Department of Mechanical Engineering

MEMS1049

MechatronicsChapter 9

Vibration Sensors 9-5

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PiezoelectricityPiezoelectricity

– In 1880, Pierre Curie and Paul-Jacques Curie (Curie Brothers) studied pyroelectricity in the 1880s, leading to their discovery of some of the mechanisms behind piezoelectricity

– Generating an electric charge in a material when subjecting it to applied stress, and conversely, generating a mechanical strain in response to an applied electrical field

Piezoelectric mat’l

Force or strain

Induced ∆Q, ∆V Piezoelectric mat’l

Induced force or strain

V

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Piezoelectric Effect

In some dielectric materials (crystals, ceramics, polymers) without center symmetry, an electric polarization can be generated by the application of mechanical stresses.----Piezo-electricity

– D = d X, direct effect– x = d E , converse effect

P: polarizationd: piezoelectric coefficient (pC/N or m/V)

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Piezoelectric Effect

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Piezoelectric Effect

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Piezoelectric Effect

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Piezoelectric materials and properties

Piezoelectric Materials– Ceramics

Pb(ZrTi)O3 (PZT), PbTiO3 (PT), etc.– Single crystals

Quartz, LiTaO3, LiNbO3, PZN-PT,etc– Polymers

PVDF and copolymers, nylon, etc.– Composites

PZT-polymer 0-3, 2-2, 1-3 composites, etc.– Thin/thick films

PZT, PT, ZnO and AlN films

Important parameters for piezo- materials– piezoelectric strain coefficient d

(m/V)– piezoelectric voltage coefficient g(V.m/N)– electromechanical coupling k33, k31, kt

– dielectric constant K– electrical resistivity ρ– dielectric loss tangent tanδ– mechanical quality factor Q– acoustic impedance ρc

Property Unit PZT ceramic

PVDF ZnO film

PZT film (4 µm on Si)

d33 (10-12)C/N 220 -33 12 246 d31 (10-12)C/N -93 23 -4.7 -105 d15 (10-12)C/N 694 -12 ? Κ3 ε33/εo 730 12 8.2 1400

tanδ 0.004 0.02 0.03 k31 0.31 0.12 Q 400 ρc (106)kg/m2-

sec 30 2.7

Typical properties of PZT, PVDF, ZnO

Crystalline quartz

0000000000

000

2625

141211

ddddd

d11 = -d12 = -d26/2 = 2.31 pC/N, d14 = -d25 = 0.73 pC/N

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For PZT, BaTiO3 , PbTiO3piezoelectric ceramics

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Piezoelectric Effect

∆L=d31 ·V · L/t, ∆W=d31 ·V · W/t , ∆t=d33 ·V

- When a voltage is applied across the thickness of the piezoelectric materials

- When a force F, is applied, in the length, width or thickness direction

Q3=d31 ·F1/(L/t), Q3=d31 · F/(W/t), Q3=d33 · F

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Be careful about this elastic constant

Piezoelectric Effect

Open circuit voltage

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Piezoelectric Effect

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Piezoelectric Effect

nmtVV

VpmdVdt

tVd

tt

Edx

37.01

/37033

33

333

3333

=∆=

==∆

=∆

=

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Piezoelectricity Piezoelectric Materials

– CeramicsPb(ZrTi)O3 (PZT), PbTiO3 (PT), etc.

– Single crystalsQuartz, LiTaO3, LiNbO3, PZN-PT,etc

– PolymersPVDF and copolymers, nylon, etc.

– CompositesPZT-polymer 0-3, 2-2, 1-3 composites, etc.

– Thin/thick filmsPZT, PT, ZnO and AlN films

Important parameters for piezo- materials– piezoelectric strain coefficient d (m/V)– piezoelectric voltage coefficient g(Vm/N)– electromechanical coupling k33, k31, kt

– dielectric constant K– dielectric loss tangent tanδ– mechanical quality factor Q– acoustic impedance ρc

Property Unit PZTceramic

PVDF ZnOfilm

PZT film(4 µm on Si)

d33 (10-12)C/N 220 -33 12 246d31 (10-12)C/N -93 23 -4.7 -105d15 (10-12)C/N 694 -12 ?Κ3 ε33/εo 730 12 8.2 1400

tanδ 0.004 0.02 0.03k31 0.31 0.12Q 400ρc (106)kg/m2-

sec30 2.7

Typical properties of PZT, PVDF, ZnO

33

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Piezoelectric longitudinal andtransverse effect

Piezoelectric multilayer andbimorph actuators

Piezoelectric Shear mode actuator

Longitudinal multilayer actuatorLarge output force, low displacement

Shear mode actuatorMedium force and displacement

Bending mode actuatorLow force, large displacement

Piezoelectric actuators and sensors

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Piezoelectric actuators and sensors

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Device Considerations

Considering piezoelectric sensors such as vibration sensors (dynamic strain sensor), accelerometers, energy harvesting devices

A simple mass-spring-damper structure

PZT is most often usedFor high temperature transducers.- AlN- Bismuth titanate ceramic (Bi4Ti3O12)- LiNbO3

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Device Considerations

Dynamic equation for forced vibration

( )sFKZDsZZMs a=++2

KDsMssF

sZ a

++= 2

)()(

22

2

21)(

nn

n

ssKFsZ

ωζϖω

++=

ζγγ 2111)(

2 jKFsZ

+−=

( ) ( ) ( )

( )tFtF

tMXtKztzDtzM

a==−=++

ωωω

sinsin2

Mechanical Transfer Function

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Device Considerations

For accelerometers

( ) ( )222 211

ζγγ +−=Y

ζγγωωζϖω 2111

21)(

22222 jssXsZ

nnn +−=

++=

−

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Device Considerations

Electrical Transfer FunctionEquivalent circuit of

piezoelectric Transducers( ) ( )tzKtQ q= ( ) ( )sZKsQ q=

22

2

2)(

nn

nq

ssKK

FsQ

ωζϖω

++=

222 21)(

nnq ss

KX

sQωζϖω ++

=−

The governing equation of the equivalent circuit

ppq R

VdtdVC

dtdzK +=

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Device Considerations

Electrical Transfer Function

τ)()()( sVssVssZ

CK

p

q += 1)()(

+=

ss

CK

sZsV

p

q

ττ

12)(

22

2

+++=

ss

ssKCK

FsV

nn

n

p

q

ττ

ωζϖω

12111)(

222 ++−=

− ss

jCK

XsV

np

q

ττ

ζγγωω

( ) 22

22

2

2

2

124sF

ss

ssKCK

sPnn

n

p

q

+

++

=τ

τωζϖ

ω

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Device Considerations

For multilayer piezoelectric stack

233

3333

233 k

sd

KKC

KTEq

p

q ==⋅ε

( ) 23

22

233

233

1211

4T

ss

jsk

spE

+

+−

=ττ

ζγγ

The maximum output power density

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Device Considerations

Transducer power vs. frequency for different damping coefficient and time constant