Optimal analysis on coil and rotor in a diamagnetically airflow energy harvester

Abstract

In this paper, the proposed diamagnetic levitation structure was studied to explore its potential in energy harvesting. It is proved that the floating magnet rotor can be levitated stably under the joint action of two highly oriented pyrolytic graphite (HOPG) sheets and the lifting magnet. Simulation calculation was carried out to analyze the influence of different coil radius and wire diameter on peak voltage and average power in scheme A or scheme B, so as to obtain appropriate layout and wire diameter for the coils which was built the experimental platform. Subsequently, the center hole, notch radius and thickness of the floating rotor are analyzed by experiment. And the influence of different parameters on rotation speed of the rotor and peak output voltage of coils is obtained. Through experimental results, it is found that the notch radius of the floating rotor has the greatest influence on the rotation speed of the rotor. Based on the experiment, a new-type rotor was designed, with an outer shell to reduce the notch radius. Compared with the original floating rotor, there was 49.73% increase in voltage, 55.70% increase in rotation speed and 124.50% increase in power according to the experimental results. Test was performed with the optimization, the LED array of Zhengzhou University logo, which was composed of 60 LED lights, was lighting up. According to the oscilloscope measurement, the diamagnetic levitation energy harvester has an output voltage up to 1.294 V and average power of 60.67 mW under gas flow rate of 3000 sccm and nozzle exit velocity of 6.173 m/s. Obviously, the new-type rotor proposed in this paper could significantly increase the energy conversion efficiency, and make the future application of airflow energy harvester a step further.

Keywords

New-type rotor diamagnetic levitation structure gas flow

1. Introduction

In recent years, energy harvesting has attracted more and more research interest. It could become a favorable alternative to traditional fossil energy sources with further research. Energy harvesting devices have the advantages of being self-powered [1,2], long lasting and portable by converting the energy of light [3], airflow [4] and vibration [5] into electricity in daily life. There have been numerous and complex energy collectors that can be applied to a wide variety of life scenarios as more and more researchers have focused on the subject of energy harvesting. Energy harvester based on diamagnetic levitation [6–8] can realize passive and static stable levitation at room temperature without external energy input. The airflow energy is collected only affected by air resistance and electromagnetic damping force [9] generated by the coil under this diamagnetic stable levitation structure. Gao et al. [10] designed a novel bistable vibration energy harvester using the diamagnetic levitation mechanism, which can work effectively at extremely low frequency ( <5 Hz) and has a peak power of 333.7 μW. Wang et al. [11] proposed a tunable electromagnetic energy harvester, which can collect vibration energy during human movement and a maximum average output power of 10.66 mW was obtained with a total weight of 218.7 g from the swing motion of leg at speed of 8 km/h. Palagummi et al. [12] proposed a new type of bi-stable system based on the passive horizontal diamagnetic levitation mechanism. In the case of 1.5-mm input amplitude from 5 Hz to 8 Hz, the floating magnet underwent chaotic and interwell [13] motions, which enabled it to enhance frequency [14] bandwidth [15] operation over the monostable diamagnetic levitation systems previously [16].

In this paper, the force analysis of floating magnet is mathematically described by formula [17]. The levitation state of the diamagnetic stable levitation structure [18] is analyzed by finite element analysis (FEA) simulation. And different levitation states of the floating magnet in the different levitation distance are analyzed. The influence of coil position and wire diameter on the output voltage and power is also studied through simulation. According to the of simulation results, the experimental platform was built. Rotor rotation speed and peak voltage obtained by the coil are studied by doing a control experiment on different center hole, notch radius and thickness of floating rotor under different airflow conditions. According to the above experimental results, a new-type rotor is designed and manufactured which is a floating rotor overmatched with a shell. Experimental results show that the new-type rotor achieves higher rotation speed, peak voltage and average power compared with the original floating rotor.

2. Force analysis

As shown in Fig. 1(a), the structure of the diamagnetic stable levitation is composed of a lifting magnet, an upper HOPG sheet [18], a lower HOPG sheet, and a floating magnet. We can see from Fig. 1(b) that the floating magnet is subjected to the magnetic attraction force of the lifting magnet, its own gravity, and the diamagnetic force from the upper and lower HOPG sheet. According to Earnshaw’s theorem [19]. It can’t generate three-dimensional potential energy required for stable levitation in free space by combination of magnetostatic and gravitational force. Since the magnetic susceptibility of diamagnetic substance is negative, a local minimum value of magnetic field can be formed and exist in free space under the repulsive forece of external magnetic field. The floating magnet is stably levitated between the two HOPG sheets under the action of the four forces by introducing the HOPG.

