Proceedings of the 2009 IEEE
International Conference on Robotics and Biomimetics
December 19 -23, 2009, Guilin, China
A Fluttering-to-Electrical Energy Transduction System for
Consumer Electronics Applications
Fei Fei and Wen J. Li *
Centre for Micro and Nano Systems, The Chinese University of Hong Kong, Hong Kong SAR, China
Abstract—This paper presents a novel type of energy
transducer which converts ambient wind power into electrical
energy based on electromagnetic induction principle. Different
from traditional wind turbine generators, flexible belts were
designed and demonstrated to harvesting energy using
aerodynamically -induced fluttering. Essentially, airflows are
used to drive a specifically designed belt to vibrate periodically
during fluttering. Nd-Fe-B magnets and outer coils were
implemented with the fluttering belt to induce current in the
coils. The parameters of the coil are optimized for power output
using a FEM tool. Experiments in controllable lab conditions
were conducted to compare the performance of the prototype.
We propose that such energy transducer can be used as an
alternative or complementary power supply to batteries in low
power consumer electronics applications.
transmitter. Leonov et al. designed a thermoelectric generator
to convert human heat into usable electrical energy, which
had a power density of ~20 μW/cm2 [4, 5]. Beside these
systems, low level vibration based energy harvesting
technologies were also widely explored [6-9]. There are
mainly three transduction mechanisms to convert energy
from mechanical motion or vibration: electrostatic,
piezoelectric and electromagnetic. For electrostatic
generators, electrostatic charges of opposite signs are
developed and rendered to two conductors using mechanical
means. For piezoelectric transducers, deformation caused by
environmental force induces voltage based on piezoelectric
effect. In electromagnetic transducers, the relative motion of
magnet and coils caused an output voltage based on
electromagnetic induction.
However, electrostatic and
piezoelectric generators are currently still difficult to build in
batch for practical applications due to the limitations of
fabrication technologies and material performance.
Keywords – aerodynamic fluttering, wind-based generator,
electromagnetic generator, energy harvesting
I. INTRODUCTION
TABLE II [2]
DEMONSTRATED ENERGY HARVESTING CAPABILITIES
Electronic devices will continue to perforate the consumer
market in the coming decades. Although chemical batteries
are still the dominant energy source for electronic devices
(e.g., some of the common devices are listed in Table I [1]),
harvesting energy from the ambient environment in which the
devices operate in becomes an alternative or replacement
solution as producers strive to extend device operation time.
Energy source
Ambient radio frequency
Ambient light
Thermoelectric
Vibration source
TABLE I [1]
EXAMPLES OF BATTERY-SUPPORTED SYSTEMS
Device type
Smartphone
MP3 player
Hearing aid
Wireless sensor node
Cardiac pacemaker
Quartz watch
Power
consumption
1W
50 mW
1 mW
100 μW
50 μW
5 μW
Ambient airflow
<1 μW/cm
100 mW/cm2 (directed toward bright sun)
100 μW/cm2 (illuminated office)
60 μW/cm2
4 μW/cm3 (human motion - Hz)
800 μW/cm3 (machines - kHz)
1 mW/cm2
In this paper, we discuss a novel type of energy converter
using aerodynamic fluttering principle, which aims to harvest
energy from low speed wind flow to support electronic
applications such as wireless sensor networks and outdoor
lighting systems, etc. We have demonstrated a prototype that
consists of three parts: a) a wind-belt specifically designed to
which transfers the wind flows of ~3 m/sec into periodic
mechanical vibration; b) an electromagnetic resonant device
which have two coils fixed on a supporting housing and a
permanent magnet inside a movable bolt (i.e., as a piston); c)
a power management circuit which copes with the output AC
voltage of the resonant device and store the transduced
energy into a rechargeable super capacitor that could be used
as a battery for various applications. The energy flow of the
described system is shown in Fig. 1.
Energy autonomy
5 hours
15 hours
5 days
Lifetime
7 years
5 years
Ambient energy source exists in many sources, e.g.,
human motion, structural vibration, thermal, light and
wind/hydraulic flow, etc. Table II lists some of the possible
power that could be obtained from environmental sources [2].
