Smart Materials inSystem Sensing and Control

Dr. M. Sunar

Mechanical Engineering DepartmentKing Fahd University of Petroleum & Minerals

INTRODUCTION

SMART MATERIALS

Definition

• Media where different fields interact in a distributed fashion

• These fields could be mechanical, thermalelectrical, magnetic and/or optical

Example Phenomena

• Piezoelectricity: Mechanical

and Electrical Fields

• Magnetostriction: Mechanical

and Magnetic Fields

• Thermopiezoelectricity: Mechanical,

Thermal and Electrical Fields

Smart Sensors

• Piezo Ceramic/Piezo Film (PZT, PVDF): Input is mechanical strain, output is electrical charge.

• Pyro Ceramic (PZT): Input is temperature gradient, output is electrical charge.

• Fiber Optic Strain Gauge: Input is mechanicalstrain, output is optical.

Smart Actuators

• Piezo Ceramic/Piezo Film (PZT, PVDF): Input is electrical signal, output is mechanical strain.

• Magnetostrictive (Terfenol): Input is magnetic field, output is mechanical force/moment.

• Shape Memory (Nitinol): Input is electrical heating, output is mechanical strain.

MATHEMATICAL FORMULATION

Linear Theory of Thermo-Piezoelectro-Magnetism

(Mechanical, Thermal, Electrical and Magnetic Fields)

• Define a thermodynamic potential G as

G = G (S, E, B, ) =

1/2(STcS ETE + BT1B 2) STeE ETP ST ST B BTr BTbE

where

S: vector of strain E: vector of electrical fieldB: vector of magnetic flux density : small temperature changec, , , , P, , e, r, b:constitutive coefficients

2

112

12

312

12

3

Constitutive Equations of Thermo-Piezoelectro-Magnetism

T = cS eE B

D = eTS + E bTB P

H = TS bE 1B r

= TS + PTE rTB

where

/G,/G

,/G,/G

BH

EDST

Differential Equations of Thermo-Piezoelectro-Magnetism

V ST

V S'E

TTV Sv

ST

V VT

dSdV)W(

dSHdVdSdV

dVdVdV)G(

nh

nAJA

PuPu sb

Define two energy functionals and

where: entropy density

: absolute temperature

u: vector of mechanical displacement

Pb, Ps: vectors of body and surface forces

: electrical potential

v: volume charge density

: surface charge

W: heat source density

A: vector of magnetic potential

J: vector of volume current density

h: vector of external heat flux

A: vector normal to the surface

HE`: matrix of external magnetic field intensity

K2

1 T

K: matrix of heat conduction coefficients

Define Hamilton’s Principle as

0dt

and

0dt)Ki(

2

1

2

1

t

t

t

t

where

Ki = Kinetic Energy =

dt2

1 TV

uu

Note the variation

G = ST T ET D + BT H

and the relations

AAB

AE

uS

A

u

L

L

We obtain the following fundamental equations:

)EquationHeat(0W

)Equations'Maxwell(0

)Equations'Maxwell(0

Motion) of(Equation 0L

T

vT

Tu

q

JHD

D

PTu b

FINITE ELEMENT METHODNote the following FE approximations

ue = Nu ui

e = N i

Ae = NA Ai

e = N i

where

N: shape function matrix

Note that

iie AAAE AiAiee NN]N[

Se = Lu ue = [Lu Nu] ui = Bu ui

Be = LA Ae = [LA NA] Ai = BA Ai

iie B]N[

Finite Element Equations

FA

uuu

K-K

-KKC M

uuA

uuuuAuu

GAuA KK K-K C- AuA

MAu

Au A

-KKK

- C- C C C-M

AAAAu

AAAAAuAA

QAuA K- C- C- C C- M AuA

PIEZOELECTRICITYLinear Equations of Piezoelectricity (Mechanical and Electrical Fields)

T = cS eE

D = eTS + E

Finite Element Equations of Piezoelectricity

Fuu KK M uuuuu

Gu K-K u

Piezoelectric Bimorph Finger

Poling Direction

Poling Direction

Piezoelectric Layer

Piezoelectric Layer

+V

-V

Finite Element Mesh

Analytical Result

w(x) = 1.5 e31V/Y (x/h)2

where

e31: piezoelectric constant

Y: Young’s modulus

h: thickness of piezoelectric layer

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-5

x

w

Tip Deflection (w) vs Horizontal Distance (x)

Thermopiezoelectricity

Linear Equations of ThermoPiezoelectricity (Mechanical, Thermal and Electrical Fields)

