Displacement andExternal Forces aConstant Force bChanging Force

L Like any other actuator, a piezoactuator is compressed when a force is applied. Two cases must be considered when oper- ating a piezo actuator with a load: a) The load remains constantduring the motion process.b) The load changes during themotion process. Zero-point is offset Displacement is reduced A mass is installed on thepiezo actuator which applies a force F = M · g (M is the mass, g the acceleration due to gravity). The zero-point will be shiftedby For piezo actuator operationagainst an elastic load differ- ent rules apply. Part of the displace-ment gene-rated by the piezo effect is lost due to the elas- ticity of the piezo ele-ment (Fig.21). The to- tal avail- able displa- cement can be related to the spring stiff- ness by the following equa-tions:(Equation 6)Maximum displacement of apiezo actuator acting against a spring load.(Equation 7)Maximum loss of displace-ment due to external spring force. In the case where the restraint is infinitely rigid (k Note To keep down the loss of travel,the stiffness of the preload spring should be under 1/10 that of the piezo actuator stiff- ness. If the preload stiffnesswere equal to the piezo actua-tor stiffness, the travel would be reduced by 50 %. For prima- rily dynamic applications, the resonant frequency of the pre- load must be above that of thepiezo actuator.
N F/k
T , where k
T is thestiffness of the actuator. If this force is below the spe- cified load limit (see product technical data), full displace-ment can be obtained at full operating voltage (see Fig. 20). (Equation 5)Zero-point offset with con-stant force
Fig. 21. Case b: Effective displacement of a piezo actua-tor acting against a spring load. Where: L
N =zero-point offset [m]F = force (mass x accel-eration due to gravi- ty) [N]k
T = piezo actuator stiff-ness [N/m] Example How large is the zero-pointoffset of a 30 µm piezo actua-tor with a stiffness of 100N/µm if a load of 20 kg isapplied, and what is the maximum dis- placement with this load?The load of 20 kg generatesa force of 20 kg x 9.81 m/s
s Example = ), the piezo actuator canproduce no displacement butacts only as a force generator. Q: What is the maximum dis- placement of a 15 µm piezo translator with a stiffness of 50 N/µm, mounted in an elas-tic restraint with a spring constant k Where: L = displacement with ex-ternal spring load [m]
S (stiffness) of 100 N/µm?A: Equation 6 shows that thedisplacement is reduced in anelastic restraint. The springconstant of the external restraint is twice the value of the piezo translator. The achievable displacement is therefore limited to 5 µm (1/3 of the nominal travel).

M

2 L =nominal displacementwithout external force or restraint [m] =196 N. With a stiffness of 100 N/µm, the piezo actuatoris compressed slightly lessthan 2 µm. The maximum displacement of 30 µm is not reduced by this constant force.

Fig. 20. Case a: Zero-point offset with constant force. L
R = lost displacementcaused by the exter- nal spring [m]k
s = spring stiffness [N/m] k
T = piezo actuator stiff-ness [N/m]
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