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.

On the frequency up-conversion mechanism due to a soft stopper by the example of an electrostatic kinetic energy harvester

“…In this paper, we focus on the modeling of an eKEHs with a gap-closing variable capacitor as an example of a harvester whose nonlinearity arises in the electrical domain, as shown in Figure 1(a). Study (Li et al, 2020) presents an interesting mathematical model of the spring, electromechanical coupling and the hard-stopper force and predicts hardening effects in the investigated eKEH very well. However, the presented model does not explain in detail the frequency up-conversion occurring in the system.…”

“…The effect is known in the literature as frequency up-conversion. Since the first observation of this effect, there have been attempt to explain and quantify it, as well as to improve the design of the devices to enhance frequency up-conversion (Abedini and Wang, 2019; Fu and Yeatman, 2019; Guo et al, 2020; Jung and Yun, 2010; Kulah and Najafi, 2008; Lensvelt et al, 2020; Li et al, 2019, 2020, 2020; Naito and Uenishi, 2019; Speciale et al, 2020; Vysotskyi et al, 2016; Zhang et al, 2018; Zorlu et al, 2011).…”

Broadband Vibration-Based Energy Harvesting for Wireless Sensor Applications Using Frequency Upconversion

“…There are various strategies explored to increase the output power of e-VEHs. They include geometry optimization [31], combining power from parallel connected devices [32], and frequency upconversion [33]. The first approach, geometry optimization, has been explored in several works [21,31,34].…”

“…Finally, the frequency upconversion involves producing high-frequency mechanical vibrations in response to a low-frequency excitation, usually by triggering a free oscillation due to the impact of the electrodes [2,33]. The impact is facilitated by large excursions of the mobile electrodes in the presence of soft suspension springs of the shuttle mass.…”

Smart Wearable Sensors Based on Triboelectric Nanogenerator for Personal Healthcare Monitoring

“…They do not only make wearable sensors bulky and uncomfortable to wear, but also requires frequent charging or regular replacement. Wearable energy harvesters, based on different principles, were widely developed, such as electrostatic [ 3 , 4 ], electromagnetic [ 5 , 6 , 7 ], thermoelectric [ 8 , 9 , 10 ], piezoelectric [ 11 , 12 ], and triboelectric [ 13 , 14 ]. As an energy harvester device, triboelectric nanogenerator (TENG) based on a coupling effect of triboelectrification and electrostatic induction was proved to be very effective to precisely convert mechanical energy (especially low frequency) in the environment into electricity [ 15 , 16 , 17 , 18 ].…”