4.    NOTES ON TECHNICAL DATA

4.1.  Voltage ranges, polarity, depolarization
The piezoelectric stacks described in the following data sheet are designed for 3 basic voltage ranges:
150 V (multilayer-types)
500 V (discrete stacking)
1000V (discrete stacking)

The maximum voltage has to be applied with the right polarity, indicated for the actuators. The ceramic is thereby operated with internal electrical field strength of 1-2 kV/mm. Counter voltages (showing opposite polarity than indicated) can be applied to 15-20% of the stated max. voltage, e.g. approx. -20 V for +150 V multilayers. The limit is defined by the onset of depolarization (inactivation) of the PZT material.

• Bare stacks are electrically insulated at their front faces and surfaces and can be operated potential free with respect to environment. Notice the polarity of the leads: black -, red +
• For piezoelectric stacks with casing, the operating ground reference is connected to the casing, therefore, the polarity of the driving voltage is fixed and is positive for the actuators and supply electronics. This allows free combination of actuators and supplies to match different application needs. On request actuators with casing for negative voltage polarity are available.
• Depolarization - Piezoelectrically active PZT ceramic becomes partially or completely inactive by destroying the original remnant polarization of the ceramic by applying too high mechanical pressure, temperature or countervoltage. This phenomenon is reversible and an actuator can be reactivated by applying the maximum operating voltage. The (potential) onset of depolarization is one criterion for the max. load force limit for the actuators. Low voltage multilayer actuators can be easily repolarized by applying 100 V and even polarization reversal is possible without any loss of performance.

4.2.  Electrical Capacitance

From the design and operating principles of piezoelectric stacks it is obvious, that the electrical behavior of such actuators resembles simple electrical capacitors (under non resonant driving conditions). The indicated data for the electrical capacitance's of the stacks are small signal values for low driving voltages/electrical fields measured at room temperature. The capacitative nature of piezoelectric actuators imply that electrical power is needed only for changing an actuator's position and no power is needed to hold a position (in contrast to magnetic actuators, where a permanent current is needed to sustain a position). To estimate the required power or currents to supply a dynamically operated actuator, an increase of the nominal capacitance by 50% has to be accepted. The reasons are due to variations of the PZT material characteristics, elevated temperature and large signal effects (application of large electrical fields).

NOTICE: the dielectric constant of high strain PZT (used for actuators) is sensitive to temperature variations and is increased up to 50% at 90^oC (compared to room temperature value). The electrical resistance of piezoelectric stacks is very high and ranges from of MegaOhm (for large volume multilayers) to GigaOhm (for high voltage stacks). An expanded (charged) actuator can be disconnected from the supply and can hold its position for a long time due to the very slow self discharging of the actuators by leakage currents (time constant hours to days).

4.3   Maximum Expansion

The maximum expansion is defined as the stroke for a voltage step 0V to maximum voltage at room temperature. Exceeding the max. voltage rating will potentially show onset of saturation in actuator's expansion characteristic and reduction of lifetime. The tolerances in the expansion rates are due to variation of materials composition from batch to batch.

• Low voltage actuators: The maximum voltage is 150 V. Further the 100 V expansion rate is stated to make easier the comparison with multilayer stacks from competitors. Tolerance of the stated ratings is +10%. Experience shows, that usually the nominal values are reached or slightly exceeded.
• High voltage actuators: Tolerance of the stated ratings is +10%. Experience shows, that usually the nominal values are exceeded.

4.4   Maximum Load, Mechanical prestress

• Piezoceramic elements resist large compressive forces, but are sensitive to tensile forces. The stated maximum compressive (m.c) force load is defined by the potential onset of depolarization under adverse circumstances such as additional countervoltage or elevated temperature. For large length/diameter ratios of a stack, the risk of buckling damage further limits the load force.
• Mechanical prestress - To handle higher tensile forces, a common trick is to prestress the piezoelectric stacks (see section 1.3.2.). Tensile forces are allowed as long as they are compensated by the prestress force. For dynamic operation, the prestress is necessary to compensate acceleration forces by overshooting and during the resetting of the actuator. For this case, a minimum prestress force Fres is needed, so that the masses coupled to the piezoelectric actuators are sufficiently fast accelerated, that the contracting PZT stack never pulls the external mass load:

F_res = m ^ I / ( ^ t )²
m = mass load
^ I = max. travel
^ t = minimum reset time

4.5.  Stiffness

Like any other solid body, piezoceramics show elasticity and therefore stiffness of the piezoelectric stacks can be defined. The resonance frequency of a PZT actuator under mass load depends on stiffness and can be estimated according the simple mass/spring-model. Furthermore, the loss of travel/force generation of an activated actuator can be estimated, when in operation against a varying counterforce. The stated data for stiffness are approximate, and were measured at a prestress 10% of the maximum force load.

