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Vibration Energy harvesting: non-linear approaches
NiPS Summer School
July 14-18th, 2014
Perugia, Italy
Francesco Cottone
NiPS lab, Physics Dep., Università di Perugia
francesco.cottone at unipg.it
1
Summary
• Vibration energy harvesting applications and principles
• Limits of linear vibration energy harvesters
• Beyond linear VEH systems: nonlinear approaches
• Wideband technique comparison
• Conclusions
2
Energy harvesting applications
02/07/2014 - Belo Horizonte (Brazil)
(birdge at FIAT factory)
Wireless Sensor Networks
Energy Harvesting could enable 90% of WSNs applications (IdTechex)
Environmental MonitoringStructural Monitoring
Transportation
Wearable sensing for health
applicationsEmergency medical response
Monitoring, pacemaker, defibrillators
Military applications
3
Vibration-driven wireless sensor node
4
Objective : 1cm3 with less than 100 µW power consumption
Temporary storage
and conditioning electrinics:
• Ultra capacitors
• Rechargeable Batteries
Energy harvesting system:
• piezoelectric,
• electromagentic,
• electrostatic,
• magnetostrictive
Sensor node and
transceiver
Mechanical vibrations
Vibration Energy Harvesters (VEHs): basic operating principles
Inertial generators are more flexible than direct-force devices because they require only one point of attachment to a moving structure, allowing a greater degree of miniaturization.
Load (ULP sensors, MEMS actuators)
Bridge Diodes Rectifier
Cstorage
ZL
Vout
AC/DC converter Vibration
Energy Harvester
RL
Transducer
k
i
F(t)
zRL d
m
fe
k
i
Transducer
F(t)=mÿ
zd
m
fe
y
zinc oxide (ZnO) nanowiresWang et al. 2008
Energy harvesting from moth vibrations Chang. MIT 2013
Energy Harvesting from dancing
5
Vibration energy harvesting versuspower requirements
ICT
Dev
ice
Po
we
rC
on
sum
pti
on
Time
VEH
sP
ow
er
De
nsi
ty
Zero Power ??
100-300W/cm3 ?
6
Vibration HarvestingGenerator
Magnetostrictive
Piezoelectric
Electromagnetic
Vibration Energy Harvesters (VEHs): basic principles
V
Moving magnet
Spring
Coil
(a) (b)
(c)
Electrostatic/Capacitive
Proof mass
Springs
Vb
7
Conversion techniques comparison
Technique Advantages Drawbacks
Piezoelectric • high output voltages • well adapted for
miniaturization• high coupling in single crystal• no external voltage source
needed
• expensive• small coupling for
piezoelectric thin films • large load optimal
impedance required (MΩ)• Fatigue effect
Electrostatic • suited for MEMS integration• good output voltage (2-10V)• possiblity of tuning
electromechanical coupling• Long-lasting
• need of external bias voltage• relatively low power density
at small scale
Electromagnetic • good for low frequencies (5-100Hz)
• no external voltage source needed
• suitable to drive low impedances
• inefficient at MEMS scales: low magnetic field, micro-magnets manufacturing issues
• large mass displacement required.
8
Human activity
Gorlatova, M et al (2013). Movers and shakers: Kinetic energy harvesting for the internet of things.
Example of vibration sources
9
Example of vibration sources
10
Chicago North Bridge
http://realvibration.nipslab.org
Car in highway
Walking person
A general model for VEHs
RL
k
i
coil
magnet
ÿ
z
Bz
Electromagnetic transduction Piezoelectric transduction
k
i
Piezo bar or cantilever beam
ÿ
z
RL
Seismic massmagnet
Vibrations
( )
( )
L
L c i L c
dU zmz dz V my
dz
V V z
11
A general model for VEHs
22
0 2
2
2 2 2
( )2 ( )( )
e
c
L c c
PY m j
R j m d j k j
0
j ty Y e
( )
L
L c i L c
mz dz kz V my
V V z
Case of LINEAR mechanical oscillator
21( )
2U z kz
2
0c c
Z mYms ds k
Vs s
Z mY
det A(s
c)
mY (sc)
ms3 (mc d)s2 (k
c d
c)s k
c
,
V mY
det A
cs
mY cs
ms3 (mc d )s2 (k
c d
c)s k
c
.
