The double H-coil method was proposed to detect magnetic field strength on the surface of a specimen more accurately than the single H-coil method. In this paper, the distribution of magnetic field strength inside exciting coil of a single sheet tester (SST) is measured simultaneously by the single H-coil method using four separated H-coils. They are placed at different distances from the surface of the specimen and thereby enable us to evaluate the influence of the position of the H-coil on the measurement accuracy of magnetic properties. As a result, it was revealed that the magnetic field strength and specific total loss increase linearly as the distance of the H-coil from the surface of the specimen increases. However the increasing rate of the specific total loss is smaller than that of the magnetic field strength and within the range of required measurement reproducibility.
I. INTRODUCTION
When measuring magnetic properties of magnetic materials by means of a single sheet tester (SST), an H-coil method is used for detecting magnetic field strength. In the previous paper, it was reported that the magnetic field strength inside the exciting coil of SST increases as the distance of the H-coil from the surface of a specimen increases.1 In order to suppress the gradient of magnetic field inside exciting coil, the double H-coil method was proposed.2,3 However, there are few studies of the influence of the distance between H-coil and a specimen surface for on magnetic properties such as specific total loss. In this paper, the magnetic field distribution near a specimen in the SST was investigated to evaluate the influence of the position of the H-coil on the measurement accuracy of magnetic properties. Moreover, the necessity of double H-coil method in measuring specific total loss as well as magnetization properties by the SST was discussed. Three kinds of specimens, i.e., grain-oriented electrical sheet, non-oriented electrical sheet and Fe-based amorphous strip, were prepared. The magnetic field strength was measured simultaneously by the single H-coil method using four separated H-coils, which are placed at different distances from the surface of the specimen.
Fig. 1 shows the specification of the four H-coils. Their area-turns are shown in Table II, which are measured by a cylindrical solenoid with enough length compared to its diameter. The distance d of each H-coil from the surface of the specimen are 0.78 mm, 2.53 mm, 4.30 mm and 6.05 mm, respectively. Magnetic properties were measured by the H-coil method with the double and single yoke construction. In order to evaluate the influence of the position of the H-coil on the measurement accuracy of magnetic properties, we discuss the relationships of d with the magnetic field strength Hb and the specific total loss Ps, where Hb is the magnetic field strength at the instant of the maximum flux density Bm in each symmetric loop.
II. MEASUREMENT METHODS
Fig. 2 shows the dimensions of the coil unit and yokes of the SST. Rectangular specimens of M155-35S5 (hereafter, GO), M230-35A5 (hereafter, NO) and Metglas® 2605HB1M (hereafter, AM) are measured. The dimensions of the specimens are 60 mm × 360 mm for GO and NO, and 60 mm × 335 mm for AM, respectively. The flux density is detected by a B-coil, and its amplitude Bm was controlled from 0.1 T to 1.9 T (GO), 0.1 T to 1.7 T (NO) and 0.1 T to 1.6 T (AM) at the interval of 0.1 T under the sinusoidal flux condition. Table I shows the convergence conditions for waveform control. Exciting frequency is 50 Hz.
Convergence criteria for waveform control.
The maximum flux density in the specimen | within 0.05 % of target value |
Form factor of induced voltage of the B-coil | 1.111 ± 0.05 % |
Distortion factor of induced voltage of the B-coil | within 2 % |
The maximum flux density in the specimen | within 0.05 % of target value |
Form factor of induced voltage of the B-coil | 1.111 ± 0.05 % |
Distortion factor of induced voltage of the B-coil | within 2 % |
III. DISTRIBUTION OF MAGNETIC FIELD STRENGTH INSIDE EXCITING COIL
The relationships of d with Hb and Ps are evaluated by the relative difference ε and the rate of change of ε with respect to d. ε is defined as follows:
where, H and H0 are the magnetic field strength measured by each H-coil and determined by the linear approximation for four measured magnetic field strength, respectively. In addition, m is defined as the slope of ε – d curve.
Fig. 3 shows the relative difference ε of Hb and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type and single-yoke type SST. Hb is a function of the distance of the H-coil from the surface of the specimen. m depends on the specimen, 1.50 %/mm (GO, single yoke), 1.32 %/mm (GO, double yoke), 0.08 %/mm (NO, single yoke), 0.11 %/mm (NO, double yoke), 1.54 %/mm (AM, single yoke), and 1.45 %/mm (AM, double yoke). Moreover, Hb and the distance from the surface of the specimen have strong positive correlation. Correlation coefficient R is 0.98 or more.
Relative difference ε of Hb and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type (b) or single-yoke type SST (a) at 50Hz.
Relative difference ε of Hb and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type (b) or single-yoke type SST (a) at 50Hz.
To investigate the cause of difference of m depending on specimen, compare with the relationship between m and the relative permeability μs on measuring GO, NO and AM. Fig. 4 shows the relationship between m and μs for GO, NO and AM measured by H-coil A placed at closest to the specimen with the double-yoke type or single-yoke type SST as one of typical examples. When magnetizing specimens from 0.1 T to near the saturation, μs varies from 200 to 1,000,000 resulting in wide range of m. It implies that distribution of magnetic field strength depends on specimen’s magnetic properties.
Relationship between m and relative permeability μs measured by H-coil A with the double-yoke type (b) or single-yoke type SST (a) at 50 Hz when measuring GO, NO and AM.
Relationship between m and relative permeability μs measured by H-coil A with the double-yoke type (b) or single-yoke type SST (a) at 50 Hz when measuring GO, NO and AM.
