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Effect of grain diameter on iron loss properties of non-oriented silicon steel sheets
Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
E!ect of grain diameter on iron loss properties of non-oriented silicon steel sheets H. Denma , Y. Ishihara *, T. Todaka , M. Doi Department of Electrical Engineering, Doshisha University, Tanabe-eho, Kyotanabe, Kyoto 610-0321, Japan Sumitomo Metal Industries, LTD, Amagasaki, Hyogo 660-0891, Japan
Abstract The iron loss properties of the non-oriented silicon steel sheets as a function thickness, silicon contents, cutting angle and grain diameter were measured by single-sheet tester (SST). The specimens were excited by sinusoidal waveform (50 Hz), fundamental waveform (50 Hz) with a single high-order harmonic component and PWM waveform. The averaging loss of three directions is de"ned as (¸#2;C#¹)/4 (called as A3D loss). The increase ratio of nonsinusoidal waveform exciting condition's A3D loss against the sinusoidal waveform one was di!erent despite the equal levels of the A3D loss under sinusoidal waveform exciting condition. This is because it depends on a di!erence of iron loss constitution. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Non-sinusoidal waveform excitation; Eddy current loss; Non-oriented silicon steel sheet
1. Introduction
2. Method of measurement
In recent years, the induction motors are exited by PWM inverter because of high e$ciency, easy control, etc. It is expected that the loss under non-sinusoidal waveform condition is bigger than that under sinusoidal waveform condition. So it is important to grasp magnetic characteristic of non-oriented silicon steel sheets under the non-sinusoidal waveform exciting condition. In this paper, the iron loss properties of the silicon steel sheets changing in thickness, silicon contents, cutting angle and grain diameter were measured by SST under the sinusoidal and the non-sinusoidal waveforms excitation. As non-sinusoidal waveforms, fundamental waveform (50 Hz) with a single high-order harmonic component (called as ACSH waveform) and PWM waveform were chosen. These results were compared with the results of a former research [1].
The iron loss properties were measured by single-sheet tester (SST) on the horizontal, double-yokes type by the Double H-coil method [2]. The measurement area of the specimen was 85;200 mm at the center of the specimen.
* Corresponding author. Tel.: #81-774-656327; fax: #81774-656813. E-mail address: [email protected], kharada@ duaic.doshisha.ac.jp (Y. Ishihara).
2.2. Condition of excitation
2.1. Condition of specimens The specimens were non-oriented silicon steel sheets. The two levels of thickness (0.35 and 0.50 mm), two Si contents (1% and 2%) and three cutting angles (03, 453 and 903 to the rolling direction of the specimens) were prepared. These specimens' grain diameters were varied in the range of 30}200 lm. The crystallographical texture of the specimens did not change much with a change of grain diameter. Each specimen was 100 mm wide and 500 mm long. Table 1 shows the details of the specimens.
The maximum #ux density was 1.5 T and the fundamental frequency was 50 Hz under all exciting
0304-8853/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 0 8 6 - X
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
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Table 1 Condition of specimens Specimen Thickness Silicon contents Grain diameter (lm) [mm] (%) 35S1 35S2 50S1 50S2
0.35 0.35 0.50 0.50
1 2 1 2
36.6, 59.3, 97, 146, 158 37.3, 56.4, 105, 150, 153 37.3, 59.1, 116, 188, 209 34, 50.7, 159, 175, 200
conditions. (a) Sinusoidal waveform excitation: Induced voltage waveform of B coil is controlled to sinusoidal waveform. (b) ACSH waveform excitation: Induced voltage waveform of B coil is controlled with < (t)"<
sin(ut)#r< sin(nut), (1) where < is the induced voltage of fundamental waveform, r is the ratio of a high-order harmonic, n is the order of harmonic. The value of r was 0.5. The parameter n was 19th harmonic order (950 Hz) and 39th harmonic order (1950 Hz). (c) PWM waveform excitation: Signal waveform was sinusoidal waveform and carrier waveform was triangular waveform. It was output when the amplitude of sinusoidal waveform was bigger than that of triangular waveform. The orders of harmonic carrier waveform were 20th (1000 Hz) and 40th (2000 Hz). The modulation ratio was 1.0. (d) Iron loss separation: It was done by the two-frequency method (20 and 100 Hz).
