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 other piezo-actuation principles. For more comprehensive studies, refer to the available specialized literature. © All pictures, photos and product descriptions ar the intellectual property of Piezomechanik Dr. Lutz Pickelmann GmbH. Utilisation and copies by third parties have to be authorized. All rights reserved.
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 dri- ves with unlimited period of unidirectional action. Smart material: Special materials providing controllable features and properties beyond the classical behavior Solid-state materials: showing induced deformation: memory alloys, piezo-effect, magneto-striction Liquids: electro- and magneto-rheological systems with con- trollable viscosity
Solid-state actuator:
Based on all kinds of solid-state materials providing a controllable motion or force generation by mate- rial’s internal structure or texture (prime mover effect)
Piezo-actuator:
Solid-state actuator, using the inverse piezo-electri- cal effect Synonyms: piezo-translators, piezo-transducers Piezo stack actuators: Piezo stack actuators use the variation of the stack- length 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 the piezo-effect (in contrast to the “piezo-electrical” generator effect).
Smart structures
Mechanical arrangements based on smart materials to control the mechanical properties of the arrange- ment 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 sophisticated electronics to get a kind of “learning process” and self-adaption for getting an optimum system’s behavior. Synonyms: Actuator displacement = stroke = shift = expansion = elongation
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 the consequence of the variation of the electrical char- ge content of the piezo-actuator. Piezo-actuators are based on a special smart mate- rial: The electro-active piezoceramic material, known as PZT made of Pb (lead)-Zr (zirconium)-Ti (Titanium) mixed-oxides. Fig. 1.1: Schematic of a piezo-mechanical system based on a piezo stack, mounted on a solid base, moving the attached mechanics 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
1.1 Basic game rules
Decision guidance for using piezo-technology ● Verify that piezo-actuators will benefit your application 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 suit- able “piezo” match of your mechanical design. Only with a well-adapted application design, you can make complete use of an actuator’s perfor- mance including the benefits of high reliability, reproducibility and long operating life. The “upgrade” of existing old-fashioned mechan- ical designs by simply replacing a conventional drive by an “innovative” piezo-actuator will usual- ly fail. Systems must be designed with the piezo- actuator in mind. ● The lifetime and reliability of actuators depend strongly on the wide variety of the interacting operational parameters and the conditions of the individual application. Therefore, it is impossible to define a single test procedure, applied to an isolated element for evaluating 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 new suitability evaluation. ● A 100% general purpose piezo-actuator, covering all kinds of applications, does not exist. Piezo- actuators are typically optimized for distinct oper- ation profiles. This degree of specialization may not explicitly be e pressed in the data sheet. Therefore, care is needed when replacing suc- cessfully operating products by ones from other sources. ● 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 actua- tor’s performance can vary from supplier to sup- plier. Pay attention to the parameter definitions, when comparing elements from different sources. Do not misinterpret catalogue data: Notice, that not all operating specifications can be realized at the same time due to simple physical facts. Example: ● Maximum displacement/shift/stroke and maximum force generation /max. blocking force cannot be generated at t he same time, only either-or. ● The real operating frequency of a piezo- mechanical system is usually held far below the actuator’s resonance frequency!

Stroke (shift) – force balances – dynamics – performance limits
Fig.1.2 shows a solid state actuator made by stacking PZT ceramic layers, which are electrically contacted individually resulting in a multilayer ca- pacitor structure. The application of a voltage to the stack generates an electrical field within the ceramic layers resulting in a mechanical strain of the stack. The generated axial expansion of piezo stack’s length L is used for actuation. Coupling to external mechanics is done via the end faces (cross section area A). Achievable maximum strains typically range be- tween 0.1% and 0.15% of L. A piezo stack with a length L = 50 mm usually possesses a maximum stroke of 50−70 μm. The load capability and max. force generation of a piezo-actuator depend on stack’s cross section area A. The load and force limits are in the range of 7 – 8 kN/cm² (70 – 80 MPc). The mechanical work capability “stroke x force” is therefore proportional to the active ceramic volume L x A. piezoceramic discs Working axis: length L Active cross section area A (mechanical coupling face).
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 and dynamic 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 Forces: Stacks with small to medium sized cross sections (up to approx. 10 x 10 mm²) => Forces ranging from Tens to several Thousands of Newtons. Low voltage actuators preferred. Dynamics Depends strongly on actuator dimensions Non-resonant cycling with maximum strain: < 1 kHz Non-resonant cycling with reduced strain: < 10 kHz
Performance limits
Exotic and expensive, mostly prototypes or singular applications 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 Dynamics: Piezo shock generator < 10 μsec rise-time for 100 μm stroke Acceleration > 100.000 m/sec²
Low voltage stacks: Co-fired multilayer actuators (CMA): also called “monolithic” stacks, involve no gluing, 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 and medium cross section (1 mm² up to approx. 14 x 14 mm²) fig. 1.3: B. High voltage actuators cover needs for larger stack cross sections (fig. 1.3: A, C). Ring actuators offer a wider range of design- options for piezo-mechanical assemblies (fig. 1.3: C, D, E). Manufacturing of ring actuators is more elaborate and expensive than for bulk stacks. (B), (D), (E) low voltage bulk stack, ring actuator and ring chip
2.1 The piezo-mechanical effect Piezo 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 with acceptable voltage levels (100 V to 1000 V), the individual 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 are used 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 inter- nal electrodes are a very thin metal film (thick- ness 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 of approx. 500 V up to 1000 V are made from com- pletely sintered and finished individual PZT discs or plates prior to stacking. The inserted layer electrodes 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 kind of composite material. (green, right), mouse and USB stick for size comparison.
Most customers relate the functionality of a piezo stack only to the used piezoceramic material. However, it is a common experience that all aspects of the stack design, manufacturing technique and finish 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 are subject to strongly varying mechanical and electrical 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 from general-purpose elements for low and medium dynamic applications up to specially designed elements for very high mechanical dynamics. of a piezo stack into a preloaded casing Further upgrades of the stack actuator are the use of metal casings with internal pre-stress mechanisms (fig. 2.2) and other options like internal heat management, position sensing etc. (=> chap. 6: Options)
Piezo tubes are simple ceramic cylinders with metalized inner and outer surfaces. For mechanical stability reasons, the wall thickness of such tubes needs to be about ≥ 0.5 mm (fig. 2.3, A). To get maximum displacement, high voltages are applied. Piezo tubes are sometimes used as simple positioning mechanism, when access to the system’s axis is needed. Piezo ring actuators can be a much more efficient alternative. By applying a center bore, piezo stacks can be built up as hollow cylindrical elements, (fig. 2.3, B) offering a much wider range of design opportuni- ties for piezomechanics. Piezo ring actuators were first offered to the market 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
Attention:
Piezo tubes make use of the contractive d 31 piezo- effect. Piezo ring actuators make use of the expanding d 33 piezo-effect showing doubled strain efficiency of the d 31 operation. The change of sign in motion shall be kept in mind when setting up e.g. a feed back controlled system. (B))
Ring actuators show specific features and advanta- ges 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, this larger diameter results in an increase of mechan- ical 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 capaci- tance increases dramatically for mechanical sta- bility reasons only. The electrical power con- sumption increases equivalently, but is not need- ed 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 with- out the increase of electrical capacitance. ● Efficient heat management: Piezo-actuators generate heat when operated dynamically with high repetition rates. This heat must be removed from actuator ceram- ic. Overheating will lead to worsening of actuator performance and/or cause damage. It is a fact that piezoceramic is characterized by poor thermal conductivity that rules all heat management measures. The length of the heat diffusion path and the available actuator surface determines the quantity of heat removed from the ceramic 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. Fig. 2.4: Ring stack versus bulk stack
All structural components of piezo-actuators are subject to potentially high mechanical loading not only during operation, but also during handling and mounting. Be careful: piezoceramic components are mechani- cally sensitive devices. ● Local mechanical stress concentration creates potentially “cracks” within the  piezoceramics, leading to a weakening of the electrical “stability” of the ceramic. ● The electrical and mechanical stability of the supply electrodes is important for the overall reliability of a stack actuator when operated dynamically. ● A major design topic is the handling of the neces- sary insulation gap between internal electrodes and supply electrodes of opposing polarity. Point of attention is a potential local distortion of electrical field in the vicinity of such an insulation region. By the piezo-mechanical coupling, this leads to a local mechanical stress concentration with subsequent crack generation and a potential failure of the stack by electrical short-circuiting. PIEZOMECHANIK takes care about these risks by using two different insulation concepts for different actuator applications. ● 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 The insulation gap is prepared on stack's surface. Therefore the piezoceramic cross ection of a stack is 100% electroded and activated homogeneously. ● highest actuator performance, high blocking forces ● no local field distortion etc. ● no local stress spots are induced => no cracks are generated etc. Last, but not least: osi-designed stacks show high resistance to bending forces. Fig. 2.6: on stack insulation (osi)-design, insulation is done outside the active stack
● in stack insulation (isi-design) Used for PIEZOMECHANIK’s PSt-HD 200 stacks Piezo chips (H)PCh 150 This 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 minia- ture stack cross sections. Here occurs additionally the stress spot concentra- tion problem. To avoid catastrophic crack generation and propagation different countermeasures are provided. One technique applies small notches or grooves to the stack’s surface for getting a “soft” surface to reduce mechanical stress concentration. Isi- stacks are less stable against bending forces due to surface weakening by the notch-effect (in comparison to osi-stacks). To improve the mechanical stability, isi-stacks are mostly used in a high-preloaded arrangement. 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 are needed to transfer high powers without losses to the ceramic structure. PIEZOMECHANIK is the expert for this kind of non-resonant actuator operation. Suitable insulation and contact techniques allow the reliable operation of its actuators with high power levels.
