Vibration Energy Harvesting:
Machinery Vibration, Human Movement and Flow Induced Vibration

49
The electrical tuning method realizes resonant frequency tuning by adjusting electrical
loads. This method consumes little energy as it does not involve any change in mechanical
properties. In addition, it is much easier to implement than mechanical methods. However,
this method normally has a small tuning range.
The suitability of different tuning approaches depends on the application but in general
terms, the key factors for evaluating a tuning mechanism are:
• energy consumed by the tuning mechanism should be as small as possible and must not
exceed the energy produced by the energy harvester;
• the mechanism should achieve a sufficient operational frequency range;
• the tuning mechanism should achieve a suitable degree of frequency resolution;
• the strategy applied should not increase the damping over the entire operational
frequency range.
Energy harvesting from human movement is another important area in vibration energy
harvesting. As human movement is random, linear energy harvesters are not suitable for
this application. Broadband, non-linear or non-resonant devices are preferred. At the
moment, the most common locations on human body for the energy harvesters are feet and
upper body due to large displacement or force produced during movement. Up to date,
some reported energy harvesters successfully produced useful amount of electrical energy
for portable electronic devices. However, consideration needs to be taken to improve design
of the energy harvesters so that they will not cause discomfort for human body.
Furthermore, another potential solution to energy harvesting from human movement is to
print active materials on fabrics, such as jackets and trousers, so that electrical energy can be
generated while human body is moving.
Energy harvesters from flow-induced vibration, as an alternative to turbine generators, have
drawn more and more attention. Useful amount of energy has been generated by existing
devices and the start flow speed has been reduced to as low as 2.5m·s
-1

0946-7076
Beeby, S. P.; Torah, R. N.; Tudor, M. J.; Glynne-Jones, P.; O’Donnell, T.; Saha, C. R. & Roy, S.
(2007). A micro electromagnetic generator for vibration energy harvesting, In:
Journal of Micromechanics and Microengineering, Vol.17, pp. 1257-1265, ISSN 0960-
1317
Bernitsas, M. M.; Raghavan, K.; Ben-Simon, Y. & Garcia, E. M. H. (2006). VIVACE (Vortex
Induced Vibration for Aquatic Clean Energy): A new concept in generation of clean
and renewable energy from fluid flow, Proceedings of OMAE2006 25th International
OMAE Conference, Hamburg, Germany, 4-9 June, 2006
Blevins, R. D. (2001). Formulas for Natural Frequency and Mode Shape, Krieger, ISBN 1-57524-
184-6, Malabar, Forida, USA
Burrow, S. G. & Clare, L. R. (2007). A Resonant Generator with Non-Linear Compliance for
Energy Harvesting in High Vibrational Environments, IEEE International Electric
Machines and Drives Conference, pp. 715-720, Antalya, Turkey, May 3-5, 2007
Burrow, S. G.; Clare, L. R.; Carrella, A. & Barton, D. (2008). Vibration energy harvesters with
non-linear compliance, In: Active and Passive Smart Structures and Integrated Systems
2008, Proceedings of the SPIE, Vol.6928, 692807
Cammarano A.; Burrow S. G.; Barton D. A. W.; Carrella A. & Clare L. R. (2010). Tuning a
resonant energy harvester using a generalized electrical load, In: In: Smart Materials
and Structures, Vol.19, 055003(7pp), ISSN 0964-1726
Carroll, D. & Duffy, M. (2005). Demonstration of wearable power generator, Proceedings of
the 11
th
European Conference on Power Electronics and Applications, ISBN: 90-75815-09-
3, ISBN: 90-75815-09-3, Dresden, Germany, September 11-14, 2005
Charnegie, D. (2007). Frequency tuning concepts for piezoelectric cantilever beams and
plates for energy harvesting, MSc Dissertation, School of Engineering, University of
Pittsburgh, USA
Ching, N. N. H.; Wong, H. Y.; Li, W. J.; Leong, P. H. W. & Wen, Z. (2002). A laser-
micromachined vibrational to electrical power transducer for wireless sensing