Fig. 5 shows the comparison of magnetization properties of GO. In this figure, HH-coil D is the measured values with H-coil D, H0 is the surface magnetic field estimated by eq. (1). In the case of using the single H-coil method, if the distance of the H-coil from the surface of the specimen is far, there is a possibility that the difference of magnetization property may be as shown in Fig. 5.
Comparison of magnetization properties of GO. (a) Single-yoke type SST and (b) Double-yoke type SST.
Comparison of magnetization properties of GO. (a) Single-yoke type SST and (b) Double-yoke type SST.
IV. INFLUENCE OF DISTRIBUTION OF MAGNETIC FIELD STRENGTH INSIDE EXCITING COIL ON SPECIFIC TOTAL LOSS
Fig. 6 shows the relative difference ε of Ps and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type or single-yoke type SST. Ps is a function of the distance of the H-coil from the surface of the specimen. m is 0.29 %/mm (GO, double yoke), 0.15 %/mm (NO, double yoke) and 0.46 %/mm (AM, single yoke). Moreover, Ps and the distance from the surface of the specimen have positive correlation. Correlation coefficient R is 0.90 or more. The reproducibility of measurement of the specific total loss required in IEC standards4 and the results of the round robin test5 is 1 % at 1.7 T in GO (double yoke), 2 % at 1.5 T in NO (double yoke), and 3 % at 1.3 T in AM (single yoke). When the magnetic field strength is measured by a H-coil (thickness 1 mm) built in the SST, the distance of the H-coil from the surface of the specimen is about 2 mm. ε at this position of the H-coil is estimated as 0.6 % (GO, double yoke), 0.3 % (NO, double yoke), and 0.9 % (AM, single yoke). These differences are sufficiently smaller than the measurement reproducibility on measuring NO and AM, and the double H-coil method is not always essential. However, the measurement reproducibility on GO is close to ε compared with NO and AM.
Relative difference ε of Ps and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type (b) and single-yoke type SST (a) at 50 Hz.
Relative difference ε of Ps and its slope m when measuring GO at Bm = 1.7 T, NO at Bm = 1.5 T and AM at Bm = 1.3 T with the double-yoke type (b) and single-yoke type SST (a) at 50 Hz.
Fig. 7 shows the difference between slope m of Hb and Ps on measuring GO at Bm = 0.1 ∼ 1.9 T, NO at Bm = 0.1 ∼ 1.7 T and AM at Bm = 0.1 ∼ 1.6 T with the double-yoke type and single-yoke type SST. The slope of Ps tends to be smaller than Hb on measuring GO, NO and AM. In addition, the slope of Ps is substantially constant value regardless of Bm.
Difference between slope m of Hb and Ps on measuring (a) GO at Bm = 0.1 ∼ 1.9 T, (b) NO at Bm = 0.1 ∼ 1.7 T and (c) AM at Bm = 0.1 ∼ 1.6 T with the double-yoke type and single-yoke type SST at 50Hz.
Difference between slope m of Hb and Ps on measuring (a) GO at Bm = 0.1 ∼ 1.9 T, (b) NO at Bm = 0.1 ∼ 1.7 T and (c) AM at Bm = 0.1 ∼ 1.6 T with the double-yoke type and single-yoke type SST at 50Hz.
To investigate the cause of difference of the slope of Ps and Hb, compare with fundamental component of magnetic field waveform h1 on measuring at each H-coil. Fig. 8 shows the fundamental component of the induced voltage waveform υb1 measured by the B-coil and h1 measured by H-coil A, B, C and D when measuring GO at Bm = 1.7 T with the single-yoke type SST. The fundamental component of the magnetic field strength H1 increase as the distance of the H-coil from the surface of the specimen increases. Fig. 9 shows the amplitude of H1 and cosθ, where θ is the phase difference between h1 and υb1 when measuring GO at Bm = 1.7 T with the single-yoke type SST. As the distance of the H-coil from the surface of the specimen increases, H1 increases but cosθ decreases. Thus the slope of the specific total loss is smaller than that of the magnetic field strength.
Fundamental component of induced voltage waveform υb1 measured by the B-coil and that of magnetic field waveform h1 measured by H-coil A, B, C and D when measuring GO at Bm = 1.7 T with the single-yoke type SST at 50Hz.
Fundamental component of induced voltage waveform υb1 measured by the B-coil and that of magnetic field waveform h1 measured by H-coil A, B, C and D when measuring GO at Bm = 1.7 T with the single-yoke type SST at 50Hz.
Amplitude of the fundamental component of the magnetic field strength (a) H1 and (b) cosθ when measuring GO at Bm = 1.7 T with the single-yoke type SST at 50Hz.
Amplitude of the fundamental component of the magnetic field strength (a) H1 and (b) cosθ when measuring GO at Bm = 1.7 T with the single-yoke type SST at 50Hz.
V. CONCLUSION
The double H-coil method is effective for the measurement of magnetization properties of Fe-based amorphous strip as well as electrical steel sheets because it can estimate the surface magnetic field strength more accurately.
The slope of the specific total loss is smaller than that of the magnetic field strength on measuring electrical steel sheets and Fe-based amorphous strip with the double-yoke type and single-yoke type SST. Therefore, specific total loss can be accurately measured by the single H-coil method. However, the specific total loss is a function of the distance of the H-coil from the surface of specimen. Moreover, they have strong positive correlation. Therefore, in the case using the single H-coil method, the H-coil should be set near to the specimen as much as possible.
ACKNOWLEDGMENTS
We are thankful for the support and advice from the Japanese National Committee for IEC/TC68.