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Piezo Engineering Tutorial
In a very general sense, it is typically the first (lowest) resonant frequency of the positioning system that
limits the achievable servo bandwidth. The design of the flexure, supporting mechanics and piezo actuator
stiffness govern the location of this resonant frequency. Aerotech has optimized the dynamics of our
nanopositioning piezo stages to provide a stiff, high-resonant frequency design in an optimal stage package.
By adding an applied mass to the piezo stage, the resonant frequency will decrease by the following
relationship:
Equation 15
where mload is the mass of the applied load.
In lever amplification designs, the stiffness can change throughout travel, as mentioned above. As a result,
the resonant frequency will change by the square root of the change in stiffness. For example, if the stiffness
changes by 7%, the resonant frequency will shift by approximately 3.4% throughout travel.
Equation
15 will provide a first-order approximation of resonant frequency in piezo nanopositioning systems.
Complex interactions of the dynamics due to damping, nonlinear stiffnesses and mass/inertia effects cause
these calculations to provide only an approximation of the resonant frequency. If a more exact value is
required for your application or process, please contact us and we will assist in the design and analysis of an
engineered solution.
Aerotech specifies the resonant frequency of our piezo nanopositioning stages at a nominal value with a
±20% tolerance along with the given payload (unloaded, 100 grams, etc.).
C.4.6 Load Ratings
Piezo actuators are ceramic materials and are brittle. As with most ceramics, PZTs have a higher
compressive strength than tensile strength. The actuators used in our stage designs are preloaded so as to
always maintain a compressive load state during standard operational limits. On our data sheets, we specify
push and pull load limits that refer to loading applied in the direction of travel. For some stages, the load
rating may be different depending on the direction of the applied load. All Aerotech load ratings are a
maximum value. If you require larger load ratings than what is provided in our data sheets, please contact an
Aerotech Applications Engineer as we may be able to easily modify or customize a design to meet your
exact needs.
C.4.7 Expected Lifetime
The critical guidance elements in Aerotech piezo actuator flexure stages are sized using FEA and analytical
techniques to ensure long, reliable operation. The materials and dimensions chosen for these flexure
elements ensure elastic bending and stresses in critical areas well below the endurance limit.
Factors such as humidity, temperature and applied voltage all affect the lifetime and the performance of
piezo actuators. As discussed in Section 3.7, our actuators are sealed and life-tested to ensure thousands of
hours of device life. Based on empirical data developed over years of testing, we can provide lifetime
estimates based on the desired move profiles and expected environmental conditions where the piezo
nanopositioning system will reside.
56
Appendix C
QNP3 Hardware Manual
Equation 14
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and
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