This article presents a compact magnetic levitation energy harvester (MLEH) with tunable resonant frequency. Unlike many of the reported tunable harvesters with unknown tuning results, the proposed MLEH can be tuned toward designated resonant frequency values within its tuning range. The targeted tuning processes is realized by a nonlinear magnet repulsive force exerted on a Halbach magnet array, combined with a calibrated scaling system. At a sinusoidal acceleration of ±0.15 g, the maximum frequency tuning range of the proposed MLEH is 6.3 Hz (8.1–14.4 Hz), which is 77.8% of its resonant MLEH (8.1 Hz). At a frequency of 9.7 Hz, the output power is 462.1 μW and the calculated normalized power density is 496 μW cm^{−3} g^{−2}.

## HIGHLIGHTS

A magnetic levitation energy harvester (MLEH) with tunable resonant frequency based on a Halbach magnet array is proposed.

The MLEH has the advantages of low resonant frequency, wide tuning range, and simple tuning procedure.

It can be precisely tuned toward a specific target frequency in a one-off manner without the need for repeated frequency scanning.

## I. INTRODUCTION

Electromagnetic vibrational energy harvesters (EVEHs) are devices that transform vibrational energy into electric power. The energy transformation process is often carried out through the induction effect between a permanent magnet and a solenoid coil. EVEHs are considered as important alternatives to traditional batteries as power sources for both consumer and industrial electronic devices. Early implementations of EVEHs are based on macroscopic magnets and coils, whereas the recent development of EVEHs has focused more on miniaturized EVEHs implemented with printed circuit board (PCB)^{1–3} or microelectromechanical systems (MEMS)^{4–6} technologies. Two major goals in EVEH design are high power output and miniaturization, and trade-offs between these two goals must be carefully weighed to achieve the optimal performance of an EVEH.

Common approaches to increase the output power of EVEHs include increasing the number of turns in the coil and increasing the magnetic field gradient on the coil. The number of coil turns is limited by the size and technology of an EVEH, whereas the magnetic field gradient is often limited by the material and size of the magnet. One effective approach to enhance the output power of EVEHs is to increase the effective magnetic field gradient by using a Halbach array formed by several oppositely arranged magnets.^{7–9} In this way, the magnetic field can be concentrated within the small gaps between the magnets, which consequently enhances the harvesting efficiency of the coil.

For applications in practical industrial scenarios, one of the main bottlenecks encountered by EVEHs is the frequency matching issue. As most EVEHs are resonant structures, they only output maximum power when their resonant frequency matches the ambient vibrational frequency. Therefore, both band-broadening^{10–12} and frequency tuning techniques have been developed to match the resonant frequency between EVEHs and ambient vibrations. For EVEH devices based on Halbach arrays, the most common frequency tuning techniques are based on adjusting the mechanical parameters and on magnetic levitation. In the case of mechanical tuning, the spring length,^{13} proof mass,^{14,15} and nonlinear spring stiffness^{16} can be tuned to tune the resonant frequency. In the case of magnetic levitation,^{17–20} the resonant frequency of the EVEH is tuned by changing the repulsive force exerted on the magnet and thus the effective stiffness of the system.^{21–23} However, for these tuning techniques, there is still one major issue to be addressed, namely, that in spite of the tunable resonant frequency, most of the reported tunable EVEHs are still incapable of being tuned toward a specific target value in a one-off manner, and only by continuous frequency scanning can the target frequency be obtained. This is not practical in industrial applications. Therefore, we need a device that can directly tune to the target frequency.

In this work, we propose a magnetic levitation energy harvester (MLEH) with tunable resonant frequency based on a Halbach magnet array (hereinafter referred to as the harvester magnet). This device has several advantages:

Low resonant frequency. The original resonant frequency of the MLEH is 8.1 Hz, which makes it suitable for low-frequency vibrations (the vibration generated during walking and running is composed of frequencies ≤10 Hz, and the vibration generated on bridges is typically 8 Hz).

