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An Introduction to ElectrostaticActuator
a Device Overview and a
Specific Applications
Prepared By: Eng. Ashraf Al-Shalalfeh
Mechanical Engineering Dept.
Faculty Of Engineering & Tech.
University Of Jordan
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What Is The MEM S ?
It stands for: Micro-Electro-MechanicalSystems.
It is an integration of elementssensors actuators and electronics ona com mon silicon substrate.
Micro-fabrication technology formaking microscopic devices.
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What Is The Actuator ?
The actuator is an elementwhich applies a force to someobject through a distance
Various actuation mechanisms:
Electrostatic actuationThermal actuationPiezoelectric actuation
Magnetic actuation
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Electrostatic Actuation:
d wl
d A
C r or o
2
21
V x A
F 2
21
V x A
F
A voltage is applied between metal
plates to induce opposite charges andCoulomb attraction
plateeachof Area A
Force F
cedis seperationd m F space freeof ty permittivi
t consdielectricrelative
factor field dringing
Where
o
r
:
:
tan:])/[1085.8(:
tan:
:
;
12
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22
221
V d
wl CV W r o
Electrostatic Energy Force:
Electrostatic Energy :
Electrostatic Force :
221
4
1
x
qq F
r o
Coulombs Law: Force between two point charges
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2
2
2 z wlV
z W
F z
Electrostatic Actuators Types:
Force Normal to Plate :
Force Parallel to Plate
d wV
yW
F y 2
2
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Why Comb Drive Micro Actuator ?
Force doesnt drops rapidly whenincreasing gap
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FringingCurves
Electrostic Micro-actuator consists of many fingers
that are actuated by applying a voltage.
The thickness of the fingers is small in comparisonto their lengths and widths.
The attractive forces are mainly due to the fringingfields rather than the parallel plate fields.
Electrostatic Actuation Mechanism:
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StationaryComb
Moving Comb
Anchors
Ground Plate
Folded Beam(Movable CombSuspension)
Comb Drive Micro Actuator Parts:
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Comb Drive Micro Actuator Video:
Sorry Video is too big to upload ton t
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Electrostatic actuators Advantages:
Low power dissipation.
Can be designed to dissipate nopower while exerting a force.
High power density at micro scale.
Easy to fabricate.
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d x Lt
N C ocomb)(
Electrostatic force in comb-drive actuator
N
d
tV V C
x x
W F ocombcomb
22
22
Fingersof Number N :
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Scaling
Challenges for Actuators
Noise & Efficiency
Nonlinearity
Range of force, motion and frequency
Repeatability
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Model Description
x L EI F 312
Small deflection
large deflection
331 xk xk F
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)1(),()(22
xt F x F dt dx
cdt xd
m er
ANALYSIS:
Where: x: is displacement.m: is mass.c: is damping.
1-D motion of the device can be described by thefollowing equation:
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331)( xk xk x F r
Where:
k 1 : linear stiffness.k 3 : cubic stiffness.
Considering nonlinearity, the recovery force canbe expressed as:
When voltage signal being applied on comb drivefingers, Fe is:
t At F e cos)(
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the equation can be rewritten as a harmonicoscillator with normalizing:
t A xk xk dt dxc
dt xd m cos3312
2
Substituting Fe and Fr in equation (1) :
)cos(3
12
2
t P x xdt dx
dt xd
m
k
m
k
m
cWhere 31
1 ,,;
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Sub-Harmonic Resonance, Its Stability, Bifurcation And Transition to chaos
Case Study target ?
A dynamic system operating at high rotationalspeed may undergo a sub-critical loss ofstability which leads to violent and destruction
sub-harmonic vibrations.
Why the 1/3 sub-harmonic resonance?
What is the sub-harmonic resonance?
3/1
The harmonic component whose frequency is
is called an order sub-harmonic
3/
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Solution Approaches:
1. Method Of Multiple Scales ( MMS )
2. 2 M ode Harmonic BalanceMethod ( 2MHB )
3. Chaos Diagnostic Tools:
Phase Plane PlotPoincare Maps Frequency Spectrum
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Method Of Multiple Scales ( MMS )
Why the (MMS)?The Method Of Multiple Scales (MMS), is oneof the most commonly used procedure foranalyzing various resonances in nonlinear
systems.
Where fast and slow time scales are definedrespectively by:
t T 0 1, nt T n
n
10)cos(31 t P x x x x
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In terms of these time scales, the time derivativesbecome :
...22
...
212
21
22
2
22
1
D D D D D Ddt d
D D Ddt
d
ooo
o
nn T DWhere;
assumes a power series expansion for the dependentvariable x :
212221121 ,,,,,,, T T T xT T T xT T T xt x oooo
a detuning parameter is give by:
22 91
1
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Harmonic Balance Method ( 2MHB )
3sin
3coscos 3/13/11
t B
t At At x
A two modes harmonic approximation to thesteady state 1/3 sub-harmonic resonanceresponse of the above oscillator takes the form:
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SIMULATIONRESULTS
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.0)0(,1)0(,4,14,1.0,1.0,0,1
.':)(:)(
:)(:)(::)2(.
21 uu P
map Poincared plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
.0)0(,1)0(,4,14,1.0,1.0,1
.':)(:)(
:)(:)(::)1(.
1 uu P
map Poincared plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
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.0)0(,5)0(,4,14,1.0,1.0,1
.':)(:)(
:)(:)(::)2(.
1 uu P
map Poincared plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
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.0)0(,5)0(,4,4,02.0,1.0,1
.':)(:)(
:)(:)(::)3(.
1 uu P
map Poincared plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
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.0)0(,5)0(,4,8,02.0,1.0,1
.':)(:)(
:)(:)(::)4(.
1 uu P
map Poincared plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
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.3,01.0,2.0,1
.:.)(,:)(:)(:)5(.
1 P curveStability solution MMS results MMS e Approximat Fig
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.5,01.0,02.0,1
).2)((:.)(
,2:)(:2:)6(.
1
1
P
solution MHB Aamplitudel Fundamenta
solution MHB solution MHBe Approximat Fig
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.5)0(,6)0(,1,100,01.0,2.0,1
:)(
:)(:)(::)8(.
1 uu P
plot plane Phasec
transform Fourier b solution seriesTimea solution Numerical Fig
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