Feenstra, J.; Granstrom, J.; and Sodano, H. A. (2008). Energy harvesting through a backpack
employing a mechanically amplified piezoelectric stack, In: Mechanical Systems and
Signal Processing, Vol.22, pp. 721–734, ISSN 0888-3270
Ferrari, M.; Ferrari, V.; Guizzetti, M.; Marioli, D. & Taroni, A. (2008). Piezoelectric
multifrequency energy converter for power harvesting in autonomous
Microsystems, In: Sensors Actuators A: Physical, Vol.142, pp. 329–335, ISSN 0924-
4247
Ferrari, M.; Ferrari, V.; Guizzetti, M.; Andò, B.; Baglio, S. and Trigona, C. (2009). Improved
Energy Harvesting from Wideband Vibrations by Nonlinear Piezoelectric
Converters, Proceedings of Eurosensors XXIII, Lausanne, Switzerland, September 6-9,
2009
Gieras, J. F.; Oh, J H.; Huzmezan, M. & Sane, H. S. (2007). Electromechanical energy harvesting
system, Patent Publication Number: WO2007070022(A2), WO2007070022(A3)
Glynne-Jones, P.; Tudor, M. J.; Beeby, S. P. & White, N. M. (2004). An electromagnetic,
vibration-powered generator for intelligent sensor systems, In: Sensors and
Actuators A: Physical, Vol.110, pp. 344-349, ISSN 0924-4247
Goldschmidtboeing, F. & Woias, P. (2008). Characterization of different beam shapes for
piezoelectric energy harvesting, In: Journal of Micromachining and Microengineering,
Vol.18, 104013, ISSN 0960-1317
Granstrom, J.; Feenstra, J.; Sodano, H. A. & Farinholt, K. (2007). Energy harvesting from a
backpack instrumented with piezoelectric shoulder straps, In: Smart Materials and
Structures, Vol.16, pp. 1810-1820, ISSN 0964-1726
Hoffmann, D.; Folkmer, B. & Yiannos, M. (2009). Fabrication, characterization and
modelling of electrostatic micro-generators, In: Journal of Micromechanics and
Microengineering, Vol.19, No.9, 094001, ISSN: 0960-1317
Huesgen, T.; Woias, P. & Kockmann, N. (2008). Design and fabrication of MEMS
thermoelectric generators with high temperature efficiency, In: Sensors and
Actuators A: Physical, Vol.145-146, pp. 423-429, ISSN 0924-4247
Humdinger Wind Energy, LLC, (accessable on 13 May
2011).

for Optimal Power Generation, In: Smart Materials and Structures, Vol.17, 065026,
ISSN 0964-1726
Liu, F.; Phipps, A.; Horowitz, S.; Ngo, K.; Cattafesta, L.; Nishida, T. & Sheplak, M. (2008).
Acoustic energy harvesting using an electromechanical Helmholtz resonator, In:
Journal of Acoustical Society of America, Vol.123, Vo.4, pp 1983-1990, ISSN: 0001-4966
Lo, H. & Tai, Y. C. (2008). Parylene-based electret power generators, In: Journal of
Micromachining and Microengineering, Vol.18, 104006, ISSN: 0960-1317
Marzencki, M.; Ammar, Y; & Basrour, S. (2008). Integrated power harvesting system
including a MEMS generator and a power management circuit, In: Sensors and
Actuators A: Physical, Vol.145-146, pp. 363-370, ISSN 0924-4247
Matova, S. P.; Elfrink, R.; Vullers, R. J. M. & van Schaijk, R. (2010). Harvesting energy from
airflow with micromachined piezoelectric harvester inside a Helmholtz resonator,
Proceedings of PowerMEMS 2010, Leuven, Belgium, November 30 - December 3,
2010
MicroBelt tech sheet,
(accessable on 13 May 2011)
Mitcheson, P.; Stark, B.; Miao, P.; Yeatman, E.; Holmes, A. & Green, T. (2003). Analysis and
optimisation of MEMS on-chip power supply for self powering of slow moving
sensors, Proceedings of Eurosensors XVII Conference, pp. 48-51, Guimaraes, Portugal,
September 21-24, 2003
Nguyen, D. S. & Halvorsen, E. (2010). Analysis of vibration energy harvesters utilizing a
variety of nonlinear springs, Proceedings of PowerMEMS 2010, Leuven, Belgium,
November 30 - December 3, 2010
Norman, B. C. (2007). Power options for wireless sensor networks, In: IEEE Aerospace and
Electronic Systems Magazine, Vol.22, No.4, pp. 14-17, ISSN 0885-8985
Vibration Energy Harvesting:
Machinery Vibration, Human Movement and Flow Induced Vibration