T = cS eE

D = eTS + E P

= TS + PTE

Finite Element Equations for Thermopiezoelectricity

Fuu K-KK M uuuuuu

Gu K K-K u

Qu K- C- C C- u

MAGNETOSTRICTION

Linear Equations of Magnetostriction (Mechanical and Magnetic Fields)

T = cS B

H = TS 1B

Finite Element Equations of Magnetostriction

FAuuu KKC M uAuuuAuu

MAuAu A AAAuAAAuAA KK- C C-M

Piezoelectro-Magnetic Composite Beam

Poling Direction

Magnetostrictive Layer

Piezoelectric Layer

-V

h

Finite Element Mesh

Analytical Result

u3(x) = e31Vb (yn-h/4) / (2YmI) x2

where

b: depth of system

yn: distance of neutral axis from system’s bottom surface

Ym: Young’s modulus of elasticity for magnetoceramic

I: area moment of inertia of system about its neutral axis

Analytical Method Finite Element Method

0 0.02 0.04 0.06 0.08 0.10

0.2

0.4

0.6

0.8

1

1.2x 10

-6

x (m)

u3 (

m)

Tip Deflection (u3) vs Horizontal Distance (x)

Magnetic Field H3 in A/m

for Magnetostrictive Layer

Analytical FEM

Top Surface 11.4411.42

Bottom Surface -21.99 -21.88

APPLICATIONS

• Tactile/acceleration sensing and trajectory tracking of robotic manipulators

• Blade vibration measurement and control in turbo-machinery

• Noise control in acoustical systems• Damage detection in composites

Sensors and actuators have load carrying capabilities.

Controller

smart material

Smart Structures

Highly Integrated Sensors and Actuators

Composites, Electronics & Functions

Instability Control

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Nor

mal

ized

Col

umn

Leng

th

Normalized Deflection

Initial Shape

Buckled Shape

P X

y

V

M a

M a

Rotorcraft System

SENSING OF BLADE VIBRATIONS

Objectives

• To investigate validity of using piezoelectric layers

• To investigate method of sandwiching piezoelectric layers

at the connection between blade and disk

• To select appropriate methods for transmitting measured

signals

Current Status

• Measurement and control of blades are essential in turbo-machinery

• Current methods: laser doppler, strain gages and casing accelerometers

• Laser doppler: need of many sensors, sensitivity and limitations with regard to rotations

• Strain gages: not resistant to high temperature and location

• Casing accelerometer: modes of vibration not identified

Piezoceramic Materials

• Resistant to high temperature• Ability of high strains• Precision • High bandwidth

Method

Stationary Cantilever Beam

Blade

Piezoceramic

Piezoceramic

Figure 5.13 Experimental instrumentation schematicExperimental Schematic

Figure 5.7 : Beam-PZT material Frame experimentExperimental Setup

Figure 5.6 : BM500 piezoelectric material

BM500 Piezoelectric Material

0 0.02 0.04 0.06 0.08 0.10

1

2

3x 10

-3

Time (s)

Ver

tical

Tip

Dis

plac

emen

t (m

)

0 0.02 0.04 0.06 0.08 0.1-15

-10

-5

0

5x 10

-5

Time (s)

Vol

tage

at

Nod

e 9

(V)

0 100 200 300 400 5000

1

2

3

4

5x 10

-5

Frequency (Hz)

PS

D o

f Dis

plac

emen

t

0 100 200 300 400 5000

1

2

3

4

5x 10

-8

Frequency (Hz)

PS

D o

f Vol

tage

Transient Response to a Step Input

0 0.2 0.4 0.6 0.8-4

-2

0

2

4x 10

-3

Time (s)

Ver

tical

Tip

Dis

plac

emen

t (m

)

0 0.2 0.4 0.6 0.8-1

-0.5

0

0.5

1x 10

-4

Time (s)

Vol

tage

at

Nod

e 9

(V)

0 20 40 60 80 100 120 1400

2

4

6x 10

-4

Frequency (Hz)

PS

D o

f Dis

plac

emen

t

0 20 40 60 80 100 120 1400

2

4

6

8x 10

-7

Frequency (Hz)

PS

D o

f Vol

tage

Steady-State Response to a Sinusoidal Input

Future Work

• Sensing and Control of Blade Vibrations using Piezoelectric and Magnetostrictive Materials

• Modeling of Nonlinearities in Thermo-Piezoelectricity and Magnetostriction(dependence of material constants ontemperature, hysteresis, etc.)

CONCLUSION• Research in smart materials will continue to grow in

different directions.

• Development of smart sensors which are very sensitive to the mechanical states of host structures, and that of smart actuators which have high strain capacities, resistant to environmental effects and cost-effective are essential.

• Efficient power, signal processing and conditioning units for smart sensors and actuators are needed.