three parts:
Part 1: Investigation of existing actuators and sensors for use in active vibration
control concerning:
Working principles (different implementations of the technologies).
Technical specification/strengths and weaknesses, e.g. force and frequency ranges,
sensitivity, max amplitudes.
Part 2: Characterization and generation of parameterized models of selected
Generate parameterized models of selected actuators.
Identification of parameters.
Validate the actuator models against experimental data.
Develop a method for use in specification dependent design.
Part 3: Characterize and generate parameterized model of a complete active
hydraulic engine mount:
Generate parameterized model of a complete active engine mount.
Validate the complete active engine mount model against experimental data.
In Chapter 2 the benchmark of actuators conduced in part 1 is presented. Chapter 3 is a
brief discussion of the most commonly used sensors in AVNC. In Chapter 4 the different
actuators are compared and other factors that influence the AVNC system are briefly
discussed. Chapter 5 continue the discussions about piezoelectric and electromagnetic
actuators. The two are modelled and guidelines for voice coil actuator design from
frequency-domain specifications are given. Chapter 6 is the main chapter and present a
complete model of an active engine mount. In the last chapter, Chapter 7, conclusions
and recommendations are found.
Chapter 2
One of the objectives is to find an actuator that is suitable to be used in active vibration
control. Depending on the application, the actuator requirements can be very different in
size, power, energy source, achievable forces, frequencies, displacements etc. An
actuator is a device that transforms energy into controllable motion and/or force, which
performs useful work on the environment.
An active vibration control system consists of a sensor and an actuator together with a
control unit. The development of the systems is often limited by the chosen actuator
technology. The usual effects that limit the potential of actuators are restrictions of
bandwidth, displacement and placement, according to Hersle and Svensson [4].
Furthermore, difficulties with producing actuators that manage high temperatures and
mechanical stress have been confirmed.
In the field of active engine-vibration isolation some principles have been well tested
over many years, while research on other principles is just beginning. The development
of new actuator principles has been forced by the space industry’s high demands on
systems and actuators.
Smart materials are materials that can change shape and/or have the ability to affect their
characteristics with an applied voltage, change in temperature or magnetic field.
Examples of well-known smart materials are shape memory alloys, electrorheological
fluids, electrostrictive, magnetostrictive materials and piezoelectric materials.
Components that are based on utilization of smart materials have shown to be very
useful in active vibration damping systems, both as actuators and sensors.
In the field of active vibration control, piezoelectric ceramics, electrostatic,
magnetostrictive, electromagnetic, and hydraulic devices are used as actuators. In both
[30] and [39], each of them meets the classification of a fully-active actuator, which is
defined as:
“A fully-active actuator is able to supply mechanical power to its system”.
The other group of actuators is semi-active, which dissipates energy similar to passive
elements. The difference is that semi-active actuators can adjust their passive mechanical
properties by a control signal.
In this thesis, an actuator technology is defined as a physical phenomenon to create
motion and/or force, and a principle is a realization or an application of a technology.
The following sub-chapters deal with promising actuator technologies and principles,
selected actuator technologies and principles, and other actuator technologies and
principles. The first sub-chapter introduces technologies possible to be used for active
vibration control applications. The next sub-chapter deals with the two actuator
technologies we have chosen to investigate more. And the third treats actuator
technologies that are not yet ready to be used in ANVC-applications. We give some
information about different actuator technologies, such as benefits, drawbacks and
commercial products. For more detailed information refer to Appendix A.
2.1 Promising Actuator Technologies and Principles
The intention of this sub-chapter is to discuss some actuator technologies and principles
that are promising for use in active vibration control. We are told by researchers that
some technologies face a very good future and that we have still not seen their actual
potential. Several technologies have a good possibility to succeed as actuators for active
vibration control. These include electrorheological, electrostatic, electrostrictive,
hydraulic, magnetorheological, magnetostrictive, and pneumatic.
2.1.1 Electrorheological and Magnetorheological
In 1947 Willis M. Winslow discovered that the flow resistance of certain fluids increases
with field strength when exposed to alternating current electric fields in the order of 4
kV/mm [17]. The response of the electric field of these fluids is very quick, in the region
of milliseconds. When an electrorheological fluid is exposed to an electric field it
changes the viscosity of the fluid or its flow rate (rheology). Electrorheological fluids
consist of non-conducting fluid and micro-sized polarized particles.
This technology is very sensitive to ambient temperatures, separation between fluid and
particles, and wear due to abrasion from particles in the fluid. In the worst case every
one of them can lead to device failures. The electrorheological fluids that exist today can
operate at higher temperatures than their predecessors. These fluids are improving as
new objectives are being set by the customer. This technology has a great potential
according to some laboratory tests, but still there are some problems with quality of the
available fluids and their long-term stability. It is still difficult to reproduce the
manufacturing process for electrorheological fluids, because the stability of the electrical
and rheological properties of the fluids may change over time. They also have high
power consumption and are sensitive to moisture. There are not many commercial
products and devices based on this technology despite the fact that it has been known for
over 50 years. Electrorheological devices are primarily used in macro scale applications.
According to Ushijima, Takano and Kojima [25], a semi-active engine mount based on
utilization of the electrorheological fluid has been tested. An electrorheological actuator
can be built very simply, because only fluid and electrodes are necessary to create
actuation. High bandwidth can be achieved according to Lind, Kallio and Koivo [28].
Magnetorheological fluids operate very much like electrorheological fluids, but their
flow rate is instead controlled by the strength of a magnetic field. Magnetorheological
dampers are available, commercially, from Lord Corporation based on hydrocarbon,
silicone or water fluids.
In both [20] and [26], the electrorheological actuator is tested to improve a passive
hydraulic engine mount. In [20] was an active engine mount prototype working with
electrorheological fluid or ferrofluid (magnetorheological fluid) tested. Both fluids have
shown to be controllable, but there were some problems with resonance in the inertia
track due to high viscosity. Therefore, Gennesseaux tried to minimize the amount of
particles in the fluid, but this resulted in drastic changes in control. In [26] was an
adaptive control system tested, with the result that stiffness and damping could be
controlled, but the vibration amplitude affected the characteristics of a controllable
2.1.2 Electrostatic
An electric field and a force emerge between positive and negative charged particles.
The property that electrostatic fields arise and disappear rapidly is utilized for very fast
operational speed. Through special structures it uses the electrostatic force to create
Electrostatic actuators are not affected by ambient temperatures and are often used in
active vibration control. These devices have extremely low current consumption,
because of high efficient actuation. They can generate great forces, but the forces are
generally limited to very short distances. To preserve a given force for a longer distance,
higher voltage is required. A dust particle can, at worst, cause breakdown due to a small
air gap. Short stroke is another limitation of linear electrostatic actuators.
Electrostatic devices are widely used in small regions. One simple commercial
electrostatic actuator which is used commonly in micro-electromechanical systems
(MEMS) is the parallel plate capacitor [32]. The lower plate is fixed, while the upper
plate can move. Most electrostatic actuators are still at the research stage.
2.1.3 Electrostrictive
Electrostriction refers to the process in which a material is deformed when it is exposed
to an electric field. Commercially available actuators exist, which are based on
electrostrictive crystals. They use a stack design in which displacement is a
superposition of the strain from several thin crystal layers. Electrostrictive crystals are
not polarized like piezoelectric ceramics. The displacement direction depends on the
voltage applied: positive or negative. Electrostrictive ceramics produce a strain, which is
in the same order as the strain from piezoelectric ceramics. Electrostrictive ceramics and
piezoelectric ceramics have different advantages. The electrostrictive ceramics provide
better characteristics of hysteresis and creep (slow deformation), but their strain
sensitivity to temperature is much higher than for piezoelectric ceramics. Most
commercial electrostrictive actuators exist in the micro region. They use materials that
are based upon solid solutions of PMN (lead magnesium niobate) and PT (lead titanate).
Swanson [22] has investigated whether electrostrictive actuators can be used in passive
hydraulic engine mounts, but they can still be too costly and produce too small
displacement outputs for many engine mount applications. It is proved that these devices
can be built with high stiffness, high forces and high frequencies (several kHz). They can
also be built extremely compact.
2.1.4 Hybrid
Sometimes it is possible to merge two or more technologies together to utilize the
advantages of each. Hybrids are used to produce compact devices. Piezoelectric is a
common technology in hybrids because a piezoelectric actuator produces very large
forces with small displacement. Together with some other technology, such as hydraulic,
it is possible to convert force to displacement through special structures. Smart materials
such as electrostrictive, magnetostrictive and piezoelectric have proven their usefulness
in precision applications, but they are normally not considered for use in actuators that
require large linear displacements. Anderson, Linder and Regelbrugge [38] present a
hybrid actuator that combines smart materials, specifically piezoelectrics, with a closed
hydraulic system. This actuator produces large displacements, without affecting the high
force capacity. The net power output is high. The hydraulic system acts as a transmission
to convert smart material output to useful mechanical work. "Solid-fluid hybrid"
actuation is a common name in articles concerning smart material-hydraulic actuation.
According to Hallinan, Kashani and Bartsch [16], it is possible to create an
electrostatically-driven phase change actuator for vibration control, which is capable of
generating forces over 300 N with displacements of a few millimeters and extremely
rapid response time for pressure (force). This micro-actuator consists of two electrodes
with a porous ceramic between them, and a vapor cavity and diaphragm above.
2.1.5 Hydraulic and Pneumatic
Hydraulic and pneumatic devices can establish a counterforce without any energy
consumption, and they have damping capabilities. Pneumatic actuators are quite similar
to hydraulic actuators, but the big difference is that hydraulic use a fluid and pneumatic
use gas or air. These actuators are both often simple devices with few mechanical parts.
Fully-active and semi-active hydraulic actuators exist, they are light in weight in relation
to the power they can admit and emit, and they have fast reaction time. Fully-active
actuators have been used in commercial products for damping. One application where
they have been used is to damp vibrations in helicopters. Valves or pumps control the
pressure in hydraulic actuators. In a valve-controlled actuator, there is a servo-valve that
controls the flow while the pump works at constant power. In a pump-controlled actuator
the flow is changed with the power of the pump. Valve-controlled actuators are quicker,
but pump-controlled actuators are more efficient.
This technology is often used in large sizes with high output forces. A benefit is that they
can, in special situations, have zero friction and nearly backlash- (recoil-) free power
transmission [28]. There are small piston and rod systems with special seals and
coatings. For instance, Teflon is widely used. A hydraulic actuator consists of piston, rod
systems, metallic bellows and rubber components.
Bormann, Ulbrich, and Abicht [15] have developed a fist-sized hydraulic actuator that
can apply forces of several kN with displacements up to ±1 mm and with a frequency
range of up to 100 Hz. The objective was to give flexibility to the system together with
high radial stiffness; this is accomplished through two annular membranes that are
connected to the lower and upper body. Servo-valves control the oil pressures in the two
Swanson [22] has investigated the suitability of servo-valve hydraulic actuators for
active extension to passive hydraulic engine mounts. These devices can produce
extremely high forces, but they are costly and have limited bandwidth. They also require
high maintenance and a hydraulic power supply. According to Gennesseaux [20], active
hydraulic systems were in engine mounts discarded, because of their cost and the need
for high pressure.
According to Stein [18], an active control system with a pneumatic spring actuator has
been developed to improve vibration in heavy vehicle seats, including agricultural
tractors and off-road vehicles.
2.1.6 Magnetostrictive
The magnetostrictive effect comes from a ferromagnetic crystal that changes its shape
when subjected to a magnetic field. Magnetostrictive actuators output large forces and
have quick dynamic responses, but they have small displacements: typically less than 1
percent of total length. This is the main disadvantage of magnetostrictive actuators.
Devices can harness these high forces to create moving mechanisms. They require high
magnetic biases for operation, but can operate at low voltages. Magnetostrictive
materials are generally very brittle, difficult to manufacture and develop heat during
operation, which must be dissipated to prevent damage to the actuator. High ambient
temperatures generally decrease the performance, for some, over 400 ºC.
Magnetostrictive materials transform electrical energy to mechanical motion very
rapidly via an induced magnetic field from the coil. Other advantages with this
technology are that these types of actuators have a long life and can be used in highfrequency and high-precision applications. These actuators are quite complicated both in
mechanical and electrical construction. To control the magnetic field, a magnetic coil is
required. Bigger magnetostrictive materials appear nonlinear, for which special models
must be worked out.
Magnetostrictive materials generally are low weight with high extension, and the
characteristics do not change in time. These materials give new possibilities to
development of components with high density, rapid reaction time and extremely good
precision. These materials have been used successfully in actuators and sensors for
vibration control. They have also been used in hearing aids, operated into teeth and in
In [28] it is explained that the actuator is typically composed of a magnetostrictive rod
(for example Terfefenol-D) placed inside a coil. According to Gennesseaux [20],
magnetostrictive materials are still too costly to be used as actuators in active engine
mounts. Therefore, they are limited to be used in military or space applications.
2.2 Selected Actuator Technologies and Principles
One of the objectives was to find the most suitable actuators to be used in active
vibration control and implemented in an active engine mount. After studying different
technologies the conclusion was that electromagnetic and piezoelectric technologies
were the most interesting, because they exert great forces, have linear relation between
electrical quantity and force, wide bandwidth, quick responses, and are well investigated.
See section 4.1.1 for details on choice, i.e. comparison between different technologies
due to different characteristics. One principle of electromagnetic technology and one
principle of piezoelectric technology are investigated further in Chapter 5. Existing
commercial actuators, from different suppliers, based on different principles of
electromagnetic and piezoelectric technologies are presented with technical data in
Appendix D.
2.2.1 Electromagnetic
When electric current is flowing through a conducting material an electromagnetic field
is produced. The actuation physics is based on the magnetically induced motion caused
by the interaction between a coil and a magnet. This technology can generate attractive
and repulsive forces, which are proportional to the current in the conductor.
Electromagnetic actuators are well investigated and these devices are used in many
different applications. Typical examples of principles that use this technology are
electromagnetic motors, solenoids and voice coil actuators.
An electromagnetic actuator has very quick operating speed, scale ability, extreme
positioning accuracy that is independent of load or velocity and can operate over a wide
range of temperatures (up to approximately 180 degrees). The performance of an
electromagnetic actuator is primarily limited by the properties of the material used in
constructing it. These actuators are highly efficient in converting electrical energy into
Electromagnetic actuators also exist in the micro and nano region, but it is complicated
to build small electromagnetic coils. A voice coil is the most commonly used linear
motor, because of good characteristics such as high force and good displacement. Voice
coils are of two types: moving coil and moving magnet. They are well tested and often
cheaper than other alternatives. This technology produces the fastest actuators in electro-
mechanics according to Compter [55]. To obtain the highest available force it is
important that the current conductor and the magnetic field are perpendicular.
Fursdon, Harrison, and Stoten [40] have proposed an active engine mount with an
electromagnetic actuator using a self-tuning cancellation algorithm. The engine mount is
a combination of a conventional hydraulic engine mount and a voice coil actuator. The
actuator is turned on for frequencies over 25 Hz. It generates a force output greater than
40 N over a 25 to 200 Hz frequency range. The coil is attached to a diaphragm, which
replaces the decoupler. By controlling the motion of the diaphragm, the pressure in the
upper chamber is changed and as a result the net output force from the mount to the
chassis and engine is controlled. The active engine mount is capable of reducing road
induced engine shake and active cancellation of engine induced chassis vibration.
Swanson [22] concludes that voice coils and solenoids are interesting for use as actuators
in active engine mounts. They fulfill the requirements stated for the actuator concerning
force, stroke and power. And it is mentioned that it requires a force of 20 N to reduce
vibration at 60 Hz. Voice coils are compact, have high frequency bandwidth (up to few
kHz) and generate output forces that are both linearly proportional to current and
independent of stroke. Solenoids generate nonlinear forces to current and stroke, but they
offer higher force outputs in smaller package than voice coils.
2.2.2 Piezoelectric
In 1880, the brothers Pierre and Jacques Curie discovered the piezoelectric effect, when
certain crystalline materials (ceramics) are compressed they produce a voltage
proportional to the applied pressure. Conversely, when an electric field is applied across
the ceramics they mechanically deform. This is known as the indirect piezoelectric
effect. Piezoelectric devices are used commonly as both actuators and sensors, with
success accordingly to the indirect and direct effects.
Piezoelectric actuators have some advantages such as good resolution, high output force,
and quick response to input voltage changes. The energy consumption for keeping a load
at a fixed position is very low. The only limiting factor in the positional resolution is
power supply noise. Piezoelectric devices have two sources of loss, these are mechanical
and electrical.
Piezoelectric actuators still have some problems with small total strain and hysteresis,
and they are expensive in comparison to other technologies. Another drawback is that
drift and lifetime are not even known by suppliers. Furthermore, there is a problem to
obtain durable attachment between the piezoelectric actuator and the structure.
Cyanocrylates (super glue) and two-part epoxies have proven useful in many
applications. Manufactures have different solutions to specific bonding requirements,
such as extreme ambient temperatures, unusual shear stress requirements or the type of
metal surface that are to be joined together.
The principles that can be of interest are amplified piezoelectric actuators and
multilayered stacks as they have bigger strain than the other principles. In [19]
piezoelectric materials are discussed and the prospect of them to be used for impact
applications in future automobiles.
According to Gennesseaux [20] a piezoelectric can hardly be used as an actuator in an
active engine mount for low frequencies and large amplitude vibrations, because of very
limited stroke.
Ushijima and Kumakawa [23] have proposed and tested an active engine mount with
piezoelectric ceramic actuators. The piezoelectric actuators have some disadvantages,
such as very small displacement and large temperature dependency, but they have
significant advantages too, such as large output forces and high speed of response. To
provide enough displacement required for the active mount the actuators are built with
alternating ceramic layers and electrodes along with a hydraulic multiplication
mechanism. The engine mount is limited to idling vibration control, but the high speed
of response gives it a significant potential even in higher frequency regions of booming
noise and road noise. In [24] an active engine mount is introduced, for large amplitude
idling vibrations working with piezoelectric actuator. It is quite similar to the one
discussed in [23]. The engine mount is able to absorb large amplitude vibration, such as
the idling vibration of a two-cylinder engine.
