THE RELATIONSHIP OF DOMAIN SPACING, GRAIN SIZE, SHEET THICKNESS AND POWER LOSS

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THE RELATIONSHIP OF DOMAIN SPACING, GRAIN SIZE, SHEET THICKNESS AND POWER

LOSS

K. Overshott

To cite this version:

K. Overshott. THE RELATIONSHIP OF DOMAIN SPACING, GRAIN SIZE, SHEET THICK- NESS AND POWER LOSS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-383-C1-385.

�10.1051/jphyscol:19711132�. �jpa-00213950�

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JOURNAL DE PHYSIQUE Colloque

C

I, fuppl&nent au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1

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383

THE RELATIONSHIP OF DOMAIN SPACING, GRAIN SIZE, SHEET THICKNESS AND POWER LOSS

K. J. OVERSHOTT,

Wolfson Centre for the Technology of Soft Magnetic Materials, U. W. I. S. T., Cardiff, U. K.

RBsum6. - On a mesurk la position des parois de Bloch parallMes dans des grains individuels de tale de transfor- mateur (Fe-Si a 3 %). Les mesures ont etk faites sur deux kpaisseurs de tale, en diffkrents points du cycle d'hystkrkses, dans la gamme de frkquence 20-150 Hz. Les parois se deplacent uniformkment de manikre rkpktitive, la distance entre parois reste indkpendante de la frkquence mais les parois prennent une certaine courbure.

La puissance totale perdue dans les rngmes grains a ktk mesuree pour diverses densrtks de flux dans la gamme 10-1 50 Hz.

Le minimum de perte survient dans les materiaux de 0,013 in (0,033 cm) d'epaisseur pour une taille de grain de 0,7 cm, et B 0,010 in (0,025 cm) pour une taille de grain inferieure.

Abstract. - Measurements of the position of parallel-bar domain walls at various points on the magnetizing cycle have been made over the frequency range 20-150 Hz in individual grains in two thicknesses of 3 % s~licon-iron transformer steel. The walls moved uniformly and revetitivelv. and the wall spacing was independent of the frequency, but wall - , - -

bowing was found to occur.

The total power loss in the same grains has been measured at various flux densities in the frequency range 10-150 Hz.

Minimum total Dower loss occurs in 0.013 in (0.033 cm) thick material at a grain size of 0.7 cm and a similar result is found to apply io 0.010 in (0.025 cm) at a smaller grain length. ^-

1. Introduction. - The total power loss in grain- oriented siliconiron is greater than would be expected from the sum of the static hysteresis loss and the eddy-current loss calculated on classical theory. The difference is known as the anomalous loss. The ratio of the sum of this anomalous loss and the classical eddy-current loss component to the classical eddy- current loss is known as the anomaly factor, and is represented by y.

2. Experimental Techniques.

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Observations were recorded on the position of parallel-bar domain walls at various points on the magnetising cycle over the frequency range 25-100 Hz in an individual grain of transformer steel, using the Kerr magneto-optic technique with stroboscopic illumination. The power loss in the same grain was measured at various flux densities in the frequency range 10-150 Hz using the rate-of-temperature-rise technique.

3. Experimental results.

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A number of grains \ \ -0'

were chosen, in both 0.013 in (0.033 cm) and 0.010 in

(0.025 cm) thick 3.25

%

grain-oriented silicon-iron 0.4 0.6 0.8 1-0

for detailed studv. which exhibited well defined bar- G R A I N S I Z E cm domain structures.' This feature showed that the grains

were well aligned to G~~~ orientation, as was deter- ^FIG.1. -Relationship between the total power loss at

1.5 Wb/mz at 50 Hz and the grain dimension for 0.013 in mined using an X-ray goniometer. A range of grain (0.033 cm) thick grain-oriented silicon-iron. ^xgrain length lengths from 0.3 to 1 cm was possible in both thick- (in rolling direction)

.

o grain width.

nesses of material.

Figure 1 shows the variation of the total power loss at 50 Hz and 1.5 Wb/m2 with grain length and grain width for the 0.013 in (0.033 cm) material.

A minimum is apparent in both cases at about 0.6- 0.7 cm. Equivalent results are plotted in (Fig. 2) for the thinner material. A minimum is found with the grain length at about 0.5 cm, but no similar minimum is observed for the grain width.

