Vibration Energy Harvesting - N.i.P.S) Lab · Vibration Energy Harvesters (VEHs): basic operating...

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

http://realvibration.nipslab.org/

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


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


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


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


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


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.


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.


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


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


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


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


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


Velocity-amplified mulitple-mass EM VEH


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


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



39



40



41


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


Prototype 2 with transversal magnetic flux

42


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


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

Vibration Energy Harvesting - N.i.P.S) Lab · Vibration Energy Harvesters (VEHs): basic operating...

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