Researchers have developed various kinds of energy
transducers to obtain ambient power according to source
types. For example, Kymissis et al. [3] presented a PVDF
system that would scavenge energy during walking; this
system provided approximately 2 mW to power up a radio
________________________________________________________
* Contact Author: wen@mae.cuhk.edu.hk.
978-1-4244-4775-6/09/$25.00 © 2009 IEEE.
Capabilities
2
580
Wind-Belt
Interation
Wind
Energy
Electromagnetic
Transducer
Vibrational
Energy
Electrical
Energy
Power
Conditioning
Circuit
always neglected because the attack angle α is very small in
practical conditions. In the simplest form, the flutter motion
could be considered as a two degree of freedom motion. The
motion equation can be represented as [14]:
Energy
Storage
(Battery/
Capacitor)
mh ch h k h h L ½
¾
ID cD D kD D M ¿
Fig. 1. Energy flow of the wind belt fluttering transducer.
h = vertical displacement
α = angular displacement
m = mass per unit length
I = section polar moment per unit length
ch = vertical damping coefficient
cα = rotational damping coefficient
kh = vertical stiffness coefficient
kα = rotational stiffness coefficient
where
II. AERODYNAMIC FLUTTERING SYSTEM
A. Wind Power and Flutter Energy Harvesting
Wind is a renewable energy source that does not produce
carbon dioxide like coal or petroleum. The energy in wind is
actually a derivation of solar energy as it is generated by the
uneven heating of the atmosphere by the sun. The power
density in wind is related to the cube of wind speed, the
equation representing this is:
(1)
P 1/ 2 ˜ U ˜U 3
Where is the air density and U is the wind speed, this
equation shows that the wind speed is very important for the
wind energy harvesting technique. For example, a 20%
increase in wind speed of 5 m/s results in a power density
increase of 73%.
Wind turbines are the most common device to obtain wind
energy now. They perform well when the wind is powerful
enough, but when they work at very low Reynolds numbers
or low wind speeds, performance deteriorates drastically.
Although the flutter effect is often considered as destructive
and unsafe, especially for long span structures such as airfoils
and suspension bridges, some researchers have investigated
energy harvesting based on elastic flutter model in order to
improve low wind speed energy harvesting efficiency.
Duncan [10] built the “flutter engine” to illustrate the flutter
phenomenon in his publication. McKinney and Delaurier [11]
demonstrated a wing windmill to extract energy from
oscillation wing. Isogai et al. [12] also proposed an elastic
wing system driven by electric motor to optimize the
efficiency. Recently, Shawn [13] and his group provided an
idea to create a new type of wind generator based on
belt-flutter phenomenon, which could be considered as a
good progress in utilizing elastic structures to harvest energy
from air flows. Fig.2 shows the basic working principle of his
design.
vibrating belt
(2)
L
U
M
α
Y
h
Reference position
X
Fig. 3. Cross section view of a fluttering flat structure.
Eq. (2) has a similar form as a second order response
system. So in terms of the critical damping ratio ,
and
the natural circular frequencies , , (2) can represent as:
m(h 2[ hZ h h Z h2 h)
L ½
°
¾
2
I (D 2[D ZD D ZD D ) M °
¿
(3)
Because of the difference of shapes and complex flow
around the structure, it is impossible to express the
self-excited lift force L and rotational moment M in an
empirically uniform equation. Scanlan and Tomko [15]
established the linearized relations between forces and
motion condition represented as:
m( H 1 h H 2D H 3D )½°
¾
M I ( A1 h A2D A3D ) °¿
L
(4)
In (4), the terms related to , and h are neglected due to
their little influence to L and M. The coefficients and are
called “flutter derivatives” and are usually measured
experimentally from low turbulence section tests in wind
tunnels. It turns out that the derivatives are functions of
reduced wind velocity (
, which consists of the
structure flutter frequency , structure width B and wind
velocity U.
To evaluate the accessibility of flutter, (3) and (4) can be
rewritten as:
coils
magnet
Fig. 2. Wind flutter generator proposed by Shawn [13].
