Vibration Energy Harvesting usingMulti-Frequency and Nonlinear
Piezoelectric ConvertersVittorio FerrariDepartment of Information EngineeringUniversity of Brescia - ITALY
Davide Alghisi Marco BaùSimone DalolaMarco Demori
Acknowledgments and credits to:
Marco Ferrari Michele GuizzettiDaniele MarioliEmanuele Tonoli
V.Ferrari London, March 28, 2012
ContentsIntroductionMulti-frequency piezoelectric harvester arraysNonlinear piezoelectric harvestersConclusions
V.Ferrari London, March 28, 2012
ContentsIntroductionMulti-frequency piezoelectric harvester arraysNonlinear piezoelectric harvestersConclusions
V.Ferrari London, March 28, 2012
vibrations
Vibration Energy Harvesting
Energy
CONDITIONING LOAD
Electrical domain
CONVERSION
The load can be sensors with wireless communication: → Autonomous Sensors
If available power is insufficient for continuous operation → Intermittent operation
PiezoelectricConverter
Rectifier andStorage element
Comparator andtriggered switch
Sensor andInterface electronics
RF Transmitter
Energy management
PiezoelectricConverter
Rectifier andStorage element
Comparator andtriggered switch
Sensor andInterface electronics
RF Transmitter
Energy management
vibrations1/15
V.Ferrari London, March 28, 2012
Piezoelectric Power Conversion
vibrating structure
m
k r z
x
y
piezo
Z L jωY
E 1 / k
V
I C
S
α : 1
m
F y r
1 / k
Z L F y mX ω 2 = -
ram
rXmP x
88
2222
lim ==&&
A maximum exists to the power that can be extracted by an ideal converter, irrespective of the conversion principleThis power limit occurs at resonance and for a converter with a purely resistive mechanical impedance adapted to r:
leA
=αl
A
F, X
V
I
V.Ferrari London, March 28, 2012
Piezoelectric Power Conversion
vibrating structure
m
k r z
x
y
piezo
Z L jωY
E 1 / k
V
I C
S
α : 1
m
F y r
1 / k
Z L F y mX ω 2 = -
r
at resonance
A maximum exists to the power that can be extracted by an ideal converter, irrespective of the conversion principleThis power limit occurs at resonance and for a converter with a purely resistive mechanical impedance adapted to r:
ram
rXmP x
88
2222
lim ==&& Same results as in:
C.B. Williams, R.B. Yates,, Sens. Actuat. A 52, 8-11 (1996).
V.Ferrari London, March 28, 2012
Limitations with Resonant Converters
This is problematic to guarantee with frequency-varying vibrations and is considerably sub-optimal for broadband and random vibrations frequency f 0
frequency f 0
Lowering the converter quality factor increases the bandwidth, but worsens the peak response
Best harvesting effectiveness is when the converter operates at mechanical resonance
frequency f 0
V.Ferrari London, March 28, 2012
Broadband Approaches
Resonance tuningMulti-modal/multi-frequency harvestersFrequency-up conversion Nonlinear
V.Ferrari London, March 28, 2012
ContentsIntroductionMulti-frequency piezoelectric harvester arraysNonlinear piezoelectric harvestersConclusions
V.Ferrari London, March 28, 2012
Multi-Frequency Converter ArrayMultiple differently-tuned converters combined to obtain a wider equivalent bandwidth:
-80
-70
-60
-50
-40
-30
-20
-10
0
0 100 200 300 400f [Hz]
Vo/V
i [dB
]
31 2
Measured frequency response.
m3
m2
m1 V2
V3
Conductive base
V1
Bimorph commercial cantilevers (RS 285–784): 15 mm×1.5 mm×0.6 mm, m1 = 1.4 g, m2 = 0.7 g, m3 = 0.6 g.
Mechanical Vibrations
SENSOR
Switched-Supply
Unit
MultiFrequency Converter Array
Impedance-Controlled Oscillator RF Transmitter
VOSC
Measured voltage acrossthe storage capacitor.
