MicroPositioning, NanoPositioning, NanoAutomation Tutorial ... · Coefficient of Thermal Expansion...

MicroPositioning, NanoPositioning, NanoAutomation®

Tutorial: Piezoelectrics in Positioning

Tutorial

Piezoelectrics in Positioning

Different Ways of Designing Multi-Axis NanoPositioning Flexure Stages

Piezoelectric NanoPositioning Systems: small (e.g. data storage), medium (e.g. fiber optics), large (e.g. precision machining).

Flatness of a NanoPositioning stage with active trajectory control isbetter than of 1 nanometer over a 100 x 100 µm scanning range.

A) Stacking 2 single-axis stages.

Pro: Simple.Con: Slower response (lower stage carriesinertial mass of upper stage); orthogonalityerror is mounting-angle dependant; runout inY cannot be monitored/ compensated bythe sensor in the X stage or vice versa.

B) Single module (monolithic) but nested(serial) X and Y.

Better response than A) but X and Y stillwork without "knowledge" of each other.

C) Single-module parallel-kinematics X and Y (with crosstalk compensation).

Best solution. Same low inertia for X and Y motion, pro-viding higher responsiveness and axis-inde-pendent performance. Best orthogonality. X sensor can monitorand correct for Y runout and vice versa.Additional rotation axis ( �z) feasible with3 actuators / sensors and digital controller.

Patented InputShapingTM feedforward algorithm eliminates resonance-driven vibration of parts on and around the NanoPositioning system.

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PZT unit cell: 1) Perovskite-type lead zirconate titanate (PZT) unit cell in thesymmetric cubic state above the Curietemperature. 2) Tetragonally distorted unit cell below the Curie temperature

Ceramic spray dryer at PI Ceramicensures piezo ceramics quality.

Variety of multilayer piezo stack and bender actuators.

Response of an open-loop piezo actuator to triangule-wave drive signalshows sub-nanometer resolution.

Sputtering (vacuum plating) process ofpiezo ceramic discs at PI Ceramic.

Equipment for multilayer piezo actuator production,at the PI Ceramic factory.

PI offers the largestselection of research and

industrial-reliability Piezo Actuators,PiezoNanoPositioning Systems,

Steering Mirrors and Control Electronicsworldwide.

In addition to the hundreds of models presented in this catalog, we manufacture

custom designs tailored to the customer's requirements.

PI is highly vertically integrated, controllingeach manufacturing step from PZT raw

materials to finished systems thus ensuring the best quality.

Variety of "cofired" and "classical" piezo stacks and rings.

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Advantages of Piezoelectric Positioning

A piezoelectric actuator (PZT) canproduce extremely fine position changes down to the sub-nanometerrange. The smallest changes in operating voltage are converted intosmooth movements. Motion is notinfluenced by stiction, friction orthreshold voltages.

Piezo actuators offer the fastest response timeavailable (microsecond time constants).Acceleration rates of more than 10,000 g‘s canbe obtained.

Unlimited Resolution

Rapid Response

PZTs can generate forces of several 10,000 N. PI offers units that move loads upto several tons and position over a range ofmore than 100 µm with sub-nanometer resolution (see "PZT Actuators" section).

Large Force Generation

The piezoelectric effect isrelated to electric fields. PZTactuators do not produce mag-netic fields nor are theyaffected by them. Piezodevices are especially wellsuited for applications wheremagnetic fields cannot be tol-erated.

No Magnetic Fields

Elongation and contraction of a piezo disk when a voltage is applied.

Variety of digital motion controllers forpiezoelectric NanoPositioning systems.

Heavy-duty closed-loop piezoelectric positioning systems for machining applications. Principle of a simple motion-

amplified NanoPositioning stage.

Variety of piezoelectric flexure nanopositioners.

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PZT Active Optics / Steering Mirrors

Tutorial: Piezoelectrics...

Capacitive Position Sensors

PZT Control Electronics

MicroPositioners / Hexapod Systems

Photonics Alignment & Packaging Systems

Motor Controllers

Index

PZT Flexure NanoPositioners

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PZT Actuators

Piezo actuators employ ceramic elements that donot need any lubricants and exhibit no wear or abra-sion. This makes them clean-room compatible andideally suited for ultra-high-vacuum applications.

The piezo effect is based on electric fields and functions down to almost zero Kelvin.

In a PZT electrical energy is converteddirectly into motion, absorbing elec-trical energy during movement only.Static operation, even holding heavyloads, consumes virtually no energy.

Low Power Consumption

Advantages of Piezoelectric Positioning...(continued)

Vacuum and Clean-Room Compatible

Operation at Cryogenic Temperatures

A piezo actuator has neithergears nor rotating shafts. Its displacement is based on solid-state phenomena andexhibits no wear and tear. PI has conducted endurance tests on PZTs in which virtuallyno change in performance was observed after several billion cycles.

No Wear and Tear

Life Science, Medicine,Biology

� Scanning microscopy� Patch-clamp � Gene manipulation � Micromanipulation� Cell penetration� Micro-dispensing devices

Optics, Photonics, Fiber Optics Metrology and Measuring Technology

� Fiber optic alignment & switching � Image stabilization� Adaptive optics � Scanning microscopy� Auto-focus systems� Interferometry� Adaptive and active optics� Laser tuning� Mirror positioning

Data Storage

� MR head testing� Pole tip recession� Spin stands� Disk testing� Vibration cancellation

Semiconductors,Microelectronics

� Nano-metrology� Wafer and mask positioning / alignment� Critical-dimension measurement� Microlithography� Inspection systems� Vibration cancellation

Applications for Piezo Positioning Technology

Precision Mechanics and Mechanical Engineering

� Fast tool servos� Out-of-roundness finishing (boring, drilling, turning)� Vibration cancellation� Smart structures / structural deformation� Wear correction� Needle-valve actuation� Micro-pumps� Knife edge control in extrusion tools� Micro-engraving systems

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PZT Actuators

Tutorial: Piezoelectrics in Positioning

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

Advantages of Piezoelectric Positioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

Applications for Piezo Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4

Tutorial Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7

Symbols and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8

Basic Introduction to NanoPositioning with Piezoelectric Technology. . . . . . . . . . . . . . . . . 4-9

Low-Voltage and High-Voltage PZTs

Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10

Open and Closed-Loop Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

Mechanical Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12

Power Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12

Different Piezo Actuator Designs to Suit Various Applications . . . . . . . . . . . . . . . . . . . . . . . . 4-13

Design Points to Remember . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14

Fundamentals of Piezoelectricity and Piezo Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

PZT Ceramics Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16

Definition of Piezoelectric Coefficients and Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17

Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18

Amplifier Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18

Displacement of Piezo Actuators (Stack & Contraction Type) . . . . . . . . . . . . . . . . . . . . . . . 4-19

Hysteresis (open-loop PZTs). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

Creep (Drift) (open-loop PZTs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

High-Resolution Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21

Strain Gauge Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21

Linear Variable Differential Transformers (LVDT’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21

Capacitive Position Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22

Mechanical Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23

Maximum Applicable Forces (Compressive Load Limit, Tensile Load Limit) . . . . . . . . . . . . . 4-23

Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23

Static Large-Signal Stiffness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24

Dynamic Small-Signal Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24

Force Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25

Displacement with External Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26

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Mechanical Considerations for Dynamic Operation of PZTs . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27

Dynamic Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27

Resonant Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28

How Fast Can a Piezo Actuator Expand? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29

Electrical Requirements for Piezo Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30

Static Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30

Dynamic Operation (Analog) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Dynamic Operating Current Coefficient (DOCC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32

Dynamic Operation (Switched) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32

Heat Generation in a PZT in Dynamic Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33

Position Servo-Control (Closed-Loop Operation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34

Methods to Improve Piezo Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36

Input Shaping™ Stops Structural Ringing Caused by High-Throughput Motions . . . . . . . . . . . . . 4-36

SignalPreshaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37

Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38

Linear Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38

Temperature Dependency of the Piezo Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38

Environmental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

PZT Operation in Normal Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

PZT Operation in Inert Gas Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

Vacuum Operation of PZTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

Lifetime of PZTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40

Basic Designs of Piezoelectric Positioning Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41

Stack Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41

Laminar Design (Contraction-Type Actuator) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41

Tube Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42

Bender Type Actuators (Bimorph and Multimorph Design) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43

Piezo Actuators with Integrated Lever Motion Amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-44

PZT Flexure NanoPositioners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-45

Electrostrictive Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-46

Mounting Guidlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

Units of Measure and Conversion Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-48

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See also “MicroPositioningTerms,” page 7-10.

Actuator:

A device that produces motion(displacement).

Blocked Force:

The maximum force an actua-tor can generate if blocked byan infinitely rigid restraint.

Ceramic:

A polycrystalline, inorganicmaterial.

Closed-Loop Operation:

The actuator is used with aposition sensor which providesfeedback to the position servo-controller, compensating fornonlinearity, hysteresis andcreep (see “open-loop”).

Compliance:

Displacement produced perunit force. The reciprocal ofstiffness.

Compressive Force:

Force tending to compress thepiezo material. Opposite oftensile force.

Creep:

An unwanted change in thedisplacement over time.

Curie Temperature:

The temperature at which thecrystalline structure changesfrom a piezoelectric (non-sym-metrical) to a non-piezoelectric(symmetrical) form whenheaded up. At this temperaturea PZT ceramic looses its piezo-electric properties.

Domain:

A region of permanent electricdipoles with the same orienta-tion.

Drift:

See “creep”

Effective Mass:

Ideal mass having same reso-nant frequency as the actual,non-ideal mass.

HVPZT:

Acronym for high voltage PZT(actuator).

Hysteresis:

Hysteresis is based on crys-talline polarization and molecu-lar effects and occurs whenreversing driving direction.Hysteresis is not to be con-fused with backlash.

LVPZT:

Acronym for low voltage PZT(actuator).

Load Capacity:

Maximum working load. Loadcapacities are generally speci-fied at levels that allow longlifetime. Note that compressiveand tensile capacities differ.

Load Limits:

Maximum force that a PZTdevice can survive without da-mage. Note that the compres-sive and tensile limits are different. Also called the “max-imum compressive / tensileforce.” See also “load capa-city.”

Maximum Compressive/

Tensile Force:

Same as “load limit”, seeabove.

Multilayer Actuator:

An actuator manufactured in afashion similar to multilayerceramic capacitors. PZT cera-mic and electrode material are“co-fired” in one step. Layerthickness is typically on theorder of 20 to 100 µm.

Normal:

At right angles to, as in “nor-mal force” or “displacementnormal to the field”.

Open-Loop Operation:

The actuator is used without aposition sensor. Displacementroughly corresponds to thedrive voltage. Creep, nonlinear-ity and hysteresis remain com-pensated.

Piezoelectric Materials:

Materials that change theirdimensions when a voltage isapplied and produce a chargewhen pressure is applied.

Piezo Gain:

Strain coefficients d33

and d31

.

Polarization:

The electric orientation of mol-ecules in a piezoelectric mate-rial.

PZT:

Acronym for plumbum (lead)zirconate titanate. Polycrystal-line ceramic material withpiezoelectric properties. Oftenalso used as acronym for piezotranslator.

Stiffness:

The spring constant (of a piezoactuator).

Tensile Force:

Force tending to stretch thepiezo material.

Trajectory Control:

Measures taken to reduce off-axis motion. Used are bothpassive measures (e.g. flexureguiding) and active measures(compensation with additionalactive axes.)

Translator:

An actuator which produceslinear motion.

Glossary







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PZT Actuators

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A Surface area [m2] (meter2)

� Coefficient of Thermal Expansion (CTE) [K-1] (1 / kelvin)

C Capacitance (F) [A�s / V]

dij

Piezo modulus (tensor components) [m/V] (meter/volt)

ds

Distance, thickness [m] (meter)

� Dielectric constant [A�s/V�m] (ampere � second � volt � meter)

E Electric field strength [V/m] (volt/meter)

f Operating frequency [Hz] (hertz = 1/second)

F Force [N] (newton)

f0

Unloaded resonant frequency [Hz] (hertz = 1/second)

g Acceleration due to gravity: 9.81 m/s2 (meter/second2)

i Current [A] (ampere)

kS

Stiffness of restraint (load) [N/m] (newton/meter)

kT

Stiffness of piezo actuator [N/m] (newton/meter)

L0

Length of non-energized actuator [m] (meter)

�L Change in length (displacement) [m] (meter)

�L0

Nominal displacement with zero applied force, [m] (meter)

�Lt=0.1

Displacement at time t = 0.1 sec after voltage change, [m] (meter)

m Mass [kg] (kilogram)

P Power [W] (watt)

Q Charge [C] (coulomb = ampere � second)

S Strain [�L/L] (dimensionless)

t Time [s] (second)

U voltage [V] (volt)

Up-p

Peak-to-peak voltage [V] (volt)

Symbols and Units

Basics

The piezoelectric effect is oftenencountered in daily life. Forexample, in small butane ciga-rette or gas grill lighters, a leverapplies pressure to a piezo-electric ceramic creating anelectric field strong enough toproduce a spark to ignite thegas. Furthermore, alarm clocksoften use a piezoelectric ele-ment. When AC voltage isapplied, the piezoelectric mate-rial moves at the frequency ofthe applied voltage and theresulting sound is loud enoughto wake even the strongestsleeper.

The word “piezo” is derivedfrom the Greek word for pres-sure. In 1880, Jacques andPierre Curie discovered thatpressure applied to a quartzcrystal creates an electricalcharge in the crystal; theycalled this phenomena thepiezo effect. Later they alsoverified that an electrical fieldapplied to the crystal wouldlead to a deformation of thematerial. This effect is referredto as the inverse piezo effect.After the discovery it took sev-eral decades to utilize thepiezoelectric phenomenon. Thefirst commercial applicationswere ultrasonic submarinedetectors developed duringWorld War I. In the 1940’s sci-entists discovered that bariumtitanate ceramics could bemade piezoelectric by applica-tion of an electric field.

As stated above, piezoelectricmaterials can be used to con-vert electrical energy intomechanical energy and viceversa. For NanoPositioning, theprecise motion which resultswhen an electric field is ap-plied to a piezoelectric materialis of great value. Actuatorsusing this effect first becameavailable around 30 years agoand have changed the world ofprecision positioning.

