Piezoelectric Sensors

Yongrae Roh

Kyungpook National UniversityDaegu, Korea

ContentsContentsI. Piezoelectricity

II. Electromechanical Equivalent Circuit

III. Sensing Principles of Piezoelectric Sensors1. Charge detection sensor2. Resonant sensor3. Ultrasonic wave sensor

IV. Design Methods

V. Application of Piezoelectric Sensors1. Impedance measurement2. Sensor system for SHM3. Bulk wave measurement4. Other examples

VI. Future trend of piezoelectric sensorsFuture trend of piezoelectric sensors

Linear conversion of electro-mechanical energy: reversible

Electrical Energy ↔ Mechanical Energy

(1) direct effect: mechanical energy → electrical energy- sensor, microphone, generator

(2) converse effect: electrical energy → mechanical energy- actuator , speaker, motor

☞ electrostriction, piezomagneticity, magnetostriction

I. PiezoelectricityI. Piezoelectricity

energy(electric)mechanicalinputenergyl)(mechanica electrictoconvertedenergy(electric) mechanical2 =effk

σεσκ σ EsEddED +=+=

Piezoelectric constitutive equations

D = electric displacement field, κσ = permittivityE = electric field, d = piezoelectric constantσ = stress, sE = elastic complianceε = strain

Variations

EeC

EeDE −=

+=

εσ

κε ε

DgE

gDsT

D

βσ

σε

+−=

+=

DhE

hDC D

εβε

εσ

+−=

−=

Anisotropy for piezoelectricity

Elastic stiffness

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

66

5655

464544

36353433

2625242322

161514131211

][

cccsymmetriccccccccccccccccccc

c

Permittivity

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

33

2322

131211

.][

εεεεεε

εsym

Piezoelectric constants

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

363534

262524

161514

333231

232221

131211

][eeeeeeeee

eeeeeeeee

e

V. M. Ristic, John Wiley & Sons, 1983

① Cubic ; o90, ===== γβαcba

② Tetragonal ; o90, ===≠= γβαcba

③ Orthorhombic ; o90, ===≠≠ γβαcba

④ Monoclinic ; βγα ≠==≠≠ o90,cba

⑤ Triclinic ; o90, ≠≠≠≠≠ γβαcba

⑥ Hexagonal ; oo 120,90, ===≠= γβαcba

⑦ Rhombohedral (trigonal); oo 60,90, ===≠= γβαcba

z

y

x

αβ

γa

b

c

Bravais lattice structures

Symmetric groups in crystals

Crystal symmetric groups

Material constants of PZT

2,

000000000000

][ 121166

66

44

44

33

1311

131211

ccc

ccsymmetric

ccccccc

c −=

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

Elastic stiffness

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

33

11

11

.000

][ε

εε

εsym

Permittivity Piezoelectric constants

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

0000000

000000

][ 24

15

333231

ee

eeee

1211

212

112

ccc

cE+

−=1211

12cc

c+

=νEquivalent isotropic properties:

Hexagonal 6mm Symmetry

Vibration modes

Thermodynamic energy conversion

Corresponding material constantsHeckman Diagram

Pyroelectricity - thermal effects

0 2000 4000 6000 8000 100003820

3822

3824

3826

3828

3830

3832

3834

3836

Freq

uenc

y [k

Hz]

T im e [10sec]

Oscillation frequency vs. time Pyroelectricelement

Wi

FET

Meas. or displaysystem

DS

FET bias resistor

RG RACA

)()(

etemperaturTonpolarizatiPp

ΔΔ

=

crystal

oscilloscope cTTA−

='κ

Curie-Weiss Law for “ferroelectrics”

A = Curie constant

Tc = Curie-Weiss temperature

Nonlinearity

Hysteresis Loop (Sawer-Tower circuit)

Piezoelectric materials

Single crystals(SiO2, LiNbO3, LiTaO3)

Polycrystalline ceramics(PZT, PbTiO3, BaTiO3)

Polymer: PVDF, Co-Polymer Thin films

Fabrication of piezoceramics

Raw Materials and Weighing

Mixing & Milling

Calcination

Remixing & Remilling

Shaping

Sintering

Post Processing

Characterization

Fabrication process

Crushing roller

Hammer mill

Ball mill

* two sphere sintering mode * densification by sintering

Crystal growth -Growth by a change of state from liquid or gas to solid, or from liquid solution to solid around nucleus

-Nucleus : a small single crystal (seed)

-Growth should be a slow process with a precise control over temperature, composition, time and so on.