2.3 Other Actuator Technologies
This sub-chapter deals with remaining technologies that so far are used for other
purposes than active vibration control. Diamagnetism and electrohydrodynamic are
referred to only in the Appendix A.
2.3.1 Electrochemical
Electrochemical technology transforms electrical energy into mechanical energy and is
based on using the electrolysis field to build up a gas pressure of an aqueous solution.
Electrochemical actuators use forces that originate from an electrochemical cell, which
consists of two metal electrodes immersed into an electrolyte with electrode reactions
occurring at the electrode-solution surfaces.
Electrochemical actuators are used in the micro region. Electrochemical actuators have
the big benefit of a liquid to gas phase transformation, which gives the huge change in
volume and/or pressure that can be obtained. They have been investigated to be used for
regulating the pressure in the eye [36].
According to Cameron and Freund [27], an electrochemical phase transformation
actuator with great theoretically efficiency, strain and stress has been developed. It is
based on the electrolysis of water to oxygen and hydrogen. The intention is to find new
actuation methods based on electrolysis of liquids and gases. This method enables the
making of smaller, more efficient and lighter machines from micro-region and larger.
2.3.2 Phase change
When certain phase change materials experience changes between phases such as solid,
liquid and gas, they force dimensional changes to the system. These dimensional
changes are expansion or contraction. Phase change actuators are built to utilize the
forces exerted by the materials, and they generally demonstrate full reversibility. These
devices can create a phase change effect over a wide range of speeds and pressures
through electrical, thermal or ultrasonic input; depending on which material is used.
Phase change actuators can exert great forces, but the forces are generally across very
short distances. Higher voltage is required if the actuator is to manage to maintain a
given force for longer distances. These devices are sensitive to ambient temperature, but
they give highly efficient actuation because of the extremely low current consumption.
Phase change materials are fairly new, and they attract interest within many different
2.3.3 Pyrotechnical
Explosive and pyrotechnic devices transform a small input of mechanical or electrical
energy into a higher level of mechanical or thermal energy that is applied to perform
practical work on a one-time basis. Therefore, they are not used for vibration control.
These devices store chemical energy until it is released by mechanical or electrical input.
The original gas generators used in airbags consist of a pyrotechnical charge only, while
the new generation of gas generators by Autoliv is a hybrid of a canister of compressed
argon gas and a pyrotechnical charge.
2.3.4 Shape Memory
In 1932, the Swedish physicist Arne Olander discovered that an alloy of gold and
cadmium could be plastically deformed when cooled and then be heated to return to the
original dimensional configuration. Shape memory actuators are constructed to use these
property changes in the material when the temperature reaches certain transition levels.
This is known as the shape memory effect. This transformation involves changes in
strength of the material, deformability and Young's Modulus, as well as the ability of the
material to return to a previously conditioned physical shape. Shape memory belongs to
a group of materials that are called smart materials, to be able to use shape memory as a
phase change actuator through heating, the material must first be educated.
There are shape memory alloys and shape memory polymers, but the only ones of
interest to us are shape memory alloys. Polymers require a built-in squeezing mechanism
to be used for purposes other than on one-time basis. Shape memory alloys have some
benefits such as considerable temperature-dependent expansion/contraction, relatively
linear control, very high stress (often over 200 MPa), arbitrary shapes and simple
actuation, and have achieved a million cycles in laboratory tests, but life time is still
fairly uncertain. Disadvantages are that special alloy materials are needed: high
temperature annealing, low efficiency (energy conversion efficiency is approximately 3
%) and long-term thermal constants.
Shape memory alloys have strain of 5-8 % depending on the number of cycles [28]. The
main disadvantage with shape memory alloys is the slow speed of response. If they
could be made smaller they would be faster, since heating and cooling is faster with
small devices. Actuators based on this technology can only be used in low frequency and
low precision applications. They are not yet suitable for active vibration control [30].
Shape memory alloys have been tested to improve passive-hydraulic engine mounts,
through SMA-wires inside rubber bellows [37]. Changes in current will affect the SMA
that changes its temperature and phase. The upper chamber compliance can be changed
by 50 percent, and it is shown that this is an effective parameter for use in an adaptive
mount, where it is sufficient with a simple on/off control. The dynamic stiffness is
reduced by 30 percent for low frequencies and 40 percent for high frequencies.
2.3.5 Thermomechanical
Thermomechanical devices are built to utilize the physical dimensional changes
(expansion or contraction) as they undergo temperature changes without changing their
phase. Thermal changes are the result of the conduction of heat energy into a material.
These changes may occur over a wide range of speeds.
Since the material need is sensitive to changes in ambient temperature, insulation may be
required. To improve the reverse transformation, the actuator would require some
passive or active cooling system. There are different methods to induce temperature
changes into the system: resistive heating at low voltages, thermally, radioactively, or
The thermomechanical actuator can be more useful in the micro region. The heat
dissipation is directly related to the volume to be cooled. Therefore, thermal cycling
occurs faster in micro devices than in macro devices. A common micro actuator using
the thermomechanical principle is a bimetallic cantilever.
Chapter 3
The intention with this chapter is to briefly discuss suitable sensors for measuring
vibrations. According to both [5] and [30], the piezoelectric accelerometer is the most
widely used sensor for vibrational measuring, that is the reason why our focus is within
piezoelectric accelerometers. Another popular sensor is the piezoelectric force sensor,
but neither piezoelectric acceleration nor piezoelectric force sensor can measure D.C.
components, or very low frequency vibrations. According to Colla [30], nonpiezoelectric devices are generally based on inductive, capacitive or optical technologies.
In Appendix B, other types such as optical sensors are presented. According to Sensor
technology information exchange (Sentix) [56], the definition of a sensor is:
"A device or system that responds to a physical or chemical quality to produce an output
that is a measure of that quality".
The active vibration control system consists of three parts, actuators, control units and
sensors. The most relevant quantities to be measured are position, velocity, acceleration,
strain and force, see [30]. There exist a number of different commercial sensors with
varying price and performance. In general, sensors used in active vibration control
systems exist in three forms, they are point acting sensors, arrays of point sensors or
continuously distributed sensors. Distributed sensors measure over an area and the
motion are integrated over the segment in the structure.
According to Lindahl and Sandqvist [5], sensor can be seen as three main parts, a
sensing element, a transducer and a device for internal signal processing, see figure 3.1.
The sensing element is directly affected by the input quantity and its task is to transform
the physical input to a dimension, which is possible to be transformed into an electrical
signal by the transducer. It is the sensing element that determines the nature, selectivity
and sensitivity of the sensor. The internal signal processing consists of electrical
equipment, which transforms the electrical signal to a useful output signal. (For example,
the sensing element can be a diaphragm, which is deformed in proportion to the
surrounding pressure. The transducer can be a tensiometer that converts the deformation
to a change in resistance and the internal signal processing can be an amplifier.)
Figure 3.1 Block diagram of a sensor
The choice of sensors is dependent on the application for which they are going to be
used. The selection of sensors is influenced by the price, performance, and the
requirement for the systems, such as need of precision, reliability, etc. In Chapter 4, the
relationship between actuators and sensors is discussed, and their affect on the closed
loop etc. Bandwidth, sensitivity, and price are three important properties of a sensor.
3.1 Piezoelectric sensors
Piezoelectric sensors are widely used as force and accelerometer sensors. When a
piezoelectric material is subject to a force it deforms elastically and generates electrical
charges, this is the direct piezoelectric effect. The change in charge that is detected on
the surface of the material originates from rotation of the crystals [13]. To detect the
change in charge two conductive coatings are applied to the material. It exhibits good
linearity and when the force changes direction the charge changes polarity. There exist
several different designs of piezoelectric sensors based on utilization of the different
piezoelectric effects, which are forces that affect the material to produce a parallel
electrical field (length effect) or perpendicular electrical field (side effect), and shear
forces of the plates producing a perpendicular electrical field (shear effect) [49], see
figure 3.2.
Figure 3.2 Three different effects on piezoelectric materials
Force and pressure sensors are in general utilizing the length effect and side effect,
respectively. In Appendix B different designs of piezoelectric accelerometer is
Piezoelectric sensor materials originate from two broad classes, ceramics and polymers
which both have been used for active vibration control. Quartz, lead zirconate titanate
(PZT) and crystalline are examples of piezoelectric ceramics that have been used widely.
Piezoelectric ceramics are used extensively for a wide range of frequencies both as
actuators and sensors. The piezoelectric polymers are used mostly as sensors, because
they require high voltages and they have a limited control authority (amount of force,
moment, strain or displacement, etc.). The best-known piezoelectric polymer is the
polyvinylidene fluoride (PVF2 or PVDF) [13]. Research is going on with porous
Magnetostrictive and electrostrictive are two materials that remind of piezoelectric
materials. These materials and other smart materials can often be used instead of
piezoelectric materials in many sensor applications. Piezoelectric is still a step ahead in
research and there exist many commercial products based on piezoelectric materials.
Piezoelectric sensors are being used in the automotive industry as knock sensors, for
distance measurements, acceleration sensors in airbags, flow sensors and liquid level
measurements [49].
3.1.1 Piezoelectric accelerometers
There exist several designs of piezoelectric accelerometers, as mentioned earlier there
exist designs that harness the different piezoelectric effects, see Appendix B. Some
advantages with piezoelectric accelerometers compared to other sensor types. Are that
they have no moving parts, are robust, easy to fit, low cost and they have a wide
frequency response [48]. There are other advantages that often are mentioned such as
high temperature range, high sensitivity, long service life and small spring travel. A
disadvantage is that they do not have static measurement.
The piezoelectric material can be suspended between a rigid post and a seismic mass. A
force on the piezoelectric element is generated when the accelerometer is subjected to
vibration. The size of this force is according to Newton's second law the product of
acceleration and the constant seismic mass. A charge output proportional to the applied
force is generated due to piezoelectric effect. The sensing element in an accelerometer
often consists of a quartz wafer that serves both as sensor and spring. The quartz wafer is
used in both compression and shear devices [33]. It produces a charge proportional to the
strain. To measure the charge are voltmeters with high input impedance used. A charge
amplifier converts the charge to an output voltage, which can then be measured with
standard instrumentation. The charge is actually not amplified, it is collected in a
capacitor with well-known capacitance and high insulated impedance. The charge
amplifier consists often of an OP amplifier together with the capacitor [5]. An enclosed
integrated circuit piezoelectric (ICP) is the same as a charge amplifier, which is built into
the sensor housing and powered by a constant current [31]. Thus, the piezoelectric
sensor output can be either charge or low voltage signal. A benefit with ICP is that it can
easy be transferred over long distances without need of special cables.
Accelerometers can be attached to the structure in many ways; some of them are by
screwing, by a magnet, silicon, cement, epoxy, or by stud mounting [31, 48]. The choice
of mounting technique affects the attachment between the accelerometer and the
structure with different strength. It is important to find the best suitable attachment
solution for the specific case to minimize influence in the frequency response.
Chapter 4
The purpose of this chapter is to briefly discuss how the choice of actuators and sensors
will influence the ability to model, update, and control the system. The process of sensor
and actuator selection is as important as designing the controller. The process is usually
ad hoc, because there is no cohesive approach to designing and selecting actuators and
sensors [10, 43].
According to Uhlbrich, Wang and Bormann [29], the realization of an efficient control is
distinctly influenced by the choice of actuators and sensors, their positioning within the
whole system, and the control concepts.
First, is a discussion about selection of an actuator and comparison of existing
technologies. This is followed by a brief discussion about how actuator and sensor
parameters are related and their influence on controllability and observability. Finally,
the placement of actuator and sensors is briefly discussed.
4.1 Actuator Selection
Historically, passive techniques, such as rubber and hydraulic mechanisms have been
used to reduce vibrations. As actuator technology and control design has matured,
different types of actuators could be used for active vibration control. To make the right
choice of actuator, knowledge is needed of the attributes and technical options for an
actuator. According to Crawley, Campbell, and Hall [10], five important parameters can
be used to describe the attributes and function of an actuator. They are:
Relative size
The actuator can be either linear or angular. It can act in different directions (along
different axis) and act at a local point or distributed over an area.
The location of the actuator is somewhat limited: it has a great influence on the behavior
of the system, because it affects the controllability and observability of the system. The
numbers of actuators to be used and where they should be placed are important factors in
design. Regarding the number of actuators, it is advantageous to have as few as possible
because the stability of the system is reduced and adaptation-time will increase. This of
course depends on the control algorithm. Furthermore, if there are more actuators than
necessary for a problem the result can be that the actuators will try to cancel out each
other, which gives a strong deteriorating damping. This is the case if the control
algorithm has not considered knowledge of interactions between actuators.
The impedance of an actuator defines whether the actuator commands force or
displacement. Actuators with low impedance command force, high impedance command
displacement and those with intermediate impedance command both force and
The relative size is defined as the size of the actuator that is needed to produce a
specified force, torque, strain or displacement. Relative size is hard to change because it
depends on the actuator physics.
The bandwidth describes the operating frequency. Usually, the bandwidth is limited by
the dynamics of the actuator or by the power amplifier or a combination of both.
4.1.1 Comparison between Actuator Technologies and Principles
This section attempts to make a simple comparison of technologies described in Chapter
2. Most of them have been tested in laboratories, but not all have been applied in
commercial products. For use in linear motion control, there are a number of actuator
alternatives. This section gives guidelines to find a proper actuator for a specific
application with certain requirements, such as amplitude, bandwidth, force, response
time, and size.
It is difficult to make a comparison of all actuator technologies, because the performance
of different systems varies greatly, and they can be either voltage or current driven. A
direct comparison of the transfer function between input and output can only be carried
out with all actuators if the mechanical output is referred to the input electrical power.
Apart from that, the development of actuators based on different technologies has
reached different stages. A comparison could be made where the actual limit for the
technology is dependent on some physical restriction, such as size, weight.
Electromagnetic, hydraulic, piezoelectric and pneumatic actuators have been compared
through relations between force/displacement and force/response time, see [6] and [42].
Electromagnetic actuators can create high forces, large displacements and fast responses,
and with large bandwidth. Piezoelectric actuators can create high forces at very short
response time, but the displacements are very small. Electrostrictive ceramics have the
same order of strain, force and response time as piezoelectric ceramics. Hydraulic and
pneumatic actuators can exert very high forces and at the same time large displacements,
but they are often slower than other solutions, and the bandwidth is often small. Figure
4.1 shows two perspicuous graphs for comparison of well-known actuator technologies.
Most existing principles of the electromagnetic, electrostrictive, hydraulic, pneumatic
and piezoelectric technologies suitable for active engine mounts applications are within
the respective areas in Figure 4.1.
Figure 4.1 Comparison between some actuators concerning force/displacement and
force/response time (Earlier presented in [6] and [42])
Even though the main disadvantage with magnetostrictive actuators is their small
displacement, the strain in some solutions has been about two times larger than the strain
of a stacked piezoelectric actuator. Magnetostrictive can create high forces at very short
response time similar to electrostrictive and piezoelectric actuators. However, the
amount of force can often be converted into displacement through utilization and
modification of hydraulic or mechanic mechanisms. Similar to piezoelectric materials,
electrostrictive and magnetostrictive materials are used in high precision applications.
They consist of ferromagnetic materials, which experience an elastic strain when
exposed to an electric or magnetic field, respectively. Magnetostrictive materials can
undergo lower input voltages then most piezoelectric and electrostrictive materials. In
addition, magnetostrictive materials have advantages against piezoelectric, for example
low weight, no change in characteristics related to age and they can operate at higher
temperatures than piezoelectric and electrostrictive actuators. A disadvantage with
magnetostrictive materials is that they are not easily embedded in control structures.
Magnetostrictive materials are similar to shape memory alloys but the difference is that
they react on a magnetic field instead of changes in temperature. A big advantage with
magnetostrictive materials is that they are much faster in transforming electrical energy
to mechanical motion in comparison to traditional memory metals (shape memory
Uhlbrich, Wang and Bormann [29] have compared electromagnetic, hydraulic and
piezoelectric technologies. Depending on the desired characteristics, they have created a
measurement of how well the three different technologies handle each characteristic. For
example, both electromagnetic and piezoelectric actuators have higher regulating
frequencies and simpler transfer characteristics than the hydraulic ones. Their transfer
characteristic depends on fluid dynamics. On the other hand, hydraulic actuators can be
made compact. Hydraulic actuators are hard to beat in applications where strong forces
are needed. Furthermore, these actuators can establish counterforce without any energy
consumption in contrast, for example, to electromagnetic actuators. In Table 4.1,
electromagnetic, hydraulic and piezoelectric actuator technologies are compared for each
characteristic. This table is carried out through studying [29].
Table 4.1
Three widely used actuator technologies with a simple comparison of
each characteristic
↓ Characteristic Technology →
Realizable force/weight (Active
element without periphery)
Realizable force/size
Realizable force/total weight
Possibility of stimulation of
vibrations due to non-linearities
Very wide
Very high
Very large
Very wide
Very small
Very high
Electromagnetic and piezoelectric actuators are highly efficient, generally over 90 and
95 percent, respectively. Piezoelectric is especially well suited when dealing with small
amplitude vibrations or in high precision constructions within µm-range. Very low
material damping and small realizable regulating distances are two crucial disadvantages
of piezoelectric devices. The third technology, hydraulic, can typically have high radial
stiffness. It can apply regulating movements without friction and ensure high safety
against tilting effects. In general, servo-valve is used to control the pressure in a twochamber device. Unfortunately, the regulating pressure depends greatly on all fluid
mechanical losses of the hydraulics and the dynamic of the servo valve. The maximum
material stress in the membranes gives the design limits.
According to Brennan, Garcia-Bonito, Elliot, David and Pinnington [46], the principles
of the magnetostrictive, piezoelectric and electromagnetic actuator technologies have
been experimentally tested for active vibration control. Before the choice of an actuator
can be made, it is explained that the requirements of the actuator must be specified in
terms of force, displacement, bandwidth and power. They compare actuator principles
through study of the input-output transfer functions for current and voltage driven
principles, respectively. Another common method of comparing different actuator
technologies is to compare the energy density per unit weight or volume. The energy of
density for electromagnetic has been calculated to be 4 J/cm3 to compare with 0.1, 0.2,
5-10 and 5 J/cm3 for electrostatic, piezoelectric, SMA and thermomechanical, see
Appendix C. This method is often used to compare miniaturized principles. The force is
dependent on how strong the magnetic field is in magnetic-based technologies, because
the possible magnetic field is dependent on the specific volume or weight.
