2021 Volume 62 Issue 12 Pages 1798-1801
The performance of vibration power generation using the inverse magnetostrictive effect increases with increasing its device size. In this study, grain-oriented electrical steel that can be largely produced was investigated as a core material, using a U-shaped unimorph device at a laboratory scale. The device using a grain-oriented electrical steel core (16 mm long with a 1.4 mm2 cross-section) with the rolling direction (RD) along the stress direction exhibited the effective open-circuit voltage of 0.89 V under an optimum bias magnetic field, when the free-end of the device was vibrated with a maximum amplitude of 2.0 mm at a mechanical resonance frequency of 108 Hz. In addition, an average output power of 300 µW was obtained by adjusting the load resistance. The above-mentioned properties of the RD unimorph core device were superior to those of the transverse direction (TD) unimorph core device, because the magnetic flux density change in the RD core was approximately 0.65 T, which was larger than that in the TD core. Therefore, grain-oriented electrical steel with the RD direction is a useful core material for developing large-sized devices with high performance.
Vibration power generation using the inverse magnetostrictive effect has been actively investigated, as this technology can generate electrical power from various ambient vibration, such as production machinery, human movement, ocean currents, etc.1–3) In this type of device, a coil is wound around the magnetic core and a bias magnetic field is applied. The periodic stresses caused by vibration induce magnetic flux density changes in the magnetic core due to the inverse magnetostrictive effect (the Villari effect). The electrical power is obtained by the magnetic flux changes in the coil in accordance with Faraday’s law. High-performance devices are desirable for expanding the fields of application.
Fe–Ga alloy single crystals have attracted significant attention as core materials for vibration power generation because of the large magnetic flux density change ΔB due to the inverse magnetostrictive effect.4–7) The magnetic domain observation of Fe–Ga alloy single crystals has been actively performed to understand the mechanism of large ΔB.8–11) A U-shaped unimorph device using Fe–Ga alloy single crystals is promising, owing to its simple fabrication, robustness, and high sensitivity.5–7) For example, it has been reported that the device using an Fe–Ga alloy single crystal core with a length of 16 mm, width of 4 mm and thickness of 0.5 mm (16 mm × 4 mm × 0.5 mm) exhibits an open-circuit voltage of 4 V and an average output power of 2.0 mW at a vibration frequency f of 88.7 Hz and an acceleration a of 6.0 m/s2 because of large ΔB of approximately 1.2 T.5) The operation of the wireless sensor has also been successfully demonstrated by the device.5) It should be noted that the vibration power generation performance increases with increasing devise size.7,12) A larger device with an Fe–Ga alloy single crystal core with dimensions of 125 mm × 40 mm × 4 mm has already been reported to exhibit an average output power of 0.22 W at a = 1.96 m/s2 and f = 18.5 Hz.6) Thus, the development of large-sized devices is effective for achieving high performance. However, further upsizing of Fe–Ga alloys single crystal cores is costly and challenging in the present crystal growth technology. To develop larger devices with higher performance, inexpensive core materials that can be largely produced are necessary.
Recently, it has been reported that a parallel cantilever device using an Fe–3 mass% Si alloy single crystal core with dimensions of 4.01 mm × 44.9 mm × 0.229 mm exhibits ΔB = 0.49 T.13) It is well known that polycrystalline Fe–Si alloys can be designed to grow grains with (110) [001] easy-axes parallel to the rolling direction, referred to as grain-oriented electrical steel.14,15) Grain-oriented electrical steel can be largely produced as a rolled sheet. In addition, it has been reported that the magnetization curve of grain-oriented electrical steel is sensitively changed by the application of stress.16–19) For example, it is expected from the changing magnetization curve that a ΔB value of approximately 1.4 T is obtained by applying 40 MPa compressive stress.19) Thus, grain-oriented electrical steel is an interesting core material for developing large-seized devices. However, the vibration power generation properties of the U-shaped unimorph device using grain-oriented electrical steel remain unclear.
In this study, grain-oriented electrical steel was applied to a U-shaped unimorph device on a laboratory scale. The influence of the rolling direction of a grain-oriented electrical steel core on the vibration power generation properties was investigated.