-Otherwise, there may be random orientation, coring, and trapping of disordered regions.

Czochralski method① Keeping a melt of a powder in a chamber, just above its melting point

② Insertion of a seed crystal fixed to a rotating tube into the chamber.

③ Placing the seed at the surface of the melt; inoculent

④ Slow withdrawing of the tube with rotation; cooling

⑤ Continuous crystallization of the melt,

while serving as a subsequent nucleus

Single crystal growth

Piezoelectric single crystals

2”3”

0.6210.5050.49kt

0.9220.750.705k33

7,84075007,750Density(Kg/m3)

4,9903,4002,000ε33T at 1KHz

(after poling)

PMN-PTPZT-5A

4,350

28.2

3,600

1,560

34

374

34Acoustic Z

(Mrayl)

4,560Sound velocity

593d33(pC/N)

PZT-5H

Pb(Mg1/3Nb2/3)O3-PbTiO3 Comparison of properties

0-0 1-0 2-0 3-0

1-1 2-1 3-1 2-2

3-2 3-2 3-3 3-3

: polymer

: piezoceramic

Piezocomposite materials

⇒ Tailoring material properties to achieve desired performance

Macro Fiber Composite

*Smart Materials Inc., USA

*NASA, Langley

Electromechanical Analogue

u

R

+

-

V

L Ci

m

k Rm

f

uRkxma

uRdtukdtdumf

m

m

⋅++=

∫ ++= ∫ ++= RIdtICdt

dILV 1

Impedance analogue: u → Im → LRm → R1/k = Cm → C, Cm : mechanical compliance

II. Electromechanical Equivalent CircuitII. Electromechanical Equivalent Circuit

Za Za

Zb-C0

C0

1: Φ

330hC=φ

lWcZkt

ZiZ

ktiZZ

Dt

b

a

ρ=

−=

=

0

0

0

sin

2tan

Equivalent circuit of a piezoceramic plate

KLM (Krimholtz, Leedom and Matthei)

Mason

Redwood

t

W

lPZT

Thickness mode

)1(

1 2

00

Lm

mLm

MEINX

CMiRR

CiR

YYY+−++

++=+=

ωω

φω

LZmM mC

0C0RmR

φ:1

u+

_-V

2/φLZ

2/φmM 2φmC

0C0R

22/φmR

Mi+

_

V

Valid only around a resonance

Input admittance

R0 = electrical resistance

C0 = electrical capacitance

Rm = motional resistance

Cm = motional capacitance

Mm = motional inductance

φ = turning ratio

ZL = load impedance = RL + iXL

V = driving electrical voltage

u = im = motional flux (velocity)

Simplified circuit around a resonance

PZT

Load

Resonance: .electromechanical impedance becomes minimum.electromechanical admittance becomes maximum

Anti-resonance: .electromechanical impedance becomes maximum.electromechanical admittance becomes minimum

→ functions of load impedance ZL = RL + iXL

Impedance curve (magnitude & phase) Admittance curve (conductance & susceptance)

Impedance & Admittance analysis

fm = frequency of maximum admittance

& minimum impedance

fn = frequency of minimum admittance

& maximum impedance

fs = series (motional) resonance

fp = parallel resonance frequency

fr = electrical resonance frequency

fa = electrical anti-resonance frequency

Impedance & Admittance analysis

2

22

2

22

2

22

10

12

n

mn

a

ra

p

speff

fff

fff

f

ffCC

Ck−

≅−

≅−

=+

=

1. Charge detection sensor- accumulation of electric charges- D = κε E + e ε

2. Resonant sensor- change in dynamic properties of the sensor- resonant frequency, Q-factor (f0/Δf)

3. Ultrasonic wave sensor- propagation of ultrasonic waves- flight time, phase shift, amplitude attenuation

III. Sensing PrinciplesIII. Sensing Principles

1. Charge Detection Sensor

D = electric displacement, E = electric field,σ = stress, ε = strainκσ , κε = permittivity e, d = piezoelectric constant

