Optimization of Magnet and Back-Iron Topologies in Electromagnetic Vibration Energy Harvesters

This paper proposes an approach to systematically find the optimal geometry of electromagnetic energy harvesters through topology optimization. The energy harvesters designed herein have a pickup coil and permanent magnets (PMs) integrated with a magnetic back iron, completing a closed-loop magnetic circuit. The configuration and geometries of the PMs and back iron are simultaneously determined using topology optimization. The optimization goal is to maximize the root-mean-square (rms) value of the harvested output voltage, which is calculated based on the Lagrange polynomial interpolation with finite-element analysis. The sensitivity needed to solve the optimization problems is obtained using the adjoint variable method. The proposed optimization approach successfully determines the optimal design of the PMs and back irons. The optimized design consists of two PM pieces with opposite magnetization directions (to rapidly alternate the magnetic field direction) and shaped back irons (to minimize the magnetic reluctance). The optimized design significantly improves the electromagnetic performance of harvesters (a 42.5× increase in the rms output voltage with decreases in the volumes of the PM and iron), compared with an initial benchmark design determined through intuition.