Vibration Actuators and Sensors

Professor Mike Brennan

Institute of Sound and Vibration ResearchUniversity of Southampton, UK

Active Vibration ControlWHY ?

• Structures become lighter

• Space and weight constraints

Actuators Sensors

ControlledStructure

Controller

Vibration actuators and sensors

• Actuators Piezoelectric Magnetostrictive Electrodynamic Hydraulic

• Sensors Piezoelectric

• Controllability/Observability

• Shaped actuators/sensors (spatial filtering)

• Applications

Piezoelectric actuators and sensors

Piezoelectric effect(sensor)

An electric field is generated due to a change in dimensions of a material(Curie brothers 1880)

+

-

-

+

Converse Piezoelectric effect (actuator)

A change in dimensions ofa material due to theApplication of an electric field

Polarisation of a piezoelectric material

• Subject a piezoelectric material to a large voltage near the Curie temperature then the dipoles align

• Curie temperature is the temperature above which the material loses its piezoelectric property

dipole

Piezoelectric actuators and sensors

Property PZT (PC5H) type VI PVDF

Curie temperature (°C)

Longitudinal Young’s modulus (Nm-2)

Piezoelectric constant – d31 (mV-1)

Max E-field (Vm-1)

212

93 10959.5 10

100

12212 10 1223 10

60.4 10 640 10

• Piezoceramic (PZT) • Relatively stiff• Large piezoelectric constant

• Piezopolymer (PVDF) • Relatively flexible• Large voltage capacity

Direct piezoelectric effect (sensor) (element in free-space)

+

-

FA

Stress ( )T F A

33Generated field ( )E g T

33Charge ( )q d F

Indirect piezoelectric effect (actuator) (element in free-space)

L

H

W

+

-

L L

H HW W

+

-

H H

L LW WP

olin

g ax

is

31

Ld E

L

32

Wd E

W

33strain ( ) V

S dH

Electric field ( ) V

EH

Conventional use of piezoelectric material in transducers

• Used in accelerometers and force transducers. Generates an electrical charge proportional to strain

• Typical materials are polycystalline materials, e.g. barium titanate and lead zirconate

Modes of deformation

ceramic

+

-

compression

+

-

shear

ceramic

+

-

elongation

ceramic

qpiezoelectric capacitance

Equivalent electrical circuit

• Charge devices have a low capacitance (high impedance) and hence require pre-amp with a very high impedance

Practical Accelerometer Designs

Advantages– Few Parts / Easy to Fabricate– High Resonant Frequency

Compression Type

Disadvantages– Very high thermal transient

sensitivity– High base strain sensitivity

Practical Accelerometer Designs

Advantages– Few Parts– Small Size and Low Profile– Low Base Strain Sensitivity– Low Thermal Transient Sensitivity

Bending Type

Disadvantages– Low Resonant Frequency

Practical Accelerometer Designs

Advantages– Low Thermal Transient Sensitivity– Very Low Base Strain Sensitivity– Small Size

Disadvantages– ???

Shear Type

Force Transducer

Principle of Operation

Force, F

Material of cross-sectional area A and Young’s modulus E

The stress is related to the applied force by

F

A

and the stress is related to the strain by

ES

Therefore the strain is related to the force by F

SEA

As the electrical output is proportional to the strain, and the strain is proportional to the applied force, then the electrical output is proportionalTo the applied force

Piezoelectric Force Transducer

Preload stud

Piezoelectric element

• Can be used in tension and compression

• Fragile to moments

Electrical output

One-dimensional piezoelectric equations

Conductiveelectrodes

Piezoelectricmaterial of thickness t

• The piezoelectric equations are

3 31 3 33 3D d T E

113 3 33 3ES S T d E

mechanical electrical

strainS stressT

electric fieldE V t piezoelectric constantd

1 1 modulus of elasticityES Y

permittivity

dielectric displacment (charge area)D

+

-

Piezoelectric elements as strain sensors

• The piezoelectric equations are

3 31 1 33 3D d T E

111 3 31 3ES S T d E

1

3

q cV

is the capacitance of the sensorc

is the voltage generatedV

is the charge generatedq

V

CVoltage generator

C

q

Charge generator

Flexural (bending) vibration sensor

l

31 10

Aq d T dA

b

which evaluates to

31 ( ) (0)p pq d w Y b w l w

pwbw

If a flexural wavelength is much greater than l, then

31p

pb

wqd Y bl

S w

x

w

Longitudinal vibration sensor

l

31 10

Aq d T dA

b

which evaluates to

31 ( ) (0)pq d Y b u l u

If a longitudinal wavelength is much greater than l, then

31 p

qd Y bl

S

u

2-dimensional sensor

plate

PVDF sensor

1

3 2

Recall for the one-dimensional case (for no applied field)

