The full phase space dynamics of a magnetically levitated electromagnetic vibration harvester

We consider the motion of an electromagnetic vibrational energy harvester (EMVEH) as function of the initial position and velocity and show that this displays a classical chaotic dynamical behavior. The EMVEH considered consists of three coaxial cylindrical permanent magnets and two coaxial coils. The polarities of the three magnets are chosen in such a way that the central magnet floats, with its lateral motion being prevented by enclosion in a hollow plastic tube. The motion of the floating magnet, caused by e.g. environmental vibrations, induces a current in the coils allowing electrical energy to be harvested. We analyze the behavior of the system using a numerical model employing experimentally verified expressions of the force between the magnets and the damping force between the floating magnet and the coils. We map out the phase space of the motion of the system with and without gravity, and show that this displays a fractal-like behavior and that certain driving frequencies and initial conditions allow a large power to be harvested, and that more stable states than two exists. Finally, we show that at leasts fifth order polynomial approximation is necessary to approximate the magnet-magnet force and correctly predict the system behavior.