Evaluation of magnetic properties of two kinds of permendurs by vector magnetic measurement

Abstract

Vector magnetic properties of various electrical steel sheets have been investigated by using a vector magnetic property measurement apparatus to select a magnetic material suitable as a motor core material. However, a magnetic material with a higher saturation magnetization than an electrical steel sheet is useful for increasing torque of a motor. Therefore, a permendur with higher saturation magnetization than an electrical steel sheet is selected as a measurement sample. It is known that a permendur does not have magnetic anisotropy. In this paper, vector magnetic properties of two kinds of permendurs made by VACUUMSCHMELZE (VAC) and Hitachi Metals are measured. Moreover, maximum magnetic field intensities and core losses of two kinds of permendurs to an inclination angle of magnetic flux density vector locus from rolling direction are evaluated for investigation of those magnetic anisotropies. As a result, differences of vector magnetic properties of two kinds of permendurs are revealed.

Keywords

Magnetic anisotropy permendur vector magnetic properties

1. Introduction

Recently, a demand of a motor with high power and high efficiency is increasing with development of a drone and a power assist suit. Generally, an electrical steel sheet is used as a magnetic material of iron core of a motor. However, a magnetic material with a higher saturation magnetization than an electrical steel sheet is useful for increasing torque of a motor. A permendur has extremely high saturation magnetic flux density and very low core loss [1]. Moreover, magnetic anisotropy of permendur is smaller than that of electrical steel sheet [2]. Therefore, it is expected that a permendur is useful as a core material of a motor with high power and high efficiency. On the other hand, vector magnetic properties of various electrical steel sheets have been investigated by using a vector magnetic property measurement apparatus to select a magnetic material suitable as a motor core material [2–4]. Moreover, vector magnetic properties is useful as a material’s data for finite element analysis in order to investigate an detailed core loss distribution in a motor core [5–7]. However, there are few detailed reports on the vector magnetic properties of permendur [2]. Therefore, it is necessary to investigate the vector magnetic properties of the permendur, especially on an anisotropy, in detail.

In this paper, vector magnetic properties of two kinds of permendurs made by VACUUMSCHMELZE (VAC) and Hitachi Metals are measured. Moreover, maximum magnetic field intensities and core losses of two kinds of permendurs to an inclination angle of magnetic flux density vector locus from rolling direction are evaluated for investigation of those magnetic anisotropies.

2. Vector magnetic properties

It is well known that both an alternating magnetic flux density condition and a rotating magnetic flux density condition occurs in a motor iron core. However, they cannot be measured by using single sheet testing or Epstein method which measures magnetic flux densities and magnetic field intensities as scalar quantities. A magnetic flux density B and magnetic field intensity H should be evaluated as vector quantities by using vector magnetic properties. A vector magnetic properties measurement apparatus can measure alternating magnetic flux conditions and rotating magnetic flux conditions in any directions. The vector magnetic property measurement apparatus is shown in Fig. 1. Dimensions of measurement samples are 80 × 80 [mm]. This measurement apparatus is original, isn’t a commercial product. Vector magnetic measurement is a measurement method that have been used from 1990s [8]. However, vector magnetic measurement is not an international standard measurement method. The sample is excited from two-directions by vector magnetic property apparatus. Various magnetic flux density conditions are made in the center of the sample by the vector magnetic properties measurement apparatus, and a magnetic flux density and magnetic field intensity are measured as vector quantities. Figure 2 shows a definition of magnetic flux density condition. It is possible to define a magnetic flux density vector locus as a magnetic flux density condition because magnetic flux densities of x- and y-direction are completely controlled as a sinusoidal waveform by the vector magnetic property measurement apparatus. A magnetic flux density condition is defined by three parameters: maximum magnetic flux density B_max, axial ratio 𝛼(= B_min∕B_max), and inclination angle θ_B. B_max is calculated by the following equation: $\begin{eqnarray}\displaystyle B_{\max }=\sqrt{B_{x}^{2}+B_{y}^{2}}. & & \displaystyle\end{eqnarray}$ (1) An alternating magnetic flux density condition is a magnetic flux density vector locus in the axial ratio 𝛼 = 0, and a rotating magnetic flux density condition is a magnetic flux density vector locus in the axial ratio 0 < 𝛼 ≤ 1. The θ_B is an inclination angle of the magnetic flux density vector locus from the rolling direction. A rolling direction of the sample is set to the x-direction (0 deg.), and a direction perpendicular to the rolling direction is set to the y-direction (90 deg.).

