ArticlePDF Available

Output power and efficiency of electromagnetic energy harvesting systems with constrained range of motion

Authors:

Abstract and Figures

In some energy harvesting systems, the maximum displacement of the seismic mass is limited due to the physical constraints of the device. This is especially the case where energy is harvested from a vibration source with large oscillation amplitude (e.g., marine environment). For the design of inertial systems, the maximum permissible displacement of the mass is a limiting condition. In this paper the maximum output power and the corresponding efficiency of linear and rotational electromagnetic energy harvesting systems with a constrained range of motion are investigated. A unified form of output power and efficiency is presented to compare the performance of constrained linear and rotational systems. It is found that rotational energy harvesting systems have a greater capability in transferring energy to the load resistance than linear directly coupled systems, due to the presence of an extra design variable, namely the ball screw lead. Also, in this paper it is shown that for a defined environmental condition and a given proof mass with constrained throw, the amount of power delivered to the electrical load by a rotational system can be higher than the amount delivered by a linear system. The criterion that guarantees this favourable design has been obtained.
Content may be subject to copyright.
1
M. Hendijanizadeh1, S. M Sharkh1, S. J. Elliott2, M. Moshrefi-Torbati1
1Electro-Mechanical Engineering Research Group, Engineering Science,
Southampton, SO17 1BJ, UK
2ISVR, University of Southampton, Southampton, SO17 1BJ, UK
E-mail: m.hendijanizadeh@soton.ac.uk
Abstract. In some energy harvesting systems, the maximum displacement of the seismic mass
is limited due to the physical constraints of the device. This is especially the case where energy
is harvested from a vibration source with large oscillation amplitude (e.g., marine environment).
For the design of inertial systems, the maximum permissible displacement of the mass is a
limiting condition. In this paper the maximum output power and the corresponding efficiency of
linear and rotational electromagnetic energy harvesting systems with a constrained range of
motion are investigated. A unified form of output power and efficiency is presented to compare
the performance of constrained linear and rotational systems. It is found that rotational energy
harvesting systems have a greater capability in transferring energy to the load resistance than
linear directly coupled systems, due to the presence of an extra design variable viz. the ball
screw lead. Also, in this paper it is shown that for a defined environmental condition and a
given proof mass with constrained throw, the amount of power delivered to the electrical load
by a rotational system can be higher than the amount delivered by a linear system. The criterion
that guarantees this favorable design has been obtained.
Keywords- Constrained systems; Efficiency; Energy harvesting; Scaling effect; Vibration,
1. Introduction
Generating electricity from ambient vibration has been the subject of significant research and
development in the last decade. Piezoelectric [1, 2] ,electrostatic [3] and electromagnetic [2, 4-8]
transducers are the most commonly used methods that are utilized to convert ambient vibrations to the
electrical energy. However, due to the limitation of geometry and limited permissible deformation of
electrostatic and piezoelectric transducers, the electromagnetic induction method is the more appropriate
choice for large scale applications [9]. Movement of a backpack carried by a human during walking [10],
all-terrain-vehicle vibration [11], vertical movement of a sailing boat [12] are some examples of
relatively large scale vibration resource.
However, in addition to the configuration of energy conversion device, maximizing the output power and
efficiency are the main concerns in the process of design and optimization of vibration energy harvesters.
Efficiency is a fundamental parameter used to compare all kinds of energy harvesters with various sizes
and designs [13-15]. Usually the main goal of an energy harvesting system is to extract the maximum
power from the environment. In this paper, the efficiency of such systems when achieving maximum
power is studied. To achieve the maximum power condition, the parameters of the system need to be
selected and tuned carefully. Tuning the load resistance to its optimum value to ascertain impedance
matching in electromagnetic energy harvesters is reported in many research works to have improved
energy capture [16-18]. However, none of these works considered the maximum allowable displacement
of the oscillating mass as a constraint in the process of calculating the optimum load resistance. More
specifically, the optimum load resistance for harvesting maximum amount of energy is generally
calculated regardless of its effect on the relative displacement of the oscillating mass. However, it is
known that the load resistance can influence the overall system damping and hence the relative
displacement of the mass. In many transducers that are used in large size applications, due to size
limitations, the oscillating mass only moves within a specified range. Now, if the load resistance of the
transducer is selected without considering the maximum permissible through of the seismic mass, there is
a risk that the amplitude of the oscillating mass will exceed the physical dimensions of the transducer
Output Power and Efficiency of Electromagnetic Energy
Harvesting Systems with Constrained Range of Motion
2
thus affecting the performance of the device. Therefore, for these cases, at the design stage, the physical
parameters such as load resistance should be selected with regard to the constraints on the oscillating
mass.
In this paper, the maximum output power and the corresponding efficiency of two types of
electromagnetic energy harvesting systems (i.e. linear and rotational) for those with constraints on their
range of motion are studied. In linear electromagnetic energy harvesting systems (henceforth referred to
as linear system) such as those studied in [11, 19-21] a linear generator is employed. However, in a
rotational energy harvesting system (henceforth referred to as rotational system), an intermediate
mechanism, such as rack and pinion[7, 10, 22] or a ball screw[23-26], is utilized to convert linear motion
of the mass to rotational one to drive a rotary generator.
The paper is distinguished by three main contributions. First it investigates the optimum load resistance
for both constrained linear and rotational systems to address the maximum output power condition. It is
shown that for constrained systems the optimal load resistance is different from that of unconstrained
energy harvesting systems that is reported in literature [16]. Then the efficiency of both systems
corresponding to their maximum output power is obtained. For each system, an expression for the load
resistance corresponding to maximum efficiency is also derived. It is shown that for linear systems it is
not possible to achieve maximum efficiency when the maximum power is extracted from the transducer.
However, for rotational systems maximum efficiency occurs at maximum output power point.
The second contribution is the derivation of equations for power and corresponding efficiency of both
systems in unified forms so that proper comparison between them can be made. These unified forms are
developed based on the non-dimensional electromechanical coupling coefficient of systems introduced
by Elliott and Zilletti [27]. The comparison reveals that in the case of a linear system, the maximum
amount of power that can be transferred to the load is half the mechanical power transferred by the
harvester and the efficiency of system is always less than 50%. However, a rotational system can be
designed so as to have an efficiency greater than 50%. The criterion that guarantees the efficiency of a
rotational system is more than 50% is derived.
The third contribution is studying the effect of scaling the size of electromagnetic generator component
of the energy harvesting system on the output power and efficiency. It is shown that by increasing the
size of energy harvesting system the efficiency is increased for both constrained linear and rotational
systems.
2. Power generation from a constrained inertia system
2.1 Power Generation from a constrained linear energy harvesting transducer
A schematic diagram of a linear energy harvesting system using an electromagnetic generator is shown in
figure 1. In this diagram, m is the seismic mass, k is the spring stiffness,
m
c
represents the mechanical
viscous damping coefficient, and
e
c
is the electrical damping coefficient corresponding to the combined
power dissipated in the generator’s internal resistance and the power delivered to the load.
Figure 1. Schematic diagram of a linear energy harvesting system
3
The governing differential equation of motion for the system shown in figure 1, with respect to the
relative displacement of the seismic mass
z x y
, is
 
.
em
m z c c z k z m y  
(1)
For a harmonic base excitation
, when the driving motion is assumed to be independent
of the mechanical loading due to the harvester, the amplitude of the relative displacement Z, can be
shown to be
 
