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NiPS Laboratory – Department of Physics and Geology – University of Perugia

Kinetic Energy Harvesting

NiPS Summer School 2017

June 30th - July 3rd - Gubbio (Italy)

Francesco CottoneNiPS lab, Physics Dep., Università di Perugia, Italy

francesco.cottone at unipg.it


Outline

NiPS Summer School 2017 – June 30th - July 3rd - Gubbio (Italy) – F. Cottone

• Motivations of energy harvesting

• Introduction to Kinetic Energy Harvesting

• Theoretical model

• Macro to micro/nano Kinetic Energy Harvesting: scaling problems and examples

• Final considerations



Wasted thermal energy

Transmitted EM energySolar

Vibrations

Traffic

Hydro/wind

RF

Biochemical

Thermal energy Radioactivity

What is an energy harvester ?

El. Interface

Energy Storage

Temporary Energy Storage: battery/supercap

EH WSN

Wirelesssensor node


Power budget


Dev

ice

Po

we

rC

on

sum

pti

on

Time

VEH

sP

ow

er

De

nsi

ty

Zero Power ??

100-300W/cm3 ?

10 – 40W

100 mW – 2 W

1 mW – 100 mW

1 – 10 W

< 10W


Historical human-made energy harvesters


Crystal radio - 1906Sailing ship (XVI-XVII century)

Self-charging Seiko wristwatch 1988

First automatic wristwatch, Harwood, c. 1929 (Deutsches Uhrenmuseum, Inv. 47-3543)

First automatic watch. Abraham-Louis Perrelet, Le Locle. 1776

Wind mill (Origin: Persia,3000 years BC)

SELF-powered by Radio Frequencies !!!

http://en.wikipedia.org/wiki/Abraham-Louis_Perrelet



Energy havesting applications

02/07/2014 - Belo Horizonte (Brazil)(birdge collapse at FIAT factory)

Environmental MonitoringStructural Monitoring

Nanomedicine

Healthcare sensorsEmergency medical responseMonitoring, pacemaker, defibrillators

Military applications


Vibration sources


Chicago North Bridge

http://realvibration.nipslab.org

Car in highway

Walking person

http://realvibration.nipslab.org/


Vibration sources


An average human walking up a mountain expends around 200 Watts of power.

The most amount of power your iPhone accepts when charging is 2.5 Watts.

Source: White Paper - Texas Instruments 2005


Vibration Energy Harvesting: research


Energy Harvesting

Devices

Energy Conversion Techniques

Materials



Macro

Magnetic energy harvesters

Piezoelectric

devices

Vibrational Structures with Magnetic Shape

Memory Alloy (NiMnGa)

Micro

Electrostatic Generators

Piezo Micro beams of stripes

ZnO, BaTiO3

Electrets SiO2, Parylene, Teflon

base

Nano

Piezoelectric nanopillars,

nanoribbons etc.

Triboelectric generators

Electrets nano-spheres

Vibration Energy Harvesting: scale


Vibration energy harvesting


Kinetic to electricity conversion techniques

MagnetostrictivePiezoelectric

Electromagnetic

V

Moving magnet

Spring

Coil

(a) (b)

(c)

Electrostatic/Capacitive

Proof mass

Springs

Vb


Dynamical model of VEH


RL

Transducer

k

i

F(t)

zRL d

m

fe

k

i

Transducer

F(t)=mÿ

zd

m

fe

y

At micro/nano scale direct force generators are much more efficient because not limited by the inertial mass!!!

( )

( )

L

L c i L c

dU zmz dz V my

dz

V V z

( )( )

( )

L

L c i L c

dU zmz dz V F t

dz

V V z

Inertial generatorsrequires only onepoint of attachmentto a movingstructure, allowinga greater degree ofminiaturization.




RL

Transducer

k

i

F(t)

zRL d

m

fe

k

i

Transducer

F(t)=mÿ

zd

m

fe

y

Inertial generatorsrequires only onepoint of attachmentto a movingstructure, allowinga greater degree ofminiaturization.