εκ ε eED += σκσ dED +=or

Mechanical stress or strain → electrical charge

Accumulation of electric charges

F = ma with a known “m”→ Measured F is proportional to “a”

AamtgAFtg

tgtEVgE

//⋅⋅⋅=

⋅⋅=⋅⋅=

⋅=→⋅=σ

σ

Piezoelectric accelerometer

Vibrating structure

PZTPZT

Mass, m

F

Piezoelectric force & pressure sensor

Force sensor Impact hammer

Pressure sensor On-road pressure sensor

Piezoelectric gyroscope

Coriolis Force:

F = 2 m ω × v

m : mass of the gyroscope

ω : angular velocity

v : linear velocity

Wx

X

Y

Z

Fy

Wx

Z

X

Y

v

ωx

ωx

v

v

×ωx

F

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5

Angular Velocity (Hz)

Output V

oltage (arb.unit)dVab

dVcd

Angular velocity vs. voltage

PZT

2. Resonant Sensor

Attachment of a piezoelectric resonator to a structure

⇒ Change of structural property

⇒ Change of sensor property

.resonant frequency

.Q-factor (f0 /Δf)

► change in impedance spectra

Change in dynamic properties of a sensor

Electromechanical Impedance Sensor

Output display

PC

Impedance analyzer

3200 3300 3400 3500 3600

2

Impe

danc

e [O

hm]

Frequency [kHz]

Non N=1 N=3 N=5 N=7 N=9

Impedance analysis method

d=1cm, Crack N=1

d=1cm, Crack N=11d=1cm, Crack N=9

d=1cm, Crack N=7d=1cm, Crack N=5

d=1cm, Crack N=3

FEM simulation

Impe

danc

e [O

hm]

Frequency [Hz]2M 3M 4M 5M 6M

1

10

100 -N=1N=2N=3N=4N=5N=6N=7N=8N=9N=10N=11

*N = number of cracks on the aluminum plate

Impedance spectrum vs. N

Piezoceramic Oscillator Sensor

Piezoelectric oscillator sensor - piezoelectric vibrator + oscillator circuit

⇒ simple, accurate, reliable

⇒ high sensitivity⇒ limited detection area Piezoceramic

vibrator

electrode

Oscillatorcircuit

AGC(Automatic Gain Control) AmplifierMaintain amplitude ~ 1Vpp

VariableGainAmp.

VariablePhase Shifter

Piezo-vibrator

Resonant frequency vs. Cracks

PZT-Oscillator sensor

d=1 d=2 d=3 d=4 d=5 d=6 d=7

7000

8000

9000

10000

11000

12000

13000

Cha

nge

in re

sona

nt fr

eque

ncy

[Hz]

Crack length

N=1 N=3 N=5 N=7 N=9 N=1126000

25900

25800

25700

25600

25500

Number of cracks

Cha

nge

in re

sona

nt fr

eque

ncy

[Hz]

Oscillator circuitPiezoceramic patch

+

3. Ultrasonic Wave Sensor

Active method- transmit waves of known properties- receive the wave after through-transmission or reflection- compare transmitted and received wave properties

- Through-transmission or Pulse-echo method

Passive method- detect waves transmitted by external sources- waves of unknown properties - event count, ringdown count, energy distribution analysis, etc.- Acoustic emission method

Type of acoustic waves

Bulk longitudinal (P) wave Bulk transverse (S) wave

Plate mode (Lamb) waveSurface (Rayleigh) wave

Properties of acoustic waves

2/1])21)(1(

)1([ννρ

ν−+

−=

EgVP

Elastic wave velocity

. P wave:

