First Steps towards Piezoaction

Thermograph of a dynamically operated piezo stackThe intention of this paper is to give newcomers to the field of “piezo-actuation” or “piezo-mechanics”
a brief overview of the topic.
In discussing stack based piezo-actuators, many aspects reviewed can easily be applied to otherpiezo-actuation principles.
For more comprehensive studies, refer to the available specialized literature.

© All pictures, photos and product descriptions ar the intellectual propertyof Piezomechanik Dr. Lutz Pickelmann GmbH.
Utilisation and copies by third parties have to be authorized.
All rights reserved.

Contents

1.

■ Piezo stack actuators: A survey

7

1.1

Basic game rules

7

1.2

Characterizing piezo stack actuators

9

Stroke (shift) - force balances - dynamics - performance limits
1.3

Actuator designs

112.

■ Basic stack designs

12

2.1

The piezo-mechanical effect

12

2.2

High Voltage versus Low Voltage: a comparison

12

2.3

Stack configurations

14

2.4

Ring stacks versus piezo tubes: a comparison

15

2.5

Ring stacks versus bulk stacks: a comparison

16

2.6

Advantages of PIEZOMECHANIK’s piezo stacks

17

3.

■ Precision positioning

19

3.1

Shift versus voltage characteristic

19

3.2

Precision positioning by piezo stacks

21

3.3

Limits of positioning accuracy

224.

■ Motion and Forces

23

4.1

Beyond simple positioning

23

4.2

Examples for force/shift relations

24

4.3

Piezo-actuator as an active spring

25

4.4

Selecting a piezo stack

25

4.5

Force generation

27

4.6

Stiffness

29

4.7

Force limitations, load capabilities

31

4.8

Dynamic operation

31

4.9

Mechanical preloading (pre-stress)

32

Contents

5.

■ Dynamic operation of piezo stacks

35

5.1

Definitions

35

5.2

Short-term excitation

36

5.3

Long-term operation

37

5.4

Typical operating frequencies

38

5.5

Resonance

40

6.

■ Extended functionality, options

42

6.1

Heat management “Thermostable”

42

6.2

Temperature sensing

43

6.3

Low temperature operation

43

6.4

Position sensing

44

6.5

Further modifications
Enhanced mechanical preload - Vacuum operation - Rotating systems -45

Non-magnetic configurations - Special materials

7.

■ Operation instructions

46

7.1

Basic comment on actuator reliability

46

7.2

First check of a piezo-actuator

47

7.3

Thumb rules

48

Handling and operation

49

7.4

Mechanical aspects - Electrical aspects - Thermal aspects
7.5

Adhesives - Electrical contacts - Chemistry

54

7.6

Further aspects
Environmental influences - Vacuum operation - Noble gases, hydrogen atmospheres -56

Radiation - Space-borne application

8.

■ Properties of piezoceramics
Voltage versus Shift diagrams, hysteresis, Materials data, Temperature-related properties,
Special ceramics (ultrasound ceramics, electrostriction)

57

Contents

9.

■ Electrical powering of piezo-actuators

62

9.1

Electrical input and piezo-mechanical reaction
Noise - Peak currents - Mean currents - Energy-/power-balances, energy dissipation -62

Electrostriction - Unipolar/semi-bipolar/bipolar operation
9.2

Alternatives: charge versus voltage control

66

9.3

Basic piezo amplifier functions

68

10.

■ Selecting a proper actuator

69

11.

■ New trends

70

11.1

Piezo action for material testing

70

11.2

Motion control

72

11.3

Electrical energy generation73

Force transducers - Energy harvesting, scavenging - Piezo transformers

Glossary

Actuator:
Mechanical actuator is synonym for motor, motion
generator, mover; often used in context with linear
displacements of limited range.
The term motor is commonly used for rotating drives with unlimited period of unidirectional action.
Smart material:
Special materials providing controllable features andproperties beyond the classical behavior
Solid-state materials:
showing induced deformation: memory alloys,
piezo-effect, magneto-striction
Liquids:
electro- and magneto-rheological systems with controllable viscosity
Solid-state actuator:
Based on all kinds of solid-state materials providing
a controllable motion or force generation by material’s internal structure or texture (prime movereffect)Piezo-actuator:
Solid-state actuator, using the inverse piezo-electrical effectSynonyms: piezo-translators, piezo-transducers
Piezo stack actuators:Piezo stack actuators use the variation of the stacklength under electrical activation. This is in contrast
to other kinds of moving profiles like shear elements
or bending elements (bimorphs).

Piezo-mechanics:
Shorter expression than “inverse piezo-electric”
describing the motor or actuator application of thepiezo-effect (in contrast to the “piezo-electrical”
generator effect).
Smart structures
Mechanical arrangements based on smart materials
to control the mechanical properties of the arrangement e. g. by electrical means.
Adaptronics:
Wide cross over with “mechatronics” or “smart
structures”:
the science of mostly mechanical systems using“smart materials” together with a sophisticatedelectronics to get a kind of “learning process” andself-adaption for getting an optimum system’s
behavior.

Synonyms:
Actuator displacement = stroke = shift = expansion= elongation

StandPiezo stack
der actuators:Piezo-Multilayer-Technik
A survey

1

1.1 Basic game rules

Piezo stack actuators are used as linear electromechanical drives or motors.
They act mainly like an expanding element (“pusher”) generating a compressive
force. The complete motion cycle is nearly proportional to the voltage signal input
from DC up to high frequencies.

From an electrical point of view, piezo-actuators
behave like electrical capacitors:
The induced motion can also be described as theconsequence of the variation of the electrical charge content of the piezo-actuator.

mounting basepiezo stackPiezo-actuators are based on a special smart material: The electro-active piezoceramic material,
known as PZT made ofPb (lead)-Zr (zirconium)-Ti (Titanium) mixed-oxides.

moved
mechanics

electronics

Fig. 1.1: Schematic of a piezo-mechanical system based on a
piezo stack, mounted on a solid base, moving the attachedmechanics by electrically induced strain of the stack.

The main characteristics of piezo motion are:● Small shifts● High force generation● High mechanical load capability● High stiffness (low compliance)● High dynamics

PIEZOMECHANIK

7

1.1 Basic game rules

Decision guidance for using piezo-technology● Verify that piezo-actuators will benefit yourapplication in a way that alternative solutions(e.g. magnetic actuation) cannot. Piezo-actuators
will be ruled out otherwise simply for cost reasons.
● Analyze your application correctly for the needed

force-shift-characteristic. Pay attention to a suitable “piezo” match of your mechanical design.
Only with a well-adapted application design, you
can make complete use of an actuator’s performance including the benefits of high reliability,
reproducibility and long operating life.
The “upgrade” of existing old-fashioned mechanical designs by simply replacing a conventional
drive by an “innovative” piezo-actuator will usually fail. Systems must be designed with the piezoactuator in mind.

● The lifetime and reliability of actuators depend

strongly on the wide variety of the interacting
operational parameters and the conditions of theindividual application.
Therefore, it is impossible to define a single test
procedure, applied to an isolated element forevaluating its reliability for all kinds of operations.
The only strategy is system testing under a set of
realistic operation conditions.
Even for a working piezo-mechanical system,
small alterations of the driving conditions or
system’s design may result in the need for a newsuitability evaluation.

● A 100% general purpose piezo-actuator, covering

all kinds of applications, does not exist. Piezoactuators are typically optimized for distinct operation profiles. This degree of specialization may
not explicitly be expressed in the data sheet.
Therefore, care is needed when replacing successfully operating products by ones from othersources.
● The product data have been derived under

distinct test conditions. The actuators may show
a different behavior, when operated in a different
way. The definitions of specifications for actuator’s performance can vary from supplier to supplier. Pay attention to the parameter definitions,when comparing elements from different sources.

8

PIEZOMECHANIKDo not misinterpret catalogue data:
Notice, that not all operating specifications canbe realized at the same time due to simple
physical facts.
Example:● Maximum displacement/shift/stroke andmaximum force generation /max. blocking
force cannot be generated at the same time,
only either-or.
● The real operating frequency of a piezo-

mechanical system is usually held far below
the actuator’s resonance frequency !

1.2 Characterizing piezo stack actuators

Stroke (shift) - force balances - dynamics - performance limits
Fig.1.2 shows a solid state actuator made bystacking PZT ceramic layers, which are electricallycontacted individually resulting in a multilayer capacitor structure. The application of a voltage to thestack generates an electrical field within the ceramiclayers resulting in a mechanical strain of the stack.
The generated axial expansion of piezo stack’s
length L is used for actuation. Coupling to externalmechanics is done via the end faces (cross section
area A).

A

L

Achievable maximum strains typically range between 0.1% and 0.15% of L. A piezo stack with alength L = 50 mm usually possesses a maximum
stroke of 50 – 70 µm.
The load capability and max. force generation ofa piezo-actuator depend on stack’s cross section
area A. The load and force limits are in the range of7- 8 kN/cm² (70 - 80 MPc).
The mechanical work capability “stroke x force” istherefore proportional to the active ceramic volume
L x A.

A
Fig. 1.2 : Piezo stack built up from individually contacted
piezoceramic discs
Working axis: length L
Active cross section area A (mechanical coupling face).

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9

1.2 Characterizing piezo stack actuators

Specific features of piezo stack actuators
Shift:
unlimited positioning sensitivity(actually proven down to the picometer range)
Forces:● High load capability up to tons
● High force / pressure generation (kiloNewtons)● Superposition of high static payload anddynamic force modulation● Low mechanical compliance (high natural
frequencies), solid-state body!

Dynamics: (depends also on electronics)● No delay in mechanical reaction● Very high acceleration rates● Very high mechanical power generation
Design advantages:● “Exotic” driving conditions applicable (vacuum,
cryogenic temperatures etc.)● Compact design● High mechanical power density even in miniature
structures (MEMS/NEMS)● Power consumption only when motion is
generated.
● No stand-by / no sustainer energy consumption.

Actuator market’s main emphasis:
Shift:
Typical stack lengths 2 -100 mm=> shifts from µm up to approx. 100 µm

Dynamics
Depends strongly on actuator dimensions
Non-resonant cycling with maximum strain: < 1 kHz
Non-resonant cycling with reduced strain: < 10 kHz

Forces:Stacks with small to medium sized cross sections(up to approx. 10 x 10 mm²)=> Forces ranging from Tens to several Thousandsof Newtons.
Low voltage actuators preferred.

Performance limits
Exotic and expensive, mostly prototypes or singularapplications
Shift:High voltage stack actuators with length > 600 mm
for 1 mm shift (= 1,000 µm)
Forces:
Large cross section elements with diameters up to
70 mm for load capabilities, blocking forces > 100 kN
Mostly high voltage (HV) piezo stacks

10 PIEZOMECHANIKDynamics:
Piezo shock generator < 10 µsec rise-time for100 µm stroke
Acceleration > 100.000 m/sec²

1.3 Actuator designs

Low voltage stacks: Co-fired multilayer actuators (CMA): also called “monolithic” stacks, involve nogluing, but a high temperature sintering of the complete ceramicelectrode pile. Operating voltages are
up to 200 V. Rectangular cross sections are typical due to the ease of cutting processes in production.
High voltage stacks: Composite structures made by the stacking of separately finished piezoceramic
discs and metal electrode foils that are joined through the use of adhesives. Operating voltages ranging
from 500 V thru 1000 V are typical. Cylindrical shapes are most common.
Ring actuators: A stack with center bore: made with rings instead of discs.
This type of actuator is available in both low and high voltage form.

Low voltage actuators are used for small andmedium cross section (1 mm2 up to approx.
14 x 14 mm2) fig. 1.3: B.

Ring actuators offer a wider range of designoptions for piezo-mechanical assemblies(fig. 1.3: C, D, E).

High voltage actuators cover needs for larger stackcross sections (fig. 1.3: A, C).

Manufacturing of ring actuators is more elaborate
and expensive than for bulk stacks.

A

B

C

D

E

Fig. 1.3 : (A), (C) high voltage bulk stack and ring actuator, large cross section(B), (D), (E) low voltage bulk stack, ring actuator and ring chipPIEZOMECHANIK

11

Basic stack designs

2

2.1 The piezo-mechanical effectPiezo stack actuators are electrical multilayer capacitors, whose outer dimensions
vary when the electrical charge status is changed. Usually the axial strain is used
for actuation purposes.
The mechanical reaction like shift and force balance
depends on the applied internal electrical field(typical values up to 2 kV/ mm).
To get the above stated levels of field strength withacceptable voltage levels (100 V to 1000 V), theindividual layer thickness of the multilayer stack will
be adapted accordingly (e. g. 0.5 mm for a 1000 V
high voltage actuator (fig.1.2)).

2.2 High Voltage versus Low Voltage: a comparison

Two completely different stacking techniques areused for low and high voltage stack actuators:● Low voltage actuators ( 200 V): ceramic layers

and internal metal electrode layers are stacked
before the final high temperature sintering, while
the ceramic is in the soft (green) state. The internal electrodes are a very thin metal film (thickness 1 µm) and are made e.g. of AgPd-alloy or
Cu. This kind of actuator technique is often called
as “monolithic cofiring”.
● High voltage actuators for voltage ranges ofapprox. 500 V up to 1000 V are made from completely sintered and finished individual PZT discs
or plates prior to stacking. The inserted layerelectrodes are made from separate thin metal
foils. The whole arrangement is fixed together by
a special high quality adhesive. Therefore HV
actuators are not a ceramic monolith, but a kindof composite material.

12 PIEZOMECHANIK

Fig. 2.1: High voltage stack (black, left) and low voltage stack(green, right), mouse and USB stick for size comparison.

2.2 High Voltage versus Low Voltage: a comparison

High voltage (HV)-stacks

Low voltage (LV)-stacks

Preferred use

large cross sections > 15 mm
For special actuator designs,
small and medium quantities

small and medium crosssections miniature elements,
lower costs for large quantities

Individual ceramic layer thickness

up to 0.5 mm typ.

< 0.1 mm typ.

Manufacturing process

gluing of individualcompletely finished
PZT-ceramic parts
like discs or plates

piling up of soft, non-sintered
PZT-ceramic sheets and electrodes.
High temperature sintering ofcomplete stack structure

Max. driving voltage

500 V - 1000 V

up to 200 V

Max. electrical fieldsame for both types: approx. 2kV/mm typelectrical capacitance/cm³(order of magnitude only)

100 nFarad

2.5 µFarad

Elastic modulus

lower for HV elements, when notmechanically preloaded

high: up to 90% of
theoretical value ofthe original PZT-ceramicMax. strainsame for NV and HV stacks: approx. 0.1 – 0.15%

Max. pressure loadsame for NV and HV stacks

Max. force generation

same for NV and (preloaded) HV stacks

Positioning accuracy

same for NV and HV stacks

Max elec. energy densities

same for NV and HV stacks(approx. 0.3 Ws/cm³, depends on PZT material)

PIEZOMECHANIK

13

2.3 Stack configuration

Most customers relate the functionality of a piezo
stack only to the used piezoceramic material.
However, it is a common experience that all aspectsof the stack design, manufacturing technique andfinish of the whole component are essentials
regarding performance and reliability.
Following points require attention:● joining techniques● electrode design● internal insulation techniques● surface insulation techniques
All of the structural components of a stack aresubject to strongly varying mechanical andelectrical load conditions during dynamic cycling.

This leads to very different levels of reliability when
considering different actuator concepts for a
distinct application.
Piezo stacks from different sources will differ not
only in the used ceramic, but also in different
manufacturing techniques. These differences are
not necessarily expressed in the short term
performance data. Careful evaluation of the
proposed piezo stacks must be undertaken when
an application requires high reliability.
PIEZOMECHANIK stack actuators range fromgeneral-purpose elements for low and medium
dynamic applications up to specially designed
elements for very high mechanical dynamics.