Fig. 1.

Schematic diagram of the diamagnetic stable levitation.

In the magnetic field formed by the lifting magnet, the potential energy of the suspended magnet can be expressed as follow: $\begin{eqnarray}\displaystyle U=-\vec{M}\cdot \vec{B}+mgz=-MB+mgz. & & \displaystyle\end{eqnarray}$ (1)

Where M is the magnetic dipole moment of the floating magnet and B is the magnetic flux density of the lifting magnet, obviously, m is the mass of the floating magnet, g is the acceleration of gravity, and z is the distance between the lower surface of the floating magnet and the ground surface.

We can introduce the term C _z z ² and C _r r ² which represent the axial and radial diamagnetic influence, and Eq. (1) could be overwritten as [20]: $\begin{eqnarray}\displaystyle U=-M\left[B_{0}+\left\{B^{\prime }-\frac{mg}{M}\right\}z+\frac{1}{2}B^{\prime \prime }z^{2}+\frac{1}{4}\left\{\frac{B^{\prime 2}}{2B_{0}}-B^{\prime \prime }\right\}r^{2}+\ldots \right]+C_{z}z^{2}+C_{r}r^{2}. & & \displaystyle\end{eqnarray}$ (2)

When the floating magnet is in levitation equilibrium, the expression in the first brace of (2) must equal zero. That is, the magnetic force of the floating magnet is equal to its own gravity in the non-uniform magnetic field of the lifting magnet. Furthermore, according to (2), the conditions for stable suspension of the floating magnet in vertical and horizontal directions can be deduced: $\begin{eqnarray}\displaystyle K_{v}\text{} & \equiv \text{} & \displaystyle C_{z}-\frac{1}{2}MB^{\prime \prime }>0∼(\text{vertical stability})\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle K_{h}\text{} & \equiv \text{} & \displaystyle C_{r}+\frac{1}{4}M\left\{B^{\prime \prime }-\frac{m^{2}g^{2}}{2M^{2}B_{0}}\right\}>0∼(\text{horizontal stability}).\end{eqnarray}$ (4)

In Fig. 1(b), it could be clearly seen that the resultant force of the floating magnet in z-axis direction can be expressed as: $\begin{eqnarray}\displaystyle F=F_{\text{Lift}}+F_{\text{Lower}}-G_{\text{Float}}-F_{\text{Upper}}. & & \displaystyle\end{eqnarray}$ (5)

3. Simulation analysis

3.1. Analysis of optimal levitation state

As shown in Fig. 2, according to Table 1, FEA models were established in COMSOL Multiphysics 5.6, so as to calculate the attractive force of the lifting magnet F _Lift, the repulsive forces F _Lower and F _Upper by the lower HOPG sheet and the upper HOPG sheet respectively. In ZOY plane, the contour bar means that the distribution of magnetic flux inside the lifting magnet, the floating magnet. And the diamagnetism generated in the diamagnetism HOPG under the action of the floating magnet can be observed.

Fig. 2.

FEA model for force calculation.

Table 1

Structure parameters of the diamagnetically stabilized Levitation

Parameter	Value/material
Lifting magnet and floating magnet	NdFeB-52
Residual flux density of lifting and floating magnet	1.45 (T)
Density of lifting magnet and floating magnet	7. 65 × 10⁻³ (g∕cm³)
Lifting magnet	∅12. 5 × 10 (mm)
Radius of floating magnet	9 (mm)
Radius of floating center hole	0 (mm)
Thickness of floating magnet	1.5 (mm)
Notch radius of floating magnet	2.5 (mm)
Diamagnetic sheet	HOPG
Size of diamagnetic sheet	∅15 × 5 (mm)
Magnetic susceptibility 𝜒 of diamagnetic sheet	[8,8,45] ×10⁻⁵

Fig. 3.

Influence of displacement on resultant force and potential energy at different levitation distances.

