Einar Halvorsen

Energy Harvesters Driven by Broadband Random Vibrations

Simple analytical models have proved very useful in understanding vibration energy harvesters driven by a sinusoidal acceleration. Corresponding analyses for broadband excitations have been absent. In this paper, we present new closed-form results on the output power, proof mass displacement, and optimal load of linear resonant energy harvesters driven by broadband vibrations. Output power dependence on signal bandwidth is also considered. The results are compared with those that are already well established for a sinusoidal acceleration. We formulate a stochastic description of more general energy-harvester models and show that the influence of elastic mechanical stoppers on the output power is dependent on the electrical load for large amplitude vibrations.

Nonlinear Behavior of an Electrostatic Energy Harvester Under Wide- and Narrowband Excitation

This paper investigates an electrostatic vibration energy harvester that displays rich nonlinear behavior including jumps during frequency sweeps and broadening of the spectrum with increasing levels of broadband vibration. We demonstrate that the measured nonlinear phenomena can be adequately described by a lumped model with a nonlinear beam displaying both spring softening and hardening. Our results show that considerable bandwidth enhancements can be achieved by use of nonlinear springs without relying on mechanical stopper impacts, resonance tuning, or large electromechanical coupling.

Fabrication and characterization of a wideband MEMS energy harvester utilizing nonlinear springs

This paper presents the fabrication, characterization and modeling of a wideband MEMS electrostatic energy harvester utilizing nonlinear springs. The experimental results show that the vibration energy harvester displays a strong softening spring effect. For narrow band vibration, the energy harvester exhibits a widening bandwidth during frequency down-sweeps. For increasing levels of broadband random noise vibration, the energy harvester displays a broadening bandwidth response. Furthermore, the vibration energy harvester with softening springs not only increases the bandwidth, but also harvests more output power than a linear energy harvester at a sufficient level of broadband random vibration. At a broadband random vibration of 7.0 × 10−4 g2 Hz−1, we found that the bandwidth increases by more than 13 times and the average harvesting output power increases by 68% compared to that of a linear vibration energy harvester. Numerical analysis confirmed that the softening springs are responsible for the band broadening.

Modeling and experimental verification of low-frequency MEMS energy harvesting from ambient vibrations

Micro-fabricated piezoelectric vibration energy harvesters with resonance frequencies of 31–232 Hz are characterized and deployed for testing on ambient vibration sources in the machine room of a large building. A survey of 23 ambient vibration sources in the machine room is presented. A model is developed which uses a discretization method to accept measured arbitrary acceleration data as an input and gives harvester response as output. The modeled and measured output from the energy harvesters is compared for both vibrometer and ambient vibration sources. The energy harvesters produced up to 43 nWrms g−2 on a laboratory vibrometer and 10 nW g−2 on ambient vibration sources typically in large buildings.

Fundamental issues in nonlinear wideband-vibration energy harvesting

Mechanically nonlinear energy harvesters driven by broadband vibrations modeled as white noise are investigated. We derive an upper bound on output power versus load resistance and show that, subject to mild restrictions that we make precise, the upper-bound performance can be obtained by a linear harvester with appropriate stiffness. Despite this, nonlinear harvesters can have implementation-related advantages. Based on the Kramers equation, we numerically obtain the output power at weak coupling for a selection of phenomenological elastic potentials and discuss their merits.

Nonlinear Springs for Bandwidth-Tolerant Vibration Energy Harvesting

We experimentally investigate the usefulness of softening springs in a microelectromechanical systems electrostatic energy harvester under colored noise vibrations. It is shown that the nonlinear harvester has performance benefits when the vibrations center frequency varies in the frequency range of its softening response. With a vibration 3-dB bandwidth of 50 Hz, less than 3-dB variation in output power can be obtained over a 85-Hz wide range of vibration center frequencies. Compared to a simulated linear-spring device, the nonlinear device gives more output power for a wide range of vibration bandwidths. The nonlinear device shows less than 1-dB variation in output power when the vibration bandwidth varies from 12 to 120 Hz and is centered on the resonant frequency.

Piezoelectric MEMS energy harvesting systems driven by harmonic and random vibrations

Switching power conditioning techniques are known to greatly enhance the performance of linear piezoelectric energy harvesters subject to harmonic vibrations. With such circuits, little is known about the effect of mechanical stoppers that limit the motion or about waveforms other than harmonic vibrations. This work presents SPICE simulations of piezoelectric micro energy harvester systems that differ in choice of power conditioning circuits and stopper models. We consider in detail both harmonic and random vibrations. The nonlinear switching conversion circuitry performs better than simple passive circuitry, especially when mechanical stoppers are in effect. Stopper loss is important under broadband vibrations. Stoppers limit the output power for sinusoidal excitations, but result in the same output power whether the stoppers are lossy or not. When the mechanical stoppers are hit by the proof mass during high-amplitude vibrations, nonlinear effects such as saturation and jumps are present.

Microscale electrostatic energy harvester using internal impacts

This article presents a new concept for electrostatic energy harvesting devices that increase output power under displacement limited inertial mass motion at sufficiently large acceleration amplitudes. The concept is illustrated by two demonstrated electrostatic energy harvesting prototypes in the same die dimension: a reference device with end-stops and an impact device with movable end-stops functioning as slave transducers. Both devices are analyzed and characterized in small and large excitation regimes. We found that significant additional energy from the internal impact force can be harvested by the slave transducer. The impact device gives much higher, up to a factor of 3.7, total output power than the reference device at the same high-acceleration amplitude. The bandwidth of the response to frequency sweeps is beneficially enlarged by up to a factor of 20 by the nonlinear mechanisms of the impact device.

Bistable springs for wideband microelectromechanical energy harvesters

This paper presents experimental results on a microelectromechanical energy harvester with curved springs that demonstrates an extremely wide bandwidth. The springs display an asymmetrical bistable behavior obtained purely through their geometrical design. The frequency down-sweep shows that the harvester 3-dB bandwidth is about 587 Hz at 0.208-g acceleration amplitude. For white noise excitation at 4×10−3 g2/Hz, we found that the bandwidth reaches 715 Hz, which is more than 250 times wider than in the linear-spring regime. By varying the bias voltage, an output power of 3.4 μW is obtained for frequency down-sweep at 1-g amplitude and 150-V bias.

An electrostatic energy harvester with electret bias

We have designed, fabricated and characterized a MEMS electrostatic energy harvester using an electret as internal bias. The device operates in continuous mode and features a high voltage output, a large travelling distance of a big mass within a compact design using full bulk silicon thickness. The output power is about 1μW at an acceleration power spectral density of 0.03g2/Hz.