Further upgrades of the stack actuator are theuse of metal casings with internal pre-stressmechanisms (fig. 2.2) and other options likeinternal heat management, position sensing etc.
(=> chap. 6: Options)Fig. 2.2 : Schematic of integrationof a piezo stack into a preloaded
casing

14 PIEZOMECHANIK

2.4 Ring stacks versus piezo tubes: a comparison

Piezo tubes are simple ceramic cylinders withmetalized inner and outer surfaces. For mechanicalstability reasons, the wall thickness of such tubes
needs to be about ≥ 0.5 mm (fig. 2.3, A).
To get maximum displacement, high voltages areapplied.
Piezo tubes are sometimes used as simple
positioning mechanism, when access to thesystem’s axis is needed.

Piezo ring actuators can be a much more efficient
alternative.
By applying a center bore, piezo stacks can bebuilt up as hollow cylindrical elements, (fig. 2.3, B)
offering a much wider range of design opportunities for piezomechanics.
Piezo ring actuators were first offered to themarket by PIEZOMECHANIK in the 1980’s .

Compared to piezo tubes, a ring actuator offers
the following advantages● Higher strain rates achievable (axial strain
efficiency at least better by a factor 2)=> compact design● Low voltage types available● Wall thickness independent from driving
voltage levels

A

B

Fig. 2.3 : Piezo tube (A) versus stacked cylinder (ring actuator(B))

Attention:
Piezo tubes make use of the contractive d31 piezoeffect.
Piezo ring actuators make use of the expanding d33
piezo-effect showing doubled strain efficiency of thed31 operation.
The change of sign in motion shall be kept in mind
when setting up e.g. a feed back controlled system.

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15

2.5 Ring stacks versus bulk stacks: a comparison

Ring actuators show specific features and advantages in comparison to bulk stacks.
● Higher bending stability:

When comparing the same volume of active
ceramic material a ring actuator has a larger total
diameter than the bulk stack. Accordingly, thislarger diameter results in an increase of mechanical stability against bending and buckling.
This is important, when long-stroke stacks are
set up showing a rather critical aspect ratio
length/diameter. To compensate for this, larger
diameters are needed.
When using a bulk design, the electrical capacitance increases dramatically for mechanical stability reasons only. The electrical power consumption increases equivalently, but is not needed on the mechanical output side. The overall
power efficiency is going down (mismatch).
By using the hollow cylinder ring actuators
design, the mechanical stability is enhanced without the increase of electrical capacitance.

Fig. 2.4 : Ring stack versus bulk stack

16 PIEZOMECHANIK● Efficient heat management:

Piezo-actuators generate heat when operated
dynamically with high repetition rates.
This heat must be removed from actuator ceramic. Overheating will lead to worsening of actuator
performance and/or cause damage.
It is a fact that piezoceramic is characterized bypoor thermal conductivity that rules all heat
management measures. The length of the heatdiffusion path and the available actuator surface
determines the quantity of heat removed from theceramic volume. In terms of heat management
efficiency, the ring design is favored over the bulk
stack with respect to these parameters.
(=> chap. 5.3) Hence, ring-type actuator can run
much higher non-resonant frequencies than bulk
stacks without the risk of heat damage.
Ring actuators are more elaborate and expensive
than bulk elements.

2.6 Advantages of PIEZOMECHANIK’s piezo stacks

All structural components of piezo-actuators are
subject to potentially high mechanical loading not
only during operation, but also during handling andmounting.

● The electrical and mechanical stability of the

Be careful: piezoceramic components are mechanically sensitive devices.
● Local mechanical stress concentration creates
potentially “cracks” within the piezoceramics,
leading to a weakening of the electrical “stability”
of the ceramic.

● A major design topic is the handling of the neces-

PIEZOMECHANIK takes care about these risks byusing two different insulation concepts for different
actuator applications.

supply electrodes is important for the overall
reliability of a stack actuator when operated
dynamically.

sary insulation gap between internal electrodes
and supply electrodes of opposing polarity.
Point of attention is a potential local distortion ofelectrical field in the vicinity of such an insulation
region. By the piezo-mechanical coupling, thisleads to a local mechanical stress concentration
with subsequent crack generation and a potential
failure of the stack by electrical short-circuiting.

100%
internal electrode● on stack insulation (osi-design) (fig. 2.6)

Used for PIEZOMECHANIK’s
high voltage actuators (H)PSt 500 /1000
low voltage stacks (H)PSt 150
PZT-layers

The insulation gap is prepared on stack’s surface.
Therefore the piezoceramic cross ection of a stackis 100% electroded and activated homogeneously.
● highest actuator performance, high blocking

forces● no local field distortion etc.
● no local stress spots are induced

insulation
supply electrodeFig. 2.6 : on stack insulation (osi)-design, insulation is done
outside the active stack=> no cracks are generated etc.
Last, but not least: osi-designed stacks show highresistance to bending forces.

PIEZOMECHANIK

17

2.6 Advantages of PIEZOMECHANIK’s piezo stacks● in stack insulation (isi-design)

Used for PIEZOMECHANIK’s
PSt-HD 200 stacks
Piezo chips (H)PCh 150

insulation gap(no internal electroding)internal
electrodeThis is a widely used “classical” technique using an
insulation gap within the stack’s volume (=> fig. 2.7).
The stack volume is not completely activated.
Therefore performance reduction occurs for miniature stack cross sections.
Here occurs additionally the stress spot concentration problem. To avoid catastrophic crack generationand propagation different countermeasures areprovided.
One technique applies small notches or grooves tothe stack’s surface for getting a “soft” surface toreduce mechanical stress concentration.
Isi- stacks are less stable against bending forces
due to surface weakening by the notch-effect (incomparison to osi-stacks).
To improve the mechanical stability, isi-stacks aremostly used in a high-preloaded arrangement.

supplyelectrode+-Fig. 2.7 : in stack insulation (isi)-design, insulation is done
inside the PZT-stack● High cycle fatigue resistant electrodes

All piezo stacks show the supply electrodes
attached onto the piezo stack’s side faces.
These electrodes are subject to remarkable strain
and acceleration induced stress during dynamic
cycling.
Additionally a high electrical current loading
occurs, where special contact techniques areneeded to transfer high powers without losses tothe ceramic structure.

PIEZOMECHANIK is the expert for this kindof non-resonant actuator operation.
Suitable insulation and contact techniques
allow the reliable operation of its actuatorswith high power levels.

18 PIEZOMECHANIKPrecision Positioning

3

Piezo stacks are widely used for precision positioning tasks: a component shall be
moved with sub-micron accuracy from one position to another.
Most piezo-mechanical systems for this purpose show a special trait:
nearly no alteration of system’s internal force balance occurs during piezo action.
Only then, piezo stack’s expansion maximum is achieved.

Piezo stack actuators expand, when they arecharged up from a voltage Umin to Umax
The motion is reversed, when the actuator isdischarged. The (reasonable) maximum strain rates
are about 0.1 - 0.15 % of the actuator length.
Exaggerating strain by applying too high electricalfields is adverse to reliability.

Precision positioning is mostly done by voltage
control of piezo stacks.

For sub-resonant operation, the piezo stack motion
follows the applied voltage signal instantaneously.
The electrical behavior of piezo-actuators is like thatof a capacitor.

● load capability is reduced to 1/n

The stroke of a piezo-mechanical system can beincreased by lever-constructions, where amplifying
factors n of 10 are achieved without big efforts.
But keep in mind:● the compliance of the complete system increases

by n² compared to the original stack data.

3.1 Shift versus voltage characteristic
Correlation of piezo stack’s open-loop cycle over a
voltage range Umin - Umax - Umin leads to the hysteresis
diagram fig. 3.1.

strokelAttention:
do not over-interpret the open-loop stroke-/voltagediagrams, they are not high resolution calibration
curves for practice !
● The exact shape of the hysteresis cycle (fig. 3.1)

depends on the applied cycling voltage range.
For very small voltage variations, the response
looks much more linear rather than like a loop(small signal versus large signal excitation).
● An acceptable reproducibility of the hysteresis

Uminvoltage

Umax

Fig. 3.1: Schematic of a piezo stack’s stroke/voltage diagram
by cycling the stack within the voltage range Umin – Umax – Umin .

diagram is achieved only after reaching an equilibrium attained by cycling the system many times
while all other operation parameters like temperature, force and load are held very constant. If thecycling conditions are changed the system will
adjust towards a new equilibrium after the application of a sufficient number of cycles.

PIEZOMECHANIK

19

3.1 Shift versus voltage characteristic● The exact shape of the diagram fig. 3.1 depends

on the cycle time.
The slower the cycling is applied, the wider thehysteresis becomes due to the slow poling effectsof the piezoceramic structure. These poling effects
are also the reason for creep upon the applicationof a voltage step to the piezo stack.

strokel● When an open-loop random (non-periodic) settingof the voltage input is applied, a field of positions
is generated, where the cycling hysteresis is theenvelope of this field (fig. 3.2).
With other words: the final position of the stack
upon application of a distinct voltage level
depends on the “history” of stack’s operation(memory-effect for open-loop)

A lot of attempts have been made to overcome theneed for position feedback for piezo precision positioning, but the success was limited
A, algorithms have been developed for piezoactuator computer control to compensate for the“ferro-effects” of PZT ceramic like non-linearity,hysteresis and memory-effect.
B, electro-strictive ceramics have been used(=> chap. 8) instead of PZT ceramics.
C, charge or current control has been appliedinstead of voltage control (=> chap. 9.2)
All methods have been limited in effectiveness e.g.
to non-linearity etc. of about 1% and are not reallysuited for open-loop ultra-precise positioning.
Options A and B are not used in common practice.
Option C, is an interesting technique for dynamic
actuator operation for other reasons, but not for
precision positioning.

20 PIEZOMECHANIK

Umin

voltage

Umax

Fig. 3.2 : Field of positions by open loop random generationof voltage steps. The uncertainty in positioning by random
position setting is about 10% of the operation range, definedby Umin , Umax .

Notice:Even when an open-loop perfect actuator would beavailable, it only partially solves the problems ofprecision positioning.
In most cases, piezo stacks are prime movers ofcoupled mechanical devices for motion transfer.
In practice, these mechanics possess inherent
imperfections. Without high accuracy position
sensing and information feedback to the actuator,
these deficits are not recognized and are selfevidently not compensated for by open-loop
actuation.
Even the simplest adjustment procedure inlaboratory by turning the voltage control knob of amanually set voltage supply is a kind of feed-backcontrol: The operator checks for the correct result(e.g. a distinct interference pattern in optics)

3.2 Precision positioning by piezo stacks

The unique feature of piezo-actuators:
the infinitely high relative positioning sensitivity Piezoceramic converts an infinitely
small voltage variation into an infinitely small motion.
This has been proven explicitly down to the picometer range.

As seen in chapter 3.1. very high precision
positioning with an accuracy better than 1% ofactuators maximum stroke position-sensing andfeed-back control is needed.
Then the piezo-actuator is able to carry out thefinest corrections to come nearest to a desired
pre-set position. In this case, hysteresis, creep, andnon-linearities are ruled out automatically.

strokelopen-loop

closed-loop

Umax
0

+5 V
rated value
signalFig. 3.3 : Schematic comparison of the open loop and feedback controlled closed-loop operation of a piezo-system

Notice:A feedback philosophy handles only all
misalignments of the piezo-mechanics between
actuator and position sensor. Misalignments outside
the closed loop path are not compensated for.
Piezo-actuators with integral position sensor canhandle all internal “imperfections” (hysteresis, drift,
non-linearity) and all effects as long as they are
acting back to the actuator’s strain (e.g. load
variations).

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21

3.3 Limits of positioning accuracy

The accuracy of a piezo-positioning system isusually not limited by the piezoceramic or piezo
stack. This has been explicitly proven down to thepicometer range. Nevertheless, in a complex piezomechanical positioning system, there are influences
outside the actuator resulting in a potential limitationof accuracy.
● quality of electronics:

any noise and electrical fluctuations will be converted in its mechanical equivalent● the accuracy of the position sensor and its loca-

tion within the piezo-mechanical system(extension of the control path)● quality of the attached mechanical transfer-mechanisms Microscopic friction, stick-slip effects
in bearings, hinges, preload mechanisms will limit
the overall accuracy of the piezo-mechanicalsystem● Tilting of stack’s end faces:

A piezoceramic stack shows, to some extent, atilting of its end-faces during the axial expansion.

Simply laboratory style optical arrangements witha glued sandwich of substrate/piezo stack/mirror
work tilt-free only over short shifts (=> 7.6).
Tilting can be reduced by mechanical preloadingof the stack (=> chap. 4.9). A tilting up to severalµrad / µm shift occurs typically. Consequent cancellation of tilt for a longer stroke is only possibleby adding a guiding mechanism.
● piezo-based stabilization circuits

A special kind of precision control is the stabilization of position sensitive physical effects.
The optical output power of laser resonators
depends on the alignment of the whole optomechanical set-up. To keep the resonator in its
power maximum despite misaligning influences
the optical output power is monitored. By applying a proper tracking algorithm to discriminate thepower maximum, the laser can be kept by piezoin its (relative) power maximum (see: dithering
principle, optical tracking, OptiSeek controller).
Similar set-ups are also used for free optical fiber
coupling.

Tips to catalogue data
● The maximum actuator shifts (strokes) in data

sheet are only valid under constant load conditions (no force variation !).
● Two values for l are stated in the data sheet

A, for the unipolar activation 0 V / + Umax
B, for semibipolar operation - Umin / + Umax
The semi-bipolar operation increases the openloop stroke of a stack by 20 - 30 %.
Any kind of stack actuator is suitable for semibipolar operation at room temperature.

22 PIEZOMECHANIK■ Example
Piezostack PSt 150/5x5/20
Unipolar operation 0 V/ + 150 V: stroke 20 µm e. g.
with a PIEZOMECHANIK LE 150 unipolar
power amplifier
Semi-bipolar operation - 30 V/+150 V: stroke 27 µm
with a PIEZOMECHANIK SVR 150 amplifier

Motion and Forces

4

4.1 Beyond simple positioning

New applications of piezo-actuators are often requiring force generation together
with the variation of position.
Attention has to be paid then to a few additional aspects compared to chapter 3.

To select a suitable piezo-actuator careful analysis of the actuated mechanics by
the user is required as follows;A, required mechanical shift lmech to move the mechanics properly?
B, force level Fc within the mechanics at the beginning of piezo action?
C, total force level within the mechanics at the end of piezo action at maximum voltage?
The difference of B,C defines the required force generation Fmech by the piezoactuator
The ratio lmech /Fmech is the compliance (inverse stiffness) of the mechanical system

PIEZOMECHANIK

23

4.2 Examples for force /shift relations

Fig. 4.1:
Gravitational mass load of a piezo-actuator
The force level Fc remains absolutely constantduring piezo action. The maximum piezo shift lmax
is achieved (according data sheet).
The piezo-actuator generates a translatoric mechanical energy Fc lmax .

FFmech = 0

Fc

0

lmax

Umin

Umax

l

Applications: precision positioning of heavy loads
like telescopes, precision manufacturing machines.

