Forces and Stiffness
PDF: More Information on Forces and Stiffness of Piezo Actuators
Maximum Applicable Forces
(Compressive Load Limit,
Tensile Load Limit)
The mechanical strength values
of PZT ceramic material
(given in the literature) are
often confused with the practical
long-term load capacity of
a piezo actuator. PZT ceramic
material can withstand pressures
up to 250 MPa (250 x 106 N/m2)
without breaking. This value
must never be approached in
practical applications, however,
because depolarization
occurs at pressures on the
order of 20 % to 30 % of the
mechanical limit. For stacked
actuators and stages (which
are a combination of several
materials) additional limitations
apply. Parameters such
aspect ratio, buckling, interaction
at the interfaces, etc. must
be considered.
The load capacity data listed for PI actuators are conservative values which allow long lifetime.
Tensile loads of non-preloaded piezo actuators are limited to 5% to 10 % of the compressive load limit. PI offers a variety of piezo actuators with internal spring preload for increased tensile load capacity. Preloaded elements are highly recommended for dynamic applications.
The PZT ceramic is especially sensitive to shear forces; they must be intercepted by external measures (flexure guides, etc.).
Stiffness
Actuator stiffness is an important parameter for calculating force generation, resonant frequency, full-system behavior, etc. The stiffness of a solid body depends on Young’s modulus of the material. Stiffness is normally expressed in terms of the spring constant kT, which describes the deformation of the body in response to an external force.
This narrow definition is of limited application for piezoceramics because the cases of static, dynamic, large-signal and small-signal operation with open and shorted electrodes must all be distinguished. The poling process of piezoceramics leaves a remnant strain in the material which depends on the magnitude of polarization. The polarization is affected by both the applied voltage and external forces. When an external force is applied to poled piezoceramics, the dimensional change depends on the stiffness of the ceramic material and the change of the remnant strain (caused by the polarization change). The equation ΔLN = F/kT is only valid for small forces and small-signal conditions. For larger forces, an additional term, describing the influence of the polarization changes, must be superimposed on the stiffness (kT). Since piezo ceramics are active materials, they produce an electrical response (charge) when mechanically stressed (e.g. in dynamic operation). If the electric charge cannot be drained from the PZT ceramics, it generates a counterforce opposing the mechanical stress. This is why a piezo element with open electrodes appears stiffer than one with shorted electrodes. Common voltage amplifiers with their low output impedances look like a short circuit to a piezo actuator.
Mechanical stressing of piezo actuators with open electrodes, e.g. open wire leads, should be avoided, because the resulting induced voltage might damage the stack electrically. Quasi-static characteristic mechanical stress/strain curves for piezo ceramic actuators and the derived stiffness values. Curve 1 is with the nominal operating voltage on the electrodes, Curve 2 is with the electrodes shorted (showing ceramics after depolarization)
Note
There is no international standard for measuring piezo actuator stiffness. Therefore stiffness data from different manufacturers cannot be compared without additional information.
Quasi-static characteristic mechanical stress/strain curves for piezo ceramic actuators and the derived stiffness values. Curve 1 is with the nominal operating voltage on the electrodes, Curve 2 is with the electrodes shorted (showing ceramics after depolarization)