 
 
2
1/2
22
2.
em
Zm
Yk m c c


 


(2)
Figure 2. Equivalent circuit of an electromagnetic generator connected to a resistive load.
In many papers on generating energy from vibrations, the effect of the generator’s internal inductance is
ignored. Cammarano et al. [17] show that even in cases where the effect of internal inductance cannot be
ignored, due to a high oscillation frequency, the undesirable effect of the internal resistance can be
compensated by adding a capacitor in series with the circuit. The equivalent electrical circuit of the
energy harvesting device is shown in figure 2, in which a capacitor is added in series with the load
reactance to cancel the effect of the generator's inductance. Assuming that an electrical generator with an
emf constant
,
t
K
is directly coupled to the seismic mass, then the generated emf voltage is given by
.
emf t
V K z
(3)
Also, the electrical damping coefficient (
e
c
), corresponding to the power dissipated in the generator’s
internal resistance and transferred to the electrical load, is
where
and
where
ii
jL

and
1/
ll
jC

. In [17] it is shown that to deliver the maximum power to the load
l
R
, the effect of internal inductance should be compensated by tuning the capacitor such that
li


.
For a spring stiffness of k, the natural frequency of system is equal to the base excitation frequency
when
2
km
at which the corresponding relative displacement
r
Z
can be derived from (2) (for
n

).
2,
t
eli
K
cZZ
(4)
,
i i i
ZR

(5)
,
l l l
ZR

(6)
4
Then
sin( )
r n z
z Z t


and
cos( )
r n n z
z Z t
 

, by substituting the electrical damping coefficients
from (4) and considering
2
1/ n
li
CL
, the amplitude of the relative displacement is
2.
n
r
t
mil
m
Z
YK
cRR
(7)
The power delivered to the load resistance is
22
2
1 1 1 .
2 2 2
emf t
l out l l l
l i l i
VKz
P R i R R
R R R R

 




(8)
Substituting the maximum value for
z
, which is
rn
Z
in (8), the power supplied to the load is given by
 
2 2 2
2
1.
2l
l out n t r
li
R
P K Z
RR
(9)
Equation (9) shows the relationship between the relative displacement, excitation frequency, load
resistance and the harvested power from a given generator.
Now, we design an optimum energy harvesting system to extract maximum energy from a given
vibration source with known amplitude and frequency of oscillation. This design will be accomplished
based on the parameters of a given generator that has given
t
K
and
i
R
values. It is also assumed that, due
to the transducer size limits, the maximum displacement of the oscillating mass is specified. Therefore,
the aim of design is the optimal selection of system parameters including k,
l
R
and m to harvest the
maximum power from the given generator within the specified range of motion. To this end, considering
0
r
Z
as the maximum allowable relative displacement of mass (i.e.,
0
rr
ZZ
is constant), the maximum
value of (9) is obtained when the load resistance is equal to the internal resistance of the generator in
which the output power is
0
2 2 2 /8
n t r i
k Z R
. The mass can then be selected from (7) to limit its maximum
displacement to
0
rr
ZZ
,
The natural frequency of system is equal to the excitation frequency when
2
km
, considering
n

in this condition the spring stiffness is given by
2.2 Power Generation from a constrained rotational energy harvesting transducer
A rotational energy harvesting system comprising a sprung mass coupled to an electrical generator
through a motion transmission system. The Ball screw is a conventional mechanism that converts linear
motion to the rotational one. A schematic diagram of this type of system is shown in figure 3. In this
device the base movement causes the mass to vibrate. The ball screw then converts the low frequency
linear motion of the seismic mass to high speed rotation. The governing differential equation of motion,
having an ideal ball screw, igure 3 is written as
 
22
22 .
e bg
m J z c c z k z my
ll


   

 
   

   

(12)
02.
2
rt
m
ni
ZK
mc
YR





(10)
02.
2
rt
nm
i
ZK
kc
YR





(11)
5
Figure 3. Schematic diagram of an energy harvesting system consisting of a sprung mass coupled to a
generator through a ball screw
Considering
l
as the ball screw lead, the equivalent reflected moment of inertia of the ball screw and the
generator is given by
 
2
2/Jl
, where J refers to the total moment of inertia of the system including the
moment inertia of the ball screw
b
J
and generator
g
J
and is defined as
Also
bg
c
includes the mechanical viscous damping of the combined ball screw connections
mb
c
and
generator
mg
c
, i.e.,
For a harmonic base excitation
, the amplitude of the relative displacement is
The systems operates at its natural frequency when
n

where
n
is given by
In this condition, the relative displacement of the mass is given by
where
i
T
is the rotary generator emf-constant which is equivalent to
t
K
in linear systems. Then the
output power is therefore expressed as
.
gb
J J J
(13)
.
bg mb mg
c c c
(14)
 
2
1/2
22
22
2
.
22
e bg
Zm
Y
k m J c c
ll




 
   


 
 
   

 

   
 



(15)
1/2
2.
2
nk
mJ l










(16)
22,
2
n
ri
bg il
mY
ZT
c
l R R







(17)
6
Now, we assume that we wish to determine the parameters of a rotational system (i.e., l, m and Rl), based
on a specific generator and given mass (i.e., known
i
T
,
i
R
and m), such that the maximum energy can be
extracted from a specified vibration source (i.e., known Y and
).
Considering the maximum allowable displacement of mass
0
rr
ZZ
,
 
2
2/l
is then obtained from (17)
as
By replacing (19) in (18), the output power for the constrained system is obtained from the following
equation
From (20), the optimum load resistance to harvest the maximum power is obtained from
/ 0,
b out l
PR
 
which results in
the optimum ball screw lead can be derived as
and the spring stiffness can be calculated from (16).
3. Power and efficiency comparison between linear and rotational systems
3.1 Power and efficiency of an electromagnetic constrained transducer
Efficiency is a fundamental term that has been studied for different energy harvesting systems. Relying
solely on the assessment of the output power of energy harvesters does not reflect their quality of
performance and their capability to harvest the maximum amount of power. However, in the context of
vibration harvesting systems, the concept of efficiency has received less attention in the literature than
that of maximizing output power. Traditionally, efficiency is defined as the ratio of the electrical power
output to the mechanical input power; whilst, in a vibration-based energy harvester, the input
mechanical power itself is related to the device characteristics. Also, the efficiency cannot be defined in
terms of the potential mechanical power available from the source as, in some applications, the loading
by the harvester does not influence the dynamics of the source of vibration. Hence, the potential
mechanical power available from the source is effectively limitless [14]. To compare the power output
of various transducers, a dimensionless figure of merit, called effectiveness e, is introduced by Roundy
[28] which is defined as
 
2
2 2 2
2
12
.
2l
b out i r
li
R
P T Z
l
RR



(18)
0
2
2
2.
n
i
r bg il
mY
lT
Zc RR

 




(19)
 
0
0
2 2 2
22
1.
2ln
b out i n r
i
li r bg il
R mY
P T Z
T
RR Zc RR




(20)
max
1/2
2
2
,, ,
i
l rotational P i i bg
T
R R R c





(21)
0
1/2
2
1/2
2
2
2,
ri
bg
ni
i i i bg
ZT
lc
mY T
R R R c






















(22)
22
0 max ,eQ


(23)
7
where, Q is the quality factor and is related to the damping ratio of the system,
is the coupling
coefficient of the transduction mechanism,
is the actual density of the device,
0
is a baseline density,
is the actual transmission coefficient and
max
is the maximum transmission coefficient. However, in
the effectiveness” index,
Q
is related to the damping ratio of the system and does not have a
fundamental limit. Hence, this metric comparison does not reveal how well the device is optimized [8].
To investigate how close a device is to its optimum performance and distinguish between different
proof mass densities and geometries, Mitcheson et al. [14] introduce a volume figure of merit”,
defined as
43
3
00
.
1
16
out
V
Au
P
FoM
YV