FFmech

Fc

0

lmax

Umin

Umax

l

F

FmechFc

0lmech < lmax

Umin

Umax

l

F
FsealFmechFeFc

0lmech < lmax

Umin

Umax

24 PIEZOMECHANIKlFig. 4.2:
Piezo-actuator expands against the counterforce
of a weak spring(elastic medium with high compliance/low stiffness)
The actuator is preloaded with a force Fc.
The expansion of the piezo-actuator leads only to asmall increase Fmech of the force balance.
It is found, that the piezo-actuator produces (nearly)
its maximum shift (data sheet).
A mechanical energy Fc lmax is produced (firstorder). Application: common optomechanics withreset springs.
Fig. 4.3:
Piezo-actuator produces a shift against a strong
spring(elastic medium with low compliance / high stiffness)
The actuator is preloaded by the spring with a force
Fc. The expansion of the piezo-actuator leads to aremarkable increase Fmech (= elastic force Fe)of the total force balance. The piezo shift lmech is
reduced compared to the data sheet value. The
total energy generation is (Fc + ½ Fe) · lmech,½ Fe l is the elastic energy put into the system
by piezo action. Application: motion control.
Fig. 4.4:
Valve actuation: piezo-actuator shift closes valve
The actuator is again preloaded by a hard spring
resulting in a base force Fc and an elastic force Fewhen moving. The final step of the voltage swing
Umin - Umax is used to build up the sealing force(press fit). This final force variation Fseal is not accompanied by a motion (so-called blocking condition).
The total achievable stroke is again less than the
maximum shift specified in data sheet.
Fig. 4.1 – 4.4: Different kinds of stroke-force profiles ofmechanical arrangements

4.3 Piezo-actuator as an active spring

From a physical point of view, the piezo stack is anactive spring:
When a piezo-actuator generates an external force
F, it does not only compress the mechanical partner, but the force acts back on the stack itself.
This “self-compression” of the actuator reduces theeffective external stroke of a piezo stack correspondingly (depending on actuator’s stiffness).

ance. Because no shift can be generated, the complete piezo activation is used to build up a force
variation.
This maximum force generation limit of a piezo
stack is called “blocking force”.
In data sheet, the max. blocking force for maximum voltage ratings are shown (both, for unipolaror semi-bipolar activation).

Blocking force
The force generation limit is reached, when thepiezo-actuator is clamped rigidly with zero compli-

The blocking force Fblock of a piezo stack
depends on stack’s cross sectional area A(fig. 1.2), but not on length L.

4.4 Selecting a piezo stackYou have analyzed your mechanics and application with regard to the required stroke-force activation
profile (Fmech , lmech), no dynamic forces (=> chap. 4.1, => chap. 10).
■ Example to 1st stepYour mechanism needs a preload Fc of 2 kN and aforce generation of 1 kN.
This is covered by piezo stacks PSt 150/10x10/xx
or PSt 150/14/xx VS 20 actuators with casing

1st step:
Select the suitable actuator group with respect toits force balance, which is related to actuator’s
crosssection.
● sufficient high load capability● data sheet blocking force at least double the

2nd step:
Within the actuator group selected according step
1, a suitable actuator length is chosen by numericalor graphical means .

needed force generation Fmech for yourapplication.

A, numerical solution
Remember that a piezo-actuator is an active spring!
The stroke is reduced the more as the ratio oflmech ≤ lmax (1 – (Fmech / FBlock))Fmech /Fblock increases. To get the needed strokelmech for activating your mechanics, the actuatorwith data sheet stroke lmax is required.

lmax = lmech FBlock / (FBlock - Fmech )lmax (max. stroke) and Fblock (blocking force) are found in actuator’s data sheet.
lmech, Fmech actuation data, required by the attached mechanics

PIEZOMECHANIK

25

4.4 Selecting a piezo stack

B, Graphic solution
Fig. 4.5 shows a coordinate triangle defined by thedata sheet values lmax and Fblock of a potential
piezo-actuator candidate.
The actuation data lmech , Fmech define an origin
based stiffness line with the intersection with thetriangle at point A.
If the coordinates A (l, F) of an actuator are
equal with your requirements (lmech , Fmech), thenthe actuator is suitable to drive your mechanics.
Usually, an actuator is selected to keep the point A
in the upper half of the triangle.

Comments:● The above mentioned strategy is a linear approximation of the more complicated ferro-electric
behavior of a piezo stack. Utilize a reasonable
tolerance range and do not aim for unreasonable“point-precision”.
● Surprise is sometimes created by the fact, that aheavy, but constant load does not reduce actuator’s maximum stroke.
The reason is rather simple: the load condition isapplied to the piezo stack before operating thestack e.g. a mass load or a low stiffness preload
is applied during mounting the system!
This compression of the stack creates the necessary counterforce to bear the load, so the system
is in force equilibrium before starting the piezoaction.
No additional force generation  F by piezo
needed => full piezo stroke!
● When actuator and the driven mechanics show

the same stiffness Sactuator = Smech
lmax

Smech

Smech = 0

Smech = SAktor
l
50%

A

E = 1/8  lmax Fmax
50 %F 50 %

FBlock

Smech = Fig. 4.5 : stroke/force-triangle with intersecting stiffness-line
defined by the operated mechanics.

26 PIEZOMECHANIKThe effective shift and generated force show 50%of the data sheet values.
This configuration allows the highest elastic energy transfer E

Dynamic operation:
For dynamic operation, acceleration forces of theinvolved masses need to be taken into account.
A good method for selecting an actuator is to aim
for a resonance frequency of the system to beat least twice the desired maximum operation
frequency.

4.5 Force generation

In a formal way, the blocking force is defined as theachieved force generation of a stack when it isclamped with “zero compliance”. “The actuator
does not move, when a voltage is applied.” In realnature, all materials show a limited elastic modulus
that does not allow infinitely high stiffness bypassive means.

But using a closed-loop active arrangement, theblocking situation can easily be verified as shown
below: A piezo-actuator is equipped with strain
gauges and mounted into a mechanical press.
A load cell is applied in series with the actuator.
The whole system is electrically operated with
PIEZOMECHANIK’s feedback control positioning
system, PosiCon 150.

D
E

A
B
C

Fig. 4.6 : arrangement for blocking force determination with a PSt 150/10x10/40 piezo stack

A Piezo stack (green)
B strain gage on stack
C load cell

D compression springs
E position control electronics PosiCon 150

PIEZOMECHANIK

27

4.5 Force generation

Experiment:● Used piezostack: PSt 150/10x10/40,
maximum operating voltage 150V
a, Zero-position of piezostack defined by setting of
the “Offset” voltage
Case 1:0 V unipolar operation
Case 2: - 30 V semi-bipolar operationb, “0 V” to input of PosiCon electronics(closed-loop-mode)
With this condition, the control-loop tries to keep
stack’s zero-position constant, when load force
varies.

Results:● The piezostack PSt 150/10x10/40 shows thefollowing maximum blocking forces
Case 1: unipolar mode(equivalent 0 V / +150 V activation) : 6500 Newtons
Case 2: semi-bipolar mode(equivalent -30 V/+150 V activation) : 7800 Newtons● Test procedure: The pressure load on the stack is

now increased continuously and monitored by
the load cell. The position of the actuator is held
constant via closed-loop-control (see b).
=> the piezo voltage is increased correspondingly
by the PosiCon-electronics to compensate forthe compression of stack’s length. The load limit
is reached, when the compensating voltage
reaches + 150 V.
This arrangement reflects exactly the blocking
condition: force variation within the piezo-mechanical system without a motion of the actuator(virtually infinitely high stiffness of actuator).

force F
(kN)
8

Fblock, max., s-bipol
Fblock, max., unipol● A linear relation between the force variation andcompensating voltage has been found for thePSt 150/10x10/40 stack (fig. 4.7).
● The blocking force is equivalent to the maximum

load variation on a piezo stack that can be compensated for by a feedback closed-loop position
control.
■ Example
A piezo stack PSt 150 (max.operation voltage+150 V) is set to a distinct position by 90 V activation. This position shall be kept constant by closedloop operation.
The maximum increase of load force what can becompensated for corresponds to the “60 Voltsblocking force” of the stack.

28 PIEZOMECHANIK

-30

0

+150

UPiezo (V)Fig. 4.7: Blocking force versus excitation voltage for piezo
stack PSt 150/10x10/40 (uni-polar and semi-bipolar operation
range)

4.6 Stiffness

A very significant feature of a piezo-mechanical actuator is the dependence of its
stiffness (inverse compliance) on the electrical operating conditions.

Test arrangement:● A piezo stack PSt 150/10x10/20 (with straingage) is compressed by a 2 kN axial load force
and the resulting compression is measured in asimilar arrangement as shown in fig. 4.6.
The compression of the stack is measured via thestrain gage together with a DSM 01 strain gage
amplifier or the PosiCon 150 electronics in its
open-loop mode.

● The actuator stack is subject to a compressiveload
A: with the leads short circuited
B: with the leads open : fig. 4.8
The load force is monitored by the load cell
(fig. 4.6).

remains within the stack. Hence a voltage at theleads is generated by mechanical means!
This is equivalent to the electrical field within thepiezoceramics. This electrical field stabilizes thepiezoceramic against compression.

A

B

Fig. 4.8 : Piezostack PSt 150/10x10/20 with closed (A) andopen (B) leads

Results:
Two different stiffness values F/l have been found(A) => approx. 200 N/µm
(B) => approx. 450 N/µm
Physical background:
The reason for the varying stiffness is the original
piezo-electric effect:
electrical load generation by mechanical pressure.
In case (A), this charge can flow and is removed
from the stack, whereas in case (B) the charge

Consequences for practice:
The situation (A) with closed leads is equivalent theoperation of piezo stacks by voltage control.
Mechanically generated electrical charge flows
towards the voltage supply to keep the actual voltage constant. The mechanically generated electricity
is dissipated!
Case (B) is equivalent the charge- or current control
philosophy (=> 9.2).
The mechanically induced electrical charge remains
in the actuator, the actual actuator voltage varies
with the load variations.
The advantage of the lower open-loop complianceby current control is preferentially used in dynamic
motion control.
The highest system stiffness is achieved by closed
loop position control (virtually infinitely high stiffness, (=> 4.5)). However, the response-time (bandwidth) of feedback controlled systems is slower
when compared to the open-loop current control.

PIEZOMECHANIK

29

4.6 Stiffness

Piezo-actuators with casing
The stiffness values shown in data sheet are
defined for force coupling via the end-pieces of theactuator.
When actuators with casing are mounted via thecasing tube (by clamping or front threads of thepiezo cartridges FPSt), a reduction in the overall
stiffness must be taken into account, because theforce path involves both the stack and the casing.
Notice:The overall stiffness of a piezo-mechanical systemdepends on all involved mechanical parts :“Weak” points are often poorly designed coupling
joints.
The implementation of “motion magnifiers” likelevers reduces the overall stiffness for basic
physical reasons:Hybrid systems with motion magnification(factor n) reduces● the blocking force down to 1/n.
● the total stiffness of a piezo-actuated systemdown to 1/n² !
(compared to actuator’s original data)

30 PIEZOMECHANIKComments on data sheet
A voltage controlled piezo stack shows approx.
20% of the stiffness of a steel rod of same
dimensions.
The elastic property of poled piezoceramics
differs remarkably from common materials● it is anisotropic (depends on the direction offorce and poling axis)● it depends on the applied field variation(small signal versus large signal excitation)(=> 8: PZT materials data)● stiffness depends to some extent on the
pre-load conditions
The data sheet values for stiffness are definedfor small-signal variation and voltage control.
Keep a tolerance range of +/-20% in mind.
Catalogue data are best used for a kind oftrend analysis.

4.7 Force limitations, load capabilities

The maximum load force shown in the data sheet isthe steady load Fc according chapter 4.2.
Within this preload range, the full motion and force
generation capability of an actuator can be used.
For higher preloads Fc , the PZT-ceramic performancedecreases as a consequence of de-poling effects(reversible!). Mechanical damage does not occur(Damage threshold up to 10 times larger than the
de-poling limit)
Only for very large aspect ratios length /diameter> 15, bending and buckling of the stack becomes aconcern.

4.8 Dynamic operation
Piezo stacks can be operated with very high dynamics with acceleration levels of
thousands of g.

Mechanical aspects
A rapid activation of a piezo stack creates potentially tensile forces by negative acceleration.
(e.g. when slowing down stack’s velocity after apulse excitation or by a stack’s contraction).
Even for an otherwise unloaded stack pre-stressing
is recommended, when switching rise-/fall-times
below 1 msec occur.
The necessary preload level can be high as 50% of
the maximum load level depending on the individual
configuration.
Generally, for every highly dynamic application, thestack design needs to be adapted accordingly.
Standard actuators from catalogue will fail.

Electrical aspects
Use power supplies well-matched to your application
with respect to voltage and current levels (power).
Oversizing electronic’s performance leads to potential mechanical or electrical overload of the piezomechanical system.
Take care for correct electrical installations: pulsed
actuator discharge by accidental short circuiting is aproper way to kill the stack.

PIEZOMECHANIK

31

4.9 Mechanical preloading (pre-stress)

Data sheet for the mechanical properties of PZTceramics show a small tensile load capability of afew percent of the compressive damage threshold.
Nevertheless it is strongly recommended to avoid
piezo-mechanical designs that systematically place
the stack under a tensile load.
Even when the regular operation keeps the actuator
within the “safe” tensile stress area, any accidental
mechanical or electrical overload (by external
shocks or irregular signals) can kill the ceramic
stack.
A piezoceramic stack is mainly a pusher-element:
Any demanding application uses mechanicalpreloading (= pre-stress) to keep a stack in any
situation and moment under compression.
(antagonistic operating principle).
Preload systems are mostly based on passively
acting force-storing principles like mechanical,
hydraulic or pneumatic springs.

32 PIEZOMECHANIKDesigning a preload mechanism:● The maximum stroke of a piezo-actuator shall not
be reduced by the preload mechanism.
According chap. 4.2, the spring constant (stiffness) of the preload spring needs to be very low:a few percent of piezo-actuator’s stiffness inmaximum.
● The preload force shall be sufficiently high toaccelerate all incorporated masses sufficiently
fast during the actuator’s contraction to avoid
tensile loading of the ceramic.
The dynamic force Fdyn can be estimated by thewell know acceleration/force-law
Fdyn = m l/t²
Notice:the preload mechanisms shall not only take into
account the force balances during regular operation, but shall also stand potential external shocks.

4.9 Mechanical preloading (pre-stress)

VSF

Fig. 4.9. Internal preloading:
The preload mechanism VS is integrated into theactuator casing. Typical configuration of actuatorswith casing like PIEZOMECHANIK’s PSt … VSelements.
Externally applied tensile forces can be handled up
to the preload level.
Dynamic cycling of an external mechanic leads toforce loads with alternating sign. Coupling joints
need careful design to handle this situation without
fatigue and play/backlash.

moved
mechanics

piezostack

+F

moved
mechanics

VS

Fig. 4.10. External preloading:
The complete mechanics is pre-loaded by the
spring VS towards the stack.
The whole arrangement is under permanent compressive load, no alternating force directions occur
during cycling. Backlash is avoided.

piezostack

VS 1

piezostack

+F

moved
mechanics

VS 2

Fig. 4.11. Split preloading:Two preload mechanisms are implemented:- the individual preload of the stack (VS 1)- the system’s preload (VS 2).
This setup has advantages for piezo-mechanicalsystems with a high mass load:
The mechanical coupling between actuator andmechanics is only compressive.
Preload VS 2 can be kept low according the regulardriving conditions.
Preload VS 1 acts as protection for the piezo stackfor handling irregular high tensile forces (within thesystem).
In this case, actuator and mechanic parts can separate upon tensile stress.
VS 1 keeps the stack safe and sound.

PIEZOMECHANIK

33

4.9 Mechanical preloading (pre-stress)+F

piezostack 1

moved
mechanics+F

piezostack 2

Fig. 4.12. Active preloading / reset:
Instead of the actuator-passive spring combination,
two complementary acting piezo-actuators are used(differential drive).
The whole system is mounted into a mechanicalsupport frame with high static stiffness.