. S wave: 2/1])1(2

[νρ +

=EVS

Transmission and Reflection

. Transmission coeff.:

. Reflection coeff.:

01

12ZZ

ZT+

=

01

01

ZZZZ

R+−

=

E = Young’s modulusρ = densityν = Poisson’s ratio

Applications:

1. Medical Diagnosis

2. Nondestructive Evaluation Test

3. Imaging, Holography Sensor

4. Distance, Level Sensor

5. Thickness Sensor

6. Flow Sensor

7. Structural Health Monitoring

Ultrasonic transducers

wear plate

piezoelectricelement

connector

matchingcircuit

backinglayer

matchinglayer

backingmaterial

Characteristics of ultrasonic transducers

1. center frequency (f0)2. sensitivity (Vp-p)3. S/N ratio4. ringdown time (t-20dB)5. bandwidth (Δf)6. impedance7. directivity (beam pattern)8. distance area characteristics (focus)

Ultrasonic test equipment

Through-Transmission Test

Pulse-Echo Test

transducer

structure

d

A1 A2

Pulse-Echo Test

Sound velocity = 2d /(t2 - t1)Attenuation = 20log | A2 /A1 |

Active ultrasonic wave method

A1 ,t1

A2,t2

A0,t0

defects

A1,t1

structure

Trx Trx

d

Through-Transmission Test

Sound velocity = d /(t1 - t0)Attenuation = 20log |A1 /A0|

A0,t0

Active ultrasonic wave method

Image scanning method

TrxTrx y

x

A scan - line depth scan B scan - vertical plane scan C scan - horizontal plane scan

3.02.01.000

0

.0-1

.01

.1

1

frequency (MHz)

|impe

danc

e|

PS

thickness modepiezoelectric

element

thickness shear modepiezoelectric

element

Impedance spectrum

Types of bulk wave transducers

P wave transducer S wave transducer P-S wave transducer

Single element transducer

Side scan transducer

Flat transducer Point focus transducer

Line focus tranducer

*Panametrics (Olympus)

Dual element transducer

Internal structure Sensor operation

Line array transducer

Array of multiple piezoelectric elements

Linear array Convex array

Linear phased array transducer

Adjustment of the time delay of each element-initial phasing to control beam pattern (beam steering) and focusing (dynamic focusing)

High inspection speedFlexible data processing capabilityHigh resolutionThe capability of scanning without mechanical movement

Beam steering Dynamic focusing

Phase shiftTime delay

Excitation by bulk wave transducers

Excitation by inter-digital transducers

Lamb wave transducer

inputIDT

outputIDT

piezoelectric substrate

Snell’s law→ critical angle for total reflection

Excitation by a piezoceramic patch

Lamb wave propagation

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

1000

2000

3000

4000

5000

6000

Gro

up v

eloc

ity(m

/s)

Frequency(MHz)

S0 A0

S0

A0

Positio

n o

f transducer

from

the P

ZT s

ensor

5 cm

10 cm

30 cm

20 cm

40 cm

25 cm

35 cm

15 cm

Volta

ge(v)

Waveform(thickness of a plate : 1 mm

S0 mode

Time(ms)

Origin

A0 mode

0.064 0.068 0.072

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4B->C, X= 0.05 mNumber of cracks = 1

Volta

ge(V

)

Time(ms)

Crack Length = 0 m Crack Length = 0.02 m Crack Length = 0.04 m Crack Length = 0.06 m Crack Length = 0.08 m

Plate mode (Lamb) wave

Acoustic emission test

Causes of acoustic emission- metallurgical transformation- dislocation movements- plastic yielding- micro-cracking- etc.

Objective.to monitor structural integrity.to detect and locate incipient discontinuities.to monitor the presence and severity of growing cracks,

plastic deformation or delaminations

Passive ultrasonic wave method

Acoustic emission sensor

Passive sensor to detect AE activity

.good sensitivity

.wide bandwidth: audible – several MHz

.low directivity

Applications

Pressure vessels, storage tanks, heat exchangers, piping, reactors, aerial lift devices, nuclear power plantsetc.

