INFLUENCE OF THE MAGNETISING FREQUENCY ON THE BARKHAUSEN NOISE POWER OF NON-ORIENTED Si-STEEL SHEETS

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INFLUENCE OF THE MAGNETISING FREQUENCY ON THE BARKHAUSEN NOISE POWER OF

NON-ORIENTED Si-STEEL SHEETS

M. Komatsubara, J. Porteseil

To cite this version:

M. Komatsubara, J. Porteseil. INFLUENCE OF THE MAGNETISING FREQUENCY ON THE

BARKHAUSEN NOISE POWER OF NON-ORIENTED Si-STEEL SHEETS. Journal de Physique

Colloques, 1985, 46 (C6), pp.C6-175-C6-178. �10.1051/jphyscol:1985630�. �jpa-00224878�

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JOURNAL DE PHYSIQUE

Colloque C6, suppldment a u n09, Tome 46, s e p t e m b r e 1985 page C6-175

I N F L U E N C E OF THE M A G N E T I S I N G FREQUENCY ON THE BARKHAUSEN N O I S E POWER OF NON-ORIENTED S i - S T E E L SHEETS

M. Komatsubara and J . L . ~ o r t e s e i l '

S i l i c o n S t e e l Laboratory of Kawasaki S t e e l Corp., Chiba, Japan

+Laboratoire Louis Ne'eZ, CNRS-USMG, 166 X , 38042 GrenobZe Cedex, France R6sum6

-

On 6 t u d i e 1 1 6 n e r g i e par c y c l e Ef du b r u i t Barkhausen dans d e s f e u i l l e s d ' a c i e r a u s i l i c i u m non o r i e n t 6 en f o n c t i o n d e l a f r 6 q u e n c e f m du champ m a g n 6 t i s a n t . Ef c r o i t d ' a b o r d e x p o n e n t i e l l e m e n t p u i s p l u s l e n t e m e n t , comme f $

.

Ces r 6 s u l t a t s m o n t r e n t que l e s i m p u l s i o n s Barkhausen t e n d e n t a s e grouper l o r s q u e f m c r o i t . On d i s c u t e l e s r e s u l t a t s en t e r m e s de f o n c t i o n de d i s t r i b u t i o n d e s i n t e r v a l l e s e n t r e s a u t s .

A b s t r a c t

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The Barkhausen n o i s e e n e r g y per c y c l e ( E f ) of n o n - o r i e n t e d s i l i c o n s t e e l s h e e t s was measured a s a f u n c t i o n of t h e f r e q u e n c y f, of t h e m a g n e t i z i n g f i e l d . A s f m i n c r e a s e s , Ef f i r s t grows e x p o n e n t i a l l y , t h e n i n c r e a s e s more g r a d u a l l y l i k e f$. T h i s shows t h a t t h e tendency t o c l u s t e r i n g of Barkhausen p u l s e s i s enhanced by i n c r e a s i n g f,. The r e s u l t s a r e d i s c u s s e d i n t e r m s of t h e d i s t r i b u t i o n f u n c t i o n of time i n t e r v a l s between p u l s e s .

I

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I N T R O D U C T I O N

Much a t t e n t i o n was p a i d t o t h e d i s c o n t i n u o u s movements of 180" Bloch w a l l s i n c e t h e y a r e r e l a t e d t o t h e p h y s i c a l o r i g i n o f eddy c u r r e n t l o s s e s i n t e c h n i c a l m a t e r i a l s , i n p a r t i c u l a r SiFe s h e e t s / I / . However,the d e t a i l e d dynamical and s t a t i s t i c a l f e a t u r e s of t h e s e movements a r e n o t e n t i r e l y e l u c i d a t e d a t p r e s e n t .

I n t h e c r u d e s t models / 2 , 3 / , t h e Barkhausen n o i s e power (BNP) i s r e g a r d e d a s simply p r o p o r t i o n a l t o t h e m a g n e t i s i n g f r e q u e n c y f,, s o t h a t t h e e n e r g y of Barkhausen n o i s e per c y c l e E~ =

1%

BNP.dt ( T o p e r i o d of c y c l e s ) is e x p e c t e d t o be c o n s t a n t . T h i s p r e d i c t i o n p o o r l y a g r e e s w i t h experiment / 4 / . R e c e n t l y t h e l a c k of p r o p o r t i o n a l i t y of t h e BNP t o f m was e x p l a i n e d by a v a r i a b l e d e g r e e of c l u s t e r i n g among Barkhausen p u l s e s , which t e n d s t o d e c r e a s e a t h i g h m a g n e t i z i n g f r e q u e n c i e s u n t i l a l l p u l s e s u l t i m a t e l y behave l i k e independent e v e n t s / 5 / . I n t h e p r e s e n t s t u d y , Ef was measured a s a f u n c t i o n of f m i n v a r i o u s t y p e s of n o n - o r i e n t e d s i l i c o n s t e e l s h e e t s . The measurements were performed a t v e r y low m a g n e t i z i n g f r e q u e n c i e s s i n c e t h e Barkhausen n o i s e was s c a r c e l y i n v e s t i g a t e d i n t h i s range.

I1

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EXPERIMENTAL METHODS

The s h e e t s of commercial n o n - o r i e n t e d s i l i c o n s t e e l from Kawasaki S t e e l Corp.