Actively preloaded systems are by definition symmetrical push-/pull-systems. The static preload
force level can be kept low even for high dynamics.
Therefore, higher external payloads are acceptable.
The advantages compared to passive resetting are:● compensation of thermal drifts● higher bandwidth
Even, when two actuators need to be powered, theoverall power consumption can be kept low byusing electronics with energy recuperation.
Nevertheless, the total efforts for an actively preloaded system are higher than for simple conventional drive.

PIEZOMECHANIK actuators with integral
preloadPIEZOMECHANIK offers all kinds of piezo
stacks in a cased version with internal preload.
The standard preload shows forces of about
10 - 20 % of the maximum load. This design
covers a very wide range of applications.
Preloaded actuators with casings are much
more rugged than the bare ceramic stacks andare more likely to withstand “rough” handlingand operation, or the impact of other environmental influences.
On request, PIEZOMECHANIK provides actuators with increased preload levels up to symmetrically acting push-pull arrangements withregard to the force balance.

34 PIEZOMECHANIKDynamic operationof piezo stacks

The expression “dynamic operation” is used for
operation modes where the actuator and the whole
piezo-mechanical system are facing additional reactions compared to a nearly static driving situation.
Most standard actuators are designed mainly for
positioning with a slow shifting of components fromposition A to B.
Dynamic operation adds effects like higher acceleration rates and forces superimposed on to the staticforce balances. The increased electrical power consumption results in self-heating of the actuator
stack.

5

Application examples for high dynamic actuator
excitation are: scanning, motion control, vibration
generation, pulsed operation, fuel injection, shock
generators and shakers.
Piezo-actuators are mostly operated non-resonantly
and can cover therefore a wide frequency range
from DC up to > 10 kHz. This is in contrast to resonating systems like ultrasound generators.
Those are operating continuously on a single highfrequency > 20 kHz with large amplitude (=> 5.4/5.5).

5.1 Definitions
Dynamic operation has two aspects● Short-term effects relevant even for a single

occurrence of excitation.
The short-term time balance of a piezo activation
deals mainly with acceleration effects and related
forces. The achievable motion profile is also
determined by the peak power capability of thepower supply.

■ Examples:
1. Pulsed operation (square wave excitation) of apiezo stack shows a huge short-term power level
during the switching rise and fall.(Power levels up to
the >> kW range).
On the other hand: when the repetition rate is verylow (e.g. 1/sec), the average power is rather small.

● Long-term effects related to permanent

dynamic cycling.
The long-term dynamic operation of a piezoactuator defines the mean electrical power consumption of the system. This power is to be provided by the electronic supply.
Points of consideration are the self-heating of thepiezoceramics and potential high cycle fatigue
problems of the mechanical set-up.

2. For a periodic excitation profile (e.g. harmonic
waves), the peak power and average power of the
dynamic operation shows a fixed ratio.

PIEZOMECHANIK

35

5.2 Short-term excitation

The dynamic response of a piezo-actuator depends
on how fast the actuator capacitance C is electrically charged
Actuator velocity v ~ I = C dU/dt
dU : variation of piezo voltage during charging
Actuator acceleration dv/dt ~ dI/dt = İ
dt : electrical charging time of capacitance C(valid for the sub-resonant excitation of piezo stack)■ Example:
A piezo-actuator with capacitance C = 10 µFarads
generates a displacement of 100 µm
by a 0 V/ +200 V excitation. Different charging times
are considered
Charge time t:
100 msec
1 msec100 µsec

Charge current I Q/t:
20 mA
2 Amperes

20 Amperes

Electric power (1/2 CU )/t:
2 Watt200 Watt

2 KiloWatt

Acceleration (constant):
0,02 m/sec²
200 m/sec²

20.000 m/sec²

2

The maximum displacement velocity by piezo
ranges over a few m/sec(requiring highest acceleration levels)

Mechanical requirements:
Design rules for a piezo-mechanic setup to transfer
dynamic motion efficiently● low compliance of the attached mechanics● the natural frequency of the mechanics shall belarger than twice the desired operation frequency● sufficient durability of mechanical couplingelements to high-pressure levels (acceleration
forces)Preloaded actuators will be needed in all cases
involving high dynamic excitation.
For extreme acceleration excitation (activation time<< 1 msec), specially adapted actuator designs areneeded beyond the standard techniques. Standard
actuators will fail.

36 PIEZOMECHANIKElectrical requirements:
An actuator’s maximum velocity is defined by power
supply’s peak current.
An actuator’s acceleration response depends on
power supply’s slew rate (band width).
If very high dynamic excitation with high peak
power requirements is expected, switching
amplifiers or high current 2-level switches are used(not linear amplifiers).
See PIEZOMECHANIK switching amplifiers RCV,High Voltage Switches: HVP.

5.3 Long-term operation

Prior to the analysis of long-term dynamic actuator operation, the short-term
dynamics within the individual cycle need to be discussed (see chap. 5.2).
Mechanics:
High frequency mechanical cycling rapidly results inhigh cycle numbers and the question about structural durability of the whole piezo-mechanicalsystem (e.g. material fatigue etc.).
To increase the reliability of such a construction,
there must be a perfect match of its design topiezo-specific design rules. “Compromises” violatingsuch design-rules will simply result in failures duringlong-term operation.

the “internal structure” of the ceramics cannot
move, therefore no “structural friction” is present
within the ceramics.

Electrics:
The average power consumption Pav of a cycled
piezo-actuator can simply be derived from thecharge/discharge rate (frequency) f and the energy
content of the piezo-actuator applied per activation
cycle.

Piezo stack’s temperature is defined by the equilibrium between heating power (energy dissipation)
and applied cooling power (heat management).

Pav = ½ CU² f
U voltage level of charged actuator
C actuator’s capacitanceIn a similar way, the mean (average) charging
current Ī can be determinedĪ = Q f = CU f
Q electrical charge quantity contained in a
powered stack
Notice: actuator’s stroke is proportional Q
Continuous wave harmonic sine-oscillation shows afixed ratio Īpeak : Īav = .

Further, the losses disappear nearly completely,when the piezoceramics are operated under cryogenic low temperature conditions. The ferroelectric
nature of piezoceramics is “frozen” with the consequence of strongly reduced capacitance, strain andlosses. Energy dissipation and self-heating are noconcern.

Standard designed actuators for positioning do notcontain explicit heat management measures. Power
cycling can therefore only applied short-term until
the stack has heated up to a distinct limit. Hightemperatures will reduce actuator performance andreliability.
PIEZOMECHANIK offers, for its cased actuators,
the heat-management “thermo-stable” option for
long-term power operation (=> chap. 6.1).
The temperature aspect can further be handled byusing suitable PZT-ceramics with a wider operating
temperature range.

clamp mount

Thermal aspects
During cycling piezoceramics, electrical energy is
dissipated into heat due to “internal friction” of themoving piezoceramic structure.
Approx. 5 - 20% of the electrical energy input isconverted into heat (fig. 5.1).
The loss mechanisms are rather complex and are
not represented in a realistic way in the standard
material data sheet for piezoceramics.
The heat generation depends to some extent on themechanical operating conditions (stroke-force).
Blocked actuators show rather low losses, because

Fig. 5.1: Thermal image of a dynamically cycled high voltage
actuator, clamped at its end faces. Environment: ambient air
convection. Notice the cooling effect at the end-faces due tothe clamping mechanics
PIEZOMECHANIK

37

5.4 Typical operating frequencies

A standard (incomplete) question is:what frequencies can be achieved by (non-resonant) piezo action?
The necessary counter-question is this: for what
amplitudes? What other operating conditions?
Another typical misinterpretation of data sheet parameters is concerning the “resonance frequency”:
The actuator cannot be operated up to this limit
with full strain !

For technical reasons in most cases, the operating
frequency needs to be kept well below resonance!
The main limitation for the operation frequency isdefined by the power consumption (frequency andamplitude!) and the self-heating of the actuator
stack.
An actuator’s shape and volume/surface ratio rules
the heat transfer rate as shown below.

■ Example:
Self-heating and actuator dimensions

oscillation

Different kinds of low voltage bulk and ring stacks(H)PSt 150 made of same PZT-material and layerstructure have been mounted with one side to a
substrate, the other side is moving freely (fig. 5.2).
The temperature of actuator’s top is monitored.
No special cooling means are applied (free air convection)
The elements are cycled @ 0 V/ +150 V.

temperature sensor
bare
PZT
stack

air 20 °C

metal base 20 °C

Fig. 5.2: Schematic test arrangement for the self-heating ofdifferent kinds of low voltage piezo stacks and rings

Actuator type

dimensions

equilibrium
temperature@ 100 Hz

operating frequency
for heat up to 80 °C

Bulk stacks
PSt 150/2x3/20
PSt 150/5x5/20
PSt 150/10x10/20

2 x 3 x L = 18 mm
5 x 5 x L = 18 mm
10 x 10 x L = 18 mm

27 °C
42 °C
60 °C

1,300 Hz340 Hz160 Hz

38 °C
39 °C

440 Hz430 HzRing-stacks (hollow cylinders)
HPSt 150/14-10/12
Ø 14 x Ø 10 x L = 13.5 mm
HPSt 150/20-15/12
Ø 20 x Ø 15 x L = 13.5 mm

38 PIEZOMECHANIK

5.4 Typical operating frequencies

It is easily seen that the self-heating phenomenon isless critical for ring type actuators and tiny stacks.
The more bulky stacks are, the poorer is the heattransfer.

Notice:Bulky stacks can show a remarkably higher temperatures in the ceramic’s core than on the surface.
A proper heat-management technique will allow anincrease in frequency ranges (=> chap. 6.1).
The achievable maximum amplitude oscillation
frequency limits are in the range of several kilohertz
range for small and medium sized elements.

Oscillations with reduced strain
Power consumption and self-heating depend not
only on frequency, but also on the strain applied tothe actuator.
When the piezo stack is operated at reduced voltage levels, they can run much higher frequencies.
For a lot of applications, it is attractive to combine ahigh voltage actuator with a low voltage/high current
power supply.

energy content of the actuator from cycle to cycle
to create a forced motion.
There is no mechanical energy-storing-mechanism
from cycle to cycle within the actuator, when operated non-resonantly. Therefore a high electrical power
is needed to drive the actuator resulting in correspondingly high losses => self-heating !

■ Example:
A ring-actuator HPSt 1000/15-8/20 VS 22 thermostable is combined with a large bandwidth amplifier
LE 150/100 EBW a +/-2 µm oscillation can be generated up to about 10 kHz.

A good resonator like an ultrasonic device has amechanical energy storing mechanism:
the mechanical resonance.
With a rather low electrical energy transfer (lowlosses !), a huge mechanical oscillatory energy canbe piled up over a distinct quantity of cycles. This
results finally in a large oscillating amplitude.

Ultrasonic oscillators can run very large amplitudes at high frequencies > 20 kHz.
What is their trick? They are using an enhancementeffect by mechanical resonance.
Hence, they can only run a single fixed frequency.
A normal non-resonantly operated piezo-actuatorneeds to charge /discharge the complete electrical

How behaves a normal actuator at resonance:
The resonant accumulating effect is present tosome extent, but it is much weaker than for an optimized ultrasonic device (up to 100 times smaller).
The background is the use of different kinds ofpiezoceramics used for actuators resp. ultrasoundgeneration (=> chap. 8) due to the different application profiles.

PIEZOMECHANIK

39

5.5 Resonance

The shorter the stack is, the higher the natural frequency of a piezo stack’s axis is. For piezo-chips
with a length of a few millimeters it is >> 100 kHz.
Very long stacks for long strokes can show lower
values in the kilohertz range. Natural frequencies
and resonances describe an inherently oscillating
system. The equivalent circuit diagram of a resonating piezo is therefore no longer a pure capacitor,
but an oscillator circuit (capacitor + inductance).
Actuator based piezo-mechanical systems do notshow only one natural frequency, but a variety ofthem with potential influence on the axial displacement (cross-talk).
For a lot of applications it is important that thepiezo-actuator shift strictly follows the input signal.
In the case of resonances, there is a phase-shift
between the excitation signal and mechanical reaction remains.

● Any attached mechanics show natural frequen-cies that will be super-positioned with the original
actuator motion. By using piezo-actuators, theseresonances of the coupled mechanics can be
excited or damped (motion control). Resonanceexcitation leads to large amplitudes with reduced
power consumption.
Resonant excitation of structures is used withminiature mechanics (MEMS, piezo motors).

amplitudelA● Piezo stacks with a high aspect ratio length /diameter show a bending mode with a lower
natural frequency than the axial mode.
● Piezo elements also show natural frequencies ofthe stack’s diameter. When the diameter is remarkably larger than the stack length, then the diameter resonance is lower than the axial mode.
● Common piezo-actuators for non-resonant ope-

ration are made from so-called soft piezoceramics
with a high strain efficiency. This type of ceramicshows a rather high mechanical damping.
Therefore, a piezo stack is a rather “bad” oscillator, expressed by a rather low quality factor. In
the case of resonance, the resonant amplitudeenhancement is typically < 10 (see fig. 5.3).
In contrast to the broadband piezo-actuators,
ultrasonic devices are a single frequency resonating system, using “hard” piezoceramics with very
low mechanical damping (quality factor> 1.000)

40 PIEZOMECHANIK

B
exciting
frequency

Fig. 5.3: Schematic of resonance behavior of oscillators withsame natural frequency, but different damping.
(A) Low damping, high quality factor: ultrasonic devices(B) High damping, low quality factor: soft PZT-actuators

Precision positioning set-ups with closed loop feedback control are usually operated well below thenatural frequencies of a piezo-mechanical system toavoid feedback problems due to electro-mechanicalphase shifting.

5.5 ResonanceResonance frequencies are usually defined for
actuators with one side fixed to a base and theother end freely moving. (Freely suspended

actuators with both sides free will show the double
resonance frequency). The electrical excitation isusually based on low field variations.

When an external mass is added to a piezoactuator, its resonance frequency will be reduced.
The resonance frequency fA-M of such an actuatormass system can be estimated:● the added mass Mext is significantly larger than

● the added mass Mext is small compared toactuator’s own mass MA

the actuator mass => the simple spring/mass formula is valid
fA-M = 1/2  (SA/Mex) 1/2
SA actuator stiffness(spring rate = inverse compliance)

fA-M = fres Meff/(Mex+Meff)
Meff : effective mass of actuator ~ ¹/³ MA

Magnifying mechanisms:
A motion magnified actuator hybrid system (factor n)shows a reduction of stiffness by a factor 1/n²
compared to actuator’s original value. Resonancefrequencies are therefore strongly reduced!

Catalogue data
The resonant response of a stack depends onmounting conditions (e.g. mechanical prestress). Variation of PZT-materials properties
due to the manufacturing process have some
impact on the electro-mechanical behavior of
the ceramics.
Data sheet values and calculations show
therefore pronounced tolerances.

PIEZOMECHANIK

41

Extended functionality,
options

The performance of piezo-actuators for various
applications is not only defined by piezoceramics
used. It depends on a lot of other features like thefinish of the stack structure or other added features.
The most frequently requested actuator upgrades
concern:

6

PIEZOMECHANIK offers comprehensive assistance in all cases where special solutions are
required to cope even with “exotic” piezoactuator applications.
Ask the experts at PIEZOMECHANIK.