Industrial reliability PZT materi-als can achieve a strain on theorder of 1/1000 (0.1%); thismeans that a 100 mm long PZT actuator can expand by 100 micrometers when themaximum allowable field isapplied.

NotesFor more detailed information see“Fundamentals of Piezoelectricity and Piezo Actuators”, page 4-15.

Basic Introduction to NanoPositioning

with Piezoelectric Technology

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PZT Actuators

� Repeatable nanometer

and sub-nanometer

steps at high frequency

can be achieved with

PZTs because they

derive their motion

through solid state

crystal effects.There

are no moving parts

(no “stick-slip” effect).

� PZTs can be designed

to move heavy loads

(several tons) or can be

made to move lighter

loads at frequencies of

several tens of kHz.

� PZTs act as capacitive

loads and require very

little power in static

operation, simplifying

power supply needs.

� PZTs require no main-

tenance because they

are solid state and

their motion is based

on molecular effects

within the crystalline

cells.

Features of PZT Actuators

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Basic Introduction . . . (cont.)

Resolution

Piezo actuators have no “stickslip” effect and therefore offertheoretically unlimited resolu-tion. This feature is importantsince PZTs used in atomicforce microscopes are oftenrequired to move distancesless than one atomic diameter.In practice, actual resolution

can be limited by a number offactors, such as the piezo con-trol amplifier (electronic noiseresults in unwanted displace-ment) and sensor & controlelectronics (noise and sensitiv-ity to EMI affect the positional resolution and stability). Mech-anical parameters are also

important (design and mount-ing precision of the sensor,actuator and preload influencemicro-friction which limits res-olution and accuracy). PI closed-loop PZT actuators provide sub-nanometer resolu-tion and stability.

Two main types of piezo actua-tors are available: low-voltage(multilayer) devices requiring100 volts or less for full motionand high-voltage devices re-quiring about 1000 volts for fullextension. Modern piezo cera-mics capable of greater motionreplace the natural materialused by the Curies, in bothtypes of devices. Lead zir-conate titanate (PZT) basedceramic materials are mostoften used today. Actuatorsmade of this ceramic are oftenreferred to as PZT actuators.

The maximum electrical fieldPZT ceramics can withstand ison the order of 1 to 2 kV/mm.In order to keep the operatingvoltage within practical limits,PZT actuators consist of thinlayers of electroactive ceramicmaterial electrically connectedin parallel (Fig. 1). The total displacement is the sum of the displacements of the indi-vidual layers. The thickness of the individual layer deter-mines the maximum operating

voltage for the actuator (formore information see“Displacement of PiezoActuators (Stack & ContractionType)”, page 4-19).

High-voltage piezo actuatorsconsist of bulk ceramic diskswhich are 0.4 to 1 mm thickand glued together to form astack.

Low-voltage piezo actuatorsare manufactured in a lamina-tion process, where thick-filmelectrodes are printed ongreen ceramic foils. The layersof ceramics and electrodes arethen pressed together andcofired to form a monolithicblock.

Typical layer thicknesses are inthe range of 20 to 100 µm.After cutting the individualstacks to size, wire leads areapplied.

Both types of piezo actuatorscan be used for many applica-tions: Low-voltage actuatorsfacilitate drive electronics de-sign, high-voltage types oper-ate to higher temperatures(150 °C compared to 80 °C).

Due to manufacturing technol-ogy, high-voltage ceramics canbe designed with larger cross-sections suitable for higher-load applications (up to severaltons) than low voltage ceram-ics.

+

+

+

+

+

+

+

+

+

Fig.1. Electrical connection of disks in a PZT stack actuator.

Low-Voltage and High-Voltage PZTs

PZT actuators can be operatedin open- and closed-loop modes. In open-loop mode,displacement roughly corre-sponds to the drive voltage.This mode is ideal when theabsolute position accuracy isnot critical, or when the posi-tion is controlled by data pro-vided by an external sensor(interferometer, CCD chipetc.). Open-loop piezo actua-tors exhibit hysteresis andcreep behavior, just like otheropen-loop positioning sys-tems.

Closed-loop actuators are idealfor applications requiring highlinearity, long-term positionstability, repeatability and ac-

curacy. PI closed-loop PZTactuators & systems areequipped with position meas-uring systems providing sub-nanometer resolution or band-width up to 10 kHz. A servo-controller (digital or analog)determines the voltage tosend to the PZT by comparinga reference signal (com-manded position) to the actualposition, as reported by thefeedback position sensor (formore information see “Posi-tion Servo-Control,” page 4-34).

PI has designed multi-axis,closed-loop PZT positionersthat offer the possibility ofrepeatedly locating a pointwithin a 1 x 1 x 1 nm cube (see

the “PZT Flexure Nano-Positioners” section for moreinformation). It is important toremember that such accuracyis obtainable only if the sur-rounding environment is con-trolled, since temperaturechanges and vibration willcause changes in position atthe nanometer level.

Dynamic Behavior

A piezo actuator can reach itsnominal displacement in ap-proximately one third of theperiod of its resonant fre-quency. Rise times on theorder of microseconds andaccelerations of more than10,000 g’s are possible. Thisfeature makes PZTs suitable for rapid switching applica-tions. Injector nozzle valves,hydraulic valves, electricalrelays, adaptive optics andoptical switches are a fewexamples of fast switchingapplications.

Resonant frequencies of indu-strial-reliability piezo actuatorsrange from a few tens of kHzfor actuators with total travelof a few microns to a few kHzfor actuators with travel ofmore than 100 microns. Thesefigures are valid for the piezoitself; an additional load willdecrease the resonant fre-quency as a function of thesquare root of the effectivemass (quadrupling the masswill halve the resonant fre-quency).

Piezo actuators are not de-signed to be driven at resonantfrequency (with full stroke andload), as the resulting highdynamic forces can endangerthe structural integrity of theceramic material.

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PZT Actuators

Open- and Closed-Loop Operation

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Stiffness

In a first approximation, a piezoactuator can be regarded as aspring/mass system. The stiff-ness or spring constant of apiezo actuator depends on theYoung’s Modulus of theceramic (approximately 25 %that of steel), the cross sectionand length of the active mate-rial and a number of other non-linear parameters (for more information see “Stiffness,”page 4-23).

Load Capacity and Force Generation

PZT ceramics can withstandhigh pushing forces and carryloads to several tons. Evenwhen fully loaded, the PZT willnot lose any travel as long asthe maximum load capacity isnot exceeded.

Load capacity and force gener-ation must be distinguished.The maximum force (blockedforce) a piezo can generate isdetermined by the product ofthe stiffness and the nominaldisplacement. A piezo actuator(as most other actuators) push-ing against a spring load willnot reach its nominal displace-ment. The reduction in dis-placement is dependent on theratio of the piezo stiffness tothe spring stiffness. As thespring stiffness increases, thedisplacement decreases andthe generated force increases(for more information see”Stiffness”, page 4-23).

Protection fromMechanical Damage

Since PZT ceramics are brittleand cannot withstand highpulling or shear forces, themechanical actuator designmust isolate these undesirableforces from the ceramic. Forexample, spring preloads canbe integrated in the mechani-cal actuator assembly to com-press (preload) the ceramicinside and increase theceramic’s pulling capabilitiesfor dynamic push/pull applica-tions (for more information see “Mounting Guidelines”,page 4-47).

Mechanical Considerations

Power Requirements


Piezo actuators operate ascapacitive loads. Since the cur-rent leakage rate of theceramic material is very low(resistance typically 10 M�),piezo actuators consumealmost no energy in a staticapplication and therefore pro-duce virtually no heat.

In dynamic applications thepower consumption increaseslinearly with frequency andactuator capacitance. High-load actuators with largerceramic cross sections havehigher capacitance than smallactuators.

For example, a typicalmedium-load LVPZT actuatorwith a motion range of 15 microns and 10 kg load

capacity requires only fivewatts to be driven at 1000 Hzwhile a high-load actuatorcapable of carrying a few tonsmay require hundreds of wattsfor the same frequency (formore information see “Elec-trical Requirements,” page4-30).

Stack Actuators(Translators)

The most common form ofpiezo actuator is a stack ofceramic layers with two elec-trical leads. To protect theceramic against external influ-ences, a metal case is oftenplaced around it. This case mayalso contain built-in springs tocompress the ceramic to allowboth push and pull operation.

The P-845 closed-loop LVPZTtranslator (Fig. 2) is one ex-ample of a low voltage transla-tor with internal spring preloadand integrated high-resolutionstrain gauge position sensor.This translator is available withdisplacements up to 90 mic-rons. It can handle loads up to300 kilograms and withstandpulling forces to 700 N (seethe “PZT Actuators” sectionfor details). Applicationsinclude vibration cancellation,shock wave generation andmachine tool positioning forfabrication of non-sphericalcontact lens surfaces.

PI offers PZT stack translatorswith travel ranges from a fewmicrons for small designs to asmuch as 200 microns for 200 mm long units. In someapplications, space restrictionsdo not allow for such longstacks. In these cases, it ispossible to use mechanicallever amplifiers to decreasethe length of the ceramicstack. The increase in travelgained with a mechanicalamplifier reduces the actua-tor’s stiffness and maximumoperating frequency.

Other Basic Actuators

Apart from stack translators, anumber of other basic PZTactuators are available: benderactuators providing long travel(millimeter range), contractionactuators, tube actuators,shear actuators etc. See“Basic Designs,” page 4-41 fffor more information.

Actuators with MotionAmplifiers & TrajectoryControl

In some applications a stackactuator alone is not enough toperform complex tasks. Forexample, when straight mo-tion is needed and onlynanometer deviation from theideal trajectory can be toler-ated, a stack translator cannotbe used because it may tilt asmuch as a few tens of arcsec-onds while expanding. If thestack and the part to be movedare decoupled and a precisionguiding system is employed,exceptional trajectory controlcan be achieved. The best guid-ing precision can be achievedwith flexures.

Fig. 3 shows one example of apiezoelectrically driven minia-ture flexure stage with inte-grated flexure guiding systemand motion amplifier. Thestage is made of stainlesssteel and all flexures are wireEDM (electrical discharge machining) cut. The flexuresare computer designed by anFEA (Finite Element Analysis)program. The central part of thestage can move +/- 40 micro-meters along one axis. Themovement is accomplished byan integrated 3:1 lever, drivenby a PZT stack pushing aspherical tip built into to the

Different Piezo Actuator Designs

to Suit Various Applications

Fig. 3. P-780 PZT Flexure Nano-Positioner and scanner with integratedmotion amplifier.

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Fig. 2. P-845 Closed-loop LVPZT translator

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lever. The resonant frequencyof the unloaded stage is 1 kHz(high when the lever amplifica-tion is considered).

The lever is connected to theplatform by a flat spring whichis very stiff in the push/pulldirection but flexible in the lat-eral direction. This flexibilityensures straight stage motionwith minimum tilt and lateraldeviation. The system runoutand flatness are in the

nanometer realm and even thislow figure can be reduced with a larger flexure base.Sub-nanometer, sub-microra-dian flatness can be achievedwith multi-axis systems usingactive error compensation (seethe “PZT Flexure NanoPosi-tioners” section for details).The flexure design is not lim-ited to single-axis stages; sys-tems with up to six degrees offreedom are available.

Single- and multi-axis flexurepositioners are used in research, laboratory and indus-trial applications. Examples aredisk drive testing, mask align-ers for X-Ray steppers, adap-tive optics, precision machin-ing, fiber aligners, scanningmicroscopy, autofocus sys-tems for surface profilers andhydraulic servo valves.

Piezo Actuators Com-bined with MotorizedLong-Travel PositioningSystems

Piezo actuators can be com-bined with other actuators toform long-travel, high-resolu-tion systems. A good exampleis the combination of a P-250piezo actuator with a closed-loop motor-driven leadscrew(Fig. 4). This combination pro-vides 25 mm coarse range(versions with 50 mm are avail-able) but preserves the high-resolution characteristics in-trinsic to PZTs. Coarse motionis provided by a micrometerwith a non-rotating tip drivenby a DC motor/encoder/gear-head unit capable of < 0.1 µmresolution. A short PZT stackproviding sub-nanometer reso-lution is mounted inside themicrometer tip. Both piezo andDC motor can be computercontrolled.

{bk xtx4140}

Piezo actuators offer uniqueand compelling advantages innanometer resolution andhigh-speed applications. Toobtain maximum performancewhile avoiding problems, how-ever, piezoelectric characteris-tics need to be considered.Pulling, shear and torsionalforces can damage the PZT ceramic. Standard PZT ceram-ics are limited to a maxi-mum operating temperature of 150 °C. PZT ceramics must beprotected from humidity or

fluid contamination (like otherelectric materials and actua-tors).

Close contact between thePZT user and the manufacturerassures that the right actuatordesign is chosen for your appli-cation. PI has more than 30 years of experience indesigning piezoelectric actua-tors and systems and offers awide variety of options whichcan adapt PZTs to various envi-ronmental conditions.

Design Points to Remember

Fig. 4. Combination of a DC-Mike linear drive and P-250 PZT translator


Since the piezo effect exhibitedby natural materials such asquartz, tourmaline, Rochellesalt, etc. is very small, polycrys-talline ferroelectric ceramicmaterials such as bariumtitanate and lead (plumbum) zir-conate titanate (PZT) withimproved properties have beendeveloped. These ferroelectricceramics become piezoelectricwhen poled.

PZT ceramics are available inmany variations and are stillthe most widely used materi-als for actuator applicationstoday. At temperatures belowthe Curie temperature, PZTcrystallites exhibit tetragonalor rhombohedric structure.Due to their permanent electri-cal and mechanical asymme-try, these types of unit cellsexhibit spontaneous polariza-tion and deformation. Groupsof unit cells with the samepolarization and deformationorientation are called domains.Because of the random distri-bution of the domain orienta-tions in the ceramic material, aferroelectric poling process isrequired to obtain any macro-scopic anisotropy and theassociated piezoelectric prop-erties (see Fig. 5.).