Fig. 1. Relationship between loss of the ring specimen and A3D loss. (B "1.5 T, frequency"50 Hz).
Fig. 2. A3D loss under sinusoidal waveform. (B "1.5 T, fre quency"50 Hz).
ACSH waveform (19th harmonic) and PWM waveform (20th harmonic) were referred to as low order, and ACSH waveform (39th harmonic) and PWM waveform (40th harmonic) were referred to as high order.
3. Result and discussion The average loss of three directions (A3D) is de"ned by ¸#2;C#¹ , A3D" 4
(2)
where ¸, C, and ¹ are iron losses in the rolling direction, the diagonal direction and the transverse direction, respectively. Fig. 1 shows the relationship between loss of the ring specimen and A3D loss. It is e!ective when measurement preparation is considered. Fig. 2 shows the relationship between A3D loss and grain diameter under sinusoidal waveform excitation. We
Fig. 3. Hysteresis loops of non-sinusoidal waveform excitation. (B "1.5 T, fundamental frequency"50 Hz).
have classi"ed these samples into three groups with A3D loss. Table 2 shows details of each group. Fig. 3 shows hysteresis loops that were compared under the ACSH waveform excitation (19th harmonic
108
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
Table 2 A3D loss level of each group Specimen
Grain diameter (lm)
A3D loss (W/kg)
Eddy current loss (W/kg)
Ratio of Eddy current loss (%)
(a) Group 1 35S2 35S1 35S1 35S1
56.4 59.3 97 158
2.66 2.69 2.78 2.78
0.68 0.87 0.98 1.05
25.70 32.23 35.10 37.65
(b) Group 2 35S1 35S2 50S2 50S2
36.6 37.3 50.7 200
3.15 3.09 3.11 3.02
0.82 0.64 1.27 1.28
26.10 20.78 40.93 42.28
(c) Group 3 50S2 50S1 50S1 50S1
34 116 188 209
3.71 3.55 3.70 3.60
1.22 1.68 1.75 1.76
32.81 47.21 47.30 48.70
Fig. 4. Ratio of increase of non-sinusoidal condition's A3D loss of low against sinusoidal waveform. (B "1.5 T, fundamental
frequency"50 Hz).
Fig. 5. Ratio of increase of non-sinusoidal condition's A3D loss of high against sinusoidal waveform. (B "1.5 T, fundamental
frequency"50 Hz).
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
order) and PWM waveform excitation (20th carrier order). Figs. 4 and 5 show the increase ratio of non-sinusoidal condition's A3D loss against the sinusoidal waveform one. Except for group 3, the increase ratio di!ered from ratio of eddy current loss. Eddy current loss was in#uenced by material factors such as the grain diameter, the thickness and the silicon contents. These results indicate that samples in the same iron loss level under sinusoidal waveform excitation show di!erent iron loss under non-sinusoidal waveform excitation. In the case of ACSH waveform excitation, the increase ratios of each harmonic order did not change much. But in the case of PWM waveform excitation, the increase ratio of high order was less than that of low order. The increase ratio of ACSH waveform exciting condition's A3D loss was bigger than the increase ratio of PWM waveform exciting condition's A3D loss. This result suggested that the hysteresis loop of ACSH wave-
109
form excitation swells and that of PWM waveform excitation is hollow.
4. Conclusion Di!erences in average loss between non-sinusoidal and sinusoidal exciting varied with material factors such as the grain diameter, the thickness, the silicon contents and electricity resistance. This is because it depends on di!erence of Eddy current loss and ratio of Eddy current loss, namely, di!erence of composition of iron loss.
References [1] M. Yamada, Y. Ishihara, T. Todaka, M. Doi, H. Yashiki, J. Phys. 4 (8) Part 2 (1998) 495. [2] JIS H 7152 (1991).
