Keywords

1 Introduction

As ultra-compact electric vehicles (EVs) employ electric motors as their power source, the noise within the vehicle primarily comprises road and wind noise [1]. This is because the bodies of ultra-compact EVs are compact and lightweight owing to the rigidity of their lower outer plates. Generally, hard felt and urethane are employed on the interior walls and roofs of vehicles to minimize external noise. However, the installation of these passive noise control materials in an ultra-compact EV is difficult owing to interior-space limitations. Additionally, the demand for ultra-compact EVs is expected to increase in the future. However, the research and development of noise control systems for ultra-compact EVs have been insufficient. To address this issue, we investigated an active noise control (ANC) system for ultra-compact EVs using a giant magnetostrictive actuator (GMA) [2,3,4]. Giant magnetostrictive materials (GMMs) feature an elastic displacement exceeding 1000 ppm, high-speed response, and high durability [5]. Therefore, a GMA can output low to high frequencies.

In this study, we determined the output characteristics of GMAs using the finite element method to develop two GMA models for ultra-compact EVs. Their output performance was evaluated through electromagnetic field analysis based on the differences in the material properties of the proposed GMAs.

2 Giant Magnetostrictive Material

Terefenol-D, exhibits the largest room-temperature magnetostriction. Terefenol-D is an alloy composed of terbium, dysprosium, and iron. GMMs are functional materials that can transform energy into other forms and generate 100 times more magnetostriction than conventional magnetic materials. Furthermore, their magnetostriction force and Curie temperature can be changed by altering their metal structure [6, 7]. Most GMMs developed thus far feature a metal composition of Tb0.3Dy0.7Fe1.9–2.0. The selected Tb/Dy ratio minimizes their anisotropy energy at room temperature owing to the competition of the TbFe-DyFe pseudo-dielement system. The characteristics of GMMs can be altered by altering their manufacturing method and the compounding ratio of the metal powder. Table 1 lists the physical properties of Terfenol-D [8].

3 GMA Structure and Flux Density Generated by GMM

3.1 GMA Structure

Figure 1 shows the structure of a GMA comprising a columnar GMM, permanent magnet (that applies a bias magnetic field), solenoid coil, and spacer. The coil is connected to an alternating current (AC) source and a magnetic field is generated as the current flows through the coil. The magnetic field stretches the GMM, and the control sound is output by the wall surface, generating vibrations via the shaft and spring. Table 2 lists the fundamental components and materials of the GMA.

Table 1. Nominal physical properties of Terfenol-D.
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Fig. 1.
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GMA structure.

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Table 2. Nominal physical properties of the GMM.
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3.2 Magnetostriction Force Generated by AC Flowing Through the Coil

Figure 2 shows a model of the GMA along the longitudinal cross-section. The N pole of the permanent magnet around the GMM is on the shaft side and the S pole is on the opposite side. In this scenario, the magnetostrictive force generated on the surface in contact with the shaft has a positive value. This is because, as shown in Fig. 2, the x-axis originates from the shaft side, and the left direction is positive. Therefore, the direction in which the stretched GMM is pushed out of the shaft is positive. This GMA employs permanent magnets as the bias magnets. Therefore, it can generate a constant magnetostrictive force under the effect of the magnetic field applied by the permanent magnet, even though no AC flows through the coil. Subsequently, when an AC flows through the coil, the magnetostriction force generated by the operating GMM increases or decreases. This magnetostrictive force causes the shaft to transmit vibrations to the wall surface, resulting in the generation of sound waves.

Fig. 2.
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Model of the GMA along the longitudinal cross-section.

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3.3 Analysis Model and Material Characteristics of the GMM

In this study, we considered the magnetic flux density for the output band of road noise using finite element models of the GMA through an electromagnetic field analysis using JMAG Designer Version 16.0 (JSOL Corporation). A permanent magnet was magnetized along the axial direction of the GMM. The coil conductor featured a diameter of 0.5, 1000 turns, and an inductance of 3.5 μH.

In this analysis, the characteristics of the GMM were used as the values for the magnetic field and flux density, based on the research conducted by Sugawara [9]. The size change under the effect of an external magnetic field applied to the GMM was determined according to the method proposed by Mori [10]. The Young’s modulus of the GMM was set to 26.5 GPa and its Poisson’s ratio was 0.3. Based on these, a 3D analysis was conducted. The number of divided elements and nodes was 29653 and 5570, respectively. The electromagnetic field analysis considered the eddy currents in the shaft and GMM.

4 GMA Structures and Magnetic Flux Density Generated by the GMM

Figure 3 shows the finite element models of the two GMAs employed in this study. Figure 4a shows a GMA in which two Terfenol-D components with lengths and diameters of 20 and 4 mm, respectively, are arranged in series. By contrast, the GMM shown in Fig. 4b has a length of 43 mm and comprises two permanent magnets. As GMAs output the displacement owing to the axial strain of the material, we analytically examined the magnetic flux density characteristics of the two GMMs by changing the AC voltage and varying the frequency applied to the coil from 100–500 Hz based on the road-noise frequency band. In this analysis, a sampling frequency of 20 kHz and voltage amplitude of 1–5 V were employed.

Figure 4 shows the vector plots of the magnetic flux densities for each model under an applied voltage of 3 V. Model A exhibits a large magnetic flux density at the interface between the GMM and permanent magnet, whereas Model B exhibits a large magnetic flux density at the center of the GMM. Figure 5 shows sample vector plots for the amplitude of the magnetic flux density of each model when the AC voltage was changed from 1–5 V. In both figures, the vertical and horizontal axes represent the magnetic flux density and AC frequency, respectively. The magnetic flux density is the value at the surface center on the shaft side. These were higher for Model A than for Model B at 100 and 300 Hz. Based on these results, we determined that the magnetic flux density changes depending on the GMM shape and the arrangement of the permanent magnets. However, a detailed study of the correlation between the magnetic flux density and the magnetostriction force is required.

Fig. 3.
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Finite element models of the two GMAs: Models (a) A and (b) B

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Fig. 4.
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Vector plot samples of the magnetic flux density for each model at the maximum voltage: Models (a) A and (b) B.

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Fig. 5.
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Sample vector plots of the magnetic flux density for each model at the maximum voltage: Models (a) A and (b) B.

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5 Conclusion

This study analyzed the output performances of two GMAs with different material properties to develop an acoustic device for an ANC system for ultra-compact EVs. We determined the low-frequency output control sound via electromagnetic field analyses of finite element models of the GMA. The analysis results indicated that the magnetic flux density changes depending on the shape of the GMM and the arrangement of the permanent magnets. However, a more detailed study on the correlation between the magnetic flux density and the magnetostriction force is required. Therefore, in future studies, we plan to vary the size, weight, shape, and components of the actuator, and employ a material with a higher magnetic permeability.