Lecture 5: Electrostatic Sensors and Actuators - Engineeringmech466/MECH466-Lecture-5.pdf · 3 Introduction to Electrostatic Transducers Electrostatic sensors and actuators operate

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MECH 466Microelectromechanical Systems

University of VictoriaDept. of Mechanical Engineering

Lecture 5:Electrostatic Sensors and Actuators

© N. Dechev, University of Victoria

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Introduction to Electrostatics

Overview of Electrostatic Actuators and Sensors

Parallel Plate Capacitors

Electrostatic Interdigitated Finger Capacitors (Comb-Drives)

Overview


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Introduction to Electrostatic Transducers

Electrostatic sensors and actuators operate on the principle of electric charge.

Electrostatics work well for micro-scale devices, since the (surface area/volume) ratio is higher for micro-devices.

The electrostatic effect is based on surface area, while mass is based on volume, and hence electrostatic force is good for microsensing and microactuation.


Accelerometer [Analog Devices] DLP Micromirror Matrix [Texas Instruments]

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For ‘sensors’, capacitive devices can be used.

- A typical capacitor is comprised of two conductive elements, physically separated from each other, using some kind of dielectric material.

- The capacitance of a capacitor may be varied by:

______________________

______________________

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Ad

Dielectric Material Properties

Overlap Area A, of Electrodes

Distance d, between Electrodes

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For ‘actuators’, movable structures carrying accumulations of electric charge can be used.

There are two possible cases for using electric charge to generate force, and hence motion.

Consider two parallel plates.


+ + + ++++

+ + ++++ + ++++++++++++ ++

Positive Charge

- - - - - - ------------ --

Negative Charge

+ + + ++++

+ + ++++ + ++++++++++++ ++

Positive Charge

+ + + + + + ++++++++++++ ++

Positive Charge

Attractive Force Repulsive Force

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Electrostatic Micromotor

One of the first electrostatic actuators was a micromotor.

Consider the principle of operation:- Central rotor has one charge.- Radial stator poles have opposite charge.- Six stator phases (pair of poles) as shown below, are turned on and off in a sequence to cause the rotor to turn.


(Shown above) Single Phase Driving Sequence: 1,2,3,4,5,6,1,2,3,4,5,6,...(Alternate) Dual Phase Driving Sequence [1,4], [2,5], [3,6], [1,4], [2,5], [3,6],...

1 2

3

4

12

3

4

5

5

6

6

1 2

3

4

12

3

4

5

5

6

6

1 2

3

4

12

3

4

5

5

6

6

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Electrostatic Micromotor


SEM of an early Electrostatic Motor[Mehregany, MIT]

Movie of Electrostatic Motor, (720 stator poles)[M. Basha, U of Waterloo]

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Electrostatic Comb-Drive

Electrostatic actuators can also be used to create ‘linear motion’ using a ‘comb-drive’ that makes use of interdigitated fingers.

The principle of operation:- Central comb has one charge.- Two outer combs are sequenced with opposite charge.


Generic Comb-Drive (Sensor or Actuator)[D. Freeman, MIT]

Movie of Comb-Drive Actuator[J. Levitan, MIT]

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Electrostatic Transducers

Benefits of electrostatic devices:

- simplicity- very low power use for low frequency applications- fast response:

- speed is governed by the charge and discharge time constants, which are small for good conductors.- switch time of 21us for DMDs.

- deflection can be accurately controlled

There are also disadvantages:

- Actuators require drive voltages in the 50 - 150 Volt range.- Sensors require carefully designed circuits to measure capacitance change in presence of noise and interference.

- Static capacitance values are in the picoFarad range, while capacitance changes are in femtoFarad range.

- Large surface area is required for comb-drives to generate forces equivalent to other micro-actuators.


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Parallel Plate Electrostatic Devices

Example of a parallel plate electrostatic system, is the DMD (Digital Micromirror Device), developed by Texas Instruments.