B. Long Span Flat Structure Flutter Analysis
Fig. 3 shows the cross section view of long span structure
in a uniform flow of velocity U. As shown, a vertical
aerodynamic force L and an aerodynamic pitching moment M
act on the structure. The horizontal aerodynamic force is
h 2[ h Z h h Z h2 h
H 1 h H 2D H 3D ½°
¾
D 2[ D ZD D ZD2 D A1 h A2D A3D °¿
(5)
In (5), the flutter accessibility or stability depends on the
581
bending stiffness will allow better energy transfer and less
deformation than the center portion of the belt. For the
convenience of adjusting belt length or tension and
portability for future outdoor experiments, the belt and the
electromagnetic resonator are fixed on the extendable
supporting beam as shown in Fig. 4.
magnitudes and signs of the flutter derivatives. If the
and
related terms are moved to the left side of the equation, (5)
can be represented as:
h (2[ hZ h H 1 )h Z h2 h
H 2D H 3D ½°
¾
D (2[ D ZD A2 )D ZD D A1h A3D °¿
(6)
2
and
could be seen as negative
Then the
damping terms which extract energy from around airflow. If
the magnitude of the negative aerodynamics damping
coefficient
is greater than the structural damping
coefficient
, the entire system vibration amplitude will
increase until it reaches the equilibrium state. In the
equilibrium point, a steady flutter phenomenon will occur, at
which the vertical displacement and angular displacement can
be represented as
and
. So,
the critical flutter wind speed is very important in the
understanding of the dynamics of fluttering systems. Except
for the above theoretical stability analysis, Selberg [16]
proposed an empirical equation for critical flutter speed,
which can be written as:
v
(7)
U F 0.44B (ZT2 ZV2 )
P
Where
and
; r is radius of
gyration of the cross-section (
); m is the mass per
unit length; B is the structure width;
is the airflow density;
and
are the circular frequencies in rotational direction
and vertical direction, respectively. However, this empirical
formula is not very accurate and only used for coarse
prediction of critical flutter wind velocity because of the
complex geometries of the structures in practical
applications.
III. ELECTROMAGNETIC RESONANT
POWER GENERATOR DESIGN
A. Mass-Spring Resonator Design
In Shawn’s wind belt flutter system [13] as sketched in Fig.
2, magnets are fixed directly on the belt, which has several
problems if used for practical applications. For example, the
vibrating belt may encounter the coils when its amplitude is
increased at high wind speeds, and the location of magnets on
the belt should be systematically designed to ensure
maximized magnetic flux linkage between the magnets and
coils. To address these problems and increase the energy
harvesting efficiency from the fluttering belt, we propose a
new type of flutter resonant system design which is described
in Fig. 4 and Fig. 5. Below we present our analysis to
systematically optimize the system.
magnet
moveabl
e bolt
outer
coils
50mm
house
spring
base
60mm
Fig. 5. Architecture of the electromagnetic resonator.
C. Flutter Energy Harvesting System
For a typical second order mass-spring system, the motion
equation could be represented as:
(8)
mx cx kx F0 cos(Zt )
1.2 m
In (8), c is the system damping coefficient, k is the spring
constant, and
is the input excitation force.
,
Substituting the natural circular frequency
, and damping ratio into (8),
excitation amplitude
the equation becomes:
(9)
x 2]px p 2 x X 0 p 2 cos(Zt )
In addition, the system transmissibility, which is described
as the amplify factor, is given by:
1
X
, J Z
(10)
E
2
2
p
X0
(1 J ) (2]J )
Fig. 4. Wind flutter energy transduction system housed on an extendable
beam. The inset shows a close-up view of the electro-magnetic resonator.
Eq. (10) implies that when input frequency is near the natural
frequency, “resonance” of the mechanical structure will occur.
Structural resonance is in general considered hazardous, but
in micro/mini electromagnetic generator designs, it is an
important objective to match a vibrating structure’s natural
frequency within a known environmental excitation
In our experiments, a thin polymer belt (width = 25mm,
thickness = 0.2mm, length = 1.2m) is used to interact with the
impinging airflow. An electromagnetic resonator is placed
near the end of belt due to the larger bending stiffness of the
portions of the belt that are close to the fixed ends. The larger
582
frequency band in order to obtain the largest energy
transduction.