Fig. 1.

Vector magnetic property measurement apparatus.

Fig. 2.

Definition of magnetic flux density conditions.

3. Measurement results

3.1. Vector locus evaluation

In this paper, two kinds of permendurs which are VACODUR49 made by VAC and YEP-2V made by Hitachi Metals are measured. Details of the measured samples are shown in Table 1. These permendurs are measured at excitation frequency 50 Hz, B_max = 1.0 T to investigate the rolling magnetic anisotropy. Figure 3 shows measured results of two kinds of permendurs at θ_B = 45 deg. under an alternating magnetic flux density condition (𝛼 = 0). Figure 4 shows measured results of two kinds of permendurs at θ_B = 45 deg. under an rotating magnetic flux density condition (𝛼 = 0.4). It is possible to draw B-H loop in each of the x- and y-directions by using vector magnetic properties. As shown in (b) of Figs 3 and 4, both inclination angles of H vector loci are almost the same as those of B vector loci. Therefore, an influence of a roll magnetic anisotropy on the permendurs is small. In B-H loops shown in Figs 3(c) and 3(d), although there are few differences in both shapes of H vector loci between two kinds of permendurs, the coercive force of YEP-2V in the x-direction is 5 A/m larger than that of VACODUR49, the coercive force of YEP-2V in the y-direction is 14 A/m larger than that of VACODUR49.

Fig. 3.

B and H vector loci and B-H loops of permendurs under the alternating magnetic flux density condition at excitation frequency 50 Hz, B_max =1.0 T, 𝛼 = 0, θ _B = 45 deg.

Fig. 4.

B and H vector loci and B–H loops of permendurs under the rotating magnetic flux density condition at excitation frequency 50 Hz, B_max = 1.0 T, 𝛼 = 0.4, θ_B = 45 deg.

3.2. Magnetic field intensity evaluation

In a vector magnetic property, since a magnetic flux density is controlled as shown in (a) of Figs 3 and 4, the difference in vector magnetic property appears in a magnetic field intensity. Therefore, detailed comparisons in a magnetic field intensity are carried out to investigate the differences between the two kinds of permendurs. Figures 5 and 6 respectively show relation between maximum magnetic field intensity and inclination angle θ_B of two kinds of permendurs at 𝛼 = 0 and 0.4. The inclination angle θ_B is changed every 15 deg. in the range of 0 to 90 deg. The maximum magnetic field intensity H_max is calculated by the following equation: $\begin{eqnarray}\displaystyle H_{\max }=\sqrt{H_{x}^{2}+H_{y}^{2}}. & & \displaystyle\end{eqnarray}$ (2) The variation in the H_max under an alternating magnetic flux condition of VACODUR49 is about 14%, and that of YEP-2V is about 11% as shown in Fig. 5. Additionally, under rotating flux density condition as shown in Fig. 6, the variation in the H_max of VACODUR49 is about 11%, and that of YEP-2V is about 8%. On the other hand, Fig. 7 shows relationship between maximum magnetic field intensity and inclination angle θ_B of non-oriented electrical steel sheet (50JN600) at 𝛼 = 0 and 0.4. In non-oriented electrical steel sheet, a variation in a H_max to an inclination angle under an alternating magnetic flux condition is about 44%, and variation in a H_max to an inclination angle under a rotating magnetic flux condition is about 31%. Therefore, the magnetic anisotropy of two kinds of permendurs is small compared with a non-oriented electrical steel sheet. However, it is difficult to quantitatively compare H_max of the electrical steel sheet and permendur because both thicknesses are different. As shown in Figs 5 and 6, the H_max of VACODUR49 increases from 0 to 45 deg., and decreases from 45 to 90 deg. The H_max of VACODUR49 in both 𝛼 = 0 and 𝛼 = 0.4 takes the maximum when θ_B is about 45 deg. On the other hand, the H_max of YEP-2V increases from 0 to 90 deg. The H_max of YEP-2V in both 𝛼 = 0 and 𝛼 = 0.4 takes the maximum when θ_B is about 90 deg. In H_max of two kinds of permendurs, both variations to the inclination angle are different. As a result, the magnetic anisotropies of two kinds of permendurs are different. The results in Figs 5 and 6 indicate that the difference of anisotropies may have been caused by the difference of composition between two kinds of permendurs as shown in Table 1.

