1. 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

2. 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.

3. What Is The Actuator ? Various actuation mechanisms:
The actuator is an element which applies a force to some object through a distance
Various actuation mechanisms:
Electrostatic actuation
Thermal actuation
Piezoelectric actuation
Magnetic actuation

4. Electrostatic Actuation:
A voltage is applied between metal plates to induce opposite charges and Coulomb attraction

5. Electrostatic Energy & Force:
Electrostatic Force :
Coulomb’s Law: Force
between two point charges

6. Electrostatic Actuators Types:
Force Normal to Plate :
Force Parallel to Plate

7. Why Comb Drive Micro Actuator ?
Force doesn’t drops rapidly when
increasing gap

8. Electrostatic Actuation Mechanism:
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.
Fringing Curves

9. Comb Drive Micro Actuator Parts:
Moving Comb
Folded Beam
(Movable Comb Suspension)
Ground Plate
Stationary
Comb
Anchors

10. Comb Drive Micro Actuator Video:
Sorry Video is too big to upload to net…

11. Electrostatic actuators Advantages:
Low power dissipation.
Can be designed to dissipate no power while exerting a force.
High power density at micro scale.
Easy to fabricate.

12. Electrostatic force in comb-drive actuator

13. Challenges for Actuators
Scaling
Noise & Efficiency
Range of force, motion and frequency
Repeatability
Nonlinearity

14. Model Description
Small deflection
large deflection

15. ANALYSIS:
1-D motion of the device can be described by the following equation:
Where:
x: is displacement.
m: is mass.
c: is damping.

16. Considering nonlinearity, the recovery force can
be expressed as:
Where:
k1: linear stiffness.
k3: cubic stiffness.
When voltage signal being applied on comb drive
fingers, Fe is:

17. Substituting Fe and Fr in equation (1) :
the equation can be rewritten as a harmonic oscillator with normalizing:

18. What is the sub-harmonic resonance?
Case Study target ?
Sub-Harmonic Resonance, Its Stability, Bifurcation And Transition to chaos
What is the sub-harmonic resonance?
The harmonic component whose frequency is
is called an order sub-harmonic
Why the 1/3 sub-harmonic resonance?
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.

19. Solution Approaches: 1. Method Of Multiple Scales (MMS)
2. 2 Mode Harmonic Balance Method (2MHB)
3. Chaos Diagnostic Tools:
Phase Plane Plot
Poincare’ Maps
Frequency Spectrum

20. Method Of Multiple Scales (MMS)
Why the (MMS)?
The Method Of Multiple Scales (MMS), is one
of the most commonly used procedure for
analyzing various resonances in nonlinear
systems.
Where fast and slow time scales are defined respectively by:

21. In terms of these time scales, the time derivatives become :
Where;
assumes a power series expansion for the dependent variable x :
a detuning parameter is give by:

22. Harmonic Balance Method (2MHB)
A two modes harmonic approximation to the
steady state 1/3 sub-harmonic resonance
response of the above oscillator takes the form:

23. SIMULATION RESULTS