In electromagnetic, electrostatic and piezoelectric actuators the generated forces are
directly in proportion to the voltage level. The main advantages of these technologies are
their rapid actuation potential and low power consumption. Piezoelectric micro actuators
have been capable of cycle rates in thousands of cycles per second range. Electrostatic
actuators can often operate as fast as the electromagnetic actuators. Both of them are
usually only limited by their mechanical design and their driving electronics.
Electrostatic actuators usually require high operating voltages.
Shape memory alloys can be considered when a large strain is preferred, because
compared to piezoelectric they have a larger strain. The main problem with shape
memory alloys is the slow response, so fast response can not be a requirement when
choosing this type of actuator. Neither can thermally driven actuators be used, because
they generally exhibit slower cycle rates than other methods. Actuators that are based on
the technologies phase change, thermomechanical and shape memory alloy require heat
as a primary driving mechanism. These thermally driven actuators lose heat to the
environment and are, typically, low in efficiency.
After we have studied and compared different actuator technologies to be used in an
active engine mount our conclusion was that electromagnetic and piezoelectric
technologies were the most promising alternatives. These two technologies are already
introduced as the selected technologies in sub-chapter 2.2. For a specific application of
active vibration isolation one of them is usually better than the other. Piezoelectric
actuators are preferred when low power consumption is desired. For example,
piezoelectric actuators can be designed to replace almost any solenoid to use less power,
but the result is always bulkier and often heavier.
4.2 Relationship between Actuators and Sensors
The relationship between actuator and sensor parameters, together with the interaction
with the closed loop system, determines their effectiveness for control and force changes
in actuator and sensor design. The choice of actuators and sensors influence each other
and the controllability and observability of the system.
An actuator and sensor pair can influence the characteristics of the transfer function and
the ability to control vibrations. For some less successful choices there can be pole-zero
cancellation of system modes in the transfer function from the input to output, which
gives uncontrollable and unobservable results.
If an actuator and a sensor are the same type, the pair is called dual. If an actuator acts
and a sensor measures at the same point they are said to be collocated. If a pair is both
dual and collocated they will create a transfer function with residues of the same sign,
this creates alternating pole-zero pattern [10]. There are actuator and sensor pairs that are
not dual, but still have alternating pole-zero pattern. These are called pseudo-dual pairs.
Alternating pole-zero pattern is discussed further is sub-chapter 4.3.
Both the actuator and sensor impedances can have large effects on the structural transfer
function characteristics. Actuator and sensor impedances can be low, intermediate, or
high. Sometimes the best transfer function characteristics are obtained when the
impedances between actuators and sensors are matched, because good pole-zero spacing
is obtained. When the impedances are different pole-zero cancellation can occur, leaving
the system in an unobservable and/or uncontrollable state. Therefore, it can be
worthwhile to examine the choices of actuator and sensor impedances. Usually, the
actuator impedance is set to match an application and the next choice is the impedance
of the sensor. The best choice is to match the selected actuator impedance in order to
obtain the largest pole-zero spacing.
To form an opinion of which size of actuator is necessary can generally not be done
before reaching halfway in the design process. Usually, a number of studies are
performed after the structure has been designed. In simplistic cases the relative size can
be analysed after the dominated mode: this rule of thumb is derived from an example of
one degree-of-freedom [10]. Before deciding the relative size of the actuator,
consideration must be given to how much noise that can be present in a sensor in order
to close the loop, see [10].
Actuator and sensor bandwidth depends on the dynamics of the device, or roll-off within
the controller. A normal method is to select the frequency to, at least, mode-controlled.
4.3 Estimate the Effectiveness for Control
With the great number of available options of sensor and actuator designs, the most
obvious question is whether it is possible to estimate the best choices for attaining the
closed loop objectives. This will be discussed briefly in this sub-chapter.
The choice of a proper actuator and sensor is based upon achieving the best performance
and stability robustness in the closed loop control design. To verify if the chosen array of
actuators and sensors for the control design is capable, there exist different methods to
form an opinion of the capability of the system. Open loop controllability and
observability and the closed loop stability are two methods respectively discussed in the
sections 4.3.1 and 4.3.2.
4.3.1 Open Loop Controllability and Observability
The effectiveness of an actuator and a sensor regarding the controllability and
observability of the system is investigated, together with a static test. This method is
creates an idea of how observable and controllable the actuator and sensor pair are in
achieving a good control of the closed loop system. The classical test for observability
and controllability is to examine the rank of the observability and controllability
matrices, but these tests do not give relative information on the observability and
controllability of different pair of actuator and sensor. There also exists a test that is
based on the size of the modal residue, but it is out of scope of this thesis.
According to Crawley, Campbell, and Hall [10], the best approach to test the static
effectiveness of an actuator or sensor is by using the observability and controllability
gramians. By combining the gramians, the Hankel Singular Values for each mode can be
found and the effectiveness of actuator and sensor pair can be analyzed. According to
Campbell [60], the gramians are really a measure of the observability and controllability
of the dynamic modes. They do not really take into account the static portion. One way
to compare different actuator pairs would be, given a set of sensors, to calculate a
different set of gramians for each actuator, and then find the Hankel singular values
(HSV). The overall level of these HSV's will give some measure of static effectiveness.
Another approach is to do the same thing, but to calculate the DC value (i.e. when xdot =
0 in a regular state-space model), which is another measure of the static effectiveness.
For an internally balanced system the observability gramian Ox and controllability
gramian Sx are equal and diagonal, according to Glad and Ljung [3].
S x = Ox =
= diag {σ 1 , σ 2 ,..., σ n }
where σi are called the Hankel Singular Values. Large Hankel Values correspond to
highly controllable and observable states, while small Hankel Singular Values
correspond to almost uncontrollable and unobservable states [10]. Observability and
controllability gramians are often used to simplify system models derived from
physically built models. This makes it easier to do an analysis, and control design and
realization. Non-observable and controllable modes can be removed without affecting
the input-output signal relationship [3].
4.3.2 Closed Loop Stability
The stability of the controller is largely affected by choice of actuator and sensor such as
type and location. To ensure good closed loop stability there must be stability robustness
of the loop to modal parameter errors and variations, along with the ability to measure
and control the system modes. To get the most effective transfer function the following
four characteristics should be fulfilled [10]:
(Nearly) alternating poles and zeros.
No non-minimum phase zeros in the bandwidth.
Good pole-zero spacing.
Good roll-off.
Alternating pole-zero pairs gives good robustness in the closed loop [10]. According to
Campbell [60], the main issue with alternating poles and zeros are that they give a
bounded phase system, which is a lot easier for the controller to cope with. When a zero
pair is missing it is still possible to control in that region, but there will be a gain drop
and loss of performance somewhere. It is similar to the non-minimum phase zero, but in
this case it is impossible to control in this region. In the frequency region where control
is desired, it is preferred to have alternating poles and zeros, and perhaps a missing zero
pair near the end of one of these regions, so that the gain drop and loss of performance
falls in a less important region, such as after roll-off.
We do not want non-minimum phase zeros in the bandwidth, because for systems with
zeros in the right half plane the phase curve will have a larger negative phase shift than
for a minimum phase system with the same amplitude curve [3].
Good pole-zero spacing is similar to having modes that are highly controllable and
observable [10]. This allows the controller to be more easily designed.
For high frequencies it is important to have high roll-off if the model is not good, thanks
to the requirement for sensitivity function and the complementary sensitivity function.
4.4 Placement
There is no easy way of dealing with this problem, and object in this sub-chapter is to
just present the problem and give a brief discussion. In consideration placement of
actuators and sensors there are alternatives such as direction, location and number of
units. Placement of an actuator or sensor influences only the direction and location.
It was briefly discussed in sub-chapter 4.2, however, an actuator and sensor collocated
pair usually creates an alternating pole-zero pattern that is quite beneficial to closed loop
control. The placement of actuators and sensors influences the controllability,
observability and the closed loop performance. There have been many studies on
optimization of placement and how it influenced the control design, see [10, 43, 44].
Chapter 5
Piezoelectric and electromagnetic actuators are two popular choices for AVNC and are
promising technologies for use in active engine mounts. In this chapter we will discuss
them and their characteristics. To predict the performance of the actuators and to
investigate design parameters, models are crated using Matlab/Simulink. A good model
of the actuator is also advantageous when designing its control algorithm.
5.1 Electromagnetic Actuators
In this section the principle of a voice coil actuator is discussed and how different
parameters affect its behaviour. To enable that discussion, a model of a voice coil is
developed. It will be shown that the derived model, with minor modifications, represents
a wide range of electromagnetic actuators. Guidelines are given at the end of the chapter
on how to design an electromagnetic actuator for specific needs.
5.1.1 Model of a Typical Voice Coil
The voice coil consists of two basic parts: a magnet and a coil. The magnet creates a
magnetic flux that passes through the coil. When current passes through the coil a force
will be generated that is proportional to the current, the length of the wire in the flux
field and the magnetic flux passing through the coil. The arrangement of a typical voice
coil is shown in Figure 5.1.
Figure 5.1 Typical voice coil actuator
The intense magnetic field that is required by the voice coil is created by a permanent
magnet or an electromagnet, as shown in Figure 5.1. Soft iron is used to transmit the
magnetic flux to the air gap between the face of the north-polarized inner pole piece,
which is round, and the hole in the south-polarized outer pole piece where the armature
coil is placed. This creates a radial flux field in the air gap between the outer and inner
pole piece. The air gap between the pole pieces is minimized to reduce the reluctance of
the magnetic circuit and thus maximizing the intensity of the fixed magnetic field.
The force that is exerted on the coil is given by:
F X = 2πRN ( µ 0 H 0 i +
µ 0 Ni 2
Fx: axial force
R: radius
N: number of turns
µ0: permeability of free space
H0: magnetic field intensity
i: current
g: gap between the outer and inner pole pieces
The first term in equation 5.1 is due to the interaction between the coil (current) and the
magnetic field, H0. The last term is due to the interaction between the wires in the coil
itself. H0 is usually made much larger than Ni2/2g to achieve linear operation by reducing
the importance of the last term. Thus, FX becomes simply 2πRNµ0H0i. The force that is
exerted on the coil is then simply proportional to the current, i.e. F = k1·i.
In Figure 5.2 the mechanical components of the shaker are shown and in Figure 5.3 the
electrical components. The two are cross-coupled because the back electromotive force
eback in Figure 5.3 depends on the movements of the coil according to equation 5.5. In the
model the shaker is divided in four different masses: body (MB), coil (MC), table (MT)
and Load (ML). The connections between them are modelled with a spring and a damper
Figure 5.2 Mechanical diagram of a voice coil
diagram of a voice coil
Figure 5.3 Electrical circuit
KB and CB are stiffness and damping of the voice coil mounts. The values for KC and CC
depend on coil design. In early designs, the coil was wound around a stiff thin walled
tube. Modern armatures use epoxy bonding techniques to fasten a rigid epoxy-stabilized
coil to a light magnesium table structure [12]. The load table is assumed rigid and is held
in place by the support structure, which has stiffness, KS and damping CS. The armature
is only allowed to move axially and it needs to be restrained from all other motions. To
accomplish this and accurately centre the armature in the gap the support structure must
be soft in the axial direction.
Applying Newton's Second Law of motion, three equations of motion will be derived,
one for each mass. The first equation is for the coil, the second for the table and the load,
and the last one is for the body.
M C xC + C C x& C − C C x&T + K C x C − k C xT − k1i = 0
(MT + ML )&x&T − CC x&C + (CC + CS )x&T − CS x&B − KS xC + (KS + KC )xT − KS xB = 0
M B &x&C − C S x& T + (C B + C S ) x& B − K S xT + ( K B + K S ) x B + k1i = 0
The voice coil's electrical model includes the resistance and inductance of the coil. The
resistance, R, defines the minimum impedance exhibited at the voice coil input. The
resistance increases by about 40% per 100°C for copper, and slightly with frequency.
The coil inductance, L, is large because the coil is attracted strongly to the iron of the
pole pieces. This cause the complex electrical impedance to be equal to R + jωL, which
hence increase with frequency.
When the coil begins to move in response to the generated force, a voltage is induced in
the coil caused by its motion in a magnetic field. This voltage is called back
electromotive force or "back emf" and is proportional to speed, magnetic field strength
and current. It reduces the voltage across the coil, thus lowering the current and the rate
of acceleration. It is modelled as:
eback = k 2 ( x& C − x& B )
According to Kirchhoff's second law for an electric circuit, the equation for the electrical
circuit in Figure 5.3 is:
( x&C − x& B )k 2 + L ⋅
+ Ri = e
Equation 5.2 to 5.6 now yields:
− CC
0 0&x&C  CC
 0 M + M 0 0&x&  − C C + C
  + 
MB 0&x&B  0
0 0 0   k2
− k2
0 x& C   KC
− KC
− k1xC 0
0 xT  0 (5.7)
0 x& T  − KC KS + KC − KS
 +
 = 
0 x& B   0
− KS KB + KS k1 xB 0
  
   
Ldi/dt  0
R  i  e
KB and CB are the stiffness and damping of the voice coil mount and are not part of the
actuator itself, therefore can they be set to infinity. The mass MB is then directly
connected to the ground, thus xb will be zero, has no impact on the system and can
therefore be removed from the model. The equation (5.7) is then simplified to:
0&x&C   CC
0  x& C   KC
− CC
− KC
− k1 x C  0
    (5.8)
 0 M + M 0&x&  + − C C + C 0  x&  + − K K + K
0 xT  = 0
 T   C
 T   C
0 0   k2
Ldi/dt  0
R  i  e
 0
5.1.2 Parameter Identification
To enable the use of the model obtained in the previous section, to predict the behaviour
of voice coil actuators, two methods have been developed for identification of the
parameters in Table 5.1. The first is called the Heuristic method and is based on
knowledge obtained by experiment. The second is based on the least square method
which is a more automatic method.
Table 5.1
Parts of a Voice Coil with moving magnet
Parts and property for voice
coil with moving coil
Load, mass
Table, mass
Table, stiffness
Table, damping
Coil, mass
Coil, stiffness
Coil, damping
A problem that has been noted is that some manufacturers only provide the magnitude of
the frequency response and let the phase be unknown. In this case we can assume that
the system is linear and the poles and zeroes are placed in the left half plane. This makes
it possible to re-create the phase from the magnitude. This can be done with the use of
the Bode relation [3]. However when the input data is experimentally obtained we can
assume that it is not well conditioned. A better solution is then to use a data-fitting
method on a parameterized model to obtain the phase [53]. This will be the case in both
method one and method two. Method 1: The Heuristic Method
Unlike algorithms, the heuristic method does not guarantee optimal solutions and has no
theoretical guarantee. This method is based on experimental knowledge and educated
guesses. Therefore, it is suitably described by an example, as in example 1, section The results can be summarized: The damping CB and stiffness KB control gain
and frequency for the first peak. The second peak depends similarly on the values of CS
and KS. Values CC and KC respectively, affect the last peak. And k1 affects the gain for
all frequencies. Figure 5.4 shows a typical frequency response for a voice coil.
Figure 5.4 A typical frequency response for a Voice Coil
Damping CS, CC and CB can be calculated with the 3dB-method. For a single degree of
freedom system SDOF the damping ratio is:
ζ =
c 0 2mω 0
2 mk
c : damping coefficient
c0 : critical damping coefficient
ω0 : resonant frequency
m : oscillating mass
k : stiffness coefficient
The 3dB-method gives the damping ratio for a SDOF system:
ζ =
∆ω 3dB
2 ⋅ ω0
Equations (5.9) and (5.10) now give the damping coefficient:
∆ω 3dB
⋅ m⋅k
The stiffness KS, KC and KB can be calculated from data given in Figure 5.4, with the
regular method, K = m ⋅ ω n .
This method of calculating the parameters has been shown to give good results. The
drawback is that it does not guarantee an optimal solution. It could be profitable to use
the Least Square method described in section as a complement to this method. Method 2: The Least Square Method
The second method is the least square method, and can be used by itself or as a
complement to the heuristic method. It is based on the least square method and uses a
frequency response, which can be found in product information given by manufactures.
To solve the curve-fitting problem a solution based on the Matlab function lsqcurvfit is
used. This function is based on the interior-reflective Newton method described by
Coleman, T.F. and Y. Li in SIAM Journal on Optimization [45]. The function that will
be minimized is:
F ( x, freq) − mag ( freq)
∑ ( F ( x, freq ) , − mag ( freq ))
where magi is the magnitude at the frequency given by freqi. The resulting "best fit"
coefficients is here called x for the parametric model. F is the transfer function for the
system of equations (5.8).
The method is implemented in Matlab. The least square algorithm is implemented in the
m-file parest.m. It needs the user to implement the transfer function into the m-file. Then
the function inputs are start values for the parameters, frequency and amplitude data.
Outputs from the function are the estimated values for the parameters. For an example of
this method we direct the reader to example two in subsection
A problem that has been noted with this way of calculating parameters is that the least
square method can find a local minimum that gives a good magnitude correspondence
but incorrect phase. The problem is minimized if the initial values are chosen with care.
The second problem that may arise is that the masses can be estimated to be abnormal.
In that case it is better to have them fixed.
Besides the least square algorithm implemented in the m-file parest.m, an additional tool
for converting pictures to transfer functions is found in the m-file tfpic2tfvalues.m. It
takes a picture of a frequency response and converts that to magnitude and frequency
data in vector form that is used in parest.m.
5.1.3 Validity of the Model
The voice coil actuator model (5.8) can be used for both regular voice-coil actuators and
voice-coil, reaction-mass actuators (RMA) with either moving-magnet or moving-coil
design. The difference is that the parameters symbolize different parts of the actuator.
The differences can be seen in Table 5.2.
