Design and experimental study of a bistable magnetoelectric vibration energy harvester with nonlinear magnetic force scavenging structure

Abstract

A bistable magnetoelectric vibration energy harvester using nonlinear magnetic force is proposed. It consists of a planar spring, a magnetoelectric transducer with an annular magnetic circuit, and a coil assembly with a ferrite bobbin inside. Based on these, a nonlinear magnetic force between the ferrite bobbin and permanent magnet arrays can be generated when the relative displacement changes, which can broaden the operating frequency bandwidth of the harvester. The nonlinear magnetic force makes the harvester demonstrate some special dynamic behaviors including the inter-well and chaotic motions, which are performed by the finite element analysis. And, the experimental validations are also carried to verify the performance of the proposed harvester. The results show that the output power can reach 10 mW in a relatively wide operating frequency range with a 90 Ω resistance load under 1 g harmonic excitation. In addition, a real vehicle road’s vibration signals from a highway bridge are acquired to estimate the practical energy harvesting performance of the harvester. The results show that the RMS output voltage and load power of the harvester can reach 3.16 V and 110.95 mW under 10× road spectrum excitations, respectively.

Keywords

Vibration energy harvester broadband magneto electric nonlinear magnetic force bistable

1. Introduction

With the increasing development of microelectronics technology, the electronic devices have a tendency to be miniaturized and integrated. Meanwhile, the emergence of ultra-low power communication standards like Bluetooth and Zigbee has urged the electronic devices to be wireless [1–3]. Currently, the Internet of Things (IoT) develops rapidly all over the world. However, one of the key technical problems is how to supply long-term energy for these ultra-low power wireless sensor network nodes [4–7]. Energy harvesting technology has the potential to liberate these low-power devices from their traditional power-supply methods such as electric wire and battery, and makes their applications easier as well as more flexible. Moreover, compared with supplying power by chemistry battery, energy harvesting technology is cleaner.

Harvesting solar energy, thermal energy and wind energy are usually used to power high-power electric devices. There is no doubt that they can be used to power sensor networks, while some sensor networks only need low power. Vibration energy harvesting technology has its advantages in portability and integration with MEMS technology, as well as no limit of light condition, temperature gradient, and wind speed. In addition, ambient vibration exists almost everywhere [8–12].

However, ambient vibrations are usually distributed over a wide frequency range. To harvest the ambient vibration energy efficiently, many researchers have already presented different works to broaden the working frequency range of the Vibation Energy Harvesters(VEHs). Multiple novel vibration scavenging structures have been proposed to achieve this goal. A broadband Vibration Energy Harvester(VEH) with multiple cantilever beams was proposed by Wa [13]. The analysis results show that the multiple cantilever beams with different natural frequencies can effectively broaden the frequency bandwidth. A broadband piezoelectric energy harvesting device using multiple bimorphs with different operating frequencies is proposed by Xue [14]. As can be seen from these works, the application of multiple vibration scavenging structures can effectively achieve the broadening of the frequencies, while the power density is not high compared with single scavenging structures.

Frequency tuning technology is another popular method in broadband vibration energy harvesting. Lallart proposed a self-sensing method for ensuring the resonance excitation of vibration-based seismic energy harvesters [15]. The cost-effective stiffness tuning mechanism uses piezoelectric material switch to reduce the self-consumption of power. Vinod develops a self-tuning VEH prototype that can tune from −27% to +22% of its untuned resonance frequency and output a peak power of about 1 mW. It consumes maximum energies of 3.3 J and 3.9 J to tune to the farthest source frequencies respecting to the untuned resonance frequency of the device [16]. However, there are some cases that the ambient vibration level is not sufficient to supply enough power for self-tuning. Therefore, how to reduce the power consumption of self-tuning further is one of the key points in this type of technical methods.

Recently, a type of bistable piezoelectric cantilever vibration energy harvester with an elastic support external magnet is proposed [17]. It has been proved that elastic support systems have better power output performance than rigid support systems when it is excited at low-intensity vibrations. The bistable effect due to the elastic support external magnet increases the frequency bandwidth of the device. Besides, some other nonlinear vibration energy harvesters also have been proposed to enhance the energy harvesting performance [18–21]. In these schemes, the magnetic force is frequently used to regulate the dynamics of the harvester. Accordingly, the magnetic force-based technique has been a promising way.

