Actuation efficiency in piezoelectricly driven linear and non-linear systems

Standard assumptions about the efficiency of active systems working against a load neglect, the electro-mechanical coupling inherent in these systems. This paper 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(1) 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. Finally, a custom built testing facility measures 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 tests performed on a discrete actuator closely match the expected work outputs and efficiencies predicted by the theory.