Hence, the transfer functions between displacement and voltage over input acceleration are given by
H
ZY(s)
Z
Y, (a) H
VY(s)
V
Y. (b) By substituting s=j in , we can calculate the electrical
power dissipated across the resistive load
Laplace transform
12
• narrow bandwidth that implies constrained resonant frequency-tuned applications
• Non-adaptation to variable vibration sources
• small inertial mass and high resonant frequency at micro/nano-scale -> most of vibration sources are below 100 Hz
Main limits of resonant VEHs
At 20% off the resonance
the power falls by 80-90%
13
Beyond linear harvesting systemsFrequency tuning
Wu et al. 2008
Challa et al. 2008
Roundy and Zhang 2004
Piezoelectric cantilever with
a movable mass
Piezoelectric cantilever with magnetic tuning
Piezoelectric beam with a
scavenging and a tuning part
Zhu, et al. (2010). Sensors and Actuators A: Physical
14
Beyond linear harvesting systemsFrequency tuning
Tang et al. 2010
15
Multimodal Energy Harvesting
Beyond linear harvesting systems
Ferrari, M., et al. (2008). Sensors and Actuators A: Physical
Hybrid harvester with piezoelectric and electromagnetic transduction
mechanisms
Tadesse et al. 2009
Shahruz 2006
Piezoelectric cantilever arrays
with various lengths and tip masses
16
H. Kulah and K. Najafi, IEEE Sensors Journal 8 (3), 261 (2008).
D.G. Lee et al. IEEE porc. (2007)
Frequency-up conversion
Jung, S.-M. et al. (2010). Applied Physics Letters
Beyond linear harvesting systems
Le, C. P., Halvorsen (2012). Journal of Intelligent Material Systems and
Structures
Impact electrostatic MEMS generator
17
Burrow, S.G and Clare, L.R. IEEE porc. (2007)
Nonlinear systems
Beyond linear harvesting systems
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009).
18
2 0 1 2
2 2 3/2
1( , )
2 2 ( )eff
M MU x K x
x
Magneto-elastic potential
Governing equations of a single-DOF
piezo-magnetoelastic model
( , ) ( ) ( ) ( ) ( ) ( )
1( ) ( ) ( );
eff v
c L p
U xmx t x t K x t K V t my t
x
V t V t K x t R C
Mechanical vibrations
Piezoelectric beam
x
ÿ
m
Opposing magnets
Vout
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009).
Beyond linear harvesting systemsNonlinear systems for vibration energy harvesting
19
Bistable oscillators for vibration energy harvesting
Resonant monostableBistable: inter-well and
intra-well oscillations
Bifurcation point
x
U(x,)
=25mm
x
U(x,)
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009). 20
Bistable oscillators for vibration energy harvesting
Resonant monostableBistable: inter-well and
intra-well oscillations
Bandwith enhancement
when interwell jumps occur
x
U(x,)
=25mm
x
U(x,)
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009). 21
Buckled beam piezoelectric harvesters
Snapping between buckled states
Cottone, F., Gammaitoni, L., Vocca, H., Ferrari, M., & Ferrari, V. (2012). Smart materials and structures, 21(3), 035021
stretching
bending
stretching
PP
Bistable oscillators for vibration energy harvesting
22
L L
x
L0
z
w(x,t)
hp
hs
Steel support
Piezoelectric layer
V (t)ip(t) Cp RL
RL
b
zk+1
zk
P
Buckled piezoelectric beams
1( , ) ) ( , )(w x t w v x tx
stretching
bending
stretching
0( ) (1 cos(2 / )) / 2x h x L
the initial buckling shape function is
P
by applying Euler-Lagrange equations
( ), ( )d d
F t I tdt q q dt
L L L L
gives two coupled second order nonlinear differential equations
governing the motion of the piezoelectric buckled beam
Where the output voltage is related to the flux linkage
0 1
33 2 1 0
2
,
2 2 .L p P P
V V
k kV V
R C C C
mq cq k q k k q k z
q qq
P
V
Bistable oscillators for vibration energy harvesting
23
Experimental and numerical results
Cottone, F., L. Gammaitoni, H. Vocca, M. Ferrari & V. Ferrari (2012)
Piezoelectric buckled beams for random vibration energy harvesting. Smart materials and structures, 21.
Bistable oscillators for vibration energy harvesting
24
Experimental and numerical results
Cottone, F., L. Gammaitoni, H. Vocca, M. Ferrari & V. Ferrari (2012)
Piezoelectric buckled beams for random vibration energy harvesting. Smart materials and structures, 21.
