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of a Piezoelectric Converterfor Energy Harvesting
M. Guizzetti1, V. Ferrari1, D. Marioli1 and T. Zawada2
1Dept. of Electronics for Automation, University of Brescia, Italy
erroperm ezoceram cs , egg , v s gaar , enmar
Presented at the COMSOL Conference 2009 Milan
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Mechanoelectrical energy conversion
onvers on ec n ques
electromagnetic (inductive)
electrostatic (capacitive)
Direct piezoelectric effect: surface charge induced by a mechanical stress
Piezoelectric energy converter
unimorph cantilever shape (thick-film, MEMS technologies)
piezoelectric layer+ V
Thick ness Opt im iza t ion o f a Piezoe lec t r ic Conv er t e r fo r Energ y Harvest ing
mechanical substrate -2 / 1 2
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Use of COMSOL
mprovemen o e conver e energy
Optimization of the dimensions
piezoelectric layer thickness
Application modes piezoelectric: mechanical / electrical behaviour
sinusoidal vertical acceleration application
generated charge / voltage
moving mesh: thickness change
a+ V
Q PZT+ + + ++ + + ++ + ++ + + +
Thick ness Opt im iza t ion o f a Piezoe lec t r ic Conv er t e r fo r Energ y Harvest ing
-3 / 1 2
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Geometry
lenght L = 27 mm;
width w= 3 mm;
steel
piezoelectric layer thickness tPZT = 60 m (poled along thickness)
t
L
piezoelectric layer
s ee
Thick ness Opt im iza t ion o f a Piezoe lec t r ic Conv er t e r fo r Energ y Harvest ing
w
4 / 1 2
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Mesh
appe mes
320 quad elements; 11808 degrees of freedom
2 elementslinearly spaced
4 elementslinearly spaced
20 elementsex onentiall s aced
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Governing equations
ezoe ec r c ayer
strain-charge form11210
0070000
000502020
000205020
000202050
PasE
7000000
0700000
0110000
dTED
s
T
S = mechanical strain
T= mechanical stress [N/m2] E -1
11210
00055.25.2
0011000
CNd
d= piezoelectric coefficient [C/N]
D = electric displacement [C/m2]
E= electric field [V/m]
0
5000
0500
0050
T
= dielectric permittivity [F/m]
112
33000 mkg
Steel layer
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s
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Subdomain and boundary conditions
Body load Fz = a
a = 0.1 g
=
Mechanical boundary conditions clamped end
Electrostatic boundary conditions
bottom surface: grounded floating potential dt = 0 ; dn = deltaThick upper sur ace: oa ng po en a
other surfaces: zero charge
Mesh boundary conditions bottom surface: clamped
vertical surfaces: normally clamped
fixed dn = 0GNDfixed
zero charge
Thick ness Opt im iza t ion o f a Piezoe lec t r ic Conv er t e r fo r Energ y Harvest ing
upper sur ace: angen a y c ampe ,
normally displaced (deltaThick)
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Solver parameters
arame r c segrega e so ver
group 1: moving mesh, static analysis
deltaThick:-50 m340 m
group : p ezoe ec r c var a es, requency response
frequency = 10 Hz
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Results tip displacement
ment[nm]
tipdisplace
100
10 100 1000
piezoelectric layer thickness [ m]
tPZT =
m
PZT rigidity > steel rigidity
tip displacement nPZTt
1tPZT = 400 m
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Results electrical output
3.E-03
4.E-03
5.E-03
oltage[V]
6.E-13
7.E-13
8.E-13
[C]
voltage
charge
PZT rigidity > steel rigidity
0.E+00
0 100 200 300 400
piezoelectric layer thickness [ m]
3.E-13
1.4
]
voltage const
0.8
1.0
1.2
ricalenergy[fJ
Stored electrical energy
0.2
0.4
.
storedelect
QVE1
05.1
substrate
PZT
t
t
Thick ness Opt im iza t ion o f a Piezoe lec t r ic Conv er t e r fo r Energ y Harvest ing
.
0 100 200 300 400piezoelectric layer thickness [ m]
1 0 / 1 2
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Results influence of the geometry
eren geome r es Substratethickness
[m]
Width
[mm]
Length
[mm]
reference 200 3 27
geometry 1 300 3 27
geometry 2 200 6 27
geometry 3 200 3 10
geom 1
geom 2
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geom 3
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Conclusions
FEM simulations used for optimizing the geometrical dimensions of apiezoelectric energy converter
Geometry with parametrized thickness
piezoelectric application mode
moving mesh application mode
The optimal tPZT/tsubstrate was found for maximizing the electrical energy
The optimal tPZT/tsubstrate value is independent from the converter
This model is a specific example of using moving mesh for device
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