Fundamentals of Piezomechanics

Forces and Stiffness

Maximum Applicable Forces(Compressive Load Limit, Tensile Load Limit)
T ). 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 counterforceopposing the mechanical stress. This is why a piezo ele- ment 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 piezoactuators with open electrodes, e.g. open wire leads, should be avoided, because the resulting induced voltage might damagethe stack electrically. The mechanical strength val-ues of PZT ceramic material(given in the literature) are often confused with the practi- cal long-term load capacity of a piezo actuator. PZT ceramic
T ,which describes the deforma- tion of the body in response to an external force. This narrow definition is of lim-ited application for piezoce- ramics because the cases ofstatic, dynamic, large-signaland small-signal operation with open and shorted elec- trodes must all be distin- guished. The poling process of piezoceramics leaves a rem- nant strain in the material which depends on the magni-tude of polarization. The pola- rization is affected by both theapplied voltage and external forces. When an external force is applied to poled piezoceram- ics, the dimensional changedepends on the stiffness of theceramic material and the change of the remnant strain (caused by the polarization change). The equation

Piezo · Nano · Positioning

material can withstand pressures up to 250 MPa (250 x 10
6 N/m
2 )without breaking. This value must never be approached inpractical applications, howev-er, 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 severalmaterials) additional limita-tions apply. Parameters such aspect ratio, buckling, interac- tion at the interfaces, etc. must be considered.The load capacity data listedfor PI actuators are conserva- tive values which allow long lifetime.Tensile loads of non-preloadedpiezo actuators are limited to5% to 10% of the compressive load limit. PI offers a variety of piezo actuators with internal spring preload for increased tensile load capacity. Preloadedelements are highly recom-mended for dynamic applica- tions.The PZT ceramic is especiallysensitive to shear forces; they must be intercepted by exter-nal measures (flexure guides,etc.). Stiffness Actuator stiffness is an impor-tant parameter for calculating force generation, resonant fre- quency, full-system behavior, etc. The stiffness of a solid body depends on Young’s modulus of the material. Stiff- ness is normally expressed interms of the spring constant k L
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) N =F/k
Note T is only valid for smallforces and small-signal condi- tions. For larger forces, an additional term, describing the influence of the polarization changes, must be super- imposed on the stiffness (k There is no international stan-dard for measuring piezo actu- ator stiffness. Therefore stiff- ness data from different manu- facturers cannot be compared without additional information.
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