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 are charged up from a voltage U min to U max The motion is reversed, when the actuator is discharged. The (reasonable) maximum strain rates are about 0.1 – 0.15 % of the actuator length. Exaggerating strain by applying too high electrical fields is adverse to reliability. For sub-resonant operation, the piezo stack motion follows the applied voltage signal instantaneously. The electrical behavior of piezo-actuators is like that of a capacitor. Precision positioning is mostly done by voltage control of piezo stacks. The stroke of a piezo-mechanical system can be increased by lever-constructions, where amplifying factors n of 10 are achieved without big efforts. But keep in mind: ●  load capability is reduced to 1/n ● 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 U min-U max-U min leads to the hysteresis diagram fig. 3.1. by cycling the stack within the voltage range U min – U max – U min
Attention:
do not over-interpret the open-loop stroke-/voltage- diagrams, 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 diagram is achieved only after reaching an equilib- rium attained by cycling the system many times while all other operation parameters like tempera- ture, force and load are held very constant. If the cycling conditions are changed the system will adjust towards a new equilibrium after the appli- cation of a sufficient number of cycles.
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 the hysteresis becomes due to the slow poling effects of the piezoceramic structure. These poling effects are also the reason for creep upon the application of a voltage step to the piezo stack. ● When an open-loop random (non-periodic) setting of the voltage input is applied, a field of positions is generated, where the cycling hysteresis is the envelope 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) Fig. 3.2: Field of positions by open loop random generation of voltage steps. The uncertainty in positioning by random position setting is about 10% of the operation range, defined by Umin, Umax. A lot of attempts have been made to overcome the need for position feedback for piezo precision posi- tioning, but the success was limited A,  algorithms have been developed for piezo- actuator 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 applied instead 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 really suited 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.
Notice:
Even when an open-loop perfect actuator would be available, it only partially solves the problems of precision positioning. In most cases, piezo stacks are prime movers of coupled 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 self- evidently not compensated for by open-loop actuation. Even the simplest adjustment procedure in laboratory by turning the voltage control knob of a manually set voltage supply is a kind of feed-back control: The operator checks for the correct result (e.g. a distinct interference pattern in optics)
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% of actuators maximum stroke position-sensing and feed-back control is needed. Then the piezo-actuator is able to carry out the finest corrections to come nearest to a desired pre-set position. In this case, hysteresis, creep, and non-linearities are ruled out automatically. back 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 can handle 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).
The accuracy of a piezo-positioning system is usually not limited by the piezoceramic or piezo stack. This has been explicitly proven down to the picometer range. Nevertheless, in a complex piezo- mechanical positioning system, there are influences outside the actuator resulting in a potential limitation of accuracy. ● quality of electronics: any noise and electrical fluctuations will be con- verted 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-mechanical system ● Tilting of stack’s end faces: A piezoceramic stack shows, to some extent, a tilting of its end-faces during the axial expansion. Simply laboratory style optical arrangements with a glued sandwich of substrate/piezo stack/mirror work tilt-free only over short shifts (=> 7.6). Tilting can be reduced by mechanical preloading of the stack (=> chap. 4.9). A tilting up to several µrad / µm shift occurs typically. Consequent can¬ cellation of tilt for a longer stroke is only possible by adding a guiding mechanism.
● piezo-based stabilization circuits
A special kind of precision control is the stabiliza- tion of position sensitive physical effects. The optical output power of laser resonators depends on the alignment of the whole opto- mechanical set-up. To keep the resonator in its power maximum despite misaligning influences the optical output power is monitored. By apply- ing a proper tracking algorithm to discriminate the power maximum, the laser can be kept by piezo in 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 condi- tions (no force variation!). ● Two values for ΔI are stated in the data sheet A, for the unipolar activation 0 V/+U max B, for semibipolar operation -U min /+U max The semi-bipolar operation increases the open- loop stroke of a stack by 20 – 30 %. Any kind of stack actuator is suitable for semi- bipolar operation at room temperature. ■ 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
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 Imech to move the mechanics properly? B, force level F。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 ΔF mech by the piezo- actuator ➡ The ratio Δlmech/ΔFmech is the compliance (inverse stiffness) of the mechanical system

Fig. 4.1:
Gravitational mass load of a piezo-actuator The force level F c remains absolutely constant during piezo action. The maximum piezo shift Δ l max is achieved (according data sheet). The piezo-actuator generates a translatoric mecha- nical energy Fc △ Imax • Applications: precision positioning of heavy loads like telescopes, precision manufacturing machines.
Fig. 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 F c. The expansion of the piezo-actuator leads only to a small increase △F mech of the force balance. It is found, that the piezo-actuator produces (nearly) its maximum shift (data sheet). A mechanical energy F c Δ l max is produced (first order). Application: common optomechanics with reset 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 a remarkable increase Δ F mech (= elastic force Δ F e ) of the total force balance. The piezo shift Almesh is reduced compared to the data sheet value. The total energy generation is (F c + ½ Δ F c) · Δ l mech; ½ ΔF。ΔI 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 Δ F。 when moving. The final step of the voltage swing U min - U max is used to build up the sealing force (press fit). This final force variation F see is not accom- panied 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 of mechanical arrangements
From a physical  point of view, the piezo stack is an active spring: When a piezo-actuator generates an external force ΔF, it does not only compress the mechanical part- ner, but the force acts back on the stack itself. This “self-compression” of the actuator reduces the effective external stroke of a piezo stack corre- spondingly (depending on actuator's stiffness). Blocking force The force generation limit is reached,  when the piezo-actuator is clamped rigidly with zero compli- ance. Because no shift can be generated, the com- plete 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  maxi- mum voltage ratings are shown (both, for unipolar or semi-bipolar activation). The blocking force AF ы ock 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 stack
You have analyzed your mechanics and application with regard to the required stroke-force activation profile (AFmech, Almech), no dynamic forces (=> chap. 4.1, => chap. 10). 1st step: Select the suitable actuator group with respect to its force balance, which is related to actuator’s crosssection. ● sufficient high load capability ●  data sheet blocking force at least double the needed force generation ΔF mech for your application. ■ Example to 1st step Your mechanism needs a preload F c of 2 kN and a force generation of 1 kN. This is covered by piezo stacks PSt 150/10x10/xx or PSt 150/14/xx VS 20 actuators with casing 2nd step: Within the actuator group selected according step 1, a suitable actuator length is chosen by numerical or graphical means .
A, numerical solution
Remember that a piezo-actuator is an active spring! The stroke is reduced the more as the ratio of AFmech/AFblock increases. To get the needed stroke Almech for activating your mechanics, the actuator with data sheet stroke Δ l max is required. Almech < Almax (1 - (AFmech / AFBIock))
ft
Almax = Almech AFBlock / (AFBlock - AFmech) Δ l max (max. stroke) and Δ F block (blocking force) are found in actuator's data sheet. Almech, AFmech actuation data, required by the attached mechanics
4.4 Selecting a piezo stack
B, Graphic solution
Fig. 4.5 shows a coordinate triangle defined by the data sheet values Δ l max and Δ F block of a potential piezo-actuator candidate. The actuation data △ l mech , △ F mech define an origin based stiffness line with the intersection with the triangle at point A. If the coordinates A (ΔΙ, ΔＦ) of an actuator are equal with your requirements (Δ l mech , Δ F mech ), then the actuator is suitable to drive your mechanics. Usually, an actuator is selected to keep the point A in the upper half of the triangle. defined by the operated mechanics.
