Nonlinear Electromagnetic Energy Harvester Research Articles

Nonlinear electromagnetic vibration energy harvester comprising dual helical-plane springs and multiple Halbach arrays for low-frequency and small-amplitude vibrations

Electromagnetic vibration energy harvesters are widely investigated for self-powered wireless sensors and nonlinearity has been introduced for low-frequency and broadband vibration energy harvesting. But how to realize the nonlinearity with small amplitudes, high reliability and few complexities is still a challenge in real-world applications. In this paper, a novel electromagnetic vibration energy harvester comprising dual helical-plane springs and multiple Halbach arrays is proposed. The structural characteristics are analyzed, which indicate that the helical-plane springs can have nonlinear stiffness under small-amplitude vibrations and multiple Halbach arrays can greatly enhance the magnetic field. Then a magnet-electro-mechanical model is built by combining mechanical dynamics &electrodynamics, which is numerically solved by using the Runge-Kutta algorithm. Finally, the feasibility of the nonlinear electromagnetic vibration energy harvester is validated both numerically and experimentally. The results show that it has a nonlinear stiffness, a resonance bandwidth of 3 Hz and a peak power of 14 mW when the excitation amplitude is only 0.5 g. In particular, the resonance frequency range depends on the excitation amplitude. Furthermore, the prototype of a self-powered wireless temperature sensor is constructed and testified. The results of this study indicate that the proposed structure can be utilized and extended to build compact, reliable and nonlinear electromagnetic vibration energy harvesters for low-frequency, small-amplitude and broadband vibrations in real-world applications.

Design and characterization of non-linear electromagnetic energy harvester with enhanced energy output

This paper presents design, analysis, and characterization of a compliant non-linear electromagnetic energy harvester operating on the principle of bi-stability incorporated with a displacement amplification mechanism. The energy harvester engenders energy from ambient vibrations at multiple modes and with frequencies ranging from 80 to 120 Hz. The energy harvester is analytically modeled using the mechanic’s elastic beam theory. Finite Element Analysis (FEA) has been carried out using commercial Finite Element Method (FEM) based software to perform static, fatigue, dynamic and electromagnetic analysis. Bi-stable mechanism has been used to harness energy at a wider frequency bandwidth while lever mechanism is acting as a displacement amplifier for enhancing low frequency vibration amplitude with the amplification factor of 6.24. With such amplification factor, the energy harvester can be deployed to extract vibrations of diminutive level and recast them into electrical energy in the form of generated voltage. Spring steel material, owing to its structural sensitivity, stiffness and higher value of ultimate stress, was used for its fabrication. The use of Neodymium (N52) magnets, copper coils and shaker were put into practice for testing of this device. The coil resistance is 2.5 Ω with number of turns kept at 350. The maximum output voltage of 1.86 V was generated at 106 Hz with root mean square value of 548 mV. Testing results are in accordance with the results obtained through simulations and thus useful electrical power of 11.1 mW can be generated from ambient vibrations at a wider bandwidth of 18 Hz with operating frequency ranging from 99 to 117 Hz.

Nonlinear energy harvesting from rotating system

A simple electromagnetic energy harvester with a cubic nonlinear stiffness is proposed and dynamic responses as well as the potential power harvested are studied in this paper. The proposed nonlinear electromagnetic vibration energy harvester can be installed on a host base that is rotating at a constant speed and vibrating vertically. Considering the combination of the vertically vibrating and rotating frequency of the host base, the 1:1 primary resonance is investigated by the method of multiple scales. The dynamic characteristics of responses in terms of system parameters are studied and bifurcation curves are constructed. In addition to possessing the resonance characteristics, some saddle–node bifurcations occur for the steady-state solutions under certain conditions. Moreover, the effects of system parameters on the output average power are investigated as well. The results of analysis show that multiple frequency bands and parameter regions exist where a large power can be harvested due to the nonlinear resonances. Introducing the nonlinearity not only can increase the power output but also expand the frequency bands and parameter regions to harvest more power. A carefully selected system parameters can help to optimize the average power harvested in the design.