Note that when the mass of magnet is optimized to the
largest acceptable volume for a particular application, the
only designable parameter is the spring constant . Listed
below in Table III are three spring designs used in our
experiments, which will be described later in this paper.
Wire
diameter d
(mm)
0.4
0.5
0.6
TABLE III
SPRING CONSTANTS
Spring
Effect
Spring
diameter
turns
height H
D (mm)
N
(mm)
9
6
20
9
6
20
9
6
20
energy harvesting application, the frequency of input force is
lower than 1 kHz, so the influence of the inductance term can
be neglected. Also to maximize the flux linkage, several
design rules should be followed, such as the selection of
magnet material, proper numbers of turns for coils, and
relative positioning of magnets and coils, etc.
There are generally three types of permanent magnets that
could be utilized for electromagnetic generator designs. Table
IV [18] lists the main properties of them. Comparing with the
other two, Nd-Fe-B magnet has high flux density
performance and reasonable cost, so it is widely adopted in
applications.
Calculated
spring constant
k (N/m)
25.2
61.6
127.7
TABLE IV [18]
PROPERTIES OF PERMANENT MAGNETIC MATERIALS
Material
type
Ferrite
Ne-Fe-B
Sm-Co
B. Linear Electromagnetic Generator Design
The basic principle of almost all electromagnetic
generators is based on Faraday’s law of electromagnetic
induction. The voltage and electromotive force induced in a
coil circuit is proportional to the change rate of magnetic flux
linkage [17]:
d)
dI
(11)
V N
dt
dt
In (11), is the generated voltage and is the total flux
linkage. As in most such electromagnetic design, hundreds of
turns of coils are utilized to gain higher voltage. So the turn
coefficient N is multiplied to calculate the flux linkage. For
most linear vibration generators, the relative motion between
the coils and the magnet is in a single direction, and the
voltage induced in the coil can then be expressed as the
product of a flux linkage and the velocity.
dI dx
(12)
V N
dx dt
The electromagnetic force
, which is proportional to
the induced current in coils , acts against the environment
excitation force, and is given by:
dx
(13)
Fem Dem
dt
Where
is the electromagnetic damping coefficient. So in
order to harvesting maximum power from such linear
electromagnetic generator,
should be well designed
when the relative velocity
is limited. Moreover, the
dissipated power extracted by electromagnetic force can
represent as:
dx
V2
(14)
P Fem
dt RL Rc jZLc
Where RL and RC are load and coil resistances, LC is the coil
inductance. Then from (11) and (14), the expression of
electromagnetic damping coefficient can be derived as:
Flux density
(Br: mT)
300 - 500
1,100 - 1,500
1,000 – 1,200
Cercive force
(Hc)
High
High
High
Density
(kg/m3)
~4980
~8400
~7470
Cost
Low
Normal
High
Assuming that the vibration amplitude of inner magnet (as
shown in Fig. 5) follows the vibration amplitude and
frequency of the belt, then the two coils could be designed to
be adjusted vertically to obtain the largest flux linkage. Fig.6
shows the flux linkage distribution when the magnet is at
initial, up and down positions using Maxwell 2D FEM
analysis. The analysis indicates that when the magnet is
vibrating at a peak to peak amplitude of 10mm, the magnitude
of flux linkage along the edge of coils in vertical direction
could vary significantly, as shown in Fig.7. This simulation
result is then used to help optimize the location of outer coils.
coils edge
line
coils
magnet
adjustabl
e
z=0
initial
up
down
Fig.6. Flux lines between magnet and coils.
2
1
§ d) ·
(15)
¸
¨
RL Rc jZLc © dx ¹
From (15), RL, RC and LC terms should be reduced to
maximize the
. However, for a typical environmental
Dem
Fig. 7. Plot of flux magnitude along the edge of coils at three states.