If heated above the Curie tem-perature, however, the PZTcrystallite unit cells take oncubic centrosymmetric (iso-tropic) structure. When cooled,the domains reform, but withrandomized orientations, andthe material does not regain itsmacroscopic piezoelectric pro-perties.

The asymmetric arrangementof the positive and negativeions imparts permanent elec-tric dipole behavior to the crystals. Before the polingtreatment, the domains are randomly oriented in the raw PZT material. During pol-ing, an intense electric field (> 2000 V/mm) is applied tothe piezo ceramic. With thefield applied, the materialexpands along the axis of thefield and contracts perpendicu-lar to that axis as the domainsline up. When the field isremoved, the electric dipolesstay roughly, but not com-pletely, in alignment. The mate-rial now has a remanent polar-ization (which can be degradedby exceeding the mechanical,thermal and electrical limits ofthe material).

Subsequently, when a voltageis applied to the poled piezo-electric material, the ions inthe unit cells are shifted and,additionally, the domains chan-ge their degree of alignment.(see Fig. 6.). The result is a cor-responding change of thedimensions (expansion, con-traction) of the PZT material.

{bk xtx4148}

NotesThe following pages give a detailedlook at piezo actuator theory and theiroperation. For basic knowledge read “Basic Introduction to NanoPositio-ning with Piezoelectric Technology”,page 4-9. For definition of units,dimensions and terms, see “Glossary”on page 4-7.

Fundamentals of Piezoelectricity

and Piezo Actuators

Fig. 5. PZT unit cell: 1) Perovskite-type lead zirconate titanate (PZT) unit cell in the symmetric cubic state above the Curie temperature. 2) Tetragonally distorted unit cell below theCurie temperature Fig. 6. Electric dipoles in domains; (1) unpoled ferroelectric ceramic, (2) during and

(3) after poling (piezoelectric ceramic)

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PZT Actuators

Material Properties

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Fundamentals . . . (cont.)

PZT Ceramics Manufacturing Process

PI manufactures its own piezoceramic materials at the PICeramic factory. The processstarts with mixing and ballmilling of the raw materials.Next, the mixture is heated to75% of the sintering tempera-ture to accelerate reaction ofthe components. The polycrys-talline, calcinated powder isball milled again to increase itsreactivity. Granulation with thebinder is next, to improve pro-cessing properties. After shap-ing and pressing the greenceramic is heated slowly toburn out the binder.

The next phase is sintering attemperatures between 1250°Cand 1350 °C. Then the ceramicblock is cut, ground, polished,lapped, etc., to the desiredshape and tolerance. Electro-des are applied by sputteringor screen printing processes.The last step is the polingprocess which takes place in aheated oil bath at electricalfields up to several kV/mm.

Multilayer PZT actuatorsrequire a different manufactur-ing process. After milling, aslurry is prepared. A foil cast-ing process allows layer thick-ness down to 20 µm. Next, thesheets are screen printed andlaminated. A compacting pro-cess increases the density of the green ceramics andremoves air trapped betweenthe layers. The final steps arethe binder burnout, sintering(co-firing) at temperaturesbelow 1100 °C, wire lead termi-nation and poling.

All processes, especially theheating and sintering cycles,must be controlled to verytight tolerances. The smallestchange affects the quality andproperties of the PZT material.100% final testing of the piezomaterial and components at PICeramic guarantees the high-est product quality.

NotesIt should be clearly understood that thepiezoelectric coefficients describedhere are not independent constants.They vary with temperature, pressure,electric field, form factor, mechanicaland electrical boundary conditions etc.The coefficients only describe materialproperties under small-signal condi-tions.

Compound components such as PZTstack actuators, let alone preloadedactuators or lever-amplified systemscannot be described sufficiently bythese material parameters. This is whyeach component or system manufac-tured by PI is characterized by specificdata such as stiffness, load capacity,displacement, resonant frequency, etc.,determined by individual measure-ments.

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Because of the anisotropicnature of PZT ceramics, piezo-electric effects are dependenton direction (see Fig. 7). Toidentify directions, the axes 1,2, and 3, will be introduced(corresponding to X, Y, Z of theclassical right-hand orthogonalaxis set). The axes 4, 5 and 6identify rotations (shear), �x, �y,�z, also known as U, V, W.

The direction of polarization(axis 3) is established duringthe poling process by a strongelectrical field applied bet-ween two electrodes. Foractuator applications, the piezoproperties along the polingaxis are the most important(largest deflection).

Piezoelectric materials arecharacterized by several coeffi-cients

Examples are:

� di j: Strain coefficients [m/V]

or charge output coeffi-

cients [C/ N]: Strain devel-oped [m/m] per unit of elec-tric field strength applied[V/m] or (due to the sensor /actuator properties of PZTmaterial) charge densitydeveloped [C/m2] per givenstress [N/m2].

� gi j: Voltage coefficients or

field output coefficients

[Vm/N]:

Open-circuit electric fielddeveloped [V/m] per appliedmechanical stress [N/m2] or

(due to the sensor / actuatorproperties of PZT material)strain developed [m/m] perapplied charge density[C/m2].

� ki j: Coupling coefficients

[dimensionless].

The coefficients are energyratios describing the con-version from mechanical toelectrical energy or viceversa. k2 is the ratio ofenergy stored (mechanicalor electrical) to energy(mechanical or electrical)applied.

Other important parametersare the Young’s modulus Y (describing the elastic prop-erties of the material) and therelative dielectric coefficients(permittivity) � r.

To link electrical and mechani-cal quantities, double sub-scripts (e.g. dij) are introduced.The first subscript gives thedirection of the excitation, thesecond describes the directionof the material response.

Example: d33

applies when theelectric field is along the polar-ization axis (direction 3) andthe strain (deflection) is along

the same axis. d31

applies if theelectric field is in the samedirection as before, but thestrain is in the 1 axis (orthogo-nal to the polarization axis)

In addition the superscripts S,T, E, D are introduced. Theydescribe an electrical ormechanical boundary condi-tion for the mechanical ordielectrical parameters.

Definition:

S for strain = 0 (mechanicallyclamped)

T for stress = 0 (not clamped)

E for field = 0 (short circuit)

D for charge displacement(current) = 0 (open circuit)

The individual piezoelectricparameters are related by sev-eral equations that are notexplained here.

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Fig. 7. Orthogonal system describing the properties of a poled piezoelectric ceramic. Axis 3 is the poling direction.

Definition of Piezoelectric

Coefficients and Directions

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Since the displacement of apiezo actuator is based onionic shift and orientation ofthe PZT unit cells, the resolu-tion depends on the electricalfield applied and is theoreti-cally unlimited. Infinitesimallysmall changes in opera-ting voltage are converted to smooth movements (see Fig. 8).

No threshold voltages influ-ence the constant motion.

Piezo actuators are used inatomic force microscopes toproduce motion less than thediameter of an atom. Since dis-placement is proportional tothe applied voltage, optimumresolution cannot be achievedwith noisy, unstable voltagesources.

Amplifier Noise

As stated above, amplifiernoise directly influences theposition stability (resolution) ofa piezo actuator. Some ven-dors specify the noise value oftheir PZT driver electronics inmillivolts. This information is oflittle use without spectral infor-mation. If the noise occurs in afrequency band far beyond theresonant frequency of themechanical system, its influ-ence on mechanical resolution

and stability can be neglected.If it coincides with the reso-nant frequency, it will have amore significant influence onthe system stability. Therefore,meaningful data can only beacquired if resolution of thecomplete system�piezo actu-ator and drive electronics�ismeasured in terms of nanome-ters rather than millivolts. For further information see p. 4-34 ff.

NotesThe level of performance describedcan only be attained by frictionless andstictionless solid state actuators suchas PZTs. “Traditional” technologiesused in motion positioners (stepper orDC servo-motor drives in combinationwith dovetail slides, ball bearings, and roller bearings) all have varyingdegrees of friction and stiction. Thisfundamental property limits resolution,causes wobble, hysteresis, backlash,and an uncertainty in position repeatability. Their practical usefulnessis limited to a precision of two ordersof magnitude less than with PI PZTNanoPositioners.


Resolution

Fig. 8. Response of a P-170 HVPZT translator to a ± 1V, 200 Hz triangular drive signal. Note that one division is only 2 nanometers.

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Displacement of PZT ceramicsis primarily a function of theapplied electric field strength E,the piezoelectric material usedand the length L of the PZTceramics. The material proper-ties can be described by thepiezoelectric strain coefficientsd

i j. These coefficients describe

the relationship between theapplied electrical field and themechanical strain produced.

The displacement �L of anunloaded single-layer piezoactuator can be estimated bythe following equation:

(Equation 1)�L = S�L

o� ±E�d

i j�L

o

Where:

S = strain (relative lengthchange �L/L, dimension-less)

Lo

= ceramic length [m]E = electrical field strength

[V/m]d

ij= piezoelectric coefficient

[m/V]

d33

describes the strain parallelto the polarization vector of theceramics (thickness) and d

31

the strain orthogonal to the

polarization vector (width). d33

and d31

are sometimes referredto as “piezo gain”. See Fig. 9for explanation. The straincoefficient d

33applies for PZT

stack actuators, d31

applies fortube and strip actuators.

Note:

For the material used in stan-dard PI piezo actuators, d

33is

on the order of 450 to 650 x 10-12 m/V, d

31is on the

order of -200 to -300 x 10-12 m/V.These figures only apply to theraw material at room tempera-ture under small-signal condi-tions.

For standard PI PZTs, theallowable field strength rangesfrom 1 to 2 kV/mm in the poling direction and up to 300 V/mm inverse (short termonly) to the poling direction(semi-bipolar mode), see Fig.10 for details. The maximumvoltages depend on the cera-mic properties and the insulat-ing materials. Exceeding the

maximum voltage may

cause dielectric breakdown

and irreversible damage to

the PZT.

With the inverse field, nega-tive expansion (contraction)occurs giving an additional20% of the nominal displace-ment. If both the regular andinverse electric fields are used,a relative expansion (strain) upto 0.2 % is achievable withPZT stack actuators. Stackscan be built with aspect ratiosup to 12:1 (length:diameter).Maximum travel for mediumsize piezo stack actuators (15 mm diameter), is thereforelimited to approximately 200 µm. Longer travel rangescan be achieved by mechanicalamplification techniques (see“Lever Motion Amplifiers” onpage 4-44).

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Fig. 9. Elongation and contraction of a PZT disk when a voltage is applied. Note that d31

(affecting lateral deformation, �D) is negative.

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Displacement of Piezo Actuators

(Stack & Contraction Type)

NotePI PZTs are designed for industrial reliability. Displacement, operatingvoltage range and load capability inthe technical data tables are realisticfigures with regard to safe operationunder conditions not restricted toresearch labs. Since we manufactureour own ceramics (in contrast to mostother PZT vendors) we could modifymaterial parameters to trade lifetimefor displacement. When you are choosing piezo actuators for yourapplication, “maximum displacement”may not be the only important designparameter.

Fig. 10. Response of a PZT actuator to a bipolar drive voltage. When a certain threshold voltage (negative to the polarization direction) is exceeded, reversal of polarization can occur.

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Hysteresis (Open-Loop PZTs)

Hysteresis can be virtuallyeliminated in closed-loop PZTactuators (see page 4-34 ff).Similar to electromagnetic de-vices, open-loop piezo actuatorsexhibit hysteresis (they, too, arereferred to as ferroelectric actu-ators). Hysteresis is based oncrystalline polarization effectsand molecular effects.

The absolute displacement gen-erated by an open-loop PZTdepends on the applied voltageand the piezo gain, which isrelated to the remanent polar-ization. Since the remanent polarization, and therefore thepiezo gain, is affected by theelectric field applied to thepiezo, the deflection dependson whether the PZT was previ-ously operated at a higher or alower field strength (and someother factors). Hysteresis is typ-ically on the order of 10% to15% of the commanded

motion (see Fig. 11).

For example, if the drive volt-age of a 50 µm piezo actuatoris changed by 10%, (equivalentto about 5 µm displacement)the position repeatability is stillon the order of 1% full travel orbetter than 1 µm. Classicalmotor-driven leadscrew posi-tioners will have difficulty beat-ing this repeatability.

In PI closed-loop piezo actuatorsystems hysteresis is fullycompensated. PI offers thesesystems for applications re-quiring absolute position infor-mation, as well as motion withhigh linearity, repeatability andaccuracy in the nanometer andsub-nanometer range (seepage 4-34 ff).

For positioning where thetravel is controlled by an exter-nal servo loop (e.g. the eyesand hands of the operator or asophisticated electronics sys-tem), hysteresis behavior andlinearity are of secondary im-portance, since they can becompensated for by the exter-nal loop.

Example: Piezoelectrically dri-ven fiber aligners derive thecontrol signal from the opticalpower transmitted from onefiber to the other. The goal is tomaximize the optical signallevel, not to determine theexact position. An open-loopPZT system is sufficient forthis application, offering unlim-ited resolution, fast response,zero backlash and zerostick/slip effect.

Creep (Drift) (Open-Loop PZTs)

Creep only occurs in open-loopoperation, and can be elimi-nated by servo-control (seepage 4-34 ff ). Like hysteresis,creep is related to the effect ofthe applied voltage on theremanent polarization of thepiezo ceramics. Creep is theexpression of the slow realign-ment of the crystal domains ina constant electric field overtime. If the operating voltageof a PZT is changed, after thevoltage change is complete,the remanent polarization(piezo gain) continues tochange, manifesting itself in aslow creep. The rate of creepdecreases logarithmically withtime.

The following equation des-cribes this effect:

(Equation 2)

�L(t) � �Lt=0.1[1+��lg( t___

0.1)]Creep of PZT motion as a func-tion of time.

where:

�L(t) = creep as a function of time [m]

�Lt=0.1

= displacement 0.1 seconds after the voltage change is complete [m].

� = creep factor, which is dependent on theproperties of the actuator (on the orderof 0.01 to 0.02 whichis 1 to 2% perdecade).

Maximum creep (after a fewhours) can add up to a few per-cent of the commanded mo-tion

Aging

Aging refers to reduced piezogain, among other things as aresult of the depoling process.Aging can be an issue for sen-sor or charge-generation appli-cations (direct piezo effect),but with actuator applications itis negligible because repolingoccurs every time a higherelectric field is applied to theactuator material in the polingdirection.