Wide tuning range. The frequency tuning range of the proposed MLEH device is 8.1–14.4 Hz (77.8% of the original resonant frequency of the MLEH).

Simple tuning process. Compared with most of the reported tunable devices, the frequency of the MLEH can be tuned to a specific target value via a compact system with scales. This compact system includes a tuning structure, where the rotation movement of a bolt is transformed to up/down movement of a slider along the

*Z*axis. The slider then changes the repulsive force between the tuning magnets and the harvester magnet array and induces a change in the suspension stiffness, ultimately changing the resonant frequency. Also, the proposed tuning structure will not change its position (elongation) when rotated, tuning the resonant frequency without increasing the device size.

The rest of this article is organized as follows: Sec. II introduces the system design of the tunable MLEH device, Sec. III describes the experimental procedures, including manufacturing and characterization, Sec. IV presents the characterization results and a discussion of the tunable MLEH device, and Sec. V concludes the work.

## II. SYSTEM DESIGN

### A. Concept of the system

The proposed MLEH and its exploded view are schematically illustrated in Figs. 1(a) and 1(b), respectively. The device is composed of a harvester magnet array levitated within the internal surface of a cylindrical solenoid coil. The levitation force is generated by two tuning magnets mounted on the bottom plate and slider, respectively. The slider is free to move along the *Z* axis under the pushing force provided by the nut when the bolt is rotated, as shown in Fig. 1(c). The advantage of this design is that the bolt will not change its position (elongation) when rotated, meaning that it will not increase the device size when tuning the resonant frequency. Instead, it transforms its rotational movement to the sliding motion of the nut and the slider. The movement of the slider changes the position of the top tuning magnet, which consequently varies the repulsive force between the tuning magnets and the harvester magnet array. The repulsive force variation then induces a change in the suspension stiffness of the harvester magnet array, and this changes the resonant frequency. The coil is fixed on the bottom plate within a high-reliability coil-holder. The external vibration induces relative movement between the harvester magnet and the coil, thereby generating an electrical potential within the coil.

The magnetic levitation system of the device consists mainly of a magnetic levitation structure formed by four cylindrical magnets (M1, M2, M3, and M4), the magnetization directions of which are shown in Fig. 1(d). Among these, M1 and M4 are small tuning magnets mounted on the slider and bottom plate of the package, and they are used to provide a magnetic repulsive force for suspending the harvester magnets M2 and M3. The harvester magnets M2 and M3 are bonded together with a polymer pole layer sandwiched in between, to form a high-efficiency harvester magnet array. Compared with MLEHs with a single magnet (or multiple magnets with the same magnetization direction), the harvester magnet array is capable of generating a much larger magnetic field gradient within the same volume, which is essential to increase the output power of the device. The harvester magnetic array is packaged in a cylindrical stainless steel tube, to provide a strong clamping force and to reduce the friction between the guiding tracks and the magnet during operation. In fact, the sliding motion of the magnet in this work is confined and guided by three 1 mm-diameter tungsten steel pins with smooth surfaces, which minimizes the friction force exerted on the magnet. In addition, the surface of the harvester magnet is covered with a Teflon film to further reduce friction. The entire device is packaged in an anodized aluminum housing for mechanical support and protection.

Many of the reported tunable energy harvesters have the capability of tuning their resonant frequency. However, most of the tuning process is “blind” in terms of the unknown tuning result, let alone the possibility of tuning the device toward a specific resonant frequency. The tuned resonant frequency must be obtained by complicated frequency scanning measurements. In this work, the targeted frequency-tuning capability is realized by a simple scale and indicator (the slider) system. The scales are laser-engraved on the outer surface of the aluminum case. The resonant frequency values are calibrated by the position of the slider on the scales. Specific resonant frequency values can be obtained by simply rotating the bolt and pushing the slider to a designated value.

