3. OPERATING PERFORMANCE OF PIEZOELECTRIC STACKS

The main applications of piezoelectric actuators include:

• ultraprecise positioning,
• generation/handling of high forces/pressures either static (e.g. high mass loads, elastic forces) or dynamic (acceleration forces)

3.1.  Positioning by piezoelectric stacks

When a piezoelectric stack is cycled within a distinct voltage range, the displacement follows the well known hysteresis curve as shown in fig. 5 nonlinearity and hysteresis are a consequence of the ferroelectric properties of PZT materials.

The hysteresis diagrams for standard actuators are very similar for low voltage and high voltage types and are therefore not a relevant criterion for selection between these stacktypes for a distinct application. The displacement curves are valid for constant force load, meaning that an applied force does not vary during piezoelectric stack's travel. Even for very high (but static) load forces, the full extension is achieved.

• Relative positioning accuracy (positioning sensitivity).
  Piezoelements show an infinitely high positioning sensitivity: An infinitely small change of the operating voltage (charge content of the actuator) results in an infinitely small change in position. This is a very important feature e.g. for scanning tunnel microscopes to get atomic resolution (by feedback control via the tunnel current). Therefore, piezoelectric actuators show a continuous steady motion with no discrete "small steps". The positioning sensitivity of a system consisting of actuator and supply electronics is determined by the stability of the supply electronics and not by the actuator.
• Absolute positioning.
  Most positioning applications of PZT actuators aim for a travel of a distinct length or a travel to reach a distinct point with highest accuracy. The philosophy to get this is obviously not based on a simple voltage controlled motion by presetting a distinct voltage, because the resolution of this strategy would be limited by the hyteresis as shown in fig. 5. The main point is, that piezoelectric stacks are controlled by feed back: the position of interest is defined by some position sensitive effect (e.g. tunnel current of a STM, optical effects, interferogramms) or a position sensor and the voltage is regulated as long as there exist a deviation from the nominal value to eliminate this. The final absolute positioning accuracy is determined again by the precision of the position detection and the stability of the supply electronics (see relative positioning), and not by the PZT.

3.2.   Force generation by piezoelectric actuators, Interaction with externally applied forces.
A lot of applications show varying forces acting on the piezoelectric stacks during operation e.g.

• piezotraval against an elastic counterforce e.g. spring, clamping mechanism etc.
• acceleration forces during dynamic operation e.g. generation of vibrations, pulsed operation
• varying massload

Under all these conditions, the piezoelectric actuator reacts on the varying force with elastic compression or dilatation according its stiffness and the variation of force (Hook's law). piezoelectric stacks can be used as force generators where they are operated against a proper counterforce e.g. an elastic clamping mechanism. The produced force depends on the driving voltage and the stiffness relation between actuator and clamping mechanism. The maximum force (blocking force) which can be produced by an actuator is achieved for infinite stiff clamping at maximum voltage. The blocking force can also be defined as the required force to press back a fully elongated actuator to its zero-position. Some general relations between the geometrical dimensions of a stack and its properties are stated below

• The maximum travel of a stack is proportional to its length: (approx. 1 to 1.5%)
• Load/blocking force is proportional to the stack's crossection the blocking force F_B can be estimated according F_B=I_oxS: I_o max, travel of stack/S stiffness of stack
• Stiffness is related both to the actuators length and crossection.

fig.6 Schematic representation of force/travel relations of 3PZT actuators Actuator 1: showing travel I1,blocking force Fb(1) Actuator 2: double length, same crossection as actuator 1: double travel, same blocking force. Actuator 3: same length, double crosssection as actuator 1: same travel, double blocking force

EXAMPLE: an actuator is operated versus an elastic clamping, showing the same stiffness as the actuator: the achieved travel is half the maximum travel, the generated (additional) force is half the blocking force.

3.3.  Piezoelectric actuators as Force Sensors and Electrogenerators

Besides the actuator effect, PZT stacks shows normal piezoelectricity, meaning, that a mechanical force generates a voltage signal (electrical charge). Piezoelectric actuators can therefore be used for force sensing, which is very effective due to the high currents involved. Any arrangement incorporating a piezoelectric actuator can be checked for its mechanical resonances or mechanical response by combining the actuator with a signal analyzer and exciting the mechanics by an external mechanical knock/shock. In the widest consequence, PZT actuators can also be used as generators to convert mechanical power to electrical power.

| 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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