4.6.  Resonance Frequency

The stated resonance frequencies are defined for actuators with one side fixed/without external mass/for small electrical signals. The frequencies refer to the basic axial oscillation mode of the actuator. Note, that an actuator shows different oscillation modes and the resonance frequencies of these modes may be lower than those for the axial mode (e.g. radial mode axial mode for a short actuator with large diameter). Additional mass load applied to the actuator lowers the overall axial resonance frequency. Therefore the resonance frequency of an internally prestressed actuator with casing is lower than that of the bare stack due to the mass of the prestress mechanism. Standard stacks show low resonance gain (high damping) due to the PZT ceramic used and the compound layer) structure. Resonance has to be kept in mind during the installation of feedback control systems. The onset of phaseshifting between the exciting signal and the mechanical response of the actuator limits the operating frequency range. Note: not only the actuator shows resonance, but also any coupled mechanics. Such parasitic resonance's can be excited by the piezoelectric actuator with high efficiency (large gain factor of the mechanics), even when the actuator itself is not operating in resonance. In many applications, resonance's are unwanted and the operating frequency of these systems should be well below resonance. However, some applications exists, where resonance is used directly for high power conversion efficiency e.g. to excite large oscillation travels (ultrasonic etc.). Resonantly working actuators and transducers show a different design compared with the standard actuators.

4.7.   Thermal Effects

• Thermal expansion - Especially for positioning application, the thermal drift of a stack has to be observed, because it can reach the order of magnitude of the piezoelectical travel. The following values are valid for the ceramics. For more complex designs (e.g. casing with prestress) the contribution of other mechanical parts has to be included. The stated values should then be corrected by the addition of up to 5x10^-6

Multilayer -stacks: -3x10^-61/^oC

Discrete stacks: 7x10^-61/^oC

• Temperature dependence of the piezoeffect
  The piezoelectric properties of actuators (e.g. maximum travel) depend to some extent on the temperature of the stack (e.g. by environmental conditions or self heating). Within the operating temperature limit, the discretely stacked high voltage actuators shows an increase of travel of approx. 20 % at 90^oC whereas multilayers reduce their expansion by a few percent with respect to the room temperature value. For cryogenic temperatures below LN2, all systems show strongly reduced travel of about 25% of the room temperature value. A principle limit of the piezoeffect results from for the Curietemperature of the material (see 4.8.). Pyro-electricity: beside the piezoeffect, PZT ceramics show the generation of electrical charges (voltage) due to temperature charges, but this effect is not really relevant for stack application.

• Operating Range
  piezoelectric stacks of standard design can be operated in the range of -40^oC+90^oC
  High voltage actuators:
  Temperature limitations are due to the application range of peripheric materials such as insulation material, mechanical properties of adhesives etc. Curietemperature is not a critical aspect in this case, because it is rather high (above 250^oC). Low temperature versions for application at cryogenic temperatures (down to LHe) are offered, in which case special adhesives and insulation materials have to be used to avoid brittleness at low temperature. Low voltage multilayer stacks: Here the Curietemperature is only about 150^oC and above 100^oC, the properties of the stacks after significantly: electrical capacitance and electrical losses during dynamic operation increase dramatically.

• Self-Heating
  Due to the ferroelectric nature of PZT ceramic, about 5-15% of the supplied electrical power is converted into heat: A bare stack CTC-PSt 150/5/15 heats up to approx. 90^oC for dynamic cw-operation with sinewave U 150 Vpp/600 Hz. A further increase of frequency is only possible with forced cooling or by reducing the driving amplitude. Self-heating prevails in large volume actuators because of the unfavorable ratio surface/volume compared to smaller stacks. The actual temperature of a stack under dynamic operation depends on a lot of environmental conditions and has to be checked individually. As a measure for stack's temperature, the change of stack's electrical capacitance can be used (see sec 4.2.).

4.8.   General Material Data
(approx. values for standard actuator PZT-ceramic/room temperature)
rel. dielectric constant: approx. 4000
piezoel. Charge constant d33: approx. 500x10^-12m/V
coercive field strength: approx. 600 V/mm
Young's modulus: 6x10^-10 N/m²
Density: 7.5x103kg/m³
Mech.gain factor: 50-100
Thermal conductivity: approx. 1W/^oK ^. m
Spec. heat: approx. 380 Ws/kg ^{. o}K
Curie-temperature:
Low voltage multilayers: 150 ^oC to 200^oC
High voltage types: 250^oC to 350^oC
Depolarizing pressure (see sec.4.1./4.4.): approx. 4000N/cm²
Compressive strength: 6x10⁴N/cm²
Failure strain: approx. 1%

NOTICE: The electrical and piezoelectrical properties depend on the special type of PZT ceramic. Discrete high voltage stacks can be optimized with respect to these parameters for distinct applications.

| Classification of piezoelectric stacks | Mounting of Piezoelectric actuators |
| Operating Performance of Piezoelectric actuators |
| | Notes on Technical Data | Selection Guide | Custom Designed Actuators | Safety Instructions |

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