Force Generation
PDF: More Information on Forces and Stiffness of Piezo Actuators
PDF: More Information on Displacement Modes of Piezo Actuators
PDF: More Information on Dynamic and Electric Operation of Piezoelectric Actuators
In most applications, piezo actuators are used to produce displacement. If used in a restraint, they can be used to generate forces, e.g. for stamping. Force generation is always coupled with a reduction in displacement. The maximum force (blocked force) a piezo actuator can generate depends on its stiffness and maximum displacement. At maximum force generation, displacement drops to zero.
(Equation 4)
Maximum force that can be generated in an infinitely rigid restraint (infinite spring constant).
where:
ΔL0 = max. nominal displacement
without external
force or restraint [m]
kT = piezo actuator stiffness
[N/m]
In actual applications the spring constant of the load can be larger or smaller than the piezo spring constant. The force generated by the piezo actuator is:
(Equation 5)
Effective force a piezo actuator can generate in a yielding restraint
where:
ΔL0 = max. nominal displacement
without external
force or restraint [m]
kT = piezo actuator stiffness
[N/m]
kS = stiffness of external
spring [N/m]
Example
What is the force generation of a piezo actuator with nominal displacement of 30 µm and stiffness of 200 N/µm? The piezo actuator can produce a maximum force of 30 µm x 200 N/µm = 6000 N When force generation is maximum, displacement is zero and vice versa (see below for details).Example
A piezo actuator is to be used in a nano imprint application. At rest (zero position) the distance between the piezo actuator tip and the material is 30 microns (given by mechanical system tolerances). A force of 500 N is required to emboss the material.
Q: Can a 60 µm actuator with a stiffness of 100 N/µm be used?
A: Under ideal conditions this actuator can generate a force of 30 x 100 N = 3000 N (30 microns are lost motion due to the distance between the sheet and the piezo actuator tip). In practice the force generation depends on the stiffness of the metal and the support. If the support were a soft material, with a stiffness of 10 N/µm, the piezo actuator could only generate a force of 300 N onto the metal when operated at maximum drive voltage. If the support were stiff but the material to be embossed itself were very soft it would yield and the piezo actuator still could not generate the required force. If both the support and the metal were stiff enough, but the piezo actuator mount was too soft, the force generated by the piezo would push the actuator away from the material to be embossed.
The situation is similar to lifting a car with a jack. If the ground (or the car’s body) is too soft, the jack will run out of travel before it generates enough force to lift the wheels off the ground.
Force generation vs. displacement of a piezo actuator (displacement 30 µm, stiffness 200 N/µm). Stiffness at various operating voltages. The points where the dashed lines (external spring curves) intersect the piezo actuator force/displacement curves determine the force and displacement for a given setup with an external spring. The stiffer the external spring (flatter dashed line), the less the displacement and the greater the force generated by the actuator. Maximum work can be done when the stiffness of the piezo actuator and external spring are identical
