Basic Analytical Tools for the Design of Resonant Vibration Transducers

Abstract

The presented review of existing work on electromagnetic inertial vibration transducers in Chap. 1 shows that there has been much interest in the design of vibration energy harvesting devices. Consequently excellent work has been done by numerous research facilities and a multiplicity of micro– and centimeter scale prototype vibration transducers has been developed. The basic analytical theory behind most of the presented devices is commonly known in the energy harvesting society. It is based on a well understood linear second–order spring–mass–damper system with base excitation. Specific analysis of vibration transducers was first proposed by Williams and Yates [15]. Since then the theory has been modified and described in various ways even though the basic findings are more or less the same. In this respect, an analytical expression for the maximum output power that can be extracted from a certain vibration was derived (also for constrains such as the limitation of the inner displacement of the seismic mass [64]) and the optimization of parameters such as the optimal load resistance or the electromagnetic damping factor was discussed. However, as will be shown, in most of these cases it is rather difficult even impossible to use the results of the analytical modelling directly for the design process of application oriented developments. This is because the theory does not consider geometrical parameters and is based on simplifying assumptions which often do not correlate well with the “real world” (e.g. random vibration instead of harmonic excitation, complex load circuit instead of simple resistance or appreciable magnetic flux leakage instead of homogeneous magnetic field distribution). However the analytical modelling is useful for understanding the influence of the most important system parameters. Furthermore it offers a deeper insight into the overall system behavior.