Comments:
● The above mentioned strategy is a linear approxi- mation 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 a heavy, but constant load does not reduce actua- tor’s maximum stroke. The reason is rather simple: the load condition is applied to the piezo stack before operating the stack e.g. a mass load or a low stiffness preload is applied during mounting the system! This compression of the stack creates the neces- sary counterforce to bear the load, so the system is in force equilibrium before starting the piezo- action. No additional force generation ΔF by piezo needed => full piezo stroke! ● When actuator and the driven mechanics show the same stiffness Sactuator = Smech The effective shift and generated force show 50% of the data sheet values. This configuration allows the highest elastic ener- gy transfer E
E = 1/8 Almax AFmax
Dynamic operation:
For dynamic operation, acceleration forces of the involved 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 be at least twice the desired maximum operation frequency.
In a formal way, the blocking force is defined as the achieved force generation of a stack when it is clamped with “zero compliance”. “The actuator does not move, when a voltage is applied." In real nature, all materials show a limited elastic modulus that does not allow infinitely high stiffness by passive means. But using a closed-loop active arrangement, the blocking 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. A  Piezo stack (green) B  strain gage on stack C  load cell D  compression springs E  position control electronics PosiCon 150
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 0 V unipolar operation Case 1: Case 2:  -30 V semi-bipolar operation b, “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. ● 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 for the 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-mechan- ical system without a motion of the actuator (virtually infinitely high stiffness of actuator).
Results:
● The piezostack PSt 150/10x10/40 shows the following maximum blocking forces Case 1: unipolar mode (equivalent 0 V/+150 V activation) : 6500 Newtons Case 2: semi-bipolar mode (equivalent -30V/+150V activation) : 7800 Newtons ● A linear relation between the force variation and compensating voltage has been found for the PSt 150/10x10/40 stack (fig. 4.7). ● The blocking force is equivalent to the maximum load variation on a piezo stack that can be com- pensated 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 activa- tion. This position shall be kept constant by closed- loop operation. The maximum increase of load force what can be compensated for corresponds to the “60 Volts blocking force” of the stack. Fig. 4.7: Blocking force versus excitation voltage for piezo stack PSt 150/10x10/40 (uni-polar and semi-bipolar operation range)
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 strain gage) is compressed by a 2 kN axial load force and the resulting compression is measured in a similar arrangement as shown in fig. 4.6. The compression of the stack is measured via the strain 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 compressive load 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). Fig. 4.8: Piezostack PSt 150/10x10/20 with closed (A) and open (B) leads Results: Two different stiffness values ΔF/ΔI 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 remains within the stack. Hence a voltage at the leads is generated by mechanical means! This is equivalent to the electrical field within the piezoceramics. This electrical field stabilizes the piezoceramic against compression. Consequences for practice: The situation (A) with closed leads is equivalent the operation of piezo stacks by voltage control. Mechanically generated electrical charge flows towards the voltage supply to keep the actual volt- age 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 compliance by current control is preferentially used in dynamic motion control. The highest system stiffness is achieved by closed loop position control (virtually infinitely high stiff- ness, (=> 4.5)). However, the response-time (band- width) of feedback controlled systems is slower when compared to the open-loop current control.
4.6 Stiffness
Piezo-actuators with casing
The stiffness values shown in data sheet are defined for force coupling via the end-pieces of the actuator. When actuators with casing are mounted via the casing tube (by clamping or front threads of the piezo cartridges FPSt), a reduction in the overall stiffness must be taken into account, because the force path involves both the stack and the casing. Notice: The overall stiffness of a piezo-mechanical system depends on all involved mechanical parts : “Weak” points are often poorly designed coupling joints. The implementation of “motion magnifiers” like levers 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 system down to 1/n²! (compared to actuator's original data)
Comments 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 of force 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 defined for small-signal variation and voltage control. Keep a tolerance range of +/-20% in mind. Catalogue data are best used for a kind of trend analysis.
The maximum load force shown in the data sheet is the 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 F c , the PZT-ceramic performance decreases 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 a concern.
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 potential- ly tensile forces by negative acceleration. (e.g. when slowing down stack’s velocity after a pulse 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, the stack 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 poten- tial mechanical or electrical overload of the piezo- mechanical system. Take care for correct electrical installations: pulsed actuator discharge by accidental short circuiting is a proper way to kill the stack.
Data sheet for the mechanical properties of PZT- ceramics show a small tensile load capability of a few 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 mechanical preloading (= 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. Designing 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 (stiff- ness) of the preload spring needs to be very low: a few percent of piezo-actuator’s stiffness in maximum. ● The preload force shall be sufficiently high to accelerate all incorporated masses sufficiently fast during the actuator's contraction to avoid tensile loading of the ceramic. The dynamic force F dyn can be estimated by the well know acceleration/force-law Fdyn = m ΔΙ/Δt²
Notice:
the preload mechanisms shall not only take into account the force balances during regular opera- tion, but shall also stand potential external shocks.

Fig. 4.9. Internal preloading:
The preload mechanism VS is integrated into the actuator casing. Typical configuration of actuators with casing like PIEZOMECHANIK’s PSt … VS elements. Externally applied tensile forces can be handled up to the preload level. Dynamic cycling of an external mechanic leads to force loads with alternating sign. Coupling joints need careful design to handle this situation without fatigue and play/backlash.
Fig. 4.10. External preloading:
The complete mechanics is pre-loaded by the spring VS towards the stack. The whole arrangement is under permanent com- pressive load, no alternating force directions occur during cycling. Backlash is avoided.
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-mechanical systems with a high mass load: The mechanical coupling between actuator and mechanics is only compressive. Preload VS 2 can be kept low according the regular driving conditions. Preload VS 1 acts as protection for the piezo stack for handling irregular high tensile forces (within the system). In this case, actuator and mechanic parts can sepa- rate upon tensile stress. VS 1 keeps the stack safe and sound.
4.9 Mechanical preloading (pre-stress)
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 mechanical support frame with high static stiffness. Actively preloaded systems are by definition sym- metrical 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, the overall power consumption can be kept low by using electronics with energy recuperation. Nevertheless, the total efforts for an actively pre- loaded system are higher than for simple conven- tional drive.
PIEZOMECHANIK actuators with integral
preload
PIEZOMECHANIK 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 and are more likely to withstand “rough” handling and operation, or the impact of other environ- mental influences. On request, PIEZOMECHANIK provides actua- tors with increased preload levels up to sym- metrically acting push-pull arrangements with regard to the force balance.
The expression “dynamic operation” is used for operation modes where the actuator and the whole piezo-mechanical system are facing additional reac- tions compared to a nearly static driving situation. Most standard actuators are designed mainly for positioning with a slow shifting of components from position A to B. Dynamic operation adds effects like higher acceler- ation rates and forces superimposed on to the static force balances. The increased electrical power con- sumption results in self-heating of the actuator stack. 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 reso- nating systems like ultrasound generators. Those are operating continuously on a single high frequency > 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 the power supply. ● Long-term effects related to permanent dynamic cycling. The long-term dynamic operation of a piezo- actuator defines the mean electrical power con- sumption of the system. This power is to be pro- vided by the electronic supply. Points of consideration are the self-heating of the piezoceramics and potential high cycle fatigue problems of the mechanical set-up.
■ Examples:
1. Pulsed operation (square wave excitation) of a piezo 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 very low (e.g. 1/sec), the average power is rather small. 2. For a periodic excitation profile (e.g. harmonic waves), the peak power and average power of the dynamic operation shows a fixed ratio.
The dynamic response of a piezo-actuator depends on how fast the actuator capacitance C is elec- trically charged Actuator velocity v ~ l = C dU/dt dU : variation of piezo voltage during charging Actuator acceleration dv/dt ~ dl/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 Δt: 100 msec
100 μsec Charge current l △Ω/△t: 20 mA 2 Amperes 20 Amperes Electric power (1/2 CU²)/Δt: 2 Watt 200 Watt
Acceleration (constant): 0,02 m/sec² 200 m/sec² 20.000 m/sec² 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 be larger than twice the desired operation frequency ● sufficient durability of mechanical coupling elements 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 are needed beyond the standard techniques. Standard actuators will fail. Electrical 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.
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 in high cycle numbers and the question about struc- tural durability of the whole piezo-mechanical system (e.g. material fatigue etc.). To increase the reliability of such a construction, there must be a perfect match of its design to piezo-specific design rules. “Compromises” violating such design-rules will simply result in failures during long-term operation.
Electrics:
The average power consumption P ay of a cycled piezo-actuator can simply be derived from the charge/discharge rate (frequency) f and the energy content of the piezo-actuator applied per activation cycle.
P ay = ½ CU² f
U voltage level of charged actuator C actuator’s capacitance In a similar way, the mean (average) charging current I can be determined
I = 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 a fixed ratio Īpeak : Īav = π.