53
Peters, C.; Maurath, D.; Schock, W. & Manoli, Y. (2008). Novel electrically tunable

based on the forces generated by the Karman street around a rectangular prism, In:
Journal of Microelectromechanical Systems, Vol.18, No.2, pp. 449-457, ISSN 1057-7157
Sari, I.; Balkan, T. & Kulah, H. (2007). A wideband electromagnetic micro power generator
for wireless Microsystems, Proceedings of International Solid-State Sensors, Actuators
and Microsystems Conference 2007, pp 275-278, Lyon, France, June 10-14, 2007
Shen, D.; Park, J.; Ajitsaria, J.; Choe, S.; Wikle, H. C. & Kim, D. (2008). The design, fabrication
and evaluation of a MEMS PZT cantilever with an integrated Si proof mass for
vibration energy harvesting, In: Journal of Micromechanics and Microengineering,
Vol.18, No.5, 55017, ISSN 0960-1317
Spreemann, D.; Folkmer, B.; Maurath, D. & Manoli, Y. (2006). Tunable transducer for low
frequency vibrational energy scavenging, Proceedings of EurosensorsXX, Göteborg,
Sweden, September 17-20, 2006
St. Clair, D.; Bibo, A.; Sennakesavababu, V. R.; Daqaq, M. F. & Li, G. (2010). A scalable
concept for micropower generation using flow-induced self-excited oscillations, In:
Journal of Applied Physics, Vol.96, 144103, ISSN 0021-8979
Taylor, G. W.; Burns, J. R.; Kammann, S. M.; Powers, W. B. & Welsh, T. R. (2001). The energy
harvesting eel: a small subsurface ocean/river power generator, In: IEEE Journal of
Oceanic Engineering, Vol.26, No.4, pp. 539-547, ISSN 0364-9059

Sustainable Energy Harvesting Technologies – Past, Present and Future

54
Torah, R. N.; Glynne-Jones, P.; Tudor, M. J.; ODonnell, T.; Roy S. & Beeby S. P. (2008). Self-
powered autonomous wireless sensor node using vibration energy harvesting, In:
Measurement Science and Technology, Vol.19, 125202, ISSN 0957-0233
Mann, B. P. & Owens, B. A. (2010). Investigations of a nonlinear energy harvester with a
bistable potential well, In: Journal of Sound and Vibration, Vol.329, pp. 1215–1226,
ISSN 0022-460X
von Buren, T. (2006) Body-Worn Inertial Electromagnetic Micro-Generators, PhD Thesis,
Swiss Federal Institute of Technology Zurich, Zurich, Switzerland