3 31 1 31 1 1D d T d Y S

For the two-dimensional case

31 2 32 1 13 32 1 31

2 22

1

1

1D dY S d Yd d S

1 2where and are Poisson's ratios

Thus the electrical output is proportional to both S1 and S2

Strain or Strain-rate measurement

+

-

R

V

Piezoelectric sensor connected to a current amplifier measures “strain rate”

+

-

C

V

Piezoelectric sensor connected to a charge amplifier measures “strain”

Piezoelectric actuators

h

hV

Single element

33Free strain, h V

dh h

Connected electrically in parallel and mechanically in series

33For a stack of disks, h V

n n dh h

Stack

h

h

Coupling an Actuator to a structure

Actuator

Structure

ak

sk

sx

bF

sF

The piezoelectric equation is

33a

aa a

T VS d

Y l

is the actuator straina a aS x l is the actuator stressaT is the actuator Young's modulusaY is the actuator lengthal is the applied voltageV

Set 0 to get the blocked forceaS

Now and b a aa a

a a

F Y AT k

A l

where actuator cross-sectional area

and actuator longitudinal stiffnessa

a

A

k

33So b aF d k V

Coupling an Actuator to a structure

Actuator

Structure

ak

sk

sx

bF

sF

1Now

1s b

a

s

F Fkk

33So 1

as

a

s

d kF V

kk

33and 1

ss

a

dx V

kk

displacement

forc

e

Increasing voltagebF

( free)sx

Max power transfer

a sk k

If then will be smalls a sk k x

Flat piezoelectric actuators

High displacement – Low force actuators

Some piezoelectric actuator configurations

Fans

Bimorphs (benders)

Stacks

Curved actuators

Amplified piezoelectric actuators

PZT actuators for beam vibration

beam

PZT element

PZT element

actuators driven out-of-phase – bending vibration induced

beam

PZT element

PZT element

actuators driven in-phase – longitudinal vibration induced

PZT actuators for beam vibration

beam

PZT element

PZT element

actuators driven out-of-phase – bending vibration induced

M M

2

2

1

6 12 8b b bt Y b T

MT T

p

b

tT

t b b b

p p p

Y b t

Y b t 31

p

Vd

t

Ratio of thicknesses

Ratio of stiffnesses

Free strain

PZT actuators for beam vibration

2

6b b bt Y b

F

b b b

p p p

Y b t

Y b t 31

p

Vd

t

Ratio of stiffnesses

Free strain

beam

PZT element

PZT element

actuators driven in-phase – longitudinal vibration induced

FF

Piezoceramic Elements

The two piezoelectric elements can be excited:

• in phase to generate longitudinal vibration• out-of-phase to generate flexural vibration FF

LONGITUDINAL VIBRATION

Piezoceramic Elements

FLEXURAL VIBRATION

Works best at high frequencies when the length of the actuator is equal to half a wavelength

Excitation of a plate

plate

PZT patch

Controllability and Observability

Example - beam

Mode 1 Mode 2 Mode 3

A

• A sensor positioned at point A will observe modes 1 and 2 but not mode 3

• An actuator positioned at point A can control modes 1 and 2 but not mode 3

Shaped piezoelectric film bonded to a beam structure

Simply supportedCantilever

Mode 1

Mode 2

Modal filters

Modal filters experimental results

Point accelerance

Modal filters experimental results

Mode 1 filter Mode 2 filter

Shunted Piezoelectric Absorber

1n LC

The Smart Ski (ACX.com)

The Smart Ski (ACX.com)

Piezo patches

The Smart Bat (ACX.com)

                                         

Second bending mode (670 Hz)

                                         

Third bending mode (1252 Hz)

                                         

                                     

Fundamental bending mode (215 Hz)

The Smart Bat (ACX.com)

Electro / Magneto -Rheological Fluids

• micron sized, polarizable particles in oil

What do they do?

• Newtonian in absence of applied field

• develop yield strength when field applied

What are they ?