E!ect of grain diameter on iron loss properties of non-oriented silicon steel sheets H. Denma , Y. Ishihara *, T. Todaka , M. Doi Department of Electrical Engineering, Doshisha University, Tanabe-eho, Kyotanabe, Kyoto 610-0321, Japan Sumitomo Metal Industries, LTD, Amagasaki, Hyogo 660-0891, Japan
Abstract The iron loss properties of the non-oriented silicon steel sheets as a function thickness, silicon contents, cutting angle and grain diameter were measured by single-sheet tester (SST). The specimens were excited by sinusoidal waveform (50 Hz), fundamental waveform (50 Hz) with a single high-order harmonic component and PWM waveform. The averaging loss of three directions is de"ned as (¸#2;C#¹)/4 (called as A3D loss). The increase ratio of nonsinusoidal waveform exciting condition's A3D loss against the sinusoidal waveform one was di!erent despite the equal levels of the A3D loss under sinusoidal waveform exciting condition. This is because it depends on a di!erence of iron loss constitution. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Non-sinusoidal waveform excitation; Eddy current loss; Non-oriented silicon steel sheet
1. Introduction
2. Method of measurement
In recent years, the induction motors are exited by PWM inverter because of high e$ciency, easy control, etc. It is expected that the loss under non-sinusoidal waveform condition is bigger than that under sinusoidal waveform condition. So it is important to grasp magnetic characteristic of non-oriented silicon steel sheets under the non-sinusoidal waveform exciting condition. In this paper, the iron loss properties of the silicon steel sheets changing in thickness, silicon contents, cutting angle and grain diameter were measured by SST under the sinusoidal and the non-sinusoidal waveforms excitation. As non-sinusoidal waveforms, fundamental waveform (50 Hz) with a single high-order harmonic component (called as ACSH waveform) and PWM waveform were chosen. These results were compared with the results of a former research [1].
The iron loss properties were measured by single-sheet tester (SST) on the horizontal, double-yokes type by the Double H-coil method [2]. The measurement area of the specimen was 85;200 mm at the center of the specimen.
* Corresponding author. Tel.: #81-774-656327; fax: #81774-656813. E-mail address: [email protected], kharada@ duaic.doshisha.ac.jp (Y. Ishihara).
2.2. Condition of excitation
2.1. Condition of specimens The specimens were non-oriented silicon steel sheets. The two levels of thickness (0.35 and 0.50 mm), two Si contents (1% and 2%) and three cutting angles (03, 453 and 903 to the rolling direction of the specimens) were prepared. These specimens' grain diameters were varied in the range of 30}200 lm. The crystallographical texture of the specimens did not change much with a change of grain diameter. Each specimen was 100 mm wide and 500 mm long. Table 1 shows the details of the specimens.
The maximum #ux density was 1.5 T and the fundamental frequency was 50 Hz under all exciting
0304-8853/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 0 8 6 - X
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
107
Table 1 Condition of specimens Specimen Thickness Silicon contents Grain diameter (lm) [mm] (%) 35S1 35S2 50S1 50S2
0.35 0.35 0.50 0.50
1 2 1 2
36.6, 59.3, 97, 146, 158 37.3, 56.4, 105, 150, 153 37.3, 59.1, 116, 188, 209 34, 50.7, 159, 175, 200
conditions. (a) Sinusoidal waveform excitation: Induced voltage waveform of B coil is controlled to sinusoidal waveform. (b) ACSH waveform excitation: Induced voltage waveform of B coil is controlled with < (t)"<
sin(ut)#r< sin(nut), (1) where < is the induced voltage of fundamental waveform, r is the ratio of a high-order harmonic, n is the order of harmonic. The value of r was 0.5. The parameter n was 19th harmonic order (950 Hz) and 39th harmonic order (1950 Hz). (c) PWM waveform excitation: Signal waveform was sinusoidal waveform and carrier waveform was triangular waveform. It was output when the amplitude of sinusoidal waveform was bigger than that of triangular waveform. The orders of harmonic carrier waveform were 20th (1000 Hz) and 40th (2000 Hz). The modulation ratio was 1.0. (d) Iron loss separation: It was done by the two-frequency method (20 and 100 Hz).
