231575 Piezo-Mechanics GB

3.6. StiffnessesLike any other solid state body, a piezo actuator showsa distinct elasticity.This elasticity is described by Hooke’s law, where adeformation ∆l is related to the applied ∆F force by∆F = S ∆ldefining thereby thespring constant = stiffness S = inverse complianceIn contrast to “normal” passive materials the uniquefeature of piezo-ceramic is to show a variable stiffness,depending on the electrical driving scheme as it isshown by following simple experiments:A compressive force ∆F shall be applied to the piezostack and the resulting compression ∆l of stack’s lengthis measured.Following situations can now be distinguished:a) the actuator leads are short circuited or connectedto a voltage amplifier with constant output voltagesetting,b) the actuator leads are open,c) the actuator is connected to a position feedbackcontrol unit.In a) a distinct actuator stiffness S volt = const. = ∆F/∆l isderived.In b) roughly the double stiffness compared to a, isobserved (depends on type of PZT material andto some extent on manufacturing technique of thestack)In c) a nearly infinitely high stiffness is seen, nocompression occurs (within the feedback controlrange).The reason for the difference in a) and b) is easily understood:The application of a compressive force to PZT leads tothe generation of electrical charge via the normal piezoelectriceffect.In case a): short circuiting the leads (or holding the voltagelevel constant via a voltage amplifier) the generatedelectrical charges can flow and equilibrate.In case b): the generated charges cannot flow due toopen leads and a voltage is generated creating astabilizing electrical field acting against the mechanicalcompression => higher stiffness than a)The case c) leads self-evidently to virtual infinitely highstiffness, because the feedback makes any compressivedeflection to zero.These basic phenomena find their equivalents in differenttypes of electrical supplies for driving a piezo actuator:a) corresponds to open loop voltage controlb) corresponds to open loop charge (or current)controlc) is realized by closed loop position control.Voltage control fits excellent to the needs of low dynamicprecision positioning, where no high requirementsfor dynamic stiffnesses are given. This was the situationfor the past decades.Motion control by open loop charge or current controlof piezo actuators leads to remarkably higher stiffnessesthan the open loop voltage control. Currently applicationsare becoming more and more important, wherehigh dynamic stiffnesses are requested to modulatehigh stiffness structures (see chapter 7).The data sheet show the actuator stiffnesses forvoltage control.3.7. Blocking forceThe maximum blocking force shown in the data sheet isdefined for maximum semi bipolar voltage swing. Detailsfor blocking forces see section 1.3.2.3.8. ResonancesAs any other solid state body, a piezostack shows resonantmodes. In the data sheet the axial resonances for aone side fix oscillation of the stack are shown.Usually piezostacks are operated broadband non resonantlywell below stack’s resonance frequency.When the piezo actuator is attached to a mechanicalsystem, the resonance of the total system will be lowerfor several reasons:ABDue to the mass m of the attached mechanics,which results in a new actuator resonance frequencyaccording the spring/mass system’s law(where the stack acts as the “spring”)f res = 1 /2π (S/m)The resonant modes of the attached mechanics(e.g. optomechanical components like translationstages have resonances in the 100 Hz region).Mechanical resonances of a piezo-actuated system canbe easily detected by using the piezo-stack as vibrationsensor. When the piezo-actuator is connected to anoscilloscope, the ringing signal can be monitored, whenthe mechanics is excited by a short knock.15