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

Tobias Willemoes Jensen, Andrea R. Insinga, Johan Christian Ehlers, Rasmus Bjørk*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

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.
Original languageEnglish
Article number16607
JournalScientific Reports
Volume11
Issue number1
Number of pages15
ISSN2045-2322
DOIs
Publication statusPublished - 2021

Bibliographical note

This work is funded by the Independent Research Fund Denmark – Technologies and Productions Sciences, project no. 8022-00038B.

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