Characterization and Modeling of Nonlinearities in In-Plane Gap Closing Electrostatic Energy Harvester

Abstract

This paper investigates in detail a micro scale in-plane gap closing electrostatic energy harvester with strong nonlinearities in squeeze-film damping, electromechanical coupling, and impacts on end-stops. The device shows softening response on increasing the bias voltage and saturation behavior on impact with end-stops at high enough acceleration amplitude. We demonstrate that a lumped model can adequately describe the measured nonlinear behavior for a range of operating conditions with nonlinear fluid damping force and impact force included in the model. While modeling capacitances, a finite-element method (FEM) is used to analyze fringing field effects on the capacitance variation for gap closing electrodes. The nominal capacitance is obtained from FEM analysis, for a range of under-cut values in the fabrication process treated as a free parameter in the model. The device modeled for linear and nonlinear squeeze-film damping force highlights the importance of nonlinear damping force to understand the device behavior over the range of operating conditions. With the compliant end-stops treated as spring-dampers and with proper choice of end-stop damping-coefficient, the model successfully captures the end-stop nonlinearities for a particular operating point and reproduces the dynamic pull-in phenomena at 8 V bias, and rms acceleration 0.6 g, as observed in the experiments. Thus, the model described in this paper reproduces the subtle nonlinear effects dominating the dynamics of an in-plane gap closing electrostatic energy harvester.[ 2015-0107]Index Terms-Electrostatic devices, energy harvester, nonlinear systems, vibrations. 1057-7157

Parameter sensitivity of an in-plane gap closing electrostatic energy harvester with end-stop impacts

“…Then we highlight the similarities and differences between the experiments and current simulations. To this end, we first present a comparison that goes further than the previous work (Kaur et al, 2015) in demonstrating the ability of the SPICE simulation to fit the experimental results for acceleration that are small enough to avoid end-stop impacts. We emphasize that even these accelerations are large in the sense that the device operates well beyond its linear small-signal regime and displays clear softening spring characteristic due to the electrostatic transducer.…”

“…In this section, we first give a brief overview of the device test setup and model that is the basis for this work and was presented in detail in Kaur et al (2015). Then we highlight the similarities and differences between the experiments and current simulations.…”

“…The damping in the end-stop is treated as the fitting parameter in order to fit the simulated behavior to measured behavior at particular operating point. A similar end-stop model is presented in Kaur et al (2015) where the simulation data fit to the measured data at a particular operating point with adjustment in end-stop damping. One such model of a relatively low-Q piezoelectric harvester with one-sided compliant mechanical end-stop is presented in Blystad and Halvorsen (2011).…”

“…In this article, a lumped model of an electrostatic vibration energy harvester presented in Kaur et al (2015) is checked for sensitivity in jump frequencies to end-stop parameters. End-stop position, end-stop stiffness and end-stop damping are varied.…”

Research of piezoelectric energy harvesting systems based on cantilevers with irregular cross-sections

“…On the other hand, electrostatic energy harvesters can be adapted to micro scale electronic systems due to low mounting volume and highly scalable design. These advantages gives possibility to combine electrostatic energy harvesters with extra low power systems and to use them where mounting space is limited (Kaur and et al 2015;Jia and et al 2013).…”