IV. Design MethodsIV. Design Methods

1. Analytic analysis

2. Equivalent circuit analysis

3. Finite element analysis

r’r

P

σ

x

zθ

22 aS π=

Rigidbaffle

)](2

sin[2 22)(2

00

00

22

22

rarkecui

deckuip

rarki

arr

ik

−+=

=

−+−

+ −∫

ρ

ηρ η

P nearfield

farfield

P θθρ ω

sin)sin(2

21)(

2

00

kakaJe

rkaAuci krti −=

)(θsax HPP •= ,

where 1J = first order Bessel Function.

A = piston radius

Pax = on-axis pressure

Hs(θ) = directional factor

At a far field

1. Analytic Analysis - single piston source

)(

)sin21sin(

)sin2

sin(),,( krtie

kdN

kdN

rNAtrP −⋅⋅= ω

θ

θθ

)()(),( θθ eax HrPrP •=∴

factor ldirectiona)sin

21sin(

)sin2

sin()( ==

θ

θθ

kdN

kdN

He

pressure axis-on)( where, ==r

NArPax

d

z

x y

12…

N

Radiation pattern

Linear array of simple sources

Accurate, complicatedLimited applicability

1. Analytic analysis - linear array

2/φmRREMM EMC

0C0R

22/φEMR

Mi+

_e

branch motionalin dissipatedPower /Rin dissipatedPower

powerinput elec. Totalbranch motionalin dissipatedPower

powerinput elec. total Radiatedpower Acoustic

2mR φη

η

η

=

=

=

MA

EM

EA

0

2

222

222

2)(||

21

)(||21

ReRRi

RRi

mREMM

mREMM

EM

++

+=

φφ

φφη

cycleperRRindissipatedpowerresonanceatMinstoredenergypeakQ

MMR

MM )(

(2+

=π

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++

+=

20

20

00/)(

φ

φEMmR

EMmRE RRR

RRRCwQ

mEM

EM

CNst

NC

NM

NtM

22

112

2

22

4)/(

4

441

πωπ

ωρ

=≅

=≅

l

l

2. Equivalent Circuit – piezoelectric patch

Pσ

x

z

θ

22 aS π=

Rigidbaffle

2. Equivalent circuit – ultrasonic transducer

backingload

piezoceramic matchinglayer 1

matchinglayer 2

acousticlens

acousticload

C MRZ

04Z02Z 03Z 05Z

V0

piezoelectricceramics

connector

matchingcircuit

backinglayer

matchinglayer

backingmaterial

time domain frequency domain

Impedance analysis

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧Φ⎟

⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−

QFu

KK

KKM

u

uuu

φφφ

φω0002

3. Finite Element Analysis

M = mechanical mass matrix,Kuu = mechanical stiffness, Kφφ = electrical stiffnessKuφ, Kφu = electromechanical stiffnessu = displacement, φ = electrical potentialF = force, Q = electric charge

Commercial FEA software packages

ANSYS®, PZFlex®, ATILA®, CAPA®, …

Accurate, multi-dimensional, various analysesexpensive, time consuming

3. Finite element analysis

0 1x106

2x106

3x106

4x106

5x106

6x106

0

500

1000

1500

2000

2500

2.473 MHz

at 1 mm

at 2 mm

at 3 mm

Mag

nitu

de

frequency

15000 20000 25000 30000 35000 400000

200

400

600

800

1000

1200

1400

1600

1800

2000

19.9 kHz

1(upper PZT)

28 kHz, 308Ω

2(lower PZT)

28 kHz, 213Ω

Impe

danc

e(|Z

|)

frequency

spatial domain frequency domain impedance analysis

음압(소자 전면으로 mesh size를 lamda/8로 동일하게 함)

