lecture 12: piezoelectric sensors & actuators - …mech466/mech466-lecture-12.pdf · given the...

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MECH 466Microelectromechanical Systems

University of VictoriaDept. of Mechanical Engineering

Lecture 12:Piezoelectric Sensors & Actuators

© N. Dechev, University of Victoria

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Examples of piezoelectric sensors and actuators making use of cantilever beams

Example of piezoelectric sensors and actuators making use of a thin plate

Case Studies:

• Membrane Accelerometer

• Hard Drive Scanning Head Correction

Future Applications of Piezoelectric Sensors:

• The Daintiest Dynamos

Overview


Given the following actuator:

Q: Find the vertical displacement (direction 3) at the end of the beam, when voltage V is applied across the piezoelectric material, via the electrodes.

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Example #3: Piezoelectric Actuator


3 2

1

Silicon beam

Piezoelectric layer

electrode layers

w

t(piezo)

L

LA

LB

tb

V

Note: Only the portion of the beam ‘LA’ will be bent due to the piezoelectric strip.

This is a case of the ‘inverse effect’, therefore:

Since there are no applied forces, this reduces to:

4© N. Dechev, University of Victoria


Under the applied voltage, V:

Note: this equation can be re-written indicating the directions as:

(In other words, the electric field along direction 3, will cause strain along direction 1.)



The equation for the strain due to the ‘inverse effect’ can be written in matrix format as:

In the case of this example, we know that:



Additionally, we know that for typical piezoelectric materials, many values of the peizoelectric coefficient matrix are zero. For example, for ZnO, the matrix is:

Therefore, given the applied electric fields, and assuming the use of ZnO, the equation for strain due to the ‘inverse effect’ is:



Due to the applied voltage V, the piezoelectric element will expand (strain) in direction 1. Since it is firmly attached to the beam, this expansion (strain) will cause segment LA to be curved into an arc with a radius r, as defined by:

where s(long) is the longitudinal strain = s1 in this example



Therefore, since only segment LA of the beam will be bent, we can define the displacement (along direction 3) at the end of segment LA as:

where:

Therefore:



3

1

rφ

δ(x=LA)

Since the rest of the beam does not bend, the tip deflection of the entire beam can be defined as:



3

1

r

φ

δ(x=LA)

δ(beam)

Straight Portion of beam

Given the same actuator as in Example #3:

Q: Find the tip deflection given the following values:



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1

Silicon beam

Piezo = ZnO (see table 7.2 for properties)Beam = polysilicon (see past notes for properties)Vapplied = 100 Vtpiezo = 10 umtbeam = 5 umLA = 100 umL = 400 umwbeam = wpiezo = 30 um

V

w

t(piezo)

LLA LB

tb



See Class Notes


Case Study 7.2: Membrane Piezoelectric Accelerometer

A membrane based accelerometer is made using the piezoelectric effect, using the following design:

Figure 7.6. Piezoelectric Accelerometer [Chang Liu]

Top Electrodes

Bottom Electrode

Cross-SectionA-A’


Case Study: Hard Drive R/W Head Correction

Disc drives store information on the surface of a ‘hard platter’ using magnetic ‘read/write heads’ to create magnetic ‘bits’ of info.

As the density (# of bits/unit area on the surface) of hard drives increased over the past two decades, mechanical factors such as ball bearings, manufacturing errors and inertial effects have created bottlenecks on the possible read/write speeds and data density.

Inside of a typical hard drive, with platter, voice coil, and scan arm visible.[How Stuff Works.com]

Multi-platters and Multi-scan heads visible.[How Stuff Works.com]



To overcome these problems, recent hard drives incorporate a ‘self-correction system, using piezoelectric (or other) microactuators, to keep the read/write head centered on the ‘data track’.

Illustration of hard drive internals.[IBM-Almaden-Research-Center]

Movie of hard drive operation,without and with ‘error correction’ from a microactuator[IBM-Almaden-Research-Center]



SEM (scanning electron microscope) image of a typical hard drive head, with microactuator.

SEM image of hard drive head (upside down)[IBM-Almaden-Research-Center]


Case Study: The Daintiest Dynamos

A proposal for creating small sized generators for energy storage.

Seeks to take advantage of high energy densities available in some radioisotopes.

Operation of Piezoelectric Beam Generator [IEEE Spectrum, Sept 2004]

Beta particles (high-energy electrons) fly spontaneously

from the radioactive source and hit the copper sheet,

where they accumulate.

Electrostatic attraction between the copper sheet and

the radioactive source bends the silicon cantilever

and the piezoelectric plate on top of it.

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Piezoelectric plate

Silicon cantilever

Copper sheet

High-energyelectrons

Radioactive source

When the cantilever bends to the point where the copper

sheet touches the radioactive source, the electrons

flow back to it, and the attractive force ceases.

The cantilever then oscillates, and the mechanical stress in

the piezoelectric plate creates an imbalance in its

charge distribution, resulting in an electric current.

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ENERGY CONTENTENERGY DENSITY

TECHNOLOGY (MILLIWATT-HOUR/MILLIGRAM)

Lithium-ion in a chemical battery 0.3

3

85057 000

*llec leuf a ni lonahteM

Tritium in a nuclear battery**

Polonium-210 in a nuclear battery** *Assuming 50 percent e!ciency

**Assuming 8 percent e!ciency and 4 years of operation


Case Study: The Daintiest Dynamos

Issue for discussion:

• How can you use new “MEMS technology” to extract power from materials with high energy density?

Proposed Solution:

• MEMS based power generator, based on extracting energy from radio isotopes.

Benefits:

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Problems:

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