In this paper, we present a bistable magneto electric vibration energy harvester used for powering wireless sensor networks. Due to the proposed structure, a nonlinear magnetic force between the ferrite bobbin and permanent magnet arrays can be generated when the relative displacement changes, which can broaden the operating frequency bandwidth of the harvester. It makes the harvester demonstrate some special dynamic behaviors including the inter-well and chaotic motions. The paper mainly aims at the design, analysis and test of the VEH. It is organized as follows. In Section 2, we outline the concept structure design, finite element analysis and dynamic analysis. In Section 3, we describe the experimental set-up and experiment results of the bistable VEH, in comparison with the theoretical predictions. Conclusions are finally provided in Section 4.

2. Design and analysis

In this section, we first demonstrate the detailed structural configurations of the proposed bistable VEH; then, analyze the magnetic field distribution, magnetic force and coil flux-linkage of the magneto electric transducer using the popular COMSOL software; finally, research the dynamic behaviors and energy harvesting performance of the proposed device based on the classical dynamic analysis.

Fig. 1.

The structural configuration of the bistable VEH: (a) overall isometric view; (b) inside cutaway view.

2.1. Concept structure design

Figure 1 shows the structural configuration of the proposed bistable VEH including the overall isometric view and the inside cutaway view. The bistable VEH contains an oscillating system with a planar spring, an acrylic frame, a coil with ferrite core, and a copper magnetic housing with four permanent magnets and two iron plates embedded. The planar spring is used as its elastic component because its spiral shape can increase the length of the flexible beam and reduce its stiffness without the increase of its area. The four permanent magnets are arranged as an annular magnetic circuit to redirect the magnetic fluxes going across the copper magnetic housing gap. When the coil moves inside the magnetic field of the gap, a voltage can be induced accordingly.

Fig. 2.

The diagram and parameters of the transducer: (a) Front cutaway view; (b) Top cutaway view.

Table 1

The main structural parameters of the magneto electric transducer

Symbol	Value	Description
L	42 mm	the length of the transducer
H	25 mm	the height of the transducer
W	22 mm	the width of the transducer
l	10 mm	the length of the permanent magnets
h	10 mm	the height of the permanent magnets
w	20 mm	the width of the permanent magnets
D	10 mm	the diameter of the coil
d	3 mm	the diameter of the ferrite core
l _c	14 mm	the length of the coil
t _i	3 mm	the thickness of the iron plate
t	1 mm	the thickness of the magnet housing
B _r	1.21 T	the remnant flux density of the permanent magnets
𝜇_r	100	the relative permeability of the ferrite core
N	1000	the turn number of the coil

Figure 2 shows the diagram and the main structural parameters of the magneto electric transducer. The main parameters of the magneto electric transducer are summarized in Table 1.

Fig. 3.

The magnetic field distribution of the magneto electric transducer: Surface: Magnetic flux density, component in the direction of the coil length (T); Arrow Surface: Magnetic flux density (Spatial): (a) The coil in the neutral position; (b) The coil deviated from the neutral position.

Fig. 4.

The relationship between the flux-linkage of the coil and the relative displacement between the coil and the magnet assembly.

2.2. Finite element analysis

The finite element analysis FEA of the magneto electric transducer is conducted using the popular COMSOL software. Based on it, the magnetic field distribution, the relationship between the coil magnetic fluxlinkage and the relative displacement, and the relationship between the magnetic force and the relative displacement can be obtained. These relationships are the key points for the further analysis of the dynamic behaviors and energy harvesting performance of the VEH.

Fig. 5.

The relationship between the magnetic force and the relative displacement between the coil and the magnet assembly.

Fig. 6.

The relationship between the potential energy of the VEH and the relative displacement between the coil and the magnet assembly.

Figure 3 shows the magnetic field distribution of the magneto electric transducer. As can be observed in the figure, when the coil moves in the range of gap, the magnetic flux goes through the coil change. When the coil is located in the neutral position, the magnetic flux goes through the coil is zero. When the coil goes across the neutral and moves up or down, its magnetic flux will first increase and then decrease.