Nonlinear Electromagnetic Energy Harvester–Structure System under Seismic Excitation: Vibration Mitigation and Energy Scavenging

Nonlinear Electromagnetic Energy Harvester–Structure System under Seismic Excitation: Vibration Mitigation and Energy Scavenging

A nonlinear electromagnetic vibration energy harvester lubricated by magnetic fluid for low-frequency vibration

Using vibration energy harvesters (VEHs) to achieve self-power is an effective method to ensure long-term use of sensor networks. This paper proposes a nonlinear electromagnetic VEH lubricated by magnetic fluid (MF) for low-frequency vibration energy harvesting. The VEH uses fixed small magnets to reduce natural frequency and prevent moving a magnet stack from flipping, MF for lubrication to improve output voltage under weak vibration, and elastomers to prevent magnet damage under strong vibration. In addition, MF and elastomers can increase the nonlinearity of restoring force, broadening the response frequency of VEHs. The motion state of the VEH is analyzed, and a crank-slider mechanism is used to test the output performance of VEHs. The influence of shell conductivity, the number of fixed small magnets, and length of VEH on output voltage is studied, and the results show that the VEH with an insulated shell, fewer fixed small magnets, and suitable length generates higher output voltage. The MF mainly plays a damping role in strong vibration but mainly plays a lubricating role in weak vibration. For experiments with 15 mm amplitude at 7.9 Hz, the output power density of the VEH without MF and lubricated by MF are 2.436 and 1.862 mW/cm3, respectively. MF damping reduces the output power density by 23.56%. However, for experiments with 7.5 mm amplitude at 3 Hz, the output power for VEHs without MF and lubricated by MF are 0.065 and 0.254 mW, respectively. The output power is increased by 291% with MF lubrication.

Non-transient optimum design of nonlinear electromagnetic vibration-based energy harvester using homotopy perturbation method

Abstract In this paper the coupled differential equations governing the vibration of nonlinear electromagnetic energy harvesters are solved by the homotopy perturbation method. The amplitudes of odd harmonics of displacement of the magnet, coil current, and load voltage are derived up to the 5th harmonic. The frequency response of output power is plotted and it peaks at the linear mechanical resonance frequency. It should be noted that the optimum design of coil and load parameters, optimum electromagnetic coupling coefficient, and optimum vibration frequency of the magnet attached to a non-linear spring resulted in a stationary or non-transient vibration. Paying insufficient attention to this point and using typical parameters instead of optimum ones will result in transient vibration. The research aims at a rigorous semi-analytical method on a nonlinear problem which has previously solely investigated by numerical or experimental method.

Dynamic analysis and design of power management circuit of the nonlinear electromagnetic energy harvesting device for the automobile suspension

A nonlinear electromagnetic energy harvester (EMEH) for the automobile suspension is designed. The magnetic flux density and the magnet repulsive force of the mechanical model are determined by finite element analysis. The dynamic model of a quarter car with the nonlinear EMEH under random road excitation is established. The influence of structure parameters on output characteristics of the nonlinear EMEH is studied. In order to further improve the output power, effects of the road class, the car speed, and the load resistance are investigated in detail. Studies have revealed that the higher the road class and the larger the car speed are, the better output characteristics of the nonlinear EMEH become. In order to prove that the nonlinear magnet repulsive force can significantly improve the output power, output characteristics of the nonlinear EMEH and the linear EMEH are compared. Finally, the power management circuit matching with the nonlinear EMEH is designed, which can convert the unstable alternating voltage into the stable direct voltage, and directly supply power to electronic devices. There are two innovations in this paper. One is the introduction of the nonlinear magnet repulsive force and the amplification bar in the structural design. Another is to design the power management circuit of the high energy conversion efficiency, which is up to 74.3% for the car speed 25 m/s on the road of class C.

