Department of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical Engineering

Piezoelectric actuators and sensors

Lecture Lecture 9

Department of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical Engineering

Piezoelectric equations

◆ EquationsS s T d E

D d T E

ij ijklE

kl kij k

j ikl kl jkT

k

= +

= +

ε

i,j,k,l = 1 to 3

T c S e E

D e S E

ij ijklE

kl kij k

j ikl kl jkS

k

= −

= +

ε

S s T g D

E g T D

ij ijklD

kl kij k

j ikl kl jkT

k

= +

= − +

β

T c S h D

E h S D

ij ijklD

kl kij k

j ikl kl jkS

k

= −

= − +

β

s sijklE

ijklD, elastic compliance at constant electrical field and constant

electrical displacement conditions

c cijklE

ijklD, elastic stiffness at constant electrical field and constant

electric displacement conditions

ε εjkS

jkT, dielectric permittivity at constant strain and constant stress conditions

β βjkS

jkT,

dielectric impermittivity at constant strain and constant stress conditions

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Piezoelectric equations

◆ Equations

d e s gijk ilm lmjkE

ljk ilT= = ε

e d c hijk ilm lmjkE

ljk ilS= = ε

g h s dijk ilm lmjkD

ljk ilT= = β

h g c eijk ilm lmjkD

ljk ilS= = β

d e g and hijk ijk ijk ikl, , ,piezoelectric coefficients which represent piezoelectric coupling between the electrical and mechanical variables

For a particular problem, the choice of which coefficient to use becomes clear when the boundary conditions of the materials are considered.

In compressed matrix notation, ij and klis replaced by p and q with

11 →1;

22 →2,

33 →3;

23, 32 →4;

13, 31 →5;

12, 21 →6;thus p, q = 1 to 6.

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◆ Pump structures

Piezo-MicropumpsA micro diaphragm pump with active valves

(a) Principle set-up of a "piston type" micropump.

(b) Schematic set-up of the saliva dispensing micropump of "Graphosoma lineatum".

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Pump structures

Piezo-Micropumps

A planar peristaltic micropump

Micro diaphragm pump with piezoelectric actuation

Electrostatically actuated micro diaphragm pump

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Pump structuresPiezo-Micropumps

Valve-less micro diaphragm pump with piezoelectric actuation: schematic diagram,and pumping principle

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Pump structures

Piezo-Micropumps

A compact pump and integrated microvalves Li et al, 1 of 2 Sensors and Actuators A: Physical Volume 11, 2005, pp.325-330

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◆ Accelerometer structures

Piezoelectric accelerometers

Piezoelectric thin film elements are connected in (a) series or (b) in parallel.

A Schematic piezoelectric thin film micro-accelerometer

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◆ Accelerometer structures

Piezoelectric accelerometers

(a) parallel and (b) serial connection of the two sensing elements

When subjected to the temperature change

When subjected to applied acceleration

Applying an acceleration along the z direction, one piezoelectric layer is compressed while the other is extended due to the intrinsic mass of each device.

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◆ Accelerometer structures

Piezoelectric accelerometers

When subjected to the temperature change

An aluminum case containing the sensing elements and the electronics

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◆ Sensor structures

Piezoelectric shear stress sensor

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◆ Optical beam deflector

Piezoelectric devices

Schematic of the optical beam deflector. Big arrows indicate thedirection of the polarization of the piezoceramics.

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◆ Beam resonators

Piezoelectric resonatorSensors and Actuators A: Physical Volume 118, 2005, pp.63-69

Ferguson and DeVoe

Theoretical, finite element, and experimental resonance frequencies for fabricated free�free resonator structures

Fundamental resonator mode shapes from composite ANSYS analysis: (a) free�free flexural beam, and (b)torsional anchor.

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◆ Thin film resonator

Thin film resonators

Principle of BAW resonator operation: A longitudinal standing acoustic wave is excited electrically in a thin piezoelectric film. The layer thickness of the piezoelectric film and of the electrodes determines the resonance frequency of the BAW resonator.

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◆ AlN FBAR

Thin film acoustic wave resonators

XRD pattern of AlN film

Micro-machined FBAR fabrication process flow

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◆ Thin film resonator

Thin film acoustic wave resonators

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◆ Thin film resonator and filter

Thin film resonator and filter

BAW filter principle: the electrical impedance curve of the parallel resonator p is shifted in frequency relative to the series resonator s by ∆f=fa−fr. This creates a band-pass filter characteristics in S21

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◆ QCM for sensors

Acoustic wave sensors

NO2 gas sensor

BVD equivalent circuit for an unperturbed AT-cut quartz resonator (a) or modified BVD equivalent circuit for a loaded AT-cut quartz crystal resonator (b).

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◆ Bimorph beam splitter

Piezoelectric devices

◆ Unimorph pressure sensor

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◆ Vibration sensor

Piezoelectric devices

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◆ For surface roughness

Piezoelectric devices

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◆ For AFM cantilever

Piezoelectric devices

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Piezoelectric devices

◆ Scanning tunneling microscopy

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◆ Data read/write cantilever

Piezoelectric devices

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Multilayer actuators

Piezoelectric devices

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Piezoelectric devices◆ Mechanical amplifier

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◆ Mechanical amplifier

Piezoelectric devices

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◆ Impact drive mechanism using piezoelectric actuator

Piezoelectric devices

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Piezoelectric devices

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Piezoelectric devices◆ A micro gripper using

unimorph actuator◆ Swimming device

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Piezoelectric devices

◆ A dynamic focusing lens

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Piezoelectric devices

◆ A dynamic focusing lens