Fig. 5.

Relationship between maximum magnetic field intensity and inclination angle θ_B of permendur under the alternating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0, θ_B = 0−90 deg.).

Fig. 6.

Relationship between maximum magnetic field intensity and inclination angle θ_B of permendur under the rotating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0.4, θ_B = 0−90 deg.).

Fig. 7.

Relationship between maximum magnetic field intensity and inclination angle θ_B of non-oriented electrical steel sheet (50JN600). (B_max = 1.0 T, 𝛼 = 0 and 0.4, θ_B = 0−90 deg.).

Table 1

Details of measurement samples

Sample	VACODUR49	YEP-2V
Composition [%]	Fe 49.0, Co 49.0, V+Nb 2.0	C ≤ 0.015, Si ≤ 0.10, Mn ≤ 0.15,
		Co 49.0, V 2.0, Fe BAL.
Thickness [mm]	0.20	0.20
Density [kg/m³]	8120	8160
Coercive force H_c [A/m]	50 (thickness 0.35 mm)	48
Maximum permeability μ_m	15000 (thickness 0.35 mm)	15000
Magnetic flux density B [T]	2.10 [at 800 A/m] (thickness 0.35 mm)	2.15 [at 800 A/m]

3.3. Core lose evaluation

Next, core loss of the two kinds of permendurs was compared. Figures 8 and 9 respectively show relation between a core loss and inclination angle θ_B of two kinds of permendurs at 𝛼 = 0 and 0.4. These results are measured at excitation frequency 50 Hz, B_max = 1.0 T. The inclination angle θ_B is changed every 15 deg. in the range of 0 to 90 deg. Core loss is calculated by the following equation. $\begin{eqnarray}\displaystyle P_{i}=\frac{1}{{\rho}T}\int _{0}^{T}\left(H_{x}\frac{\partial B_{x}}{\partial t}+H_{y}\frac{\partial B_{y}}{\partial t}\right)dt. & & \displaystyle\end{eqnarray}$ (3) As shown in Figs 8 and 9, in VACODUR49, the core loss is constant from 0 to 90 deg. On the other hand, in YEP-2V, the core loss of YEP-2V at 𝛼 = 0 increases from 0 to 45 deg., and decreases from 45 to 90 deg. The core loss at 𝛼 = 0.4 decreases from 0 to 90 deg. The Core loss of YEP-2V is about 0.1 W/kg larger than that of VACODUR49 at any inclination angles. In the core loss of two kinds of permendurs, both amounts of the variation to an inclination angle and both value of core loss are different. To investigate the difference in core loss, θ_BH is compared in the two kinds of permendurs. θ_BH is a spatial phase difference between a magnetic flux density vector B and a magnetic field intensity vector H . Generally, θ_BH is related to a speed of magnetic wall movement in a low magnetic flux density region such as B_max = 1.0 T. Therefore, the core loss is small when θ_BH is small because the magnetization vector is easy to be oriented to an excitation direction and the magnetic energy is low. Figures 10 and 11 respectively show θ_BH waveform of two kinds of permendurs at 𝛼 = 0 and 0.4. As shown in Fig. 10, the θ_BH waveform increases like a square wave every half cycle under an alternating flux density condition. Although the rising of θ_BH waveform in YEP-2V is earlier than that in VACODUR49, the maximum value of θ_BH in VACODUR49 is larger than that in YEP-2V. Therefore, the effective values of θ_BH waveforms in Fig. 10 are calculated. The effective value of θ_BH waveform in VACODUR49 is 86.9 deg. and that in YEP-2V is 87.1 deg. The effective value of θ_BH of YEP-2V and VACODUR49 is almost the same. Consequently, the difference in core loss between the two permendurs under the alternating magnetic flux density condition is not due to difference of θ_BH. As shown in Fig. 11, the θ_BH