Numerical analysis of a magnetic-spring-based piecewise nonlinear electromagnetic energy harvester

Numerical analysis of a magnetic-spring-based piecewise nonlinear electromagnetic energy harvester

Dynamic responses of a two-degree-of-freedom bistable electromagnetic energy harvester under filtered band-limited stochastic excitation

This study investigates the dynamic responses of a two-degree-of-freedom (2DOF) nonlinear bistable electromagnetic energy harvester under filtered band-limited stochastic excitation. The mathematical model of the 2DOF bistable energy harvester is derived, and its fidelity is experimentally verified. A comprehensive numerical investigation is conducted under filtered band-limited stochastic excitation (which is the white Gaussian noise filtered by a second-order filter). Comparative studies are performed between the 2DOF bistable energy harvester, the 2DOF equivalent linear energy harvester, and the single-degree-of-freedom (SDOF) linear energy harvester when subjected to white Gaussian noise and the exampled band-limited stochastic excitation. The comparative results show that the 2DOF bistable energy harvester can significantly improve the average power compared to the equivalent 2DOF and SDOF linear energy harvesters. The study reveals the insights of the excitation strength, bandwidth, and center frequency into the system performance. Finally, structural parametric studies demonstrate that the bigger frame mass and the larger spring stiffness coefficient will increase the oscillation velocity which has great significance for energy harvester.

Nonlinear multi-mode electromagnetic insole energy harvester for human-powered body monitoring sensors: Design, modeling, and characterization

The current research in wearable electronics is trending towards miniaturization, portability, integration, and sustainability, with the harvesting of biomechanical energy seen as a promising route to improve the sustainability of these wearable electronics. Efforts have been made to prolong operational life of these harvesters, to overcome energy dissipation, lowering resonant frequency, attaining multi-resonant states as well as widening frequency bandwidth of these biomechanical energy harvesters. Herein, an electromagnetic insole energy harvester (EMIEH), capable of efficiently harvesting low-frequency biomechanical energy, has been designed, fabricated and experimentally tested. The core component in the device is the vibrating circular spiral spring, holding two magnets as the driving force on the central platform of the circular spiral spring, and just in-line with the upper and lower wound coils. It has been shown that the harvester exhibits higher sensitivity to low-frequency external vibrations than conventional cantilever-based designs, and hence allows low impact energy harvesting such as harvesting energy from walking, running and jogging. The experimentally-tested four resonant frequencies occurred at 8.9 Hz, 28 Hz, 50 Hz, and 51 Hz. At the first resonant frequency of 8.9 Hz under base acceleration of 0.6 g, the lower electromagnetic generator can deliver a peak power of 664.36 µW and an RMS voltage of 170 mV to a matching load resistance of 43.5 Ω. The upper electromagnetic generator can contribute an RMS voltage of 85 mV, corresponding to the peak power of 175 µW across 41 Ω under the same experimental condition. Finally, the harvester has been integrated into the shoe and it is able to charge a 100 µF capacitor up to 1 Volt for about 8 minutes foot movement. The result has remarkable significance in the development of wireless body monitoring sensors applications.

Physical realisation of a nonlinear electromagnetic energy harvester for rotational applications

Control and structural health monitoring sensors are becoming increasingly common in industrial and household applications due to recent advances reducing their manufacturing costs, size and power consumption. Nevertheless, providing power for these sensors poses a key challenge to engineers, particularly in system locations where limited access renders regular maintenance infeasible due to high associated costs. In the present work, the design and physical prototype testing of a nonlinear electromagnetic vibration energy harvester is presented based on a previously reported concept of the authors. The harvester is activated by the torsional speed fluctuations of a rotating shaft. Experimental testing in a rig driven by an electric motor confirms the harvester’s properties and the modelled oscillatory behaviour. This novel rotational vibration energy harvester concept may generate over 10 mW of electrical power for a broadband speed range of approximately 400 rpm (in the examined rotational system with set fluctuating speed) for wireless sensing purposes on rotating shafts.