Another advantage of proposed design is the compact tuning structure that transforms the rotary motion of the bolt into linear motion of the nut, which is inspired by a ball screw structure. The designed tuning structure also includes a set screw to keep the distance between the two tuning magnets constant during the vibration process. The detailed design of the slider is shown in Fig. 1(e). The head is designed with a dovetail groove and forms a linear slider with the side wall (diagonal position). The middle part includes three round holes for mounting the guide (the aperture is larger than the diameter of the guide). The tail and the nut form a sliding block. By rotation of the bolt, the slider can be moved up and down parallel to the bottom plate.

### B. System model

*m*

_{m}is the effective mass of the harvester magnet,

*c*is the damping, including mechanical and electromagnetic damping,

*z*is the relative displacement of the harvester magnet and the base,

*y*is the external vibration applied to the base, and

*F*

_{m}is the magnet force.

^{24}

^{,}

**is the magnetization vector,**

*M**V*is the magnet volume, and

**is the magnetic field, which is given by**

*B*^{25}

*μ*

_{0}is the vacuum permeability, and

**(**

*r**r*,

*z*) is the vector between the centers of the two magnets. Thus, Eq. (2) can be written as

*M*

_{m}is the magnetization for both the tuning magnet and the harvester magnet (they are the same type of magnet), and

*V*

_{f}and

*V*

_{m}are the volumes of the tuning and harvester magnets, respectively.

*z*= 0 and that the magnets in the MLEH are arranged coaxially, the total force exerted by the two tuning magnets on the harvester magnet can be expressed as

*d*is the distance between the centers of the tuning magnet and harvester magnet, and

*d*

_{top}=

*d*

_{bottom}=

*d*, ignoring the influence of gravity on the harvester magnet.

*z*= 0 and the higher-order terms neglected:

*k*

_{1}and

*k*

_{3}are the linear and nonlinear coefficients of the magnetic force, respectively. The equivalent stiffness

*k*is given by

*z*

_{0}is the equilibrium position,

*F*

_{m}(

*z*

_{0}) =

*mg*.

Figure 2 shows the resonant frequency as a function of the distance between the two tuning magnets (M1 and M4). The resonant frequency is simulated using finite element method (FEM) model analysis in COMSOL Multiphysics. Here, the resonant frequency changes from 10.9 Hz to 16.9 Hz when the distance changes from 40 mm to 18 mm.

*z*direction and ignoring the torsional tendency in the

*x*or

*y*directions, according to Faraday’s law, the induced voltage in the coil can be written as

*N*is the number of turns of the coil,

*ϕ*is the magnetic flux, and

*A*is the area of the coil. The magnetic flux density

*B*can be obtained from Eq. (3), and the calculation can be simplified by using a 2D axisymmetric FEM model in COMSOL Multiphysics.

Figure 3 shows the distribution of magnetic flux density for the MLEH, with the arrowed lines indicating the magnetic flux lines of the magnet with *z*-axis magnetization. The distribution is symmetrical along *z* = 0, and the maximum magnetic flux density is concentrated at the center of the pole layer. When the radial distance between the magnet’s symmetry axis and the inner side of the coil is 8.5 mm (the minimum design distance), the maximum magnetic flux density along the *z* axis is 0.21 T. This distribution of the harvester magnet represents the origin of the induction process of the MLEH under vibrational excitation.

*R*

_{MLEH}(the inductance of a commercial coil is much smaller than its resistance, and so the inductance of the coil is ignored in the model), the electrical system model can be simplified as the voltage source

*e*(

*t*), the internal resistor

*R*

_{MLEH}, and the external load resistor

*R*

_{load}connected in series. The instantaneous power

*P*

_{load}(

*t*) and voltage

*V*

_{load}(

*t*) in the load are given by

*P*

_{load}can then be expressed as

*V*

_{rms}is the root-mean-square (rms) voltage across the external resistor and

*e*

_{rms}is the open-circuit rms voltage produced by the MLEH.