waveform is repeated its maximum and minimum values like a sine wave every half cycle under a rotating flux condition. The θ_BH waveform under the rotational flux density condition is quite different from that under the alternating flux density condition. The θ_BH of YEP-2V is larger than that of VACODUR49 in most phases. The effective values of θ_BH waveform in VACODUR49 is 52.8 deg. and that in YEP-2V is 58.4 deg. The effective value of θ_BH in YEP-2V is larger than that of VACODUR49. However, it cannot be concluded that the cause of the difference of core loss in Fig. 9 is the difference of θ_BH as shown in Fig. 11. As a result, the θ_BH waveforms of the two kinds of permendurs in both 𝛼 = 0 and 𝛼 = 0.4 are different. The results in Figs 10 and 11 indicate that the difference of θ_BH waveforms may have been caused by the difference of composition between two kinds of permendurs.

Fig. 8.

Relationship between core loss and inclination angle θ_B of permendur under the alternating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0, θ_B = 0−90 deg.).

Fig. 9.

Relationship between core loss and inclination angle θ_B of permendur under the rotating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0.4, θ_B = 0−90 deg.)

Fig. 10.

θ_BH waveform of permendur under the alternating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0, θ_B = 45 deg.)

Fig. 11.

θ_BH waveform of permendur under the rotating magnetic flux density condition. (B_max = 1.0 T, 𝛼 = 0.4, θ_B = 45 deg.)

4. Conclusion

In this paper, vector magnetic properties of two kinds of permendurs, VACODUR49 and YEP-2V, is measured. Firstly, vector loci of B and H, and B–H loops are evaluated under an alternating magnetic flux density condition and an rotating magnetic flux density condition. The roll magnetic anisotropy of the permendur is small because inclination angles of H vector loci are almost the same as those of B vector loci. However, coercive forces in x- and y-direction of YEP-2V are larger than that of VACODUR49. Secondly, maximum magnetic field intensities H_max of two kinds of permendurs to an inclination angle θ_B of magnetic flux density vector locus from rolling direction are evaluated for investigation of those magnetic anisotropies. Variations in H_max of two kinds of permendurs to the inclination angle θ_B are quite different. Moreover, variations and values in core loss of two kinds of permendurs to the inclination angle θ_B are different. Finally, the θ_BH waveforms of two kinds of permendurs are evaluated. The θ_BH waveforms of two kinds of permendurs in both 𝛼 = 0 and 𝛼 = 0.4 are different.

As a result, differences in the maximum magnetic field strength and the core loss depending on the manufacturing company are clarified. However, the cause of the differences has not been clarified yet and it is necessary to investigate more in the future. Moreover, we confirmed that the magnetic property of permendur is superior to that of electrical steel sheet. However, the current situation is that permendur is used only in a limited field because cobalt used as a material of permendur is much more expensive than an iron and a silicon which are materials of an electrical steel sheet. In addition, it is necessary to investigate a vector magnetic property measured under high magnetic flux density conditions, such as a saturation region in the future.

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