Bistable oscillators for vibration energy harvesting
25
Nonlinear electromagnetic generators for wide band vibrational energy harvesting
26
2 2
3
2 2
( ) 1 ( ) ( )( ) ( ) ( ) ,
d q dq d yq q V
d Q d d
2( )( )
1,
em
dV dqV k
d d
0 / ( )R L 2 2
2
1 1
( ).em
c c
Blk
k L k L
22
1 0
pzkk C
Nonlinear electromagnetic generators for wide band vibrational energy harvesting
27
Bandwidth
enhancement of 2.5x
with bistability at 0,2 grms
Université Paris-Est, ESIEE Paris,
Silicon MEMS-based electrostatic harvesters.
• Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F. and T. Bourouina. Non-linear MEMS electrostatic kinetic energy harvester with a
tunable multistable potential for stochastic vibrations, (2013) Conf. Proceeding. IEEE TRANSDUCERS 2013.
• Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F. and T. Bourouina. Bistable multiple-mass electrostatic generator for low-frequency
vibration energy harvesting, (2012) Conf. Proceeding. IEEE MEMS (2013).
• R., Guillemet, Basset., P, Galayko, D., Cottone, F., Marty, F. and T. Bourouina. Wideband MEMS electrostatic vibration energy harvesters
based on gap-closing interdigitated combs with a trapezoidal cross section, (2012) Conf. Proceeding. Accepted for publication at IEEE MEMS
2013.
• Cottone, F., Basset, P., Vocca, H. and Gammaitoni, L. Electromagnetic buckled beam oscillator for enhanced vibration energy harvesting, Conf.
Proceeding. 2012 IEEE International Conference on Green Computing and Communications, Conference on Internet of Things, and Conference
on Cyber, Physical and Social Computing. (2012).
Electrostatic generators
28
Nonlinear MEMS electrostatic kinetic energy harvester
Basset, P., Galayko, D., Cottone, F., Guillemet, R., Blokhina, E., Marty, F., & Bourouina, T. (2014). Journal of Micromechanics and Microengineering
24(3), 035001
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013). 2013 Transducers & Eurosensors.
29
Guilllemet, R., Basset, P., Galayko, D., Cottone, F., Marty, F., & Bourouina, T. (2013).
Micro Electro Mechanical Systems (MEMS), 2013 IEEE 26th International Conference on (pp. 817-820): IEEE.
𝑘𝑠𝑝
𝑘𝑠𝑡
𝑔0
𝑚𝑠
𝑅𝐿
𝑉0
𝑑
Mathematical modeling
2 2
2 2
( ),a i
d x dx dU x d ym c c m
dt dt dx dt
0( ) ,L
dR C V V U
dt
2 2
0 lim
2 2
0 lim
1 1( ) , for
2 2( )
1 1( ) ( ) , for
2 2
sp
sp st
k x C x U x x
U x
k k x C x U x x
0 0
0 0
2 21( ) ln ln ,
2par f f
d x hr d x hrC x C N l
r d x d x
Governing equations
30
Nonlinear MEMS electrostatic kinetic energy harvester
𝑘𝑠𝑝
𝑘𝑠𝑡
𝑔0
𝑚𝑠
𝑅𝐿
𝑉0
𝑑
Mathematical modeling
2 2
0 lim
2 2
0 lim
1 1( ) , for
2 2( )
1 1( ) ( ) , for
2 2
sp
sp st
k x C x U x x
U x
k k x C x U x x
31
Nonlinear MEMS electrostatic kinetic energy harvester
Electrostatic generators
F. Cottone, P. Basset Université Paris-Est, ESIEE Paris,
Silicon MEMS-based electrostatic harvesters.
32
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013).
Transducers & Eurosensors.
33
Nonlinear MEMS electrostatic kinetic energy harvester
Basset, P., Galayko, D., Cottone, F., Guillemet, R., Blokhina, E., Marty, F., &
Bourouina, T. (2014). JMM 24(3), 035001.
Bistable multiple-mass electrostatic generator for low-frequency vibration energy harvesting
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013).
Bistable multiple-mass elecrostatic generator for low-frequency vibration energy
harvesting (MEMS), 2013 Conference.