NotesFor periodic motion, creep and hys-teresis do not affect repeatability.


Fig. 11. Hysteresis curves of an open-looppiezo actuator for various peak voltages. The hysteresis is related to the distancemoved.

Fig. 12. Creep of open-loop PZT motion after a 60 µm change in length as a function of time.Creep is on the order of 1% of the last com-manded motion per time decade.

Strain Gauge Sensors

A resistive film bonded to thePZT stack changes resistancewhen strain occurs. Up to fourstrain gauges (the actual con-figuration varies with the PZTconstruction) form a Wheat-stone bridge driven by a DCvoltage (5 to 10 V). When thebridge resistance changes,electronics converts the result-ing voltage change into a signalproportional to the displace-ment.

Resolution: better than 1 nm(for 15 µm actuator)

Repeatability: to 0.1% of nominal displacement

Bandwidth: to 5 kHz

Advantages:

� High bandwidth

� Vacuum compatible

� Extremely small (no extramounting space, no reduc-tion of active cross-sectioncausing reduced stiffness)

� Cost-effective

Other characteristics:

� Low heat generation (0.01to 0.05 W sensor excitationpower)

Examples:

Most PI LVPZT and HVPZTactuators are available withstrain gauge sensors forclosed-loop control (see the“PZT Actuators SelectionGuide” p. 1-6).

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Notes:The description explains the featuresof different high-resolution sensortypes used for closed-loop control ofPZT actuators. The bandwidth givenis the open-loop bandwidth of thesensor. Closed-loop bandwidth of aPZT sensor / servo-controller systemis limited by the mechanical andelectrical properties of the system.

Linear VariableDifferential Trans-formers (LVDTs)

A magnetic core, attached tothe moving part, determinesthe amount of magneticenergy induced from the pri-mary windings into the twodifferential secondary wind-ings. The carrier frequency istypically 10 kHz.

Resolution: to 5 nm

Bandwidth: to 1 kHz

Repeatability: to 5 nm

Advantages:

� Good temperature stability

� Very good long-term stability

� Controls the position of themoving part rather than theposition of the PZT stack

� Cost-effective


� Outgassing of insulationmaterials may limit applica-tions in vacuum

� Extra space for mountingrequired

Examples:

P-780, p. 2-16; P-721.10, p. 2-10;P-762, p. 2-38 ; etc., (see “PZTFlexure NanoPositioners” sec-tion).

Fig. 14. Operating principle of an LVDT sensor

Fig. 15. LVDT sensor, coil and core.Paper clip for size comparison

Fig. 13. Strain gauge sensors. Paper clip for size comparison

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Capacitive PositionSensors

The sensor consists of two RF-excited plates that are part of acapacitive bridge. One plate isfixed, the other plate is con-nected to the object to be posi-tioned. The distance betweenthe plates is inversely propor-tional to the capacitance,which is a measure for the dis-placement. Resolution on theorder of picometers is achiev-able with short range capaci-tive position sensors. (See“Capacitive Displacement Sen-sors” section for details).

Resolution: better than 0.1 nm

Repeatability: to 0.1 nm

Bandwidth: to 10 kHz

Advantages:

� Highest resolution of all commercially availablesensors

� Excellent long-term stability

� Excellent frequencyresponse


� Extra space for mountingrequired

� Parallelism of the platesmust be controlled for opti-mal performance

Examples:

P-500 series of Flexure Stages,p. 2-32; P-753 LISA NanoAuto-mation® Actuators, 2-22.

Fig. 17. Operating principle of two-plate capacitive position sensors


Fig. 16. Two-plate capacitive position sen-sors provide up to 10,000 times higher reso-lution than calipers

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Maximum ApplicableForces

(Compressive Load Limit, Ten-sile Load Limit)

The mechanical strength val-ues of PZT ceramic material(given in the literature) areoften confused with the practi-cal long-term load capacity of aPZT actuator. PZT ceramicmaterial can withstand pres-sures up to a few hundredMPa (a few 10,000 psi) beforeit breaks mechanically. Thisvalue must not be approachedin practical applications, because depolarization occursat pressures on the order of20% to 30% of the mechanicallimit. For stacked actuators(which are a combination ofseveral materials) additionallimitations apply. Parameterssuch asaspect ratio, buckling,interaction at the interfaces,etc. must be considered. If thespecified “maximum com-pressive force” for a PZT isexceeded, mechanical damageto the ceramics as well asdepolarization may occur.

The load capacity data listedfor PI actuators are conserva-tive values which allow longlifetime. Standard PI PZT stackactuators can withstand com-pressive forces to several10,000 N (several tons).

Tensile loads of non-preloadedPZTs are limited to 5 � 10% ofthe compressive load limit(maximum compressive for-ce). PI offers a variety of piezoactuators with internal springpreload for extended tensileload capacity. Preloaded ele-ments are highly recom-mended for dynamic applica-tions. Shear forces must beisolated from the PZT ceram-ics by external measures (flex-ure guides, etc.).

Stiffness

When calculating force gener-ation, resonant frequency, sys-tem response, etc., piezoceramic stiffness is an impor-tant parameter. In solid bodiesstiffness depends on theYoung’s modulus of the mate-rial, i.e. the ratio of stress(force per unit area) to strain(change in length per unitlength). Stiffness is generallydescribed by the spring con-stant k

T, relating the influence

of an external force to thedimensional change of thebody.

This narrow definition is of lim-ited application for PZT ceram-ics because the cases of stat-ic, dynamic, large-signal andsmall-signal operation withopen and shorted electrodesmust all be distinguished. Thepoling process of PZT ceram-ics leaves a remanent strain inthe material which depends onthe magnitude of polarization.The polarization is affected byboth the drive voltage andexternal forces. When anexternal force is applied topoled PZT ceramics, the di-mensional change depends on

the stiffness of the ceramicmaterial and the change of theremanent strain (caused by thepolarization change). The equa-tion L

N= F/k

Tis only valid for

small forces and small-signalconditions. For larger forces,an additional term describingthe influence of the polariza-tion changes, must be super-imposed on the stiffness (k

T).

Since piezo ceramics areactive materials, they producean electrical response (charge)when mechanically stressed(e.g. in dynamic operation).When the electric charge can-not be drained from the PZT, itgenerates a counterforce op-posing the mechanical stress.(This is why a PZT elementwith open electrodes appearsstiffer than one with shortedelectrodes). Mechanical stres-sing of PZT actuators withopen electrodes, e.g. openwire leads, should be avoided,because the resulting inducedvoltage might damage thestack electrically.

NotesThere is no international standard formeasuring piezo actuator stiffness.Therefore stiffness data of differentmanufacturers cannot be comparedwithout additional information.

It must be understood that a piezoactuator can only generate appreciableforce if it is directly coupled (no slack!)to an element which is stiff comparedto the PZT.

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The curves expressing the dis-placement of piezoelectricceramics under mechanicalstress are similar to those forelectrically induced displace-ment. The action of high pres-sures on the domains withinthe material cause it to exhibita non-linear response, withhysteresis, that has beencalled “ferro-elastic” behavior.

The curves are strongly influ-enced by the state of the elec-trodes. Fig. 18 shows the twocases of nominal operatingvoltage (for maximum dis-placement) applied (1), andshorted electrodes with theceramics depoled (2). A thirdcase, that with open contacts(not shown in the graph) givesa very different result withhigher stiffness.

Since Hook’s law is notobeyed, no single stiffnessvalue can reasonably be given.If, for example, stiffness is de-termined using very low-ampli-tude displacements (small-sig-nal stiffness), the value meas-ured may be almost twice ashigh as that measured usinglarge-amplitude displacements(large-signal stiffness).

The relevant value is, in thefinal instance, dependent onthe details of the application.

Static Large-Signal Stiffness

The static large-signal stiffnessis calculated from the slope ofthe secant between the end-points of the response curve,measured with the nominaloperating voltage on the elec-trodes (e.g. Curve 1 in Fig. 18).The values are obtained with a quasi-static, triangle-waveforce signal of 0.02 Hz, andany “memory” anomalies arecleared by measuring the thirdcycle. The end points of theforce curve are chosen in con-junction with the cross sectionof the piezo actuator, such thatthe variation in mechanicalstress is from 10 MPa to 40 MPa.

Dynamic Small-Signal

Stiffness

Dynamic small-signal stiffnessis another term sometimesused to characterize PZTceramics. This value is calcu-lated from the observedmechanical resonant fre-quency of the actuator inresponse to very low-ampli-tude mechanical stress withthe electrodes shorted. Thedynamic small-signal stiffnessand the resonant frequencyprovide information about thedynamic characteristics thatcan be expected of the sys-tem�for example, how it willrespond to a change in load.

For the use of piezo ceramicsin positioning systems, thestatic large-signal stiffness isusually far more importantthan the small-signal value, asit describes the behavior of theactuator when working againstan elastic load.

With piezoelectric positioningsystems and actuators (com-pound structures of differentactive and passive materials)the stiffness scenario is evenmore complicated. This factexplains why the (dynamicallymeasured) resonant frequencyof a piezo actuator or position-ing system does not necessar-ily match the results calculatedwith the simple harmonicoscillator equation:

f0= 12�

___��k T

meff

___

For more details see “Reso-nant Frequency,” p. 4-28.


Fig. 18. Quasi-static characteristic mechanical stress/strain curves forpiezo ceramic actuators and the derived stiffness values (note that displacement is negative because the applied force is compressive). Curve 1 is with the nominal operating voltage (voltage giving nominalmaximum displacement) on the electrodes, Curve 2 is with the elec-trodes shorted (showing ceramics after depolarization)

Force Generation

In most applications, piezoactuators are used to producedisplacement. If used in arestraint, they can generateforces. Force generation isalways coupled with a reduc-tion in displacement. The maxi-mum force (blocked force) apiezo actuator can generatedepends on its stiffness andmaximum displacement. Seealso “Displacement withExternal Forces,” page 4-26.

(Equation 3)

Fmax

� kT��L

0

Maximum force that can begenerated in an infinitely rigidrestraint (infinite spring con-stant). At maximum force gen-eration, displacement is zero.

where:

�L0

= max. nominal displace-ment without externalforce or restraint [m]

kT

= PZT actuator stiffness[N/m]

In actual applications the loadspring constant can be largeror smaller than the PZT springconstant. The force F

max effgen-

erated by the PZT is:

(Equation 4)

Fmax eff

� kT��L

0 (1- kT

kT+kS

_____)Effective force a piezo actuatorcan generate in a yieldingrestraint

where:

�L0

= displacement (withoutexternal force or res-traint) [m]

kT


ks

= stiffness of externalspring [N/m]

Example: Force generation ofa PZT actuator with nominal dis-placement of 30 µm and stiff-ness of 200 N/µm. The PZT canproduce a maximum force of30 µm 200 N/µm = 6000 N.When force generation is max-imum, displacement is zeroand vice versa (see Fig. 19 fordetails).

Example: A piezo actuator isto be used in a metal sheetembossing application. At rest(zero position) the distancebetween the PZT tip and thesheet is 30 microns (given bymechanical system toleran-ces). A force of 500 N isrequired to emboss the metal.

Q: Can a 60 µm actuator with astiffness of 100 N/µm beused?

A: Under ideal conditions this actuator can generate a force of 30 100 N = 3000 N(30 microns are lost motiondue to the distance betweenthe sheet and the PZT tip). Inpractice the force generationdepends on the stiffness ofthe metal and the support. Ifthe support were a soft mate-rial, with a stiffness of 10N/µm, the PZT could only gen-erate a force of 300 N onto themetal when operated at maxi-mum drive voltage.

If the support were stiff butthe metal itself were very soft(gold, aluminum, etc.) it wouldyield and the piezo actuatorstill could not generate therequired force. If both the sup-port and the metal were stiff

enough, but the PZT mountwas too soft, the force gener-ated by the PZT would pushthe actuator away from thematerial to be embossed. Thesituation is similar to lifting acar with a jack. If the ground(or the car’s body) is too soft,the jack will run out of travelbefore it generates enoughforce to lift the wheels off theground.

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Fig. 19. Force generation vs. displacement of a PZT actuator (displacement 30 µm, stiffness 200 N/µm) at various operating voltages. The points where thedashed lines (external spring curves) intersect the PZT force/displacement curvesdetermine the force and displacement for a given setup with an external spring.Maximum work can be done when the stiffness of the PZT actuator and externalspring are identical.

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NotesWhen designing (internally or exter-nally) preloaded PZT systems, the stiffness of the preload spring shouldbe less than 1/10 of the PZT stiffness.Otherwise too much of the unloadeddisplacement would be sacrificed. If the preload spring has the same stiffness as the PZT, displacement will be cut in half.

Displacement withExternal Forces

Like any other actuator, a piezoactuator is compressed whena force is applied. Two casesmust be considered whenoperating a PZT with a load:

a) The load remains constantduring the motion process

b) The load changes during themotion process.

Constant Force

Zero-point is offset

A mass is installed on the PZTwhich applies a force F = M � g(M: mass, g: acceleration dueto gravity). The zero-point will be offset by an amount �L

N�F/k

T, where k

Tequals the

stiffness of the PZT. If thisforce is within the specifiedload limit (see product techni-cal data), full displacement canbe obtained at full operatingvoltage (see Fig. 20).

(Equation 5)

�LN

� FkT

____

Zero-point offset withconstant force

where

�LN

= Zero-point off-set [m]

F = Force (gener-ated by massand gravity) [N]

kT

= PZT actuatorstiffness [N/m]

Example:

Q: How large is the zero-pointoffset of a 30 µm PZT actuatorwith a stiffness of 100 N/µm ifa load of 20 kg is applied andwhat is the maximum dis-placement with this load?

A: The load of 20 kg generatesa force of 20 kg x 9.81 m/s2 = 196 N. With a stiffness of 100 N/µm, the piezo actuator iscompressed slightly less than2 µm. The maximum displace-ment of 30 µm is not reducedby this constant force.