I t has been shown [I] that the degree of wall bowing could be seen by studying the relationship between a parameter which represented the degree of magnetic saturation expressed by the domains, and the value

of BIB,,, as measured by the search coil. When these two parameters are equal, the walls must be perfectly planar, and any deviation from this indicated domain- wall bowing. (Fig. 3) shows the resultant curves of ( A

-

B)/(A

+

B) and BIB,,, for various frequencies from 25-150 Hz for a grain of length 1.01 cm and sheet thickness 0.013 in (0.033 cm). Similar results are plotted in (Fig. 4) for a grain 0.25 cm in length in 0.010 in (0.025 cm) material.

4. Discussion of Experimental Results. - The basic role of domain walls, and the relevance of their

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711132

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C 1

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384 K. J. OVERSHOTT

0.2 0.4 C.6 0.8

G R A I N S I Z E c m

FIG. 2. - Relationship between the total power loss at 1.5 Wb/m2 at 50 Hz and the grain dimensions for 0.010 in (0.025 cm) thick grain-oriented silicon-iron. x grain length

in rolling direction). o grain width.

FIG. 3.

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Relationship between B/Bsat as obtained from the Kerr magneto-optic measurements compared with those from the search coil at various frequencies. If no bowing occurred, the solid line would be followed. Material 0.013 in (0.033 cm) thick and of grain length 1 .O1 crn. (a) 25 Hz, (b) 40 HZ,-(c) 60 Hz,

( d ) 80 Hz, (e) 100 Hz,

Cf)

150 Hz.

0.2 0.4 0.6

S E A R C H C O I L

FIG. 4. - Relationship between B/Bsat as obtained from Kerr magneto-optic measurements compared with those from the search coil at various frequencies. If no bowing occurred, the solid line would be followed. Material 0.010 (0.025 cm) of grain length 0.25 cm. Note that the domains do not behave in a simple pattern as the frequency is changed. (a) 20 Hz, (b) 25 Hz,(c) 30 Hz, ( d ) 40 Hz, (e) 60 Hz, (f) 100 Hz, (g) 150 Hz.

spacing mobility and bowing, in eddy-current theory is important. Houze [2] has stated that pinning could be responsible for a substantial part of the anomalous loss, while Boon and Robey 131, with similar results, came to the same basic conclusions. They believed that the anomalous loss could be accounted for in a satisfactory way by variations in wall mobility.

However, in the present work, such problems were much simplified, since individual grains could be studied and the ones having simple well defined bar structures used. Domain-wall bowing is taking place (see Fig. 3 and 4) which is capable of explaining the magnitude of the anomalous loss [I]. The theoretical anomaly factor due to the classic calculations of Polivanov [4] does not vary with frequency.

Carr [5] showed that the average domain-wall spacing decreased with increasing frequency, and considered that this feature could explain the cur- vature of the loss-per-cycle/frequency. The present experimental results do not show this feature.

5. Conclusions.

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Experiments on individual grains of silicon-iron in polycrystalline oriented production strip have shown that :

(a) There is an optimum grain diameter of about 0.7 cm that gives the minimum total power loss in 0.013 in (0.033 cm) thick material. Similar results are thought to apply to 0.010 in (0.025 cm) material

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THE RELATIONSHIP OF DOMAIN SPACING, GRAIN SIZE, SHEET THICKNESS C 1

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³⁸⁵

at a smaller grain length. (Grains tended to be shor- tened in the rolling direction.)

(b) In the grains chosen for detailed study with simple bar structures, the walls move uniformly and repetitively ; and the wall spacing is independent of frequency. Thus, modifications to Polivanov's theory, involving changes in domain-wall spacing and in the mobility spectrum with frequency, do not explain

the relationship between anomalous loss and frequency and it is necessary to include some degree of wall bowing.

The experimental findings could have practical siaficance, but it might be difficult to vary the grain size in a material on a production basis without, at the same time, changing the degree of preferred orientation and purity.

References

[lj OVERSHOTT (K.), F'REECE (I.) and THOMPSON (J.), Proc. I. E. E.. 1968. 115. 1840.

[2] Houz~ (G.), J. A ~ ~ Z . P~YS.', 1969, 38, 1089.

[3] BOON (C.) and ROBEY (J.), Proc. I. E. E., 1968, 115, 1535.

[4] POLIVANOV (K.), IZV. Akad. Nauk SSSR Ser piz, 1952, 16, 449.

[5] CARR (W.), J . Appl. Phys., 1959, 30, 905.