A network model for piezoelectric flexure actuators

Abstract

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 anglethe 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  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.