Fundamentals ... (cont.)
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Displacement of Piezo Actuators (Stack & Contraction Type)
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Displacement of PZT ceramics is primarily a function of the applied electric field strength E, the piezoelectric material used and the length L of the PZT ceramics. The material properties can be described by the piezoelectric strain coefficients dij. These coefficients describe the relationship between the applied electrical field and the mechanical strain produced.
The displacement DL of an unloaded single-layer piezo actuator can be estimated by the following equation:
(Equation 1)
Where:
S = strain (relative length change DL/L, dimensionless)
Lo = ceramic length [m]
E = electrical field strength [V/m]
dij = piezoelectric coefficient [m/V]
d33 describes the strain parallel to the polarization vector of the ceramics (thickness) and d31 the strain orthogonal to the polarization vector (width). d33 and d31 are sometimes referred to as "piezo gain". See Fig. 9 for explanation. The strain coefficient d33 applies for PZT stack actuators, d31applies for tube and strip actuators.
Note:
For the material used in standard PI piezo actuators, d33 is on the order of 450 to 650 x 10-12 m/V, d31 is on the order of -200 to -300 x 10-12 m/V. These figures only apply to the raw material at room temperature under small-signal conditions.
For standard PI PZTs, the allowable field strength ranges from 1 to 2 kV/mm in the poling direction and up to 300 V/mm inverse (short term only) to the poling direction (semi-bipolar mode), see Fig. 10 for details. The maximum voltages depend on the ceramic properties and the insulating materials. Exceeding the maximum voltage may cause dielectric breakdown and irreversible damage to the PZT.
With the inverse field, negative expansion (contraction) occurs giving an additional 20% of the nominal displacement. If both the regular and inverse electric fields are used, a relative expansion (strain) up to 0.2 % is achievable with PZT stack actuators. Stacks can be built with aspect ratios up to 12:1 (length:diameter). Maximum travel for medium size piezo stack actuators (15 mm diameter), is therefore limited to approximately 200 µm. Longer travel ranges can be achieved by mechanical amplification techniques (see "Lever Motion Amplifiers" see link).
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Fig. 9. Elongation and contraction of a PZT disk when a voltage is applied. Note that d31 (affecting lateral deformation, DD) is negative.
Fig. 10. Response of a PZT actuator to a bipolar drive voltage. When a certain threshold voltage (negative to the polarization direction) is exceeded, reversal of polarization can occur.
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