Smart Materials in System Sensing and Control

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Smart Materials inSystem Sensing and Control

• Dr. M. Sunar
• Mechanical Engineering Department
• King Fahd University of Petroleum Minerals

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INTRODUCTION

• SMART MATERIALS
• Definition
• Media where different fields interact in a
  distributed fashion
• These fields could be mechanical, thermal
• electrical, magnetic and/or optical

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Example Phenomena

• Piezoelectricity Mechanical
• and Electrical Fields
• Magnetostriction Mechanical
• and Magnetic Fields
• Thermopiezoelectricity Mechanical,
• Thermal and Electrical Fields

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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 mechanical
• strain, output is optical.

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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.

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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 - ET?E BT?-1B - ??2) - STeE - ETP? -
  ST?? - ST ? B - BTr? - BTbE

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where
S vector of strain E vector of electrical
field B vector of magnetic flux density ? small
temperature change c, ?, ?, ?, P, ?, e, r,
b constitutive coefficients
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Constitutive Equations of Thermo-Piezoelectro-Mag
netism
T cS - eE - ? B - ?? D eTS ?E bTB
P? H - ? T S - bE ?-1B - r? ? ?TS PTE
rTB ?? where
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Differential Equations of Thermo-Piezoelectro-Mag
netism
Define two energy functionals ? and ?
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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
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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
K matrix of heat conduction coefficients
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Define Hamiltons Principle as
where Ki Kinetic Energy
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Note the variation ?G ?ST T - ?ET D ?BT H -
?? ?
and the relations
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We obtain the following fundamental equations
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FINITE ELEMENT METHOD
Note the following FE approximations ue Nu
ui ?e N? ?i Ae NA Ai ?e N? ?i where
N shape function matrix
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Note that
Se Lu ue Lu Nu ui Bu ui Be LA Ae LA
NA Ai BA Ai
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Finite Element Equations
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PIEZOELECTRICITY
Linear Equations of Piezoelectricity
(Mechanical and Electrical Fields) T cS -
eE D eTS ?E Finite Element Equations of
Piezoelectricity
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Piezoelectric Bimorph Finger
Poling Direction
Finite Element Mesh
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Analytical Result
w(x) 1.5 e31V/Y (x/h)2 where e31 piezoelectric
constant Y Youngs modulus h thickness of
piezoelectric layer
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Tip Deflection (w) vs Horizontal Distance (x)
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Thermopiezoelectricity

Linear Equations of ThermoPiezoelectricity
(Mechanical, Thermal and Electrical Fields)
T cS - eE - ?? D eTS ?E P? ? ?TS
PTE ??
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Finite Element Equations for Thermopiezoelectricit
y
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MAGNETOSTRICTION
Linear Equations of Magnetostriction
(Mechanical and Magnetic Fields) T cS - ?
B H - ? T S ?-1B Finite Element Equations of
Magnetostriction
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Piezoelectro-Magnetic Composite Beam
Finite Element Mesh
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Analytical Result
u3(x) e31Vb (yn-h/4) / (2YmI) x2
where b depth of system yn distance of neutral
axis from systems bottom surface Ym Youngs
modulus of elasticity for magnetoceramic I area
moment of inertia of system about its neutral axis
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Tip Deflection (u3) vs Horizontal Distance (x)
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Magnetic Field H3 in A/m for Magnetostrictive
Layer
Analytical FEM Top Surface
11.44 11.42 Bottom Surface -21.99 -21.88
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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

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Controller
smart material
Sensors and actuators have load carrying
capabilities.
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Smart Structures
Composites, Electronics Functions
Highly Integrated Sensors and Actuators
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Instability Control
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Rotorcraft System
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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

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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

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Piezoceramic Materials

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

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Method
Stationary Cantilever Beam
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Experimental Schematic
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Experimental Setup
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BM500 Piezoelectric Material
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Transient Response to a Step Input
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Steady-State Response to a Sinusoidal Input
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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 on
• temperature, hysteresis, etc.)

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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.