Displacement andExternal Forces aConstant Force

bChanging Force

Maximum displacement of apiezo actuator acting against a spring load. 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 shifted by For piezo actuator operationagainst an elastic load differ- ent rules apply. Part of thedisplace-ment gene- rated by the piezo effect is lost due to the elas- ticity of the piezo ele-ment. Thetotal avail- able displa- cement can be related to the spring stiffness by the following equations: (Equation 8)

Piezo · Nano · Positioning

Note Maximum loss of displace-ment due to external springforce. In the case where therestraint is infinitely rigid (k 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 the piezo actuator.
N â‰ˆ 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. (Equation 6)
Case b: Effective displacementof a piezo actuator actingagainst a spring load Zero-point offset with con-stant force where: L
N =zero-point offset [m]F = force (mass x acceleration due togravity) [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 100 N/µm if a load of 20 kg isapplied, and what is the maximum dis- placement withthis load?The load of 20 kg generates a force of 20 kg x 9.81 m/s
s Example = âˆž ), 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 of50 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 7 shows that thedisplacement is reduced in anelastic restraint. The spring constant 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 forceor 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. L
Case a: Zero-point offset with constant force 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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