In the analysis of this work, the plane of symmetry between two HOPG sheets is chosen as zero-plane, and the direction of the magnetic attraction force of the lifting magnet F _Lift is defined as the positive direction. When the floating magnet is levitated steadily between two HOPG sheets, the resultant force F in (5) is equal to zero. From the results shown in Fig. 3(a), there is only one zero-point at the distance between two HOPG sheets L _HOPG is greater than 1.9 mm and less than or equal to 3.5 mm. The number of zero-points increases to three when L _HOPG is from 3.9 mm to 5.5 mm. These zero-points only mean that the floating magnet can be in equilibrium at these positions, but it does not imply that the floating magnet can be levitated steadily. A necessary condition for a magnet to achieve stable levitation is that the potential energy of the floating magnet is the lowest point. Namely, the floating magnet is in the deepest point of the potential energy trap [21 ]. According to the principle of minimum potential energy, a system is in a stable state when it has minimum potential energy. Thus, the floating magnet will be in stable levitation [22 ] as the floating magnet in the minimium potential position. Figure 3(b) shows that the floating magnet has minimum potential energy point as the space between two HOPG sheets is between 1.9 mm and 3.5 mm. And there are two minimum potential energy points as the notch between the two HOPG sheets is between 3.9 mm and 5.5 mm. When the potential energy of the floating magnet has only one minimum point, it is suspended in the zero-plane, which could be called symmetric monostable levitation state. At this time, the floating magnet can remain stable in the z-axis direction. Furthermore, the floating magnet can be levitated stably on both sides of the zero plane as the potential energy of the floating magnet has two minimum points. In this case, the two minimum potential energy points projected on the displacement axis are not symmetric about the zero displacement point, this levitation state is called asymmetric bistable levitation state.

3.2. Analysis of the coils layout

The rotation speed of the floating rotor, the structure parameters of airflow energy harvester and arrangement form of coils are the key factors affecting the induced electromotive force generated by the coils. When structure parameters of coils are constant, the induced electromotive force is linear with the speed of floating rotor. Therefore, it is only need to study the influence of coils layout on the induced electromotive force at a certain speed.

Fig. 4.

Analysis of coil scheme by FEA model.

The analysis simulation was conducted by COMSOL Multiphysics 5.6. Figure 4(a) is the FEA model of floating rotor. The single-layer coil is wound by a wire with a diameter 0.55 mm. The outer diameter of the coil is 10 mm, and its number of turns is 93. The parameters of floating magnet rotor are shown in Table 1.

As shown in Fig. 4(b) and (c), there are two coils distribution schemes. In scheme A, the three coils are concentrically arranged with the three notches around the rotor. In scheme B, the three coils are tangent to each other, and their centers coincide with the center of the floating rotor.

Fig. 5.

Influence of coil radius and diameter on peak voltage, average power or coil resistance.

Figure 5(a), (b) and (c) are the calculated voltage and average power for schemes A and B. For scheme A, when the outer diameter of the coil is smaller than 4.5 mm, the average power and peak voltage generated change linearly with its outer diameter. The average power will reach the maximum value 0.96 mW as the radius of the coil is 4.5 mm. While the radius of the coil is larger than 4.5 mm, the average power decreases slowly with the increase of the radius. For scheme B, it could be seen that when radius of coil is 6.5 mm, the average power reaches its maximum value 0.85 mW, which is 11% lower than that of scheme A. While the radius of coil is larger than a threshold value, the average power collected by coil decreases slowly with the increase of coil radius no matter in both scheme A or scheme B. It can be seen from Fig. 5(c) that the average power of the coil is positively correlated with the wire diameter of the coil, and the peak voltage decreases with the increase of the wire diameter of the coil. Obviously, the variation of the wire diameter changes the resistance of coil and further affects the average power and peak voltage.

Scheme B is more compact than scheme A. From Fig. 5(a) and (b), it can be found that the average power of scheme A and scheme B almost coincide, and the peak voltage of scheme B is slightly lower when the radius of the coil is 6 mm. It can be seen from Fig. 5(c) that smaller wire diameter of coils leads to lower average power, bigger wire diameter will lead to lower peak voltage, which will affect the collected energy. In the experiment of the Section 4, we choose the coil of scheme B with outer radius of 6 mm and wire diameter of 0.1 mm.