0123456789
0 10 20 30t [s]
V Cb
[V]
2ALL
tswitching
tswitching
M. Ferrari et al., Sens. Actuat. A 142, 329-335 (2008).
V.Ferrari London, March 28, 2012
L
W
W = 18 mmL = 31 mmFilm Thickness = 125 µm
Screen-Printed Piezoelectric Films
parameter BULK CERAMIC THICK FILM rel. permittivity εΤ/εo 4100 100density ρ [g/cm3] 7.5 4.5 piezoelectric coeff. d33 [pC/N] 590 < 10
Alumina substrate
Harmonic steel substrate
Lead zirconate titanate (PZT) powder in polymeric binderCuring: (10 min @ 150°C)
Electrodes: Ag polymeric inkPoling: (10 min @ 4 MV/m @130°C)
W
LC
LP
W = 5 mmLC = 35 mmLP = 30 mm
W
LC
LPW
LC
LP
W = 5 mmLC = 35 mmLP = 30 mm
Top electrode (20µm)
Steel shim (200µm)
PZT (100µm)
Piezokeramica-APC 856 powder (soft material)
V.Ferrari London, March 28, 2012
Steel Implementation of a MFCA
Open-circuit voltages @ 1 gpk acceleration
Converter 1 Converter 2 Converter 3
VP (V
)
Steel cantilevers (40 mm×5 mm×0.5 mm)Cured thickness of PZT film: 75 µmSeries bimorph configuration
Internal impedance:400 pF || 20 MΩ @ 100 Hz
V.Ferrari London, March 28, 2012
Output Combinations in a MFCA
Parallel-like combination:Rectified currents are fed to a single capacitor
Series-like combination: Rectified voltages on different capacitors are summed
m 3
m 2
m 1 V 2
V 3
V 1
8/15
V.Ferrari London, March 28, 2012
Output Combinations in a MFCA I1 ICb
VP1
CP1
RP1 D
D C
VP2 D
D C
VP3 D
D C
Cb
CP2
RP2
CP3
RP3
VCb
V1
V2
V3
I2
I3
The storage capacitor is charged prevalently by the converter with the highest instantaneous levelThe voltage is determined by the dominant converterUnder wideband excitation, all the converters contribute to shorten the charging time
R L
SW
9/15
Series
VP1
CP1
RP1 D
D C
VP2 D
D C
VP3 D
D C
Cb2
CP2
RP2
CP3
RP3 Cb3
Cb1
VCb
V1
V2
V3
VCb1
VCb2
VCb3
Each storage capacitor is charged by the corresponding converterThe voltage is given by the sum of the single voltagesInactive converters worsen energy transfer to the load due to charge redistribution upon switching
Parallel
M. Ferrari et al., Proc. SENSORDEVICES-2010, (2010).
V.Ferrari London, March 28, 2012
Experimental Results on Steel MFCA
Converter 1 Converter 2 Converter 3
VP (V
)
Series-like configuration
Parallel-like configuration
The series-like configuration outputs a higher voltage at parity of excitationThe series-like configuration reaches the threshold to trigger the RF transmission
10/15M. Ferrari et al., Proc. SENSORDEVICES-2010, (2010).
