On the electromechanical coupling in electromagnetic vibration energy harvesters

Abstract

This paper presents a theoretical and numerical analysis of the electromechanical coupling occurring in levitation-based electromagnetic vibration energy harvesters. The relevant mathematical and physical aspects of its formulation are analyzed; the focus is put on the practical consequences of the hypotheses made during the derivation process. Its effects on the dynamical response of the harvester are addressed. A detailed mathematical description of the harvester equations of motion is also presented; this includes a derivation of the expressions that describe both the mechanical and electromagnetic phenomena that take place in the device. Numerical tests are conducted in order to compare two formulations of the electromechanical coupling. It is found that a consistent electromechanical coupling is obtained if it is written in terms of the electric current; also, the classical formulation in terms of the electromechanical damping coefficient leads to an inconsistent description of the electromechanical coupling phenomenon; which, among other things, does not conserves the total energy.