-5.0E+04

-3.0E+04

-1.0E+04

1.0E+04

3.0E+04

5.0E+04

1.00E-05 1.18E-05 1.33E-05 1.48E-05 1.63E-05 1.78E-05 1.93E-05

시간

음압

(dyne/c

m2)

at 1mm

at 2 mm

at 3 mm

time domain

V. Application of Piezoelectric SensorsV. Application of Piezoelectric Sensors

1. Impedance measurement

2. Piezoelectric Sensor System for platesOscillator sensor: Local measurementLamb wave sensor: Global measurement

3. Bulk wave measurement

4. Other examples

1. Impedance Measurement

Mechanical load- function of structural

conditions

Input Admittance

ZL= mechanical impedance of the plate = RL + i XL

V = input voltage, im = mechanical fluxR0 = internal electrical resistance C0 = electrostatic capacitanceRm = mechanical resistance Cm = mechanical capacitanceLm = mechanical mass ω = frequency

PZT

Thickness Mode Resonator

mmCLπ21

m

m

m CCCC

L 0

0121 +π

fs = unloaded series resonance

fp = unloaded parallel resonance

2/φLZ

2/φmL 2φmC

0C0R

22/φmR

Mi+

_

V

)1(

1 2

00

Lm

mLm

MEINX

CMiRR

CiR

YYY+−++

++=+=

ωω

φω

0 00

2

L L

ZA C

ωω ρΔ Δ

∝ −Frequency Shift:

Frequency (Hz)

Impe

danc

e (O

hm)

Does not require Modal Parameters / Failure ModesMonitor Local Modes at High Frequencies(>100 kHz)

: It Can Detect Incipient-type Damages

Monitoring the of the PZT bonded on the Structure in relation to Structural Damages

0ω

= Initial resonant frequency

= Frequency Shift in response to ΔZ

0ω

ωΔ

1. Impedance measurement

Experimental setup and Procedure

1. Impedance measurement

Measured data (S. H. Park)

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

x 106

100.3

100.4

100.5

100.6

100.7

100.8

Frequency (MHz)

Imp

edan

ceNo damageDamage Case I-1Damage Case I-2

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

x 106

100.4

100.5

100.6

100.7

100.8

Frequency (MHz)

Imp

edan

ce

No damageDamage Case I-1Damage Case I-2

PZT 1

PZT 2

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

x 106

100.3

100.4

100.5

100.6

100.7

100.8

Frequency (MHz)

Imp

edan

ce

No damageDamage Case I-1Damage Case I-2

PZT 3

2 cracks near PZTs 2 & 3Damage Case I-2

Crack near PZT 3Damage Case I-1

-40000

-30000

-20000

-10000

0

10000

Damage Case

Fre

qu

en

cy

Sh

ift(

Hz)

PZT 1

PZT2

PZT3

No damage

Damage I-1

Damage I-2

Impedance vs. Crack configuration

*N = number of cracks on the aluminum plate

Frequency [Hz]

2M 3M 4M 5M 6M1

10

100 -

Impe

danc

e [O

hm]

N=1N=2N=3N=4N=5N=6N=7N=8N=9N=10N=11

856 858 860 862 864 866 868

32.72

32.73

32.74

32.75

32.76

32.77

32.78

32.79

Frequency [kHz]

No crackd=3cm, N=1d=4cm, N=1d=5cm, N=1d=7cm, N=1

Impe

danc

e [O

hm]

Impedance spectrum vs. Crack lengthImpedance spectrum vs. N

2. Piezoelectric Sensor System for plates

PZT oscillatorUltrasonic transducer

local major cracksat a weak region

global minor cracksdistributed over arbitrary places

Oscillator circuit

PZT oscillator sensor: Local measurementUltrasonic sensor: Global measurement

Portable ultrasonic measurement system

Local Detection: PZT Oscillator Sensor

Piezoelectric oscillator sensor - piezoelectric vibrator + oscillator circuit

⇒ diagnosis of the number of cracks⇒ diagnosis of the length of cracks

Piezoceramic vibrator

electrode

Oscillatorcircuit

thickness mode lateral mode

1000 2000 3000 4000 5000 6000

1

10

100

1000

10000

100000 Impedacne Phase

Frequency [kHz]

Impe

danc

e [O

hm]