V.Ferrari London, March 28, 2012
MEMS Implementation of a MFCA
500 ? m500 ? m500 ? m500 µm
Design: University of BresciaFabrication: CNM, BarcelonaPZT paste: MEGGIT/Ferroperm
Screen-printed PZT filmIDT electrodes (d33 mode)
V.Ferrari London, March 28, 2012
New Designs of MEMS MFCAsDesign: University of BresciaFabrication: CNM, Barcelona
BE-SOI process (10 mm × 10 mm) dieCantilever resonant frequencies: 4.5÷9 kHz - 3.5÷6.5 kHz
Array of straight and tapered cantilevers
V.Ferrari London, March 28, 2012
Deposition of Piezoelectric Film
PZT paste: MEGGIT/Ferroperm
Sputtered Cr bottom electrode (tCr ≅ 0.5 µm) Screen-printed PZT film (tPZT ≅ 30 µm)
1 mm
1 mm
V.Ferrari London, March 28, 2012
Top Electrode and PolingTop electrode: direct writing* of Ag polymeric inkPoling: 120 V @100°C, 10 min
* Manual artwork in the first prototype
V.Ferrari London, March 28, 2012
Preliminary Results
-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.250.30
0 0.002 0.004 0.006 0.008Time [s]
Am
plitu
de [V
]
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.001 0.0012 0.0014 0.0016 0.0018 0.002Time [s]
Am
plitu
de [V
]
f = 9787 Hz-0.50-0.40-0.30-0.20-0.100.000.100.200.300.400.50
0 0.002 0.004 0.006 0.008Time [s]
Am
plitu
de [V
]
-0.50-0.40-0.30-0.20-0.100.000.100.200.300.400.50
0.001 0.0012 0.0014 0.0016 0.0018 0.002Time [s]
Am
plitu
de [V
]
f = 9298 Hz
Internal impedance @ 10 kHz:CP = 7÷10 pF; RP = 10 ÷30 MΩ
Impulse response tests:
V.Ferrari London, March 28, 2012
Preliminary Results
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-0.1 0.0 0.1 0.2 0.3 0.4 0.5Time [ms]
Volta
ge [V
]
R2_2R2_7R2_8Sinusoidal excitation of
the shaker (apk ≈ 1 g) Measurement of open-circuit voltage
Brüel & KjærPower amplifier
type 2719
Brüel & KjærVibration exciter
type 4808Agilent Waveform generator 332200A
LeCroyDSO LT374M
Brüel & KjærPower amplifier
type 2719
Brüel & KjærPower amplifier
type 2719
Brüel & KjærVibration exciter
type 4808
Brüel & KjærVibration exciter
type 4808Agilent Waveform generator 332200AAgilent Waveform
generator 332200A
LeCroyDSO LT374M
LeCroyDSO LT374M
V.Ferrari London, March 28, 2012
ContentsIntroductionMulti-frequency piezoelectric harvester arraysNonlinear piezoelectric harvestersConclusions
V.Ferrari London, March 28, 2012
Nonlinear ConverterBistability is exploited to amplify displacement induced by broadband vibrations
For decreasing values of d:Quasi linearityNonlinearity Bistability
Collaboration with Univ. Catania (S. Baglio) and Univ. Perugia (L. Gammaitoni)
M. Ferrari et al., Sens. Actuat. A 162, 425-431 (2010).
V.Ferrari London, March 28, 2012
Nonlinear Converter: ExperimentBimorph cantilever beam fabricated with:
Stainless steel substrate (thickness 200 µm)Low-curing-temperature PZT films
White-noise excitation filtered in the bandwidth 1-100 Hz
M. Ferrari et al., Sens. Actuat. A 162, 425-431 (2010).
V.Ferrari London, March 28, 2012
Nonlinear Converter: ResultsFor suitably low gap d, jumps occur between stable statesThe output voltage spectrum broadens and VPrms increases
-15
-10
-5
0
5
6 9 12 15Time [s]
Out
put v
olta
ge V
P [V
]
-10
-5
0
5
10
15
20
25
30
35
Bea
m d
efle
ctio
n [m
m]
Stable states
d = 2.5 mm
Out
put v
olta
ge V
P [V]
Tip
disp
lace
men
t x [m
m]
0.0001
0.001
0.01
0.1
1
10
1 10 100Frequency [Hz]
FFT
mod
ule
mag
nitu
de
25mm8mm5mm2.5mm
Distance d [mm] rms output voltage VPrms [V]25 4.27
5 6.112.5 7.99
arms = 0.3 g
M. Ferrari et al., Sens. Actuat. A 162, 425-431 (2010).
Complex dynamics, see: S.C. Stanton et al., Physica D 239, 640-653 (2010).
