Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
A MULTI-FUNCTIONAL CANTILEVER FOR ENERGY SCAVENGING FROM
VIBRATIONS
M. Wischke, P. Woias
Laboratory for Design of MEMS
Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany
Abstract: To overcome the drawbacks of battery technology in embedded sensors, environmental energy is
scavenged to power MEMS systems. Piezoelectric materials and electromagnetic set-ups are widely spread to
transduce vibrations into electrical energy. This paper presents the merging of a piezoelectric with an
electromagnetic transducer. The resulting hybrid energy generator shows a higher power density and an enhanced
power output. Two power sources within one system feature different interconnection possibilities, and two
different optimal load resistances.
Key Words: energy harvesting, vibration energy scavenging, piezoelectric, electromagnetic
acceleration, the cantilever is bent due to inertia forces,
and charge can be extracted from the piezoelectric
material. In the electromagnetic setup [5, 6], a coil (or
magnet) is fixed at a suspension. Again, inertia forces
lead to an oscillation with respect to the static magnet
(or coil). In the piezoelectric layout, the tip mass
material itself is functionless, only its mass is
important to tune the resonance frequency and enlarge
the tip amplitude. The suspension in the
electromagnetic layout serves as mounting for the
oscillator, but features no material functionality.
Replacing in each layout the parts without functional
material with functional ones creates a hybrid
piezoelectric electromagnetic generator. A schematic
setup is shown in Figure 1.
1. INTRODUCTION
The progress in the recent past brought along a
growing request for a more “intelligent” environment.
Modern buildings, for example, feature a technical
equipments, e.g. to incorporate the outside weather
conditions to achieve a pleasant climate inside, and
furthermore, to decrease the building’s power
consumption. Beside the improvement of comfort, the
safety of critical infrastructure such as bridges and
tunnels is of vital importance. Hence, many different
sensors are patched into urban infrastructures. In
general, these sensors can be considered as devices
using external energy to gather information of the
environment and transmit them. Due to the great
efforts in wireless communication the data
transmission requires a decreasing amount of space
and energy. Instead, the power feed-in appears
challenging since a wired supply is too extensive for
reconditioned systems or wide area networks. An
ambitious solution is that each sensor node supplies
itself by gathering energy from its environment.
Among the ambient energy sources, vibrations are
favorable as they are present in almost every building
and in machines with rotating parts. By far the best
suited transducers to retrieve energy from mechanical
vibrations are piezoelectric and electromagnetic
setups, as worked out in [1]. Up to now, each principle
is always employed in a separate system. The
following sections present the merging of both
principles into one hybrid generator, which combines
the advantages of both principles and features multifunctionality.
Fig. 1: Schematic setup of the hybrid generator.
Due to the functional principles involved, the
voltage of the piezoelectric part is in phase with the tip
displacement, whereas the output from the
electromagnetic part is in phase with the tip velocity.
With this p/4-phase shift, four power maxima are
deserved per period, furnishing the power more evenly
over the time.
Type
s11 [m2/N]
d31 [C/Vm]
e
t [µm]
PZT A
14.2*10-12
-315*10-12
4500
260
-12
4000
200
PZT B
16*10
-12
-290*10
2. DESIGN & FABRICATION
Tab. 1: Material properties of the two PZT ceramics.
Generally, piezoelectric materials are integrated in
cantilever structures [2-4] with a tip mass. Under
The cantilevers are fabricated in our proven piezopolymer-composite technology [7], where a two
73
Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
Fig. 2: Piezoelectric bimorph cantilever
electromagnetic parts before assembling.
and
compound epoxy resin is cast onto the piezo-ceramic
in a PDMS mold. For a benchmark of the output
power, two different PZT ceramics were used here.
The essential material properties are shown in Table 1.
The basic unimorph cantilever is 20 mm long, 5 mm
wide and has a total thickness of 500 µm. As structural
improvement [8], cantilevers with a varying width
have been fabricated. Neglecting the cantilever’s own
weight, this trapezoidal shape equilibrates the strain
across the beam length. The PZT area is equal in both
layouts. In order to increase the output from the
piezoelectric part, bimorph cantilevers with both
ceramics types and with constant and varying width
were manufactured (length 20 mm, 0.6mm thick). The
cylindrical coils are self-made from a 50 µm copper
wire with 500, 750 and 1000 windings. The inner coil
diameter is 2.2 mm, the coil height 1.5 mm, and the
outer diameter depends on the number of windings. In
the experimental setup, cylindrical NdFeB magnets,
2.0 mm in diameter and in height, and with a residual
induction of 1.17 Tesla are used. All components
(before assembling) are depicted in Figure 2.