Table 5.2
Parameters for different electromagnetic actuators
Load, mass
Table, mass
Coil, mass
Coil, stiffness
Coil, damping
Magnet, mass
moving coil:
Moving magnet:
Some assumptions have been made when deriving the model. The following
phenomenon have been ignored: temperature dependency, nonlinearity because the
magnetic field that affects the coil depends on the coil displacement, the resistance in the
coil is temperature and frequency dependent, and friction losses.
The nonlinearity because of the magnetic field that affects the coil is assumed small.
When it is possible to construct the pole pieces higher than the coil, the results will be
that the coil is always in the area where the radial flux is constant. This is also discussed
in section 5.1.1.
Temperature dependency tests have been made on the SA10 actuator at CSA
Engineering. According to Eric Anderson at CSA Engineering, the conclusion is that
there is no significant change in actuator output gain for current input over the -40ºC to
+60ºC temperature range. The magnetic properties of the system did not change
significantly over the range. But CSA also recommended that a more comprehensive test
may be necessary in the future. The test done by CSA Engineering was carried out in an
ambient environment of 24ºC. They measured at four different amplifier inputs: 0.1, 0.2,
0.5 and 1.0 Vrms at 200 Hz, and found that the output was nearly linear with the drive
amplitude. The use of a current amplifier rather than a voltage amplifier means the
change in resistance over this temperature range does not influence the current applied
for a given drive input. This is because it is not affected by changes in impedance with
temperate. Assuming that the coil resistance changes with temperature in the same way
as the conductor it is approximately 0.4%/ºC [5]. Data for conductor materials are given
in Table 5.4. The high temperature extreme presents the largest voltage requirements
because of ambient temperature increases and temperature rise due to self heating. The
results of the test are presented in Table 5.3.
Table 5.3
Results of temperate measurements for the SA10 actuator.
Room T (24 C)
-40 C
+60 C
Measured response
40.5 N/A
42.17 N/A
42.12 N/A
Difference from RT
Resistance re RT and
implied voltage increase
for same current
Table 5.4
Data for conductor materials [5]
Temperature coefficient
Melting point
Tensile strength
Permitted tensile stress
per ºC
5.1.4 Examples of parameter identification
In this chapter the model of a typical voice coil has been developed. In this section two
examples of model parameter identification will be shown. The first example is a voice
coil with a moving magnet, SA–100 from Data Physics. The second example is a voice
coil reaction mass actuator, SA10 from CSA Engineering. Both the heuristic and the
more automated least square method will be exemplified. Example A: Voice Coil Reaction Mass Actuator
To identify parameters for a typical voice coil with moving coil, we contacted Henrik
Isaksson at Saven Hitech, agent for Data Physics in Sweden. He contributed with some
estimated values for the voice coil actuator S-100 [54] as follows:
MD = 10 kg
MT + MC = 1.4 kg
MB = 80 kg
KS = 22 kN/m
KC = 10 GN/m
R = 4.3 ohm
L = 0.31 mH
k1 = 44
The remaining values were calculated from Figure 5.5 which is extracted from the article
by George Fox Lang and Dave Snyderin Sound & Vibration, October 2001 [12]. The
upper curve shows gain of the transfer function from current to table acceleration and the
lower curve shows the same for voltage.
Figure 5.5 Frequency response for model of S-100 in Sound & vibration [12].
Upper curve is gain from current to table acceleration, and lower curve
is gain from voltage to table acceleration.
Damping CS, CC and CB was calculated with the 3dB-method according to (5.11).
∆ω 3dB
⋅ mk
The remaining stiffness KB was calculated from data given in the Figure 5.5 with the
regular method, K = mω n . The values were calculated to be:
CS = 340 Ns/m
CC = 273 000 Ns/m
CB = 167 Ns/m
KB = 19 739 Ns/m
In Figure 5.6, the frequency response can be seen for transfer function 5.7. The dotted
line is from the article in Sound & Vibration [12]. The amplitude is ten times what is
expected. The conclusion is that k1 is ten times higher than that used in the article. And
the damping for the second and last peak seems too high. Figure 5.7 shows the frequency
response for k1, CC, CB ten times smaller: k1 = 4.4, CC = 273 00, CB = 16 which seems
more accurate.
Figure 5.6 Bode diagram, voice
coil, given values.
Figure 5.7 Bode diagram, voice
coil with smaller values.
The two different methods were tried, to obtain the right values of the parameters. The
first, heuristic method, is based on experimentally identifying the effect the parameters
on the model. The second used to calculate the parameters was the least square method.
As expected, the damping CB and stiffness KB control gain and frequency for the first
peak. The second peak depends similarly on the values of CS and KS. Values CC and KC
respectively, affect the last peak.
After some adjustments of the values the following results were obtained:
Table 5.5
Estimated vales for a voice coil
MD = 10 kg
MT + MC = 1.3 kg
MB = 78.8 kg
k1 = 4.4
KS = 24 kN/m
KC = 0.44 GN/m
KB = 20 kN/m
CS = 43 Ns/m
CC = 1350 Ns/m
CB = 500 Ns/m
The resulting frequency response is compared to those in the article by George Fox Lang
and Dave Snyder in Sound & Vibration, in Figure 5.5. The conformity with the
frequency response in their model is high. The results can be seen in Figure 5.8.
Figure 5.8 Bode diagram for S-100 voice coil, relating table acceleration to applied
current as a function of frequency. Solid line is voice coil model with
values in Table 5.5. Dotted line is values from Sound & Vibration [12].
Figure 5.9 Bode diagram for S-100 voice coil, relating table acceleration to applied
current as a function of frequency. Solid line is voice coil model without
mount, with values in Table 5.5. Dotted line is values from Sound &
Vibration [12].
The second method based on the least square method can be used by itself or as a
complement to the method discussed above. The method was used for the transfer
function representing system one (5.7) and two (5.8). The same initial values in Table
5.6 were used in both cases:
Table 5.6
Initial values for parameter estimation
MD = 0.1
MT + MC = 1
MB = 10
k1 = 10
KS = 104
KC = 107
KB = 104
CS =10
CC =103
CB =103
The results can be seen in the Figure 5.10 below and the agreement with the Figure 5.5 is
Figure 5.10 Bode diagram for S-100 voice coil, relating table acceleration to applied
current as a function of frequency. Solid line is least square parameter
estimation of acceleration. Dotted line is values from Sound & Vibration
Figure 5.11 Bode diagram for S-100 voice coil, relating table acceleration to applied
current as a function of frequency. Solid line is least square parameter
estimation. Dotted line is values from Sound & Vibration [12].
It can be noted that the first peak in Figure 5.10 is missing. The reason is that the least
square method does not weight that small change high. In Figure 5.11 it is also missing
as expected, because it is originally from the body moment and in this model the body is
rigidly connected to the ground. But the results for both the heuristic and the least square
method are satisfying. Example B: Voice Coil Reaction Mass Actuator
In this example the least square method will used to identify the model parameters for a
reaction mass actuator from CSA Engineering, SA10. The specifications for SA10 are
taken from a data sheet published by CSA Engineering [62]. The Bode diagram is shown
in Figure 5.10.
Table 5.7: Specifications for SA10
Rated Force Output:
Motor Constant (Typical
Resonant Frequency:
44.48 N
Resistance (Userspecified):
Total Mass:
2 Ohm
2.49 kg
93 mm
92 mm
Figure 5.12 Bode diagram for SA10 [62].
The method used was to guess the initial values and then use the least square method
discussed in sub-chapter The initial values that were used are presented in Table
5.8. The results are shown in Figure 5.13 and in Table 5.9.
Table 5.8
Initial values for SA10
MC = 0.1
MT + MD = 1.6
k1 = 90.0
KS = 6.0·103
KC = 2.0·107
CS = 20.0
CC = 200.0
Figure 5.11 Bode diagram for SA, parameters estimated with least square method.
Table 5.8
Results for SA10 with least square method
MC = 0.28
MT + MD = 1.88
k1 = 88.70
KS = 3.33·104
KC = 1.43·107
CS = 101.93
CC = 311.29
The results correlate well with the measured response that can be seen in Figure 5.12.
What can be noted is that the total mass given in the specification, Table 5.7, is 2.49 kg
and the total mass of the modelled parts is estimated to 2.16 kg. We can assume that the
actuator housing weight is approximately 0.4 kg and that gives a total estimated mass of
2.56 kg, which is close to the given value. If the results had been unusual, the masses
could have been fixed and the least square method could have been used again. This is
not necessary this time.
5.1.5 Specification-dependent Design
To be able to use the voice coil actuator capacity to its maximum, consideration must be
given to the wanted frequency response for the specific application. This enables the
system designer to use a smaller actuator then otherwise would be needed. This can save
space, weight and money.
For instance, the actuator resonance frequencies can be placed close to where the largest
forces are needed. Thus enable the use of a smaller actuator and less power. Another
desired effect can be that the actuator should give the same response in the entire
operating range. That can be accomplished by placing the resonance frequencies outside
the actuator’s operating range.
Voice coil response characteristics with constant current or voltage amplifier coupling
can be seen in Figure 5.4. When choosing between controlling the actuator with current
or voltage, both the wanted frequency response and the accessibility must be considered.
The following steps can be used as guidelines for voice coil actuator design from
frequency-domain specifications. The steps are given for the moving coil, the moving
magnet, and the reaction mass actuator cases:
Figure 5.14 Bode diagram, specification-dependent design
Step 1:
Moving coil:
Moving magnet:
RMA (moving coil):
RMA (moving magnet):
Step 2:
Decide the weight of the masses:
Coil MC, table MT and load MD.
Magnet MC, table MT and load MD.
Coil MC, table MT and reaction mass MD.
Magnet MC, table MT and reaction mass MD.
Place the resonance frequencies:
First resonance: ω 01 =
M C + MT + M D
Second resonance: ω 02 =
Step 3:
Chose the damping coefficients:
First resonance:
∆ω 01:3dB
CS =
⋅ K S (M C + M T + M D )
ω 01
Second resonance:
∆ω 02:3dB
CC =
⋅ KC M C
ω 02
Step 4:
Adjust amplitude A:
A now
k 1:wanted = k 1:now
A wanted
Step 5:
Are the parameters reasonable?
No, go back to step 1. and adjust the values.
When choosing the parameters, the values must be considered so they are physically
possible. For example, as discussed in section 5.3.1, the force from the coil which is
described by the constant k1 depends on the size of the coil. This makes k1 coupled to the
mass of the coil MC. And the generated heat depends on the resistance in the wiring,
which depends on its area, and which will also affect the possible weight of the coil, as
discussed in subsection 5.3.3.
5.2. Piezoelectric Actuators
Among the different actuator technologies that are available today piezoelectric actuator
devices offer a number of benefits for use in active vibration control. Their high stiffness
results in isotopic high actuator performance. Piezoelectric actuators give fast response,
are small in size and weight, and are easily controlled. [7]
5.2.1 Piezoelectric Model
This section will describe the behaviour of the piezoelectric material. The notations used
are the IEEE standard on piezoelectricity:
Table 5.9
The IEEE standard notations for piezoelectricity
D : Electric Displacement, Coulumb/m2
E : Electric field, V/m
ε : Dielectric constant of the material, Farad/m
εT : Dielectric constant under constant stress
S : Strain
T : Stress, N/m2
s : Compliance of the material, m2/N
sE : Compliance under constant electrical field, m2/N
When the material is unstressed the electric displacement, D, is simply related to the
electric field, E, in the one-dimensional case by:
D = εE
Strain and stress are similarly related in a zero electric field:
S = sT
For a piezoelectric material, the electrical and mechanical equations are coupled. In the
pseudo-static case the equations become [7]:
S = sET + dE
D = dT + εTE
Equations (5.14) and (5.15) are transformed for easier understanding of the physical
phenomenon they describe. The quantities that will be used are displacement u [m],
force F [N], applied voltage V [V], charge Q [C], height h [m] and area A [m2]. Using
the following variable transformations:
T =−
the new equations will then describe actuator displacement as a function of force:
hs E
F + dV
and the force as a function of displacement:
hs E
(−u + dV )
In the unloaded actuator case, the displacement as a function of applied voltage is shown
in Figure 5.15. One relevant feature for practical applications is the hysteresis behaviour
of the piezoelectric material. This originates in the movement of ferroelectric domain
walls in the piezoelectric material. [7] This creates a practical problem for using applied
voltage for controlling displacement. In general, additional sensors are needed to
monitor the actual displacement.
The problem with hysteresis can be reduced by controlling the transferred charge instead
of the voltage. In Figure 5.15, displacement is shown as a function of voltage (dashed
line) and displacement as a function of charge (solid line). The hysteresis in the later
case is almost suppressed.
Figure 5.15 Example of displacement. The dashed line is displacement as a function
of voltage and the solid line is displacement as a function of charge for a
free actuator
When the actuator is subjected to an external force, there are two basic situations that
must be considered. The first case is when the external force is proportional to the
displacement, like a spring. The other case is when the actuator is subjected to a constant
If no internal forces are considered and the actuator is assumed to be in a quasi-static
case, the counterforce will increase with displacement as, k∆u. That will decrease the
maximum actuator displacement. The final position will be reduced by k∆u/K, where K
is the stiffness of the actuator.
The second case is with a constant load F on the actuator. The "displacement" of the
actuator will initially be "reduced" by F/K, where g is the gravitational constant. The
displacement due to an applied charge or voltage will then be approximately the same as
in the free case. The two restraint cases and the free case are shown in Figure 5.16.
Figure 5.16 Upper curve shows free displacement, middle curve shows displacement
with proportional counter force, and the lower curve shows displacement
with constant load.
Another important property is the blocking force at "maximum" applied voltage. With
free displacement it can be used to decide if the actuator can fulfil the requirements. The
blocking force is the force that the actuator gives when it is restrained so no strain can be
developed, but a force will be developed against the object. To illustrate the applicability
of an actuator, a plot over displacement and force can be drawn. A line is drawn from the
maximum blocking force (zero displacement) to the free displacement (zero force). An
example can be seen in Figure 5.17. The relation between displacement and blocking
force can also easily be seen in equations 5.16 and 5.17.
Figure 5.17 Force versus displacement for "maximum" voltage. The grey area is
where the actuator can be operated
A simple mechanical model of a piezoelectric material can be shown in Figure 5.18. The
mass meff is effective mass, about 1/3 of the mass of the ceramic stack. KT is the actuator
stiffness. The force F is the actuators internal force.
Figure 5.18 Simple mechanical model of piezoelectric material
The resonant frequency for the spring and mass system is a function of its stiffness and
effective mass. The resonant frequency given in the technical data tables refers to
unloaded actuators, with one end rigidly attached. The resonance frequency will be
estimated to:
ω0 =
One desirable feature of a piezo actuator is fast response. The key to obtain fast response
is rapid drive voltage change, which results in a rapid position change. This is necessary
in active vibration-cancellation systems.
A piezoelement can reach its nominal displacement in approximately 1/3 of the resonant
frequency period, although with significant overshoot that can be seen in Figure 5.19.
Figure 5.19 Example of a step response for a piezoelement.
5.2.2 Piezo Stack Actuator
In this section a one degree of freedom electromechanical model of a piezoelectric
actuator will be developed. The linear, constitutive equations (5.14) and (5.15) will be
used. The resulting model can be directly coupled to a dynamic model of an amplifier
and the surrounding structure.
The equations (5.14) and (5.15) are in the axial direction (third direction):
S 3 = s 3E T3 + d 33 E 3
D3 = d 33T3 +
ε 33
First, the equations for one layer are described. D3 is the electrical displacement and can
be written as, D3 =
ql . [2] E3 is the electrical field in the piezoelement and can be
written as, E 3 = a . By use of equation 5.20 the charge ql that enters each layer can be
obtained as:
ql = ε 33 a + d 33T3
The equation can be rewritten to:
ql = ε 33
V a + d 33 lwT3 = C lV a + d 33 lwT3
By use of equation (5.21) we can state the equations for a stack with n layers. The charge
. Equation
entering all layers will be q=nql and the total capacitance C = nCl = ε 33
(5.21) for n layers becomes:
ql = CVa + d 33 nlwT3
Solving equation (2.22) for voltage:
Va =
d nlw
q − 33
T3 = q − 33 hT3
ε 33
The first component, I, is the direct capacitive effect and the second part, II, is the
contribution from the mechanical stress. Replacing the electric field with its voltage
relation in equation 5.19 the following equations are obtained:
S3 = s33T3 + d33E3 = s33T3 + d33
 d
d 1
= s33T3 + 33  q − 33 hT3  = 33 ⋅ q + (1 − k2 )s33T3
h  C ε33  nlwε33
Introducing the electromechanical coupling coefficient:
k2 =
d 33
s 33 ⋅ ε 33
Equation 5.24 could be rewritten to:
T3 =
s 33 1 − k
1 d 33
 S3 −
nlw ε 33
q 
The strain in the actuator will cause displacement according to:
x = nhS 3
The force from the stress in the actuator becomes:
Fa = lwT3
The relation between current ia and charge q are:
q = i dt
From equations (5.26) to (5.27) the connection between current, displacement and force
are conducted:
Fa =
 1
1 d 33
i dt 
nlw ε 33
lws 33 (1 − k )  nh
The equations 5.30 and 5.23 are implemented in Matlab as shown in Figure 5.18:
Figure 5.20 Electromechanical model of a piezo stack actuator
5.2.3 Amplified Piezo Actuators
The increase in displacement gained with a mechanical amplifier reduces the actuator's
stiffness and maximum operating frequency. They consist of a piezoelectric element and
either a mechanical or hydraulic displacement amplifier. A more detailed discussion is
out of scope for this thesis work.
5.2.4 Simulation of Piezoelectric Stack Actuator Model
For validation we have constructed a simple model of an actively controlled structure. It
is assumed that the actuator is bonded rigidly to the mass M. K is the parallel spring and
C is the parallel damper. The mechanical model is in Figure 5.19. The structure is
implemented in Simulink as showed in Figure 5.19.
Figure 5.21 Mechanical
diagram of the
controlled structure
Figure 5.22 Simulink block diagram of
the controlled structure
To minimize the vibration in the mounting point, the force Fa + K ⋅ x + C ⋅ x& must be
small. In this example this is obtained using proportional feedback coupling with the
constant Kreg. The simulink block diagram of the complete system is shown in Figure
Figure 5.23 Simulink block diagram of the complete system.