V.Ferrari London, March 28, 2012
Nonlinear Single-Magnet ConverterA ferromagnetic substrate is coupled to a fixed magnet
-8-7-6-5-4-3-2-1012
14 14.2 14.4 14.6 14.8 15Time [s]
Tip
disp
lace
men
t x [m
m]
-3-2-101234567
Out
put v
olta
ge V
P [V]Stable states
decreasing d
3xxFAv βα −= kxFel −= 42
42)()( xxkxU βα
−−
=
M. Ferrari et al., Sens. Actuat. A 172, 287-292 (2011).
xd
Permanent magnet
Input mechanical excitation
N S
VP
PZT film
FA
FAh
Ferromagnetic cantilever
t
Fel
V.Ferrari London, March 28, 2012
Mechanically-Induced BistabilityAn elastic beam compressed up to buckling shows bistability and double-well potentialPZT layers on the beam perform enhanced energy conversion from bending vibrations
F. Cottone et al., Smart Mater. Struct., 21, 035021 (2012).
Collaboration with Univ. Paris-Est (F. Cottone) and Univ. Perugia (L. Gammaitoni)
V.Ferrari London, March 28, 2012
Experimental Results
PZT films screen printed on steel shims (f0 = 220 Hz)Shaker driven by Gaussian noise: autocorrelation time τ = 1 ms; acceleration 1÷3 grms
F. Cottone et al., Smart Mater. Struct., 21, 035021 (2012).
Collaboration with Univ. Paris-Est (F. Cottone) and Univ. Perugia (L. Gammaitoni)
V.Ferrari London, March 28, 2012
Impact-Enhanced Multi-Beam EHTop piezo
beam
Bottom piezo beam
Driver beam (nonpiezo
high compliance)
Base excitation
PZT parallel bimorph on flexible steel
Beam dimensions: (45×19×0.58) mm3
Internal impedance @ 100Hz: CP = 270 nF; RP = 20 kΩ
V.Ferrari London, March 28, 2012
Modelling: Noninteracting Beams
T, B and D beams operate independently as uncoupled oscillatorsThe outputs of T and B peak at the respective resonant frequenciesPoor response at low frequency
sY
E 1 / k
V
I
C
S
α : 1
m
F y
Z L
1/k R m
F y mX = 2 s
Bottom piezo (B)
Toppiezo (T)
Driver (D)
m
F y F
y mX ω 2 = -
1/k R m
sY
d T d B
y
D
y
T
y
B
x
sY
E 1 / k
V
I
C
S
α : 1
m
F y
Z L
1/k R m
F y mX = 2 s
V.Ferrari London, March 28, 2012
Modelling: Interacting Beams
sY
E 1 / k
V
I
C
S
α : 1
m
F y
Z L
1/k R m
F DT
F y mX = 2 s
Bottom piezo (B)
Toppiezo (T)
Driver (D)
m
F y F
y mX ω 2 = -
1/k R m
sY
Assumptions:Impulsive impact of D on T/BZero engaging time No effect on D by T/B
( )⎪⎩
⎪⎨⎧
=
>=
0
0 0
,,
,,
BTDBDT
BTDBDT dyf
dF
&
d T d B
y
D
y
T
y
B
x
sY
E 1 / k
V
I
C
S
α : 1
m
F y
Z L
1/k R m
F DB
F y mX = 2 s
T/B voltage
off-resonance response
resonant decaying response
V.Ferrari London, March 28, 2012
Experimental ResultsEH mounted on the shaker (Brüel & Kjær Vibration exciter type 4808)Swept-frequency excitation of the shaker (apk = 1 g @ 50 Hz)
0
1
2
3
4
5
6
7
8
9
10
0 25 50 75 100 125Frequency [Hz]
rms
volta
ge [V
]
Top
Bottom
Noninteracting beams
0
1
2
3
4
5
6
7
0 25 50 75 100 125Frequency [Hz]
rms
volta
ge [V
]
Top
Bottom
Quadratic sum
Interacting beams
Power on matched load: 1÷2 mW
V.Ferrari London, March 28, 2012
Experimental Results
Handheld EH intentionally shaken RF transmissions start after 10 to 15 s and repeat every few seconds under moderate to forcible shaking
RF Receiver Piezoelectric Converter
Rectifier and storage capacitor
