We investigate flexure piezoelectric stacks to produce large force and fine position control. The network model for the free ideal stack with many layers was first worked out by Martin [Martin 1963, 1964a, 1964b]. He noted that the stack impedance model in the limit of large layer number n > 8 that a network model for this case could be developed which is identical in form to the network model of the length-thickness mode with appropriate material coefficients from the length extensional (LE 33) mode of the material. This network model allows for the additional determination of the velocities and displacements of the stack surfaces, as well as the acoustic power deliver to any elastic load. We show that this model can be extended to allow for the modelling of acoustic elements, such as non-piezoelectric endcaps and coupling to other structures including flexures. In order to demonstrate the utility of this modeling, we will present the model for a stack embedded in a simple flexure frame. Embedding the piezoelectric stack in a flexure enables preloading of the piezoelectric so that it does not experience tension during operation. This reduces the overall risk of failure. Additionally, flexures have been demonstrated to amplify in the transverse direction the stroke of the stack at low frequencies by a factor that is proportional to the cotangent of the liftoff angle – the angle the flexure makes with the axis of the stack. Impedance measurements of the flexure stack show two additional modes in addition to the stack fundamental length extensional mode. Investigations on the other modes of the flexured stack actuator show a low frequency flexure mode that is π out of phase with the stack extension and with a resistance at resonance that is smaller by the amplification factor of the flexure. A flexure breathing mode is found just below the stack resonance. At the higher frequency a clamped stack resonance in phase with the flexure displacements is shown. In the paper, we will also discuss how the flexure network model can be implemented into other structures.
The next generation of space telescopes will require large, segmented apertures for observations in the near ultraviolet through mid- and far-infrared regions to enable new science ranging from exoplanet characterization to precision astronomical observations that refine astrophysics models. To meet these challenges, we are developing instrumented (strain gauge) surface parallel actuators (SPAs) that are robust and can meet the stringent requirements of mass and cost per m2. We have developed a surface parallel mirror test piece and a set of flexured actuators that maintain compression in the piezoelectric stack elements at all times. The characterization work of these actuators is directed at understanding the performance of flexure piezoelectric multilayer stack actuator operation when embedded in the mirror. To determine the influence functions for each actuator position, we will report the measured stroke/strain and charge/capacitance versus voltage curves for all 42 preloaded actuators. Although designed to operate under close loop control via feedback from the strain gauge initial testing on bare lead zirconate titanate (PZT) stack actuators suggests that by driving the stack to a known domain state we could perform open loop control in the actuators to levels of ± 0.3 μm. We will also report on creep for the actuators and cross actuation for each unique actuator position as well as discuss approaches to mitigating the effect on open loop control error. Thermal studies of flextensional actuators embedded in analog rib structures down to 100K will also be presented.
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