## III. EXPERIMENTAL PROCEDURES

### A. Manufacturing process and results

The main components of the MLEH, including the device package, tuning structure, harvester magnet package, and slider are manufactured with a CNC machine. The package and slider are made of 6061-T6 aluminum alloy and surface-treated with an anti-scratch anodization process. A photograph of the assembled MLEH prototype is shown in Fig. 4(a). A D-size battery is placed alongside the MLEH device for size comparison. The component visible in the figure is the packaged device with tuning structure. Figure 4(b) shows the packaged harvester magnet, which is composed of two cylindrical magnets with opposite magnetization directions and a polymer pole, forming a sandwich structure (magnet–pole–magnet). The assembly process of the magnet is conducted via a home-made assembly apparatus to provide alignment accuracy under a large repulsive magnetic force. The distance between the top and bottom tuning magnets is varied by rotating the tuning structure. A cylindrical wound coil is fixed on the bottom plate within a high-reliability coil-holder, as shown in Fig. 4(c). The key design parameters of the proposed MLEH prototype are listed in Table I.

Parameter . | Design value . |
---|---|

Size of device | 30 × 30 × 46 mm^{3} |

Magnet grade | N35 |

Size of tuning magnet | Φ6 mm × 0.5 mm |

Size of polymer pole | Φ12 mm × 2 mm |

Size of harvester magnet | Φ15 mm × 14 mm |

Size of coil | Φ21.6 mm/17.6 mm × 13 mm |

Number of turns in coil | 630 |

Inductance of coil | 6 mH |

Parameter . | Design value . |
---|---|

Size of device | 30 × 30 × 46 mm^{3} |

Magnet grade | N35 |

Size of tuning magnet | Φ6 mm × 0.5 mm |

Size of polymer pole | Φ12 mm × 2 mm |

Size of harvester magnet | Φ15 mm × 14 mm |

Size of coil | Φ21.6 mm/17.6 mm × 13 mm |

Number of turns in coil | 630 |

Inductance of coil | 6 mH |

### B. Measurement setup

A schematic of the measurement setup for characterizing the fabricated MLEH device is shown in Fig. 5. The setup consists of a signal generator (AFG-2112), a power amplifier (SA-PA050 YE 5873A), a vibrational shaker (JZK-20), a data acquisition board (NI MCC USB-1608G), and a computer. The assembled MLEH is mounted on the shaker, and an accelerometer (ADXL335) is mounted between the MLEH and shaker. The exciting vibration is generated by the shaker under actuation by the electric signal from the signal generator and power amplifier. The output signals of the accelerometer and MLEH are measured simultaneously by the data acquisition board and transmitted to the computer. A LabVIEW measurement platform is implemented to process the measurement data. The built-in rms function is then applied to the collected data. A fourth-order Butterworth low-pass filter with a cutoff frequency of 150 Hz (the maximum resonant frequency of the MLEH is 14.4 Hz) is applied to filter high-frequency noise.

## IV. RESULTS AND DISCUSSION

### A. MLEH open-circuit output characteristics

To characterize the open-circuit output performance of the fabricated MLEH device, a sinusoidal acceleration of ±0.25 g is applied to the device in the frequency range of 5–25 Hz, and the open-circuit rms voltage of the MLEH device at different distances between the two tuning magnets is measured.

Figure 6 shows the open-circuit output rms voltage of the MLEH as a function of frequency at different distances between the two tuning magnets. As shown in Fig. 6, with decreasing distance between the tuning magnets, the magnetic force between the tuning and harvester magnets increases, i.e., there is an increase in magnetic stiffness. Thus, the resonant peak shifts to a higher frequency. Each of the curves in Fig. 6 shows the typical dynamical behavior of a resonant system, i.e., it reaches the maximum value at the resonant frequency. The rms voltage of the MLEH device is 237.9 mV at 8.4 Hz for a distance of 40 mm, 239.1 mV at 8.5 Hz for a distance of 36 mm, 242.8 mV at 9.2 Hz for a distance of 32 mm, 236.3 mV at 9.7 Hz for a distance of 28 mm, 224.9 mV at 11.4 Hz for a distance of 24 mm, and 167.0 mV at 14.0 Hz for a distance of 20 mm. In addition, the output rms voltage is also decreased due to the reduction in the amplitude of the harvester magnet oscillation, which is also a result of the increased magnetic stiffness.