MicroGenerator
Mass
MicrometricScrew
BuckledBeams Springs
VMicro Electrostatic
VEH
Vibrations
Bistable ExciterBase Mass
Linear springs
yz1
z2
34
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013). Bistable multiple-mass elecrostatic generator for low-
frequency vibration energy harvesting (MEMS), 2013 Conference.
35
Bistable multiple-mass electrostatic generator for low-frequency vibration energy harvesting
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013). Bistable multiple-mass elecrostatic generator for low-
frequency vibration energy harvesting (MEMS), 2013 Conference.
0 2 4 6 8 10-0.5
0
0.5
Time (s)
Voltage (
V)
0 2 4 6 8 10-0.5
0
0.5
Time (s)
Voltage (
V)
Bistable mode
Normal mode
low-freq. Inter-well jumps (a)
(b)
36
Bistable multiple-mass electrostatic generator for low-frequency vibration energy harvesting
Velocity-amplified mulitple-mass EM VEH
Beyond linear harvesting systems
1 1 2 1 22
1 2
( 1) ( )i if
e m v m em vv
m m
the final velocity of the smaller mass is
v2f = 2v1f − v2i.
In the case of equal but opposite initial velocities
v2f = − 3v2i,
which represents a gain factor of 3x in velocity.
if 𝑒 = 1 and in the limit of m1 / m2 → ∞,
37
Beyond linear harvesting systems
For a series of n−bodies of progressively
smaller mass that impact sequentially, the
velocity gain is proportional to n.
(Rodgers et al., 2008)
, 1
1,0
2 , 1
1(1 ) 1
1
nk k
n
k k k
eG e
r
38
Velocity-amplified mulitple-mass EM VEH
Beyond linear harvesting systems
39
Velocity-amplified mulitple-mass EM VEH
Beyond linear harvesting systems
40
Velocity-amplified mulitple-mass EM VEH
Beyond linear harvesting systems
41
Velocity-amplified mulitple-mass EM VEH
Moving coil
Gap magnet
expansions (iron)
High Q-factor
springs
Linear low friction
guides
Base for clamping
Top cap
NdFeB Magnets
University of Limerick (Ireland) and Bell-Labs Alcatel (USA).
F. Cottone, G. Suresh, J. Punch - “Energy Harvesting Apparatus Having Improved Efficiency”. US Patent n. 8350394B2
Beyond linear harvesting systems
Prototype 2 with transversal magnetic flux
42
Velocity-amplified mulitple-mass EM VEH
Moving coil
Gap magnet
expansions (iron)
High Q-factor
springs
Linear low friction
guides
Base for clamping
Top cap
NdFeB
Magnets
Velocity-amplified mulitple-mass EM VEH
University of Limerick (Ireland) and Bell-Labs Alcatel (USA).
F. Cottone, G. Suresh, J. Punch - “Energy Harvesting Apparatus Having Improved Efficiency”. US Patent n. 8350394B2
Beyond linear harvesting systems
Prototype 2 with transversal flux linkage
Improvement up to a
factor 10x
43
Comparison of various approaches
Zhu, D., Tudor, M. J., & Beeby, S. P. (2010). 44
Performance metrics
Mitcheson, P. D., E. M. Yeatman, et al. (2008). "Energy harvesting from human and machine motion for wireless
electronic devices." Proceedings of the IEEE 96(9): 1457-1486.
Bandwidth figure of merit
Frequency range within which the output power is less than 1 dBbelow its maximum value
45
Conclusionso Most of vibrational energy sources are random and present low frequency content.
o Linear vibration energy harvesters are limited and application dependent.
o The efficiency of Vibration Energy Harvesting can be improved with nonlinear approaches such as:
o Freqeuncy tuning
o Multimodal systems
o Freqeuncy-up converters, impacting masses
o Bistable nonlinear systems
o There’s plenty of room for improvement at level of
o nonlinear dynamics,
o material properties,
o miniaturization procedures,
o efficient conditioning electronics.
o In general nonlinear systems like bistable/multistable oscillators are the best choice for wideband vibration harvesting
46
Technical challenges
o Miniaturization issues: improving coupling coefficient at small scale and power density
o Improvements of piezoelectric-material properties
o Improving capacitive design
o Increasing remanent magnetic filed in micro magnets
o Research on electrets
o Efficient conditioning electronics
o Mechanical rectification ?
o Efficient Integrated design
o Power-aware operation of the powered device
47
Research activities done in collaboration with
2013
2011
2008
2010
Thank you
48