For small electric driving sig-nals the displacement
ij . Thesecoefficients describe the rela-
tionship between the applied
electric field and the mechani-
cal strain produced.The change in length, L, of anunloaded single-layer piezoactuator can be estimated by
the following equation: (Equation 1) L of abulk ceramic material sample
can be calculated from the fol-
lowing equation: (Equation 2)
Lj= SjL0= dijEiL0
ij , for PZTceramics 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 volt-
age of the actuator is applied.This increase leads to a veryhigh large-signal deformation
coefficient d where:S = strain (relative lengthchange
Piezo · Nano · Positioning
where: S
i : mechanical strain in direc-tion j (strain in defined as
relative length change, L/L) [dimensionless]L
: material thickness in fielddirection [m]E
i : electrical field in directioni [V/m]d
15 of 1100 pm/V atan amplitude of 250 V for
PICA L/L, dimen-sionless) L
TM ij : piezoelectric deformationcoefficient [pm/V] -Shear actuators, whichare made of PIC 255.Commonly used stack actua-tors achieve a relative displace-
ment of up to 0.2 %. Dis-
placement of
piezoceramic
actuators is primarily a func-
tion of the applied electric field
strength E, the length L of theactuator, the forces applied to itand the properties of the piezo-
electric material used. The
material properties can be
described by the piezoelectric
strain coefficients d
= ceramic length [m]E = electric field strength[V/m]d The maximum allowable fieldstrength in piezo actuators is
between 1 and 2 kV/mm in the
polarization direction.Exceeding the maximum volt-age may cause dielectric break-
down and irreversible damage
to the piezo actuator.Stacks can be built with aspectratios up to 12:1 (length:diame-
ter). Longer travel ranges canbe achieved by mechanical
amplification techniques.Equation 1 is applicable forsmall electric signals only, be-cause the piezoelectric defor-
mation coefficients, d
ij = piezoelectric coeffi-cient of the material [m/V]
V 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 41