Fig. 1. Relationship between loss of the ring specimen and A3D loss. (B "1.5 T, frequency"50 Hz).
Fig. 2. A3D loss under sinusoidal waveform. (B "1.5 T, fre quency"50 Hz).
ACSH waveform (19th harmonic) and PWM waveform (20th harmonic) were referred to as low order, and ACSH waveform (39th harmonic) and PWM waveform (40th harmonic) were referred to as high order.
3. Result and discussion The average loss of three directions (A3D) is de"ned by ¸#2;C#¹ , A3D" 4
(2)
where ¸, C, and ¹ are iron losses in the rolling direction, the diagonal direction and the transverse direction, respectively. Fig. 1 shows the relationship between loss of the ring specimen and A3D loss. It is e!ective when measurement preparation is considered. Fig. 2 shows the relationship between A3D loss and grain diameter under sinusoidal waveform excitation. We
Fig. 3. Hysteresis loops of non-sinusoidal waveform excitation. (B "1.5 T, fundamental frequency"50 Hz).
have classi"ed these samples into three groups with A3D loss. Table 2 shows details of each group. Fig. 3 shows hysteresis loops that were compared under the ACSH waveform excitation (19th harmonic
108
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
Table 2 A3D loss level of each group Specimen
Grain diameter (lm)
A3D loss (W/kg)
Eddy current loss (W/kg)
Ratio of Eddy current loss (%)
(a) Group 1 35S2 35S1 35S1 35S1
56.4 59.3 97 158
2.66 2.69 2.78 2.78
0.68 0.87 0.98 1.05
25.70 32.23 35.10 37.65
(b) Group 2 35S1 35S2 50S2 50S2
36.6 37.3 50.7 200
3.15 3.09 3.11 3.02
0.82 0.64 1.27 1.28
26.10 20.78 40.93 42.28
(c) Group 3 50S2 50S1 50S1 50S1
34 116 188 209
3.71 3.55 3.70 3.60
1.22 1.68 1.75 1.76
32.81 47.21 47.30 48.70
Fig. 4. Ratio of increase of non-sinusoidal condition's A3D loss of low against sinusoidal waveform. (B "1.5 T, fundamental
frequency"50 Hz).
Fig. 5. Ratio of increase of non-sinusoidal condition's A3D loss of high against sinusoidal waveform. (B "1.5 T, fundamental
frequency"50 Hz).
H. Denma et al. / Journal of Magnetism and Magnetic Materials 215}216 (2000) 106}109
order) and PWM waveform excitation (20th carrier order). Figs. 4 and 5 show the increase ratio of non-sinusoidal condition's A3D loss against the sinusoidal waveform one. Except for group 3, the increase ratio di!ered from ratio of eddy current loss. Eddy current loss was in#uenced by material factors such as the grain diameter, the thickness and the silicon contents. These results indicate that samples in the same iron loss level under sinusoidal waveform excitation show di!erent iron loss under non-sinusoidal waveform excitation. In the case of ACSH waveform excitation, the increase ratios of each harmonic order did not change much. But in the case of PWM waveform excitation, the increase ratio of high order was less than that of low order. The increase ratio of ACSH waveform exciting condition's A3D loss was bigger than the increase ratio of PWM waveform exciting condition's A3D loss. This result suggested that the hysteresis loop of ACSH wave-
109
form excitation swells and that of PWM waveform excitation is hollow.
4. Conclusion Di!erences in average loss between non-sinusoidal and sinusoidal exciting varied with material factors such as the grain diameter, the thickness, the silicon contents and electricity resistance. This is because it depends on di!erence of Eddy current loss and ratio of Eddy current loss, namely, di!erence of composition of iron loss.
References [1] M. Yamada, Y. Ishihara, T. Todaka, M. Doi, H. Yashiki, J. Phys. 4 (8) Part 2 (1998) 495. [2] JIS H 7152 (1991).