PZT
Layout
fR [Hz]
calculated
Q
A
unimorph, rectangular
412
404
43
A
unimorph, trapezoidal
612
600
56
A
bimorph, rectangular
715
755
40
A
bimorph, trapezoidal
1101
1113
58
B
unimorph, rectangular
420
397
46
B
unimorph, trapezoidal
616
602
54
B
bimorph, rectangular
722
740
36
B
bimorph, trapezoidal
1105
1110
52
Tab. 2: Characteristics of all cantilever layouts.
This time and position dependent differential equation
can be solved with Bernoulli’s function:
υ ( x, t ) = X ( x) T (t ) .
(2)
Using a trigonometric approach for the time function,
expression (1) can be transformed into a differential
equation with derivatives with respect to space only.
This equation can be solved by:
⎛λ ⎞
⎛λ ⎞
X ( x) = C1 Cos⎜ x ⎟ + C 2 Cosh⎜ x ⎟
⎝l ⎠
⎝l ⎠
⎛λ ⎞
⎛λ ⎞
+ C 3 Sin⎜ x ⎟ + C 4 Sinh⎜ x ⎟
⎝l ⎠
⎝l ⎠
(4)
Applying the boundary conditions for a fixed-free
cantilever generates, after some calculations, the
expression (5) that defines the first eigenvalue l of the
oscillating structure. Assuming no damping, the first
eigenfrequency w (6) is equal to the basic resonance
frequency of the cantilever.
− 1 = Cos (λ ) Cosh(λ )
ω=
Fig. 3: Cantilever element with force and moment
resultants.
λ2
l
2
EI
δA
(5)
(6)
EI is the cantilever’s bending stiffness, dA the mass
resultant of inertia, l the cantilever length. Table 2
shows the calculated and measured values.
3. MODELING
For their characterization, the cantilevers are fixed
with their base to a shaker. A cantilever element
with force and moment resultants is shown in
Figure 3. From the balance of forces and
moments, the motion υ ( x, t ) can be expressed by:
EI
∂ 4υ
∂ 2υ
=
−
δ
A
.
∂x 4
∂t 2
Fig. 4: Equivalent electro-mechanical circuit of a
piezoelectric transducer.
(1)
74
Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
The electro-mechanical behavior of the piezoelectric
transducer, disregarding all nonlinear effects, can be
described by the equivalent circuit depicted in
Figure 4. The secondary part forms the mechanical
part of the piezo, which is stimulated by the velocity
u& = I2. The primary part, coupled via the inductor to
the mechanical part, embodies the electric behavior.
The voltage V of the piezo can be described by:
V = (RLoad || Cp )α u& =
RLoad
α u& .
1 + jR Load Xc
(7)
The phase shifts of this expression are written as
equation (8). Taking the phase of the velocity u& as
reference (=0°), the phase of V is only affected by the
phase shift of the impedance Z (9). In the case an of
open circuit, (RLoadض) V is shifted by 90° to the
induced voltage.
—V=—Z+— u&
(8)
—V=— (α R Load ) -— (1 + jR Load Xc)
(9)
Fig. 6: Output power and optimal load resistance of
coils with different numbers of windings.
recorded with a oscilloscope with phase measurement
capabilities. The peak acceleration was kept constant
to 1 g (9.81 m/ss) during all measurements. First, the
basic resonance frequencies and the quality factors Q
are determined (Table 2). The presented values are the
averages of five characterized devices each per layout.
For the analysis of the output power, all eight
cantilever types were combined with the three coil
sizes. Figure 6 shows the resulting output power of a
trapezoidal unimorph cantilever of PZT type B with
different coil sizes. Also the output power of a
bimorph cantilever with different electrical
interconnections between the piezoelectric layers and
the inductor were investigated (Figure 7).
With a decrease of the resistance load the phase shift
decreases until it reaches zero for the short circuit case
(RØ0). If so, the piezoelectric voltage is in phase with
velocity u& and the voltage from the coil. Figure 5
shows the transducer characteristics as a function of
the load resistance.
As RLoad impacts the current I1 it influences via the
transformer the mechanical behavior. Electrical
resistance loading leads to a higher mechanical
stiffness of the cantilever, which increases the
resonance frequency. This is synonymic to a lower
velocity and oscillating amplitude.
Fig. 7: Different interconnections of the piezoelectric
layers, and in parallel with the inductor.
Fig. 5: Phase, amplitude and output power versus load
resistacne.
6. DISCUSSION
4. EXPERIMENTAL RESULTS
Figure 5 clearly shows that the piezoelectric part and
the electromagnetic part have a significantly different
optimal load resistance. With a higher number of
windings, the inner impedance of the coil increases
and hence the optimal load increases too. However,
there is still a dip in the power between the two
The cantilever’s resonance frequency and output
power were determined on a shaker that was driven
with a sinusoidal input signal. The acceleration, the tip
deflection as well as the output voltage were
75
Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
generator parts. In the case of a bimorph cantilever, the
piezoelectric layer can be connected in parallel. Doing
this the output voltage is halved, but the electric
capacitance and the inner impedance are doubled.