DMD Operation Schematic,[Texas Instruments]

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Parallel Plate Electrostatic Devices


DMD Operation [Texas Instruments]

DLPTM Chip

Micro-MirrorElement (Pixel)

Micro-MirrorRemoved

Micro-Mirror

Actuator

Micro-Mirror

Compliant Hinge

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Consider an “ideal” parallel plate capacitor:


AWhere: A - Overlap area of two plates E - Electric Field d - distance between the two plates

E d

A dielectric material will occupy the space between the two plates:

The ‘Relative’ electrical permitivity is defined as:

The permitivity of the material is:

Where , is the permitivity of free space (vacuum)

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The capacitance between two plates is defined as:


Stored Charge Electrostatic Potential=

A

E d

The electric energy stored in the capacitor is:

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To obtain an expression for capacitance for the parallel pales, we can use Gauss’s Law, where the electric field:

This can be substituted into the capacitance equation to obtain:


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By measuring C accurately, we can sense changes in A (area), Permittivity, or d (distance between plates).

For example, Permittivity of a material can be influenced by:- Humidity- Chemical reactions - Temperature

Also, changes in the overlap of the two plates, or changes in the distance between the plates, can be made by:

- Static pressure- Acceleration- Other physical phenomena



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The force due to electrostatic attraction or repulsion between the plates is important to determine, and is defined by:



If the plates move along the axis normal to their surface, the variable of displacement is d. Therefore:

Solving:

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Example of force between two plates. (Example 4.1)



See Class Notes

Diagram of Comb-Drive:

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Interdigitated Finger Capacitors


Lo

tLc

wt xoOne Side of Comb

Other Side of Comb

Modeling of Comb-Drives

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One Comb is Anchored

Km

Mechanical ConnectionBetween Combs

CCf

Where: C - Normal Capacitance Between Beams Cf - Fringe Capacitance (Highly Non-linear)

A mechanical spring constant, Km, represents the stiffness of the compliant mechanism between the two combs

The two types of capacitance, C, and Cf, both have substantial contributions to the overall capacitance of the device.

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The total capacitance of the system is given by:

For the previous diagram:

There are two main types of Comb-Drives:

- Transverse

- Longitudinal



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The design of the flexure mechanism will determine the system stiffness and hence axis of motion


Transverse Comb-Drive

High StiffnessKm (y-axis)

Km (x-axis)Low Stiffness

AnchorPoints

FlexibleBeams

(a)

DeflectedBeams

(b)

δx

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When the upper comb is deflected to the right, the capacitance will change between the fingers as follows:



x

y

Lo

xxo

relative motion

Csr

Csl

Capacitance ofleft side:

Capacitance ofright side:

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The total capacitance is defined as:

Note: under equilibrium conditions, the net change in capacitance will be zero.



However, during motion, the rate of capacitance change can be measured, termed the displacement sensitivity, Sx:

If the comb-drive is used as an actuator, the force can be represented as:

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The capacity change associated with a single finger is:

Note: under equilibrium conditions, the net change in capacitance will be a finite amount.


Longitudinal Comb-Drive

x

y

Lo

+y

yo

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The displacement sensitivity in the longitudinal direction, Sy, is defined as:

If the longitudinal comb-drive is used as an actuator, the force can be represented as:

Note: The solution to these equations is not trivial.


Longitudinal Comb-Drive

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To compute values such as force, displacement sensitivity, and other parameters, numerical methods are required.

The contribution from ‘fringe capacitance’ is substantial, and cannot be ignored.

However, ‘fringe capacitance’ is highly non-linear and changes with different initial conditions and boundary conditions.


Computation of Comb-Drive Values

Electric Field Plot[C. Liu]

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Electromagnetic FEA (finite element analysis) is often used to compute the electric fields and intensities, and subsequently to determine capacitance, force and other parameters.


Computation of Comb-Drive Values

Electric Field Isolines[ANSYS]

Read Case 4.9 in Textbook. Example of how comb-drives are used for linear actuation of a Gear Rack, via a Pinion Gear.

28© N. Dechev, University of Victoria

Linear Actuators based on Comb-Drives

Rotational Comb-Drives

Linear Actuator[Sandia National Laboratories]

Rotational Comb-Drive[ALGOR FEMPRO]

Documents

Lecture 5: Electrostatic Sensors and Actuators - Engineeringmech466/MECH466-Lecture-5.pdf · 3 Introduction to Electrostatic Transducers Electrostatic sensors and actuators operate