The system was run with an external sinusoidal disturbance force Fext with amplitude of
20 N and frequency 100 Hz. The results are presented in Figures 5.23, 5.24; they are
plotted with the regulator on and off. The results shown that the displacement is higher
for the case with actuator and regulator which is as expected because it will decrease the
force against the ground as can seen in Figure 5.24.
Figure 5.23 The solid line is the displacement x with actuator and regulator, the
dotted line is without actuator.
Figure 5.24 The solid line is the force against the ground Fa + Kx + Cx& with
actuator and regulator, the dotted line is without actuator
The simulation results are as expected but the physical measurements must be carried
out to completely verify the model, but that is beyond the scope of this thesis.
5.2.5 Validity of the Model
Some assumptions have been made when deriving the model of a piezoelectric stack
actuator: The piezoelectric element has been seen as pseudo-static. Temperature
dependency and changes over life time have been ignored.
Temperature has two different effects on piezoelectric actuators: linear thermal
expansion and temperature dependency of the piezoelectric effect.
Thermal stability of piezoelectric ceramics is better than other materials like steel or
aluminium. The change is usually specified by the manufacturer and is given as relative
change in length ∆L/L per unit change in temperature. The following values could be
used as guidelines: 11·10-6m/°K for high voltage piezoelectric ceramics and -3.5·106
m/°K for low voltage ceramics. For example, for the piezoelectric stack actuator DPA60
from Cederat, it is 0.20·10-6m/°K and for their amplified actuator APA120ML it is
1.17·10-6m/°K. The thermal expansion values change with temperature and are normally
given for room temperature. [8]
The piezoelectric effect is based on electric field and thus works down to zero degrees
Kelvin. But temperature changes cause a voltage to appear across the electrodes. This is
due to the pyroelectric properties of piezoelectric ceramic. Temperature also affects
other properties of piezoelectric ceramics such as elastic, dielectric and piezoelectric
coupling. There is no general trend and each dependence must be measured separately.
[9] The piezoelectric effect varies with temperature for several reasons, but around room
temperature it is very stable. For example, at cryogenic temperatures (ultra-low
temperatures) it is approximately 20 to 30 % of its room temperature value. Figure 5.25
shows the temperature dependency for the piezo effect (piezo gain) given by Physik
Instrumente. [8]
Figure 5.25 Temperature dependency for the piezoelectric effect, given by Physik
Instrumente. [51]
To create the piezoelectric effect in a piezoelectric ceramic it is heated during the
polarization and an electric field is applied to allow alignment of the dipoles.
Conversely, a poled piezoelectric material will depolarize when heated above the
maximum allowed operating temperature. It can be somewhere around 100°C. But there
are piezoelectric actuators that can operate in higher temperatures.
The life time is pretty difficult to estimate but tests at Physik Instrumente have shown
that piezoelectric elements can perform billions of cycles under suitable conditions. And
at Piezo Systems they have had a piezoelectric fan running constantly since 1982. But no
conclusive tests have been done.
But some things can be said. Generally, as with capacitors, the lifetime of a Piezo is a
function of the applied voltage and the average voltage should be kept as low as
possible. But many other factors affect the life time, such as temperature, humidity,
voltage, acceleration, load, operating frequency and insulation materials.
Chapter 6
It exist different principles of active engine mounts. The one that will be presented and
modelled in this chapter are based on the commonly used passive hydraulic engine
mount. Use of the present passive hydraulic engine mount extended with an active part
would benefit from the well-known passive characteristics as well as the active. The type
of active hydraulic mount that is modelled in this chapter is a hydraulic mount with a
voice coil actuator as the active element. This seems to be the most common principle
today for an active hydraulic engine mount. Therefore, it is most interesting to construct
a model for this type of mount. During this thesis work we have not found any published
papers on construction of an active hydraulic engine mount model that works both for
low and high frequencies. The models that we have found are only valid up to around 40
Hz. To reduce the time to design the mount and its application, it is desirable to construct
a model to predict the behaviour of the system before it is physically assembled. A good
model is also a key element when designing the control algorithm for the system.
First a regular passive hydraulic engine mount will be modelled and the results will be
compared to measured data. The object is not to obtain the optimum parameters for the
passive hydraulic engine mount model. The purpose is to show that the modelling
technique is satisfactory and can serve to model the active hydraulic engine mount. It is
important that the model has a high known correspondence to reality, since the amount
of data that can be used to verify the active hydraulic mount model is limited.
After the passive hydraulic mount is modelled an actuator is included in the mount to
provide mechanical energy. The main structure will be similar to the passive hydraulic
engine mounts. The difference is that that the decoupler is replaced with a diaphragm
that is attached to a voice coil actuator. That will be shown in section 6.1.4 Complete
Active Engine Mount.
6.1 Passive part
The general principles of a hydraulic engine mount are shown in Figure 6.1. It consists
of two parts. The rubber part supports the engine weight and the hydraulic part gives the
mount its main dynamic behaviour.
Figure 6.1 Passive hydraulic engine mount
The hydraulic part consists of two fluid-filled chambers. The fluid can be a mixture of
water and anti-freeze liquid such as glycol. The bottom of the lower chamber is of thin
rubber; the chamber acting as a reservoir when fluid is forced into it. The two chambers
are connected through an inertia track (damping channel) and a decoupler. The
decoupler is a rubber or fabric diaphragm which can move freely in the passage
connecting the two chambers.
Hydraulic mounts with only an inertial track can be tuned to give high damping at low
frequencies. But this kind of mount gives higher dynamic stiffness at all frequencies for
lower amplitudes compared to an elastomeric mount. To solve that problem a decoupler
is used to make the hydraulic mount amplitude-dependent. The decouple works like a
floating piston. At low amplitudes it allows the fluid to pass between the chambers and
the mount behaves like an elastomeric mount. This gives low dynamic stiffness and
provides good vibration isolation. Higher amplitudes will force the decoupler to saturate,
which forces the fluid through the inertial track and thus increases the dynamic stiffness.
To obtain a model of a passive hydraulic engine mount, the different parts of the mount
will be modelled. The affect that the surrounding structure has on the mount is
parameterized by X, which is the displacement of the mount. It is also the input to the
system and the output will be the force FT transmitted to the frame.
The rubber around the upper chamber (chamber one) is modelled with its stiffness kr and
damping property br. The rubber will add volumetric compliance C1 to the upper
chamber. The upper rubber structure also works as a piston on the upper chamber with
an effective pumping area Ap. The lower chamber has volumetric compliance C2, which
comes from the rubber below. The flow that passes through the decoupler is called Qd
and the flow through the inertial track is called Qi.
Figure 6.3 Schematic of a hydraulic engine mount
The continuity equations for the internal dynamics of the system can now be derived:
C1 P&1 = A p X& − Qi − Qd
C 2 P&2 = Qi + Qd
6.1.1 Inertia Track
The inertia track is a long column of fluid between the two chambers which has a
damping effect. It is assigned the resistance Ri and the effective inertia Ii. The
momentum equations become:
P1 − P2 = I i Q& i + Ri Qi
This equation describes the linear behaviour of the inertia track. From experimental
results the resistance unlike the inertia does not exhibit constant behaviour [57]. Since
the resistance is dependent on the Reynolds number will it change because of the
oscillatory flow. According to A.A. Geisberger [8], the resistance is dependent on the
amplitude and frequency of the flow and can be modelled as: Ri = Ri + Ri' Qi . Where
Ri represents the laminar resistance term and Ri represents the resistance in the turbulent
region. The non-linear momentum equation becomes:
P1 − P2 = I i Q& i + ( Ri + Ri' Qi )Qi
6.1.2 Decoupler
Most of the amplitude-dependent behaviour originates from the decoupler. When the
flow is oscillating across the decoupler orifice and the decoupler plate does not have
contact with the cage it is considered to be free. In that case the decoupler system
behaves like a simple orifice. The decoupler is assigned inertia and a resistance value,
similar to the inertia track. The non-linear equation for the free decoupler now becomes:
P1 − P2 = I d Q& d + ( R d + R d' Q d )Q d
When the decoupler contacts the cage it will stop the flow. To model this flow stop a
large resistance is added to the equation (6.4) and the equation become:
P1 − P2 = I d Q& d + ( Rd + R d' Qd + R stop )Qd
The position of the decoupler plate is called Xd and is related to the decoupler volume Vd
by Vd = XdAd where Ad is the decoupler area. The decoupler volume can be integrated
from the flow of fluid through the decoupler. In Figure 6.4 the corresponding position of
the decoupler can be seen. The expression for Xd becomes:
Xd =
Vd =
∫ Q dt
Figure 6.4 The positions and sign for the decoupler
When the decoupler contacts the cage the resistance Rstop should be high to reduce the
flow to zero in the decoupler, and when it is free it should be low so it doesn't have any
affect on the flow. The resistance Rstop should also be low when the decoupler contact
the cage but the flow change direction. This because the decoupler then can move freely
in the wanted direction even if it still contact the cage. The desired values of Rstop
resistance can be seen in Figure 6.5.
Figure 6.5 The nonlinear switching function of the resistance Rstop
To describe the function in Figure 6.4 an exponential function is used with an arctangent
function to get the switching behaviour of the exponential function [8]. Three constants
R0, X0 and Q0 are also used to get the resistance Rstop in the right domain. The function
Rstop will be R stop = R0 e
( X d / X 0 ) arctan( Qd / Q0 )
. The momentum equation for the decoupler
P1 − P2 = I d Q& d + ( Rd + R d' Qd + R0 e ( X d / X 0 ) arctan(Qd / Q0 ) )Qd
6.1.3 Transmitted Force
When the decoupler comes into contact with the cage, the transmitted force will be as in
equation 6.8. That is, because the force can work on the total area Ap it can be seen as
the decoupler area Ad becomes almost zero and the flow Qd become negligible.
FT = k r X + br X& + A p P1
The force from the rubber is modelled as krX and br X& like a normal spring and damper
system. The force from the pressure in the upper chamber is ApP1. The lower chamber's
bottom rubber is soft and acts as a reservoir; therefore it only contributes with a
negligibly small force.
To capture the force from the decoupler, a similar method as in the decoupler resistance
case is used. To model the changes in force from the decoupler, the decoupler area will
be modelled as dependent on the decoupler position and the pressure differential. The
total area which the upper chamber pressure affects will be Ap – Ad_fnc, and this describes
the behaviour discussed. When the decoupler plate comes into contact with the cage the
decoupler is modelled as zero. Though, when the pressure differential reverses direction
the decoupler will appear open even if the inertia still holds the decoupler at rest. The
difference from the conditions used for decoupler resistance is that the area is directly
related to pressure differential and not flow. The desired behaviour for the switching
function can be seen in Figure 6.6.
Figure 6.6 The decoupler area function Ad_fnc
According to A. A. Geisberger [57], the function can be modelled as:
Ad _ fnc =
 (2 / π ) X d arctan((P1 − P2 ) / P0 − X d _ max )  
  (6.9)
Ad  − arctan
π 2
Where P0 and X1 is constants and Xd_max is the maximum displacement in the decoupler
as can be seen in Figure 6.4.
The transmitted force now becomes:
FT = kr X + br X& + ( Ap − Ad _ fnc )(P1 − P2 ) + Ap P2 + Ad (Rd + Rd' Qd )Qd (6.10)
6.1.4 Complete Passive Mount Model
The total model of the hydraulic mount can now be summarized from equation (6.1) to
The continuity equations for the mount:
C1 P&1 = A p X& − Qi − Q d
C 2 P&2 = Qi + Q d
The momentum equations for the mount:
P1 − P2 = I i Q& i + ( Ri + Ri' Qi )Qi
P1 − P2 = I d Q& d + ( Rd + R d' Qd + R0 e ( X d / X 0 ) arctan(Qd / Q0 ) )Q d
Where Xd is:
d dt
The transmitted force:
FT = k r X + br X& + ( A p − Ad _ fnc )( P1 − P2 ) + A p P2 + Ad ( Rd + R d' Q d )Q d
Ad _ fnc =
 (2 / π ) X d arctan((P1 − P2 ) / P0 − X d _ max )  
Ad  − arctan
To enable simulations the equations are implemented in Matlab. The system can then be
implemented as a numeric differential problem in Matlab.
6.1.5 Validity of the Passive Engine Mount Model
Some assumptions have been made constructing the model. The effects that have not
been taken into account are as follows:
Rubber stiffness kr depend on excitation amplitude, driving frequency and
preload force.
Damping br depend on excitation amplitude, driving frequency and preload
Effective pumping Ap depends on the preload force.
Upper chamber compliance C1 depends on driving frequency, volume
amplitude and preload force.
Some hydraulic engine mounts permit high resistance flow through the
decoupler even when the decoupler contacts the cage.
Lower chamber compliance C2 depends on the preload force.
This is according to A. A. Geisberger [4]. One solution is to measure the different
parameters' dependency and take that into account. One parameter that is heavily
influenced by frequency is the stiffness of the rubber. The rubber stiffness increases,
roughly, with 1 N/mm per frequency step (Hz); depending of course on the chosen
rubber material. This dependency is relatively linear and can easily be modelled. It could
be modelled as: k r = k r _ static + k r _ dynamic ω X where kr_static is the rubber stiffness for
very low frequencies and kr_dynamicωX is the change in stiffness by frequency and there ωX
is the frequency of excitation.
The other effects are not in order of size to have a significant affect on the model. This
conclusion is taken from studying the results that the derived model gives without
consideration of the effects and studying of measurements done [4].
F. JANSSON O. JOHANSSON Superimposed inputs
One interesting question about the validity of the model is the reaction to superimposed
input. As far as the author knows, no measurements of superimposed inputs have been
done successfully for a hydraulic mount. In an attempt to verify the correctness of the
model, measurements were performed at Volvo Cars. The results are inconclusive, most
likely because of equipment limitations.
However, measurements were also done on a conventional rubber grommet to verify the
function of the measurement equipment. The result is seen in Figure 6.8. The dynamic
stiffness for the base frequency 10 Hz with 1 mm amplitude was 661 N/mm. The 0.1 mm
superimposed force dynamic stiffness can be viewed in Figure 6.8.
The conclusion that can be made from the measurements on the rubber is that the
dynamic stiffness is lower for superimposed input then it would be without the base
frequency. This is probably a result of the higher base amplitude making the rubber
soften. To really understand the behaviour of the rubber in the case of superimposed
input, a more detailed investigation is needed. It is likely that the rubber part of the
hydraulic mount behaves in a similar way as the rubber grommet. This makes it likely
that the dynamic stiffness for the hydraulic engine mount is lower in the superimposed
case similar to the case of a rubber grommet.
Figure 6.8 Dynamic stiffness for conventional rubber grommet for superimposed
input and non superimposed input. Base frequency 15 Hz with 1 mm
amplitude and 0.1 mm superimposed.
6.1.6 Experimentally Validation of the Passive Engine Mount Model
To verify the model of the passive hydraulic mount, measurements were done on the
hydraulic engine mount. The parameters needed for the model were identified by
studying their influence on the frequency response. In Figures 6.9 to 6.19, the different
parameters' affects on the model can be studied. The model was linearized to make these
plots by letting the flow Qd be zero at low frequencies, as the amplitude normally is high
(1 mm) which makes the decoupler to bottom. And Qi becoming zero at high frequencies
because the amplitudes are normally small (0.1 mm) and all flow goes through the
decoupler. Ri´ and Rd´ is zero in the examples.
Figure 6.9 Model response for change in the rubber stiffness kr.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.10 Model response for change in the affective pumping area Ap.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.11 Model response for change in the decoupler area Ad.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.12 Model response for change in the upper compliance parameter C1
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.13 Model response for change in the inertia for inertia track Ii.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.14 Model response for change in the inertia for decoupler track Id.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.15 Model response for change in the resistance for inertia track Ri.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
Figure 6.16 Model response for change in the resistance for decoupler track Rd.
· · · · 40 % increased values of the parameter
- - - 40 % decreased values of the parameter
The resulting model and the measured results for 1 mm amplitude of X can be seen in
Figure 6.17. This result must be seen as satisfactory when the objective was not to
optimize the parameters for the model but to study the model behaviour. For higher
frequencies the results is shown in Figure 6.18. As can be viewed are the results
inconclusive after 350 Hz. This is probably an effect of the measurement equipment
Figure 6.17 Measured and calculated response for 1 mm amplitude for a hydraulic
engine mount.
Figure 6.18 Measured and calculated response for 0.1 mm amplitude for a hydraulic
engine mount.
6.2 Complete active engine mount
Different techniques exist to go from a passive engine mount to an active engine mount.
However, there are several different ways to provide controlled mechanical energy to the
engine mount system. The secondary vibrations produced by the active engine mount are
used to cancel the primary vibrations. The main principle is to replace the decoupler in
the passive hydraulic engine mount model with a diaphragm connected to a voice coil
actuator; that will be used to provide mechanical energy to the engine mount system.
Figure 6.20 Schematic of a decoupler
Figure 6.21 Schematic of a diaphragm
Figure 6.20 shows a schematic of a decoupler, and Figure 6.21 a schematic of a
diaphragm. The coil of the voice-coil actuator is mounted on the diaphragm and the dark
shaded part symbolizes the magnet. The characteristics and function of a voice coil are
described in Chapter 5. The difference between the decoupler and the diaphragm is that
the diaphragm does not have the same dynamic stiffness amplitude-dependency. This is
because it is never totally free when it is attached to the side. Instead, the dynamic
stiffness can now be controlled by controlling the diaphragm position with the voice coil
actuator. In theory this will make it possible to have a dynamic stiffness that is zero for
higher frequencies, which will give total vibration isolation at these frequencies. This
will be derived if the actuator forces the mount to follow the vibration displacements
from the engine, which will isolate the vibration from the engine to the frame. It could
also be used to make the engine mount stiffer at certain frequencies by providing an antiphase force to the mount.
