an introduction to electrostatic actuator a device overview and a specific applications an...
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An Introduction to Electrostatic Actuator
a Device Overview and a Specific Applications
An Introduction to Electrostatic Actuator
a Device Overview and a Specific Applications
Prepared By: Eng. Ashraf Al-Shalalfeh
Mechanical Engineering Dept.
Faculty Of Engineering & Tech.
University Of Jordan
What Is The MEMS? What Is The MEMS? It stands for: Micro-Electro-
Mechanical Systems.
It is an integration of elements, sensors, actuators, and electronics on a common silicon substrate.
Micro-fabrication technology, for making microscopic devices.
It stands for: Micro-Electro-Mechanical Systems.
It is an integration of elements, sensors, actuators, and electronics on a common silicon substrate.
Micro-fabrication technology, for making microscopic devices.
What Is The Actuator ?What Is The Actuator ?
The actuator is an element which applies a force to some object through a distance
The actuator is an element which applies a force to some object through a distance
Various actuation mechanisms:Various actuation mechanisms:
Electrostatic actuation Thermal actuation Piezoelectric actuation Magnetic actuation
Electrostatic actuation Thermal actuation Piezoelectric actuation Magnetic actuation
Electrostatic Actuation:Electrostatic Actuation:
d
wl
d
AC roro
2
2
1V
x
AF
2
2
1V
x
AF
A voltage is applied between metal plates to induce opposite charges and Coulomb attraction
A voltage is applied between metal plates to induce opposite charges and Coulomb attraction
plateeachofAreaA
ForceF
cedisseperationd
mFspacefreeoftypermittivi
tconsdielectricrelative
factorfielddringing
Where
o
r
:
:
tan:
])/[1085.8(:
tan:
:
;
12
22
22
1V
d
wlCVW ro
Electrostatic Energy & Force:Electrostatic Energy & Force:
Electrostatic Energy: Electrostatic Energy:
Electrostatic Force: Electrostatic Force:
221
4
1
x
qqF
ro
Coulomb’s Law: Force between two point charges
Coulomb’s Law: Force between two point charges
2
2
2z
wlV
z
WFz
Electrostatic Actuators Types:Electrostatic Actuators Types:Force Normal to Plate :Force Normal to Plate :
Force Parallel to PlateForce Parallel to Plate
d
wV
y
WFy 2
2
Why Comb Drive Micro Actuator? Why Comb Drive Micro Actuator?
Force doesn’t drops rapidly when increasing gapForce doesn’t drops rapidly when increasing gap
Fringing CurvesFringing Curves
Electrostic Micro-actuator consists of many fingers that are actuated by applying a voltage.
The thickness of the fingers is small in comparison to their lengths and widths.
The attractive forces are mainly due to the fringing fields rather than the parallel plate fields.
Electrostic Micro-actuator consists of many fingers that are actuated by applying a voltage.
The thickness of the fingers is small in comparison to their lengths and widths.
The attractive forces are mainly due to the fringing fields rather than the parallel plate fields.
Electrostatic Actuation Mechanism:Electrostatic Actuation Mechanism:
Stationary CombStationary Comb
Moving CombMoving Comb
AnchorsAnchors
Ground PlateGround Plate
Folded Beam(Movable Comb Suspension)
Folded Beam(Movable Comb Suspension)
Comb Drive Micro Actuator Parts:
Comb Drive Micro ActuatorParts:
Comb Drive Micro Actuator Video:Comb Drive Micro Actuator Video:
Sorry Video is too big to upload to net…Sorry Video is too big to upload to net…
Electrostatic actuators Advantages:
Electrostatic actuatorsAdvantages:
Low power dissipation.
Can be designed to dissipate no power while exerting a force.
High power density at micro scale.
Easy to fabricate.
Low power dissipation.
Can be designed to dissipate no power while exerting a force.
High power density at micro scale.
Easy to fabricate.
d
xLtNC o
comb
)(
Electrostatic force in comb-drive actuatorElectrostatic force in comb-drive actuator
Nd
tVVC
xx
WF ocomb
comb
22
22
FingersofNumberN :
ScalingScaling
Challenges for ActuatorsChallenges for Actuators
Noise & EfficiencyNoise & Efficiency
NonlinearityNonlinearity
Range of force, motion and frequencyRange of force, motion and frequencyRepeatabilityRepeatability
Model DescriptionModel Description
xL
EIF
3
12
Small deflectionSmall deflection
large deflectionlarge deflection
331 xkxkF
)1(),()(2
2
xtFxFdt
dxc
dt
xdm er
ANALYSIS:ANALYSIS:
Where: x: is
displacement.
m: is mass. c: is damping.
Where: x: is
displacement.
m: is mass. c: is damping.
1- D motion of the device can be described bythe following equation:
1-D motion of the device can be described by the following equation:
331)( xkxkxFr 331)( xkxkxFr
Where:
k1: linear stiffness. k3: cubic stiffness.