● improved heat management● position sensing

6.1 Heat management “Thermostable”
The dynamic charging power of a piezo-actuator ispartially dissipated into heat. The actuator temperature reflects the equilibrium between heating by
power dissipation and cooling by the heat transfer
to the environment. Too high temperatures interferewith actuator performance and reliability.
Standard versions of piezo-actuators are primarily
designed for low dynamic positioning tasks and are
not provided with extra heat management features.
PIEZOMECHANIK offers the option “thermostable”
to handle heat generation by dynamic operation.
Heat is effectively removed from the ceramic stackand transferred towards the casing.
The “thermostable” casing is made from thermallyhigh conductive metal (like copper, brass, aluminumetc.) providing effective heat sinking contact to theenvironment.

manner. Heat-management is recommended for all
applications using power amplifiers like the LE or
RCV-machines.
■ Example
A high voltage actuator PSt 1000/16/150 VS 25 withthermo-stable option + air fins + forced air coolinghas been cycled dynamically with maximum stroke(150 µm) at about 800 Hz.
The casing-temperature was held at about 80 °C.
The actuators ceramic core temperature was about
20° higher (measured via its electrical capacitance).
A standard actuator of the same type without heatmanagement would reach its temperature limit atabout 150 Hz.

Just the simple mounting of a “thermostable”
actuator to the operated mechanics provides aremarkable cooling effect.
For very high thermal loads, all common methods
for enhanced cooling can be applied to the actuatorcasing like forced air cooling (incl. addition of airfins) or liquid cooling (fig. 6.1).
Notice:
The thermo-stable option does not alter actuators
dimensions! Upgrading an existing standard based
piezo-mechanical system with “thermostable” modified elements can be done in a straight forward
42 PIEZOMECHANIK

Fig. 6.1: Various types of actuators with thermo-stable heat
management Air fin corpus can be added

6.2 Temperature sensing

For distinct applications, it is useful to explicitly
check the temperature of the ceramic stack.
For temperature measurements, PIEZOMECHANIK
provides options such as thermocouples or Pt 100/
Pt 1000-thermo resistors, mounted to the ceramic
stack’s surface.

Notice:Information about the volume temperature of an
actuator can be derived from electrical capacitanceanalysis (=> chap. 7, Operating instructions,=> chap. 8, Material properties).

6.3 Low temperature operation
Piezoceramic stacks can be operated down to thelowest temperatures near absolute zero.
Standard actuators run down to - 40 °C.
For operation at even lower temperatures, modifications maybe necessary and are offered on request.

E. g. piezo stacks can be wired with poly-imide coated manganin-leads.
Due to the reduced thermal conductivity ofManganin, the thermal loading of the cryo-station isthen kept low.

PIEZOMECHANIK

43

6.4 Position sensing

A pre-requisite for ultra-precise positioning via
closed-loop feedback control is the combination of
the actuated system with a position sensor option.
For position sensing, PIEZOMECHANIK offers highquality strain gages applied directly to the surfaceof the piezo stack. Usually, complete 4-active-gridbridges are used to ensure temperature compensation and high sensitivity (Fig. 6.2 - 6.4).
By closed loop feedback controlled positioning, thenon-linearity, hysteresis, and thermal drifting of apiezo stack are ruled out. Mechanically induced
strain variations of the stack (e.g. by changes of theexternal load) are also detected and cancelled out.

SG

1 LemoFor position sensing and control, PIEZOMECHANIK
offers the strain gage amplifier DMS 01/03 and thecomplete feedback control system PosiCon.

SG

SG

3 LemoPosition resolution:
Strain gages can detect strain variations L / L evenbelow 10-6.
Taking into account the actuator strain range ofabout 0.1 %, this motion can be resolved again toapprox. 10-3. For short stacks, position variations of
1nm magnitude can be detected.

SG

4 Lemo2 LemoFig. 6.2 : Wheatstone-configuration with 4 active grids SG:
Supply voltage to 1, 2,
Sensor signal out on 3, 4

Fig. 6.3 : 4-element strain gage-bridge configuration on a
piezo stack Typical gage resistance: 1.2 kiloOhms

Fig. 6.4 : Basic position control equipment. Piezo-actuatorwith strain gage position sensor. Position read out by DMS 01
unit. Piezo-actuator supply electronics SVR 150 (left)
44 PIEZOMECHANIK

6.5 Further modifications

Enhanced mechanical preload
Depending on the individual application, higher
mechanical preloading of the actuators may beneeded beyond what is supplied as standard (about
10 - 20% of the max. load capability). For symmetricpush-pull configurations or very high dynamic operation, preload levels up to 50 % will be necessary.
PIEZOMECHANIK offers modifications of the preload mechanisms beyond standard.
Vacuum operation
PIEZOMECHANIKs standard actuators are generally
vacuum compatible to standard laboratory highvacuum levels better 10-6 mbar. Neither the performance is impacted nor is vacuum contaminated byout gassing. In the case of a dynamic operation in
vacuum, be aware of the lack of actuator cooling by
ambient atmosphere.
For ultra high vacuum (UHV, up to 10-10 mbar range)
applications, modifications to the actuators areneeded, e.g. special coatings to avoid traces ofcontaminations. Bake out procedures can beapplied to some extent. It is recommended tocontact PIEZOMECHANIK in these cases to ensure
the proper system results.

Non-magnetic configurations
A special feature of piezo actuation is the complete
absence of magnetic fields during motion generation. Accordingly, piezo-actuators are an ideal solution for applications where any kind of interaction
with magnetic fields would cause problems.
Piezo-actuators can be built up from completely
non-magnetic materials including the casing, preload mechanisms, and wiring.
On request, PIEZOMECHANIK supplies completely
non-magnetic actuators.
Special materials
Piezo-actuators are excellent candidates for exotic
driving conditions. Attention needs to be paid not
only to the PZT ceramic itself, but to all other structural components of an actuator. PIEZOMECHANK
has experience in using a wide range of special
materials like titanium, special alloys, INVAR,
machinable ceramics, glass-or carbon-fiber based
composites.

Rotating systems
Piezo-actuators are sometimes used in rotating
mechanics. As long as the stack’s axis show radial
orientation, the centrifugal forces lead only to axial
load variations for the stack without further problems.
Problems occur when the rotational axis and stack’s
axis are parallel and the stack shows a large aspectratio length/diameter: The centrifugal force can leadto the bending or buckling of the stack. Special
mechanical requirements are needed to handle thissituation.
PIEZOMECHANIK is experienced in this field:
Ask for proposals.

PIEZOMECHANIK

45Operation instruction

7

7.1 Basic comment on actuator reliability

In most applications, piezo-actuators are usually
kept as small as possible and operated nearly totheir performance limits simply for cost reasons.
As a result, in most mechanical designs, piezoactuators become the “weakest link” from a mechanical point of view. In addition, ceramic is amaterial that is more complicated and more sensitive to issues resulting from improper handling thanmetal components.
Even when piezoceramic is “ruggedized” by placing
it in a preloaded casing, a profound understandingof the technical background of piezo devices is amust to ensure high reliability through proper designand operation. Any step in handling, mounting andthe operation of piezoceramic components muststrictly avoid any single overload situation. Impropermechanical designs, irregular mechanical and incorrect electrical driving conditions need to be identified by realistic tests and evaluation procedures tocome to a reliable solution!
“Mishandling” of piezo-actuators does not leadnecessarily to the immediate break down, but reduces the long-term reliability with failure part way
through the desired duty cycle. Piezo-actuators
operated in a short-term manner can operate at ornear their mode maximums, which would not berecommended, when long-term reliability and lifetime under long-term operation and large cycle
numbers are a “must”. Vice versa, a short-term“successful” testing of a new set-up is not at all asignal for a long-term reliable solution.

Piezo-actuator reliability is subject to a wide
range of influences from● the attached mechanics● the driving electronics● the environment via the atmosphere or othermedia

Even when a piezo-actuated configuration has been
proven for reliability, a seemingly “small modification”
of the driving conditions may require a new reevaluation of the system. In literature, usually two
extreme cases are discussed for characterizing
piezo-actuator reliability● High cycle number reliability:

This criterion is mostly used for dynamic operations with elevated mechanical stress levels by
short-term excitation.
■ Example: two-level switcher operation inpulse-width modulated processes, piezo fuelinjectors with cycle numbers up to 1010. Suchhigh cycle numbers depend strongly on the quality of the mechanical design of the whole set-up !
● Long-term static operation:

Potential degradation is coming mostly from environment influences like excessive air humidity
etc. in superposition with the piezo-mechanicaldriving parameters and temperature.
When comparing specifications about reliability,
pay attention to the applied driving conditions
like the strain levels.
■ Example: humidity problems in tropical atmosphere can best be overcome by hermetic
encapsulation of the stack.
In practice, a superposition of both kinds of operational profiles occurs. A simple extrapolation for
reliability from the above stated general “experiences” will be limited in success. Individual testingunder a realistic load duty cycle will be neededin any case to ensure high reliability of a piezomechanical system.

46 PIEZOMECHANIK

7.2 First check of a piezo-actuator

All kinds of piezo stacks show the following basic
properties, when they are in a correct proper state:● A piezoceramic stack shows electrically insulat-

ed end-faces allowing a floating potential operation. The electrical polarity of a stack is indicatedby marking dots or color of the leads. Typically,
the positive pole is indicated (e.g. by a red wire).
The piezo stack expands when the voltage withcorrect polarity is increased.
The polarity of an unknown actuator can be identified by applying a small voltage variation andchecking the sign of the resulting shift ! Alternatively, a stack can be connected to an oscilloscope. By application of a short squeeze, a small
voltage pulse is generated. Its polarity shows thewire polarity (relative to ground).
● Piezo-actuators behave like electrical capacitors

Any related test e.g. by a RCL-meter must clearly
indicate a capacitance value in the Nano or
Microfarad range.

Note:
This internal DC-resistance has nothing to do withstack’s power consumption or self-warming effects!
When you identify lower resistance, please check all
involved electrical parts, wiring, connectors, andplugs for failure, not only the stack. A failed stackwith internal short-circuiting shows very low resistance of kilo Ohms or less.
● Testing of the overall electrical circuitry can bedone acoustically by applying a harmonic signalof a few Volts to the piezo-actuator e.g. by a function generator. (Notice: discharge the piezo stack
before connecting it to the signal source).
● A piezo-actuator shows the normal piezo-elec-

trical effect (generator or sensor-effect).
Connect the actuator to an oscilloscope andapply a small knock to your piezo-mechanics.
A voltage response signal according the mechanical ringing of your piezo-mechanics will befound, containing information about natural
frequencies of your arrangement.

● Apply a DC-voltage to the stack and measure thecharging current. After a while, this charging current will decrease to a negligible value below
Microamperes. This reflects the very high internal
resistance of the stack >> Mega Ohms.

Trouble shooting:
Stack failures are often assumed when theactuator creates a “strange noise”. Keep inmind that the wrong electrical signals can be
the reason for this behavior and the stack could
be in good condition.
Rule:
Always check your complete electronic
setup and related systems in all those cases
where the actuator produces a “strange
noise” !

PIEZOMECHANIK

47

7.3 Thumb rules● Mechanical coupling and mounting of the ceram-

ics is only allowed via stack’s end-faces.
Avoid mechanical contact to the side-faces. An
air gap between actuator side-faces and the peripheral mechanics is needed, otherwise electricalinsulation break down of the actuator surface
may occur over time.
Piezo stacks show DC-insulation at the endfaces. When end-faces are made from poled
piezoceramics, a very weak electrical AC-coupling
during dynamic cycling can emerge. Set all metal
mechanics electrically to ground.
● Apply only and purely compressive axial forces

No bending, torsion, or tensile forces should bepresent.
The more “compromises” you allow on thesepoints the worse the actuator’s reliability will
become.

● To keep the long-term average voltage level low,

use a longer stack and operate it with reduced
strain. Use the semi-bipolar operation mode, if
possible.
● Do not over-size the supply electronics withrespect to voltage, current and power range.
It is a fact of experience, that an accidental overload situation will emerge over time and damage
the actuator.
● Be careful not to contaminate piezo stacks withchemical agents. Avoid traces of water, humidity,
electrolytes (no touching with bare fingers), adhesives and casting materials generating corrosive
agents during cure.
Cleaning can be done using 100% isopropyl-alcohol (propanole), avoid acetone.

● Keep the activation duty cycle of piezo-actuators

as low as possible. No inverted operation byusing high voltage levels as long-term basic stateof your piezo action.
No stand-by-operation:
Switch off the actuator, when not in use or set
the piezo signal to 0 V !

Mounting faults:
Do not squeeze bare ceramic stacks sideways
into tight-tolerance clearances.
Never apply knocks to accelerate mounting or
to overcome mechanical resistances, otherwise
you will permanently damage piezo-actuators ina very final way.

48 PIEZOMECHANIK

7.4 Handling and operation

The achievable performance and reliability of an actuator must be seen in context
with the interaction with the operated mechanical system driving characteristics.

Poorly designed mechanics like low stiffness coupling to the actuator, friction, wrong preloading,wrong force coupling, misalignment of coupling
faces from actuator to mechanics reducesignificantly usable stroke, accuracy, force
generation and make the use of piezo-actuator
more or less worlhless. Poor designing impacts
actuator's long-term reliability.
Fig. 7.1 shows the consequences of inhomogeneous
high force loading: A stack with excessive edge
squeezing/pressure of the ceramic-stack by an
improper force coupling. Cracks are generated
within the active ceramic section resulting inelectrical break down and arcing.

Coupling of actuator and mechanics
Optimum actuation performance is achieved byfollowing a few simple rules● The coupling face of the mechanics shall covercompletely actuator's end faces to achieve maximum force transfer (fig. 7.2). The contact force
shall be homogeneously distributed over thecontact area
● When a high load pressure is applied, the coupling faces of actuator and mechanics faces shallbe absolutely plain (eg. by grinding) to avoid local
overload of the ceramic front face.
● The resulting load force vector shall coincide withactuator's axis. Within a virtual cylinder of+/- 10% of actuator's cross-section (fig. 7.2) toavoid excessive bending and shear stress. Forcemisalignment tolerance becomes more criticalfor increased ratios actuator length / diameter.
For high dynamic operation, actuator’s axis shallfurther hit the centre of mass of the attachedmechanics to avoid dynamic torque.

mechanics

piezo stack

Fig. 7.1: Failed actuator stack, caused by a wrong coupling
to the actuated mechanics. Local edge pressure exceeded
ceramic's stability with subsequent electrical break down
after approx. 800 hours.

Fig. 7.2 : Perfect plain-plain coupling of piezo stack and attached mechanics by floating axis orientation of the mechanics.
Acceptable tolerance : see above .
PIEZOMECHANIK

49

7.4 Handling and operating● When the mechanical partner can readjust itself

by a free suspension (floating axis) according
actuator's plane face, no problems will occur.

In a similar way, the plain-plain coupling of an axially acting stack with a rotating lever arrangement willlead to a fundamental edge squeezing situation inany case (fig. 7.4).

● Coupling of piezo-actuators to guided mecha-

nisms (axis orientation not floating):
One of most widespread design mistake is coupling a plain-faced actuator directly to a plainfaced
guided mechanism (fig. 7.3). Even the slightest
misalignment between the orientations of theboth plains leads immediately to edge squeezing
with very high local spot pressures and subsequent ceramic damaging (fig. 7.1) especially
under high force loaded conditions.

moving partIn the above cases, it is a must to decouple theaxis orientations by using spherical / plain
coupling or flex hinges or other means!
● The above requirements are valid at any timeand any state of the system during set up andoperation.

moving part

moving partwrong
critical edge
squeezingcorrect

correct

piezo stack

piezo stack

piezo stack







Fig. 7.3 : In correct /correct coupling of Iinear guided mechanics

pivot

wrong
critical edge
squeezing

Fig. 7.4 : lncorrect /correct coupling of a rotating mechanism
50 PIEZOMECHANIK

pivot

correct

7.4 Handling and operating

Electrical aspects
The electrical controller performance determines the dynamics and motion characteristics of a piezo-actuated system.