The diaphragm is modelled with a stiffness kdia and damping properties bdia. This makes
the diaphragm model linear differing from the non-linear decoupler model. This because
the diaphragm is not free floating and we assume it never contacts the top or bottom of
its cage as the decoupler does. The force from the voice coil is called Fa. The dynamics
of the force Fa can be derived from the voice-coil actuator model in Chapter 5. Basically,
it is proportional to the current provided to the actuator. The voice coil could also be
controlled with voltage, which would give a different dynamic behaviour. Adia is the area
of the diaphragm and the force from the pressure in the upper chamber is called FP1 . The
mechanical representation of the diaphragm is seen in Figure 6.22.
Figure 6.22 Mechanical representation of a diaphragm
Because pressure is force per area a fluid momentum equation similar to the one for the
decoupler (6.7) can be derived. The pressure from the lower chamber P2 which the
decoupler was affected by is replaced with the force from the stiffness and damping of
the diaphragm, together with the force from the actuator. The equation becomes:
P1 − (kdia X dia + bdia X& dia + Fdia ) / Adia = IdiaQ&diad + (Rdia + Rdia
Qdia )Qdia
Xdia is the position of the diaphragm, Idia is the effective inertia for the liquid diaphragm
column and the coil. The resistance is assumed to be dependent on the amplitude and
frequency of the flow in the same way as in the passive hydraulic mount case. The
frequency and amplitude dependency is modelled with Rdia that represents the laminar
resistance term, and Rdia' that represents the resistance in the turbulent region.
The force is calculated in a similar way as in the passive case. The force equation (6.10)
can be simplified because the diaphragm does not flow freely in its cage. The transmitted
force then will be the sum of the force from the upper chamber pressure P1 on the
chamber floor and the force from the rubber krX and br X& : like a normal spring damper
system. The differences here, as mentioned, are that the diaphragm is not free and the
pressure affects the total floor area (effective pumping area) Ap. The effect of the
pressure in the lower chamber P2 can be negligible because the rubber below is soft and
it acts as a reservoir. The resulting force becomes:
FT = k r X + br X& + A p P1
The continuity equations will also be different in the active case. The flow into the
diaphragm chamber only affects the upper chamber and the continuity equations
C1 P&1 = A p X& − Qi − Qdia
C 2 P&2 = Qi
The momentum equation for the inertia track will be the same as in the passive hydraulic
engine mount case when no changes to the inertia track have been done:
P1 − P2 = I i Q& i + ( Ri + Ri' Qi )Qi
The final model of the active hydraulic engine mount can now be summarized from
equation (6.11) to (6.15):
The continuity equations for the mount:
C1 P&1 = A p X& − Qi − Qdia
C 2 P&2 = Qi
The momentum equations for the mount:
P1 − P2 = I i Q& i + ( Ri + Ri' Qi )Qi
P1 − (k dia X dia + bdia X& dia + Fdia ) / Adia = I dia Q& dia + ( R dia + R dia
Q dia )Qdia
The transmitted force:
FT = k r X + br X& + A p P1
In the same way as the decoupler position Xd was calculated (6.6) the diaphragm
position Xdia is calculated:
X dia =
dia dt
6.2.1 Validity of the complete active engine mount model
The assumptions made in constructing the model of the active hydraulic engine mount
are similar to the ones for the passive hydraulic engine mount model. The affects that
have not been taken into account are the same as for the passive hydraulic mount model
are as follows:
The diaphragm effective area is probably not constant when it bends.
The stiffness kdia and damping bdia of the diaphragm probably depend on the
excitation amplitude and driving frequency.
It would be useful to be able to make more accurate, conclusive measurements on a
specific diaphragm. This is, however, beyond the scope of this thesis.
6.2.2 Validation of complete active engine mount
The model has been verified with experimental data provide by a manufacturer. The
broken line in the frequency response seen in Figure 6.23 is for their active engine mount
in passive mode. The solid line is the calculated model frequency response. The
agreement is very good, as can be seen.
Figure 6.23 Frequency response for an active engine mount. Dotted line is the
measured frequency response and the solid line is the model frequency
For higher frequencies, no data was found to verify the model. If a decoupler were to be
used, similar resonance will be present at 200 Hz. This is because the resonance
phenomenon of the column of fluid in the diaphragm chamber is similar to that in the
decoupler passage. The model's frequency response for higher frequencies can be seen in
Figure 6.24. The results are as expected with a resonance peak at 200Hz. This is because
the liquid column, diaphragm and the coil of the actuator are resonating.
Figure 6.24 High frequency response for the model
6.2.3 Linearization of the Complete Active Engine Mount Model
The non-linearity in the active engine mount model origin in the non-linear behaviour of
the resistance in the momentum equations for the inertia track and the diaphragm. If we
assume that the non-linearity in the fluid column resistance for the inertia track
' Q
( Ri + Ri' Qi ) and diaphragm ( R dia + R dia
dia ) are small can they be replaced by
Ri and R dia . The loss is that the non-linear behaviour of the resistances is not taken into
account. Where this non-linearity phenomenon originates from is described in section
6.1.1, where it is added to the model. Have this affect the model has to be investigated
further but the results seen in figure 6.25 are similar to the results with the non-linear
model shown in figure 6.24. This indicates that the non-linearity is quite small. But a
more detailed investigation is out of scope of this work. The equation system for the
active engine mount becomes:
The continuity equations for the mount:
C1 P&1 = A p X& − Qi − Qdia
C 2 P&2 = Qi
The momentum equations for the mount:
P1 − P2 = I i Q& i + Ri Qi
P1 − (k dia X dia + bdia X& dia + Fdia ) / Adia = I dia Q& dia + R dia Qdia
X dia
dia dt
The transmitted force:
FT = k r X + br X& + A p P1
The equations now give the systems transfer function G1, relating the transmitted force
FT to the displacement X, dynamic stiffness. Its also gives the transfer function G2
relating the force crated by the actuator on the diaphragm Fdia to the transmitted force FT.
In this case a voice coil actuator is used and the force Fdia exerted on the diaphragm is
simply proportional to the current, i.e Fdia = k1·i.
FT =G1 X + G2 Fdia = G1 X + G2 k1i
G1 = k r + bs s + UZA 2p s
G2 =
1 + ZC1 s + WZC 2 s
k dia
+ I d s + R dia
1 + I 1C 2 s 2 + R i C 2 s
The dynamic stiffness for the linear active engine mount model in passive mode, Fdia = 0,
is seen in Figure 6.25.
Figure 6.25 Bode diagram for linear model of active engine mount, dynamic
stiffness as a function of frequency.
Chapter 7
The main objective of this thesis work was to create a complete parameterized model of
an active hydraulic engine mount. This was done with success and the model show great
potential to predict the behaviour of the active engine mount over its complete frequency
range. A benchmark of the now existing and upcoming technologies and principles was
carried out to find suitable actuators for active vibration control. The actuator technology
is placed in three groups depending on their suitability for active vibration control. The
groups are: promising actuators, selected actuators and other actuators. The actuator
technologies selected are the piezoelectric and the electromagnetic, because of their good
performance and that their wide use. These two are discussed more in Chapter 4, where
models of them are also developed. The electromagnetic actuator principle of voice coil
with moving coil was chosen for use in the active hydraulic mount model.
The model of the active hydraulic engine mount can be used to predict the behavior of
the mount before it is physically constructed. It is also important for designers of active
engine mounts and control algorithms to understand how the design parameters affect
the characteristics of the mount, which is explained in this thesis work. This can be done
because the model technique enables studies of internal behavior of liquid columns and
components of the mount. This gives an extra contribution to the work. A model can also
shorten the period of designing an active hydraulic mount system and financial savings
can be made.
Two ways to estimate the parameters for the voice coil actuator were obtained. A
method was achieved to go from specification in the frequency domain to specification
of the voice coil actuator. This could be used both for design and to understand the
possibilities of the different voice coil actuators.
To summarize, a benchmark over actuators for active vibration control was also
accomplished and an overview of the sensors used mostly for that purpose. Models for
the two chosen actuators, a common passive hydraulic engine mount and an active
hydraulic engine mount were created with good results.
Several conclusions were made in the different parts of the work:
Several actuators are suitable for use in active vibration control as discussed in
Chapter 2. A number of actuators also exist that are promising but need further
When choosing sensors for active vibration control, there are several
alternatives. The most widely used is the piezoelectric accelerometer, as
referred to in Chapter 3.
Two methods have been developed that can be used to estimate the parameters
for the voice coil model. It is also shown that they give good results
independently of whether phase information is available or not.
The models created for the voice coil actuator with moving magnet could also
be used for other types of voice coil actuators, with small changes, as described
in section 5.1.3. The actuators that could be described with this model are:
voice coil with moving magnet, voice coil with moving coil, and reaction mass
actuators with moving coil or moving magnet.
It is possible to go from a specification in the frequency domain to design
parameters of a voice coil actuator. This can be done by use of the five step
method that has been developed and is shown in section 5.1.4.
A model of an active voice coil engine mount is developed and the model
shows great potential in predicting the behavior of the mount between 0Hz and
about 300Hz. Good agreement with experimental data has been achieved.
Recommendations for future work are made as a consequence of the experience from
this thesis work:
The actuator field is developing and information on it needs to be continuously
The model of the active voice coil engine mount could be enhanced by studies
of the effects that have not been taken into account, as mentioned in section
Measurements need to be done to verify the high frequency characteristics of
the active voice coil engine mount in sub-chapter 6.2.
Study of the effect that superimposed input has on both passive and active
hydraulic mounts would be interesting; it has not been done with any success as
far as the authors is aware. A short introduction and measurements are given in
Development of an algorithm for parameter identification for both the passive
and the active hydraulic engine mount. This may be done in a similar way as for
the voice coil actuator in section and would be of great use for practical
use with the models.
The development of good hydraulic displacement expanders in recent years
makes it interesting to study the possibilities of piezoelectric engine mounts.
These have the potential advantages of smaller dimensions, less heat
dissipations, faster response time and power consumption only at expansion
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Appendix A
This appendix presents further information about the technologies and principles
presents in Chapter 2, together with diamagnetism and electrohydrodynamic
technologies for use in active vibration control. Benefits and drawbacks are presented
along with typical materials.
A.1 Diamagnetism
“Diamagnetism is the ability to reflect an external magnetic field” [35].
An external magnetic field affects the movement of electrons in a material so that it
works against the external magnetic field. The subject's magnetization is directed in the
opposite direction to the external magnetic field. Diamagnetism can be found in all
materials, but it is hard to see because of much stronger paramagnetic or ferromagnetic
qualities. The relative magnetic susceptibility is low in most diamagnetic materials
except in superconductors. Superconductor materials are associated with diamagnetism
because of their qualities. Bismuth, graphite and silicon are some non-superconducting
materials that also possessing diamagnetic ability, but at very low levels [35].
The Meissner Effect is one well-known result of the diamagnetic effect, often explained
as a magnet floating steadily above a superconductor. This technology has been
promising for devices in micro and nano regions, because of problems creating
frictionless and self-levitating bearings. In general, these devices do not force
maintenance. This technology is sensitive to ambient temperatures outside the proper
region [1]. Inside a superconductor the magnetic field becomes zero below its critical
temperature. Superconducting transition temperatures have been studied for different
materials. For example for MgB2H0.03 and MgB2 materials, the result is that the former is
Diamagnetic actuator benefits have high efficiency and fast response time, but the forces
are generally weak per unit mass. Another drawback is that diamagnetic materials are
highly susceptible to impurities.
Recently, diamagnetism has not been used for vibration control except in some unique
cases in the micro and nano region. The forces that a diamagnetic device can distribute
are generally weak per unit mass, and diamagnetic materials are highly susceptible to
A.2 Electrochemical
An electrochemical cell is a device that converts chemical energy into electrical energy
or vice versa when a chemical reaction occurs in the cell.
This technology is based on the electrolysis-field, with an electrochemical cell. An
electrochemical cell consists of two metal electrodes immersed in an electrolyte with
electrode reactions occurring at the electrode-solution surfaces. The principle of an
electrochemical actuator is to build up a gas pressure by electrolysis of an aqueous
solution [36]. There have been studies to develop new materials for actuation and
pumping to improve the use of scalable electrochemical phase transformations.
Electrochemical actuators have been developed with strains of 136% and non-optimized
work cycle efficiencies near 50% [37].
There is not much information about electrochemical actuators and those that exist, are
rarely used, but there are some actuators in the micro region. There are some practical
problems concerning the micro fabrication and operation of the device [36].
A.2.1 Principles
Electrochemical micro-actuator
Electrochemical micro-actuators have been used in medical research. The
electrochemical cell contains two electrodes, platinum and copper in a 1molar (1M)
CuSO4×5H2O solution. The platinum electrode is used as the anode and they should
have a relatively large active area because the oxygen gas has to react at the platinum
electrode to form water, when the actuator is in the pressure reduction state. The copper
electrode is used as the cathode and it should be thick enough to ensure the required
lifetime. This particular micro-actuator was developed to adjust the pressure in the eye
A.3 Electrohydrodynamic
“Electrohydrodynamic motion arises when the particle of a polar fluid are subjected to
a strong electric field” [35].
Electrohydrodynamic motion generates a fluid pressure and creates a flow or fluid
circulation. Electric force induces flow in dielectric fluids, which alternates in 3-phase
wave (positive, negative, neutral). They are often simple in design and are produced to
provide direct conversion of electricity to flow of fluid. These devices do not require
much maintenance, because of few moving parts. Drawbacks concerning
electrohydrodynamic actuators are low power density and low current, but they require
high operating voltage. The maximum efficiency is medium and they have medium
speed in comparison to other technologies [35]. Electrohydrodynamic actuator operation
is greatly influenced by the electric properties of the fluid. They can produce a high
volume of flow in comparison to piezoelectric or thermally driven pumps. They can also
be used as a driver for pumps to move other types of fluid inappropriate for
electrohydrodynamic flow.
For instance, this technology is used as motive power in submarines, to avoid the noise
of rotating propellers, by pumping huge quantities of seawater through special tubes
[35]. Another application is in the micro region, where an ethanol pump has been
developed with grids charged by etched silicon [35].
A.4 Electromagnetic
“Electromagnetism arises from electric current moving through a conducting material”
Electromagnetism is one of the four known forces in nature. Electricity and magnetism
were long seen as separate phenomena. It was not until the 19th century that they were
treated as different types of the same electromagnetic field. The motion of a charge
carrier, like an electron, will cause an electromagnetic field as a property of space. In
contrast to a stationary charge, that will only produce an electric field in the surrounding
space, if the charge is moving a magnetic field is also produced. If the magnetic field is
changing an electric field can be produced. The lines of magnetic flux are between and
around a pair of opposite magnetic poles. Equation (A.1) is Lorentz Force Law for
contribution of electric and magnetic forces.
r r
F = qE + qv × B
An electromagnetic actuator has many benefits, such as extreme positioning accuracy
that is independent of load or velocity. The scope of this thesis covers linear
electromagnetic actuators.
Electromagnetic actuators have many advantages, such as they can generate attractive
and repulsive forces, and in some principles is the force in proportion to input current.
They have usually quick responses, high efficiency, wide bandwidth, and large
displacements. The mayor reasons that have done this technology so successfully are
because it is well-used and often cheaper than other alternatives.
Some drawbacks with electromagnetic actuators are that they have an upper temperature
limit and they are difficult to miniaturize. There are two ways to create the magnetic
field, by use of a permanent magnet or an electromagnet. When an electromagnet is used
instead of a permanent magnet, the difference is increasing dimensions and a continuous
power loss. Disadvantage of permanent magnets is the upper temperature limit of 200
degrees and its cost. Usually costs are only initial investment, which are compensated
very quickly by the advantage of lower losses. The wire manages temperatures up to
approximately 180 degrees depending on which material is used in the conductor
according to Compter [55]. According to Sjöstrand [59] engine mounts will be exposed
to ambient temperatures of 90 ºC continuous and 110 ºC short duration. (Engine
overheating in driving up a steep hill.)
This technology was selected to be more investigated, because it is commonly used and
has good characteristics that match with our requirements for use in an active engine
mount. We are especially interested in the voice coil principles.
A.4.1 Principles
Voice Coil – Moving Magnet
Unlike a solenoid, a linear actuator produces a constant force regardless of actuator
position. Some advantages that are often stated with a moving magnet are higher forces,
no frictional wear, by design, and the structure can utilize heat sinking more effectively.
A voice coil with moving coil or moving magnet can be chosen if the actuator fulfills
certain requirements. These requirements are:
In an actuator built on the voice coil principal: with a single coil, force is proportional to
current and the force is generated in one direction. Furthermore, it is friction-free (noncontacting action) and the force is bi-directional and hysteresis-free.
If it is important that the moving mass is low, select a moving coil and if better heat
transfer is a desirable effect, chose a moving magnet instead.
Voice Coil – Moving Coil "Loudspeaker"
The loudspeaker is the most commonly used linear motor, thanks to good characteristics
such as high forces and good displacement. It is well-tested and often cheaper than other
alternatives. This principle produces the fastest actuators in electro-mechanics, according
to Compter [55]. Voice coils are capable of moving an inertial load at extremely high
acceleration. Voice coils are used, for example, in audio speakers and computer disk
Suppliers often call a more robust voice coil a shaker, but that is the only difference
between them. The voice coil consists of a coil of wire, suspended in a fixed radian
magnetic field. The force provided by the actuator is proportional to the current flowing
through the coil, with the assumption that there are no interactions between the coil
The performance of the voice coil is limited by displacement, moving mass, the total
mass of the voice coil, thermal power of the coil and stress safety factor of the armature
[12]. The coil resistance increases with temperature and slightly with frequency and coil
inductance depends on frequency.
Reaction Mass Actuator
Reaction mass actuator consists in essential terms of a mass suspended on a spring that is
driven by an electromagnetic circuit [14]. The suspended mass is constituted either by
the magnets and supporting structures or the coil itself.
The Slide Motor
This principle is used in some CD players for moving the laser and the lens actuator in
the radial direction of the disc [13]. The moving part is the copper coil. In a CD player
two parallel shafts are used to guarantee guidance.
Linear Motor, Long Stroke
This concept is based on moving magnets and a stationary coil. This principle achieves
positional accuracies of 100 nanometers and better, therefore this principle is used in
exposure machines for IC production [13].