583
C. Power Conditioning Circuits
In general, for most small scale generators, the primary
problem for power conditioning is to accumulate low power
electrical energy and store it into storage components such as
rechargeable batteries or super capacitors. However, due to
the high number of charge-discharge cycles (millions
compared to 200-1000 for rechargeable batteries) and quick
charging time, super capacitors are considered as the better
energy storage solution in the future. For the wind-belt
generator system, the generated power is mainly dictated by
the non-continuous ambient wind which is typically in low
frequency range, therefore, a 0.47F super capacitor is used to
store the converted power temporarily before using it to drive
electronics devices. In our experiments, the AC peak voltage
obtained from inductive coils is typically lower than 2.5 V as
seen in Fig.9 (CH2). The electrical energy stored in the
0.47F super capacitor after the charging circle is decided by
the charging voltage (
), the storage efficiency of
IV. EXPERIMENTS
To systematically analyze the performance of the prototype
generator, continuous airflow generated by an electric fan is
used to drive the belt into fluttering, which then allows the
electro-magnetic resonator to convert the wind energy into
electric power. Typical wind speed generated by the fan
during experiments is measured by a wind meter and is shown
in Fig. 10. Obviously, the wind speed is not a constant value
as an ideal laminar flow. The local turbulent flows and
vortices make the instantaneous wind speed fluctuate around
a mean speed. To estimate the wind flutter generator’s
performance, the average flow speed in a period (t = 150s) is
used to define the magnitude of wind speed, i.e., ~3 m/sec.
Bellows are other designed parameters used in experiments:
coil turns N=2000 (each); coil resistance
;
loading resistance RL=500Ohm; wind speed U = 1.5
m/s 3.5m/s (average); columnar magnets size (diameter =
10mm, thickness = 5mm, mass = 2.90 gram).
the super capacitor will be limited if the inducted AC voltage
is rectified and connected into the capacitor directly. Hence, a
voltage multiplier charging circuit is implemented to rectify
and boost the generator’s AC voltage before feeding it into
the capacitor as shown in the circuit schematic in Fig.8. Based
on this booster circuit, the charging DC voltage can be lifted
to 5.68V as shown in Fig.9 (CH1), which can increase almost
5 times the energy storage capability. Note that, for specific
applications, other supplementary circuits such as DC-DC
regulator can be added according to the input voltage and
current requirements.
Fig. 10. Plot of measured wind speed in lab conditions.
As expected, the fluttering frequency and the generated AC
voltage frequency is not only related to the wind speed but
also decided by the tension level of the belt. That is, the
tension level serves to control the belt’s spring constant, and
hence controls the vibration characteristics of the belt.
Generally, the belt vibrates at higher frequency when the
tension is higher, as shown in Fig. 11 (Spring type 1: without
spring; Spring type 2: k = 25.2 N/m; Spring type 3: k = 61.6
N/m; Spring type 4: k=127.7 N/m).
Fig. 8. Voltage multiplier booster charging circuit.
Fig. 9. AC voltage generated and DC voltage of charged capacitor.
Fig. 11. Relation between fluttering frequency and tension levels.
584
by the environmental wind speed and induced
electromagnetic force, different magnets, springs, and wind
speed were tested to characterize the resonant performance of
the system. With a wind speed of 3.1 m/s, 1.3 mW of
electrical power was extracted with our current design.
Further work will be focused on improving the
aerodynamic characteristics of flexible and deformable belt to
achieve higher energy conversion efficiency of the proposed
system.
Resonance characteristic of the electromagnetic resonator
with different springs is also compared in the experiments as
shown in Fig. 12. It is clear that when a spring is installed, the
system could harvest more power than without a spring. Note
particularly that Spring type 2 has a stable performance
during the entire experimental domain, and the peak AC
voltage value achieved by the wind flutter energy converter is
when the wind speed is nearly 3 m/s. Figure 13 shows the
effect to the voltage output of the system when different sizes
of magnets are used. Note that the largest mass does not
guarantee the highest output voltage, hence understanding of
the physical couplings between flutter, resonance, and
magnetic induction is extremely important to optimize the
system described in this paper.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Fig. 12. Comparison of different spring constants and wind speeds.
[7]
[8]
[9]
[10]
[11]
[12]
Fig. 13. Comparison of different springs and magnets at a given wind speed.