Thermal aspects
During cycling piezoceramics, electrical energy is dissipated into heat due to “internal friction” of the moving piezoceramic structure. Approx. 5 – 20% of the electrical energy input is converted 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 the mechanical operating conditions (stroke-force). Blocked actuators show rather low losses, because the “internal structure” of the ceramics cannot move, therefore no “structural friction” is present within the ceramics. Further, the losses disappear nearly completely, when the piezoceramics are operated under cryo- genic low temperature conditions. The ferroelectric nature of piezoceramics is “frozen” with the conse- quence of strongly reduced capacitance, strain and losses. Energy dissipation and self-heating are no concern. Piezo stack's temperature is defined by the equi- librium between heating power (energy dissipation) and applied cooling power (heat management). Standard designed actuators for positioning do not contain explicit heat management measures. Power cycling can therefore only applied short-term until the stack has heated up to a distinct limit. High temperatures will reduce actuator performance and reliability. 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 by using suitable PZT-ceramics with a wider operating temperature range. actuator, clamped at its end faces. Environment: ambient air convection. Notice the cooling effect at the end-faces due to the clamping mechanics
A standard (incomplete) question is: what frequencies can be achieved by (non-reso- nant) piezo action? The necessary counter-question is this: for what amplitudes? What other operating conditions? Another typical misinterpretation of data sheet para- meters 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 is defined by the power consumption (frequency and amplitude!) 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 Different kinds of low voltage bulk and ring stacks (H)PSt 150 made of same PZT-material and layer- structure 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 con- vection) The elements are cycled @ 0 V/+150 V. different kinds of low voltage piezo stacks and rings

5.4 Typical operating frequencies
It is easily seen that the self-heating phenomenon is less critical for ring type actuators and tiny stacks. The more bulky stacks are, the poorer is the heat transfer.
Notice:
Bulky stacks can show a remarkably higher tempe- ratures in the ceramic’s core than on the surface. A proper heat-management technique will allow an increase 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 to the actuator. When the piezo stack is operated at reduced volt- age levels, they can run much higher frequencies. For a lot of applications, it is attractive to combine a high voltage actuator with a low voltage/high current power supply.
■ Example:
A ring-actuator HPSt 1000/15-8/20 VS 22 thermo- stable is combined with a large bandwidth amplifier LE 150/100 EBW a +/-2 μm oscillation can be gene- rated up to about 10 kHz. Ultrasonic oscillators can run very large ampli- tudes at high frequencies > 20 kHz. What is their trick? They are using an enhancement- effect by mechanical resonance. Hence, they can only run a single fixed frequency. A normal non-resonantly operated piezo-actuator needs to charge/discharge the complete electrical 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 operat- ed non-resonantly. Therefore a high electrical power is needed to drive the actuator resulting in corre- spondingly high losses => self-heating! A good resonator like an ultrasonic device has a mechanical energy storing mechanism: the mechanical resonance. With a rather low electrical energy transfer (low losses!), a huge mechanical oscillatory energy can be piled up over a distinct quantity of cycles. This results finally in a large oscillating amplitude. How behaves a normal actuator at resonance: The resonant accumulating effect is present to some extent, but it is much weaker than for an opti- mized ultrasonic device (up to 100 times smaller). The background is the use of different kinds of piezoceramics used for actuators resp. ultrasound generation (=> chap. 8) due to the different applica- tion profiles.
The shorter the stack is, the higher the natural fre- quency 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 reso- nating piezo is therefore no longer a pure capacitor, but an oscillator circuit (capacitor + inductance). Actuator based piezo-mechanical systems do not show only one natural frequency, but a variety of them with potential influence on the axial displace- ment (cross-talk). For a lot of applications it is important that the piezo-actuator shift strictly follows the input signal. In the case of resonances, there is a phase-shift between the excitation signal and mechanical reac- tion remains. ● 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 of the stack’s diameter. When the diameter is remark- ably larger than the stack length, then the dia- meter 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 ceramic shows a rather high mechanical damping. Therefore, a piezo stack is a rather “bad” oscilla- tor, expressed by a rather low quality factor. In the case of resonance, the resonant amplitude enhancement is typically < 10 (see fig. 5.3). In contrast to the broadband piezo-actuators, ultrasonic devices are a single frequency resonat- ing system, using “hard” piezoceramics with very low mechanical damping (quality factor > 1.000) ● Any attached mechanics show natural frequen- cies that will be super-positioned with the original actuator motion. By using piezo-actuators, these resonances of the coupled mechanics can be excited or damped (motion control). Resonance excitation leads to large amplitudes with reduced power consumption. Resonant excitation of structures is used with miniature mechanics (MEMS, piezo motors). same 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 feed- back control are usually operated well below the natural frequencies of a piezo-mechanical system to avoid feedback problems due to electro-mechanical phase shifting.
5.5 Resonance
Resonance frequencies are usually defined for actuators with one side fixed to a base and the other end freely moving. (Freely suspended actuators with both sides free will show the double resonance frequency). The electrical excitation is usually based on low field variations. When an external mass is added to a piezo- actuator, its resonance frequency will be reduced. The resonance frequency f A-M of such an actuator- mass system can be estimated: ● the added mass Mext is small compared to actuator’s own mass M A fa-m = fres Meff/(Mex+Meff) M eff：effective mass of actuator ~ ¹/3 M a 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. Resonance frequencies are therefore strongly reduced! Catalogue data The resonant response of a stack depends on mounting conditions (e.g. mechanical pre- stress). 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. ● the added mass Mext is significantly larger than the actuator mass => the simple spring/mass for- mula is valid fa-m = 1/2π (Sa/Mex) 1/2 S A actuator stiffness (spring rate = inverse compliance)
The performance of piezo-actuators for various applications is not only defined by piezoceramics used. It depends on a lot of other features like the finish of the stack structure or other added features. The most frequently requested actuator upgrades concern: ● improved heat management ● position sensing PIEZOMECHANIK offers comprehensive assis- tance in all cases where special solutions are required to cope even with “exotic” piezo- actuator applications. Ask the experts at PIEZOMECHANIK.
6.1 Heat management “Thermostable”
The dynamic charging power of a piezo-actuator is partially dissipated into heat. The actuator tempera- ture reflects the equilibrium between heating by power dissipation and cooling by the heat transfer to the environment. Too high temperatures interfere with 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 stack and transferred towards the casing. The “thermostable” casing is made from thermally high conductive metal (like copper, brass, aluminum etc.) providing effective heat sinking contact to the environment. Just the simple mounting of a “thermostable” actuator to the operated mechanics provides a remarkable cooling effect. For very high thermal loads, all common methods for enhanced cooling can be applied to the actuator casing like forced air cooling (incl. addition of air fins) 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” modi- fied elements can be done in a straight forward 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 with thermo-stable option + air fins + forced air cooling has 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 heat- management would reach its temperature limit at about 150 Hz. Fig. 6.1: Various types of actuators with thermo-stable heat management Air fin corpus can be added
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 capacitance analysis (=> chap. 7, Operating instructions, => chap. 8, Material properties).
6.3 Low temperature operation
Piezoceramic stacks can be operated down to the lowest temperatures near absolute zero. Standard actuators run down to -40 °C. For operation at even lower temperatures, modifica¬ tions maybe necessary and are offered on request. E.g. piezo stacks can be wired with poly-imide coat- ed manganin-leads. Due to the reduced thermal conductivity of Manganin, the thermal loading of the cryo-station is then kept low.
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 high quality strain gages applied directly to the surface of the piezo stack. Usually, complete 4-active-grid- bridges are used to ensure temperature compensa- tion and high sensitivity (Fig. 6.2-6.4). By closed loop feedback controlled positioning, the non-linearity, hysteresis, and thermal drifting of a piezo stack are ruled out. Mechanically induced strain variations of the stack (e.g. by changes of the external load) are also detected and cancelled out.
Position resolution:
Strain gages can detect strain variations Δ L/L even below 10 . Taking into account the actuator strain range of about 0.1 %, this motion can be resolved again to approx. 10 3 . For short stacks, position variations of 1nm magnitude can be detected. For position sensing and control, PIEZOMECHANIK offers the strain gage amplifier DMS 01/03 and the complete feedback control system PosiCon. Fig. 6.2: Wheatstone-configuration with 4 active grids SG: Supply voltage to 1, 2, Sensor signal out on 3, 4 piezo stack Typical gage resistance: 1.2 kiloOhms with strain gage position sensor. Position read out by DMS 01 unit. Piezo-actuator supply electronics SVR 150 (left)

Enhanced mechanical preload
Depending on the individual application, higher mechanical preloading of the actuators may be needed beyond what is supplied as standard (about 10 – 20% of the max. load capability). For symmetric push-pull configurations or very high dynamic ope- ration, preload levels up to 50％ will be necessary. PIEZOMECHANIK offers modifications of the prelo- ad mechanisms beyond standard.