4. Experiment

4.1. Experimental analysis

As we can see in Fig. 6, in the experiment nitrogen source is used as airflow, and two mass flow controllers (AITOLY MFC300) are used to control the airflow in each nozzle. The oscilloscope (Tektronix TDS2012C) is used to measure the pulse signal of the output voltage of the energy harvester. It can be seen in Fig. 7 that the output waveform of airflow energy harvester was a sinusoidal signal whose frequency is triple of the rotation frequency of the magnet rotor.

Fig. 6.

Experimental platform of diamagnetic levitation airflow energy harvester.

Fig. 7.

Peak waveform of airflow energy harvester captured by an oscilloscope.

Fig. 8.

Influence of the diameter of floating rotor center hole on peak voltage and rotation speed at the same flowrate.

Table 2

Coil parameters.

Parameter	Value/material
Coil	Copper
Wire diameter of coil	0.1 (mm)
Thickness of coil	0.1 (mm)
Radius of coil	6 (mm)
Radius of coil center hole	1 (mm)
Number of coils	6
Number of turns of coil	93
Total resistance of coil	13.8 Ω

In order to study the influence of floating rotor geometry on output performance, Tables 1 and 2 shows the structural parameters of the energy harvester used in the experimental. During the experiment, only one parameter (center hole, notch radius or thickness) of the floating rotor was changed, and the other parameters remained unchanged.

As shown in Fig. 8(a) and (b), rotors of different center hole have little effect on the changes of peak voltage and rotation speed while the gas flow is lower than 1900 sccm, indicating that when the gas flow rate is 0–1900 sccm, the rotations of different center hole rotors have consistency. When the gas flow is greater than 1900 sccm, the speed and peak voltage of rotor with 4-mm center hole are greatly improved compared compared with 0 mm and 2 mm. When the gas flow is greater than 2600 sccm, the speed and peak voltage of the rotor with 2 mm center hole are greatly improved compared with 0 mm rotor. When gas flow reaches 3000 sccm, the rotor with 2 mm and 4 mm center hole increase rotation speed by 6.12%, 13.06% and peak voltage by 7.35%, 22.17% compared to 0 mm. Obviously, it can be seen from the figure that the rotor with larger center hole has a smaller gas flow threshold, the rotor rotation speed is greatly improved compared with the rotor with smaller center hole as the threshold is exceeded.

Fig. 9.

Influence of the radius of floating rotor notch on peak voltage and rotation speed at the same flowrate.

In Fig. 9(a), as the gas flow is 0–600 sccm, the peak voltage generated by the rotor with 1.5-mm notch radius is the largest, while when the gas flow is greater than 600 sccm, the peak voltage generated by the one with 2.5-mm notch radius is the best. Floating rotor with a notch radius of 4.5 mm performed the worst in the 0–2000 sccm gas flow range. The floating rotor with notch radius of 1.5 mm, 2.5 mm and 3.5 mm are improved by 3.35%, 20.32% and 12.64% compared with 4 mm at the gas flow reaches 2000 sccm. From Fig. 9(b), compared to the floating rotor with 4-mm notch radius, the rotation speed are increased by 585.50%, 217.28% and 56.02% for 1.5 mm, 2.5 mm and 3.5 mm notch radius respectively under gas flowrate of 2000 sccm. Basically, there may be two reasons. Firstly, the velocity of the airflow ejected from the nozzle is inversely proportional to the ejecting distance. When the notch radius of the floating rotor decreases, the distance between the notch surface and the nozzle outlet shortens, the instantaneous velocity exerted on the notch surface by the airflow will increase. Accordingly, the rotation speed of the floating rotor rises with the instantaneous velocity of gas flow. Secondly, notch surface curvature becomes bigger as the notch radius decreases. So the angle between the normal direction of the striking position on the notch surface and the flow direction is reduced. Consequently, the tangential component force exerted on the rotor by the gas flow rises, which results in the enhance of the rotor rotation speed.

Fig. 10.

Influence of the thickness of floating rotor on peak voltage and rotation speed at the same flowrate.

From Fig. 10(a) and (b), the magnet rotor with 1.5-mm thickness has the largest peak voltage and speed, and the 3.5-mm thick rotor has the worst performance as the gas flow is 0–2000 sccm. When the thickness of floating rotor is 1.5 mm and 2.5 mm, the peak voltage is 14.99% and 8.30% higher than that of 3.5 mm, and the speed is 76.05% and 28.43% higher. To sum up, the rotation speed and peak voltage of the floating rotor are the highest when the diameter of the center hole is 4 mm, the notch radius is 2.5 mm and the thickness is 1.5 mm.