Fig. 7.

The dynamic behavior of the oscillator in 15 Hz: (a) The displacement versus time; (b) Phase portrait diagram.

Fig. 8.

The dynamic behavior of the oscillator in 20 Hz: (a) The displacement versus time; (b) Phase portrait diagram.

Fig. 9.

The dynamic behavior of the oscillator in 25 Hz: (a) The displacement versus time; (b) Phase portrait diagram.

Figure 4 shows the relationship between the coil magnetic flux-linkage and the relative displacement between the coil and the magnet assembly. As can be seen from the figure, the linear relation exists between the coil magnetic flux-linkage 𝜓 and the relative displacement z. Therefore, a linear fitting method is used in the displacement range of 10 mm. The relation can be closely approximated by a linear function: $\begin{eqnarray}\displaystyle {\psi}=Kz & & \displaystyle\end{eqnarray}$ (1) where the coil magnetic flux-linkage gradient K in the relative movement direction is 0.0074 Wb/mm.

Fig. 10.

The dynamic behaviors of the oscillator in different frequencies.

When the magnet assembly moves relatively to the coil, a magnetic force will act on the magnet assembly. The magnetic force is calculated by finite element analysis and is shown in Fig. 5. Fourier curve fitting is used to derive the expression of the nonlinear magnetic force. With the planar spring stiffness of 2.5 N/mm and the expression of the magnetic force, the relationship between the potential energy of the VEH and the relative displacement can be easily obtained. The potential energy is shown in Fig. 6. As can be seen from this figure, there are two potential wells and one barrier in the potential energy function. Therefore, from the view of energy, the proposed VEH can be categorized as a bistable VEH.

Fig. 11.

The photograph of the VEH prototype.

Fig. 12.

The testing system of the VEH prototype.

2.3. Dynamic analysis

When the VEH is driven by a harmonic excitation, its dynamics governing equation can be given in following: $\begin{eqnarray}\displaystyle m\ddot{x}+c{\dot{x}}+kx=f(x)+m{\omega}^{2}Y\sin {\omega}t & & \displaystyle\end{eqnarray}$ (2) where m, c, k are the mass of the oscillator, the damping coefficient and the stiffness of the planar spring, respectively. Here, the mass of the oscillator m and the planar spring stiffness k are set to 0.13 kg and 2.5 N/mm, respectively. ω and Y are the angular frequency and the displacement amplitude of the excitation. The variable f (x) is the magnetic force operating in the oscillator. It should be noted that for an energy harvesting system with a resistor connected to the output terminal of the coil, the damping coefficient can be approximately expressed by the equation: $\begin{eqnarray}\displaystyle c\approx K^{2}/R & & \displaystyle\end{eqnarray}$ (3) where R is the total resistance value. In the dynamic analysis, the resistance value R is set to 180 Ω, which equals to the double of its coil internal resistance.

Assume that the acceleration level ω² Y of the harmonic excitation is 1 g. By numerically solving Eq. (2) and Eq. (3), we can obtain the dynamic behaviors of the oscillator in different frequencies, as is illustrated in Fig. 7, Fig. 8 and Fig. 9.

Fig. 13.

The measured output voltage: (a) 15 Hz; (b) 20 Hz; (c) 25 Hz.

Fig. 14.

The relationship between the induced electromotive force, the load power and excitation frequency.

As can be seen from the above figures, the oscillator of the VEH keeps in large amplitudes in a wide frequency range. The Root Mean Square(RMS) values of the oscillator displacement and velocity in different frequencies are calculated and presented in Fig. 10.

Fig. 15.

The typical forced vibration condition of a highway bridge: (a) The vibration waveform; (b) The power spectral density on the frequency domain.

Fig. 16.

The dynamic response of the broadband magneto electric VEH: (a) The oscillator displacement waveform; (b) The output voltage waveform.

Since the induced electromotive force of the VEH can be expressed as $emf=-K({\dot{x}}-{\dot{y}})$ , and the excitation velocity ${\dot{y}}$ is far smaller than the oscillator velocity ${\dot{x}}$ , the RMS values of the induced electromotive force are approximately proportional to the oscillator velocity. It can be observed from Fig. 10 that the oscillator keeps a high RMS velocity level as well as the induced electromotive force in the frequency range from about 15 Hz to 20 Hz.

