A predictive model for electrostatic energy harvesters with impact-based frequency up-conversion

Abstract

This paper reports a predictive model for vibration-to-electrical energy harvesters based on an in-plane, gap-closing variable capacitor with frequency up-conversion triggered by the impact between the electrodes. Since the output power is proportional to the output frequency, rectifying low-frequency ambient vibrations (1–50 Hz) to high-frequency electrical signals (200–600 Hz) increases the power output. While such a device has been previously reported experimentally, this is the first time a model able to predict the experimental data has been described. The model is based on lumped approximation. The central area supporting the mobile electrodes, or the shuttle mass, is represented by a point mass suspended by springs and has its own equation of motion. The motion of the electrodes attached to the shuttle is described by a set of two equations, each associated with a distinct dynamic mode. In these equations, the electrodes are represented by an equivalent mass and spring constant. The first equation describes the separate motion of mobile and fixed electrodes. In this mode, the electrodes experience damped free vibration due to the electrostatic and air damping between them. The second equation describes the combined motion when the two set of electrodes move together. In this mode the air damping forces between the collided electrodes is eliminated and the electrostatic force is kept constant. The motion equations are solved simultaneously with Kirchhoff’s law to compute the voltage drop across a resistor in series with the variable capacitor and a DC bias voltage source. Predictions are shown to be consistent with the experimental results, and frequency up-conversion effects are observed with exponentially decaying voltage amplitude as seen in experiments. A parametric study is also carried out to identify main parameters that affect the up-conversion, laying the foundation for future design optimization to maximize the power output.