By observing the experimental results in Figs 8, 10(a) and (b), it could be found that the speed of the floating rotor is consistent with the peak voltage obtained by the harvester. Form Fig. 9(a) and (b) we can know that the notch radius of the floating rotor has the greatest influence on the rotation speed of the floating rotor. We consider that different notch radius of the floating rotor corresponds to different energy conversion factors, which means the energy generated by each rotation of the rotor. Floating rotor with small notch radius of can produce larger rotation speed, while its energy conversion factor is relatively smaller. It could be inferred that if we can design and manufacture a new-type rotor which include a rotor with a larger energy transfer factor and a smaller notch shell, it may be possible to increase the rotor rotation speed and thus increase the energy collected.

4.2. Experimental verification

According to the experimental analysis in Section 4.1, the design criteria of the new-type rotor were determined. The new-type rotor is composed of a floating rotor and an outer shell. The shell is made of photosensitive resin, a non-magnetic material, modeled by SolidWorks software and printed by a 3D printer. The floating rotor and the shell are assembled by transition fit. The specific parameters of the new-type rotor is listed in Table 3. And its physical structure is shown in Fig. 11. To carry out comparative study, the floating rotor is used as the control group, at the same time the new-type rotor is regarded as the experimental group.

Fig. 11.

New-type rotor with outer shell.

Fig. 12.

Comparison of new-type rotor and floating rotor.

Table 3

New-type rotor parameters

Parameter	Value/material
Diameter of new-type rotor	18 (mm)
Diameter of new-type rotor center hole	4 (mm)
Notch radius of new-type rotor	2.5 (mm)
Thickness of new-type rotor	1.5 (mm)
Material of shell	Photosensitive resin
Diameter of shell	19.6 (mm)
Notch radius of shell	1.5 (mm)
Thickness of shell	1.5 (mm)

Fig. 13.

The logo of Zhengzhou University lamps was light up which is made up of 60 LEDS.

The voltage and rotation speed of the new-type rotor and the floating magnet rotor were processed and obtained in Fig. 12(a) and (b). The new-type rotor finally produced rotation speed of 22140 rpm, 1.294 V peak voltage, and 60.67 mW peak power at 3000 sccm. In Fig. 12(c), the rotation speed and voltage fitting of the two rotors overlapped linearly, which proved that the increase of output voltage was entirely attributed to the hybrid new-type rotor, rather than the change of experimental conditions. Compared with the floating rotor, the peak voltage, rotation speed and average power of the new-type rotor are 49.73%, 55.70% and 124.20% higher than that of the floating rotor respectively, indicating that adding the outer shell to the magnet rotor can greatly improve the energy conversion efficiency.

Altium Designer 17 software was used to design the schematic diagram of PCB. Open the nitrogen gas valve to regulate its output pressure at 0.8 MPa. The laptop computer is used to control the two mass flow controllers. The flow rate increases slowly from 1000 sccm to 3000 sccm. When the floating rotor is rotating stably, we can obtain the experimental photograph of the lamp array of Zhengzhou University logo composed of 60 LED lights lit by the output voltage from the coils through the twelvefold voltage rectifier circuit in Fig. 13.

5. Conclusions

In this paper, the levitation characteristics of diamagnetic stable levitation are studied. Two levitation states of the floating magnet in the structure are obtained, and suitable levitation state for the airflow energy harvester is analyzed. The appropriate coil layout and the influence of coil diameter on power and voltage are studied through simulation. The effects of the diameter of the center hole, the notch radius and the thickness of the floating magnet on the rotor rotation speed and the peak voltage were studied experimentally. According to the research results, the optimal parameters of the floating rotor were selected as the control group, and a new-type rotor with outer shell is chosen as the experimental group. Compared with the control group, the peak voltage, rotation speed and average power of the new-type rotor in the experimental group were improved by 49.73%, 55.70% and 124.20% respectively. The experimental results strongly show that the outer shell around floating rotor has a great improvement on energy conversion efficiency. In future research work, the number of lifting magnets in the airflow energy harvester and the number of notches in the floating rotor can be studied in detail, so as to improve the performance, reduce the size of the energy harvester and make it more practical in daily life.

Footnotes

Acknowledgements

This study is supported by the National Natural Science Foundation of China under grant no. U1904169.

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