an introduction to electrostatic actuator

8/10/2019 An Introduction to Electrostatic Actuator

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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




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.0)0(,5)0(,4,14,1.0,1.0,1

.':)(:)(

:)(:)(::)2(.

1 uu P




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.0)0(,5)0(,4,4,02.0,1.0,1

.':)(:)(

:)(:)(::)3(.

1 uu P




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.0)0(,5)0(,4,8,02.0,1.0,1

.':)(:)(

:)(:)(::)4(.

1 uu P




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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



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an introduction to electrostatic actuator

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