M

Fig. 20. Case a,zero-point offset with constant force (mass).

a Changing Force

(Force = Function of �L, e.g. aspring load):

Displacement is reduced

For PZT operation with springloads different rules apply. The“spring” could bean I-beam or a sin-gle fiber, eachwith its character-istic stiffness orspring constant.Part of the dis-placement ge-nerated by thepiezo effect is lostdue to the elastic-ity of the piezoelement. The totalavailable displacement can berelated to the spring stiffnessby the following equations:

(Equation 6)

�L � �L0( kT

kT+ kS

______)Maximum displacement of apiezo actuator acting against aspring load.

(Equation 7)

�LR

� �L0 (1- kT

kT+kS

______)Maximum loss of displace-ment due to external springforce. In the case where thespring stiffness k

sis � (infi-

nitely rigid restraint) the PZTonly acts as a force generator.

where:�L = displacement with

external spring load [m]�L

O= nominal displacement

without external forceor restraint [m]

�LR

= lost displacementcaused by the externalspring [m]

ks

= spring stiffness [N/m] k

T= PZT actuator stiffness

Example:

Q: What is the maximum dis-placement of a 15 µm PZTtranslator with a stiffness of 50 N/µm, mounted in an elastic restraint with a spring constant k

s(stiffness) of

100 N/µm?

A: Equation 6 shows that thedisplacement is reduced in anelastic restraint. The springconstant of the external res-traint is twice the value of the piezo translator. Theachievable displacement istherefore limited to 5 µm (1/3 of the nominal travel).

Fig. 21. Case b, effective displace-ment of a piezo actuator acting against a spring load.

b

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Dynamic Forces

Every time the PZT drive voltage changes, the piezo element changes its dimen-sions. Due to the inertia of thePZT mass (plus any additionalload), a rapid change will gen-erate a force (pushing orpulling) acting on the piezo.The maximum force that canbe generated is equal to theblocked force, described by:

(Equation 8)

Fmax

� ± kT��L

0

Maximum force available toaccelerate the piezo mass plusany additional load.

where:

�L0

= max. nominal displace-ment without externalforce or restraint [m]

kT


Tensile forces must be com-pensated for by a mechanicalpreload (inside the actuator orexternal) in order to preventdamage to the ceramics.Preload should be around 20%of the compressive load limit,with soft preload springs�softcompared to the PZT stiffness(1/10 or less).

In sinusoidal operation withfrequency f and amplitude�L/2, peak forces can beexpressed as:

(Equation 9)

Fdyn

= ±4�2�meff (�L___

2 )f2

Dynamic forces on a PZT insinusoidal operation at fre-quency f.

where:

Fdyn

= dynamic force [N]

meff.

= effective mass [kg]

�L = peak-to-peak displace-ment [m]

f = frequency [Hz]

The maximum permissibleforces must be consideredwhen choosing an operatingfrequency.

Example: Dynamic forces at1000 Hz, 2 µm peak-to-peak and1 kg load reach approximately ± 40 N.

NotesA guiding system (e.g. diaphragmtype) is recommended when heavyloads or large mechanical parts (com-pared to the piezo actuator diameter)are moved dynamically. Without aguiding system, there is a potential fortilt oscillations and other non-axialforces that may damage the PZTceramics.

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Fig. 22. Recommended guiding for large masses.

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Fig. 23. Effective mass of an actuator fixed at one end.

Resonant Frequency

In general, the resonant fre-quency of any spring/masssystem is a function of its stiff-ness and effective mass (seeFig. 23). The resonant fre-quency given in the technicaldata tables always refers tothe unloaded actuators, withone end rigidly attached.

(Equation 10)

f0= ( 1___

2�)��kT_______meff

Resonant frequency of anideal spring/mass system.

where:

f0

= resonant frequency [Hz]

kT

= actuator stiffness [N/m]

meff

= effective mass (about1/3 of the mass of theceramic stack plus anyinstalled end pieces)[kg]

Note: Due to the non-idealspring behavior of PZT ceram-ics, the theoretical result from the above equation does not necessarily match the real-world behavior of the PZT system under large signal con-ditions.

When adding a mass M to theactuator, the resonant fre-quency drops according to thefollowing equation:

(Equation 11)

f0’= f

0 ��meff_______

m’eff

Resonant frequency with neweffective mass m’

eff= additional mass M + m

eff.

The above equations showthat increasing the effectivemass of the loaded actuator bya factor of 4 will reduce theresponse (resonant frequency)by a factor of 2. Increasing thespring preload on the actuatordoes not significantly affect itsresonant frequency.

The phase response of a PZTsystem can be approximatedby a second order system andis described by the equation:

(Equation 12)

� 2 � arctan( f__f0)

= phase angle [deg]

f0

= resonant frequency [Hz]

f = operating frequency [Hz]

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How Fast Can a PiezoActuator Expand?

Fast response is one of thedesirable features of piezoactuators. A rapid drive voltagechange results in a rapid posi-tion change. This property isnecessary in applications suchas switching of valves/shut-ters, generation of shock-waves, vibration cancellationsystems, etc

A PZT can reach its nominaldisplacement in approximately1/3 of the period of the reso-nant frequency, albeit with sig-nificant overshoot (see Fig.24).

(Equation 13)

Tmin

� 1___3f0

Minimum rise time of a piezoactuator (requires an amplifierwith sufficient output currentand rise time).

For example, a piezo translatorwith a 10 kHz resonant fre-quency can reach its nominaldisplacement within 30 µs. Formore information see “Dyna-mic Operation”, page 4-31.

Fig. 24. Response of an undamped, lever-amplified PZT actuator (low resonant frequency) to a rapid drive-voltage change.

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General

When operated well below theresonant frequency, a PZTbehaves as a capacitor: dis-placement is proportional tocharge (first order estimate).

PZT stack actuators are as-sembled with thin, laminarwafers of electroactive cera-mic material electrically con-nected in parallel.

The (small-signal) capacitanceof a stack actuator can be esti-mated by:

(Equation 14)

C � n � �33T � A/d

s

Where:

n = number of layersl0___d

S

�33 T = dielectric constant

[As/Vm]

A = electrode surface area ofa single layer [m2]

ds

= distance between theindividual electrodes(layer-thickness) [m]

l0

= actuator length

The equation explains that for a given actuator length l0 = n · d

Sand a given disk thick-

ness dS, the capacitance is a

quadratic function of the ratiod

S/ d

1where d

1< d

S. There-

fore, the capacitance of a piezo actuator constructed of 100 µm thick layers is 100 times the capacitance ofan actuator with 1 mm thicklayers if the two actuators arethe same length.

Static Operation

When electrically charged, theenergy E = (1/2) CU2 is storedin a piezo actuator. Everychange in the charge (andtherefore in the displacement)of the PZT requires a current i:

(Equation 15)

i = dQ___dt

= C � dU___dt

Relationship of current andvoltage for the piezo actuator

Where:

i = current [A]

Q = charge [coulomb (As)]

C = capacitance [F]

U = voltage [V]

t = time [s]

For static operation only theleakage current has to be sup-plied. The high internal resist-ance reduces leakage currentsto the micro-amp or sub-micro-amp range. Even when discon-nected from the electricalsource, the charged actuatorwill not make a sudden move but return to its uncharged dimensions veryslowly (time constant of sev-eral minutes).

For slow position changes,very low current is required.For example, an amplifier withan output current of 20 µA fullyexpands a 20 nF actuatorwithin one second. (Suitableamplifiers can be found usingthe Control Electronics Selec-tion Guide on page 6-6).

NotesThe PZT capacitance values indicatedin the technical data tables are small-signal values (measured at 1 V, 1000 Hz,20° C, no load). The capacitance of PZTceramics changes with amplitude, tem-perature, and load, to up to 200% ofthe unloaded, small-signal, room-tem-perature value. For detailed informa-tion on power requirements, refer tothe amplifier frequency responsecurves in the “PZT Control Electronics”section.


+

+

+

+

+

+

+

+

+

Fig. 25. Design of a PZT stack actuator.

NotesLow-voltage PZTs (100 µm layers, 100 V operating voltage, high capaci-tance) require 10 times the driving current of high-voltage PZTs of similarsize (1 mm layers, 1000 V operatingvoltage, low capacitance). Powerrequirements are similar. PI high/low voltage amplifiers are specially designed to meet the different require-ments for driving high/low voltageactuators.

Electrical Requirements for Piezo Operation

Dynamic Operation(Analog)

PZTs can provide accelerationsof thousands of g’s and areperfectly suited for dynamicapplications.

Several parameters influencethe dynamics of a PZT posi-tioning system:

� If the piezo element is in-stalled in a positioningmechanism (and sufficientelectrical power is availablefrom the amplifier), themaximum drive frequencycan be limited by dynamicforces (see “Dynamic Ope-ration”, page 4-27).

� The maximum operatingfrequency is also limited bythe phase and amplituderesponse of the system(especially in closed-loopsystems). Rule of thumb:the higher the system reso-nant frequency the betterthe phase and amplitude re-sponse and the higher theusable frequency.

� The amplifier output currentand rise time determine themaximum operating fre-quency of a piezoelectricsystem.

� In closed-loop operationother parameters such assensor bandwidth, phasemargins and control algo-rithms determine the per-formance of a positioningsystem.

The following equations des-cribe the relationship betweenamplifier output current, volt-age and operating frequency.They help determine the mini-mum specifications of a PZTamplifier for dynamic operation.

(Equation 16)

ia

� f � C � Up-p

Average current required forsinusoidal operation

(Equation 17)

imax

� f � � � C � Up-p

Peak current required for sinu-soidal operation

(Equation 18)

fmax

� imax______2· CU

p-p

Maximum operating frequencywith triangular waveform as afunction of the amplifier outputcurrent limit

Where:

ia

= average amplifiersource/sink current [A]

imax

= peak amplifiersource/sink current [A]

fmax

= maximum operating fre-quency [Hz]

C = PZT actuator capaci-tance [F]

Up-p

= peak-to-peak drive voltage [V]


The average current and maxi-mum current for each PI PZTamplifier can be found in theproduct technical data tables.

Example:

Q: What peak current is re-quired to operate a HVPZTactuator with a nominal dis-

placement of 40 µm @ 1000 Vand capacitance of 40 nF with asinusoidal waveform of 1000 Hzat 20 µm displacement?

A: With a nominal displace-ment of 40 µm @ 1000 volts,approximately 500 V

p-pare

required to expand the actua-tor by 20 µm. With Equation17 the peak current is calcu-lated to be � 63 mA. (Suitableamplifiers can be found usingthe Control Electronics Selec-tion Guide on page 6-6).

The following equations des-cribe the relationship between(reactive) drive power, actuatorcapacitance, operating fre-quency and drive voltage.

The average power a piezodriver has to be able to providefor sinusoidal operation isgiven by:

(Equation 19)

Pa

� C � Umax

� Up-p

� f

Peak power for sinusoidaloperation is:

(Equation 20)

Pmax

� � � C � Umax

� Up-p

� f

Where:

Pa

= average power [W]

Pmax

= peak power [W]



Up-p

= peak-peak drive voltage[V]

Umax

= nominal voltage of theamplifier [V]







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Dynamic OperatingCurrent Coefficient(DOCC)

Instead of calculating therequired drive power for agiven application, it is easier tocalculate the drive currentbecause it grows linearly withboth frequency and voltage(displacement). Output currentcapability for all PI high-voltageand low-voltage amplifiers isgiven in the technical datatables (“PZT Control Electro-nics” section).

The Dynamic Operating Cur-rent Coefficient (DOCC) valueis provided for each PI piezotranslator to facilitate selectionof the appropriate drive/controlelectronics. The DOCC is theelectrical current that must besupplied by the amplifier todrive the PZT per unit fre-quency (Hz) and unit displace-ment (sinewave operation).E.g. to find out if a selectedamplifier can drive a given PZTat 50 Hz with 30 µm peak-to-peak displacement, multiplythe PZT’s DOCC by 50 x 30and check if the result is lessthan or equal the average out-put current of the selectedamplifier.

{bk xtx4328}

Dynamic Operation(Switched)

For applications such as shockwave generation or valve con-trol, switched operation (on/off) may be sufficient. PZTscan provide motion with rapidrise and fall times with acceler-ations up to thousands of g’s.(For further information see“Dynamic Forces,” page 4-27).

The simplest form of binarydrive electronics for PZT appli-cations would consist of alarge capacitor that is “slowly”charged and rapidly dischargedacross the PZT.

Equation 21 relates appliedvoltage (which corresponds todisplacement) to time.

(Equation 21)

U(t) = Uo+ U

p-p� (1 - e-t /RC)

Voltage on the piezo afterswitching event.

Where:

U0

= start voltage [V]

Up-p


R = resistance in drive circuit [�]


The voltage rises or falls expo-nentially with the RC time con-stant. Under static conditionsthe expansion of the PZT isproportional to the voltage. Inreality, dynamic PZT processescannot be described by a sim-ple equation. Whenever thePZT expands or contracts,dynamic forces act on theceramic material. These forcesgenerate a (positive or negative) voltage in the piezo

element which adds to thedrive voltage. A PZT can reachits nominal displacement in approximately one third of theperiod of the resonant fre-quency (see “How Fast Can aPiezo Actuator Expand?”, page4-29). For example, a piezo ele-ment with 10 kHz resonant fre-quency can reach its nominaldisplacement within 30 µs ifamplifier current and rise timeare sufficient.

If the voltage rises fast enoughto excite a resonant oscillationin the PZT, ringing and over-shoot will occur.

For charging with constant cur-rent (e.g. that provided by a linear amplifier), the followingequation applies:

(Equation 22)

t � C � (Up-p

/ imax

)

Time to charge a PZT with con-stant current. (Minimum ampli-fier rise time must also be con-sidered).

Where:

t = time to charge to Up-p

[s]

C = PZT actuator capacitance[F]

Up-p


imax

= peak amplifiersource/sink current [A]

For fastest settling, switchedoperation is not the best solu-tion. If the input signal risetime is limited to 1/f

0the over-

shoot can be reduced signifi-cantly. Preshaped input signals(optimized for minimum reso-nance excitation) reduce thetime to reach a stable position.