(24)
This dimensionless ratio compares the performance of the device with that of an ideal device. The device
has the same total package volume but with a proof mass equal to the density of gold (
Au
), occupying
half of this volume (
0
V
). The proof mass oscillates in the other half of this package. The power output
harvested by this hypothetical device is considered as the maximum possible output for the based
vibration with amplitude of
0
Y
at frequency of
. The power output of the transducer is compared with
the maximum possible output to evaluate the performance of a device as a function of its overall size.
Although the volume figure of merit” facilitates the comparison of a harvesting device performance with
a reference ideal energy harvesting system, it does not enable the calculation of input power absorbed by
the system to produce a certain amount of output power.
Elliott and Zilletti [27] conducted research into scaling of linear electromagnetic transducers for power
harvesting and shunt damping. In this study the efficiency is defined as the ratio of output power to the
sum of the mechanical dissipated power, electrical power loss and electrical output power. This definition
is closer to the original definition of efficiency. This study shows that the efficiency of a linear
electromagnetic transducer depends on a non-dimensional electromechanical coupling coefficient which
will be discussed later in this paper. The coupling coefficient scales with the transducer’s size. However,
this research does not consider the constraint on the displacement of the proof mass. The mechanical
input power absorbed by the energy harvesting structure is given by
Here, we define the efficiency of a linear system,
l
E
, as the ratio of the electrical power harvested from
(9) to the supplied mechanical power from (25), which is
The load resistance corresponding to the maximum efficiency of the system, as opposed to the maximum
power output, can be obtained from
/0
ll
ER  
, i.e,. differentiation of (26), which results in
By comparing the optimum load resistance for maximum output power (
max
,,l linear P i
RR
), and the load
resistance corresponding to the maximum achievable system efficiency derived in (27), it is realized that
the latter is always greater than the former. Therefore, in a practical linear system it is not possible to
achieve maximum efficiency at the maximum output power point. The mechanical input power absorbed
by the rotational system can be calculated as
222
1.
2t
l in m n r
li
K
P c Z
RR





(25)
 
2
22.
l out l t
ll in m l i t l i
P R K
EPc R R K R R
 
(26)
max
1/2
2
2
,, .
t
l linear E i i m
K
R R R c





(27)
2
222
12
.
2i
b in bg n r
il
T
P c Z
R R l








(28)
8
The harvesting efficiency,
b
E
, is defined as
Also, from (29), the load resistance corresponding to the maximum efficiency of the system can be
obtained from
/0
bl
ER  
, which is
Comparison of (21) and (30) reveals that in the rotational system, the optimum load resistance to obtain
the maximum efficiency is the same as the load resistance corresponding to the maximum power. In the
other words, for a constrained rotational system the maximum efficiency occurs at the maximum output
power.
3.2 Comparison of output power and efficiency of systems
By replacing (7) in (9) for
0
rr
ZZ
the load power of a constrained linear energy harvesting system for
the load resistance corresponding to the maximum output power (
max
,,l linear P i
RR
), is
where
em
is a non-dimensional electromechanical coupling coefficient of an energy harvesting system
and is defined as [27]
for linear systems and
for rotational systems. By increasing this coefficient (i.e.,
em
 
) the maximum output power, given
by (31), approaches the following expression
This shows that the maximum theoretical power is determined by the environmental vibration
characteristics (
n
,
Y
) and also the system mass and the maximum allowable displacement. Note that
n
is a characteristic of the transducer, but here the system is designed such that the undamped natural
frequency of the device is equal to the frequency of excitation.
Considering (26), the efficiency of a constrained linear system for the load resistance corresponding to
the maximum output power (
max
,,l linear P i
RR
), can readily be shown to be [27]
For weak linear coupled systems, the efficiency is low. By increasing
em
the efficiency increases until
it reaches a maximum value of 50%, i.e.
   
2
22.
b out l i
bb in i l bg i i l
P RT
EPR R c T R R

 
(29)
max
1/2
2
2
,, .
ii
l rotational E i bg
RT
RR
c





(30)
max 0
3
,,
81 2
em
l out P n r
em
P m YZ



(31)
2,
t
em mi
K
cR

(32-a)
2,
i
em bg i
T
cR

(32-b)
max 0
3
,1
lim .
4
em l out P n r
P m YZ
 
(33)
max
,.
42
em
lP em
E

(34)
(35)
9
However, considering the optimum load resistance for rotational systems from (21), the output power of
such systems from (20) can be written as
and for the case when
em
 
, the power is
Also, the efficiency of rotational systems corresponding to the maximum output power can be obtained
by replacing (30) in (28) and using (22), (32-a) and (32-b), which results in
Equation (38) indicates that in the case of a rotational system, it is possible to achieve an efficiency of
more than 50%. To achieve such favourable design, the condition below must be met
This condition is satisfied if
8
em

. Selecting the parameters according to this condition can lead to a
system with an efficiency above 50%. For the case when
em
 
, the efficiency of the rotational
system is
In the case that the a linear and a rotational system have same seismic mass, by replacing (7) in (25) and
(17) in (28), for
0
rr
ZZ
, it an be shown that the mechanical input power for both systems
is
0
3
1/ 2 nr
m YZ
, however, the linear system in the optimum condition can only transfer less than half of
this power to the load, while, the rotational system under certain condition, i.e.
8
em

, can harvest
more power.
3.3. Effect of the Scaling of constrained electromagnetic harvesters on the output power and
efficiency
It was shown earlier that by increasing
em
, the efficiency of a typical energy harvesting transducer is
improved. A question that arises here is “how do the output power and efficiency of a system change by
increasing the size of the generator?”.
Elliott and Zilletti [27] studied the relation between
em
and the characteristic length of a transducer [L].
In this study, assuming that
w
A
is the cross-sectional area of the wire used for the coil of the
electromagnetic transducer and
w
is its resistivity, the resistance of the coil is given by
Here h is the coil’s wire length, which is approximately given by
 
 
max 0
3
,2
1
1,
21 1 1 1
em em
b out P n r
em em em
P m YZ
 
     
(36)
max 0
3
,1
lim .
2
em b out P n r
P m Y Z
 
(37)
 
 
max
,2
1,
1 1 1 1
em em
bP
em em em
E  
     
(38)
 