Voltage ranges, polarity
The plus/positive -pole of a piezo-device is usuallyindicated by a dot or red wires. Typically, the coaxial
cable shield electrically grounds piezo-actuatorcasings with coaxial cable. This configuration is preferentially used together with common voltage
amplifiers.
On request, the cased versions can be built up witha floating potential setup: The stack actuator isinsulated from the metal casing by separating electrical grounding from the casing. Floating potential
wiring is most often used together with current control electronics. Ask PIEZOMECHANIK for details.
Make certain to use the correct polarity when applying the specified maximum voltage, otherwise depoling or poling reversal of the ceramics will occur.
This results in a useless irregular response of theactuator. Counter-voltages with lower levels can beused to some extent, but attention needs to be paid
to the individual driving conditions (e.g. stack’s temperature => 9.1).
Uni-polar activation
Voltage signals with the specified actuator-polarity
can be applied to the piezo-actuator up to thespecified maximum voltage ratings independently

Near-static long-term operation
When bare ceramic stacks are operated nearly statically in a highly humidity loaded atmosphere, it is
not recommended to apply the maximum voltage
Umax for long-term operation. Semi-bipolar activation can partially compensate for this reduction.
Alternatively, the humidity-problem can be dealt withby using hermetically sealed elements. Metal-foil
encapsulated stacks PSt 150/5x5/20 have withstoodsuch conditions operating for 2 years (DC – operation) @ 150 V activation / 85% rel. humidity/ 20 °C
ambient temperature without any degradation(=> fig. 7.5). The humidity problem is strongly re-from actuator’s temperature. PIEZOMECHANIK’sstandard power amplifiers LE and RCV provide unipolar output 0 V/+Umax .
Semi-bipolar activation
At room temperature, any piezo stack actuatorcan be operated up to a 20% counter-voltage((-) 0.2 Umax). Using the wider voltage range, stroke
and force generation range of piezo-actuators areenhanced by at least 20% compared to the unipolar
activation. PIEZOMECHANIK offers low power
amplifiers SVR with semi-bipolar output. At higher
temperatures, semi-bipolar operation shall only beapplied to high Curie-temperature PZT-ceramics.
Ask PIEZOMECHANIK for details.
Bipolar activation:
Successful counter-voltage operation of piezo
stacks is influenced by stack’s temperature(=> chap. 9.1). The stability of PZT-ceramics against
unwanted de-poling effects increases dramaticallyat low temperatures. For very low (cryogenic) temperatures, the piezo stacks can be operated in abipolar way within +/- Umax. By doubling the voltage
range compared to the unipolar mode, the temperature-induced reduction of piezo-mechanical efficiency (µm/Volt) can partially be compensated for.
PIEZOMECHANIK offers SVRbip amplifiers withbipolar high voltage output.
Example: Piezostacks PSt 150 can be operated
with +/-150 V at 77 °K (LN 2 temperature). The
strain efficiency µm/V is reduced down to 20 %.
Using bipolar activation, you get about 40 % of theoriginal unipolar stroke @ room temperature.

duced, when the actuator is cycled dynamically. The
elevated temperature due to self-warming repels the
diffusion of water molecules into stack’s surface.

Fig. 7.5: Metal foil encapsulated stack
PIEZOMECHANIK

51

7.4 Handling and operating

Thermal aspects● Heat management
The piezoceramic material properties depend on
temperature e.g. the electrical parameters like
capacitance and loss factor increase with temperature. Too high temperatures reduce performance and life-time.
Hence, the long-term power operation of piezoactuators requires heat-management solutions
for optimum power efficiency and lifetime.
PIEZOMECHANIK offers highly effective options
for internal heat-management for standard piezoactuators with a casing. The outer dimensions
will not be changed !
(=> 6.1: option thermo-stable)

Maximum temperature limit
The Curie-temperature Tc is usually not the limiting
factor with respect to actuator operation and storing
conditions. In most cases, actuator temperature
limits are usually significantly lower than Tc due tofollowing effects:● actuator’s performance and operation data areworsening remarkably● electrical losses/heat-dissipation increase withtemperature● the piezoceramics start to become electricallyconductive (depends on type of PZT-ceramics)● temperature limitations of used insulation-,contact- and coating materials● Ring-actuators show a better heat-managementbalance than bulk stacks (=> chap. 5.4).
● Piezo stacks can be immersed in inert fluids forheat transfer (=> chap. 7.5).
● The de-poling stability of piezoceramics depends

on temperature. Stay well within the safe area
voltage range, when applying counter-voltages(=> chap. 9.1).
● Bulky stacks can show higher core temperatures.

The thermal status of an actuator’s volume canbe determined by electrical capacitance measurements.

52 PIEZOMECHANIKIn practice, the typical operation temperature limits
are about 2/3 of the ceramic’s Tc
Piezo-actuators adapted for high temperature canbe operated up to 150 °C long-term (200 °C shortterm):
HS/HT PZT-material based components (=> chap. 8).
■ Comment:
A special case are low Tc-ceramic based stacks:
They can be stored even at high temperatures.
Potential depoling is compensated for by the firstfull voltage swing operation at normal temperaturelevels. The ceramic is repoled = reactivated then.
(useful for out-bake @ UHV)

7.4 Handling and operating

Low temperature conditions
PIEZOMECHANIK standard stacks can be stored
and operated down to low temperatures of - 40 °C.
The actuator parameters show following trend for
decreasing temperatures:● reduction of strain/Volt● reduction of hysteresis and non-linearity● reduction of electrical capacitance● reduction of loss factor● increase of electrical stability against de-poling(allows bipolar operation)
Pay attention to the overall thermal expansion behavior of your mechanical frame work, when applying
large temperature variations. Avoid mechanicaloverload due to thermally induced stress duringcool down.

Lowest temperature (cryogenic) operation
Piezoceramic stacks can be stored and operated
under LN2 or LHe conditions near absolute zero if
they have been adapted properly. Care is needed
for setting up a suitable internal actuator structure
to handle thermally induced stress during cool
down. Points of attention are the thermal conductivities, thermal capacitances and different coefficients of thermal expansion for the different materials in use (PZT-ceramic, metal electrodes, coatings).
Ask PIEZOMECHANIK for details on cryo-compatible actuators.
For low temperature operation, preloading shall beapplied to the stacks. The mechanical coupling isbest done by compressive means only (=> chap. 4.9)
to avoid any external tensile stress. At cryo-temperatures, PZT-ceramic shows very high coercive
fields. Bipolar voltage operation can be applied.

Notice:The warming up of a cold piezo-actuator needs
occur slowly. The risk is the condensation of wateron the actuator resp. the sucking of humidity inside
the casing. The ceramic core shall show even aslightly higher temperature than ambient (use a
simple heater). Check stack’s volume temperature
via the electrical capacitance.

PIEZOMECHANIK

53

7.5 Adhesives – Electrical contacts – Chemistry

Piezo-actuators have electrodes and high electricalfields in the vicinity of the ceramic stack’s surface.
It is easily understood that any mechanical orchemical impact on this surface structure results ina high risk of failure.

products must be generated by the cure processes. Do not use standard 1-component silicone
compounds: they generate traces of acids, whenreacting with air humidity. These agents will
penetrate into actuator’s surface and start electro-corrosion. Use corrosion free materials only!

● Be careful with any contaminations of actuatorsurfaces with unknown species. Even traces ofcorrosive agents will result in an actuator failure
over time. Do not touch ceramic elements withbare fingers. Avoid contact of the ceramics withwater containing fluid or electrolytes.

● Usually adhesives like epoxies, poly-urethanes,or cyano-acrylates are successfully used. Best
glue line quality is achieved for longer cure-times> 30 min at room temperature or mild heat up.
Rapid cure creates mechanical stress and poor
glue line quality.

● Be careful, when using adhesives, sealing andencapsulation materials: no corrosive reaction● Glue line quality: At first glance, a very thin andhard glue-line gives the best coupling quality interms of rigid coupling of the involved components.
Attention:
Large coupling cross sections, together with hardand inflexible glue lines:
The lateral d31 motion of the piezo-component will
be hindered and consequently the axial d33 response
too. High mechanical stress is produced within
this composite structure during piezo activation(=> fig. 7.6 /7.7).
When large area gluing is to be done, preliminary
tests must be used to find the optimum adhesive
formula and glue-line thickness to ensure unhindered motion.

hard glueline
activated PZT-Layer

substrate

Fig. 7.6 : Lateral (in-plane) clamping effect by large area hardgluing a piezo-chip on a rigid substrate. The thickness expansion of the PZT-layer is blocked also, distortions occur in theceramic (tilting, reduced stroke)activated PZT-Layer

substrate

Fig. 7.7: Bending structure of a thin substrate/piezo-layercomposite by hard adhesive coupling.Deformation of opticalflats can occur.
54 PIEZOMECHANIK

7.5 Adhesives – Electrical contacts – Chemistry

Useful Materials● Temporary bonding

Bonding waxes as used for wafer grinding,melting point 70 °C, Logitech Polishing &Lapping, Glasgow● Permanent bondingfor -50 °C to +120 °C temperature range
High quality epoxies: EpoTec, Araldite,longer cure > 30 min at room temperate orslightly elevated temperatures.

● Electrical contacting

Most multilayer piezo components fromPIEZOMECHANIK have electrical wiring.
Nevertheless it is helpful to understand how toapply electrical contacts to PZT-components,
having no wires. Such piezo-elements havevery thin metal-layers as electrical contacts(thickness µm).
These metal layers can be electrically contacted by soldering, conductive adhesives andcoatings or elastic spring contacts. Be careful:accidental removal of these original contact
layers make the piezo component unusable.

● Low outgas and cryo-compatible glue lines

Stycast 2850 FTTorrSeal● Provisional bonding

Cyano - acrylates: give thick and flexible gluelines, not recommended for long-term use

Soldering of PZT-metalization
Attention: Improper soldering dissolves the thinmetalization in the solder tin making an electricalcontacting then impossible.
● use standard solder tin● Casting, sealing●e.g. 2-component silicone rubbers RTV2
non-corrosive 1 component RTV silicone or
acrylate – based rubber● Liquids for cleaning and cooling

General requirements:
Absolutely no water content, even traces
No electrolytes, non-ionic liquids only
Test for compatibility with polymer coatings !
Paraffin oil, silicone-oils, hydrocarbons (fuel),transformer oil, alcohols have successfully beenused e.g. for cooling.

●● use a tiny solder tip for setting small solder● set solder tip 300 ° - 350 °C● keep solder melting time on metalized

ceramic rather short (max. a few seconds
should be sufficient)● use non-corrosive solder flux , remove

residues

Use 100% isopropyl alcohol (iso-propanol, IPA) for
cleaning: Avoid acetone and other ketones

PIEZOMECHANIK

55

7.6 Further aspects

Environmental influences
Piezo-actuators have electrodes and high electricalfields in the vicinity of the ceramic stack’s surface.
Any mechanical or chemical impact on this surface
structure results in a high risk of failure. One mainconcern is the operation of piezo-actuators withinvery humid and polluted atmospheres (aerosols, liketropical ambient air). This situation can be overcome
by reducing the operating voltage level of piezoactuators or hermetic encapsulation (=> fig. 7.5).
Vacuum operation
PIEZOMECHANIK stack actuators are compatible
with high vacuum conditions. Restrictions occur inthe fine vacuum in the mbar range. Especially highvoltage actuators can ignite glow discharge on theirsurface, when a distinct voltage level is exceeded.
This does not allow a regular operation of theseactuators with maximum voltage ratings. Low
voltage actuators do not show the glow discharge
problem and can be used regularly.

56 PIEZOMECHANIK

Noble gases, hydrogen atmospheres
Hydrogen and light noble gases like helium interferewith the electrical insulation conditions of a piezo
stack .The accepted maximum driving voltage isreduced. Insulation performance breaks down.
Individual tests are necessary to determine stable
operating conditions.
Radiation
Piezo-actuators are sometimes exposed to highenergy radiation or neutron fluxes (e.g. resonatortuning in synchrotrons or accelerators for spallation
neutron sources). The heavy-metal containing piezoceramics is not degraded by radiation.
Space-borne applications
Piezo stacks are compatible with vacuum, cryoconditions and radiation. Therefore they are wellsuited for space applications. Adoption to special
aspects of a mission can be implemented into an
actuator design on request.

8

Properties of
piezoceramics

Common piezo-actuators use no “quartz” or “single crystals”, but a simple oxide
ceramic made from PZT (Pb lead, Zr zirconium, Ti titanium). This compound classshows much better piezo-electrical and piezo-mechanical efficiency than quartz.

The PZT- formulation can be varied with regard tostochiometry and dopants resulting in a broad
spectrum of material properties optimized for different application profiles.
Not all desirable properties can be put into one
compound. Piezo-mechanics is to some extent the“art of best compromises”, when selecting a suitable material for a distinct application.

Piezoceramics is a ferro-electric compound. Thismeans, that the electro-mechanical conversion process for producing a motion is related to a kind ofself-enhancement process based on an internalreorganization of the material’s structure.
● This self-enhancement process results in thehigher piezo-electrical efficiency of PZT comparedto materials like quartz.
● The structural re-organization is accompanied by“internal structural friction”, resulting in energylosses. When the structural re-organization is hindered by blocking conditions or very low temperature, these losses are reduced.

Notice:PIEZOMECHANIK is using piezo-electrically “soft”
and “semi-hard” PZT-formulations.
High strain rates and high energy contents areachieved for efficient non-resonant electro-mechanical conversion.

Developing new piezo-materials is a steadily
ongoing process in the ceramic industry.
PZT is the most widely used smart material forsolid-state actuation. Alternative materials withenhanced strain capability are under study, but allthese “innovative” materials have severe drawbacks
regarding common driving conditions in practice.

● This ferro-electric structural re-organization of

PZT shows nonlinearities
 hysteresis in stroke/voltage diagram, capaci
tance varying with driving conditions
 complex elastic behavior(compliance and force balances depend on the
degree of structural variation).
A moving structure is “softer” than a static one(see blocking force experiment 4.5 in comparison to the classical compression experiment
4.6).
Literature tries to down-size this complexity bylinear approximations, but to the cost of consistencies between theory and practice.

PZT ceramics’ material data are usually definedat low field excitation where nonlinearities are
not dominant. In practice, high electrical fields
are applied to PZT actuators, resulting in a nonlinear enhanced response (“ferro-effects”) andaltered parameters. Nevertheless, for reasonsof comparison with materials from different
suppliers, the classical characterizations areused for describing actuator ceramics andshown in the tables.
The data shown in the tables are valid for room
temperature operation.

PIEZOMECHANIK

57

8 Properties of piezoceramics

Piezoceramic for stacks PSt 150
The PSt 150 stacks are a kind of “general purpose”
actuator e.g. for low and medium dynamic positioning tasks.

1
l
lmax

0

+Umax

Fig. 8.1: Schematic stroke-/voltage diagram for high field
excitation of PSt 150 stack actuators.

Piezoceramic HS/HT
for low voltage actuators PSt-HD 200,
piezo-chips (H) PCh 150,
standard high voltage actuators(H)PSt 500 and 1000
The HS/HT-piezoceramic is used as standard material for high voltage actuators. It is a high strainmaterial with a wide temperature range up to
150 °C. The actuator data do not vary strongly withtemperature. This type of material is used for piezofuel injectors.

1
l
lmax

0

+Umax

Fig. 8.2: Schematic stroke-/ voltage diagram for high field
excitation of HS/HT-piezoceramic.

