F u n d a m entals of Piezo m echanics
Displacement of Piezo Actuators (Stack & Contraction Type)
Commonly used stack actua-tors achieve a relative displace-
ment of up to 0.2 %.
Displacement of piezoceramic
actuators is primarily a func-
tion of the applied electric fieldstrength E, the length L of theactuator, the forces applied to it
and the properties of the piezo-
electric material used. The
material properties can be
described by the piezoelectric
strain coefficients d
15 mode.These figures only apply to the
raw material at room tempera-
ture under small-signal condi-
tions.The maximum allowable fieldstrength in piezo actuators is
between 1 and 2 kV/mm in the
polarization direction. In the
reverse direction (semi-bipolar
operation), at most 300 V/mm
is allowable (see Fig. 10). Themaximum voltage depends onthe ceramic and insulation
materials.Exceeding the maximum volt-age may cause dielectric break-
down and irreversible damageto the piezo actuator.With the reverse field, negativeexpansion (contraction) occurs,
giving an additional 20 % of the
nominal displacement. If boththe regular and reverse fieldsare used, a relative expansion
(strain) up to 0.2 % is achiev-
able with piezo stack actuators.
This technique can reduce the
average applied voltage with-
out loss of displacement andthereby increase piezo lifetime.
Stacks can be built with aspectratios up to 12:1 (length:diame-
ter). This means that the maxi-
mum travel range of an actua-
tor with 15 mm piezo diameter
is limited to about 200 µm.
Longer travel ranges can be
achieved by mechanical ampli-
fication techniques (see “LeverMotion Amplifiers” p. 4-42).
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 piezo
actuator can be estimated by
the following equation:(Equation 1) Where:S = strain (relative lengthchange
Polarisation L/L, dimen-sionless) L
= ceramic length [m]E = electric field strength[V/m]d
Fig. 9. Expansion and contraction of a piezoelectric disk in response to an appliedvoltage. Note that d 31 , which describes the lateral motion, D, is negative. ij = piezoelectric coeffi-cient of the material [m/V] d
33 describes the strain parallelto the polarization vector of theceramics (thickness) and is
used when calculating the dis-
placement of stack actuators;
d
31 is the strain orthogonal tothe polarization vector (width)
and is used for calculating tube
and strip actuators (see Fig. 9).
d
V 33 and d
31 are sometimesreferred to as “piezo gain”. Notes For the materials used in stan-dard PI piezo actuators, d
33 ison the order of 250 to 550pm/V, d
Fig. 10. Typical response of a “soft PZT” actuator to a bipolar drivevoltage. When a certain threshold voltage negative to the polarization
direction is exceeded, reversal of polarization can occur. © PI 1998-2005. Subject to change w/o notice. Cat 118 05/09.17 31 is on the order of
-180 to -210 pm/V. The highestvalues are attainable with
shear actuators in d
4-16