However, when the distance between the two tuning magnets is from 40 mm to 32 mm, the output rms voltage does not decrease significantly. This phenomenon can be attributed to the limited coil height. Under the same acceleration, when the distance between the two tuning magnets is from 40 mm to 32 mm, the oscillation amplitude of the harvester magnet is higher than half of the coil height (6.5 mm; when the distance is 40 mm, the harvester magnet and the coil are in vertical center alignment), and the output voltage tends to saturate. Furthermore, owing to the tilt of the harvester magnet, the distortion of the harvester magnetic field induces a distortion in the output voltage waveform, which is consistent with the time-domain waveforms in Fig. 7.

In Fig. 6, it can be observed that the nonlinearity of the device increases as the distance between the tuning magnets decreases, which can be attributed to the nonlinearly increased magnetic force. Also, the rms voltage of the MLEH gradually increases before the resonant frequency and decreases sharply after the resonant frequency. This is the typical nonlinearity caused by the hardening effect, originating from the reduction in the distance between the tuning magnets. These phenomena might be further explained by Eqs. (5) and (6): as the distance *d* decreases, the repulsive force *F*_{m} is more strongly affected by the cubic term caused by nonlinearity and increases geometrically with an exponent of 3. Therefore, the nonlinearity of the MLEH continues to increase. It is beneficial for the energy harvester to have a broader bandwidth, which make it available for a wider range of applications. The frequency tuning range of the MLEH device is from 8.4 Hz to 14.0 Hz when the distance between the two tuning magnets is reduced from 40 mm to 20 mm. By optimizing the arrangement and combination of the coil and harvester magnet, the output power and bandwidth of the proposed MLEH device can be further improved.

The open-circuit output voltage of the fabricated MLEH device as a function of time at different distances between the two tuning magnets is shown in Fig. 7, where the output signals are measured at the resonant frequencies corresponding to the different distances between the magnets. As can be seen, the time-domain waveforms have different periods and amplitudes, owing to the different output performances of the MLEHs with different distances between the tuning magnets, and the reduction in the amplitude of the output voltage is similar to the frequency-domain curves in Fig. 6, i.e., when the distance between the two tuning magnets is from 40 mm to 32 mm, the peak values of the output voltage are approximately equal, and the output voltage then decreases with decreasing distance between the magnets. In addition, the output voltage waveforms in the time domain are distorted owing to the non-optimal design of the coil height, to magnet tilt (see the discussion of Fig. 6), and to friction between the harvester magnet and the guide. Therefore, we use the output rms voltage instead of the output peak-to-peak voltage to discuss the performance of the MLEH device, and the output rms voltage is also used subsequently.