NotesRapid actuation of nanomechanismscan cause recoil-generated ringing of their load and any adjacent com-ponents. This ringing can take hun-dreds of milliseconds to damp out.The problem obviously grows moreserious as motion throughputs in-crease and resolution requirementstighten.

A patented real-time feedforwardtechnology called InputShaping™nullifies resonances before they start,rather than waiting for them to dampout (and turn into heat). The result:the fastest possible motion, with virtually instant settling.

Input Shaping™ was developedbased on research at the Massach-usetts Institute of Technology andcommercialized by Convolve, Inc.,(www.convolve.com). It is an (inter-nal) option in several PI digital piezocontrollers


4-334-33

Heat Generation in a PZT in DynamicOperation

As mentioned before, PZTsare reactive loads and there-fore require charge and dis-charge currents that increasewith operating frequency. The thermal active power, P (apparent power powerfactor, cos ), generated in theactuator during harmonic exci-tation can be estimated withthe following equation:

(Equation 23)

P � �__4

� tan � � f � C � Up-p

2

Heat generation in a PZT.

Where:

P = power converted toheat [W]

tan � = dielectric loss factor(�power factor, cos ,for small angles � and )

f = operating frequency[Hz]


Up-p

= peak-peak drive volt-age [V]

For the description of the losspower, we use the loss factortan � instead of the power fac-tor cos , because it is themore common parameter forcharacterizing dielectric mate-rials. For standard actuator PZTceramics the loss factor is onthe order of 1 to 2% (small-sig-nal conditions only). In large-signal conditions however, 8 to12% of the electrical powerpumped into the actuator isconverted to heat (varies withfrequency, temperature, ampli-tude etc.). Therefore, the maxi-mum operating temperature

can limit the PZT dynamics.For large amplitudes and highfrequencies, cooling measuresmay be necessary. A tempera-ture sensor mounted on theceramics is suggested formonitoring purposes.

In addition, a new generationof amplifiers employing energyrecovery technology has beendeveloped for high-powerapplications. Fig. 26 shows theblock diagram of such anamplifier. Instead of dissipat-ing the reactive power at theheat sinks, only the activepower used by the piezo actua-tor has to be delivered. Theenergy not used in the actua-tor is returned to the amplifierand reused as supply voltagein a step-up transformationprocess. The combination oflow-loss, high-energy PZTceramics and amplifiers withenergy recovery are the key tonew high-level dynamic piezoactuator applications.

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PZT Actuators

Fig. 26. Block diagram of an amplifier with power recovery

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Position servo-control elimi-nates nonlinear behavior ofPZT ceramics and is the key tohighly repeatable nanometricmotion.

PI offers the largest selectionof closed-loop piezo mecha-nisms and control electronicsworldwide. The advantages ofposition servo-control are:

� Very good linearity, stability, repeatability and accuracy

� Automatic compensationfor varying loads or forces

� Virtually infinite stiffness(within load limits)

� Elimination of hysteresisand creep effects

PI closed-loop PZT actuatorsand systems are equippedwith position measuring sys-tems providing sub-nanometerresolution and bandwidths upto 10 kHz. A servo-controller(digital or analog) determinesthe output voltage to the PZTby comparing a reference sig-nal (commanded position) tothe actual sensor position sig-nal.

PI closed-loop piezo actua-

tors provide sub-nanometer

resolution, repeatability and

linearity to 0.003%.

For maximum accuracy, it isnecessary to mount the sen-sor as close as possible to thepart whose position is to becontrolled. PI offers piezo actu-ators with integrated sensorsas well as external sensors.


Fig. 29. Closed-loop position control of a stage driven by a piezo actuator. For optimum performance, the sensor is mounted directly on the object to be positioned.

Fig. 28. Block diagram of a typical PI closed-loop PZT positioning system. {bk xca4349}{bk xtx4351}Fig. 27. Variety of digital piezo controllers

Position Servo-Control (Closed-Loop Operation)

Fig. 30. Response of a closed-loop PI PZT actuator (P-841.10, 15 µm, strain gaugesensor) to a 3 nm peak-to-peak square-wave control input signal, measured withservo-control bandwidth set to 240 Hz and 2 msec settling time. Note the crispresponse to the square wave control signal.

Ctrl Input /V

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PZT Actuators

PZT Calibration Data

Each PI PZT position servo-controller is calibrated withthe specific closed-loop PZT(system) to achieve optimumdisplacement range, fre-quency response and settlingtime. The calibration is per-formed at the factory and areport with plotted and tabu-lated positioning accuracydata will be supplied with thesystem. To optimize calibra-

tion, information about

the specific application is

needed. See the “PZT ControlElectronics” section fordetails.

Fig. 31. Response of a closed-loop PI PZT actuator with capacitive position sensors,shows true sub-nm positional stability, incremental motion and bidirectionalrepeatability.

Fig. 32. Open-loop vs. closed-loop performance graph of a typical PI PZT actuator (supplied with each closed-loop system).

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The dynamic behavior of apiezo positioning system de-pends on the system’s reso-nant frequency, any positionsensor, and the controllerproperties. Simple controllerdesigns limit the usableclosed-loop tracking band-width of a piezoelectric systemto 1/10 of the system’s reso-nant frequency. PI has devel-oped controllers featuring avariety of techniques for in-creased system dynamics (seetable). Two of the methods aredescribed below; additionalinformation is available onrequest.

InputShaping™ StopsStructural RingingCaused by High-Throughput Motions

Rapid actuation of nanomech-anisms can cause recoil-gener-ated ringing of their loads andany adjacent components. Thisringing can take hundreds ofmilliseconds to damp out. Theproblem obviously grows moreserious as motion throughputsincrease and resolution require-ments tighten.

Conventional wisdom sug-gests that there is nothing thatcan be done about these reso-nant reactions, since theyoccur outside the servo loopand cannot be observed by thecontrols.

A patented real-time feedfor-ward technology called Input-Shaping™ nullifies resonancesbefore they start, rather thanwaiting for them to damp out (turn into heat). The result: thefastest possible motion, withvirtually instant settling, asshown in actual vibrometertesting.

InputShaping™ was devel-oped based on research at the Massachusetts Institute of Technology and commer-cialized by Convolve, Inc.,(http://www.convolve.com). Itis a (built-in) option in severalPI digital piezo controllers, iseasy to set up for a particularOEM application and robustagainst dynamic changes inthe setup. It requires nochange to the system soft-ware, application, physicalsetup or servo parameters.InputShaping™ eliminatesunwanted motion-driven reso-nances and ringing in step-mode and continuous-motion(scanning) applications, and itgreatly improves throughputand resolution in high-speedapplications.

Various Methods to Improve Piezo DynamicsMethod Goals

Feedforward Reduce phase difference between output and input (tracking error)

Signal preshaping (software) Increase operating frequency of the system, correct amplitude and phase response. Two learning phases required; only for periodic signals.

Adaptive preshaping (hardware) Increase operating frequency of the system, correct amplitude and phase response No learning phase, but settling phase required; only for periodic signals.

Linearization (analog, in power amplifier) Compensate for piezo hysteresis

Linearization (digital, in DSP) Compensate for piezo hysteresis and creep effects

InputShaping™ Cancel recoil-generated ringing of load and any adjacent components. Reduce the settling time. Closed and open-loop.

Learning control Increase operating frequency of the system, correct amplitude and phase response in scanningprocesses. Online learning phase and trigger for start of period required. Only periodic signals


Fig. 33. InputShaping™ eliminates the recoil-driven resonant reaction of loads and neigh-boring components due to rapid NanoPositioner actuation. Top: Laser Vibrometer reveals the resonant behavior of an undamped fixture when thenanomechanism is stepped. Bottom: Same fixture, same step, with InputShaping ™. The structural ringing is eliminated.

Methods to Improve Piezo Dynamics

4-374-37

Signal Preshaping

For applications with continu-ous, repetitive (periodic) in-puts, a new preshaping tech-nique can reduce the rolloff,phase error and hysteresis ofthe servo-system. The result isto improve the effective band-width and allow more accuratetracking. Signal Preshaping isimplemented in object code,based on an analytical ap-proach in which the complextransfer function of the systemis calculated, then mathemati-cally transformed and appliedin a feedforward manner toreduce the tracking error.Signal Preshaping improvesthe effective bandwidth by afactor of 10 and is more effec-tive than classical phase-shift-ing approaches in reducingtracking error in multi-fre-quency applications.

Signal Preshaping is based onFFT (fast Fourier transforma-tion) techniques. Frequencyresponse and harmonics(caused by nonlinearity) aredetermined in two steps. Theresults are applied to the origi-nal control function and a newcontrol function is calculated.

E. g. for a PZT positioning sys-tem with 400 Hz resonant frequency, the command trans-fer function (amplitude andphase) can be improved from20 Hz to 200 Hz without affect-ing the system stability. At thesame time, the tracking erroris reduced by a factor of up to50 compared to that using theuncorrected control input sig-nal.







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Fig. 34. Signal preshaping, phase 1

Fig. 35. Signal preshaping, phase 2

Fig. 37. Signal after preshaping, phase 2. A: Expected motion (old control signal); B: Actual motion; C: New, preshaped input signal; D: Tracking error.

Fig. 36. No preshaping. A: Control input signal (expected motion). B: Actual motion of system. C: Tracking error

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Two effects must be consid-ered:

Linear Thermal Expansion

Thermal stability of PZTceramics is better than that ofmost other materials (steel,aluminum, etc.). Fig 39 showsthe behavior of several typesof PZT ceramics used by PI.The curves only describe thebehavior of the PZT ceramics.Actuators and positioning sys-tems consist of a combinationof PZT ceramics and othermaterials and their overall be-havior differs accordingly.

Temperature Dependency of the Piezo Effect

Piezo translators work in awide temperature range. Thepiezo effect in PZT ceramics isknown to function down toalmost zero kelvin. For severalreasons the magnitude of thepiezoelectric effect (piezo gain)is dependent on the tempera-ture.

{bk xtx4433}

At liquid helium temperaturepiezo gain drops to approxi-mately 20% of its room-tem-perature value. See Fig. 38, for temperature dependency.

PZT ceramics must be poled toexhibit the piezo effect. Apoled PZT may depole whenheated above the maximumallowable operating tempera-ture. The “rate” of depoling isrelated to the Curie tempera-ture of the material. PI HVPZTshave a Curie temperature of250 °C and can be operated upto 150 °C (with the high-tem-perature option). LVPZTs havea Curie temperature of 150 °Cand can be operated up to 80 °C. See “Options,” p. 1-39in the “PZT Actuators” section,for temperature range modifi-cations.

NotesClosed-loop piezo positioning systemsare less sensitive to temperature changes than open-loop systems.Optimum accuracy is achieved if theoperating temperature is identical tothe calibration temperature (22 °C). See calibration test sheet for details.


Fig. 39. Linear thermal expansion of several PZT materials.

Fig. 38. Temperature dependency of the piezo effect.

Temperature Effects

4-39

PZT Operation inNormal Atmospheres

The insulation materials usedin standard piezo actuatorsare sensitive to humidity.These PZTs are not recom-mended in environments withhigh relative humidity (morethan 60%). For higher humidityenvironments, PI offers specialsystems with enclosed stacks,or integrated dry-air flushingmechanisms.

PZT Operation in InertGas Atmospheres

Piezo actuators can be dam-aged if operated at maximumdrive voltage in a helium orargon atmosphere. Low-volt-age actuators are recom-mended for these conditions.To reduce the risk of dielectricbreakdown, the PZTs shouldbe operated at minimum pos-sible voltage (HVPZTs: < 300 V,LVPZTs: < 80 V). Semi-bipolaroperation helps to furtherreduce the electric fieldstrength, while producing rea-sonable displacement.

Vacuum Operation of PZTs

All PI piezo actuators can beoperated at pressures below0.1 hPa (~0.1 torr). When piezoactuators are used in a vacuum, two factors must beconsidered:

I. Dielectric stability

II. Outgassing

I. The dielectric breakdownstrength of a gas is a func-tion of pressure. Air dis-plays a high insulation ca-pacity at atmospheric pres-sure and below 0.1 hPa(~0.1 torr). However, in thecorona area range from 100 to 0.1 hPa (~100 to 0.1 torr), its insulation prop-erties are greatly degraded.PZTs should not be oper-ated in this range becausean electric breakdown mayoccur.

II. Outgassing (of the insula-tion materials) may limit theuse of PZTs in applicationswhere contamination or vir-tual leaks are an issue.Outgassing behavior variesfrom model to model depending on design. High-vacuum options for mini-mum outgassing are avail-able for several standardLVPZTs and HVPZTs (see“Options,” p. 1-39 ff., in the“PZT Actuators” section fordetails). UHV (ultra-high-vacuum) compatible PZTflexure positioners are avail-able on request.







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Lifetime of PZTs

The lifetime of a PZT is not lim-ited by wear and tear. Testshave shown that PI PZTs canperform billions (109) of cycleswithout loss of performance, ifoperated under suitable condi-tions.

Generally, as with capacitors,the lifetime of a PZT is a func-tion of the applied voltage. Theaverage voltage should be keptas low as possible. This is whyPI offers specially designedactuators and electronics forsemi-bipolar operation, an im-portant advantage over con-ventional actuator/driver com-binations.

There is no generic formula todetermine the lifetime of a PZTbecause of the many parame-ters, such as temperature,humidity, voltage, accelera-tion, load, operating frequency,insulation materials, etc.,which have a (nonlinear) influ-ence. PI PZTs are designedand built for maximum lifetimeunder actual operating condi-

tions. The operating voltagerange values in the technicaldata tables are based on yearsof experience with scientificand industrial OEM applica-tions. For maximum lifetime,operating voltage should notexceed the figures given in thetable.

Example: The P-842.60 LVPZT(see p. 1-18 in the “PZT Actu-ators” section) is to operate aswitch with a stroke of 100 µm.The switch is to be in operation8 hours a day. Of its operatingtime, it is to be open for 70%and closed for 30 %.