A grain-oriented electrical steel sheet (JFE Steel Corporation 35JG135) was cut into a plate-shaped core with a length of 16 mm, width of 4 mm and thickness of 0.35 mm. The length direction of the core was set parallel to the rolling direction (RD) and transverse direction (TD). A U-shaped unimorph device was used to measure the vibration power generation properties, as shown in Fig. 1(a). The device was composed of a U-shaped steel frame with shorter and longer beams, a grain-oriented electrical steel core, a coil, and a permanent magnet. A unimorph core was prepared by bonding the RD and TD cores to a shorter beam along the longitudinal direction. A coil was wound with 3638 turns around the unimorph core. A proof mass was attached on the shorter beam. A permanent magnet was placed inside the frame between the two beams to provide a bias magnetic field. Figure 1(b) illustrates the setup used to measure the vibration power generation properties. A longer beam was fixed to the base. When the base is forcibly vibrated, tensile and compressive stresses are alternately induced along the longitudinal direction of the unimorph core through the vibration of the free shorter beam. The vibration power generation properties are sensitively affected by the vibration frequency and the free-end displacement.5) The vibration power generation properties of the RD and TD unimorph core devices were compared at the same vibration frequency and the same free-end displacement. The voltage of the coil and the free-end displacement were measured using an oscilloscope and a laser displacement meter, respectively.
(a) Photograph of U-shaped unimorph device using grain-oriented electrical steel and (b) schematic illustration of setup to measure vibration power generation properties.
Figure 2 shows the time t response of (a) the free-end displacement d and (b) the open-circuit voltage V of the RD unimorph core device with a 2.28 g proof mass. In this measurement, the base was forcibly vibrated at f = 108 Hz. A permanent magnet with the surface magnetic flux of 3.9 µWb was attached to provide bias magnetic fields. The d-t curve indicates the oscillation because of mechanical resonance. The oscillation period of the d-t curve is 108 Hz, which is the same as that of the base. The V-t curve also shows that the oscillation has almost the same period as that of the d-t curve, indicating that the power generation is caused by vibration.
Time t response of (a) free-end displacement d, (b) open-circuit voltage V and (c) induced magnetic flux Φ of the RD unimorph core device with magnet of 3.9 µWb bias magnetic flux and 2.28 g proof mass at f = 108 Hz.
The vibration power generation properties have been demonstrated as sensitive to bias magnetic fields.20–22) To clarify the optimum bias magnetic field, the V-t curves of the RD and TD unimorph core devices were measured using bias permanent magnets with various magnetic fluxes. Figure 3 shows the bias magnetic flux dependence of the effective open-circuit voltage Veff obtained from the V-t curve. As the vibration of the device was affected by the bias magnetic flux, the maximum amplitude of the free-end displacement Δd in the d-t curve was set to 2.0 mm by adjusting the proof mass. The Veff values of the RD and TD unimorph core devices exhibit maximum at 3.9 µWb and 2.8 µWb, respectively. The maximum Veff value of the RD unimorph core device under an optimum bias magnetic field of 3.9 µWb is 0.89 V, which is larger than that of the TD unimorph core device at 2.8 µWb.
Bias magnetic flux dependence of the effective open-circuit voltage Veff of the RD and TD unimorph core devices. The device was vibrated with the maximum value of the free-end displacement Δd of 2.0 mm in the d-t curve at f = 108 Hz.
The output power is also an important property of power generation devices. To evaluate the output power, various load resistances were attached to the device, and the generation voltage was measured at f = 108 Hz and Δd = 2.0 mm, under optimum bias magnetic fields. Figure 4 shows the average output power Pave as a function of the load resistance RL of the RD and TD unimorph core devices. The Pave value was calculated using the following:
| \begin{equation} P_{\text{ave}} = \frac{1}{T}\int_{0}^{T}\frac{V_{\text{L}}{}^{2}}{R_{\text{L}}}\text{d}t \end{equation} | (1) |
Relationship between load resistance and average output power Pave of the RD and TD unimorph core devices at Δd = 2.0 mm and f = 108 Hz under optimum bias magnetic fields.