3. Experimental study

In this section, the experiment is carried out to verify the above analysis of the proposed bistable VEH. The experimental prototype is manufactured and fabricated shown in Fig. 11 according to the structural parameters in Section 2, and The experimental setup is shown in Fig. 12.

The prototype is fixed on the vibration table and driven by a vibration exciter (HEV-200, Force: 0--200 N, Frequency: 0--3 kHz). The vibration exciter is driven by a signal generator (Agilent 33120A) and power amplifier (HEA-200C, Power: 550 W, Frequency: 0--10 kHz). Output signal generated by the signal generator imports to exciter through power amplifier. The voltages generated by the coil are monitored by an oscilloscope (TDS 2012). The laser displacement sensor (KEYENCE LK-G3001V & LK-G155) is used to measure the amplitude of the vibration of the vibration table.

Figure 13 shows the output voltage waveforms that measured in the excitation frequencies of 15 Hz, 20 Hz and 25 Hz, respectively. The RMS values of these output voltages in the steady states are 3.32 V, 1.90 V and 1.37 V, respectively. With the approximation formula $emf=-K{\dot{x}}$ , these output voltage values can verify the dynamic behaviors of the VEH that derived by theoretical calculation. According to the measured output voltages, the relationship between the induced electromotive force, the load power and the excitation frequency is given in Fig. 14.

These results indicate that the load power can reach the 10 mW level in a wide range, approximately from 15 Hz to 20 Hz. The bistable effect of the VEH structure broadens the frequency bandwidth effectively. It should be pointed out that the maximum load power can reach 68 mW when the excitation frequency is about 19 Hz.

Figure 15(a) shows a typical forced vibration waveform of a highway bridge. It should be noted that the excitation acceleration of the waveform magnifies 10 times to show the bistable phenomenon clearly, due to the size of the bistable magneto electric VEH prototype. Figure 15b illustrates its power spectral density on frequency domain. In the following experiment, the excitation is restored through the vibration table.

When driven by the typical forced vibration, the dynamic behavior of the broadband magneto electric VEH are measured and can be seen in Fig. 16. As is shown in Fig. 16(a), the oscillator vibrates between and around the two stable positions. The bistable effect broadens the movement region of the oscillator significantly. The output voltage of the VEH is measured by oscilloscope and is shown in Fig. 16(b). It can be estimated that the RMS value of the output voltage reaches 3.16 V and the load power consumption reaches 110.95 mW. It still shows the good energy harvesting performances of the bistable VEH though compared with its size and excitation strength.

4. Conclusion

In this paper, a type of broadband magneto electric VEH using bistable vibration scavenging structure is proposed. A nonlinear magnetic force respecting to the relative displacement is generated by its ferrite bobbin and magnetic circuit and permanent magnet array. The magnetic field distribution and the coil fluxlinkage change in the relative movement range are analyzed by the FEA software COMSOL. Based on the FEA results and the dynamic governing equation, the dynamic behaviors of the VEH are predicted by ODE calculation. Validation experiments are carried out and show that the VEH can harvest high power in a relatively wide excitation frequency bandwidth. The test shows that the load power of the VEH with a load resistor of 90 Ω can reach 10 mW level in a wide frequency bandwidth when the acceleration level of the excitation keeps in 1g. A strengthened typical forced vibration waveform of a highway bridge is used to estimate its energy harvesting performance under a real working condition. The RMS value of its output voltage and its load power consumption can reach 3.16 V and 110.95 mW, respectively. It still shows good energy harvesting performances of the bistable VEH though compared with its size and the excitation strength. Further research is underway to reduce its size and to harvest energy from weaker ambient vibrations.

Footnotes

Acknowledgements

This work was supported by Natural Science Foundation of China (No. 51675265), the priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD), Jiangxi province humanities and social sciences key base project(JD17127), Key Research and Development Project of Jiangxi Province(20171BBE50049), Jiangxi Province Teaching Reform Project(JXJG-17-22-16),Ministry of Education Humanities and Social Sciences Youth Fund(18YJC760085) and Jiangxi Province Education Science Planning Project(17YB276).

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