AN ACCURATE MODELLING METHOD OF MAGNETIC FORCE IN MULTI-STABLE ENERGY HARVESTING SYSTEM

Chaos and bifurcation make the nonlinear dynamic response sensitive to structural parameters for multi-stable energy harvesting system, so that it is difficult to design the nonlinear characteristics directly from structural parameters. In order to acquire the relationship between the nonlinear restoring force and the structural parameters quantitatively, an accurate modelling method of magnetic force for multi-stable energy harvesting system is proposed. The relative distance and the rotational angle between the end magnet and the external magnet are calculated to determine the relative spatial position between magnets, and the magnetic charge theory is adopted to deduce the model of the nonlinear magnetic force in multi-stable energy harvesting system. Then, the experimental platform is carried out to measure the nonlinear magnetic force under different structural parameters for multi-stable energy harvesting system. The comparative analysis shows that the magnetic force calculated by the proposed method is in a better agreement with the experimental result than other methods. The effectiveness of the proposed method for magnetic force prediction is verified by the peak values errors of 4.3% and 6.49% for bi-stable energy harvesting system and tri-stable energy harvesting system respectively. In addition, the influence mechanism of structural parameters on potential wells is investigated to obtain the steady states critical positions of multi-stable energy harvesting system based on the proposed method, and also the influence of different structural parameters on voltage response is analysed for bi-stable and tri-stable energy harvesting systems. After parameters optimization, the maximal RMS voltage response for bi-stable system is 10.22 V in case of the vertical distance 34 mm, while for tri-stable system the maximal RMS voltage response is 12.7 V in case of the vertical distance 28 mm and horizontal distance 8 mm. This research is expected to provide the guidance for the output performance optimization of multi-stable energy harvesting system.