Optimum solution: The actua-tor should be linked to theswitch in such a way that theopen position is achieved withthe lowest possible operatingvoltage. To reach a displace-ment of 100 µm, a voltageamplitude of approximately110 Volts is required (nominaldisplacement @ 100 V is only90 µm). Since the P-842.60 can be operated down to -20 volts, the closed positionshould be achieved with 90 V,and the open position with -20 volts. When the switch isnot in use at all, the voltage onthe PZT should be 0 volts.

Statistics show that most fail-ures with piezo actuatorsoccur because mechanicalinstallation guidelines are notobserved and mechanicalstress, shear forces or torqueare allowed to exceed the per-missible limits. PI offers a

variety of preloaded actua-

tors, ball tips, flexible tips

and custom designs to elimi-

nate these critical forces.Failures can also occur whenhumidity or conductive materi-als such as metal dust degradethe PZTs insulation, leading todielectric breakdown. PI has

designed enclosed actuators

for applications in hostile

environments.

PZT Operating Guidelines Duty LVPZT Translators HVPZT Translators HVPZT TranslatorsCycle (1000 V type) (1500 V type)

Operate up to Operate up to Operate up to

100 % 50 V 250 V 500 V

35 % 70 V 600 V 750 V

15 % 100 V 750 V 1000 V

1 % 120 V 1000 V 1500 V


4-414-414-414-414-414-414-414-414-41

Stack Design

The active part of the position-ing element consists of a stackof ceramic disks separated bythin metallic electrodes. Themaximum operating voltage isproportional to the thickness ofthe disks. PI stack actuatorsare manufactured with layersfrom 0.02 to 1 mm thickness.

Stack elements can withstandhigh pressures and exhibit thehighest stiffness of all piezoactuator designs. Since theceramics cannot withstandlarge pulling forces, spring pre-loaded actuators are available.Stack models can be used forstatic and dynamic operation.For further information see“Maximum Applicable Forces”,page 4-23.

Displacement of a PZT stackactuator can be estimated bythe following equation:

(Equation 24)

�L � d33

�n � U

where:

d33

= strain coefficient (field and displacementboth in polarization direction) [m/V]

n = number of ceramic layers

U = operating voltage [V]

Example:

P-845, p. 1-20, etc. (see the“PZT Actuators” section)

Laminar Design(Contraction-TypeActuator)

The active material in the lami-nar actuators consists of thinceramic strips. The displace-ment exploited in these de-vices is that perpendicular tothe direction of polarizationand electric field application.When the voltage is increased,the strip contracts. The piezostrain coefficient d

31(negative!)

describes the relative changein length. Its absolute value ison the order of 50% of d

33

The maximum travel is a func-tion of the length of the strips,while the number of stripsarranged in parallel determinesthe stiffness and the stabilityof the element.

Displacement of a PZT con-traction actuator can be esti-mated by the following equa-tion:

(Equation 25)

�L � d31

� L � U––d

where:

d31

= strain coefficient (displacement normal to polarization direction)[m/V]

L = length of the PZT ceramics [m]


d = thickness of one ceramiclayer [m]

Example:

Laminar piezos are used in theP-280 and P-282, p. 2-24, p. 2-25 Flexure Positioners(see the “PZT Flexure Nano-Positioners” section).

Basic Designs of Piezoelectric

Positioning Elements

+

+

+

+

+

+

+

+

+

Fig. 40. Electrical design of a stack translator

Fig. 41. Mechanical design of a stack translator

Fig. 42. Laminar design

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Tube Design

Monolithic ceramic tubes areyet another form of piezo actu-ator. Tubes are silvered insideand out and operate on thetransversal piezo effect. Whenan electric voltage is appliedbetween the outer and innerdiameter of a thin-walled tube,the tube contracts axially andradially. Axial contraction canbe estimated by the followingequation:

(Equation 26 a)

�L � d31

� L � U––d

where:

d31

= strain coefficient (dis-placement normal topolarization direction)[m/V]

L = length of the PZT ceramic tube [m]


d = wall thickness [m]

The radial displacement is theresult of the superposition ofincrease in wall thickness(equation 26 b) and the tangen-tial contraction

�r___r

� d31

U___d

r = tube radius

(Equation 26 b)�d � d

33� U

where:

�d = change in wall thick-ness [m]

d33

= strain coefficient (fieldand displacement inpolarization direction)[m/V]


When the outside electrode ofa tube is separated into four90° segments, placing differen-tial drive voltages ± U onopposing electrodes will leadto bending of one end (if theother end is clamped). Suchscanner tubes that flex in X and Y are widely used inscanning-probe microscopes.

The scan range of a scanner

tube is defined by:

(Equation 27)

�x � 2��2 � d31� L2� U

� � ID � d _______________

where:

�x = scan range in X and Y (for symmetrical elec-trodes) [m]

d31

= strain coefficient (dis-placement normal topolarization direction)[m/V]

U = symmetric operatingvoltage [V]

L = length [m]

ID = inner diameter [m]

d = wall thickness [m]

Tube actuators are notdesigned to withstand largeforces. Application examplesare scanning microscopy, inkjet printers etc.

Basic Designs . . . (cont.)

Fig. 43. Tube design

Fig. 44. PZT scanner tube

Bender Type Actuators(Bimorph andMultimorph Design)

A PZT bimorph operates simi-larly to the bimetallic strip in athermostat (see Fig. 45). When the ceramic is energizedit contracts or expands propor-tional to the applied voltage.Since the metal substrate doesnot change its length, a deflec-tion proportional to the applied voltage occurs. Bimorph actua-tors providing motion up to 1000 µm and more are avail-able. In addition to the classicalstrip form, bimorph disk actua-tors where the center archeswhen a voltage is applied, areoffered.

PZT/PZT combinations, whereindividual PZT layers are oper-ated in opposite modes (con-traction/expansion), are alsoavailable.

Two basic versions exist: thetwo-electrode bimorph (serialbimorph) and the three-electrode bimorph (parallelbimorph), see Fig. 46. In theserial type, one of the twoceramic plates is always oper-ated opposite to the directionof polarization. To avoid depo-larization, the maximum elec-tric field is limited to a few hun-dred volts per millimeter. Serialbimorph benders are widelyused as force sensors.

Monolithic multilayer-type PZTbenders are also available.Similar to multilayer stack actuators, they run on a lowoperating voltage (60 to 100 V).

Bender type actuators providelarge motion in a small packageat the expense of stiffness,force and speed.

Example:

P-286 - 289 disk translators

PL122 multilayer bender actua-tors

Fig. 45. Bimorph design (strip and disk translator).

Fig. 46. Parallel bimorph and serial bimorph.

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Piezo Actuators withIntegrated LeverMotion Amplifier

Piezo actuators or positioningstages can be designed insuch a way that a lever motionamplifier is integrated into thesystem, typically increasingthe PZT displacement by a fac-tor of 2 to 20. To maintain sub-nanometer resolution with theincreased travel range, thelever system must be stiff,backlash- and friction-free,which means ball or roller bear-ings cannot be used. PIemploys a proprietary finiteelement analysis (FEA) com-puter program to design PZTflexure NanoPositioners withor without integrated levermotion amplifiers (see Fig.48.and Fig 49.).

Piezo positioners with inte-grated motion amplifiers haveseveral advantages over stan-dard piezo actuators:

� Compact size compared tostack actuators with equaldisplacement

� Reduced capacitance (= reduced drive current)

In combination with a flexureguiding system, extremelystraight multi-axis motion ispossible (see “Flexure Nano-Positioners,” page 4-45).

When using (ideal) levers toamplify motion of any primarydrive system, the followingrelations apply:

ksys

= k0___r2

�Lsys

= �L0� r

fres-sys

=fres-0____r

where:

�L = displacement [m]

ksys

= stiffness of the lever-amplified system [N/m]

k0

= stiffness of the primarydrive system (PZT stackand joints) [N/m]

r = lever transmission ratio

fres-sys

= resonant frequency ofthe amplified system[Hz]

fres-0

= resonant frequency of the primary drive sys-tem (PZT stack and joints) [Hz]

Note:

The above equations are basedon an ideal lever design withinfinite stiffness and zeromass. They also imply that nostiffness is lost at the couplinginterface between the PZTstack and the lever. In real ap-plications the design of a goodlever requires a sound under-standing of micromechanicsand nanomechanisms. A bal-ance between mass, stiffnessand cost must be found, while maintaining zero-frictionand zero-backlash conditions.

Coupling the PZT stack to thelever system is actually quitecomplex. The coupling must bevery stiff in the pushing direc-tion but should be soft in allother degrees of freedom toavoid damage to the ceramics.Even if the stiffness of theinterface is as high as that ofthe PZT stack alone, a 50%loss of overall stiffness stillresults.

Our experience shows thatmost often PZT stiffness is not the limiting factor whenusing piezo actuators in a me-chanism. PI has more than 30 years experience in design-ing piezo actuators and flexuresystems. Our engineers will behappy to help you find an opti-mal solution for your position-ing problem.

Fig. 47. Simple lever motion amplifier.

4-454-454-454-454-454-454-454-454-454-454-454-454-45

PZT FlexureNanoPositioners

For applications where extre-mely straight motion in one ormore axes is needed and onlynanometer deviation from theideal trajectory can be toler-ated, simple stacks, tubes andother basic actuators are notideal because they may exhibittoo much off-axis error. Fur-thermore, they may not pro-vide sufficient motion in asmall enough package. PI PZTFlexure NanoPositioners withpassive or active trajectorycontrol provide an excellentsolution in such situations.

A flexure is a frictionless, stic-tionless device based on theelastic deformation (flexing) ofa solid material. Sliding androlling are entirely eliminated.In addition to absence of inter-nal friction, flexure devicesexhibit high stiffness and highload capacity. Flexures are alsoless sensitive to shock andvibration than other guidingsystems.

Basic parallelogram flexureactuators show a second-ordercross-coupling (parasitic mo-tion) between two axes due toarcuate motion (travel is in anarc). This can lead to out-of-plane errors on the order of0.1% of the distance traveled(see Fig. 48). The error can beestimated by the followingequation:

(Equation 28)

�H � (± �L____2 )2 1___

2H

where:

�H = Lateral runout (out-of-plane error) [m]

�L = Distance traveled [m]

H = Length of the flexures [m]

For applications where thiserror is intolerable, PI has de-signed a zero-arcuate-error

multi-flexure guiding sys-

tem. This special design, employed in most PI flexurestages, eliminates the cross-coupling inherent in commonparallelogram guiding systemsand provides flatness andstraightness in the nanometerand micro-radian ranges res-pectively (see Fig. 49).

For applications requiring sub-nanometer and sub-µrad flat-ness and straightness, PIoffers a system with integratedmulti-axis error compensation(active trajectory control). Itmeasures and actively controlsmotion in all six degrees offreedom to sub-nanometerand sub-microradian toler-ances. The exceptional flatnessprovided by this system isshown in Fig. 50.

Examples:

P-527, P-734, p. 2-28 ff. in the“PZT Flexure NanoPositioners”section.

NotesFlexure positioners are far superior to traditional positioners(ball bearings, crossed roller bearings, dovetails etc.) in terms of resolution, straightness and flatness. Inherent friction and stiction in these traditional de-signs limit applications to thoserequiring repeatability on the order of 0.5 to 0.1 µm.

Fig. 48. Basic parallelogram flexure guiding system with motion amplification. The amplification r (transmission ratio) is given by (a+b)/a.

Fig. 49.Zero-arcuate-error flexure guiding system.

Fig. 50. Flatness (Z) of an actively error compensated flexure stage over a 100 x 100 µm scanning range.







Motor Controllers

Index


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PZT Actuators

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

http://www.pi.ws

[email protected]

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[email protected]

4-46http://www.pi.ws

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ElectrostrictiveActuators

Electrostrictive actuators aresolid state actuators similar toPZTs. The electrostrictive ef-fect can be observed in alldielectric materials, even in liq-uids. Although sometimes ad-vertised as a recent discovery,the material used has beenaround for 20 years. Electro-strictive actuators are made ofa lead magnesiumniobate

(PMN) ceramic material. PMNis a ceramic exhibiting dis-placement proportional to thesquare of the applied voltageunder small-signal conditions,for certain compositions andtemperature ranges. Underthese conditions PMN unitcells are centro-symmetric atzero volts. An electrical fieldseparates the positively andnegatively charged ions,changing the dimensions ofthe cell and resulting in anexpansion. Electrostrictive actuators must be operatedabove the Curie temperature,which is typically very lowwhen compared to PZT materi-als.

In a limited temperature range,electrostrictive actuators ex-hibit less hysteresis (on theorder of 3%) than PZT actua-tors. Despite the reduced hys-teresis, they provide highlynonlinear motion because ofthe quadratic relationship bet-ween voltage and displace-

ment. They are also unable to take advantage of the reducedelectric field strength of bipolarmode operation, becausereversing the electric fielddoes not result in contraction(see Fig. 51). Furthermore, PMNactuators show an electricalcapacitance four to five timesas high as piezo actuators andhence require significantlyhigher drive currents for dyna-mic applications.

PZT materials have muchgreater temperature stabilitythan electrostrictive materials,especially over large (10 ° C)temperature variations. Bothdisplacement and hysteresis of PMN materials are stronglydependent on the actuatortemperature. When the temp-erature increases, displace-ment decreases (see Fig. 52.;)at low temperatures, wheredisplacement is at a maximum, hysteresis also reaches a maximum (see Fig. 53.),greatly restricting application.


16

Fig. 51. Displacement vs. voltage behavior of PZT andPMN actuators (generalized)

Fig. 52. Displacement vs. temperature behavior of PZT and PMN actuators.

Fig. 53. Hysteresis vs. temperature behavior of PZT and PMN actuators.

Mounting Guidelines

for PZT Translators

Fig. 54. No pulling force without preload

Fig. 55. No lateral force or torque

Fig. 56. Ball tips or flexures to decouple lateral forces orbending forces.

4-47







Motor Controllers

Index


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[email protected]

PZT Actuators

Summary

Piezoelectric actuators

offer today’s motion

engineer a practical way

to achieve extremely high

positioning accuracy in a

wide variety of applica-

tions. Examples given

in this discussion indicate

but a few of the many

applications of piezo

actuators. In the near

future, PZT-based motion

will more and more

replace classical motion

systems. In addition, the

unique features of PZTs

will trigger development

of products that could

not exist without this

technology and help push

back the frontiers of minia-

turization, precision and

throughput.