### B. Acceleration measurement

Figure 8 shows the dependence of the MLEH output rms open-circuit voltage on the acceleration level for different distances between the two tuning magnets. All data are obtained at the resonant frequency of the MLEH at different distances (8.4 Hz for 40 mm, 8.5 Hz for 36 mm, 9.2 Hz for 32 mm, 9.7 Hz for 28 mm, 11.4 Hz for 24 mm, and 14.0 Hz for 20 mm), and the external excitation peak-to-peak acceleration increases from 0.1 g to 1 g in steps of 0.03 g. As shown in Fig. 8, the output rms voltage of the MLEH increases with increasing acceleration. All curves increase first rapidly and then slightly, with the peak-to-peak acceleration at the turning point being between 0.2 g and 0.3 g. The saturation of the output rms voltage increase is due to the limited motion of the harvester magnet that can be achieved within the two tuning magnets (when the peak-to-peak acceleration is greater than 0.3 g, the harvester magnet has collided with the tuning magnets). At an acceleration of 0.3 g, the maximum rms open-circuit voltage decreases as the distance between the two tuning magnets decreases. However, at an acceleration of 1 g, the maximum rms open-circuit voltage is 253.7 mV for 40 mm, 273.6 mV for 36 mm, 251.4 mV for 32 mm, 259.4 mV for 28 mm, 234.1 mV for 24 mm, and 165.8 mV for 20 mm. A possible explanation for this phenomenon is that the harvester magnet cannot be kept completely horizontal when it is suspended in the vibration channel formed by the guide, and the friction between the harvester magnet and the guide reduces the output voltage owing to the tilt of the harvester magnet. In addition, as a consequence of errors in device processing and the asymmetry of the magnet performance, the harvester magnet has various tilting situations, which lead to different friction conditions under the same acceleration.

Furthermore, the designed MLEH device is suitable for matching to low-frequency and low-acceleration ambient vibrations. In the remaining tests, an acceleration of ±0.15 g is used, because the output rms voltage can then be maximized without collision occurring.

### C. Impedance matching

The design goal of the MLEH is for it to act as a power source and supply power to an external load. Therefore, it is necessary to investigate the optimal output characteristics of the MLEH device under different electrical load conditions. In this study, external resistors between 1 Ω and 1000 Ω are connected to the output of the MLEH, and the output rms voltage and power across the matching resistor are measured.

Under an acceleration of ±0.15 g and a frequency of 9.3 Hz, the rms voltage and power of the MLEH as functions of load resistance are shown in Fig. 9. The MLEH device used in this test has a distance between the two tuning magnets of 28 mm (the corresponding resonant frequency is 9.3 Hz), and an internal resistance of 27.7 Ω.

As can be seen in Fig. 9, when the external load resistance is smaller than the optimal load resistance, the output power of the MLEH increases rapidly. Then, with increasing external load resistance, the output power of the MLEH decreases gradually. The maximum power of 462.1 μW is obtained under the optimal load resistance of 27.3 Ω, which is slightly smaller than the coil resistance. This slight difference between the optimal load resistance and the internal resistance originates from measurement inaccuracy as well as the neglect of the resistance of the external wires. In addition, the output rms voltage increases rapidly in the low-resistance range, and then gradually approaches saturation in the high-resistance range, which means that the voltage increases at a lower rate in the high-resistance range than in the low-resistance range. When the external load resistance approaches infinity, the closed circuit can be regarded as an open circuit, and the output rms voltage of the MLEH will be equal to the open-circuit output.

*V*and external vibrational excitation

*A*have a greater impact on device output performance, to accurately describe the latter, the normalized power density (NPD, μW cm

^{−3}g

^{−2}) is given by

The calculated NPD of the MLEH device is 496.08 μW cm^{−3} g^{−2} (for a power of 462.1 μW, a volume of 41.4 cm^{3}, and an acceleration of ±0.15 g). Table II compares the NPD of the proposed MLEH with those of other recently reported energy harvester devices. The resonant frequencies of these energy harvesters range from 8 Hz to 11 Hz. It is found that the proposed MLEH device performs well in comparison with other energy harvesters based on magnetic levitation. The devices reported in Refs. 17 and 22 have higher output power than the proposed device. However, the device in Ref. 17 is larger in size, with an effective functional volume of 48.5 cm^{3}. Furthermore, the device in Ref. 22 has a larger percentage of effective functional volume (100%), compared with 22.2% (9.2 cm^{3}) for the device proposed in this work. For future optimization of coils and magnets, the output power of the proposed MLEH device could be further enhanced.

