The blocking force Fmax is the maximum force generated by the actuator. This force is achieved when the displacement of the actuator is completely blocked, i.e. it works against a load with an infinitely high stiffness. Since such a stiffness does not exist in reality, the blocking force is measured as follows: The actuator length before operation is recorded. The actuator is displaced without a load to the nominal displacement and then pushed back to the initial position with an increasing external force. The force required for this is the blocking force.
If the piezo actuator works against a spring force, its induced displacement decreases because a counterforce builds up when the spring compresses. In most applications of piezo actuators, the effective stiffness of the load kL is considerably less than the actuator stiffness kA. The resulting displacement ΔL is therefore close to the nominal displacement ΔL0:
As an example of a load case in which a nonlinear working curve arises, a valve control is sketched in fig. 6. The beginning of the displacement corresponds to operation without a load. A stronger opposing force acts near the valve closure as a result of the fluid flow. When the valve seat is reached, the displacement is almost completely blocked so that only the force increases.
If a mass is applied to the actuator, the weight force FV causes a compression of the actuator. The zero position at the beginning of the subsequent drive signal shifts along the stiffness curve of the actuator. No additional force occurs during the subsequent drive signal change so that the working curve approximately corresponds to the course without preload (fig. 7).
An example of such an application is damping the oscillations of a machine with a great mass.
If the mechanical preload is applied by a relatively soft spring inside a case, the same shift takes place on the stiffness curve as when a mass is applied (fig. 8). With a drive voltage applied, however, the actuator generates a small additional force and the displacement decreases somewhat in relation to the case without load due to the preload spring. The stiffness of the preload spring should therefore be at least one order of magnitude lower than that of the actuator.
In longitudinal stack actuators, the actuator length is the determining variable for the displacement ΔL0. At nominal field strengths of 2 kV/mm, displacements of 0.10 to 0.15 % of the length are attainable. The cross-sectional area determines the blocking force Fmax. Approximately 30 N/mm² can be achieved here.
Accordingly, the determining parameter for the mechanical energy Emech = (Δ L0 Fmax)/2 to be attained is the actuator volume.
The energy amount Emech, that is converted from electrical into mechanical energy when an actuator is operated, corresponds to the area underneath the curve in fig. 9. However, only a fraction Eout of this total amount can be transferred to the mechanical load. The mechanical system is energetically optimized when the area reaches its maximum. This case occurs when the load stiffness and the actuator stiffness are equal. The light blue area in the working graph corresponds to this amount. A longitudinal piezo actuator can perform approx. 2 to 5 mJ/cm³ of mechanical work and a bending actuator achieves around 10 times lower values.
Efficiency and Energy Balance of a Piezo Actuator System
The calculation and optimization of the total efficiency of a piezo actuator system depends on the efficiency of the amplifier electronics, the electromechanical conversion, the mechanical energy transfer, and the possible energy recovery. The majority of electrical and mechanical energies are basically reactive energies that can be recovered minus the losses, e.g., from heat generation. This makes it possible to construct very efficient piezo systems, especially for dynamic applications.