Where:
k1: linear stiffness. k3: cubic stiffness.
Considering nonlinearity, the recovery force can
be expressed as:
Considering nonlinearity, the recovery force can
be expressed as:
When voltage signal being applied on comb drive
fingers, Fe is:
When voltage signal being applied on comb drive
fingers, Fe is: tAtFe cos)( tAtFe cos)(
the equation can be rewritten as a harmonic oscillator with normalizing:
the equation can be rewritten as a harmonicoscillator with normalizing:
tAxkxkdt
dxc
dt
xdm cos3
312
2
tAxkxkdt
dxc
dt
xdm cos3
312
2
Substituting Fe and Fr in equation (1): Substituting Fe and Fr in equation (1):
)cos(312
2
tPxxdt
dx
dt
xd )cos(312
2
tPxxdt
dx
dt
xd
m
k
m
k
m
cWhere 3
11 ,,;
m
k
m
k
m
cWhere 3
11 ,,;
Sub-Harmonic Resonance, Its Stability, BifurcationAnd Transition to chaos
Sub-Harmonic Resonance, Its Stability, BifurcationAnd Transition to chaos
Case Study target ?Case Study target ?
A dynamic system operating at high rotational speed may undergo a sub-critical loss of stability which leads to violent and destruction sub-harmonic vibrations.
A dynamic system operating at high-rotational speed may undergo a sub critical loss of stability which leads to violent and destruction sub-harmonic
vibrations.
Why the 1/3 sub-harmonic resonance?
Why the 1/3 sub-harmonicresonance?
What is the sub-harmonic resonance?
What is the sub-harmonicresonance?
3/1 3/1
The harmonic component whose frequency is
is called an order sub-harmonic
The harmonic component whosefrequency is
is called an order sub-harmonic
3/ 3/
Solution Approaches:Solution Approaches:1. Method Of Multiple Scales
(MMS)
2. 2 Mode Harmonic Balance Method (2MHB)
3. Chaos Diagnostic Tools:
Phase Plane PlotPoincare’ MapsFrequency Spectrum
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 nonlinearsystems.
Where fast and slow time scales are defined respectively by:Where fast and slow time scales are defined respectively by:
tT 0 tT 0 1, ntT nn 1, ntT nn
10)cos(31 tPxxxx 10)cos(31 tPxxxx
In terms of these time scales, the time derivatives become :In terms of these time scales, the time derivatives become :
...22
...
212
21
22
2
22
1
DDDDDDdt
d
DDDdt
d
ooo
o
...22
...
212
21
22
2
22
1
DDDDDDdt
d
DDDdt
d
ooo
o
nn T
D
n
n TD
Where;Where;
assumes a power series expansion for the dependent variable x :assumes a power series expansion for the dependent variable x :
2122
21121 ,,,,,,, TTTxTTTxTTTxtx oooo 2122
21121 ,,,,,,, TTTxTTTxTTTxtx oooo
a detuning parameter is give by:a detuning parameter is give by:
22
9
11 22
9
11
Harmonic Balance Method (2MHB)
3
sin3
coscos 3/13/11
tB
tAtAtx
A two modes harmonic approximation to the steady state 1/3 sub-harmonic resonance response of the above oscillator takes the form:
SIMULATION RESULTS
SIMULATION RESULTS
.0)0(,1)0(,4,14,1.0,1.0,0,1
.':)(:)(
:)(:)(::)2(.
21 uuP
mapPoincaredplotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
.0)0(,1)0(,4,14,1.0,1.0,1
.':)(:)(
:)(:)(::)1(.
1 uuP
mapPoincaredplotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
.0)0(,5)0(,4,14,1.0,1.0,1
.':)(:)(
:)(:)(::)2(.
1 uuP
mapPoincaredplotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
.0)0(,5)0(,4,4,02.0,1.0,1
.':)(:)(
:)(:)(::)3(.
1 uuP
mapPoincaredplotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
.0)0(,5)0(,4,8,02.0,1.0,1
.':)(:)(
:)(:)(::)4(.
1 uuP
mapPoincaredplotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
.3,01.0,2.0,1
.:.)(,:)(:)(:)5(.
1
P
curveStabilitysolutionMMSresultsMMSeApproximatFig
.5,01.0,02.0,1
).2)((:.)(
,2:)(:2:)6(.
1
1
P
solutionMHBAamplitudelFundamenta
solutionMHBsolutionMHBeApproximatFig
.5,01.0,2.0,1
).2)((:.)(,:(*)
,:(.),2:)(:2,:)7(.
1
1
P
MHBAamplitudelFundamentasolutionNumerical
solutionMMSsolutionMHBsolutionNumericalandMHBMMSFig
.5)0(,6)0(,1,100,01.0,2.0,1
:)(
:)(:)(::)8(.
1 uuP
plotplanePhasec
transformFourierbsolutionseriesTimeasolutionNumericalFig