Short Stroke Linear Motor
Draw magnets are the cheapest alternative for short stroke linear motors, as described
further in [13]. They are typically used in doorbells. Draw magnets always have nonlinear behavior between the force and the current. These actuators are not suitable for
servo applications [13].
Micro-actuators are becoming a growing field of interest. Their applications range from
low-force actuators, such as optical mirrors or magnetic printing systems, to large-force
actuators, such as motor relays and valves. As there is a demand for actuators with large
displacement and large force, in particular for applications like microrelayes, a magnetic
actuation principle has been chosen. Different approaches for the magnetic actuation of
micro-relays have been evaluated, such as magneto-thermal and electromagnetic with
magnet or without magnet.
In some way electromechanical as technology can include many other technologies, but
when using electromechanical we think of the use in a gearbox or other structure that are
used to transmit motion. This technology is one of several different types commonly
used in power-by-wire actuation [34]. In comparison to other solutions, they can be more
efficient, smaller, lighter, stiffer and more complex, because of the absence of an internal
hydraulic system.
A.5 Electrorheological and Magnetorheological
“If fluids are exposed to an electric field there are going to be some changes in their
rheology, i.e. viscosity or flow rate” [35].
With special structures, a device can be successfully built so that changes in rheology
generate or control fluid motion. According to [35], in an electrorheological fluid
subjected to an electric field, the particles can react in the millisecond range. The
particles are lining up and causing the fluid to be thicker or even non-flowing. These
devices are usually not used in micro regions. When this technology is used in an
actuator it results in medium efficiency and includes few or no moving parts.
Electrorheological actuators can be found in semi-active hydraulic systems.
The drawbacks with electrorheological fluids are some problems that in the worst case
can lead to device failures. Water-based fluids can develop thermal runaway problems if
they are not adequately cooled: thermal stresses can dry out the working fluid, and low
temperatures can cause problems, especially around the fluid's freezing point [35].
The viscosity characterizes an electrorheological fluid with mechanical tension as a
parameter. It will be affected by an electrical potential, where the change in viscosity is
proportional to electrical field strength. Electrorheological fluid is a collection name for
several different substances, but the most common construction is a polar polymer
suspended or pulverized in a fluid with the same characteristics as oil.
One variant of an electrorheological fluid is magnetorheological fluid. It functions in a
similar way to the electrorheological fluids, but the difference is that it reacts on a
magnetic field instead of an electric. There are some commercial products that use this
type of fluid. The flow rate is controlled by the strength of a magnetic field.
This technology is not presently suitable for active vibration control, because it is not
sufficiently tested, generates weak forces and is sensitive to ambient temperatures. But
one idea is to use this technology in cooperation with another technology, like a hybrid
actuator, to use the benefits of both. According to laboratory results this technology has
good potential to accomplish great things in this area if the quality of the fluids can be
A.6 Electrostatic
“Electrostatic charge arises from a build-up or deficit of free electrons in a material,
which can exert an attractive force on oppositely charged objects, or a repulsive force
on similarly charged objects” [35].
When two objects have different electrical charges and are located near each other, an
electrostatic field exists between them. There also exist electrostatic fields around any
single electrically charged object with consideration to its surroundings. Metallic objects
block electrostatic fields, unlike magnetic fields, which can pass through most metals.
According to [21], the attractive force between two conductive plates with unlike
charges (Coulombic force) is:
U 
FN = ⋅ ε ⋅ A ⋅  
The strength of the field depends on the gap size as well as surface roughness.
Electrostatic actuators are affected very little by ambient temperatures and they are
highly efficient in actuation, because of their extremely low current consumption.
This technology is better than electromagnetic in smaller dimensions [55]. Electrostatic
actuators are suitable for active vibration control, but there are not as many commercial
products as electromagnetic ones for purposes other than micro and nano regions.
A.6.1 Principles
The parallel plate capacitor
In micro-electromechanical systems, or MEMS technology, this principle is used
commonly and is very basic: consisting of two parallel plates (capacitor). The lower
plate is fixed, while the upper plate can move. To simplify the expressions we first
assume that the electrical field is uniform between the plates of the capacitor, and zero
A.7 Electrostrictive
Electrostrictive materials are deformed when they are exposed to an electric field.
Strain sensitivity is affected by ambient temperature. Commercial actuators exist in
small regions: typically micro regions [21]. The usual principles are crystal stack design
and polymers.
Electrostrictive actuators can be suitable for active vibration control, but they can in
some instances be too costly [22]. They produce small displacements, which can limit
the possibilities. The strain is sensitive to ambient temperature.
A.8 Hybrid – combination of two or more Technologies
Hybrid actuators are actuators that are built of two or more different technologies in
Sometimes it is possible to merge two or more technologies together to utilize
advantages of each technology. It may be interesting to use piezoelectric, electrostrictive
and magnetostrictive materials together with other technologies to enlarge the strain. For
instance hydraulic has been successfully used together with piezoelectric.
A.8.1 Principles
According to Anderson, Linder and Regelbrugge [38], piezoelectric and closed hydraulic
systems have been produced with large displacement and high force capacity.
Electrostatically-driven Phase Change Actuator
Electrostatically driven phase change actuators can produce large displacement and, at
the same time, high forces [16].
A.9 Hydraulic
A definition by example: a rod is forced to move because the pressure is higher on one
side of a plate attached to it than on the other side.
In constructing a hydraulic actuator is it important to try to minimize the power loss of
transmission of the fluid, through reducing the mass flow of the fluid and reducing the
frictional drags.
Semi-active hydraulic devices are filled with fluid, typically ethanediol: often divided in
two or more different chambers that are connected through channels. These channels
have an adjustable area of opening controlled by servo-valves. The damping
characteristic of semi-active hydraulic actuators with a flow through the adjustable
channels changes because the friction in the channels depends on the adjustable opening
Hydraulic actuation is the technology most often used in the majority of the earth
moving equipment. It is used, for instance, in brakes (sometimes together with
pneumatic), steering and implements for excavators implements.
Hydraulic actuators exist that are successfully used in active vibration control for
frequencies below 100 Hz [15]. They generate high forces and large displacement, but
they can be slow in response time and usually have low bandwidth.
A.9.1 Principles
Electrohydrostatic actuators are used in power-by-wire actuation, together with several
other types of actuators [34]. This principle is based on a reversible, electrically driven
pump motor to directly pump self-contained hydraulic fluid to a piston. This drives the
ram in the same fashion as a standard hydraulic actuator. They tend to be more complex,
larger, heavier, less efficient and smoother than other devices used in similar
Hydraulic actuator for vibration control
In [15] a fist-sized hydraulic actuator is presented, which can apply forces of several kN
with displacements in the region of millimeters and with a frequency range of up to
approximately 100 Hz. This actuator was developed to meet the requirement to be used
for small displacement and to avoid the disadvantages of hydraulic cylinders that have
some problems with body friction, leakage, extended length and relatively low stiffness
due to large oil volume. To accomplish this they use elastic membranes that allow small
axial movements and also act as a radial guide. The two annular membranes connect the
lower and upper body and give flexibility to the system together with high radial
stiffness. The oil pressures in the two chambers are to be controlled by servo-valves.
To obtain some specific requirements, such as maximum force, pressure, displacements
and outer diameter the parameters that should be changed are membrane thickness and
inner diameter this will also affect maximum stress in the membranes.
A.10 Magnetostrictive
“Magnetostrictive materials exhibit very small but strong shape changes when subjected
to magnetic fields” [35].
James Prescott Joule first discovered magnetostrictive materials in the 1840s. He noticed
that changes in magnetism affected the length of iron, this phenomenon he named the
Joule Effect (magnetostriction). The phenomenon magneto-mechanical effect (Villari
Effect) refers to the change in magnetic energy when a magnetostrictive material is
stretched or compressed.
These materials give new possibilities in the development of components with high
density, rapid reaction time and extremely good precision. Typically, magnetostrictive
rod is placed inside a coil to be activated by an external magnetic field, changing the
shape of the core [35].
Typical magnetostrictive materials include combinations of rare earth elements with iron
such as TbFe (Terfenol) and TbDyFe (Terfenol-D). Terfenol-D has been the most widely
used magnetostrictive material. Iron, nickel, cobalt and ferrite are examples of other
magnetostrictive materials.
Under a magnetic field these materials offer less then 0.15% strain. Advantages of this
technology are that these types of actuators can be used in high frequency and high
precision applications and have a long life. But the actuators are quite complicated, both
in mechanical and electrical construction. That is because a magnetic coil is required for
control of the driving magnetic field. One other major drawback is the need for a large
bias field. That implies the use of heavy permanent magnets. [30] The conclusion is that
this type of material can be used, but the drawback is the need for a large magnetic field
that can be complicated to create.
A.11 Phase change
“Phase Change systems use the dimensional changes, like expansion and contraction,
which occur in materials as they undergo changes between phases, such as solid, liquid
and gas” [35].
Device can be built which harness the forces exerted by the phase changes, and they
generally demonstrate full reversibility. Depending on the material, a phase change may
be induced electrically, thermally, or ultrasonically, and may happen over a wide range
of speeds and pressures.
Commercial thermal phase change actuators exist in micro-region and in MEMS
A.12 Piezoelectric
Piezoelectric ceramics generates an electric charge when mechanically deformed.
Conversely, when an external electric field is applied to piezoelectric materials they
mechanically deform.
Even though piezoelectricity can be found in several types of natural materials, most
modern devices use polycrystalline ceramics such as lead-zirconate-titanate (PZT). PZT
is the most commonly used piezoelectric ceramic since its discovery for more than 40
years ago.
There are ranges of piezoelectric actuators: high-voltage and low-voltage piezos.
Piezoelectric devices show good resolution and are used commonly as both actuators and
Basic piezoelectric modes are thickness expansion, thickness shear and face shear.
According to Compter [55], one successful application for piezoelectric actuators has
been to drive a system of an electron microscope of FEI, where magnetic fields are not
Hydraulic mechanisms can be used to enlarge the displacement. For example, a
piezoelectric multilayered stack actuator acting on a diaphragm that forces a fluid (non
compressible medium). The diameter of the rod is smaller than the diameter of the
diaphragm. A force is thus been converted into displacement.
We can not discount piezoelectric as an interesting technology. Most commercial
applications today are based on electromagnetic or piezoelectric principles. They can
exert high output forces, very quick responses, often linear to charge and they are highly
efficient. The drawbacks with piezoelectric actuators are that they are hard to attach,
expensive, hysteresis and have unknown lifetime [55].
A.12.1 Principles
Amplified Piezoelectric Actuators (APAs)
Amplified piezoelectric actuators consist of stacks that are pre-stressed inside a steel
elliptic frame, which produces a natural amplification ratio of the displacement (between
2 and 5 according to the two axes ratio) [5]. This principle will obtain deformation
between 0.3 and 3 percent with only a slight decrease of the force capability. Other
piezoelectric principles have strokes about 0.1 percent of their total length.
Two independent flat piezoelectric elements, stacked on top of each other. By driving
one element to expand while contracting the other one, the actuator is forced to bend,
creating an out-of-pale motion.
Disk bender
Disk benders consist of two piezoelectric disks separated by a central electrode and two
electrodized external surfaces. The whole sandwich is poled in one direction and can be
operated in different ways, depending on how the voltage is applied.
They appear to represent an ideal solution for many applications with demanding space
conditions. A major drawback is that disk benders are usually quite expensive because
the fabrication method requires the cutting of two thin piezoelectric disks from a ceramic
A new low-cost disk bender was recently developed and shows very little difference
from standard disk benders.
Work on the inverse piezoelectric effect, the PZT (lead-zirconate-titanate) material is
used. Applying voltage causes the material to expand.
The Moonie consists of a piezoelectric disk with electrodes and two metal caps glued on
the surface. By shrinking the disk the caps are forced to bend.
Multilayered Stacked
Actuators of this kind show quite large displacements, in the range of 10-300 µm, with
large blocking forces, up to several kN, and quite low driving voltages. The mayor
drawback is that these actuators are complicated to fabricate and therefore expensive.
The rainbow is a piezoelectric disk such as lead-lanthanum-ziconate-titanate (PLZT)
with one of the two faces of the disk reduced.
A.13 Pneumatic
Differences in pressure of air or gas in these devices create force.
Pneumatic can establish a counterforce without any energy consumption. Pneumatic
actuators are similar to hydraulic actuators, but they use another medium. There are
some problems with friction like the ones with hydraulic actuators. Pneumatic actuators
are very common in level-regulation systems.
A.14 Pyrotechnical
Explosive and pyrotechnic devices transforms a small input of mechanical or electrical
energy into a higher level of mechanical or thermal energy that is applied to perform
practical work on a one-time basis.
Some companies, such as Hirschmann, supply ignition units for pyrotechnical actuators
in restraint and safety systems in the car. This is accomplished by releasing the stored
energy in an explosive or pyrotechnic mixture through a precisely controlled reaction.
Actuator devices transform pyrotechnical-generated energy into motion to perform work
against an external load.
There is no information about this technology used for active vibration control, and that
is understandable because its use is on a one-time basis.
A.15 Shape Memory
Shape Memory effect arises in some unique metal alloys that change form with
temperature, but "remembers" the original shape and when it is cooled it reverts to its
original shape (cycle as figure below) [35].
The term shape memory refers to the ability of certain materials to cancel its deformation
and recovers its predefined or "imprinted" shape. The SM effect is based on a solid-solid
phase transition of the shape memory alloy that takes place within a specific temperature
interval [9].
These materials are best suited for heating through the phase change. Creating phase
change through heating is only possible after "education" of the material. And the
difficulties of cooling must be solved. These types of actuators can only be used in lowfrequency and low-precision applications [30]. We have only found Shape Memory
actuator solutions in the micro region. The conclusion is that SMA-actuators are not
suitable for active vibration control [30].
A.15.1 Principles
SMA - Shape Memory Alloy
Nickel Titanium is a widely used alloy. This principle is used more commonly than
SMP. Memory metals are another name for Shape memory alloys. The function of
memory metals is similar to piezoelectric elements, but the difference is that they react
to changes in temperature. This characteristic implies that after the metal has been
deformed it can recover to its original form if it warms up. The process that changes the
form is a thermo-elastic martensitic transformation. The most common memory metals
are Zn-Al, Cu-Al-Ni and Ni-Ti alloys. Memory metals have big advantages, as they are
small and not sensitive to environmental influences apart from temperature. A control
signal can be put direct into the material without transformation to or from digital form.
There exist so-called Giant magnetostrictive materials (GMM), which are in competition
with piezoelectric ceramics, but they are commonly used in specific applications such as
low voltage actuators, large force actuators, high power low frequency sensors and space
cryogenic positioning.
SMP – Shape Memory Polymer
Shape memory polymers are not based on the same physical principles as shape memory
alloys, even though they have similar names. They are thermo-elastic polymers, which
undergo a glass transition; their viscosity becomes low at high temperatures (rubber
state) and increases as the temperature decreases. Consequently, when the temperature is
sufficiently low, the viscosity becomes high enough to make the polymer stiff. This
condition is called the glassy state.
This principle has been utilized as an actuator by squeezing the polymer into a very
small volume at high temperatures, and then lowering the temperature while maintaining
the pressure bringing the polymer to the glassy state. The polymer remains compact
when the pressure is removed. When the actuator is exposed to high temperatures the
polymer strives to return to its initial value and the polymer restores its original shape. In
[11] can the amount of exploitable motion of this actuation technique can be very high
up to 4000% since the polymer can be squeezed into a very small volume. As long as
there is no built-in squeezing system, this device can only be used once.
A.16 Thermomechanical
Thermo mechanical systems use the physical expansion or contraction that occurs in
materials as they undergo temperature changes within their phase (solid, liquid or gas)
Thermomechanical materials change their dimensions with temperature. To avoid
undesirable changes in temperature in the surroundings, the materials may be forced to
be isolated. In micro devices the characteristics of usefulness and speed of a
thermomechanical actuator change radically. To re-establish the previous condition, the
heat must be removed in some way.
A.16.1 Principles
Bimetallic cantilever
A bimetallic cantilever is a micro actuator using gold on silicon with a beam length of
500 micrometer, producing deflections of up to 100 micrometers while using about 200
mW of power. A 200 micrometer long thermally activated cantilever beam made only of
silicon, silicon oxides and phosphorous doped silicon - standard elements of CMOS-type
electronic circuits - produced a displacement of 4 micrometers and operated at a
frequency of over 1 kHz [35].
Appendix B
B.1 Accelerometers
There are two main types of accelerometers, which measure either translation
accelerations or angular accelerations. Most of the translation accelerometers belong to
the category of seismic instruments, which implies that the acceleration is not measured
in proportion to a reference point [4]. Accelerometers can be either mechanical or
electromechanical devices. Further, the electromechanical accelerometers can be
classified as variable resistance accelerometer, variable inductance accelerometer,
piezoelectric accelerometer, piezoelectric transistor and servo accelerometer [4].
There are several kinds of accelerometer that are based on rotation. In one kind the
damping fluid functions as a seismic mass, and during rotation acceleration of the fluid
is relative to the chamber creating a pressure on two symmetrically placed vanes. This
pressure is a measure of the rotation acceleration.
B.1.1 Design alternatives - piezoelectric accelerometers
There are a few different types of piezoelectric accelerometer, which harness one of
three effects: length, side and shear. The following sections B.1.1.1, B.1.1.2 and B.1.1.3
present examples of different designs of piezoelectric accelerometers, which utilize each
one of the three effects.
B.1.1.1 Compression-based design
A piezoelectric sensor of the compression type consists of a seismic mass, piezoelectric
crystals and a pre-stressed spring washer, see figure B.1. This type of design harnesses
the length effect of piezoelectric materials, shown in sub-chapter 3.1. The pre-stressed
spring washer presses the movable mass towards the piezoelectric crystals. To improve
the sensitivity two piezoelectric crystals are often mechanically connected in series.
Figure B.1 Piezoelectric sensor based on compression (side view).