Actuators A: Physical, Vol.158, No.2, pp. 284-293, ISSN 0924-4247
Zhu, D.; Beeby, S.; Tudor, J.; White, N. & Harris, N. (2010). A novel miniature wind
generator for wireless sensing applications, Proceedings IEEE Sensors 2010, ISBN
978-1-4244-8170-5, Waikoloa, Hawaii, USA, November 1-4, 2010
Zhu, D.; Almusallam, A.; Beeby, S.; Tudor, J. & Harris, N. (2010). A Bimorph Multi-layer
Piezoelectric Vibration Energy Harvester, Proceedings of PowerMEMS 2010, Leuven,
Belgium, December 1-3, 2010
Zhu, D. & Beeby, S. (2011). Kinetic energy harvesting, In: Energy Harvesting Systems:
Principles, Modeling and Applications, pp. 1-78, Springer, ISBN 978-1-4419-7565-2,
New York Dordrecht Heidelberg London
Zhu, D.; Beeby S.; Tudor J. and Harris N. (2011) A credit card sized self powered smart
sensor node, In: Sensors and Actuators A: Physical, Vol.169, No.2 pp. 317-325, ISSN
0924-4247
3
Modelling Theory and Applications of the
Electromagnetic Vibrational Generator
Chitta Ranjan Saha
Score Project, School of Electrical & Electronic Engineering University of Nottingham,
Nottingham, NG7 2RD
UK
1. Introduction
There is rapidly growing interest over the last decade on the topics of energy harvesting
devices as a means to provide an alternative to batteries as a power source for medical
implants, embedded sensor applications such as buildings or in difficult to access or remote
places where wired power supplies would be difficult [1-13]. There are several possible
sources of ambient energy including vibrational, solar, thermal gradients, acoustic, RF, etc that
can be used to power the sensor modules or portable electronic devices. The most promising
ambient energy sources of these are solar, thermo-electric and vibrational. A significant
amount of research has already been done in this area over the past few years and several
energy scavenger products are already available in the market such as the solar calculator,

power could be harvested from the macro and micro level EM energy harvester and whether
micro or macro device would be suitable for particular applications. The next section will give
the brief overview of the working principle of the vibrational energy harvesters.
1.1 Kinetic/vibrational energy harvesting
Kinetic energy is the energy associated with the motion of an object. This includes
vibrational motion, rotational motion and translational motion. The kinetic energy depends
on two variables, the mass of the moving object (m) and the speed (U) of the object and is
defined by [14];

2
1
.
2
KE mU=
(1)
Kinetic energy is a scalar quantity and it is directly proportional to the square of its speed. In
kinetic energy-harvesting, energy can be extracted from ambient mechanical vibrations
using either the movement of a mass object or the deformation of the harvesting device. The
basic operating principle of ac generator or alternator
or EM harvester can be expressed
using the energy flow diagram shown in Figure 1. When this external mechanical vibration
or force is sufficient enough to overcome the mechanical damping force then the mass
component of the energy harvesting devices to move or oscillate. This mechanical energy
can be converted into electrical energy by means of an electric field (electrostatic), magnetic
field (electromagnetic) or strain on a piezoelectric material, which are commonly known as
electromechanical energy conversion principles. There also exists magnetostrictive energy
harvesting devices which combine two principles: electromagnetic and piezoelectric.

Fig. 1. Energy flow diagram of mechanical to electrical energy conversion principle.
Input mechanical

movement. This movement could be either rotational or linear due to forces arising between
the fixed and the moving parts of the machine when we describe them as a rotational or
linear machine. Another closely- related device is the transformer, which converts ac
electrical energy at one voltage level to ac electrical energy at another voltage level. These
three types of devices are very important in our everyday lives and sometimes such energy
conversion devices are called transducer. One of the common factors between these
machines is that they make use of magnetic fields to convert one form of energy to another.
How these magnetic fields are used in such devices can be described by four basic principles
[15-17];
1. A magnetic field will be produced surrounding a current-carrying conductor.
2. A time-changing magnetic field induces a voltage in a coil when it passes through it,
which is called transformer action.
3. A current carrying conductor experiences a force in the presence of a magnetic field;
this is known as motor action.
4. When a conductor such as copper wire moves in the magnetic field, a voltage will be
induced between the conductor terminals; this is known as generator action.
The fourth principle is commonly known as Faraday’s electromagnetic induction principle
which has a wide range of applications, especially in power generation and power
transmission theory. The following section will highlight the key components of the
magnetic circuits since the magnetic field analysis is required to predict the performance of
the electromagnetic device.
1.3 Magnetic materials and permanent magnet circuit model
Magnets are made from the magnetic materials and magnetic substances which consist of
different metallic alloys. The magnetic materials are classified according to the nature of its
relative permeability (µ
r
) which is actually related to the internal atomic structure of the
material and how much magnetization occurs within material. There are three categories the
magnetic materials can be classified such as ferromagnetic materials, paramagnetic