Power fluxes

3( )mP t my z l z ( ) ( ) ( )mP t F t z t

2 ( )( )L

dU zmzz dz z V z F t z

dz



( )

( )

L

L c i L c

dU zmz dz V my

dz

V V z

, , ,c i Parameters that depends only on the transduction technique!

0

j ty Y e

( )

L

L c i L c

mz dz kz V my

V V z

For LINEAR mechanical oscillators withelastic potential well

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

.

Laplace transform




22 2

0

2( )

2 ( )( )e

c

L L c c

PV Y m j

R R j m dj k j

( )

L

L c i L c

mz dz kz V my

V V z

For LINEAR mechanical oscillators

By substituting s=j in , we can calculate the electricalpower dissipated across the resistive load


In the approximate version, at resonance =n, (William et al.)

3 2 2 4 2

0

2 24( ) 2( )

e n e ne

e m e m

m Y m d YP

d d

Where c, and are included in the

electrical damping factor de



Piezoelectric conversion

Unpolarized Crystal

Polarized Crystal

After poling the zirconate-titanate atoms are off center. The molecule becomes elongated and polarized

Pioneering work on the direct piezoelectric effect (stress-charge) in this material was presented by Jacques and Pierre Curie in 1880

In 1903 Pierre received the Nobel Prize in Physics with his wife, Marie Skłodowska-Curieand and Henri Becquerel, for the research on the radiation phenomena discovered by Professor Henri Becquerel.




Man-made ceramics• Barium titanate (BaTiO3)—Barium titanate was the first

piezoelectric ceramic discovered.• Lead titanate (PbTiO3)• Lead zirconate titanate (Pb[ZrxTi1−x]O3 0≤x≤1)—more

commonly known as PZT, lead zirconate titanate is the most common piezoelectric ceramic in use today.

• Lithium niobate (LiNbO3)

Naturally-occurring crystals

• Berlinite (AlPO4), a rare phosphate mineral that isstructurally identical to quartz

• Cane sugar• Quartz (SiO2)• Rochelle salt

Polymers• Polyvinylidene fluoride (PVDF): exhibits piezoelectricity

several times greater than quartz. Unlike ceramics, long-chain molecules attract and repel each other when an electric field is applied.

direct piezoelectric effect

Stress-to-charge conversion

Biological• Bones• DNA !!!

V

http://en.wikipedia.org/wiki/Barium_titanate

http://en.wikipedia.org/wiki/Lead_titanate

http://en.wikipedia.org/wiki/Lead_zirconate_titanate

http://en.wikipedia.org/wiki/Lead

http://en.wikipedia.org/wiki/Zirconium

http://en.wikipedia.org/wiki/Titanium

http://en.wikipedia.org/wiki/Oxygen

http://en.wikipedia.org/wiki/Lithium_niobate

http://en.wikipedia.org/wiki/Berlinite

http://en.wikipedia.org/wiki/Phosphate

http://en.wikipedia.org/wiki/Mineral

http://en.wikipedia.org/wiki/Sugarcane

http://en.wikipedia.org/wiki/Quartz

http://en.wikipedia.org/wiki/Potassium_sodium_tartrate

http://en.wikipedia.org/wiki/Polyvinylidene_fluoride

http://en.wikipedia.org/wiki/DNA




Strain-charge

t

E

T

S s T d E

D d T E

Stress-charge

E t

S

T c S e E

D e S E

• S = strain vector (6x1) in Voigt notation

• T = stress vector (6x1) [N/m2]

• sE = compliance matrix (6x6) [m2/N]

• cE = stifness matrix (6x6) [N/m2]

• d = piezoelectric coupling matrix (3x6) in Strain-Charge

[C/N]

• D = electrical displacement (3x1) [C/m2]

• e = piezoelectric coupling matrix (3x6) in Stress-Charge [C/m2]

• = electric permittivity (3x3) [F/m]

• E = electric field vector (3x1) [N/C] or [V/m]

F33 Mode

V-

+

3

12

31 Mode

FV

+

-

3

1

2



Piezoelectric conversionconverse piezoelectric effect

direct piezoelectric effect

Voigt notation is used to represent a symmetric tensor by reducing its order.Due to the symmetry of the stress tensor, strain tensor, and stiffness tensor, only 21 elastic coefficients are independent. S and T appear to have the "vector form" of 6 components. Consequently, s appears to be a 6 by 6 matrix instead of rank-4 tensor.