2 1 1 .
em em
   
(39)
max
,
lim 1.
em bP
E
 
(40)
.
iw
w
h
RA
(41)
,
C
w
V
hA
(42)
10
where
C
V
is the volume of the coil. For a well-designed transducer with saturated magnetic flux density
B, the emf-constant (
t
K
for linear systems and
i
T
for rotational systems) is proportional to the magnetic
flux density times the length of the wire in the coil (i.e.,
t
K
or
i
T
=Bh). Therefore, the electromechanical
coefficient of the transducer can be re-written as
The magnetic flux density (B) and wire resistivity (
w
) of the transducer depend on their material
properties, but not on the transducer dimensions. In general, the scale of the volume of the coil (
C
V
) is
[
3
L
], whereas the mechanical damping coefficient (
m
c
for linear systems and
bg
c
for rotational systems)
is related to the structure and the detailed mechanism of the transducer, but generally scales as [
L
][29].
Therefore, the electromechanical coefficient shown in (32-a) and (32-b) is proportional to the square of
the characteristic length of the transducer [
2
L
]. Hence, an option in increasing the coupling coefficient of
a transducer is to increase its overall size. From (33) and (37) it is evident that, for both systems, by
increasing the size of device the electromagnetic coefficient and consequently the output power of the
system is increased.
In the case of a rotational system, considering the combined ball screw, mass, spring and the rotary
generator as the transducer assembly, the coupling coefficient related to the generator part of the
transducer can be defined as
where
mg
c
is the mechanical damping associated with the rotary generator. According to the discussion
presented above, it is expected that
emg
will scale with the square of the characteristic length of the
generator [L2]. This assumption will be examined in the next section by studying the specifications of a
set of commercial generators. For the rotational transducer assembly, the coupling coefficient defined in
(32-b) can be rewritten as
where
mb
c
is the mechanical damping due to the presence of other transducer’s mechanical components
such as ball screw, bearings and coupling shafts. Here, by increasing the size of the rotary generator, the
quantity
2/
ii
TR
scales as [L3], but
mg
c
scales as [L], while,
mb
c
does not scale up. Hence, it can be
understood that by increasing the generator size, the coupling coefficient of the overall transducer
assembly is increased but due to constant
mb
c
, the rate of scaling is higher than [L2]. For instance if two
rotational systems are designed based on two different rotary generators with electromechanical
coefficients
1
emg
and
2
emg
, the ratio of the non-dimensional electromechanical coefficient for these
generators scales as [L2], i.e.,
and from (45) the ratio of the overall electromechanical coefficient of the designed transducers is
 
22.
C
em wm
wm
w
Bh BV
hc
c
A
 
(43)
2,
i
emg mg i
T
cR

(44)
 
2,
i
em mg mb i
T
c c R

(45)
2
2 2 2
11
11
2
2
2,
i
emg mg i
emg i
mg i
T
cR L
T
cR



(46)
11
Therefore, if
1
/
mb mg
cc
is greater than
2
/
mb mg
cc
, then in comparison with
1
em
,
2
em
scales with a ratio
greater than [L2].
4. Numerical study
4.1. Linear system examples
This section investigates the relation between size and efficiency of energy harvesting devices under
constrained condition brought about by the employed commercial generator. It is assumed that a source
of vibration (for example a vertical movement of a boat) with a frequency of 0.5 Hz (

rad/sec) and
amplitude of 1 m (
1Y
m) is available. We are required to design an energy harvesting device such that
the maximum displacement of the seismic mass does not exceed 0.3 m.
First case is dedicated to the design of a linear energy harvesting structure based on figure 1. Table 1 lists
the parameters of a variety of linear electromagnetic actuators presented in [27] that are sorted in the
order of small to large scales. The last system represents a hypothetical case in which the size of the
actuator is much larger than model ASP400 (~8 times).
Table 1 Parameters of a number of linear electromagnetic inertial actuator models[27]
t
K
i
R
m
c
em
m
max
,l out P
P
Type
(N/A)
(Ω)
(Ns/m)
(kg)
(W)
Trust headphone actuator
0.74
8
0.38
0.18
0.03
0.007
Micromega(IA-01)
1.6
3.0
1.4
0.61
0.17
0.09
Aura
7
4.4
9
1.23
1.39
1.23
Motran (IFX 30-100)
10
1.6
44
1.42
7.18
6.93
Micromega (ADD-45N)
20
4
35
2.86
8.11
11.10
ASP 400
21
1.6
30
9.19
16.02
30.60
Hypothetical case
42
0.8
60
36.75
111.01
224.8
For each presented linear actuator type, the proof mass is calculated such that the oscillation at excitation
frequency (

rad/sec) occurs within the given constraint (i.e.,
00.3
r
Z
m). For each inertial
generator
em
and the seismic mass are calculated from (32-a) and (10), respectively. Then, at optimum
load resistance (
max
,,l linear P i
RR
), the output power is obtained from (9). As table 1 shows, by increasing
the transducer dimensions,
em
is increased and that is in agreement with the result presented in section
3. Also, by increasing the size of the linear actuator, the overall damping of the system gets larger, thus,
requiring a bigger mass to reach the same displacement (i.e.,
00.3
r
Z
). In addition, it is seen that by
increasing the size of the linear actuator, the output power increases. However, as in this case, mass is the
design variable (and for hence the absorbed mechanical power is different for each design), system
efficiency would therefore be a more appropriate criterion to be used in order to compare the different
harvesters. Figure 4 shows the efficiency of the designed system corresponding to their maximum output
power calculated from (26). It is seen that by increasing
em
due to the increase of the transducer size, the
 
 
2
22
2 2 1
11
1
2
11
2
2
1
.
1
imb
mg mb i
em emg mg
mb
em emg
i
mg
mg mb i
Tc
c c R c
c
Tc
c c R

 

(47)
12
efficiency of the energy conversion system is improved. However, even in the case of a hypothetical
system where the size has been increased dramatically, the efficiency of the system does not exceed 50%
which is in agreement with the result obtained from (35).
Figure 4. Efficiency of linear electromagnetic energy harvesting systems versus
em
for the linear
actuator shown in table 1
4.2. Rotational system examples
Table 2 presents the size and specifications of a number of commercial PM (permanent magnet)
generators where h and r, respectively, are the length and the radius of the rotary generator coupled to the
ball screw as presented in figure 3. Here, for each generator,
emg
is calculated from (44), see table 2.
Figure 5 shows the variation of the coupling coefficients of the generators in comparison with the size of
the reference generator (Model a). A reasonable fit to
emg
shows that it is linearly proportional
to
 
2
3
1
/
i
VV
, where
1
V
is the volume of generator model a, and
i
V
is the volume of the selected generator.
This result validates the statement made in section 3 that the electromechanical coupling coefficient of a
generator scales up with the square of the characteristic length of the device [L2]. Also in each case
em
which represents the electromechanical coefficient of the transducer assembly is calculated from
(45). Note that
mb
c
is not a function of the generator size and is assumed to be 3.0E-3 (mN.m.s.rad-1) for
all the designed transducers. A comparison of
em
and
emg
reveals that the
em
scales with a ratio
higher than that of
emg
. This agrees with the discussion presented in section 3.
13
Table 2. The parameters of PM motors from Faulhaber [30]
h
r
i
T
i
R
mg
c
emg
em
l
max
,b out P
P
Type
(mm)
(mm)
(mNm/A)
(Ω)
( mN.m.s.rad-1)
(mm)
(W)
a
6
20
1.13
9.1
6E-5
2.33
0.05
1.2
0.4
b
12
26
2.77
2.3
4.2E-4
6.78
0.95
1.5
6.2
c
16
28
3.86
4.3
4.8E-4
7.22
0.99
1.6
6.4
d
20
36
6.34
3.4
1.3E-3
9.20
2.75
2
12.0
e
30
56
12.74
1.6
6E-3
16.20
10.80
3.8
20.6
f
35
64
14.52
0.6
1.4E-2
24.40
20.20
6.1
24.2
g
44
90
23.83
0.23
6E-2
39.94
38.4
13.5
27.3
Figure 5. The coupling coefficient of rotary generators presented in table 2 versus ratio of their sizes to the
reference generator in power of two over 3.
Now, it is assumed that the environmental vibration condition and the constraint on the maximum
allowable displacement of the seismic mass are the same as the values considered in the first case
(
01Y
m,

