Towards Nonlinear Magnetic Rotating Pendula for Low-Frequency Weak Vibration Energy Harvesting

Energy harvesting from ambient vibrations has received significant attention as an alternative renewable, clean energy source for microelectronic devices in diverse applications such as wearables and environmental monitoring. However, typical vibrations in remote environments exhibit ultra-low frequencies with variations and uncertainty leading to operation away from resonance and severe underperformance in terms of power output. Pendulum-based energy harvesters offer a promising solution to these issues, particularly when designed for parametric resonant response to driven displacement of the pendulum pivot. Parametric excitation has been shown to trigger fast rotational motion of the pendulum VEH that is beneficial for energy generation and the necessary space utilization. Nevertheless, low-frequency ambient vibrations typically come at very weak amplitudes, a fact that establishes significant design barriers when traditional gravitational pendula are used for rotary energy harvesting. In this paper, we propose a novel concept that utilizes permanent magnet arrays to establish pendulum dynamics. Extensive investigation of the restoring torque of the proposed magnetic pendulum concept is conducted with analytical tools and FEA verification. The resulting oscillator exhibits frequency tuning that is decoupled from gravity and adjustable via the circularly arranged magnetic fields, leading to increased flexibility in the concurrently necessary amplitude tuning. Numerical integration of the nondimensional equation of motion is performed in the system’s parameter space to identify the impact on the regions triggering rotational response to parametric excitation. Finally, a theoretical case study is numerically investigated with the device space constrained within 20 cm3, showing a multi-fold improvement in the achieved power density of over 600 μW/cm3/g2/Hz over a broad range of frequencies and driving amplitudes as low as 1.1 Hz at 0.2 g.