Piezoceramic HP
with highest mechanical power density for highvoltage actuators (H)PSt 500 and 1000
Higher strain rates and blocking forces are achieved
compared to the standard PZT material HS/HT.
Depending on the individual application conditions,the useable mechanical energy output density is
doubled. This type of material is preferred for motion control, active structures, and high-pressure
hydraulic pumps. The Curie-temperature is lower
than for the HS/HT composition. For high energy
conversion rates, an efficient heat management
solution is needed.

58 PIEZOMECHANIK

1
l
lmax

0

+Umax

Fig. 8.3: Schematic stroke-/ voltage diagram for high field
excitation of HP-piezoceramic.

8 Properties of piezoceramics

Piezo-mechanical data (small signal-values at room temperature)
PSt 150 Stacks

PZT HS/HTPZT HP

loss factor (10-4)

5,400
0.200

1,850
0.130

3,800
0.160

coupling factors
Kp
K31
K33

0000.620000.340000.68000 0.62000 0.34000 0.72

0000.650000.38
0000.74

Piezoelectric charge coefficients (picometer/Volt )
0-290
d31
d33
0-635

0-190
--440

0-275
--680

Elast.compliance (10-12 m2/N)
S11E
S33E

00 14.800 18.1

00 18.500 20.7

00 15.800 23Frequency constants (m/sec)
RadialThickness
Transverse
Longitudinal

2,040
1,800
1,410
1,370

2,020
2,030
1,325
1,250

1,960
1,885
1,420
1,190

Quality factor (resonance)

0.070

00 80

00,80

density (g/cm3)

0.008

000 7.74

000 7.83

Curie-temperature °C
Spec. heat Ws/ °K kg
Thermal conductivity Ws/m K (axial)

0.150
.0380
ca. 1.5

0 340
0 380
ca. 1.5

0 215
0 380
ca. 1.5

εrel

Non-linearity:
Due the ferroelectric nature of PZT-ceramics, the above-mentioned parameters can vary significantly withthe operating electrical field strength. In practice, PZT-ceramics are operated with large field excitationlevels for actuation.
The following example for the rather stable PZT-ceramics HS/HT illustrates this trend:
small signal (E << 100 V/mm)

εd31 (picometer/Volt)
d33 (picometer/Volt)
elast. modulus 33 (109 N/m2)

1,850
000 -190
00004400000065

large signal 2 kV/mm
3,500
0-270
00640
00030
PIEZOMECHANIK

59

8 Properties of piezoceramics

Temperature effects
Electrical capacitance:
The relative dielectric constant ε of piezoceramics
varies noticably with temperature. It is not unusual
for an actuator’s capacitance to increase by approximately 40% when heated up from room temperature to 80 °C. This effect has to be taken into
account when selecting a proper amplifier for dynamic operation (=> chap. 9.3).
It is immediately understood that, for power efficiency reasons in the case of a dynamic operation, aproper heat-management option is recommended
to keep the actuator temperature low.
Thermal expansion of piezo stacks
Piezoceramic is also characterized by an anisotropy
in thermally induced expansion.
The CTE (coefficient of thermal expansion) α for
PZT-ceramic isapprox. - 5 ppm / °C in poling direction
approx. +5 ppm / °C in lateral direction(measured with short-circuited electrodes)
Low voltage stacks(temperature range -40 °C thru +120 °C)
Axial α: approx. – 5 ppm (neg. coefficient !)High voltage stacks
Axial α: 0 to + 2 ppm / °C
High voltage piezo stacks are a composite structure
made of piezoceramics and metal foil electrodes.
Hence HV actuators show a CTE differing from pure
PZT-ceramics.
PIEZOMECHANIK high voltage stacks show rather
low CTEs when compared to similar products ofother suppliers.
Notice: Metal end-pieces applied to piezoceramic
stacks contribute to the over-all thermal expansionof such a device. A piezo-actuator’s casing is usually not involved in the thermal expansion balance,
when the mounting of the actuator is done via its
end pieces.
If an actuator is fixed using the casing tube, thissituation changes: e.g. by clamping the casing or
using piezo cartridges FPSt with front thread mounting. The thermal expansion of the complete force
path needs to be taken into account.
60 PIEZOMECHANIK

Piezo strain
The achievable strain/Volt of a piezo-actuator isrepresented by the d33-coefficient (piezo-electriccharge constant) in the data sheet.
Compared to room temperature operation,● the strain/Volt efficiency decreases remarkably,

when temperature is decreased.
At cryo-temperatures, the ferroelectric selfenhancement of the piezoceramic reaction isstrongly reduced.
● the effect of an increase of temperature on thed33 parameter depends on the Curie-temperatureof the PZT-material used.
Soft-PZT-based PSt stacks show a slight efficiency reduction, when heated up to 80 °C:
A stack PSt 150/5x5/20 operated @ 0 V/+150 V
shows a shift of
20 µm @ room-temperature,
19 µm @ 80 °C
High Curie temperature material HS/HT experiences
an efficiency increase of about 5%, when heated up
to 100 °C.
Pyro-electricity
Piezoceramic is electrically self-charging, when atemperature variation is applied.
This effect is irrelevant for actuation, although theeffect can electrically shock the user when acharged actuator is touched with bare hands at theleads.

8 Properties of piezoceramics

Comparison between actuator and ultrasonic
PZT-ceramics
Ultrasonic techniques are a kind of resonant actuation, where the device is designed to run at permanent (cw continuous wave) harmonic oscillation on ahigh single (resonance) frequency with large amplitudes. The achieved large amplitudes are the consequence of resonant amplification over a large
number of cycles. The efficiency of storing mechanical oscillation energy is described by the “quality
factor Q”. A high Q indicates a low mechanicaldamping.
Usually a “normal” piezo-actuator is operated “nonresonantly” broadband from DC up to rather highfrequencies. Large amplitudes shall be generated
within one cycle. Such an operation profile is only
available for the class of “soft” or semi-hard PZTmaterials. These materials shall show a larger piezoelectric coefficient d33 and an elevated dielectric
constant. Actuator ceramics show a low quality
factor Q: common broadband piezo-actuators arerather “poor” oscillators (=> 5.5, Resonances).

Parameter

ultrasonichard PZT

actuatorsoft PZT HP

Quality factor Q> 1,000

00.70

Piezo electric charge
constant d33(picometer/Volt)> 0.240

0.680

rel. dielectr. constant ε> 1,000

3,800

Curie temperature Tc °C 0>. 310

0.215

Electrostrictors
Electrostrictive ceramics can roughly be described
as a kind of piezoceramics operated at its Curietemperature near the phase transition piezoelectricparelectric .
A special class is the PMN-PT solid solution
ceramics (lead-magnesium niobate in lead-titanate)shows a Curie-temperature around room temperature.
A stack, built up from this electro-strictive materialshows the following performance:● axial strain : up to 0.1 %● hysteresis 1- 2%● no long-term drift upon application of a voltage

step
Therefore, electro-strictive actuators have a few
advantages in open loop positioning compared to
PZT-actuators. Nevertheless, when a very highaccuracy is demanded or external influences need
to be compensated for, the electrostrictors require
closed loop feedback control like PZT-actuators.
Additionally, the above stated performance data are
only valid in a rather narrow temperature range ofabout +/-5 °C around the optimum point. Therefore,
dynamic operation is ruled out because of the selfwarming problems.
Summing up these side conditions, electrostrictive
ceramics are not commonly used.

Single frequency ultrasonic resonator systems
show strongly reduced losses and heat dissipation (in relation to oscillation power; frequency,
amplitude) compared to broad band actuators.

PIEZOMECHANIK

61

Electrical poweringof piezo-actuators

9

For actuation, electrical energy is converted into a mechanical reaction.
The energy content E of any actuator depends only on the active piezoceramicvolume and the applied electrical field strength.
Expressed in usual electrical terms, the energy content E is
E = ½ CU2
Newcomers to piezo actuation ask for actuatorswith very low capacitances to save energy or power
in a very general way. Keep in mind, that energy
conservation is valid for piezomechanics too. Highpower mechanical output cannot be achieved witha low electrical input.
The electrical parameter “capacitance” is responsi-

ble for the energy coupling on the electrical side.
Accordingly, it cannot be minimized in an arbitrary
way.
Further, capacitance itself is not an absolute measure for the power consumption. As mentioned
before, it depends further on the applied voltage
levels. Therefore it is self-evident that high-voltage
and low-voltage actuators show very different nominal capacitance values for the same energy andpower balances.

9.1 Electrical input and piezo-mechanical reaction
The electrical power supply defines, to a large extent, the performance of a piezoactuated system.
Careful selection of properly adapted electronics is therefore a must.
Electrical noise
One of the unique features of piezo actuation is theconversion of a small precise electrical signal into
an equivalently small shift in position. Consequently,
any undesired electrical signal variation like noise orother instabilities is transformed into an equivalent“mechanical” noise or uncertainty of position too.
It has been found, that the positioning accuracy of apiezo-mechanical system is not limited by the piezoactuator itself, but by the quality of the electronics.
Ultra-fine positioning needs therefore a high quality
power supply with regard to the signal/noise (S/N)
ratio.
The position noise lnoise can be estimated bylnoise = Unoise x (lmax / Umax)
lmax : max.actuator stroke at maximum voltage Umax
Unoise : voltage noise
62 PIEZOMECHANIKThe lowest noise levels are achieved by low power
analogue linear amplifiers.
High power switching amplifiers show higher noiselevels and are mainly used for dynamic motion control.
PIEZOMECHANIK offers low noise amplifiers SVR
for highly sensitive positioning tasks.

■ Example
The low noise amplifier SVR 150 shows a noise levelof about 0,3 mVpp
Combined with a piezo stack PSt 150/7/20 VS 12(stroke 20 µm @ 0 V/150 V) the equivalent nominal
uncertainty in position is 0.04 nanometers.
Because the voltage modulation by noise represents a “small-signal excitation”, the real fluctuationin position is << 1 Angstrom.

9.1 Electrical input and piezo-mechanical reaction

Pulsed operation
The mechanical response/rise time of a piezo stack
is determined by the charging time of the actuator’scapacitance. The higher the charging current is, thefaster the actuator reacts.
To get a shift in position equivalent to a voltage
variation dU(t) with a rise-time dt, an actual current
I a(t) is needed according to:
I a(t) = C dU(t)/dt

C actuator’s capacitance

The maximum rating of I a(t) is the needed peak current I peak to be deliverd by the power supply.
The peak-currents I peak for the most common signal
profiles are shown below:
Sine:
I peak =  C Upp f
Triangle:
I peak = C Upp f
Square wave: I peak = C Upp/dt
Upp total voltage swing dU = Upp.
dt voltage rise-time

For very short rise-times, the necessary peak currents can reach significantly high levels.
■ Example
A piezo-actuator with 5µFarad capacitance shallbe charged within a time dtc with a voltage step
Upp: 0 V/150 V
dtc = 100 msec

= > I peak = 7,5 mA

low dynamic positioning eg. by an amplifier SVR 150
dtc = 1 msec=> I peak = 750 mAdynamic motion control, power level of a
LE 150 /100 EBW amplifier
dtc= 150 µsec=> I peak = 5 A

piezo fuel injectors ,use power switches like HVP
dtc = 10 µsec=> I peak = 75 A

piezo shock generation using HVP switches
For rise times < 1 msec, piezo-actuators need to beadapted to the very high electrical and mechanicalload conditions. Standard actuators will fail (seechap. 4.9: mech. preloads).

Pulse-generators
Distinct applications with a fast 2-level excitation
will not need a steadily signal-varying amplifier.
For a simple pulse-width modulation of a valve withsimple “open” and “close” levels, an electricalswitch will do the job. Keep in mind, that “bigblock” actuators show large capacitances and need
therefore high charging current (up to the order ofmagnitude of 100 Amperes).

For such purposes, high power “on/off”-switches
are used for efficiency and cost reasons.
Ask PIEZOMECHANK for HVP switches and its
derivatives for shock generation.
Pulsed operation requires care adaptation of theactuator configuration to prevent mechanicaldamage of stack’s structure.
Standard actuators will fail !

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63

9.1 Electrical input and piezo-mechanical reaction

Long-term average current
For long-term cycling operation of a piezo-actuatorwith a distinct frequency f and a voltage variation
 U, the actuator’s capacitance C is charged /discharged accordingly.

Energy-/power-balances
The energy content E of a piezo-actuator is
E = ½ CU², when charged up to a voltage U.
The electrical energy input during actuator’s charging is split into

This defines an average charging current Ī accordingto:● Mechanical work (displacement, elastic defor-

Ī = C U f
To produce a permanent cycling of a distinct signal
function, the power electronics shall be selected forboth current ratings: the short-term peak current
and the long-term average current.
For a periodic signal, peak and average current will
have a fixed ratio.
Examples:harmonic cycling I peak / Ī = triangle
I peak / Ī = 1
Power amplifiers from PIEZOMECHANIK are mostly
designed for a I peak : Ī = 3 to allow a well matchedcw high dynamic cycling e.g. for motion control
applications.

Notice:a noticeable fraction of the electrical charging
power is reactive. It is redirected into the amplifier
during discharge. The standard linear amplifiers will
convert this power into heat internally, so that the
total energy per cycle is finally consumed.
A more power efficient alternative are amplifiers withenergy recycling (energy recuperation):

64 PIEZOMECHANIK

mation) (=> chap. 4.2).
● Dissipation losses = self-heating rate about

5-20% depends on detailed mechanical driving
conditions● Non-converted electrical rest energy:
is stored in actuator until discharge
Average electrical power consumption
When the actuator with an energy content E is cycled with a frequency f, an average electrical charging power P is needed according to:
P= E f■ Example:
A 10 µFarads actuator is charged @ 0 V/100 V with
100 Hz => average charging power: 5 Watts.

The reactive part of the input electrical energy, when
fed back to the amplifier, can be reused for the next
charging cycle. Switcher-type amplifiers can be
designed for energy recovery like PIEZOMECHANIK’s
RCV amplifiers.
Only this kind of strategy allows a non-resonant
actuator to cycle with high power levels with acceptable efforts.

9.1 Electrical input and piezo-mechanical reaction

Voltage ranges, voltage polarity
The classical actuator activation was done by using
unipolar voltage signal 0/Umax according the actuator’s specified voltage polarity and operating range.
This kind of operation can be applied under all
specified operating side conditions e.g. temperature
range. On the other hand, it has been experienced,
that under distinct conditions a semi-bipolar or
bipolar signal can be put into a piezo stack, enhancing its displacement and force range.
The point of attention is the de-poling stability of
PZT-ceramic, expressed by the so-called “coercive
field strength”. This de-poling threshold depends
strongly on ceramic’s temperature. A piezo-actuatorcan be operated with a counter-polar voltage, aslong as this level keeps the corresponding electricalfield well below the coercive field Edepol (fig. 9.1).

(-)E
kV/mm
5
4

(-)Edep

3(-)Esafe area

2
1
0

°K
100

200

300
(R1 )

400

500

T

(Tc )

Notice:the above mentioned aspects are valid for all kindsof piezoceramic components like bimorph benders
or shear-elements

Fig. 9.1: Schematic of the temperature dependence of PZTceramics de-poling or coercive field. Counter-field operation ofa piezo-actuator must stay in the safe-area at lower electricalfield levels compared to Edepol

Generally, three operation modes can be distinguished according the operating temperature:
Unipolar activation: can be applied over the complete operating temperature range.
Semi-bipolar operation: for room temperature or
lower.
Bipolar operation: with max. voltage ratings only
applicable at very low temperatures.
The wider the voltage swing is, the larger the displacement and force generation are. The individual
driving conditions also depend on the type of PZTmaterial used.