). In this case, based on each of the PM generators presented in table 2, a rotational
harvesting system is designed. It is assumed that the energy harvester has a mass of 8.1 kg, and the
design variables are
l
and
l
R
. The optimum load resistance for each case is obtained from (21), and then
the optimum lead size for the ball screw is calculated from (22). Table 2 presents the ball screw lead
values and the generated power of each system corresponding to the relevant selected PM generator in
each case. It is seen that by increasing the size of the generator,
em
and consequently the output power
of the system is increased which is in agreement with (37).
Figure 6 shows the efficiency of the designed rotational systems versus
em
. It is seen that by increasing
the size of PM generators, the efficiency of the system increases. Here, in contrast with linear systems, an
efficiency above 50% is achievable. This occurs for those systems whose
em
meet the criterion
presented in (39), i.e., systems designed based on generators e, f and g. However, if
em
does not satisfy
the condition presented in (39), i.e.
8
em

, designing a rotational energy harvesting system may result
in a sub-optimum energy harvesting device in comparison with the linear system. For instance
comparison of the designed systems based on the generators a, b and c with the linear system designed
based on Micromega (ADD-45N), reveals that although the rotational systems utilize the same mass, they
produce less power compared with the linear system. Therefore, for constrained applications, in the
14
design process of the energy harvesting systems, a rotary generator should be selected carefully to allow
the designer to take advantage of the superiority of the rotational systems over the linear systems.
Figure 6. Efficiency of rotational electromagnetic energy harvesting systems versus
em
for the rotary
generators shown in table 2
5. Discussion and conclusion
In some energy harvesting systems, the maximum displacement of the oscillating mass will be limited
due to the physical constraints of the device. In systems where this limitation does not exist, choosing the
optimum load resistance with the goal of maximizing the energy harvested from the environment is a
process that takes place after the machine design. This is why, in these cases, the phrase “tuning” is used
to refer to the selection of the resistance load. However, in systems where the maximum displacement of
the mass is limited (constrained systems), choosing the optimum load resistance is part of the actual
design process and cannot be done independently of choosing other parameters.
In this article, the maximum power condition and the corresponding efficiency for constrained vibration
based linear and rotational energy harvesting devices were presented. For convenience, and for enabling
the comparison of different systems, the definition for the coupling coefficient of an energy harvesting
device given by (32) is employed [27].
In a linear system, electromechanical coupling coefficient (
em
) is shown to increase with the size of the
transducer according to its characteristic length squared. However, in the case of a rotational system,
although
emg
of the rotational generator, itself, increases as [L2], the value of
em
for the whole
transducer assembly (including the ball screw) scales by a ratio greater than [L2].
It is shown that in a system with linear motion and constrained throw, even with the assumption of
negligible mechanical losses, the maximum harvestable power (at optimum condition, i.e.,
max
,,l linear P i
RR
) is half of the mechanical power that can be absorbed by the transducer.
Also, it is shown that the output power and efficiency of linear systems increase by increasing the size of
the structure. However, the maximum efficiency for such devices cannot be more than 50%.
In contrast, rotational systems with a constrained throw show greater capability in transferring energy to
the resistance load. In these systems, the ratio of the optimum load resistance and the internal resistance
of the generator can be written according to equation (21) and (32) as follows:
Therefore, by increasing
em
, this could be achieved by the enlargement of the rotary generator size, the
ratio of the generator internal resistance to the load resistance increases.
max
,, 1.
l rotational P em
i
R
R  
(48)
15
Figure 7 shows the logarithmic plot of
em
against the generator volumes over reference volume to the
power of two over three for both linear and rotational transducers, respectively presented in tables I and
II. The generators volume and the related reference volume for the linear transducers have been obtained
from [27]. It is seen that
em
for rotational systems scales with a greater ratio in comparison with the
linear systems. Hence, scaling the generator part in a rotational system, can be more beneficial in terms
of improvement the system efficiency and output power.
Figure 7. Log-log plot of
em
versus volume over the reference volume to the power of two over three for
linear and rotational systems presented in tables I and II.
It is demonstrated that these transducers can be designed to operate with efficiencies above 50%. The
criterion that guarantees this superior efficiency was derived in (39) which can be used in the design
process. This superiority of rotational systems over linear systems is due to the presence of an
intermediate mechanism viz ball screw that can provide an extra design variable, thus enabling us to
optimize the power output of the system subject to displacement constraint more desirably.
For a defined environmental condition and a given proof mass with constrained maximum allowable
displacement, the amount of power delivered to the electrical load by a rotational system can be as high
as twice the amount delivered by a linear system.
Acknowledgements
The authors are very grateful to Mr Mike Russell for providing financial support to the project.
References
1. Anton, S.R. and H.A. Sodano, A review of power harvesting using piezoelectric materials (2003
2006). Smart Materials and Structures, 2007. 16(3): p. R1-R21.
2. Khaligh, A., Z. Peng, and Z. Cong, Kinetic Energy Harvesting Using Piezoelectric and
Electromagnetic Technologies—State of the Art. Industrial Electronics, IEEE
Transactions on, 2010. 57(3): p. 850-860.
3. Naruse, Y., et al., Electrostatic micro power generation from low-frequency vibration such as
human motion. Journal of Micromechanics and Microenginering, 2009. 19: p. 1-5.
4. Bin, Y. and et al., Electromagnetic energy harvesting from vibrations of multiple frequencies.
Journal of Micromechanics and Microengineering, 2009. 19(3): p. 035001.
5. Glynne-Jones, P., et al., An electromagnetic, vibration-powered generator for intelligent sensor
systems. Sensors and Actuators A: Physical, 2004. 110(1-3): p. 344-349.
6. Beeby, S.P. and et al., A micro electromagnetic generator for vibration energy harvesting.
Journal of Micromechanics and Microengineering, 2007. 17(7): p. 1257.
16
7. Zhongjie, L., et al., Electromagnetic Energy-Harvesting Shock Absorbers: Design, Modeling,
and Road Tests. Vehicular Technology, IEEE Transactions on, 2013. 62(3): p. 1065-1074.
8. Saha, C.R., et al., Optimization of an Electromagnetic Energy Harvesting Device. Magnetics,
IEEE Transactions on, 2006. 42(10): p. 3509-3511.
9. Tang, X. and L. Zuo. Analysis of a micro-electric generator for microsystems. in IMECE. 2009.
USA.
10. Rome, L.C., et al., Generating Electricity While Walking with Loads. Science, 2005. 309: p.
1725-1728.
11. Gupta, A., et al., Design of electromagnetic shock absorbers. International Journal of Mechanics
and Materials in Design, 2006. 3(2): p. 285-291.
12. Sharkh, S.M., et al. An inertial coupled marine power generator for small boats. in Clean
Electrical Power (ICCEP), 2011 International Conference on. 2011.
13. Renaud, M., et al., Optimum power and efficiency of piezoelectric vibration energy harvesters
with sinusoidal and random vibrations. JOURNAL OF MICROMECHANICS AND
MICROENGINEERING, 2012. 22(10): p. 105030.
14. Mitcheson, P.D., et al., Energy Harvesting From Human and Machine Motion for Wireless
Electronic Devices. Proceedings of the IEEE, 2008. 96(9): p. 1457-1486.
15. Shu, Y.C. and I.C. Lien, Efficiency of energy conversion for a piezoelectric power harvesting
system. JOURNAL OF MICROMECHANICS AND MICROENGINEERING, 2006. 16(11): p.
2429.
16. Stephen, N.G., On energy harvesting from ambient vibration. Journal of Sound and Vibration,
2006. 293(1-2): p. 409-425.
17. Cammarano, A., et al., Tuning a resonant energy harvester using a generalized electrical load.
Smart Materials and Structures, 2010. 19(5): p. 055003.
18. Mansour, M.O., M.H. Arafa, and S.M. Megahed, Resonator with magnetically adjustable natural
frequency for vibration energy harvesting. Sensors and Actuators A: Physical, 2010. 163(1): p.
297-303.
19. Nakano, K., Y. Suda, and S. Nakadai, Self-powered active vibration control using a single