Design of nonlinear electromagnetic energy harvester equipped with mechanical amplifier and spring bumpers

Design of nonlinear electromagnetic energy harvester equipped with mechanical amplifier and spring bumpers

Experimental Analysis on the Transduction Coefficient of a Non-Linear Electromagnetic Energy Harvesting Device with Softening Stiffness

Nonlinear energy harvesting devices in the form of stiffness nonlinearity have emerged as among the effective solutions to overcome the performance limit of linear energy harvesting devices. However, up to now, researches on the nonlinear devices are only focusing on the ability to widen the bandwidth while the limit of employing linear transduction coefficient in a nonlinear system has yet to be heavily discussed. This paper investigates on the transduction coefficient for both linear and nonlinear systems of an electromagnetic energy harvesting device as a function of the excitation frequency. It is proven that the transduction coefficient of the nonlinear device is larger than its equivalent linear device, especially in the multi-stable solutions region. In common practice, the nonlinearity in the nonlinear system is considered weak, and its transduction coefficient is assumed to converge to the one produced by the linear system. The limits to which the transduction coefficient of a linear system can be employed on the nonlinear system were drawn based on the experimental analysis conducted on the proposed device. The device was designed to perform as a linear or nonlinear system, where the degree of nonlinearity was changed by varying the gap between the magnets. The limit of the transduction coefficient was determined from the analysis of the harmonic ratio. The results show that the linear transduction coefficient is valid to be employed to the nonlinear system when the harmonic ratio is less than five per cent at the multi-stable solutions region.

Performance of a Nonlinear Electromagnetic Energy Harvester–Structure System under Random Excitation

AbstractElectromagnetic (EM) energy harvesters have been proposed in civil engineering for simultaneous energy scavenging and structural vibration mitigation. One important component governing the ...

A hula-hooping-like nonlinear buckled elastic string electromagnetic energy harvester for omnidirectional broadband excitations

This paper reports a hula-hooping-like nonlinear buckled elastic string electromagnetic energy harvester for wideband vibration energy harvesting. The harvester is comprised of a magnetic rotor attached at the middle of a clamped-clamped buckled elastic string and a stator with an embedding coil array. Attributed to the geometric nonlinear characteristic of the elastic string, the harvester can convert the reciprocate vibration in arbitrary in-plane direction to a hula-hooping-like curvilinear translation plane motion. A hardening nonlinear wideband voltage response was demonstrated by sweep excitation from 5\\,∼\\,23 Hz. The output peak power for a single coil can reach 1.12 mW at a 5 ms−2 excitation. To overcome the phase delay effects between the voltages of three spatially distributed coils, they were rectified separately and connected serially or parallelly to provide the final output. An open circuit peak voltage of 0.53 V was obtained from the serial connection at a 4 ms−2 up-sweep excitation, under which a 100μF capacitor was successfully charged to 0.35 V within 120 s. The omnidirectional energy scavenging performance of the harvester was further validated experimentally, suggesting its great promise for practical vibration energy harvesting.

Stochastic analysis of a nonlinear electromagnetic energy harvesting system with fractional damping under additive and multiplicative stochastic excitation

Electromagnetic energy harvester has been widely concerned in recent years due to its advantages of small size and high sensing frequency. In this paper, the stochastic behaviors of a nonlinear electromagnetic energy harvesting system (NEEH) with fractional damping are investigated under the additive and multiplicative stochastic excitation. Firstly, by applying the stochastic average method to the NEEH system, the mean square of the output current, and the steady-state probability density of vibration amplitude, displacement and velocity are obtained. Meanwhile, the validity of the theoretical results is verified by comparing with the numerical results given by the Monte Carlo method. Secondly, by investigating the theoretical and numerical results, the influences of noise intensity and fractional order on the NEEH system are explored. It is obvious that a higher output voltage can be obtained by the larger intensity of the stochastic excitation, and the smaller coefficient and fractional order of the fractional damping.