Reference . | Frequency (Hz) . | Power (μW) . | Acceleration (g) . | Volume (cm^{3})
. | NPD (μW cm^{−3} g^{−2})
. |
---|---|---|---|---|---|

THE^{17} | 9 | 16 216 | 0.4 | 202.7 | 500 |

EEH-c^{17} | 11 | 69 438 | 0.4 | 220.3 | 1970 |

Reference 18 | 8 | 6900 | 1 | 52.3 | 132 |

Reference 21 | 8.2 | 101 | 0.2 | 9.9 | 255 |

Reference 22 | 8 | 6100 | 0.3 | 22.1 | 3067 |

This work | 9.3 | 462.1 | 0.15 | 41.4 | 496 |

Reference . | Frequency (Hz) . | Power (μW) . | Acceleration (g) . | Volume (cm^{3})
. | NPD (μW cm^{−3} g^{−2})
. |
---|---|---|---|---|---|

THE^{17} | 9 | 16 216 | 0.4 | 202.7 | 500 |

EEH-c^{17} | 11 | 69 438 | 0.4 | 220.3 | 1970 |

Reference 18 | 8 | 6900 | 1 | 52.3 | 132 |

Reference 21 | 8.2 | 101 | 0.2 | 9.9 | 255 |

Reference 22 | 8 | 6100 | 0.3 | 22.1 | 3067 |

This work | 9.3 | 462.1 | 0.15 | 41.4 | 496 |

### D. Frequency tuning performance

Before tuning the resonant frequency of the MLEH, the relationship between the resonant frequency and the distance between the two tuning magnets is calibrated. At a sinusoidal acceleration of ±0.15 g, the resonant frequency of the MLEH as a function of this distance is shown in Fig. 10 (the inset is a partial enlargement). The maximum frequency tuning range of the proposed MLEH is 6.3 Hz (8.1–14.4 Hz), which is 77.8% of the natural resonant frequency of the MLEH (8.1 Hz). Each of the measurement points in Fig. 10 is the average value of ten measurements: each measurement was repeated ten times, with a cycle of adjusting the distance between the two tuning magnets from 18 mm to 40 mm. As shown in Fig. 10, the curve of resonant frequency vs distance is nonlinear, and it shows a similar trend to that predicted in Fig. 2. However, the measured resonant frequencies are smaller than the simulation results in Fig. 2. This deviation may arise from the magnetic field of the magnet. The curve shifts up as the magnetic field increases.^{26} Once the resonant frequency–distance relationship has been obtained, we can try to tune the resonant frequency to a specific target value. The experimental procedure is as follows:

Step 1: select seven target frequencies from 8 Hz to 14 Hz, with a step length of 2 Hz.

Step 2: obtain the distance value by interpolating the data in Fig. 10.

Step 3: according to the scale line, rotate the tuning structure to tune the distance to each target value, and measure the resonant frequency.

Step 4: repeat steps 1–3 ten times.

The targeted frequency tuning measurement results are shown in Fig. 11 (the inset is a partial enlargement). Each data point represents the average value of ten measurements and the error bars represent the standard deviation of these ten measurements. It should be noted that to avoid the potential influence of tuning tricks based on understanding of the device structure, the targeted tuning experiments were carried out by personnel inexperienced in the tuning process of the MLEH device. At the frequencies of 9 Hz and 10 Hz, the maximum error is −0.09 Hz, and the minimum error is 0 Hz at frequencies of 8 Hz, 13 Hz, and 14 Hz. The linear fitting function is *y* = 0.968*x* + 0.318 (where *x* and *y* are the target frequency and tuned frequency, respectively). This reveals good controllability and repeatability of the tuning process.