According to Faraday’s law, the V value of the device can be related to the induced magnetic flux Φ in the unimorph core with the number of coil turns N as V = −N (dΦ/dt). Figure 2(c) shows the Φ-t curve obtained from the V-t curve in Fig. 2(b) by using Faraday’s law. When the tensile stress is induced by a decrease in d, Φ exhibits a positive value. A negative Φ value is obtained, when the compressive stress is induced by an increase in d. The above–mentioned behavior of Φ occurs in the RD unimorph core, which is composed of grain-oriented electrical steel and the steel frame. To clarify the contribution of grain-oriented electrical steel, the Φ-t curve of the device without the RD and TD cores (frame core) was also measured. Figure 5(a) shows the bias magnetic flux dependence of the peak-to-peak value of the induced magnetic flux ΔΦ in the Φ-t curves of the RD and TD unimorph cores and the frame core. The ΔΦ value of the frame core exhibits a maximum. Thus, the optimum bias magnetic flux of the frame core is 1.3 µWb, which is much smaller than those of the RD and TD unimorph cores. In addition, the maximum ΔΦ value of the frame core device is much smaller than those of the RD and TD unimorph cores. Accordingly, the vibration power generation properties of the RD and TD unimorph core devices under optimum bias magnetic fields are mainly caused by grain-oriented electrical steel.
(a) Bias magnetic flux dependence of the peak-to-peak value of the induced magnetic flux ΔΦ in the Φ-t curve of the RD and TD unimorph cores at Δd = 2.0 mm under optimum bias magnetic fields. For comparison, the data of the frame core are also indicated. (b) Bias magnetic flux dependence of the magnetic flux density change ΔB in the RD and TD cores.
Figure 5(b) shows the bias magnetic flux dependence of the magnetic flux density change ΔB of the RD and TD cores without the frame core. The ΔB value was obtained by the following:
| \begin{equation} \varDelta B = \frac{\varDelta \varPhi_{\text{unimorph}} - \varDelta \varPhi_{\text{frame}}}{S} \end{equation} | (2) |
Finally, the relationship between Δd and ΔB of the RD and TD cores under an optimum bias magnetic field are shown in Fig. 6. As the stress induced in the core increases with increasing Δd, the ΔB value increases proportionally with Δd. The ΔB value of the RD core is sensitive to Δd in comparison with that of the TD core, indicating that the ΔB value of the former is probably more sensitive to stress than that of the latter. The magnetostrictive constant in the ⟨100⟩ direction of the Fe–3.2 mass% Si alloy is 23 ppm, which is larger than the magnetostrictive constant in the ⟨110⟩ direction λ110 = 3 ppm.23) Thus, the saturation magnetostriction of the RD core with ⟨100⟩ preferred orientation was evaluated to be approximately 17 ppm from the magnetic field dependence of the length change. This value was larger than the saturation magnetostriction of approximately 9 ppm of the TD cores with ⟨110⟩ preferred orientation, implying that the difference in the stress sensitivity of ΔB between the RD and TD cores is related with the anisotropy of the magnetostrictive properties. The ΔB value of the RD core shows ΔB = 0.71 T at Δd = 2.2 mm. This value is approximately 38% of the saturation magnetic flux density. Therefore, it is important to develop large-sized devices that cause large stress in the RD core. Further investigations are also needed to clarify the energy conversion efficiency of the device using the grain-oriented electrical steel.
Relationship between Δd and ΔB of the RD and TD unimorph core devices under optimum bias magnetic fields.
The vibration power generation properties of a U-shaped unimorph device using grain-oriented electrical steel cores with a plate shape (16 mm long with a 1.4 mm2 cross-section) were investigated. When the free-end of the device was vibrated with the maximum amplitude of 2.0 mm at a mechanical resonance frequency of 108 Hz, a grain-oriented electrical steel core with the RD direction parallel to the induced stress direction exhibited a magnetic flux density change ΔB of approximately 0.65 T under an optimum bias magnetic field. As a result, the RD core device exhibited the effective open-circuit voltage Veff of 0.89 V. In addition, an average output power of 300 µW was obtained by adjusting the load resistance. As the ΔB value in the RD core was larger than that in the TD core, the vibration power generation properties of the device with an RD core were superior to those with a TD core. Consequently, grain-oriented electrical steel in the RD direction has the potential to promote the development of larger device with higher performance.
This research was supported by JSPS KAKENHI Grant Numbers 20H02424 and 20K21088, the Kansai Research Foundation for Technology Promotion and the TEPCO Memorial Foundation. The authors would like to thank Dr. Toshiyuki Ueno at Kanazawa University for the experimental support.