π
x 10
-7
H/m.
1.3.1 Ferromagnetic materials
The ferromagnetic materials have very large positive values of magnetic permeability and
they exhibit a strong attraction to magnetic fields and are able to retain their magnetic
properties after the external field has been removed. The relative permeability of
ferromagnetic material could be a few hundred to a few thousand and they are highly
nonlinear. Ferromagnetic materials those are easily magnetized called soft magnetic
materials such as soft iron, silicon steel, soft ferrites, nickel-iron alloys etc. Soft magnetic
materials have a steeply rising magnetization curve, relatively small and narrow hysteresis
loop as shown in figure 2 (a). They are normally used in inductors, motors, actuators,
transformer, sonar equipments and radars. Those ferromagnetic materials have a gradually
rising magnetization curve, large hysteresis loop area and large energy loss for each cycle of
magnetization as shown in figure 2 (b) called hard magnet or permanent magnet. Alnico,
Ceramic, Rare-earth, Iron-chromium-Cobalt, Neodymium-Iron-boron etc are few examples
of permanent magnet materials. The more details of the Hysteresis loop (B-H curve) is
explained in different literatures [16-17].
1.3.2 Paramagnetic materials
The paramagnetic materials have small, positive values of magnetic permeability to
magnetic fields. These materials are weakly attracted by the magnets when placed in a
magnetic field and the materials could not retain the magnetic properties when the external
field is removed. Potassium, aluminum, palladium, molybdenum, lithium, copper sulphate
etc are common paramagnetic materials.
1.3.3 Diamagnetic materials
The diamagnetic materials have a weak, negative magnetic permeability to magnetic fields.
Diamagnetic materials are slightly repelled by the magnets when placed in a magnetic field
and the material does not retain the magnetic properties when the external field is removed.
The examples of diamagnetic materials are bismuth, copper, diamond, gold etc.

) and the flux density at a point M(x,y,z) outside the magnet can be calculated
[18] from the following equation,

)arctan(
222
rrrr
rr
rzk
zyxz
yx
BB
++
−=
(3)
Where B
zk
is the flux density in the magnetization direction and
kr
xxx −=
,
yyy
kr
−=

and
zzz
kr
−=
. The total flux density M(x,y,z) would be the summation of the eight
corner flux densities.

μ
(4)

Fig. 3. Magnet flux density calculation
Where
c
r
p
H
B
=
μ
is the permanent magnet permeability. The electrical analogy of the
magnetic components for flux linkage (
φ
) as current (I), the magnetomotive force (F
p
) as a
voltage source (E) and the magnetic reluctance as the resistance. The voltage drop across the
magnet can be defined as [19];

ppppcp
pp
p
pp
FlH
A
l
lH −ℜ=−=
φφ

,B
p
) would not move along the non-linear demagnetization
curve, it simply moves along the centre line of the minor loop.
M(x,y,z)
N
S
+B
r
-
+B
r
-B
r
y
k
,z
k
)
N
S
+B
r
-
+B
r
-B
r
k
,

H
(
A/m
)
B
p

l
p

Ap

H
p

B
p

H
p
l
p

p
φ
pp
p
p
A
l

t
V
φ
φ
=
Δ
Δ
=
(7)
H
c
+ H
p

H
p

H
p
+ H
cModelling Theory and Applications of the Electromagnetic Vibrational Generator

63
where V is the generated voltage/induced emf and
φ
is the flux linkage.
If we consider the case where a coil moves in the x direction through a magnetic field or flux

dx
d
−ΔΔ=
φ
(9)
where B(0) and B(Δx) are the flux density at the x=0 position and the x=Δx position.
The expression for the generated voltage as the product of the flux linkage gradient and the
velocity is important for understanding the operation of the vibrational generator.