## V. CONCLUSIONS

In this work, an electromagnetic vibrational energy harvester with targeted frequency-tuning based on magnetic levitation has been designed and fabricated. The resonant frequency of the MLEH is tuned by changing the distance between two tuning magnets via rotation of the tuning structure. At a sinusoidal acceleration of ±0.15 g, the output power is 462.1 μW, the calculated NPD is 496 μW cm^{−3} g^{−2} (9.7 Hz), and the maximum tuning frequency range is 6.3 Hz (8.1–14.4 Hz), which is 77.8% of the natural resonant frequency of the MLEH (8.1 Hz). The scenarios where a frequency tuning range of 8.1–14.4 Hz is appropriate are typically those involving heavy machinery that generates vibration with low frequency (≤20 Hz) and high amplitude (≥80 mm), such as compressors or vibrating coal sifters. In addition, devices within this frequency range may also be used to harvest kinetic energy of human or animal motion.

This work has focused on developing a proof-of-concept demonstrator device with the targeted frequency tuning capability. Therefore, the device has been optimized in such a way that all the tuning components can be fitted into a rather confined space, with reasonable simplicity of tuning. In the future, we will further optimize the parameters that affect output voltage, considering, for example, new magnet arrangements, coil structure and position, and spring force, with the aim of realizing precise tunability and high output power.

## ACKNOWLEDGMENTS

This work is supported by the Key Research and Development Program of Shaanxi (Program Nos. 2022GXLH-01-20 and 2024GX-YBXM-193). The authors would like to thank Weitao Dou, Bingjian Lu, and Haijian Dong for their assistance in the characterization procedures of the harvester devices.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

## DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

## REFERENCES

**Chengbo Hu** received his Master’s degree in Electrical Engineering from Xi’an Jiaotong University, China. Since 2011, he has worked as an engineer and senior engineer at the State Grid Jiangsu Electric Power Co., Ltd., Electric Power Research Institute, Nanjing, China. He is currently pursuing his Ph.D. degree at the Southeast University, China. His main research interests include the Internet of Things and artificial intelligence with applications to power equipment. He is a member of the Intelligent Sensing Committee of the Chinese Society of Electrical Engineering.

**Xinyi Wang** received her B.E. degree in Electrical Engineering and its Automation from Xidian University, Xi’an, China, in 2017. She received her Master’s degree in Electrical Engineering from Xi’an Jiaotong University, Xi’an, in 2020. She is currently pursuing her Ph.D. degree at the School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China. Her research interests include the design, fabrication, and application of energy harvesters.

**Zhifei Wang** received his Bachelor’s degree in Electrical Engineering and Automation from the China University of Mining and Technology, Beijing, China, in 2022. He is currently pursuing his Ph.D. degree in the School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China. His research interests include the design, fabrication, and application of energy harvesters.

**Shudong Wang** received the joint Ph.D. degree in Instrument Science and Technology from Xi’an Jiaotong University, Xi’an, China, and the City University of Hong Kong, Hong Kong SAR. He is currently an Assistant Professor in the School of Electrical Engineering, Xi’an Jiaotong University. His research interests include the design and integration of microelectromechanical sensors.

**Yuanyuan Liu** received her Bachelor’s degree from the School of Resources at Chang’an Univeristy and her Master’s degree in Project Management from Xi’an Jiaotong University. She is currently an engineer at the Xi’an Space Radio Technology Research Institute. Her main research fields include optimization of manufacture and research processes.

**Yunjia Li** (Senior Member, IEEE) is a professor in the School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China. He received his Ph.D. degree from the Group of Micro and Nanosystems, ETH Zürich, Switzerland, in 2014. From 2016 to 2021, he was an Associate Professor in the School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China. His research interests include capacitive/inductive sensors, actuators, and energy harvesters, on both the device and system levels. He is the Chair of the Technical Committee on MEMS and Nanotechnologies of the IEEE Industrial Electronics Society (IES), a representative of IES in the IEEE Nanotechnology Council AdCom, a Steering Committee member of the *IEEE/ASME Journal of MEMS*, and Associate Editor of the *IEEE Transactions on Industrial Electronics*. He has served as a technical committee member, track chair, and session chair at multiple IES flagship conferences, including IECON, ICIT, and ISIE.