Adherence to the followingguidelines will help you obtainmaximum performance andlifetime from your PZT actua-tors:

I. PZT stack actuators mustonly be stressed axially.Tilting and shearing forcescan be avoided by use ofball tips, flexible tips, etc.

II. PZTs without internal pre-load are sensitive to pullingforces. An external preloadis recommended for appli-cations requiring strongpulling forces (dynamic op-eration, heavy loads, etc.).

III.Maximum torque allowableat the top-piece can befound in the technical datatables for all PZT stacks andmust not be exceeded.Proper use of wrench flatsto apply a counter-torque tothe top-piece when a mat-ing piece is installed willprotect the ceramics.

IV. When PZTs are installedbetween plates, a ball tip isrecommended to avoid ben-ding and shear forces.

Fig 57. Ball tips or flexures to decouple bending forces Fig. 58. Bolting between plates is not recommended

4-48

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Units of Measure and Conversion Tables

Length[m] [mm] [µm] [nm] [Å] [“] [in]

1 meter [m] = 1 1000 106 109 1010 39.371 millimeter [mm] = 10-3 1 1000 106 107 0.039371 micrometer [µm] = 10-6 10-3 1 1000 10000 39.37 x 10-6

1 nanometer [nm] = 10-9 10-6 10-3 1 10 39.37 x 10-9

1 angstrom [Å] = 10-10 10-7 10-4 0.1 1 39.37 x 10-10

1 inch [in], [“] = 0.0254 25.4 25,400 25.4 x 106 25.4 x 107 1

Angle Measure[°] [arc sec] [mrad] [µrad]

1 degree [°] = 1 3600 17.45 17,4501 arc second = 2.778 x 10-4 1 4.848 x 10-3 4.848-

1 milliradian [mrad] = 57.30 x 10-3 206.3 1 10001 microradian [µrad] = 57.30 x 10-6 0.2063 10-3 1

Mass*[kg] [g] [lb]

1 kilogram (of mass) [kg] = 1 1000 2.2051 gram (of mass) [g] = 10-3 1 2.205 x 10-3

1 pound (of mass,also known as a slug) [lb] = 0.4536 453.6 1

Force* (Mass x Acceleration)[N] [kg] (force) [lb] (force)

1 newton [N] = 1 0.102 0.22481 kilogram of force [kg] = 9.807 1 2.205 x 10-6

1 pound of force [lb] = 4.448 0.4536 1

Torque (Lever Arm x Force)[N�m] [mN�m] [ft�lb] [in�lb]

1 newton-meter [N�m] = 1 1000 0.7376 8.85121 millinewton-meter [mN�m] = 0.001 1 73.76 x 10-5 8.8512 x 10-3

1 foot-pound [ft�lb] = 1.3563 1356.3 1 121 inch-pound [in�lb] = 0.113 113 0.083 1

Energy (Force Acting over Distance)[N�m] [W�s] [ft�lb] [in�lb]

1 newton-meter [N�m] = 1 1 0.7376 8.851 watt-second [W�s] = 1 1 0.7376 8.851 foot-pound [ft�lb] = 1.3563 1.3563 1 121 inch-pound [in�lb] = 0.113 0.113 0.083 1

Power (Energy per Unit Time)[N�m/s] [W] [ft�lb/s] [in�lb/s]

1 newton-meter per second [N�m/s] = 1 1 0.7376 8.851 watt [W] = 1 1 0.7376 8.851 foot-pound / sec [ft�lb/s] = 1.3563 1.3563 1 121 inch-pound / sec [in�lb/s] = 0.113 0.113 0.083 1

Pressure (Stress, Force per Unit Area)[N/m2] [Pa] [hPa] [torr] [psi] [lb/in2]

1 newton per square meter [N/m2] = 1 1 0.01 750.1 x 10-5 14.50 x 10-5

1 pascal [Pa] = 1 1 0.01 750.1 x 10-5 14.50 x 10-5

1 Hectopascal [hPa] = 100 100 1 0.7501 14.50 x 10-3

1 torr [torr] = 133 133 1.33 1 19.34 x 10-3

1 pound per square inch [lb/in2] = [psi] = 689.5 689.5 6.895 51.71 1

Illumination[lm/m2] [lm/ft2]

1 lux [lm/m2] 1 0.0929foot-candle [lm/ft2] 10.76 1

Temperature[K] [°C] [°F]

kelvin [K] 1 K-273.16 K � (9/5) -459.688degree Centigrade [°C] °C+273.16 1 (°C + 40) � (9/5) -40degree Fahrenheit [°F] (°F + 459.688) � 5/9 (°F + 40) � (5/9) -40 1

* The names and abbreviations of certain units of force conflict with those of certain units of mass. Which is meant can usually be deter-mined by the context. For example, when it is stated that a Hexapod can tolerate a load of 200 kg vertically, kilograms of force are meant,but when it is a question of moving a 20 g load at 2 kHz, grams of mass are meant.

Technologies that set PI apart:

Parallel Kinematics Multi-

Axis Micro- & Nano-

positioning Systems

reduced inertia, faster response, more compact,higher stiffness, no accumulation of errors, nomoving cables (no friction),parallel metrology (highermulti-axis precision).

Parallel Metrology

monitors all controlleddegrees of freedom simultaneously; allowsactive trajectory control.

Active Trajectory Control

allows active elimination of runout and off-axis errors to sub-nanometer and sub-microradian precision.

Dynamic Digital

Linearization

reduces phase lag and non-linearity in high-speedpositioning, scanning and tracking applications. Improves effective bandwidth up to 3 ordersof magnitude.

InputShaping®

Eliminates self-generatedringing of componentsinside and outside theservo-loop. Allows settlingwithin one period of theresonant frequency.

Capacitive

Sensors

Non-contact,absolute measur-ing devices providing sub-nanometer resolution, very high linearity and high bandwidth. Excellent for parallel-metrologyconfigurations.

PICMA®

Technology

A new monolithic piezo actuator design with all-ceramic insulation, insensitive to humidity and providing significantlyhigher reliability, lifetimeand operating temperatureranges than conventionalpiezo actuators. Ideal forvacuum applications.

PIline™ Piezo Motors

are based on a novel solid-state ultrasonic piezo-ceramic drive. They arelightweight, low-profile andprovide a number of advan-tages over conventionalmotors, such as negligibleEMI, ultra-fast response,auto-locking, zero-backlashand excellent power-to-weight ratio.

PI—History of Innovation

The following examples emphasize PI’s four decades of innovation in micro- and nanopositioning technology

� First commercially available piezo translators

� First PZT translators withintegrated preload forindustrial reliability

80’s

� First commercially available closed-looppiezo actuators

� First flexure-guided piezo-driven nanopositioningsystems

� First hybrid multiaxis fiberalignment systems

� First preloaded actuatorswith monolithic low-voltage PZTs

� Nanopositioning systemswith PC interface

� First closed-loop, imagestabilization platforms

2000–

http://www.pi.ws

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70’s

� First flexure-guided, high-speed nano-focus device

� First two-plate capacitivesensors / controllers w/integrated linearization forsub-nanometer precision

� First parallel kinematicsmultiaxis piezo nanoposi-tioning stage with inte-grated parallel metrology

� First piezoelectrically driv-en high-speed tool servo

� PI becomes the firstnanopositioning systemssupplier with piezo-ceramics-manufacturingcapabilities

� First sub-micron 6-DOFHexapod

� First fully automated fiberalignment system withhigh-resolution Piezo-Walk™ drive (10 nm)

� First piezo stage with 6Dactive trajectory control

� First fully automated 6-DOF photonics alignment system withvirtual pivot point

� First piezo controller withInputShaping® vibrationelimination algorithms

90’s

With over four decades experience, PI has evolved into the world-leading supplier of nanopositioning technology.

In the 70's, when space exploration spurred new research in optics,PI introduced piezo actuators to help scientists control motion tosub-micron levels.

In the 80's, when the introduction of microcomputers created thefirst semiconductor boom and the need for smaller and smallerfeature sizes, PI nanopositioning systems were ready to take on the challenge.

The fall of the Berlin wall in the 90's marked the end of the cold warand the beginning of a new age of borderless communications. It also meant the beginning of a new age for PI: the start of thepiezoceramic division PI Ceramic.

The new millennium saw worldwide efforts advancing fiber-optictechnologies, nanotechnology and biotechnology, fields where“smaller” and “more precise” is the key to success. PI is there tolead the way with faster and higher-performance motion controlsystems.

� Patented high-forcecompact piezomotors

� First 6-axis digital piezocontroller

� First piezo controller withdynamic linearization (improves dynamic linearity by up to 3 ordersof magnitude)

� First closed-loop piezo-driven steering mirrorwith 50 mrad range

� First PICMA® monolithicpiezo actuators w/ ceramic insulation for increased lifetime andzero outgassing

� Fastest open-frame,closed-loop XY nano-positioning stage

� Lowest out-of-planemotion nanopositioningstages (< 1 nm)

Nanopositioning,NanomechanicsLeadershipPI has been developing andmanufacturing products in thefield of nanomechanics andnanotechnology for more than30 years. During this time, wehave achieved and continuallyconsolidated our position as aglobal market leader. Primeexamples of our core compe-tencies and cutting-edge tech-nology are to be found in thedevelopment of parallel kine-matics—integrated 6-axis posi-tioners based on the Hexa-pod—and in the field ofnanopositioning with piezo-ceramic actuators. PI employs more than 300staff worldwide and maintainssales, support and serviceoffices in Germany, the USA,England, France, Italy, Japanand China with nanometrologycapabilities on three conti-nents. PI is represented in manycountries around the world.

At the Heart of ourSystems: the Piezo EffectOne small step for PierreCurie—one great leap for theworld. The piezo effect—Pierre Curie’s discovery ofabout a hundred years ago—now forms the basis of thesmallest mechanical, elec-tronic or control-technologyproducts. When voltage is ap-plied to piezoelectric crystalsor ceramics, they expand. Weexploit this effect to createpositioning systems withnanometer accuracy.

PI Products—Innovation &Superior QualityPI has been ISO 9001 certifiedsince 1994. Our products arecharacterized by their qualityand innovation. Developed togive the highest degree of pre-cision, we employ the most-modern tools and software for product development like FEMcalculations and simulations.To determine the performancelevel of our products, we hadto design equipment capable ofresolving to fractions of a nanometer, pushing measure-ment accuracies to the limit.

PrecisionAdvancesOver the years we have seenmany technological advancesmake the transition from thelaboratory to daily life, ad-vances requiring the utmost inpositioning accuracy, advancesinconceivable without PI. Finerand finer structures on semi-conductor wafers for cost-effective mass-production ofhigh-performance electronics,or higher and higher density intelecommunications streamswith millisecond switchingfrom network to network, all inthe minimum amount ofspace: this is where PI is athome.

PI’s Customers PI customers come from allsectors of manufacturing, qual-ity assurance, research anddevelopment. And they arespread across many branchesof industry: � Astronomy � Semiconductors � Semiconductor Test

Systems� Medical Engineering � Bio- / Nanotechnology � Telecommunications � Precision Engineering � Aerospace Engineering PI’s customers even includenational standardization insti-tutes. As our customer, you also prof-it from our more than 30 years’experience in micro- and nano-positioning technology. You willjoin an ever-increasing numberof renowned companies andinstitutes whose products areat the cutting edge of innova-tion, research and technology.PI moves the nanoworld.

PI USA. The east coast office in Auburn, MA, also hosts a service department withnano metrology equipment.

PI Headquarters, Karlsruhe, Germany. PI employs the world’s most expe-rienced design and manufacturingteams for nanopositioning and nano-mechanics products.

Motion Controllers for MicroPositioners

Piezo Motors/Ultrasonic Motor Driven Stages

Section 9

Section 7

Photonics Alignment & Packing Systems

Section 8

Tutorial—Piezoelectrics in Positioning

Section 4

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Hexapod Parallel Kinematics 6DMicroPositioning Systems

Section 7

Products

Section 1

Piezo Actuators

Motion Controllers for NanoPositioners(Piezo Controllers, Drivers, Power Amplifers)

Section 6

Active Optics (Piezo Steering Mirrors, etc.)


Section 2

Section 5

Section 3

Section 1

Piezoelectric Ceramics

Piezoelectric NanoPositioning Systems

Linear and Rotary MicroPositioners

Section 7

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400 Page

PI Catalog:

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USA

PI (Physik Instrumente) L.P. West

1342 Bell Avenue, Suite 3A

Tustin, CA 92780

Tel: +1 (714) 850-9305

Fax: +1 (714) 850 9307

Email: [email protected]

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PI (Physik Instrumente) L.P. East

16 Albert Str.

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JAPAN

PI-Polytec Co., Ltd.

2-38-5 Akebono-cho

Tachikawa-shi

Tokyo 190-0012

Tel: +81 (42) 526 7300

Fax: +81 (42) 526 7301


JAPAN

PI-Polytec Co. Ltd.

Hanahara Dai-ni Building, #703

4-11-27 Nishinakajima,

Yodogawa-ku, Osaka-shi

Osaka 532-0011

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GERMANY

Physik Instrumente (PI)

GmbH & Co. KG

Auf der Roemerstrasse

76228 Karlsruhe

Tel: +49 (721) 4846-0

Fax: +49 (721) 4846-100

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GERMANY

PI Ceramic GmbH

Lindenstrasse

07589 Lederhose

Tel: +49 (36604) 882-0

Fax: +49 (36604) 882-25

www.piceramic.com

[email protected]

GREAT BRITAIN

Lambda Photometrics Ltd.

Lambda House

Batford Mill

Harpenden, Hertfordshire

AL5 5BZ

Tel: +44 (1582) 76 43 34

Fax: +44 (1582) 71 20 84


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FRANCE

Polytec PI S.A.

32 rue Delizy

F-93694 Pantin Cedex

Tel: +33 (1) 48 10 39 30

Fax: +33 (1) 48 10 08 03


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ITALY

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