Analysis and scaling study of vibration energy harvesting with reactive electromagnetic and piezoelectric transducers

The goal of this paper is to present a comparative study on the principal features and scaling properties of time-harmonic vibration energy harvesting with electromagnetic and piezoelectric reactive transducers. The study is organised around two prototype reactive harvesters having one end connected to ground. The two harvesters are composed respectively by a coil-magnet and a composite piezoelectric beam characterised by similar dimensions, weights and fundamental natural frequencies. The work is based on equivalent lumped parameter models and energy formulations for the two harvesters. The study shows that, to maximise the power harvesting, the electromagnetic and piezoelectric transducers should be connected respectively to a resistive load and to a resistive-reactive load. In this case, the spectra of the harvested power per unit base acceleration falls proportionally to the inverse of frequency squared and the spectra of the energy harvesting efficiency remains constant with frequency. The scaling study shows that the normalised harvested power density for the electromagnetic harvester grows proportionally to the square of dimension whereas that for the piezoelectric harvester does not vary with dimension. In parallel, the efficiency to absorb vibration energy of the electromagnetic harvester scales following a distinctive S-type law, which reaches the maximum of 0.5 for large transducers. Instead, the efficiency of the piezoelectric transducer is constant and limited to a maximum of 0.5, apart for large transducers where it drops for large scales.