-120

-100

-80

-60

-40

-20

0

20

40

Magnitude [degree]

4.55 MHz

100 200 300 400 50010

100

1000

10000

100000 Impedacne Phase

-100

-80

-60

-40

-20

0

20

40

60

80

100

Magnitude [degree]

Frequency [kHz]

Impe

danc

e [O

hm]

125 kHz

Compensation of environmental effects

Experimental plate specimen

f1 　 effects of cracks+ effects of environment

Reference plate specimen

f2 　 effects of environment

Oscillator Oscillator

PZT 10 cm

50 cm

Frequency counter Frequency counter

Output display

ΠΧ

GPIB GPIB

Experimental plate with damages PZT-Oscillator Reference sensor

Lateral mode analysis & measurement

Crack length vs. frequency shift

FEM analysisMeasurement

d=1 d=2 d=3 d=4 d=5

72200

72400

72600

72800

73000

73200

73400

73600

73800

Freq

uenc

y [H

z]

Length of crackd=1 d=2 d=3 d=4 d=5 d=6 d=7

119000

120000

121000

122000

123000

124000

125000

126000

Length of cracks

Del

ta F

requ

ency

[Hz]

Number of cracks vs. frequency shift: crack length = 3 cm

FEM analysis

N=1 N=3 N=5 N=7 N=9 N=11

124000

124200

124400

124600

124800

125000

125200

125400

125600Fr

eque

ncy

[Hz]

Number of cracks

Measurement

N=1 N=3 N=5 N=7 N=9 N=11125000

125100

125200

125300

125400

125500

Number of cracks

freq

uenc

y [H

z]

Number of cracks vs. frequency shift: crack length = 3 cm

Thickness mode vs. Lateral mode: FEA

Crack length vs. frequency shift

thickness lateral

thickness

lateral

None N=1 2 3 4 5 6

0.9980

0.9985

0.9990

0.9995

1.0000

1.0005

Num. of crack

Nor

mal

ized

freq

uenc

y

N=1 N=3 N=5 N=7 N=9 N=11123800

123850

123900

123950

124000

124050

124100

124150

Freq

uenc

y [H

z]

Num. of Crack

d=1cm 3 5 7 9 11

124000

124200

124400

124600

124800

125000

125200

125400

125600

Impe

danc

e [O

hm]

Frequency [Hz]

0 2 4 6 8 100.994

0.995

0.996

0.997

0.998

0.999

1.000

Y A

xis

Title

X Axis Title

B

Ultrasonic Transducer: (1) Bulk transducer (2) Piezeceramic patch

Crack configuration to be measured(1) Crack position (2) Crack length (3) Crack number

Global Detection: Ultrasonic Transducer

OscilloscopeBulk

transducer

PZT sensor

Piezo-patch

Damage detection scheme

0.1 m

0.05 m

0.05 mCB

0.05 m

Transducer & wedge

crack

PZT

xF

The crack position was changed in the range 5<=X<=15.The position of wedge and transducer is fixed at node B.

α : distance between crack and wedge.

α

0.15 m

Specimen

0.01 m

0.05 m

0.05 m

Transducer ->sensor(Through transmission)

Position of cracks

Number of cracks

Range of crack length

B->CE

from 1 to 3 form 0 to 0.09 mF

D->CEF

Damage scenario

D

Ultrasonic beam width

frequency P/Pax

0.5 MHz 1 MHz

-3 dB 12.7871o 12.7157o

-6 dB 17.6608o 17.5607o

Theoretical Beam Width

0.5 MHz

j i

Voltag

e(v)

1 MHz

Voltag

e(v)

j i

frequency P/Pax

0.5 MHz 1 MHz

-3 dB 10.314o 15.589o

-6 dB 17.734o 19.934o

Beam Width Measurement

Good agreement !