Hence the optimal load is decreased from 200 kW to
70 kW without affecting the power output (see
Figure 7). In the same diagram it can be seen, that
parallel connected piezos in a parallel connection to
the coil (a) lead to the highest output compared to the
in series connected piezos with the parallel coil (b) and
the pure coil (c). In summary, the parallel connection
of the piezoelectric layers in a bimorph cantilever is
beneficial for the power output. However, the
piezoelectric and electromagnetic generator parts
should be used separately to extract all power and
benefit from the two optimal load resistances.
The comparison between the unimorph and bimorph
cantilever design of PZT A is plotted in Figure 8. As
the inducted voltage is regulated by ∂B / ∂t it is
evident that the unimorph design generates more
electromagnetic power. This is due to the higher tip
velocity which in turn results from the lower resonance
frequency. With the higher stiffness, the bimorph
exhibits a much higher resonance frequency and,
consequently, a much smaller tip velocity. Therefore
the electromagnetic power output is negligible
compared to the increased piezoelectric output, which
originates from the higher strain in the stiffer layout.
inclination of the coil this problem will vanish. The
cantilever layout with varying width shows a higher
resonance frequency (Table 2) compared to the
rectangular shape. Accordingly, the tip velocity and
the electromagnetic output power are smaller. Thus the
trapezoidal shape yields no advantage concerning the
output power, but requires a more complicated
fabrication. The variations between measured and
calculated results in Table 2 originate from inaccuracy
in the fabrication. As the two PZT ceramic types show
no important difference, the results are not presented
here.
6. CONCLUSION
With the presented design of a hybrid piezoelectricelectromagnetic generator the power output was
increased up to 150% compared to a single unimorph
piezoelectric cantilever (see Figure 8 top). It was
shown that the parallel connection of the piezos in a
bimorph layout is beneficial and the different generator
parts should be tapped separately. With its two optimal
load resistances, the improved power output, and the
different frequency layouts the hybrid generator is
capable of supplying wireless sensors with energy
from ambient vibrations. Numerical analysis will be
adopted to optimize the design and electromagnetic
coupling to enhance the performance of the next
generation of harvester.
REFERENCES
[1]
S. Roundy, P. K. Wright, J. M. Rabaey, “Energy
Scavenging for Wireless Sensor Networks”, Kluwer Academic
Publishers, 2003
[2]
E. M. Yeatman, P. D. Mitcheson, A. S. Holmes, “Microengineered devices for motion energy harvesting”, Proc. of
IEDM’07, Washington, USA, pp. 375-378, 2007
[3]
E. K. Reilly, E. Carleton, P. Wright, “Thin film
piezoelectric energy scavenging system for long term medical
monitoring”, Proc. of BSN’06, Boston, USA, pp. 38-41, 2006
[4]
W. J. Choi, Y. Jeon, J.-h. Jeong, R. Sood, S. G. Kim,
“Energy harvesting MEMS devices based on thin film piezoelectric
cantilvers”. J. of Electroceramics, Vol. 15, pp. 543-548, 2006
[5]
P. Glynne-Jones, M. J. Tudor, S. P. Beeby, N. M. White,
“An electromagnetic, vibration-powered generator, for intelligent
sensor systems”, J. of Sensor and Actuators A, Vol. 110, pp. 344349, 2004
[6]
E. Koukharenko, S. P. Beeby, M. J. Tudor, N. W. White,
T.
O’Donnell,
C.
Saha,
S.
Kilkarni,
S.
Roy,
“Mircoelectromechanical
systems
virbration
powered
electromagnetic generator for wireless sensors application”,
Microsyst. Technol., Vol. 17, pp. 1071-1077, 2006
[7]
C. Friese, F. Goldschmidtboeing, P. Woias,
“Piezoelectric Microactuators in Polymer-Composite Technology”,
Proc. of Transducers’03, Boston, USA, pp. 1007-1010, 2003
[8]
F. Goldschmidtboeing, P.Woias, “Characterization of
different beam shapes for piezoelectric energy harvesting”, J.
Micromech. Microeng., in press, 2008
Fig. 8: Comparison between the output power of a
unimorph (top) and a bimorph (bottom) cantilever.
Here a trade-off has to be found between the strain in
the piezo and the velocity of the magnet, in order to
maximize the extractable power from both generator
parts. An easy strategy to meet both requirements is to
increase the tip mass by using a larger magnet. Due to
the fixed-free condition of the cantilever, its tip moves
along a parabolic track. The magnet will therefore dip
into the coil with a certain inclination which reduces
the electromagnetic coupling. With a pre-set
76