Vacuum operation
PIEZOMECHANIKs standard actuators are generally vacuum compatible to standard laboratory high vacuum levels better 10 -8 mbar. Neither the perfor- mance is impacted nor is vacuum contaminated by out 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 are need, e.g. special coatings to avoid traces of contaminations. Bake out procedures can be applied to some extent. It is recommended to contact PIEZOMECHANIK in these cases to ensure the proper system results.
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 pro- blems. Problems occur when the rotational axis and stack’s axis are parallel and the stack shows a large aspect ratio length/diameter: The centrifugal force can lead to the bending or buckling of the stack. Special mechanical requirements are needed to handle this situation. PIEZOMECHANIK is experienced in this field: Ask for proposals.
Non-magnetic configurations
A special feature of piezo actuation is the complete absence of magnetic fields during motion genera- tion. Accordingly, piezo-actuators are an ideal solu- tion 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, prelo- ad 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 struc- tural 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.
In most applications, piezo-actuators are usually kept as small as possible and operated nearly to their performance limits simply for cost reasons. As a result, in most mechanical designs, piezo- actuators become the “weakest link” from a me- chanical point of view. In addition, ceramic is a material that is more complicated and more sensi- tive to issues resulting from improper handling than metal components. Even when piezoceramic is “ruggedized” by placing it in a preloaded casing, a profound understanding of the technical background of piezo devices is a must to ensure high reliability through proper design and operation. Any step in handling, mounting and the operation of piezoceramic components must strictly avoid any single overload situation. Improper mechanical designs, irregular mechanical and incor- rect electrical driving conditions need to be identi- fied by realistic tests and evaluation procedures to come to a reliable solution! “Mishandling” of piezo-actuators does not lead necessarily to the immediate break down, but re- duces the long-term reliability with failure part way through the desired duty cycle. Piezo-actuators operated in a short-term manner can operate at or near their mode maximums, which would not be recommended, when long-term reliability and life- time 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 a signal for a long-term reliable solution. Piezo-actuator reliability is subject to a wide range of influences from ● the attached mechanics ● the driving electronics Even when a piezo-actuated configuration has been proven for reliability, a seemingly “small modification” of the driving conditions may require a new re- evaluation 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 opera- tions with elevated mechanical stress levels by short-term excitation. ■ Example: two-level switcher operation in pulse-width modulated processes, piezo fuel injectors with cycle numbers up to 10 10 . Such high cycle numbers depend strongly on the quali- ty of the mechanical design of the whole set-up! ● Long-term static operation: Potential degradation is coming mostly from envi- ronment influences like excessive air humidity etc. in superposition with the piezo-mechanical driving parameters and temperature. When comparing specifications about reliability, pay attention to the applied driving conditions like the strain levels. ■ Example: humidity problems in tropical atmo- sphere can best be overcome by hermetic encapsulation of the stack. In practice, a superposition of both kinds of opera- tional profiles occurs. A simple extrapolation for reliability from the above stated general “experien- ces" will be limited in success. Individual testing under a realistic load duty cycle will be needed in any case to ensure high reliability of a piezo- mechanical system.
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 opera- tion. The electrical polarity of a stack is indicated by 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 with correct polarity is increased. The polarity of an unknown actuator can be iden- tified by applying a small voltage variation and checking the sign of the resulting shift! Alterna- tively, a stack can be connected to an oscillo- scope. By application of a short squeeze, a small voltage pulse is generated. Its polarity shows the wire 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. ● Apply a DC-voltage to the stack and measure the charging current. After a while, this charging cur- rent will decrease to a negligible value below Microamperes. This reflects the very high internal resistance of the stack >> Mega Ohms.
Note:
This internal DC-resistance has nothing to do with stack’s power consumption or self-warming effects! When you identify lower resistance, please check all involved electrical parts, wiring, connectors, and plugs for failure, not only the stack. A failed stack with internal short-circuiting shows very low resis- tance of kilo Ohms or less. ● Testing of the overall electrical circuitry can be done acoustically by applying a harmonic signal of a few Volts to the piezo-actuator e.g. by a func- tion 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 and apply a small knock to your piezo-mechanics. A voltage response signal according the me- chanical ringing of your piezo-mechanics will be found, containing information about natural frequencies of your arrangement. Trouble shooting: Stack failures are often assumed when the actuator creates a “strange noise”. Keep in mind 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"!
✪ 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 pe- ripheral mechanics is needed, otherwise electrical insulation break down of the actuator surface may occur over time. Piezo stacks show DC-insulation at the end- faces. 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 be present. The more “compromises” you allow on these points the worse the actuator’s reliability will become. ● Keep the activation duty cycle of piezo-actuators as low as possible. No inverted operation by using high voltage levels as long-term basic state of your piezo action. No stand-by-operation: Switch off the actuator, when not in use or set the piezo signal to 0 V! ● 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 with respect to voltage, current and power range. It is a fact of experience, that an accidental over- load situation will emerge over time and damage the actuator. ● Be careful not to contaminate piezo stacks with chemical agents. Avoid traces of water, humidity, electrolytes (no touching with bare fingers), adhe- sives and casting materials generating corrosive agents during cure. Cleaning can be done using 100% isopropyl-alco- hol (propanole), avoid acetone. 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 in a very final way.
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 cou- pling to the actuator, friction, wrong preloading, wrong force coupling, misalignment of coupling faces from actuator to mechanics reduce significantly 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 in electrical break down and arcing. Coupling of actuator and mechanics Optimum actuation performance is achieved by following a few simple rules ● The coupling face of the mechanics shall cover completely actuator's end faces to achieve maxi- mum force transfer (fig. 7.2). The contact force shall be homogeneously distributed over the contact area ● When a high load pressure is applied, the cou- pling faces of actuator and mechanics faces shall be absolutely plain (eg. by grinding) to avoid local overload of the ceramic front face. ● The resulting load force vector shall coincide with actuator's axis. Within a virtual cylinder of +/- 10% of actuator's cross-section (fig. 7.2) to avoid excessive bending and shear stress. Force misalignment tolerance becomes more critical for increased ratios actuator length/diameter. For high dynamic operation, actuator's axis shall further hit the centre of mass of the attached mechanics to avoid dynamic torque. 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 at- tached mechanics by floating axis orientation of the mechanics. Acceptable tolerance α: see above .
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. ● Coupling of piezo-actuators to guided mecha- nisms (axis orientation not floating): One of most widespread design mistake is cou- pling a plain-faced actuator directly to a plainfaced guided mechanism (fig. 7.3). Even the slightest misalignment between the orientations of the both plains leads immediately to edge squeezing with very high local spot pressures and sub- sequent ceramic damaging (fig. 7.1) especially under high force loaded conditions. In a similar way, the plain-plain coupling of an axial- ly acting stack with a rotating lever arrangement will lead to a fundamental edge squeezing situation in any case (fig. 7.4). In the above cases, it is a must to decouple the axis orientations by using spherical / plain coupling or flex hinges or other means! ● The above requirements are valid at any time and any state of the system during set up and operation. Fig. 7.4: Incorrect/correct coupling of a rotating mechanism
7.4 Handling and operating
Electrical aspects
The electrical controller performance deter- mines the dynamics and motion character- istics of a piezo-actuated system.
Voltage ranges, polarity
The plus/positive -pole of a piezo-device is usually indicated by a dot or red wires. Typically, the coaxial cable shield electrically grounds piezo-actuator casings with coaxial cable. This configuration is pre- ferentially used together with common voltage amplifiers. On request, the cased versions can be built up with a floating potential setup: The stack actuator is insulated from the metal casing by separating elec- trical grounding from the casing. Floating potential wiring is most often used together with current con- trol electronics. Ask PIEZOMECHANIK for details. Make certain to use the correct polarity when apply- ing the specified maximum voltage, otherwise de- poling or poling reversal of the ceramics will occur. This results in a useless irregular response of the actuator. Counter-voltages with lower levels can be used to some extent, but attention needs to be paid to the individual driving conditions (e.g. stack's tem- perature => 9.1).
Uni-polar activation
Voltage signals with the specified actuator-polarity can be applied to the piezo-actuator up to the specified maximum voltage ratings independently
Near-static long-term operation
When bare ceramic stacks are operated nearly stati- cally in a highly humidity loaded atmosphere, it is not recommended to apply the maximum voltage Umax for long-term operation. Semi-bipolar activa- tion can partially compensate for this reduction. Alternatively, the humidity-problem can be dealt with by using hermetically sealed elements. Metal-foil encapsulated stacks PSt 150/5x5/20 have withstood such conditions operating for 2 years (DC – opera- tion) @ 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's standard power amplifiers LE and RCV provide uni- polar output 0 V/+U max •
Semi-bipolar activation
At room temperature, any piezo stack actuator can be operated up to a 20% counter-voltage ((-) 0.2 U max ). Using the wider voltage range, stroke and force generation range of piezo-actuators are enhanced 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 be applied 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 dramatically at low temperatures. For very low (cryogenic) tem- peratures, the piezo stacks can be operated in a bipolar way within +/- U max . By doubling the voltage range compared to the unipolar mode, the tempera- ture-induced reduction of piezo-mechanical efficien- cy (μm/Volt) can partially be compensated for. PIEZOMECHANIK offers SVRbip amplifiers with bipolar 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 the original 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.