electric actuator. Journal of Sound and Vibration, 2003. 260(2): p. 213-235.
20. Gargov, N.P., A.F. Zobaa, and G.A. Taylor. Direct drive linear machine technologies for marine
wave power generation. in Universities Power Engineering Conference (UPEC), 2012 47th
International. 2012.
21. Waters, R., et al., Experimental results from sea trials of an offshore wave energy system.
Applied Physics Letters, 2007. 90(3): p. 034105-034105-3.
22. Choi, S.-B., M.-S. Seong, and K.-S. Kim, Vibration control of an electrorheological fluid-based
suspension system with an energy regenerative mechanism. Journal of Automobile Engineering
2009. 223(D): p. 459-469.
23. Agamloh, E.B., A.K. Wallace, and A. von Jouanne, A novel direct-drive ocean wave energy
extraction concept with contact-less force transmission system. Renewable Energy, 2008. 33(3):
p. 520-529.
24. Matsuoka, T., et al., A Study of Wave Energy Conversion Systems Using Ball Screws
Comparison of Output Characteristics of the Fixed Type and the Floating Type, in International
Offshore and Polar Engineering Conference2002: Kitakyushu, Japan. p. 581-585.
25. Brown, P., D. Hardisty, and T.C.A. Molteno. Wave-powered small-scale generation systems for
ocean exploration. in OCEANS 2006 - Asia Pacific. 2006.
26. Cassidy, I.L., J.T. Scruggsa, and S. Behrensb, Design and Experimental Characterization of an
Electromagnetic Transducer for Large-Scale Vibratory Energy Harvesting Applications. Journal
of Intelligent Material Systems and Structures, 2011. 22: p. 2009-24.
27. Elliott, S.J. and M. Zilletti, Scaling of electromagnetic transducers for shunt damping and power
harvesting (ID 896), in ISMA2012: Leuven, Belgium. p. 463-474.
28. Roundy, S., On the Effectiveness of Vibration-based Energy Harvesting. Journal of Intelligent
Material Systems and Structures 2005. 16(10): p. 809-823.
29. Peirs, J., Design of micromechateronic systems: scales laws, technologies and medical
applications 2001, Katholike Universiteit Lueven.: Sweden.
30. Faulhaber, Brushless DC-Servomotors catalog, 2012.
... Linear devices -Up to 50 [ 109 ] 150-2300 W (For 200-500 rev) [ 147 ] -Rotatory devices -Up to 70 [ 109 ] Approx. 0.3-7000 W [ 147 ] -Electrostatic ...
... Linear devices -Up to 50 [ 109 ] 150-2300 W (For 200-500 rev) [ 147 ] -Rotatory devices -Up to 70 [ 109 ] Approx. 0.3-7000 W [ 147 ] -Electrostatic ...
Article
The increase of energy demand in the past 50 years and the targets to reach net-zero carbon dioxide emissions have led to an increase of electricity production from renewable energy sources. This paper first gives a snapshot of the word's energy mix and then reviews the most widely used renewable energy sources in the market; comparing their reliability, efficiency and cost-effectiveness, and highlighting their major advantages and weaknesses. The review concludes that marine energy, and specifically wave energy, can be the emerging energy source capable of addressing many of the problems that current renewable energy concepts and devices present, although major challenges remain. The paper is focused on the current global position of wave energy technologies in the market and under development in the past two decades, by looking at their status, reliability, energy generated, capacity installed and geographical locations. The current marine energy status of the main players, including France and South Korea, is compared with the rest of Europe and the wave energy status in Europe has been reviewed with an special interest in UK, as one of the major players, and Australia as a new emerging area of development. The main Wave Energy Converters (WECs) together with the world's wave energy density map were also discussed. This has led to a conclusion, that even though there is high energy potential, the wave technologies developed to date cannot offer a much needed breakthrough. A new concept of WEC based on a system of synchronized rotational pendula, having potential to work across-scales is introduced, which can motivate future work.
... In contrast, many studies have been conducted to optimise the power output of a vibration energy harvester. The most common example of power output optimisation in vibration energy harvesting applications is the determination of the optimum load resistance that corresponds to the maximum power output of the harvester, which have been reported in many published works [10][11][12][13], among others. Generally, optimisation of a vibration energy harvester can be divided into two streams. ...
... For macro-size cantilever beams (volume > 100 mm 3 ), the mechanical damping ratio can be divided into its thermoelastic damping, ℎ , and its material damping as shown in Eq. (13). Other forms of damping can be assumed negligible for this size range [29]. ...
Article
Full-text available
This study investigates several important considerations to be made when optimising the structural aspects of a single-degree-of-freedom (SDOF) electromagnetic vibration energy harvester. Using the critically damped stress method, the damping and power output of the harvester were modelled and verified, displaying an excellent agreement with the experimental results. The SDOF harvester was structurally optimised under a certain set of constraints and it was found that under the fixed beam's thickness condition, the harvester displayed an insignificant increase in power output as a function of volume when the device's size was relatively larger. This highlights the importance of considering a smaller practical volume for this case. Additionally, when optimising the device using a low stress constraint and a low damping material, it was observed that considering the load resistance as an input parameter to the objective function would lead to a higher power output compared to the optimum load resistance condition. Further analysis indicated that there exists a power limit when the electromagnetic coupling coefficient approaches infinity. For the case of a high electromagnetic coupling coefficient value and a small volume constraint, it is possible to achieve approximately 80.0% of the harvester's power limit. Finally, it was demonstrated that a high power output can be achieved for a SDOF electromagnetic harvester by considering a high-density proof mass centred at the free end of the beam.
... The average energy conversion efficiency can be computed as g ¼ P 1000 i¼1 P VEH;i . P 1000 i¼1 P c;i [33], where P VEH;i represents the literally harvested vibration energy under the ith realization of the random input determined from (30), while ...
Article
Full-text available
Beneficial effects of nonlinear damping on energy harvesting and vibration isolation under harmonic inputs have been investigated showing that the introduction of nonlinear damping can increase the harvested energy and reduce the vibration over both the resonant and higher frequency ranges. However, the scenario becomes more complicated when the loading inputs are of more general form such as multi-tone and random inputs, which can produce system responses that are induced by an interaction of system input components of different frequencies. In the present study, by introducing the concept of power transmissibility, the study of the beneficial effects of nonlinear damping is extended to the systems subject to general inputs including both multi-tone and random inputs. A rigorous analysis is conducted based on single degree of freedom systems subject to general inputs. The analysis reveals the conditions under which the antisymmetric nonlinear damping is beneficial for improving energy harvester performance and reducing of the power of system output in vibration isolation. Moreover, the beneficial effects are demonstrated by two case studies.
... Another fundamental quantity for the study of energy harvesters is efficiency. However, in these systems, compared to the maximum output power, it has received less attention [29]. Efficiency is the ratio of output power (electrical) to input power (mechanical). ...
Article
Full-text available
Environment vibrations are an important source of energy, often occurring at very low frequencies, but with large amplitude. The possibility to use the large amplitude of the motions is important to enhance the energy harvester's output power. In this paper, an electromagnetic energy harvester is designed and fabricated to produce electricity from low- frequency high amplitude impact motions using an elastic polyurethane cylinder. This millimeter-scale electromagnetic generator (MS-EMG) includes a movable magnet attached to a free sliding mass, a fixed coil, and a polyurethane holding chamber. Polyurethane is a very stable elastic polymer that provides continuous large-amplitude movement for the magnet and plays an effective role in impact capability. Therefore, the effect of impact excitation and the polyurethane foam was investigated simultaneously. The performance of the device was studied, experimentally, for the environment vibrations in the range of 1 to 10 Hz. The impact motions were applied using a simulator that was fabricated for this work. The fabricated MS-EMG with a volume of 1.07 cm3 and a mass of 8.74 g show the capability of producing a voltage of 44.41 mV and power of 10.48 µW over a 100 Oresistive load, using a 6 Hz frequency impact motion. Finally, an analytical model is used to simulate the device performance which showed a good agreement with the experimental results.
