The maximum force (blocked force) a piezo actuator can generate depends on its stiffness and maximum displacement. Force generation is always coupled with a reduction in displacement. If used in a restraint, they can generate forces. In most applications, piezo actuators are used to produce displacement. It must be understood that a piezo actuator can only generate considerable force if it is directly coupled (no slack!) to an element which is stiff when compared to the Piezo. Since stiffness values of Piezo actuators are not constants they can only be used to estimate the behavior under certain conditions and to compare different Piezo actuators of one manufacturer. (For more details see "Resonant Frequency"). The above discussion explains why the (dynamically measured) resonant frequency of a piezo actuator does not necessarily match the results calculated with the "simple harmonic oscillator equation": f 0 = (1/2π)*√(k T/m eff) with statically measured stiffness. With actuators (compound structures of different active and passive materials) the scenario is even more complicated. This is why a Piezo element with open electrodes appears stiffer than one with shorted electrodes. When the electric charge cannot be drained from the Piezo, it generates a counter force to the mechanical stress. Since piezo ceramics are active materials, they produce an electrical response (charge) when mechanically stressed (e.g. For larger forces, an additional term describing the influence of the polarization changes, is superimposed on stiffness (k T). The equation L N = F/k T is only valid for small forces and small signal conditions. When an external force is applied to poled Piezo ceramics, the Dimensionsal change depends on the stiffness of the ceramic material and the change of the remanent strain (caused by the polarization change). The polarization is affected by both the drive voltage and external forces. The poling process of Piezo ceramics leaves a remanent strain in the material which depends on the magnitude of polarization. This narrow definition does not apply fully for Piezo ceramics large and small signal conditions, static and dynamic operation, open and shorted electrodes must be distinguished. It is generally described by the spring constant k T, relating the influence of an external force to the Dimensionsal change of the body. In solid bodies stiffness depends on the Young's Modulus which is the ratio of stress (force per unit area) to strain (change in length per unit length). When calculating force generation, resonant frequency, system response, etc., piezo stiffness is an important parameter. Shear forces must be isolated from the Piezo ceramics by external measures (flexure guides, etc.). Preloaded elements are highly recommended for dynamic applications. PI offers a variety of piezo actuators with internal spring preload for extended tensile load capacity. Tensile loads of non preloaded PZTs are limited to 5 - 10 % of the compressive load limit. Standard PI Piezo stack actuators can withstand compressive forces to several 10,000 N several tons). The load capacity data listed for PI actuators are conservative values which allow long lifetime. If the maximum compressive force for a Piezo is exceeded, damage to the ceramics as well as depolarization may occur. Parameters such as aspect ratio, buckling, interaction at the interfaces etc. For actuators (which are a combination of several materials) additional rules apply. For practical applications, this value must not be approached because depolarization occurs at pressures on the order of 20 to 30 % of the mechanical limit. Piezo ceramic material can withstand pressures up to 250 MPa (2500 x 10 5 N/m²) before it breaks mechanically. The mechanical strength values of Piezo ceramic material (given in the literature) is often confused with the practical long term load capacity of a Piezo actuator. (Compressive Load Limit, Tensile Load Limit) Therefore stiffness data of different manufacturers cannot be compared without additional information. There is no international standard for measuring piezo actuator stiffness.
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