Reconstruction of Original Signals

fp : frequency spectrum of PZT- Sensor (known)fa : frequency spectrum of original signal (unknown)fd : frequency spectrum of distorted signal (known)

fa (ω)*fp(ω) = fd (ω)

fa (ω) = fd(ω)/fp(ω)

= fd(ω)*(1/fp=impedance spectrum(Zp))

fd(ω) ≒ signal of wavelet transformed domain

(1) Crack Position – TOF in a P/E responseTo get the position of a crack (unknown)

The crack position was changed in the range 5<=X<=15.The position of wedge and transducer is fixed at node B.

α : distance between crack and the front edge of the wedge.

0.1 m

0.05 m0.05 m

CB

0.05 m

Transducer & wedge

crack

PZT

x

α

0.2 m

Flying distance = velocity*TOF + constant

0.09 0.10 0.11 0.12 0.13 0.14

-0.10

-0.05

0.00

0.05

0.10

Vol

tage

(V)

T im e(m s)

a =0.010 m a =0.015 m a =0.020 m a =0.025 m

Time response of Pulse-echoed signalsα: 0.2 m

α: 0.15 m

α: 0.1 mThe position of the front edge of wedge : X= 0.20 mfrequency 0.5 MHzExact α 0.10 m 0.15 m 0.20 m 0.25 m

TOF (ms) 0.0898 0.1079 0.1261 0.1445

flying distance (m) 0.1995 0.3002 0.3999 0.5

estimated α(m) 0.0998 0.1501 0.1999 0.25

α: 0.25 m

(2) Crack Length –Amplitude of a T/T responseNormalized amplitude of the first peak of measured signals (driving frequency=0.5 MHz)

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nor

mal

ized

mag

nitu

de

Crack length(m)

Crack 1, X=0.05 m Crack 2, X=0.05 m Crack 3, X=0.05 m Crack 1, X=0.1 m Crack 2, X=0.1 m Crack 3, X=0.1 cm

B->C D->C

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nor

mal

ized

mag

nitu

de

Crack length(m)

Crack 1, X=0.05 m Crack 2, X=0.05 m Crack 3, X=0.05 m Crack 1, X=0.1 m Crack 2, X=0.1 m Crack 3, X=0.1 cm

B->C D->C

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nor

mal

ized

mag

nitu

de

Crack length(m)

Crack 1, X=0.05 m Crack 2, X=0.05 m Crack 3, X=0.05 m Crack 1, X=0.1 m Crack 2, X=0.1 m Crack 3, X=0.1 m

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nor

mal

ized

mag

nitu

de

Crack length(m)

Crack 1, X=0.05 m Crack 2, X=0.05 m Crack 3, X=0.05 m Crack 1, X=0.1 m Crack 2, X=0.1 m Crack 3, X=0.1 m

Normalized amplitude of the first peak of original signals (driving frequency=0.5 MHz)

The amplitudes are continuously decreasing as the crack lengths are increased to enter the ultrasonic beam.

(3) Crack Number – TOF in a T/T response

B->C, X= 0.05

TOF is increasing in proportion to the number of cracks.

Crack number =1 Crack number =2 Crack number =3

0.044

0.045

0.046

0.047

0.048

Length of Cracks(m)

X=0.05 m, B->C

0.080.070.06

TOF(

ms)

Number of Cracks = 1 EA Number of Cracks = 2 EA Number of Cracks = 3 EA

Relationship between in TOF and Flying Distance to determine the number of cracks

CDBcrack

FX

3. Bulk Wave Measurement

Nondestructive Testing Handbook, ASNT, 1991

4. Other Example

V. Giurgiutiu et al, Aerospace America, May 2003

structural neural system, G. R. Kirikera et al, Structural Health Monitoring, 2008Monitoring the health of aeronautical structures,

Igor Bovio, SPIE, 2006

4. Other Example

1. New materials: PZN-PT, PMN-PT, Li2B4O7, thin films

2. New structures: .multi-functional, micro-sensors.resistant to harsh environment

3. Smart sensors: .system integration.coupled with actuators to process self-treatment

4. Sensor network: multi-dimensional, wireless

VI. Future Trend of Piezoelectric SensorsVI. Future Trend of Piezoelectric Sensors

Sensor network application framework, E. Sazonov, et al, 2004