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 tem- perature. Too high temperatures reduce perfor- mance and life-time. Hence, the long-term power operation of piezo- actuators requires heat-management solutions for optimum power efficiency and lifetime. PIEZOMECHANIK offers highly effective options for internal heat-management for standard piezo- actuators with a casing. The outer dimensions will not be changed! (=> 6.1: option thermo-stable) ● Ring-actuators show a better heat-management balance than bulk stacks (=> chap. 5.4). ● Piezo stacks can be immersed in inert fluids for heat 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 can be determined by electrical capacitance mea- surements.
Maximum temperature limit
The Curie-temperature T c 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 T c due to following effects: ● actuator's performance and operation data are worsening remarkably ● electrical losses/heat-dissipation increase with temperature ● the piezoceramics start to become electrically conductive (depends on type of PZT-ceramics) ● temperature limitations of used insulation-, contact- and coating materials In practice, the typical operation temperature limits are about 2/3 of the ceramic’s Tc Piezo-actuators adapted for high temperature can be operated up to 150 °C long-term (200 °C short- term): HS/HT PZT-material based components (=> chap. 8).
■ Comment:
A special case are low T c -ceramic based stacks: They can be stored even at high temperatures. Potential depoling is compensated for by the first full voltage swing operation at normal temperature levels. 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 be- havior of your mechanical frame work, when applying large temperature variations. Avoid mechanical overload due to thermally induced stress during cool 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 conduc- tivities, thermal capacitances and different coeffi- cients of thermal expansion for the different materi- als in use (PZT-ceramic, metal electrodes, coatings). Ask PIEZOMECHANIK for details on cryo-com- patible actuators. For low temperature operation, preloading shall be applied to the stacks. The mechanical coupling is best done by compressive means only (=> chap. 4.9) to avoid any external tensile stress. At cryo-temper- atures, 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 water on the actuator resp. the sucking of humidity inside the casing. The ceramic core shall show even a slightly higher temperature than ambient (use a simple heater). Check stack’s volume temperature via the electrical capacitance.
Piezo-actuators have electrodes and high electrical fields in the vicinity of the ceramic stack’s surface. It is easily understood that any mechanical or chemical impact on this surface structure results in a high risk of failure. ● Be careful with any contaminations of actuator surfaces with unknown species. Even traces of corrosive agents will result in an actuator failure over time. Do not touch ceramic elements with bare fingers. Avoid contact of the ceramics with water containing fluid or electrolytes. ● Be careful, when using adhesives, sealing and encapsulation materials: no corrosive reaction ● Glue line quality: At first glance, a very thin and hard glue-line gives the best coupling quality in terms of rigid coupling of the involved compo- nents.
Attention:
Large coupling cross sections, together with hard and inflexible glue lines: The lateral d 31 motion of the piezo-component will be hindered and consequently the axial d 33 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 unhin- dered motion. products must be generated by the cure pro- cesses. Do not use standard 1-component silicone compounds: they generate traces of acids, when reacting with air humidity. These agents will penetrate into actuator's surface and start elec- tro-corrosion. Use corrosion free materials only! ● 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. Fig. 7.6: Lateral (in-plane) clamping effect by large area hard gluing a piezo-chip on a rigid substrate. The thickness expan- sion of the PZT-layer is blocked also, distortions occur in the ceramic (tilting, reduced stroke) flats can occur.

Useful Materials
● Temporary bonding Bonding waxes as used for wafer grinding, melting point 70 °C, Logitech Polishing & Lapping, Glasgow
● Permanent bonding
for -50 °C to +120 °C temperature range High quality epoxies: EpoTec, Araldite, longer cure > 30 min at room temperate or slightly elevated temperatures. ● Low outgas and cryo-compatible glue lines Stycast 2850 FT TorrSeal
● Provisional bonding
Cyano - acrylates: give thick and flexible glue- lines, not recommended for long-term use
● 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 been used e.g. for cooling. Use 100% isopropyl alcohol (iso-propanol, IPA) for cleaning: Avoid acetone and other ketones
● Electrical contacting
Most multilayer piezo components from PIEZOMECHANIK have electrical wiring. Nevertheless it is helpful to understand how to apply electrical contacts to PZT-components, having no wires. Such piezo-elements have very thin metal-layers as electrical contacts (thickness μm). These metal layers can be electrically con- tacted by soldering, conductive adhesives and coatings or elastic spring contacts. Be careful: accidental removal of these original contact layers make the piezo component unusable.
Soldering of PZT-metalization
Attention: Improper soldering dissolves the thin metalization in the solder tin making an electrical contacting then impossible. ● use standard solder tin ● 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

Environmental influences
Piezo-actuators have electrodes and high electrical fields 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 main concern is the operation of piezo-actuators within very humid and polluted atmospheres (aerosols, like tropical ambient air). This situation can be overcome by reducing the operating voltage level of piezo- actuators or hermetic encapsulation (=> fig. 7.5).
Vacuum operation
PIEZOMECHANIK stack actuators are compatible with high vacuum conditions. Restrictions occur in the fine vacuum in the mbar range. Especially high voltage actuators can ignite glow discharge on their surface, when a distinct voltage level is exceeded. This does not allow a regular operation of these actuators with maximum voltage ratings. Low voltage actuators do not show the glow discharge problem and can be used regularly. Noble gases, hydrogen atmospheres Hydrogen and light noble gases like helium interfere with the electrical insulation conditions of a piezo stack .The accepted maximum driving voltage is reduced. Insulation performance breaks down. Individual tests are necessary to determine stable operating conditions.
Radiation
Piezo-actuators are sometimes exposed to high energy radiation or neutron fluxes (e.g. resonator tuning in synchrotrons or accelerators for spallation neutron sources). The heavy-metal containing piezo- ceramics is not degraded by radiation.
Space-borne applications
Piezo stacks are compatible with vacuum, cryo- conditions and radiation. Therefore they are well- suited for space applications. Adoption to special aspects of a mission can be implemented into an actuator design on request.
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 class shows much better piezo-electrical and piezo-mechanical efficiency than quartz. The PZT- formulation can be varied with regard to stochiometry and dopants resulting in a broad spectrum of material properties optimized for dif- ferent 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 suita- ble material for a distinct application. Piezoceramics is a ferro-electric compound. This means, that the electro-mechanical conversion pro- cess for producing a motion is related to a kind of self-enhancement process based on an internal reorganization of the material's structure. ● This self-enhancement process results in the higher piezo-electrical efficiency of PZT compared to materials like quartz. ● The structural re-organization is accompanied by “internal structural friction”, resulting in energy- losses. When the structural re-organization is hin- dered by blocking conditions or very low temper- ature, these losses are reduced. Developing new piezo-materials is a steadily ongoing process in the ceramic industry. PZT is the most widely used smart material for solid-state actuation. Alternative materials with enhanced strain capability are under study, but all these “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 compari- son to the classical compression experiment 4.6). Literature tries to down-size this complexity by linear approximations, but to the cost of con- sistencies between theory and practice.
Notice:
PIEZOMECHANIK is using piezo-electrically “soft” and “semi-hard” PZT-formulations. High strain rates and high energy contents are achieved for efficient non-resonant electro-mechani- cal conversion. PZT ceramics' material data are usually defined at low field excitation where nonlinearities are not dominant. In practice, high electrical fields are applied to PZT actuators, resulting in a non- linear enhanced response (“ferro-effects”) and altered parameters. Nevertheless, for reasons of comparison with materials from different suppliers, the classical characterizations are used for describing actuator ceramics and shown in the tables. The data shown in the tables are valid for room temperature operation.
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 position- ing tasks. 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 mate- rial for high voltage actuators. It is a high strain material with a wide temperature range up to 150 °C. The actuator data do not vary strongly with temperature. This type of material is used for piezo- fuel injectors. Fig. 8.2: Schematic stroke-/ voltage diagram for high field excitation of HS/HT-piezoceramic.
Piezoceramic HP
with highest mechanical power density for high voltage 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 mo- tion 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. Fig. 8.3: Schematic stroke-/ voltage diagram for high field excitation of HP-piezoceramic.