V. CONCLUSION
[13]
[14]
A prototype of electromagnetic-based wind-fluttering
resonant transducer has been demonstrated to harvest energy
from airflows. Optimizations of coil and magnet parameters
is settled,
When the constant wind speed (
different groups of spring and magnets are tested as shown in
Fig.13. From this figure, heavier magnet which means
stronger magnetic flux linkage is benefit for energy
harvesting. And spring type 2 and mass II has get a much
higher output voltage, which could be supposed to get the
specific nature frequency near with the instantaneous exciting
force frequency. were conducted to maximize the power and
harvesting efficiency of this novel system. Because the
vibration frequency of the fluttering belt is mainly controlled
[15]
[16]
[17]
[18]
585
R. J. M. Vullers, R. Van Schaijk, C.Van Hoof, R. Mertens, “Micro
power energy harvesting,” Solid-State Electronics, vol. 53, Issue 7, pp.
684-693, July 2009.
J. A. Paradiso and T. Starner, "Energy scavenging for mobile and
wireless electronics," Pervasive Computing, IEEE, vol. 4, no. 1, pp.
18-27, 2005.
J. Kymissis, C. Kendall, J. Paradiso, and N. Gershenfeld, "Parasitic
power harvesting in shoes," Wearable Computers, 1998. Digest of
Papers. Second International Symposium on, pp. 132-139, 1998.
V. Leonov, T. Torfs, P. Fiorini, and C. Van Hoof, "Thermoelectric
converters of human warmth for self-powered wireless sensor nodes,"
Sensors Journal, IEEE, vol. 7, no. 5, pp. 650-657, 2007.
Leonov V, Fiorini P, Sedky S, Torfs T, Van Hoof C, "Thermoelectric
MEMS generators as a power supply for a body area network,"
Solid-State Sensors, Actuators and Microsystems, 2005. Digest of
Technical Papers. TRANSDUCERS '05. The 13th International
Conference on , vol.1, no., pp. 291-294 Vol. 1, 5-9 June 2005.
S. Roundy, P. K. Wright, and J. Rabaey, "A study of low level
vibrations as a power source for wireless sensor nodes," Computer
Communications, vol. 26, no. 11, pp. 1131-1144, July 2003.
S. P. Beeby, M. J. Tudor, and N. M. White, "Energy harvesting
vibration sources for microsystems applications," Measurement
Science and Technology, vol. 17, no. 12, pp. R175-R195, 2006.
C. D. Richards, M. J. Anderson, D. F. Bahr, and R. F. Richards,
"Efficiency of energy conversion for devices containing a
piezoelectric component," Journal of Micromechanics and
Microengineering, vol. 14, no. 5, pp. 717-721, 2004.
Anton, R. Steven, Sodano, and A. Henry, "A review of power
harvesting using piezoelectric materials (2003-2006)," Smart
Materials and Structures, vol. 16, no. 3, pp. R1-R21, June 2007.
J. W. Duncan, The Fundamentals of flutter, ARC/R&M, London, 1948,
pp. 1-36.
W. McKinney, and J. DeLaurie, “The Wingmill: An Oscillating-Wing
Windmill,” J. Energy, vol. 5, pp. 109-115, 1981.
M. Isogai, K. Yamasaki, Matsubara, M., and Asaoka, T., “Design
Study of Elastically Supported Flapping Wind Power Generator,”
International Forum on Aeroelasticity and Structural Dynamics,
Amsterdam, 2003.
http://www.humdingerwind.com
R. H. Scanlan, “The Action of Flexible Bridges under Wind, I: Flutter
Theory,” Journal of Sound and Vibration, vol. 60(2), pp. 187-199,
1978.
R. H. Scanlan and J. J. Tomko, “Airfoil and bridge deck flutter
derivatives,” Journal of the Engineering Mechanics Division, vol. 97,
no. 6, pp. 1717-1737, 1971.
Selberg A, “Oscillation and aerodynamic stability of suspension
bridge,” Acta Polytechnica Scandinavica, Civil. Eng. and Building
Constr. Series, No. 13, 1961.
Shashank Priya, Dan Inman, Eneryg harvesting technologies, New
York; Longdon: Springer, c2009.
http://www.asahi-kasei.co.jp/ake/en/technical/magnet.html