... In a rotational harvester, a suitable motion transmission system is used to convert low frequency linear motion to high frequency rotational one. In [82], a ball screw was employed in the vibration harvester, as shown in Figure 7.6. In this system, the base movement causes the mass to vibrate. ...
Thesis
Although magnetic gears are more expensive and larger than mechanical gears for a given power rating, they are more efficient. They also offer the advantage of physical separation between the driving and driven shafts which can be in different environments, e.g., in water and in air. Recent research has focused on rotary magnetic gears, with limited work on linear to rotary and vice versa motion conversions, which is desirable in many applications such as wave energy harvesting. This thesis focuses on the development of the theory and design optimisation of a novel linear-rotary magnetic gear derived from a variable reluctance permanent magnet (transverse-flux) rotational machine topology. The configuration of a linear to rotary magnetic gear is developed and discussed. A design optimisation methodology is implemented based on finite element analysis. Using this methodology, optimal proportions and dimensions of a linear to rotary magnetic gear demonstrator are determined. It is shown that increasing the magnet thickness results in the increase transmitted torque, but with diminishing returns. The optimal results showed that the maximum torque density obtained about 11.3 kNm/m<sup>3</sup>. The proposed design methodology is successfully applied to the design of a two-pole (on the rotor) magnetic gear. A demonstrator is built and successfully tested, and theoretical predictions are validated. Based on the demonstrator in this study, the use of a linear-rotary magnetic gear for applications such as wave energy harvesting looks promising.
... This implies excitation frequencies beyond the natural frequency reduces the efficiency of the harvester [3][4][5]. The second limitation concerns the constrained physical enclosure of the VEH, which causes the suspended mass to oscillate within a specified span [6,7]. Therefore, for best performance, the maximum excitation level is considered at the design stage. ...
Chapter
Full-text available
One of two major limitations of a vibration energy harvester (VEH), concerns its limited performance due to its confined physical enclosure. The maximum span realizable is attained at a specific excitation level. This excitation level provides the maximum energy harvested by the VEH device. Due to span constraints, VEHs are designed to operate at the maximum span achievable at the maximum excitation level existing within the region of interest. In this study, a constrained optimisation problem (for the VEH) is formulated and investigated. This paper focuses on the analysis, design and optimisation of a nonlinear VEH device.
... Hence, The equivalent model of the hybrid system is represented in Figure 2. The equivalent mass of the cantilever beam along with the MFC and the tip mass form the first mass m1. The second mass m2 represents the mass of the magnet and the equivalent mass of the spring [2]. k1, k2, and c1, cm2 are the stiffness and damping coefficient of the two subunits. ...
Article
Full-text available
The aim of this paper is to boost the power output of the hybrid energy harvester effectively and to provide electrical optimization for a hybrid energy harvesting system that produces two electrical outputs from a single source of mechanical input namely vibration. Two different electrical outputs are produced by using the concept of piezoelectricity and electromagnetic induction. In this paper, an electrical equivalent is obtained for the standalone piezoelectric system and the electromagnetic system. The rectification of the piezoelectric system along with its results is discussed. Different circuits for amplification is studied and simulated to improve the voltage. All the practical experimental outputs and the different software used to gain these outputs are recorded. The various applications of the hybrid system are reviewed and discussed.
... However, if a rotational SDOF harvester was to be considered instead, then a slight modification needs to be made in the optimisation. Based on the concept of rotational harvesters demonstrated by Hendijanizadeh et al. [12], it can be shown that the electromagnetic coupling factor for a rotational SDOF electromagnetic harvester is instead of , where is defined as the 3 2 / D 2 / 3 rotary generator emf-constant. Note that this parameter is independent of the structural aspects. ...
Article
This paper demonstrates a two-stage optimisation for a single-degree-of-freedom (SDOF) electromagnetic vibration energy harvester under a harmonic base excitation vibration. In this paper, a designed cantilever beam was used to verify the optimisation methods. The dynamics of the beam was modelled using the Euler-Bernoulli beam theory. By deriving the exact expression of the power output under the optimum load resistance condition, the correct electromagnetic coupling coefficient was determined. The first optimisation stage involves maximising this coefficient by considering several coils and magnet parameters, allowing at this stage to define the electrical efficiency of the harvester which is described as the ratio of the harvester's power output to its power limit. The experimentally determined power output for this stage was 3.51 mW. The structural aspects of the harvester were then optimised by considering the addition and placement of proof masses and the structural dimensions of the harvester. This part represents the second optimisation and determines the power limit of the harvester. An experimental power output of 7.95 mW was achieved in this stage. All experimental results displayed a good agreement with the derived theoretical model, recording an error of less than 10.0%, hence validating the theoretical model. The first optimisation stage presented here can be applied to any linear electromagnetic SDOF harvester whereas the second optimisation stage can be easily modified to suit different structural considerations. Additionally, both stages can also be slightly modified to account for rotational systems.
Conference Paper
This paper presents the result of generated electrical energy from mechanical energy using an electromagnetic generator. This generated energy is very low. Efforts are made to develop an energy storage device for this generated energy. Capacitor bank and rechargeable batteries are used for store energy. This stored energy is used to recharge the battery of wearable electronic devices for extending battery discharging time. Diode pump and voltage booster circuit are developed to enlarge output voltage. The voltage booster a circuit reaches to the maximum level of 5V at 1.2V input voltage. This generated voltage is stored in the capacitor bank and rechargeable battery.
Chapter
This chapter reviews present usage of vibration-based energy harvesting (VEH) devices and their applications. The evolution of energy resources and advancement in electronic technologies has resulted in the need for a self-sustainable wireless/portable electronic device in current modern society. Batteries are non-beneficial in the miniaturization process of electronic designing, and alternative power supplies are desperately needed to drive the advance of the wireless/portable development further. VEH has emerged as one of the most promising alternatives to replace conventional batteries and as the solution for the bottleneck. Consideration of creating an optimal vibration energy harvester is suggested through an analytical model of a mechanical transducer, including a relatively new method defined as triboelectricity. Useful applications and usages of VEH are presented, and some suggestions for improvement are also given. Lastly, the trend of energy harvesting is annotated and commented in-line with the demand of electronic sensors market.
Article
Full-text available