Piezo-mechanical data (small signal-values at room temperature)
Non-linearity:
Due the ferroelectric nature of PZT-ceramics, the above-mentioned parameters can vary significantly with the operating electrical field strength. In practice, PZT-ceramics are operated with large field excitation levels for actuation. The following example for the rather stable PZT-ceramics HS/HT illustrates this trend:

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 approx- imately 40% when heated up from room tempera- ture to 80 °C. This effect has to be taken into account when selecting a proper amplifier for dyna- mic operation (=> chap. 9.3). It is immediately understood that, for power efficien- cy reasons in the case of a dynamic operation, a proper 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 is approx. -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 of other suppliers. Notice: Metal end-pieces applied to piezoceramic stacks contribute to the over-all thermal expansion of such a device. A piezo-actuator's casing is usual- ly 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, this situation changes: e.g. by clamping the casing or using piezo cartridges FPSt with front thread mount- ing. The thermal expansion of the complete force path needs to be taken into account.
Piezo strain
The achievable strain/Volt of a piezo-actuator is represented by the d 33 -coefficient (piezo-electric charge 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 self- enhancement of the piezoceramic reaction is strongly reduced. ● the effect of an increase of temperature on the d 33 parameter depends on the Curie-temperature of the PZT-material used. Soft-PZT-based PSt stacks show a slight efficien- cy 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 a temperature variation is applied. This effect is irrelevant for actuation, although the effect can electrically shock the user when a charged actuator is touched with bare hands at the leads.
8 Properties of piezoceramics
Comparison between actuator and ultrasonic
PZT-ceramics
Ultrasonic techniques are a kind of resonant actua- tion, where the device is designed to run at perma- nent (cw continuous wave) harmonic oscillation on a high single (resonance) frequency with large ampli- tudes. The achieved large amplitudes are the con- sequence of resonant amplification over a large number of cycles. The efficiency of storing mechan- ical oscillation energy is described by the “quality factor Q”. A high Q indicates a low mechanical damping. Usually a “normal” piezo-actuator is operated “non- resonantly” broadband from DC up to rather high frequencies. Large amplitudes shall be generated within one cycle. Such an operation profile is only available for the class of “soft” or semi-hard PZT- materials. These materials shall show a larger piezo- electric coefficient d 33 and an elevated dielectric constant. Actuator ceramics show a low quality factor Q: common broadband piezo-actuators are rather “poor” oscillators (=> 5.5, Resonances).
Single frequency ultrasonic resonator systems show strongly reduced losses and heat dissipa- tion (in relation to oscillation power; frequency, amplitude) compared to broad band actuators.
Electrostrictors
Electrostrictive ceramics can roughly be described as a kind of piezoceramics operated at its Curie- temperature near the phase transition piezoelectric- parelectric . A special class is the PMN-PT solid solution ceramics (lead-magnesium niobate in lead-titanate) shows a Curie-temperature around room tempera- ture. A stack, built up from this electro-strictive material shows 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 high accuracy 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 of about +/-5 °C around the optimum point. Therefore, dynamic operation is ruled out because of the self- warming problems. Summing up these side conditions, electrostrictive ceramics are not commonly used.
For actuation, electrical energy is converted into a mechanical reaction. The energy content E of any actuator depends only on the active piezoceramic volume and the applied electrical field strength. Expressed in usual electrical terms, the energy con- tent E is E = ½ CU² Newcomers to piezo actuation ask for actuators with very low capacitances to save energy or power in a very general way. Keep in mind, that energy conservation is valid for piezomechanics too. High power mechanical output cannot be achieved with a 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 mea¬ sure 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 nomi- nal capacitance values for the same energy and power balances.
9.1 Electrical input and piezo-mechanical reaction
The electrical power supply defines, to a large extent, the performance of a piezo- actuated system. Careful selection of properly adapted electronics is therefore a must.
Electrical noise
One of the unique features of piezo actuation is the conversion of a small precise electrical signal into an equivalently small shift in position. Consequently, any undesired electrical signal variation like noise or other instabilities is transformed into an equivalent “mechanical” noise or uncertainty of position too. It has been found, that the positioning accuracy of a piezo-mechanical system is not limited by the piezo- actuator 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 Δ l noise can be estimated by Alnoise = AUnoise x (Almax/Umax) Δ l max : max.actuator stroke at maximum voltage U max △U noise：voltage noise The lowest noise levels are achieved by low power analogue linear amplifiers. High power switching amplifiers show higher noise levels and are mainly used for dynamic motion con- trol. PIEZOMECHANIK offers low noise amplifiers SVR for highly sensitive positioning tasks. ■ Example The low noise amplifier SVR 150 shows a noise level of 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 repre- sents a “small-signal excitation”, the real fluctuation in position is << 1 Angstrom.

Pulsed operation
The mechanical response/rise time of a piezo stack is determined by the charging time of the actuator's capacitance. The higher the charging current is, the faster 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 3 (t) is the needed peak cur- rent I peak to be deliverd by the power supply. The peak-currents I peak for the most common signal profiles are shown below: Sine: Ipeak = π C Upp f Triangle: Ipeak =   C Upp f Square wave:  Ipeak = C Upp/dt U oo total voltage swing dU = U oo dt voltage rise-time For very short rise-times, the necessary peak cur- rents can reach significantly high levels. ■ Example A piezo-actuator with 5μFarad capacitance shall be charged within a time dtc with a voltage step U ｡｡: 0 V/150 V dt。 = 100 msec = >  Ipeak = 7,5 mA low dynamic positioning eg. by an amplifier SVR 150 dt c = 1 msec =>  I peak = 750 mA dynamic motion control, power level of a LE 150/100 EBW amplifier dtc= 150 μsec =>  Ipeak = 5 A piezo fuel injectors ,use power switches like HVP dt c = 10 μsec =>  Ipeak = 75 A piezo shock generation using HVP switches For rise times < 1 msec, piezo-actuators need to be adapted to the very high electrical and mechanical load conditions. Standard actuators will fail (see chap. 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 with simple “open” and “close” levels, an electrical switch will do the job. Keep in mind, that “big block” actuators show large capacitances and need therefore high charging current (up to the order of magnitude 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 the actuator configuration to prevent mechanical damage of stack’s structure. Standard actuators will fail!
Long-term average current For long-term cycling operation of a piezo-actuator with a distinct frequency f and a voltage variation Δ U, the actuator’s capacitance C is charged/ discharged accordingly. This defines an average charging current Ī according to:
I = C ΔU f
To produce a permanent cycling of a distinct signal function, the power electronics shall be selected for both 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  /  I   =  π triangle I peak / I  = 1 Power amplifiers from PIEZOMECHANIK are mostly designed for a I pesk : Ī  = 3 to allow a well matched cw high dynamic cycling e.g. for motion control applications. 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 charg- ing is split into ● Mechanical work (displacement, elastic defor- 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 cy- cled with a frequency f, an average electrical charg- ing 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.
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 with energy recycling (energy recuperation): 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 accept- able efforts.

Voltage ranges, voltage polarity
The classical actuator activation was done by using unipolar voltage signal 0/U max according the actua- tor'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, enhanc- ing 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-actuator can be operated with a counter-polar voltage, as long as this level keeps the corresponding electrical field well below the coercive field E depol (fig. 9.1).
Notice:
the above mentioned aspects are valid for all kinds of piezoceramic components like bimorph benders or shear-elements ceramics de-poling or coercive field. Counter-field operation of a piezo-actuator must stay in the safe-area at lower electrical field levels compared to Edepol Generally, three operation modes can be distinguis- hed according the operating temperature: Unipolar activation: can be applied over the com- plete 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 dis- placement and force generation are. The individual driving conditions also depend on the type of PZT- material used.
Unipolar amplifiers
PIEZOMECHANIK offers power amplifiers LE and RCV for use with unipolar devices . No depoling of the PZT-ceramic occurs at elevated temperatures.
Semi-bipolar amplifiers
PZT ceramic accept counter-voltages of about 20 % of the maximum voltage rating ((-)0.2 U max ) at room- temperature. 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 the low power level, no self-heating occurs within the piezoceramic.
Bipolar amplifiers
Bipolar ceramic activation at room temperature is mostly done with shear elements or bimorph bend- ers to get symmetrical dual-sided action. Do not exceed the voltage ratings because of the de-poling effect. PZT-ceramics' stability against field-induced de- poling increases remarkably at cryogenic tempera- tures. Therefore, piezo stacks accept bipolar opera- tion with maximum voltage ratings at very low tem- peratures (below 77°K). PIEZOMECHANIK offers low power bipolar ampli- fiers SVRbip as standard.
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:
v = dl/dt ~ dQ/dt = Im ~ dIm/dt = İm Q(t) electrical charge content The relations for charge-and current-control opera- tion of piezo-actuators are only valid for sub-reso- nant activation. Due to the non-linear behavior of PZT-ceramics, the control 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.
