Study of work flow in piezoelectrically driven linear and non-linear systems

Abstract

Standard assumptions about the efficiency of active systems working against a load neglect the load coupling inherent in these systems. This thesis contains a derivation for finding the actuation efficiency and work output in electro-mechanically coupled systems working against a load. This general derivation is for fully coupled, non-linear systems working against a generalized load. Three example cases are then shown to demonstrate several key aspects of the general derivation. The first example case is a one-dimensional, linear discrete actuator working against a one-dimensional, linear spring load. This example shows the effects of electro-mechanical coupling on the actuation efficiency. The second example case is of a piezoelectric bender first presented by Lesieutre and Davis[l] in their derivation of the device coupling coefficient. The bender example demonstrates the differences between the device coupling coefficient and actuation efficiency as well as the use of the generalized derivation in mechanically complex problems. The final example presented is a one-dimensional, linear discrete actuator working against a one-dimensional, non-linear load in order to demonstrate the possibility of increasing the work output of a system through the use of non-linear loading functions. To test the theoretical derivation presented, a custom built testing facility was designed and built to measure the work output and actuation efficiency of a discrete actuator working against both linear and non-linear loads. The testing facility was designed for load application with programmable impedances and closed loop testing at frequencies up to 1 kHz. The complete design of the testing facility is presented with an overview of the rationale behind the design decisions made. Finally, tests were performed on a discrete actuator working against linear and non-linear loading functions. The tests performed on a discrete actuator working against a linear load match the expected work output predicted by the theory. Tests performed on a discrete actuator working against a non-linear load validate that increases in the mechanical work out of the actuator are possible by using non-linear loads instead of linear loads. To illustrate that this is a practical result, the design of a loading device that loads a material non-linearly while loading a spring linearly is presented with its theoretical performance. Recommendations on ways to improve the model, testing methodology, and testing machine concludes the document.