Assuming a sinusoidal vibration as input, an inertial piezoelectric harvester designed for maximum efficiency of the electromechanical energy conversion does not always lead to maximum power generation. In this case, what can be gained by optimizing the efficiency of the device? Detailing an answer to this question is the backbone of this paper. It is shown that, while the maximum efficiency operating condition does not always lead to maximum power generation, it corresponds always to maximum power per square unit deflection of the piezoelectric harvester. This understanding allows better optimization of the generated power when the deflection of the device is limited by hard stops. This is illustrated by experimental measurements on vacuum-packaged MEMS harvesters based on AlN as piezoelectric material. The results obtained for a sinusoidal vibration are extended to random vibrations. In this case, we demonstrate that the optimum generated power is directly proportional to the efficiency of the harvester, thus answering the initial question. For both types of studied vibrations, simple closed-form formulas describing the generated power and efficiency in optimum operating conditions are elaborated. These formulas are based on parameters that are easily measured or modeled. Therefore, they are useful performance metrics for existing piezoelectric harvesters.
Article
Full-text available
Vibration energy harvesting is receiving a considerable amount of interest as a means for powering wireless sensor nodes. This paper presents a small (component volume 0.1 cm 3 , practical volume 0.15 cm 3) electromagnetic generator utilizing discrete components and optimized for a low ambient vibration level based upon real application data. The generator uses four magnets arranged on an etched cantilever with a wound coil located within the moving magnetic field. Magnet size and coil properties were optimized, with the final device producing 46 µW in a resistive load of 4 k from just 0.59 m s −2 acceleration levels at its resonant frequency of 52 Hz. A voltage of 428 mVrms was obtained from the generator with a 2300 turn coil which has proved sufficient for subsequent rectification and voltage step-up circuitry. The generator delivers 30% of the power supplied from the environment to useful electrical power in the load. This generator compares very favourably with other demonstrated examples in the literature, both in terms of normalized power density and efficiency.
Article
In previous papers, the authors proposed the fixed type and floating type wave energy conversion systems using ball screws. The fixed type is composed of a pressure plate and a ball screw type turbine settled in a caisson, and the floating type is composed of a floating body and one or two wave power buoys with a ball screw type turbine. The ball screw type turbine consists of a ball screw, a one-way clutch, a flywheel and a generator. The ball screw is useful in transforming slow linear motion into fast rotary motion with a high efficiency of more than 90 %, and wave power is efficiently converted into electric power by the ball screw. In this paper, the output characteristics of the fixed type and floating type wave energy conversion systems using the ball screw type turbine are calculated and compared. Both types of experimental models were made, and tank tests were carried out. The experimental results were compared with the calculated results, and the output characteristics and the propriety of the calculations were substantiated.
Conference Paper
Direct drive generators have the potential to simplify Wave Energy Converters (WEC) and increase reliability. In the last couple of decades several technologies proposing direct drive linear generators for wave energy converters have been proposed. In this paper a review of the current technologies for direct drive generators is carried out. Moreover, the most common magnetisation types for permanent magnets used in linear machines are reviewed.
Article
In order for an electromagnetic transducer to operate well as either a mechanical shunt damper or as a vibration energy harvester, it must have good electromechanical coupling. A simple two-port analysis is used to derive a non-dimensional measure of electromechanical coupling, which must be large compared with unity for efficient operation in both of these applications. The two-port parameters for an inertial electromagnetic transducer are derived, from which this non-dimensional coupling parameter can be evaluated. The largest value that this parameter takes is approximately equal to the square of the magnetic flux density times the length of wire in the field, divided by the mechanical damping times the electrical resistance. This parameter is found to be only of the order of one for voice coil devices that weigh approximately 1 kg, and so such devices are generally not efficient, within the definition used here, in either of these applications. The non-dimensional coupling parameter is found to scale in approximate proportion to the device's characteristic length, however, and so although miniaturised devices are less efficient, greater efficiency can be obtained with large devices, such as those used to control civil engineering structures.
Article
Nowadays, harvesting energy from vibration is one of the most promising technologies. However, the majority of current researches obtain 10 µW to 100 mW power, which has only limited applications in self-powered wireless sensors and low-power electronics. In fact, the vibrations in some situations can be very large, for example, the vibrations of tall buildings, long bridges, vehicle systems, railroads, ocean waves, and even human motions. With the global concern on energy and environmental issues, energy harvesting from large-scale vibrations is more attractive and becomes a research frontier. This article is to provide a timely and comprehensive review of the state-of-the-art on the large-scale vibration energy harvesting, ranging from 1 W to 100 kW or more. Subtopics include energy assessment from large vibrations, piezoelectric materials and electromagnetic transducers, motion transmission and magnification mechanisms, power electronics, and vibration control. The relevant applications discussed in this article include vibration energy harvesting from human motion, vehicles, transportations, and civil structures. The unique challenges and future research directions of large-scale vibration energy harvesting are also discussed.
Article
This article reports on the design and experimental characterization of an electromagnetic transducer for energy harvesting from large structures (e.g., multistory buildings and bridges), for which the power levels can be above 100 W and disturbance frequencies below 1 Hz. The transducer consists of a back-driven ballscrew coupled to a permanent-magnet synchronous machine with power harvesting regulated via control of a four-quadrant power electronic drive. Design considerations between various subsystems are illustrated and recommendations in terms of minimal values are made for each design metric. Developing control algorithms to take full advantage of the unique features of this type of transducer requires a mechanical model that can adequately characterize the device’s intrinsic nonlinear behavior. A new model is proposed that can effectively capture this behavior. Comparison with experimental results verifies that the model is accurate over a wide range of operating conditions. As such, the model can be used to assess the viability of the technology and to correctly design controllers to maximize power generation. To demonstrate the device’s energy harvesting capability, impedance matching theory is used to optimize the power generated from a base-excited tuned mass damper. Both theoretical and experimental investigations are compared and the results are shown to match closely.
Article
This paper proposes a device to harvest energy from the vertical motion of small boats and yachts. The device comprises a sprung mass coupled to an electrical generator through a ball screw. The mathematical equations describing the dynamics of the system are derived. The equations are used to determine the optimum device parameters, namely its mass, spring constant, ball screw lead, within practical constraints. Simulation results are presented to determine the maximum power that can be generated and the optimum load resistance as a function of boat vibration frequency.
Article
This work presents vibration control of a vehicle Suspension system using a controllable electrorheological (ER) shock absorber activated by all energy generator Without external power sources. The ER shock absorber has a rack and pinion mechanism which converts a linear motion of the piston to a rotary motion. This rotary motion is amplified by gears and Subsequently activates a generator to produce electrical energy. The generated voltage is experimentally evaluated with respect to excitation magnitude and frequency of the ER shock absorber. After evaluating the damping force using the regenerated voltage, a quarter-car ER Suspension model is established. A skyhook controller is then formulated and experimentally implemented to attenuate vibration using the regenerated energy. It has been demonstrated via experiment that suspension vibration under bumpy and sinusoidal road conditions is significantly controlled by activating the ER shock absorber operated by the proposed regenerative energy mechanism.