Increased dynamic stiffness
The electrical charge balance of a piezo stack is not only changed via the electrical power supply, but also by load force variations (=> chap. 4.6). Voltage control dissipates this mechanically gener- ated charge to cancel out unwanted voltage varia- tions. But thereby the mechanical stiffness of the actuator is lowered. Current control handles quantitatively the charge flow between amplifier and actuator. Mechanically generated charge is not dissipated and results in an increased stiffness of the actuator. Current control is only applicable to dynamic motion. Linear relation between position and charge content Q The position-charge-characteristic shows a (near) absence of hysteresis and good linearity fig. 9.2. Fig. 9.2: Linear response of position by charge control (max. charge content of actuator at max. driving voltage)
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 para- meters. ● Higher dynamic stiffness increases the response speed of piezo-mechanical setups. ●  Open-loop control of the above parameters is faster than that of closed-loop voltage-control based systems Charge/current control and precision positioning? Open-loop charge or current control is not suited for very high accuracy positioning. Reasons are: ● linearity and hysteresis are limited to about 1% of the maximum stroke the charge/position-characteristic varies with o temperature ● 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 discrimi- nated from position related effects. External misaligning effects cannot be compen- sated for by open-loop control means. For high accuracy positioning a closed-loop feed- back control via position sensing is needed. This will allow the use of simpler and less costly voltage- controlling electronics. Comments on data sheet Carefully check the experimental basis for the definition of the actuator's capacitances stated in data 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 (capacitance- meters use 1 – 2 Volts excitation @ 1 kHz). The high field excitation of PZT ceramics at an actuator's voltage limit shows an effective capacitance larger by 50% or even more compared to the low-field excitation. In addition, capacitance increases further with temperature- rise. Real actuator capacitances maybe as large as twice the data sheet value.

1 Offset
potentiometer for manual setting of a DC-voltage level to piezo. The amplifier can be used as an autonomous power supply with a manual piezo- voltage setting. In addition, the DC-voltage level will be super- imposed to the amplified external signal from input (3)
2 Ampl
potentiometer for continuous variation of ampli- fier's gain factor for amplifying the external signal (input (3))
3 Input
putting in an analogue signal from an external source (function generator etc.) Fig. 9.3: Front panel of a piezo power amplifier from LE product line
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
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 much as possible". Putting concrete numbers on the needed piezo-parameters is helpful to avoid over- sizing and mismatch. Poorly selected system components are ineffective and therefore 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 piezo- actuator 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 the needed 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 piezo- ceramics can occur (=> chap. 6.1: heat manage- ment).

Beyond positioning
The very first application of stack-based piezo- actuation was in (coherent) optics in the 1960's to 1970’s as super-precise positioning drives for the emerging laser technology and semi-conductor industry. The other highlights like force generation and 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-/force- generation profiles over a large number of cycles. A high level of reproducibility is needed. Common mechanical drives are then limited in their repetition rates resulting in rather long test periods. For distinct test procedures, piezo-actuators pro- vide a remarkable advantage due to their ability to cycle high frequency together with high repro- ducibility. One interesting aspect is the upgrade of conven- tional test frames by adding a high frequency piezo- drive. The conventional long stroke performance can be superimposed by a high frequency fine modulation (fig.11.1). Piezo-mechanical arrangements have been success- fully used for - Fretting tests - Super high cycle fatigue test - Material testing of polymers - High frequency vibration excitation, shaker The frequency range of conventional electro- magnetic shakers is usually limited to about 5 kHz. Piezo-based shakers extend this upper frequency limit towards >> 10 kHz. added high-load, long stroke piezo-actuator for extended operating dynamics. 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.
11.1 Piezo action for material testing
Shock-generation by piezo
An alternative to high frequency harmonic excitation of structures is the application of single pulses to excite the natural frequencies of a mechanical structure. By analyzing the decay of the excited oscillation, the mechanical parameters of the system can be analyzed. Piezo-specific unique features are ● non-ballistic shock generation, mechanical contact between shock-partners prior to shock generation and transfer ●  wide tuning range of acceleration levels (100 m/sec² up to > 100,000 m/sec² ● electrical tuning of mechanical shock parameters (e.g. amplitudes, rise-time) ● single shot, bursts or continuous operations are feasible 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 is an unusual driving mode of piezo stacks: the electrical excitation is very short (< 10 μsec) compared to the acoustic transit time of sound through the stack. The propagating shock-front within the piezoceram- ic leads to a highly inhomogeneous mechanical stress distribution, both in time and place. This con- dition is usually strictly avoided in piezo-technology. Special mechanical provisions for the shock- generator design are needed to get a reliable config- uration.
Notice:
Piezo shocks shall be distinguished from common “fast acting” piezo-elements as used in fuel-injec- tors: The electrical excitation time is sufficiently long (about 100μsec) compared to the transit time of sound. The stack is mechanically excited below its natural frequency, having a near homogeneous stress distribution. A real shock actuation within a fuel injector would result in a worsening of the injec- tion balance due to ringing effects. 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 carried out with higher repetition rates in so-called split Hopkinson-Bar arrangements. Piezo-shock-generation is now in practical use at calibration services. non-ballistic piezo-shock-generation.
Motion control is a general expression for all kinds of motion generation according distinct defined cri- teria, usually done in a feed-back controlled system. A special field in this context is active vibration con- trol with: Active vibration generation Active vibration cancellation Active vibration isolation
Adaptronics, morphing
Piezo-mechanical components are used for dynam- ic active shaping of functional profiles like adaptive wings, adaptive rotors, adaptive optics, adaptive frame structures.
The following applications of piezo-elements are not part of PIEZOMECHANIK’s program. 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 an electrical charge. It is also true that this electro-mechanical conver- sion is bi-directional: Piezo-mechanics and piezo-electricity Piezo-actuators exhibit the piezo-electric generator- effect, while they are not specially adapted to this kind of use. Nevertheless a few hints shall be given: ●  the conversion efficiency is related to the g-constants shown in the PZT-material data tables ● 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 actua- tion. ● Force transducers etc. For quantitative measurements single crystalline materials are used like quartz. For high tempera- ture application the more effective GaPO 4 is used. Polycrystalline PZT is a low cost alternative, when a compromise in measurement quality is acceptable. The main advantage of PZT is the much higher generator-efficiency that makes sig- nal detection easier.Usually, force measurements are done by determining the quantity of generat- ed electrical charge, not the induced voltages. ● Energy harvesting, energy scavenging One cubic-centimeter (cm³) of PZT-material deliv- ers 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 piezo- elements into the countryside and squeezing them from time to time will not solve the world’s energy problems. Serious projects dealing with piezo-based gener- ators are talking about “micro-energy-harvesting“. Electrical power-generation by piezo depends mainly on cycling frequency. To achieve the order of Watts, cycling frequencies in at least the kilo- hertz-range are needed. Applications are autonomously operated arrange- ments with very small power consumption e.g. for information transfer, sensor units for environ- mental parameters and toys.
11.3 Electrical energy generation
● Piezo transformers
A perfect example of the bi-directional piezo-effect is a piezo-transformer. The energy coupling between input and output is done by mechanical coupling avoiding e.g. mag- netic fields from inductive elements. Fig. 11.3 shows a demo-arrangement, based on piezo stack’s d 33 effect. Two stacks are mounted into a rigid frame. Stack 1 shows a common multilayer design with a small layer-thickness “d” for low voltage actuation. The second “stack” consists only of one thick layer "D". Fig. 11.3: schematic of an axial d 33 transformer arrangement Expansion of stack 1 by a low voltage signal input squeezes stack 2 and generates a distinct electrical charge. The big “D” converts it into a high voltage output. This scheme works non-resonantly from cycle to cycle. The cycle frequency determines the average power generation. Notice: the transformer ratio U in /U gut is more compli- cated than the d/D ratio suggests!
Piezo-transformers in practice:
In practice, resonating systems are used. This iner- tia-based operation avoids the mounting into a mechanical framework. Efficient resonant operation requires hard ultrasound PZT-ceramics with a high quality factor (=> chap. 8). Typical piezo-transformers use resonances in the range of >> 20 kHz up to Megahertz. Power trans- fers are typically in the Watt-range. This demon- strates again, that power generation by piezo is mainly a matter of frequency. Fig. 11.4: Monolithic high voltage piezo transformer (Rosen- type) for voltage > 10 kV Mechanical d 33 -d 31 coupling. Low voltage signal input via d, high voltage generation by the resonating L Resonant transformers need some care for opti- mum operation: The input signal frequency needs to be matched exactly to transformer’s resonance. Any power extraction from the transformer is a kind of damping, leading to a detuning of the resonance frequency. Some kind of compensation circuitry is needed to get stable power efficiency. The main advantage of piezo-transformers is their slim design and the absence of magnetic fields. E.g. they are used within laptop-computers for ignit- ing the background illumination of the LCD screen. High power piezoelectric axial
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