Sensing and switching
Voltage regulator
Oscillator
RF Transmitter
DC
Temperature & angular position
sensors
433 MHz OOK
F. CeriniD. Roncali University of Brescia
V.Ferrari London, March 28, 2012
Nonlinear MultiFrequency Array
N S Base
Beam 3
Beam 4
Piezo-ferromagnetic beam 1
Beam 2
MFCA and NL concepts merged into a compact configurationThe beams have different frequency responses
Parameter Beams 1, 3 Beams 2, 4 Steel thickness [µm] 200 100Tip mass no yesRes. frequency [Hz] 150 30
Electrodynamic shaker (Bruel & Kjaer 4808)
Converter
-1.5
-1
-0.5
0
0.5
1
1.5
0 5 10 15 20Time [s]
Acc
eler
atio
n [g
]
D. Alghisi et al., Proc. Conv. Nazionale Sensori, (2012).
V.Ferrari London, March 28, 2012
Experimental Results
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5Time [s]
Am
plitu
de [V
]
MagnetNo magnet
Beam 1
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.1 0.2 0.3 0.4 0.5Time [s]
Am
plitu
de [V
]
MagnetNo magnet
Beam 2
-1
-0.5
0
0.5
1
1.5
2
0 0.1 0.2 0.3 0.4 0.5Time [s]
Am
plitu
de [V
]
MagnetNo magnet
Beam 3
-3
-2
-1
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5Time [s]
Am
plitu
de [V
]
MagnetNo magnet
Beam 4
Typical responses with and without the magnet
Complex dynamics: quasi linear, nonlinear, bistable In all cases the magnet increases the rms output
D. Alghisi et al., Proc. Conv. Nazionale Sensori, (2012).
V.Ferrari London, March 28, 2012
Experimental ResultsTypical responses with and without the magnet
Complex dynamics: quasi linear, nonlinear, bistable In all cases the magnet increases the rms output
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5Shaker driving level [V]
Out
put r
ms
ampl
itude
[V]
No Magnet
Magnet
Beam 1
D. Alghisi et al., Proc. Conv. Nazionale Sensori, (2012).
V.Ferrari London, March 28, 2012
Summing UpLinear MFCA harvesters: Bandwidth is not amplitude-sensitive
Good performances with multi-tone excitationsBandwidth is limited by the
resonances of the array elements
m 3
m 2
m 1 V 2
V 3
V 1
Nonlinear (NL) harvesters Bandwidth exceeds the range
of linear resonancesGood performances with random excitationsSufficient amplitude is needed for bandwidth expansion
NL- MFCA harvesters: Benefits of both classes Triggering of nonlinearity/bistability
by mutual interactions among converters and magnet(s)
N S
V.Ferrari London, March 28, 2012
ContentsIntroductionMulti-frequency piezoelectric harvester arraysNonlinear piezoelectric harvestersConclusions
V.Ferrari London, March 28, 2012
ConclusionsPiezoelectric elements and PZT thick films on different substrates investigated for energy harvestingPromising approaches studied for energy harvesting from broadbandvibrations:
Multi-Frequency converter arraysNonlinear convertersNonlinear converter arrays
m 3
m 2
m 1 V 2
V 3
V 1
T. Zawada and M. Guizzetti at MEGGIT-Ferroperm (DK):collaboration on the piezoelectric materials.P. Colombi at CSMT - Brescia for providing sputtering.MIUR:
Projects PRIN 20078ZCC92 (2008-2010); PRIN 2009KFLWJA (2011-2013).
Acknowledgments
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