When a piezoelectric sensor of the compression type is subjected to a sine curve
vibration along the direction of the symmetry axis (y), the voltage per frequency output
will be as shown in Figure B.2. The figure shows the bandwidth of the piezoelectric
compression accelerometer between the frequencies f1 and f2. In the figure, two cut-off
frequencies appear. The upper cut-off frequency is determined by the seismic system and
the lower cut-off frequency depends on which system that is used. It originates either
from leakage resistance by voltage amplification or from the time constant of the charge
amplification. The frequency f0 is the natural frequency of the seismic system, and
because the internal spring rate is really high the natural frequency in general is going to
be 10 kHz or higher.
Figure B.2 Output voltage of a piezoelectric compression accelerometer with sine
curve vibration.
The force that will affect the crystals becomes a linear function of the acceleration of the
moving part relative to the fixed part, since the crystals deform elastically. The output
voltage becomes proportional to the oscillatory movements of the movable mass if the
frequencies are low compared to the natural frequency, see equation B.1.
1 d 2s
ω 02 dt 2
Here l is sensed by its position, which is proportional to the acceleration of the test
object. The sensor is sensitive to accelerations at low frequencies if the damping ratio is
ζ ≈ 0.7, see [5, 33]. This is not the case with this piezoelectric sensor since it does not
have any damping material [5]. Manufactures typically give the bandwidth (operating
range) for the sensor instead of the damping ratio.
B.1.1.2 Shear-based design
When compression-based piezoelectric sensors are mounted on a frame that is subject to
bending stress they can be compared to force sensors, because the bending stress is
mistaken for acceleration by the crystals. This is one reason why the shear-based
piezoelectric accelerometer was developed. In contrast to compression types, it can sense
the acceleration component, which is perpendicular to the symmetry axis. It senses
acceleration in the symmetry axis direction. This design harnesses the shear effect of
piezoelectric materials. Figure B.3 shows that the crystals are mounted free from the
bottom of the housing, this makes the sensor insensitive to bending stress of the frame.
The crystals are held in place by two half-moon seismic masses and a clamping ring
(pre-load ring). During acceleration the crystals are subject to shear stress forces, and
charge is created by the transversal component of the shear stress. In new developed
accelerometers is the majority design based on shear effects
Figure B.3 Side view and top view of a piezoelectric sensor based on shear effects.
B.1.1.3 Bending-based design
Piezoelectric accelerometer designs based on bending utilize beam-shaped sensing
crystals, which are fixed in one end, with the other end having a seismic mass that
create strain on the crystals when the mass is accelerated. Bending-based design
harnesses the side effects of piezoelectric materials. The upper and lower parts of the
carrier beam, respectively, are subjected alternately to compression and expansion
effects, which is the same as the piezoelectric side effect. This design offers a low
profile, light weight, and a competitive price. Generally, bending-beam designs are well
suited for low frequency and low acceleration applications. They are sensitive to very
high acceleration, high amplitude and high frequencies. Figure B.4 gives a basic layout
sketch of a piezoelectric sensor based on bending design.
Figure B.4 Piezoelectric sensor based on bending (side view).
Comparison between the piezoelectric accelerometer designs compression, shear and
bender has been carried out through study [31] and are stated in table B.1.
Table B.1 Comparison between different piezoelectric accelerometers based on
different designs
+ high sensitivity-tomass ratio
+ robustness
+ technological
- high temperature
transient sensitivity
- high base strain
+ low temperature
transient sensitivity
+ low base strain
+ best sensitivity-tomass ratio
- lower sensitivityto-mass ratio
- fragile
- relatively high
transient sensitivity
B.1.2 Other accelerometers
The purpose of this section is to present other types of accelerometer than piezoelectric,
even though piezoelectrics are used more commonly than others.
B.1.2.1 Servo accelerometer
Servo accelerometers consist of an electromechanical servomechanism, which holds a
mass fixed in a certain position when the device is accelerated. Consequently, the force
that is consumed is a measure of the acceleration. Some servo accelerometers can
measure up to 100 g [4].
B.1.2.2 Variable inductance accelerometers
Actually, these sensors measure velocity, but can be modified to be sensitive for
acceleration [5]. The measuring instrument is supported by weak springs. Therefore, the
natural frequency of the system is low, at about 10 Hz. The system is an electrodynamic
type, having a limiting coil (copper ring) that moves in the field of a permanent magnet,
thereby inducing damping eddy currents. The damping ratio ζ becomes 0.5-0.7.
Deflections of the moving part will be in proportion to the measured velocity. The output
voltage is proportional to the velocity. Variable inductance accelerometers are
characterized by comparatively low natural frequency. The measured capacity can be as
high as 50 g with high output voltage, which means that the requirement for
amplification falls away [4]. Other information [5] specifies the upper limit of
acceleration and amplitude of oscillation to be approximately ± 10g and ± 1mm. They
exist in different sizes.
B. Geophone
The geophone is nowadays only used in investigation of vibrations associated with
blasting operations. In these applications it is generally of no importance that the sensor
responds to velocity, because it is often compared to standard specifications and
empirical values, and these values can also be based on velocity.
B.1.2.3 Variable resistance accelerometers
A variable resistance accelerometer is constructed on the principle that the electrical
resistance of the conductor is a function of its dimensions. When these dimensions
mechanically change at the same time as a constant electrical current flows through the
conductor the voltage will vary over it. The change in voltage is in proportion to the
mechanical change in dimension. They are often used to measure sluggish processes, for
instance to measure the acceleration of vehicles such as aeroplanes [5].
B.2 Microphones
Microphones can be used as sensors that can enable a system to be optimized by noise.
There are sensors that react to sonic waves. They consist of a diaphragm that interacts
with the waves. When the diaphragm moves in a condenser microphone the electrical
potential changes due to energy changing in an electrical field when one plate of the
parallel plate capacitor is moving. The fixed plate is loaded by voltage supply.
B.3 Optical Sensors
Optical sensors are used to measure velocity, amplitude or position in relation to a
reference point. One kind of optical sensor is based on fibre optics. Optical sensors can
be used to measure rotation vibration.
B.3.1 Photoelectric cells
B.3.1.1 Distance measuring
Position is often measured with a sensor that consists of photoelectric cells, a source of
light, and a movable glass plate furnished with alternating black and transparent fields
according to a certain system. When the glass plate moves light will be allowed to pass
through it to the photoelectric cells that have a transparent field between them and the
source of light. The photoelectric cells have two possible conditions, which give the
signal 0 or 1. By combining several photoelectric cells binary numbers are generated,
which correspond to a certain distance to the reference point, see figure B.5.
Figure B.5 Binary and Gray code that corresponds to 24 = 16 possible distances
(four photoelectric cells are used).
To get the correct binary number go from left to right. One problem with this technology
is how to code the different states, if regular binary numbers is used the result is that a
big change in the binary number shaping will affect the output only a minor amount.
This can give rise to disproportionately large faults, and because of this Grey codes are
commonly used when the plate changes sectors.
B.3.1.2 Amplitude measuring
For optical measuring of vibrational amplitudes a sensor is often used consisting of two
plates with thin lines engraved. One plate is fixed and the other one is attached to the
body whose movement is going to be measured. The two plates are moving relative to
each other and at the same time the amount of light that will pass through the plates is
changing: in the ideal case as a sine curve. These changes can be read off by a
photoelectric cell, which generates an output signal. A bigger output can be measured
through calculating the number of crests.
B.3.2 Optical fibre
Thanks to inner reflections, optical fibres have the ability to enclosure a light beam
inside the fibre. There is a distance and time difference between a straight fibre and a
curved fibre when a light beam is travelling through it, because the amount of reflections
is not the same. Therefore, the light beam travels much faster in a straight fibre than in a
curved one, and thus time displacement can be measured as a phase displacement
compared to the straight fibre. Unfortunately the phase displacement is not in proportion
to the deflection, so the fibre sensor must therefore be calibrated along the length of the
B.3.3 Laser
Only recently have laser sensors been used to measure direct displacement and velocity
on the surface: such sensors utilize the Doppler Effect. The lasers rely on not-contacting
the vibrating surface and they measure the phase difference between an internal
reference and the measurement beam that has been reflected to the surface. Polytec has
developed lasers that measure on rotating surfaces at speeds of 30 m/s and at frequencies
of 30 MHz.
Advantages with lasers based on Doppler Effect are insensitivity to ambient light, long
measuring ranges, measurement on any target surfaces, high resolution and repeatability.
They use high measuring frequency and permits measurement on hot, miniature or soft
surfaces, and even under water.
There are also laser sensors that measure distance through optical triangulation. HeliumNeon is a common low-power laser that is eye-safe class 2, which can operate at
distances of hundreds of meters.
B.4 Force Sensors
When piezoelectric force sensors are subjected to a stress, they produce a charge that is
proportional to the force. In force sensors, quartz is commonly used, because it has good
mechanical properties, good resistance to high temperature and the resistively is very
high. Furthermore, the piezoelectric effect becomes free from hysteresis, has
extraordinary linearity and is insignificantly dependent on temperature. They are well
suited for high precision in the nanometer range and have been used in ultrasonic
The piezoelectric polymer polyvinylidene fluoride (PVDF) has been used in force
sensors. PVDF is a flexible piezoelectric material, which produces a current proportional
to extension. This material is a polymer (semi-crystalline) with high polarity, which can
be attached to almost any surface. The characteristics of the material are dependent on
the ambient temperature. Pyroelectric application with PVDF films has been used in
thermometers. Piezorubber (PZR) is a flexible composite material (polymer) that
consists of lead titanate particles embedded in a neoprene elastomeric matrix. The U.S.
Navy has tested PZR in hydrophones. Neither PVDF nor PZR is piezoelectric naturally,
but they have been polarized in the manufacturing process by exposure to a strong
electric field during cooling down from a high temperature.
Appendix C
Max energy density comparison between different technologies is a good measure when
the objective is to compare micro actuators. In literature there exist many different
values of maximum energy of density at a specific volume or weight, depending on the
estimated conditions. The estimated conditions are obtained through a study of relevant
material and estimation. According to [61], the max energy of density is 0.025 J/cm3 for
electromagnetic to compare with 0.015, >5 and >0.1 J/cm3 for electrostatic, Shape
memory alloy and piezoelectric ceramic. Other literature has mentioned that the max
energy of density of SMA is 10 J/cm3.
Max Energy Density formulas
Estimated conditions
Approx. (J/cm3)
2 ⋅ µ0
B = magnetic field
µ0 = magnetic permeability
B = 0.1 T
ε0 ⋅ E2
~ 0.1
E = electric field
ε0 = dielectric permittivity
E = 5 V /µm
Y ⋅ (d 33 ⋅ E )
E = electric field
Y = young's modulus
~ 0.2
E = 30 V/µm
Y = 100 GPa
d33 = piezoelectric constant
d33 = 2⋅10-12 C/N
According to literature
5 - 10
Y ⋅ (α ⋅ ∆T )
α = coefficient of expansion
∆T = temperature rise
Y = young's modulus
α = 3⋅10-6 /ºC
∆T = 100 ºC
Y = 100 GPa
According to [35], high work output density the different technologies are compared:
Phase change
Shape Memory
Work output density
Very high
Very high
Appendix D
The purpose with this appendix is to more easily understand the possibilities and
restrictions of certain actuator requirements for existing commercial actuators of
electromagnetic and piezoelectric technologies. First, electromagnetic technology is
introduced and the possibilities are stated. This is following by detailed information
about different electromagnetic actuators from different suppliers.
Finally, piezoelectric technology and detailed information about commercial
piezoelectric actuators from different suppliers are presented.
Strengths/ Weaknesses
Displacements (%)
Maximum Pressure
Frequency Range (Hz)
Response Time (ms)
Relative Speed (full
Maximum Efficiency
Need of Voltage (V) /
Current (A)
• Very fast operating speeds
• Extreme positioning accuracy
• Scale ability
• High degree of efficiency
• Have an upper temperature limit (≈180ºC)
• Performance is primarily limited by the properties of the
material used in constructing the actuator
• Difficult to build small electromagnetic coils
• The most devices require perpendicularity between the
current conductor and the moving element
• Simply on/off control but relatively limited functionsusually only lift and not lift states available
See Appendix A and Chapter 2 for more detailed
Extremely high
<< 1 Theoretical [35]
Fast [35]
> 901
Dependent on relative size and principle
From micro/nano region and bigger
Depend on the force that is required. Permanent magnet
instead of electromagnet increases the weight.
Most of them have low costs.
Magnetic actuators are perhaps among the oldest types of
actuators. Magnetic actuation methods offer the possibility of
generating repulsive forces in addition to attractive forces.
Voice coils can be built with a max specific work of 30 J/kg
and up to 70 kHz (Ref.).
Extremely high
(Voice coil) These values are based on an array of 0.01 m thick voice coils,
50% conductor, 50% permanent magnet, 1 T magnetic field, 2 ohm-cm
resistivity, and 40,000 W/m2 power dissipation (http://ndeaa.jpl.nasa.gov/nasande/lommas/eap/actuators-comp.pdf)
Products Names
Max Displacements
Maximum Force (N)
Frequency Range
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Other characteristics
Nominal Impedance
Max Velocity (m/s)
Moving Mass (g)
Voice coil – moving coil (Shaker)
Data Physics Corporation
DP-V002 DP-V004 DP-V009 DP-V011 DP-V016
More robust than ordinary voice coils. The created force is
in proportion to the current. The actuator is limited by, for
example, displacement, moving mass, thermal power of the
coil and stress safety factor of the armature.
DC-7000 DC-7000 DC-7000
2.7 A
3.8 A
5.5 A
5.5 A
5.5 A
The coil resistance increases with the temperature and
slightly with the frequency. The impedance depends on the
1 Optional displacement
2 Peak force for sine instead of random
Products Names
Max Displacements
Maximum Force (N)
Frequency Range
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Reaction Mass Actuator (RMA)
Counterforce vibration control
CSA Engineering, Inc.
CSA have also two smaller actuators than SA-10, they are
SA-1 and SA-5.
Moving Element
1 The actuator have diameter instead of length and width.
Products Names
Max Displacements
Maximum Force (N)
Frequency Range
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Moving Mass (g)
1 Peak to peak, continous
Voice coil – Moving Coil (Shaker)
VP 5
• Low static support
30 A rms, max
80 A rms, max
Height: 260.9, diameter:
50 000
Height: 500.1, diameter:
234 000
The standard VP 5 will support a static load of 1.8 kg. For
heavier loads, up to 23 kg an additional load support system
may be fitted. Designed for testing of small components,
subassemblies and modal testing of large complex structures.
The VP 5 can be configured to perform “back-to-back”
calibration of piezoelectric accelerometers. Rated ouput sine
force is 222 N. Air cooled by suction type remote centrifugal
Products Names
Max Displacements
Maximum Force
Frequency Range
Frequencies (Hz)
Stiffness (N/µm)
Response Time
Efficiency (%)
Need of Voltage (V)
/ Current (A)
Size (H/L/W) (mm)
Weight (g)
Accuracy (µm)
Voice Coil – Moving Magnet
H2W Technologies, Inc.
NCM08-15-025-2 NCM02-05-005-4X
Smaller stroke than
It is a compact linear
driven actuator that
The low moving
can be controlled
mass allows high
like a servo motor.
acceleration of light
5 µm repeatability
Diameter: 38.1
NCM08-15-025-2 LB has a max acceleration of 20g.
The voice coils have very low electrical and mechanical time
Strengths/ Weaknesses
Displacements (%)
Maximum Pressure
Frequency Range (Hz)
Response Time (ms)
Relative Speed (full
Maximum Efficiency
Need of Voltage (V) /
Current (A)
• High stiffness results in isotropic high actuator performance
• Easily controlled
• Provide fast response
• Small dimensions and weight
• Simply driven by voltage
• Maximum strain under electrical field can approach 0.2%
• They can cover a wide range of frequencies
• High precession
• They can hardly be used at very low frequency and at dc.
• Very large force
• Very small displacement
See Appendix A and Chapter 2 for more detailed
Ceramics 0.2, Single Crystal 1.7, Polymer 0.1
Ceramics 110, Single Crystal 131, Polymer 4.8
> 100 kHz
<< 1
Fast [35]
> 90
From 100 V to 1000 V for full extension. Very low current
use (mA).
Depend on the design, from low to very high
The best known and most used piezoceramic, Lead Zirconate
Titanate (PZT), can deliver up to 0.1% strain.
High in closed loop design
Products Names
Strengths/ Weaknesses
Max Displacements
Maximum Force (N)
Frequency Range (Hz)
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Multilayered Stacked
Adaptronics, Inc
• High power efficiency
• Low drive voltage
-20 to 150 V
-20 to 150 V
-20 to 150 V
-20 to 150 V
DPA40, DPA60 and DPA80 have diameter 25.0 mm.
PPA40M exist with less displacement.
Products Names
Strengths/ Weaknesses
Max Displacements
Maximum Force (N)
Frequency Range (Hz)
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Adaptronics, Inc.
• Very large displacements
-20 to 150 V
-20 to 150 V
-20 to 150 V
-20 to 150 V
Response time and resonance frequency for a free actuator.
APA129ML and APA400M exist with less displacement and
higher force.
The moonie consists of a piezoelectric disk with electrodes
and two metal caps glued on the surface. By shrinking the
disk the caps are forced to bend.
Products Names
Strengths/ Weaknesses
Max Displacements
Maximum Force (N)
Frequency Range (Hz)
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Bimorph Stripbenders
Bimorph DiskBimorph Stripbenders without
benders with
Piexomechanik GmbH
BM 300/70/1.5mm
Bimorph have large displacements compared to piezoelectric
plate and multilayered stacked actuator (normally 5-10 % of
total length for strip-benders), quite small resonance
frequency, low stiffness, and low blocking force.
± 1500
± 0.70
± 0.280
± 150 V
± 100 V
± 200 V
They exist with less displacement. Bimorph Strip-benders
exist also with blocking force.
Products Names
Strengths/ Weaknesses
Max Displacements
Maximum Force (N)
Frequency Range (Hz)
Frequencies (Hz)
Stiffness (N/µm)
Response Time (ms)
Maximum Efficiency
Need of Voltage (V) /
Current (A)
Size (H/L/W) (mm)
Weight (g)
Dynamic Spring
Multilayered Spring-like
Adaptronics, Inc
-20 to 150 V
The maximum force for E400P-4 is preload. It exists with less
displacement and less force.
PPA80L exist with less displacement.
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