Due to this extended voltage range, an actuator’s
piezo-mechanical performance like stroke and force
generation is increased by at least 20%.
PIEZOMECHANK offers low power amplifiers SVR
for use with semi-bipolar devices, because of thelow power level, no self-heating occurs within thepiezoceramic.

Unipolar amplifiers
PIEZOMECHANIK offers power amplifiers LE and
RCV for use with unipolar devices .
No depoling of the PZT-ceramic occurs at elevatedtemperatures.
Semi-bipolar amplifiers
PZT ceramic accept counter-voltages of about 20 %of the maximum voltage rating ((-)0.2 Umax) at roomtemperature.

Bipolar amplifiers
Bipolar ceramic activation at room temperature ismostly done with shear elements or bimorph benders to get symmetrical dual-sided action. Do not
exceed the voltage ratings because of the de-poling
effect.
PZT-ceramics’ stability against field-induced depoling increases remarkably at cryogenic temperatures. Therefore, piezo stacks accept bipolar operation with maximum voltage ratings at very low temperatures (below 77°K).
PIEZOMECHANIK offers low power bipolar amplifiers SVRbip as standard.
PIEZOMECHANIK

65

9.2 Alternatives: charge versus voltage control

Analyzing the capacitor-description of the actuator
response leads to the following simple relationships.
Actuator position I(t) is related to voltage or charge
content:
actuator positionl(t) ~ Q(t) = C U(t)actuator velocity

v = dl/dt ~ dQ/dt = I mactuator acceleration b~ dI m/dt = İ m

The relations for charge-and current-control operation of piezo-actuators are only valid for sub-resonant activation.
Due to the non-linear behavior of PZT-ceramics, thecontrol of a piezo-actuator by voltage or charge/
current control results in a different response.
A current controlling amplifier, via the input signal,
primarily modulates an actuator’s velocity and not
the position.

Q(t) electrical charge content

Increased dynamic stiffness
The electrical charge balance of a piezo stack is not
only changed via the electrical power supply, butalso by load force variations (=> chap. 4.6).
Voltage control dissipates this mechanically generated charge to cancel out unwanted voltage variations. But thereby the mechanical stiffness of theactuator is lowered.

Linear relation between position and charge
content Q
The position-charge-characteristic shows a (near)absence of hysteresis and good linearity fig. 9.2.

strokellmax

Current control handles quantitatively the charge
flow between amplifier and actuator.
Mechanically generated charge is not dissipatedand results in an increased stiffness of the actuator.
Current control is only applicable to dynamic motion.
0

Qmax

QelectricalchargeFig. 9.2: Linear response of position by charge control(max. charge content of actuator at max. driving voltage)

66 PIEZOMECHANIK

9.2 Alternatives: charge versus voltage control

Conclusions for practice● Open-loop current control is preferentially used
for dynamic motion control or generation of
acoustic vibration. The linear open-loop response
avoids frequency side-bands (low harmonic
distortion).
● Motion control is often aiming to control the

dynamic parameters velocity and acceleration.
Current control gives direct access to these parameters.
● Higher dynamic stiffness increases the response

speed of piezo-mechanical setups.
● Open-loop control of the above parameters isfaster than that of closed-loop voltage-control
based systems

Comments on data sheet
Carefully check the experimental basis for thedefinition of the actuator’s capacitances stated indata sheet. Usually, the so-called low field values
are stated in data sheet, measured with very low
voltage excitation levels, where the non-linear
effects of PZT are not present (capacitancemeters use 1- 2 Volts excitation @ 1 kHz).

Charge/current control and precision positioning?
Open-loop charge or current control is not suited forvery high accuracy positioning.
Reasons are:● linearity and hysteresis are limited to about 1% of
the maximum stroke● the charge/position-characteristic varies withtemperature● Low dynamic positioning results in extremely
small currents, which are difficult to control.
Under static conditions, the self-discharge of a
stack by leakage currents cannot be discriminated from position related effects.
● External misaligning effects cannot be compensated for by open-loop control means.
For high accuracy positioning a closed-loop feedback control via position sensing is needed. This
will allow the use of simpler and less costly voltagecontrolling electronics.

The high field excitation of PZT ceramics at an
actuator’s voltage limit shows an effective
capacitance larger by 50% or even morecompared to the low-field excitation. In addition,
capacitance increases further with temperaturerise.
Real actuator capacitances maybe as large as
twice the data sheet value.

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9.3 Basic piezo amplifier functions

5
1

2

3

4

6

Fig. 9.3 :Front panel of a piezo power amplifier from LE product line

1 Offsetpotentiometer for manual setting of a DC-voltage
level to piezo. The amplifier can be used as anautonomous power supply with a manual piezovoltage setting.
In addition, the DC-voltage level will be superimposed to the amplified external signal from
input (3)2 Amplpotentiometer for continuous variation of amplifier’s gain factor for amplifying the external signal(input (3))
3 Input
putting in an analogue signal from an externalsource (function generator etc.)

68 PIEZOMECHANIK

4 Monitor
low power signal output parallel to piezo voltage
power output (6).
For on-line real time monitoring the piezo-voltage
dynamics e.g. via an oscilloscope.
Reduction factor 1:100 or 1:1000.
5 LC-Display
slow response: used for near static read out e.g.
together with a manual piezo voltage
setting via “Offset”
6 Output plug
supply voltage for the piezo-actuator

Caution:High voltage, high currents

10

Selecting aproper actuator

Guideline:
The main pre-requisite for selecting suitable piezo components is the precise
definition of the needed operation profile by the user !
Any supplier of piezo-mechanical components will highly appreciate precise
specifications of the requested components beyond “the system shall do as muchas possible”.
Putting concrete numbers on the needed piezo-parameters is helpful to avoid oversizing and mismatch. Poorly selected system components are ineffective andtherefore expensive (=> chap. 4).
Please try to analyze the needs for operating your mechanics successfully according to
the following:
A, what shift/stroke shall be achieved ?
B, what force variation shall be generated by the piezo action ?
C, what static preload is acting on the actuator from the beginning ?
D, what is the desired maximum operation frequency ?
E, what is the desired stroke at maximum frequency (D) ?
F, what is the desired max. frequency at maximum stroke (see A) ?
G, shortest achievable rise-/fall-time ?
H, what external masses shall be attached to the actuator ?
A, to C, allow an actuator selection for low dynamic operation according chapter 4.
D, to H, aims for the best match for the designated dynamic operation.

Selecting the amplifier
The above selection process results in a piezoactuator of distinct voltage range and electrical
capacitance. Only amplifiers with a matched voltage
range should be considered for use.
Do not use amplifiers providing higher voltage !

The dynamic operation profile D, to H, defines theneeded current levels (I peak and I average) according
chapter 9.1.
When the power consumption of the actuator
exceeds the Watt-range, self-heating of the piezoceramics can occur (=> chap. 6.1: heat management).

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11

New trends

Beyond positioning
The very first application of stack-based piezoactuation was in (coherent) optics in the 1960’s to1970’s as super-precise positioning drives for the
emerging laser technology and semi-conductor
industry. The other highlights like force generationand high dynamic operation were not a focus,
although this has changed over time.
Currently, many new applications are aiming to use
the whole spectrum of excellent features offered by
piezo-actuation.

These new applications include:- Piezo fuel injectors- Motion control- Vibration generation:
acoustical, structural excitation- Hydraulic pumps- Miniature machines (MEMS, NEMS)
etc.

11.1 Piezo action for material testing
Vibration generation by piezo
Component testing for reliability studies or material
characterization require well-defined stroke-/forcegeneration profiles over a large number of cycles.
A high level of reproducibility is needed.
piezo power piston
Piezoantrieb

Common mechanical drives are then limited in theirrepetition rates resulting in rather long test periods.
For distinct test procedures, piezo-actuators provide a remarkable advantage due to their ability
to cycle high frequency together with high reproducibility.

test
sampleProbe

One interesting aspect is the upgrade of conventional test frames by adding a high frequency piezodrive. The conventional long stroke performancecan be superimposed by a high frequency finemodulation (fig.11.1).
Piezo-mechanical arrangements have been successfully used for- Fretting tests- Super high cycle fatigue test
- Material testing of polymers- High frequency vibration excitation, shaker

Fig. 11.1: Schematic of conventional set-up for test engineering withadded high-load, long stroke piezo-actuator for extended operating
dynamics.

The frequency range of conventional electromagnetic shakers is usually limited to about 5 kHz.
Piezo-based shakers extend this upper frequency
limit towards >> 10 kHz.

100 kHz excitation by small-scale elements is not
unusual to excite vibrations in miniature structures
for mode-analysis or studies on structural borne
acoustics.

70 PIEZOMECHANIK

11.1 Piezo action for material testing

Shock-generation by piezo
An alternative to high frequency harmonic excitationof structures is the application of single pulses to
excite the natural frequencies of a mechanicalstructure. By analyzing the decay of the excitedoscillation, the mechanical parameters of thesystem can be analyzed.
Piezo-specific unique features are● non-ballistic shock generation, mechanicalcontact between shock-partners prior to shock
generation and transfer● wide tuning range of acceleration levels(100 m/sec² up to > 100,000 m/sec²

Calibration, quality control of accelerometers
PIEZOMECHANIK has supplied piezo-shocker
based test arrangements to industrial accelerometer
manufacturers since 2006.
The basic configurations of suitable arrangements
have been published by PIEZOMECHANIK in 2006
including the description of the non-ballistic
Hopkinson-bar excitation (=> fig. 11.2).
Material testing with high strain rates can be carriedout with higher repetition rates in so-called split
Hopkinson-Bar arrangements.
Piezo-shock-generation is now in practical use at
calibration services.

● electrical tuning of mechanical shock parameters(e.g. amplitudes, rise-time)● single shot, bursts or continuous operations arefeasiblepiezo stackshock

A kind of intermediate piezo-exciter between shaker
and shock-generator would be a burst-generator.
A potential application is the simulation of SRS(Shock Response Spectrum) of pyro-shock-tests.
From a technical point of view, shock generation isan unusual driving mode of piezo stacks:
the electrical excitation is very short (< 10 µsec)
compared to the acoustic transit time of soundthrough the stack.
The propagating shock-front within the piezoceramic leads to a highly inhomogeneous mechanicalstress distribution, both in time and place. This condition is usually strictly avoided in piezo-technology.
Special mechanical provisions for the shockgenerator design are needed to get a reliable configuration.

LDA Spot
accelerometer

Hopkinson-bar
Electric
power
switchHVcurrent
pulse

strain gages

HVP

triggersignalIN

Fig. 11.2 : Hopkinson-Bar arrangement for sensor-testing by
non-ballistic piezo-shock-generation.

Notice:Piezo shocks shall be distinguished from common“fast acting” piezo-elements as used in fuel-injectors: The electrical excitation time is sufficiently long(about 100µsec) compared to the transit time ofsound. The stack is mechanically excited below its
natural frequency, having a near homogeneousstress distribution. A real shock actuation within afuel injector would result in a worsening of the injection balance due to ringing effects.

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11.2 Motion control

Motion control is a general expression for all kindsof motion generation according distinct defined criteria, usually done in a feed-back controlled system.
A special field in this context is active vibration control with:
Active vibration generation
Active vibration cancellation
Active vibration isolation

72 PIEZOMECHANIK

Adaptronics, morphing
Piezo-mechanical components are used for dynamic active shaping of functional profiles like adaptive
wings, adaptive rotors, adaptive optics, adaptive
frame structures.

11.3 Electrical energy generation

The following applications of piezo-elements are not part of PIEZOMECHANIK’sprogram. Disregarding this obvious fact, a lot of inquiries are coming in looking for:
- force transducers, accelerometers- energy harvesting (energy scavenging)- piezo transformers
Therefore a few statements shall be made to discriminate between piezo-fantasy
and piezo-reality.
The original piezo-electric effect is a generator
effect converting a mechanical force input into anelectrical charge.
It is also true that this electro-mechanical conversion is bi-directional:
Piezo-mechanics and piezo-electricity
Piezo-actuators exhibit the piezo-electric generatoreffect, while they are not specially adapted to thiskind of use.
Nevertheless a few hints shall be given:● the conversion efficiency is related to theg-constants shown in the PZT-material datatables● PZT ceramics shows to some extent “ageing”,
meaning a long-term reduction of the conversion
efficiency due to de-poling. This is important for
the generator effect, but is not relevant for actuation.

● Force transducers etc.

For quantitative measurements single crystalline
materials are used like quartz. For high temperature application the more effective GaPO4 is
used.
Polycrystalline PZT is a low cost alternative,
when a compromise in measurement quality is
acceptable. The main advantage of PZT is themuch higher generator-efficiency that makes signal detection easier.Usually, force measurements
are done by determining the quantity of generated electrical charge, not the induced voltages.
● Energy harvesting, energy scavenging

One cubic-centimeter (cm³) of PZT-material delivers a few milliWattseconds (10-3 Ws) energy per
cycle even under high mechanical loading. From
this fact, it is easily seen that gluing a few piezoelements into the countryside and squeezingthem from time to time will not solve the world’s
energy problems.
Serious projects dealing with piezo-based generators are talking about “micro-energy-harvesting“.
Electrical power-generation by piezo depends
mainly on cycling frequency. To achieve the orderof Watts, cycling frequencies in at least the kilohertz-range are needed.
Applications are autonomously operated arrangements with very small power consumption e.g.
for information transfer, sensor units for environmental parameters and toys.

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11.3 Electrical energy generation● Piezo transformers
A perfect example of the bi-directional piezo-effectis a piezo-transformer.
The energy coupling between input and output isdone by mechanical coupling avoiding e.g. magnetic fields from inductive elements.
Fig. 11.3 shows a demo-arrangement, based on
piezo stack’s d33 effect.
Two stacks are mounted into a rigid frame.
Stack 1 shows a common multilayer design with asmall layer-thickness “d” for low voltage actuation.
The second “stack” consists only of one thick layer“D”.

clamping framedD

Expansion of stack 1 by a low voltage signal input
squeezes stack 2 and generates a distinct electricalcharge. The big “D” converts it into a high voltage
output. This scheme works non-resonantly fromcycle to cycle. The cycle frequency determines theaverage power generation.
Notice: the transformer ratio Uin/Uout is more complicated than the d/D ratio suggests !
Piezo-transformers in practice:In practice, resonating systems are used. This inertia-based operation avoids the mounting into amechanical framework. Efficient resonant operation
requires hard ultrasound PZT-ceramics with a highquality factor (=> chap. 8).
Typical piezo-transformers use resonances in therange of >> 20 kHz up to Megahertz. Power transfers are typically in the Watt-range. This demonstrates again, that power generation by piezo ismainly a matter of frequency.

PZT-ceramic
signal (LV)inelectrodes

d

NV in

HV
out

L
HV outelectrodeFig. 11.3: schematic of an axial d33 transformer arrangement

Fig. 11.4: Monolithic high voltage piezo transformer (Rosentype) for voltage > 10 kV
Mechanical d33-d31 coupling. Low voltage signal input via d,high voltage generation by the resonating L

Resonant transformers need some care for optimum operation:
The input signal frequency needs to be matchedexactly to transformer’s resonance. Any power
extraction from the transformer is a kind of
damping, leading to a detuning of the resonancefrequency. Some kind of compensation circuitry isneeded to get stable power efficiency.
The main advantage of piezo-transformers is theirslim design and the absence of magnetic fields.
E.g. they are used within laptop-computers for igniting the background illumination of the LCD screen.

74 PIEZOMECHANIKBerg-am-Laim-Straße 64 · D-81673 München · Telefon ++ 49 / 89 /4 31 55 83 · Fax ++ 49 / 89 /4 31 64 12
E-Mail: info@piezomechanik.com · http://www.piezomechanik.com

Stand: April 2010

Piezomechanik · Dr. Lutz Pickelmann GmbH