Depending on the independent variable choice 4 piezoelectric coefficients are defined:



22 3131

11 33

.

. E T

El energy dk

Mech energy s

Electromechanical Coupling is an adimensional factor that provides the effectiveness of a piezoelectricmaterial. It is defined as the ratio between the mechanical energy converted and the electric energy input or the electric energy converted per mechanical energy input

Characteristic PZT-5H BaTiO3 PVDF AlN(thin film)

d33 (10-10 C/N) 593 149 -33 5,1

d31 (10-10 C/N) -274 78 23 -3,41

k33 0,75 0,48 0,15 0,3

k31 0,39 0,21 0,12 0,23

𝜀𝑟 3400 1700 12 10,5





y(t)

z(t)

Mt

RL

i

strain

Lb

VL

Piezoelectric plates

( )

L

L c i L c

mz dz kz V my

V V z

hp

hs

Piezoelectric layer

Subtrate layer

Le

Lm

Ep and Es are the Young’s modulus of piezolayer and steel substrate respectively

31 2/ , ,

1 / , 1 / ,

p L

c L p i i p

kd h k R

R C R C

1 2

1 22

3 3

2

,

3 (2 )2, ,

3(2 )2

2

/, 2 ,

2 12 12

p

b m e

b m eb b m

s p b p s p b s

b p

k k k E

b l l lIk k

b l l ll l l

h h w h E E w hb I w h b

Governing equations

Inertia area moment of the beam



Equivalent circuit

i(t)

Ri

Lc

RL

RL

k

i

coil

magnet

ÿ

z

Bz

magnet ( )

L

L c i L c

mz dz kz V my

V V z

/ , ,

/ , / ,

L L

c L c i i c

Bl R Bl R

R L R L

Electromagnetic conversion

Governing equations

V

Moving magnet

Spring

Coil

(a) (b)

(c)


Electrostatic conversion


𝑘𝑠𝑝

𝑘𝑠𝑡

𝑔0

𝑚𝑠

𝑅𝐿

𝑉0

𝑑

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

Governing equations



Y. Lu, F. Cottone, S. Boisseau, F. Marty, D. Galayko, and P. Basset, Applied Physics Letters 2015.

Electrostatic conversion


Figure of merit


Galchev et al. (2011)

Bandwidth figure of merit

Frequency range within which the output power is less than 1 dBbelow its maximum value

Mitcheson, P. D., E. M. Yeatman, et al. (2008).


Figure of merit


Mitcheson, P. D., E. M. Yeatman, et al. (2008).

Bandwidth figure of merit

Frequency range within which the output power is less than 1 dBbelow its maximum value

Galchev et al. (2011)


Comparison of conversion techniques


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.


Microscale energy harvesters


MEMS-based drug delivery systems

Bohm S. et al. 2000

Body-powered oximeter

Leonov, V., & Vullers, R. J. (2009).

D. Tran, Stanford Univ. 2007

Heart powered pacemaker

Pacemaker consumption is 40uW.

