Displacement Modes of Piezoelectric Actuators
For small electric driving signals the displacement ΔL of a bulk ceramic material sample can be calculated from the following equation:
ΔLj = Sj L0 = dij Ei L0
Si: mechanical strain in direction j (strain in defined as relative length change, ΔL/L) [dimensionless]
L0: material thickness in field direction [m]
Ei: electrical field in direction i [V/m]
dij: piezoelectric deformation coefficient [pm/V]
The maximum allowable field strength in piezo actuators is between 1 and 2 kV/mm in the polarization direction.
Exceeding the maximum voltage may cause dielectric breakdown and irreversible damage to the piezo actuator.
Stacks can be built with aspect ratios up to 12:1 (length:diameter). Longer travel ranges can be achieved by mechanical amplification techniques.
Equation 1 is applicable for small electric signals only, because the piezoelectric deformation coefficients, dij, for PZT ceramics show strong electric field dependency. In fact, the coefficient value can increase by a factor of 1.5 to 2 compared to the small-signal value in Table 1 when the nominal voltage of the actuator is applied. This increase leads to a very high large-signal deformation coefficient d15 of 1100 pm/V at an amplitude of 250 V for PICA™-Shear actuators, which are made of PIC 255.
Commonly used stack actuators achieve a relative displacement of up to 0.2 %. Displacement of piezoceramic actuators is primarily a function of the applied electric field strength E, the length L of the actuator, the forces applied to it and the properties of the piezoelectric material used. The material properties can be described by the piezoelectric strain coefficients dij. These coefficients describe the relationship between the applied electric field and the mechanical strain produced.
The change in length, ΔL, of an unloaded single-layer piezo actuator can be estimated by the following equation:
ΔL = S·L0 ≈ ± E·dij·L0
S = strain (relative length change ΔL/L, dimensionless)
L0 = ceramic length [m]
E = electric field strength [V/m]
dij = piezoelectric coefficient of the material [m/V]
Table 2 illustrates the different piezoelectric actuator displacement modes for PZT ceramics.
By convention, index 3 is always aligned in the poling direction of the material. The small-signal values of the relevant piezoelectric deformation coefficients d33, d31 and d15 for the different actuator materials can be found in Table 1.
The longitudinal mode is used for most linear actuators in this catalog. In this mode, the electric field, the poling direction as well as the mechanical strain or displacement, have the same orientation. Keep in mind that the longitudinal deformation is always accompanied by a transverse deformation. When driven with a positive voltage U3, the material expands in the longitudinal direction while at the same time shrinking in the transverse direction, as can be seen from the material deformation figures in Table 2. Whether the actuator is of a longitudinal or transverse type depends only on the displacement which is used. The shear mode is different, because in the electric field and the poling direction are perpendicular to each other. The PICA™-Shear actuators use the shear displacement in the poling direction.
To get the displacements of the individual layers in a multilayer actuator to add while using the appropriate electrical contact configuration, the poling orientations of adjacent layers have to alternate (see Table 2).
Ei vector component of the electric field
P polarization direction
U applied voltage
ΔL induced displacement
Typical response of a “soft PZT” actuator to a bipolar drive voltage. When a certain threshold voltage negative to the polarization direction is exceeded, reversal of polarization can occur