ER fluids respond to electric field

MR fluids respond to magnetic field

Magneto-Rheological Fluids - Applications

Ride Mode Switch

MR Fluid Damper

Sensor/Controller

Magneto-Rheological Fluids - Applications

Seat

Sensor

Controller

SpringControllable shock absorber

Road input

Acceptable motion transmitted

Off-stateRandompattern

On-State Ordered pattern

Single Degree of Freedom System -

Heavy Duty Vehicle Suspended Seats

• off-highway, construction and agricultural vehicles • class 8 trucks ("eighteen wheelers")• buses

Change in Stiffness – shape memory alloys

When the memory metal is pulled apart, it deforms. When placed into hot water, the metal "remembers" its original shape, and again forms the letters ICE.

Memory metal is a nickel-titanium alloy

This piece has been formed into the letters ICE, heat-treated, and cooled.

Change in Stiffness – shape memory alloys

Soft

Stiff

Stiffness increasesWith temperature

Change in Stiffness – shape memory alloys

• Material whose Young’s modulus changes with temperature

Composite panel

}

Embedded SMA wires

• Activating the fibres (by passing a current through them and hence causing a temperature change) causes local stiffening and hence the natural frequencies can be shifted to avoid troublesome excitation frequencies.

Active Control of Helicopter Vibrations/Structure-Borne Sound

• Active control of rotor vibrations at about 18 Hz

• Active control of gearbox noise at about 500 Hz

Application of ACSR to the Westland/Agusta EH101 Helicopter.

Active Control of Structural Response (Westlands, 1989)

Active Control of Rotor Vibration

rotor

fuselage

Hydraulic actuators

• Active control at rotor blade passing frequency at about 18 Hz + harmonics

• Feedforward control

ACSRACSR - Actuator Installation for Production EH101

•sa

Steel downtube

CompositeCompliantElement

TitaniumLug End

ACSR Actuator

Hydraulic Supply

Main GearboxInstallation

Fwd

Support Strut/ACSR ActuatorAssembly

Magnetostrictive actuators

polepiece

polepiece

magnet

Solenoidcoil

Terfenol-D rod

Terfenol-D

Ter – Terbium

Fe – Iron

Nol – Naval Ordinance Lab

D – Dysprosium

• Needs to be pre-stressed for good operation• Low voltages required• Similar performance to PZT

Active Control of Gearbox Noise

rotor

fuselage

• Active control at gear meshing frequency at about 500 Hz + harmonics

• Feedforward control

magnetostrictive actuators

Active Control of Gearbox Noise

Kinetic energy of receiving blockmeasured using 6 accelerometers

Without control

With controlReal-time control

Active Control of Aircraft Noise

Original Equipment- 4 Tuned Vibration Absorbers per engine

Actuators 2 per engine

Active Control of Aircraft Noise (Lord Corporation)

Controller 1 in cargo bay 12”x8”x3.5” 5 lbs

Amplifier 1 in cargo bay 11”x18”x3.5” 17 lbs

Actuators 4 2 on each yoke 4.5”diax5” 15 lbs

Microphones 8 behind trim incorporated into actuator harness

Wire Harness from cockpit, overhead through cabin, to pylon 22 lbs

Active Control of Aircraft Noise

NVX™OFF

NVX™ON

Attenuation is up to 8dBC

SPL (dBC)

Active Control of Aircraft Noise

NVX Systems reduce noise by reducing vibration

Controller On Controller Off

0 50 100 150 200 250 -80

-60

-40

-20

0

Frequency (Hz)

Typical Vibration Reduction with NVX DC9 Ground Test @ 75% Power

~6.3 dB

~25.5 dB

N1 N2

Data measured on pylon

Active magnetic bearings (SKF)

bearing sensors

controller

Active Vibration isolation demonstration

Active Vibration isolation demonstration

Concluding Remarks

• Actuators and Sensors are required for all Active Control Systems:

• Actuators used•Hydraulic•Piezoelectric (PZT)•Electrodynamic•Magnetostrictive

• Sensors used•Accelerometers•Force gauges•PVDF•PZT

References

• C.R. FULLER, S.J. ELLIOTT and P.A. NELSON 1996. Active Control of Vibration. Academic Press

• P.A. NELSON and S.J. ELLIOTT 1992. Active Control of Sound. Academic Press

• C.H. HANSEN and S.D. SNYDER 1997 Active Control of Noise and Vibration. E & F.N. Spon

• R.L. CLARK, W.R. SAUNDERS and G.P. GIBBS 1998. Adaptive Structures. Wiley Interscience

• A.V. SRINIVASAN and D. MICHAEL McFARLAND 2001. Smart Structures. Cambridge University Press