Beating heart could produce 200uW of power

Micro-robot for remote monitoring

A. Freitas Jr., Nanomedicine, Landes Bioscience, 1999

The input power a 20 mg robotic fly is 10 – 100 uW




Chang. MIT 2013

Jeon et al. 2005

D. Briand, EPFL 2010

M. Marzencki 2008 – TIMA Lab (France)

ZnO nanowires Wang, Georgia Tech (2005)

Piezoelectric




EM generator, Miao et al. 2006

Cottone F., Basset P. ESIEE Paris 2013

Mitcheson 2005 (UK)Electrostatic generator 20Hz 2.5uW @ 1g

Le and Halvorsen, 2012

Electrostatic and electromagnetic


Microscale energy harvesters: scaling issues


First order power calculus with William and Yates model

h

w

l

• Low efficiency off resonance

• High resonant frequency at miniature scales

• Power A2l4 where A is the acceleration and l the linear dimension

outV2

2n n

E hC

l

3

3

Ewhk

l

Boudary conditions C1

doubly clamped 1,03

cantilever 0,162

Boudaryconditions Uniform load Point load doubly clamped 32 16

cantilever 0,67 0,25





h

w

l

outV

3

3 2

0

22 2

1 2( )

e

n

e

e m

n n

m Y

P

that is

At resonance, that is =n , the maximum power is given by

3 2 2 4 2

0

2 24( ) 2( )

e n e ne

e m e m

m Y m d YP

d d

for a particular transduction mechanism forced at natural frequency n, the power can be maximized from the equation

The instantaneous dissipated power by electrical damping is given by

2

0

1( ) ( )

2

x

T

dP t F t dx d x

dt

The velocity is obtained by the first derivative of steady state amplitude

2

0

2 2 2,

(1 ) (2( ) )e m

r YX

r r

2

24 ( )

eel

n m e

m AP

Max power when the condition e=m is verified

or with acceleration amplitude A0=n2Y0.





h

w

l

outV2

2n n

E hC

l

3

3

Ewhk

l

3 322 2

2

2

0.32( / 4) 0.32( / 4)

4 ( ) 816

si mo si moeel

n m e n m

n m

si

lwh l lwh lm AP A A

E hC

l

30.32 0.32( / 4)eff beam tip si sim m m lwh l

At max power condition e=m

By assuming

1

0.01

/ 200

/ 4

m

A g

h l

w l

2 4/ 800 0.32 64

16

200

si moel

n m

si

P A lE

C




NEMS-VEHs

MEMS-VEHs

MEMS-VEHs

NEMS-VEHs

1

0.01

/ 200

/ 4

m

A g

h l

w l

By assuming


Piezoelectric micro-pillars


ZnO nanowires forest

ZnO Pillar

Wang 2004X. Wang 2011




Hydrotermal synthesisLength: 15 mThickness: 4 – 6 um A. Di Michele, G. Clementi, M. Mattarelli, F. Cottone




Length: 17 mThickness: 5umFirst mode: 10.9 Mhz

Stress-strain equations

Strain-charge form

t

E

T

S s T d E

D d T E

A. Di Michele, G. Clementi, M. Mattarelli, F. Cottone


Piezoelectric micro-pillars, ribbons, nano-wires


• Implementation of vertically-aligned ZnO micropillars on IDE and other geometry (e.g. horionzontal)

• Use of the devive as VEH and vibration sensor• Fabrication of same device with BaTiO3 • Use of the piezo pillars as micro electro-mechanical antenna

Microfibre-Nanowire:

Wang(2008)

Yang(2009)

Piezoelectric ribbon: Microantenna

:

Onda EM

V V


Final considerations


o Kinetic energy harvesting systems are promising technology to enable autonomous low-power wireless devices

o Main transduction techniques are piezoelectric, inductive and electrostatic: large research is beign carried out for both materials and device fabrication

o Theoretical model is complete for linear oscillator based VEH

o Reducing the size to micro and nano is challenging The application decide wether it si convenient reone macro-scale VEH

o Inertial vibration energy harvesters are very limited at small scale P l3

direct force piezoelectric/electrostatic devices are more efficient at nanoscale.

Recent micro/nano structures have improved performance.

kinetic energy harvesting - nips) lab kinetic_energy_harvesting cottone.pdfself-charging seiko...

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