X
Y
Z
(0, 0, 0)
(Δx, Δy, 0)
(Δx, 0, 0)
(0, Δy, 0)
U
B

Fig. 8. Movement of a conductor in a position varying magnetic field.

Sustainable Energy Harvesting Technologies – Past, Present and Future

64
1.4.1 Loudspeaker type vibrational generator
Figure 9 shows the schematic of a typical moving coil loudspeaker type linear generator. The
loudspeaker type generator consists of a moving coil inside a static magnetic field where the
voice coil is connected to the cone and its suspension [20]. Normally the cone is made from
carbon fibre, plasticized cloth or paper. The magnet assembly consists of front plate, back
plate, yoke pole pitch which are mainly made from low cost iron material and a large ferrite

Modelling Theory and Applications of the Electromagnetic Vibrational Generator

65 Magnet
Coil
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0123
Distance(mm)
Flux density(T)Fig. 10. Air gap flux density along the coil axis of the four magnets and single coil generator
structure.
D=Coil outer diameter
L =magnet length
H = magnet
height
G= Gap between
magnet and coil
Magnetization

vibrates relative to a housing when subjected to an external vibrational force. For an
electromagnetic generator mass may consist of the magnet itself or the coil. Figure 11 shows
the typical structure of a generator as described by P.Glynne-Jones [21]. In this generator,
two opposite polarity magnets were fixed in a gap at the free end of the cantilever and a
wire-wound coil was placed in the gap between the magnets. When the external force is
applied to the generator housing, the voltage would be generated in the coil terminal due to
the relative displacement between magnets and coil. In order to have a model, it is
important to develop the equations for the various generator parts such as the magnet
parameters, the coil parameters, beam parameters and damping (D) parameters.
Figure 12 shows the schematic diagram of the electromagnetic generator. Variables z and y
are the displacements of the generator mass and housing, respectively. It is assumed that
movement of the housing is unaffected by the movement of the generator, since the moving
mass (m) is much smaller than the mass of the generator housing. For a sinusoidal
excitation,
)sin(
0
tYy
ω
=
, where Y
o
is the vibration amplitude and ω is the frequency of
vibration. The equation of motion for the mass relative to the housing at no load condition
(no electromagnetic forces considered) can be defined [4-5] by the following equation,

Modelling Theory and Applications of the Electromagnetic Vibrational Generator

67
beam spring constant where the natural resonant frequency
ω
n
is given by,
mk
n
/=
ω
. The
steady state solution of equation (4) is the displacement for the no-load condition and is
given by the following equation [4]:

222
0
)()(
)sin(
ωω
φω
p
loadno
Dmk
tF
x
+−
−
=
−
where,
)(tan
2

2
0
=

The damping ratio (ξ
oc
) determines the qualitative behaviour of the system and it compares
the time constant for decay of an oscillating system’s amplitude to its oscillating period. The
details of this parasitic damping and quality factor will be given later in this chapter.
It is well known that any mechanical, electrical or acoustic system always generates the
maximum vibration amplitude at the resonance condition. Any system can have more than
one resonance frequencies and resonance occurs when the system’s natural frequency
matches the frequency of oscillation of the external force.

Sustainable Energy Harvesting Technologies – Past, Present and Future

68
m
x
(t)
y(t)
z
(
t)
D
p
D

mass includes an extra term due to the magnetic force and becomes;

emp
FtFkx
dt
dx
D
dt
xd
m −=++
ω
sin
0
2
2
(14)
where the F
em
is the electromagnetic force.
The conductor moves along the X axis at velocity U in magnetic field B that varies with the
position x as shown in Figure 2. In this case, the force experienced on the current-carrying
conductors in the loop is;
].[.
)0,0,(
)0,0,0(
)0,,(
)0,0,(
)0,,0(
)0,,(
)0,0,0(

IF
em
φ
=