A hybrid numerical-analytical approach for modeling levitation based vibration energy harvesters

This paper presents a computational approach for the evaluation of the electro-mechanical response of levitation based vibration energy harvesters. A detailed analysis of the relevant physical, mathematical and computational aspects of the design of a harvester is presented. Several key points of the design of levitation based energy harvesters, such as the existence of the resonance phenomenon, the influence of damping in the system response, the magnetic force nonlinearity and the calculation of the magnetic flux derivative for multi-magnet configurations are addressed. The evolution in time of the electromechanical variables is investigated through a hybrid numerical-analytical approach. The evaluation of the levitational force and the magnetic flux derivative is done through a nonlinear model based on the finite element method. A performance assessment is done by comparing the results obtained with the present formulation against measurements; a physical prototype of a multi-pole-multi-coil harvester is built ad hoc. An excellent agreement between the mathematical model and the experiments was found.