Design and Research on a Nonlinear 2DOF Electromagnetic Energy Harvester With Velocity Amplification

In order to power the microelectronic devices of the Internet of Things in the low-frequency broadband vibration environment, a novel nonlinear 2DOF electromagnetic energy harvester was proposed based on the magnetic levitation structure and velocity amplification mechanism. The electromechanical coupling model was established and numerically simulated to analyze the generating characteristics. A prototype was fabricated and tested to verify the theoretical model. The influences of the key parameters, including the gap between the suspended magnet and the lower spring, excitation acceleration, spring stiffness, mass of copper cylinder, on the generating characteristics were studied. When it was subjected to a harmonic excitation with acceleration amplitude of 0.8g, the measured open-circuit voltage reached peaks of 3.13 V at 8 Hz and 2.93 V at 13.5 Hz, respectively. The optimal output power at 8 Hz was 10.18 mW with the matched load resistance of 250~Ω. Both the experimental and theoretical results demonstrated that this novel electromagnetic energy harvester had obvious advantages in increasing the output power and widening the bandwidth.

Nonlinear resonance-type electromagnetic vibration energy harvester excited by an impact ball

Nonlinear resonance-type electromagnetic vibration energy harvester excited by an impact ball

A Nonlinear Broadband Electromagnetic Vibration Energy Harvester Based on Double-Clamped Beam

The performance of vibration energy harvesters is usually restricted by their frequency bandwidth. The double-clamped beam with strong natural nonlinearity is a simple way that can effectively expand the frequency bandwidth of the vibration energy harvester. In this article, a nonlinear electromagnetic vibration energy harvester with monostable double-clamped beam was proposed. A systematic analysis was conducted and a distributed parameter analytical model was established. On this basis, the output performance was estimated by the analytical model. It was found that the nonlinearity of the double-clamped beam had little influence on the maximum output, while broadening the frequency bandwidth. In addition, the resonant frequency, the frequency bandwidth, and the maximum output all increased following the increase of excitation level. Furthermore, the resonant frequency varies with the load changes, due to the electromagnetic damping, so the maximum output power should be gained at its optimum load and frequency. To experimentally verify the established analytical model, an electromagnetic vibration energy harvester demonstrator was built. The prediction by the analytical model was confirmed by the experiment. As a result, the open-circuit voltage, the average power and the frequency bandwidth of the electromagnetic vibration energy harvester can reach up to 3.6 V, 1.78 mW, and 11 Hz, respectively, under only 1 G acceleration, which shows a prospect for the application of the electromagnetic vibration energy harvester based on a double-clamped beam.

Enhanced Bandwidth Nonlinear Resonance Electromagnetic Human Motion Energy Harvester Using Magnetic Springs and Ferrofluid

An enhanced bandwidth nonlinear resonant electromagnetic energy harvester has been designed to harness low frequency energy from basic human motions. The inertial mass of the proposed harvester is formed by four stacked ring permanent magnets (PMs), which is suspended axially by two magnetic springs and circumferentially by ferrofluid within a carbon fiber tube. The magnetic springs are made up of two button PMs adhered, respectively, to the end cap at each end of the carbon fiber tube to provide varying repulsive forces to the PM stack, resulting in enhanced resonance frequency band and higher efficiency in energy harvesting. The ferrofluid that self-assembles around the edges of the PM stack acts as its bearing system to minimize frictional losses during its movement. Copper wire is wrapped outside the tube to form the armature winding. The stiffness characteristic of the magnetic springs and the optimum equilibrium position and number of windings have been determined by finite element method analysis. As a proof of concept, a portable prototype of the proposed energy harvester that weighs 110 g and with a volume of only 37.7 cm $^3$ is fabricated. A series of experiments is carried out and the results show that the frequency band of the harvester becomes wider as the external vibration intensity increases. In addition, the effectiveness of ferrofluid in reducing friction is demonstrated under walking and running conditions. Without ferrofluid, the maximum average outputs are 10.15 and 32.53 mW, respectively, for walking and running. With ferrofluid, the maximum outputs are 17.72 and 54.61 mW, representing an increase of $74.58\%$ and $67.88\%$ , respectively. Furthermore, the prototype exhibits an average power density of 1.45 mW/cm $^3$ during running motions, which compares favorably with existing harvesters used in low power wearable devices.