Piezo

•

Nano

•

Positioning

Note: In positioning applications, piezo actuators are operated well below their resonant fre- quencies. Due to the non-ideal spring behavior of piezoceram-ics, the theoretical result fromthe above equation does not necessarily match the real- world behavior of the piezo actuator system under large signal conditions. When adding a mass M to the actua- tor, the resonant frequencydrops according to the follow-ing equation:(Equation 11)Resonant frequency withadded mass.m´ Where: Resonant Frequency In general, the resonant fre-quency of any spring/mass sys- tem is a function of its stiffness and effective mass (see Fig. 23). Unless otherwise stated, the resonant frequency given in the technical data tables for actuators always refer to theunloaded actuator with oneend rigidly attached. For piezo positioning systems, the data refers to the unloaded system firmly attached to a significant- ly larger mass.(Equation 10)Resonant frequency of an idealspring/mass system.

Piezo Actuators Piezo Actuators Nanopositioning & Scanning Systems Nanopositioning &Scanning Systems

Where:f

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= phase angle [deg]F

Industrial motion controllers Motion Controllers
max

= resonant frequency [Hz]f = operating frequency[Hz]

Ceramic Linear motors & Stages Ceramic Linear Motors & Stages Index Index
eff

= additional mass M + m

O

= resonant frequency ofunloaded actuator [Hz]k

eff

.The above equations show thatto double the resonant fre- quency of a spring-mass sys- tem, it is necessary to either increase the stiffness by a fac-tor of 4 or decrease the effec-tive mass to 25 % of its original value. As long as the resonant frequency of a preload spring is well above that of the actua-tor, forces it introduces do not significantly affect the actua- tor’s resonant frequency.The phase response of a piezoactuator system can be approx- imated by a second order sys-tem and is described by the fol-lowing equation:(Equation 12)

T

= piezo actuator stiffness[N/m]m

eff

= effective mass (about1/3 of the mass of the ceramic stack plus any installed end pieces) [kg]

Fig. 23. Effective mass of an actuator fixed at one end.

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