(approximate t h i c k n e s s 0.5 mm) were s p a r k - c u t t o t h e shape of r i n g s ( i n n e r and o u t e r d i a m e t e r s : 93.5 and 121 - 5 mm)

.

T h e i r chemical c o m p o s i t i o n s and r e l e v a n t p r o p e r t i e s a r e l i s t e d i n Table I ( a l t h o u g h t h e r e s u l t s were c o h e r e n t t h r o u g h o u t t h e s e r i e s o f m a t e r i a l s , we r e s t r a i n e d o u r s e l v e s , f o r t h e c l e a r n e s s o f t a b l e s and f i g u r e s , t o t h r e e specimens d e n o t e d h e r e a f t e r by A , B and C ) . A primary c o i l o f nl = 250 e q u a l l y d i s t r i b u t e d t u r n s Of copper w i r e was wound on e v e r y specimen, t o g e t h e r w i t h two secondary windings ^:n2 = 20 and 50 t u r n s . The m a g n e t i z i n g c u r r e n t was f e d t o t h e primary c o i l by a sawtooth g e n e r a t o r which could s u p p l y a maximum f i e l d of 200 ~ . m - l , which proved t o be a s u f f i c i e n t v a l u e ( 2 He a t l e a s t ) . I n o u r e x p e r i m e n t s , t h e m a g n e t i z i n g f r e q u e n c y f, was v a r i e d from 1.29 x 10-3 t o 2.84 x 10-2 Hz.

The n o i s e s i g n a l V ( t ) a t t h e o u t p u t of t h e s e c o n d a r y winding was f i r s t a m p l i f i e d by a h i g h - g a i n ( 1 0 5 ) , broadband g a l v a n o m e t r i c a m p l i f i e r . The v o l t a g e V ( t ) t h u s o b t a i n e d was t h e n s q u a r e d and a d e q u a t e l y f i l t e r e d by a s t a n d a r d s o l i d - s t a t e d e v i c e , which

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985630

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JOURNAL DE PHYSIQUE

TABLE 1

chemical c o n t e n t % t h i c k n e s s d e n s i t y BS H c Grain s i z e Specimen

S i A 1 Mn mm g/cm3 T e s l a A/M I J ~

u l t i m a t e l y y i e l d e d t h e BNP a s : BNP = 1 / T

1;

v 2 ( t ) d t . The time c o n s t a n t T was s e t t o 1.4 s. We checked t h e p e r f e c t q u a d r a t i c response of t h e measuring chain by feeding t o i t a sequence of c a l i b r a t e d imput s i g n a l s . Moreover, we checked t h a t t h e BNPt s measured with both secondary windings were e x a c t l y p r o p o r t i o n a l t o 202 and 502

.

111

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RESULTS AND DISCUSSION

Fig.1 shows t h e dependence of t h e BNP on t h e magnetizing f i e l d H f o r v a r i o u s frequen- c i e s f,. Only t h e r e s u l t s p e r t a i n i n g t o t h e ascending loop branches a r e p r e s e n t e d :

obviously symmetrical phenomena t a k e p l a c e on t h e descending branches. A s could be expected, t h e n o i s e power r a p i d l y i n c r e a s e s with f,, and i t s peak value is always l o c a t e d near Hc. However t h e t a i l of t h e power d i s t r i b u t i o n g r a d u a l l y extends t o higher f i e l d s a s f m i n c r e a s e d . Simultaneously t h e f i n e d e t a i l s of t h e n o i s e s t r u c t u r e a r e g r a d u a l l y l o s t . A d i r e c t o s c i l l o s c o p i c o b s e r v a t i o n of t h e Barkhausen n o i s e b e f o r e t h e o ~ e r a t i o n of q u a d r a t i c average is performed shows t h a t t h e s i g n a l c o n t a i n s more

A: 3.34Ol0SiS':eel

- - -

I

0 Hc

H

^Hm

Field ( A l m )

Fig. 1 - Noise power h a l f - c y c l e p r o f i l e s of sample A on r i s i n g magnetizing branch.

a ) f m = 1.29 x 10-3 Hz ; b) = 2.59 x 10-3 Hz ; c = 3.88 x 10-3 H Z ; d ) 11.64 x 10-3 HZ.

The PH s c a l e of t h e I'dtt r e c o r d i n g was reduced by 1/10. Each PH o r i g i n is s h i f t e d upwards i n t h e a . b , c , d sequence ( d o t t e d l i n e s ) .

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a n d more low f r e q u e n c i e s as f m is i n c r e a s e d , e s p e c i a l l y n e a r Hc. The n o i s e e n e r g y p e r c y c l e Ef is e a s i l y o b t a i n e d by g r a p h i c a l i n t e g r a t i o n o f t h e BNP o v e r t h e e n t i r e c y c l e ( a s c e n d i n g + d e s c e n d i n g b r a n c h ) . F i g . 2 i s a p l o t o f Ef vs.fm. The dependence o f Ef is e x p o n e n t i a l a t low f r e q u e n c i e s , t h e n s e t t l e s down t o a , s l o w e r r a t e .

1

0 5 10 15 20 25 30

frn ( X I O - ~ H Z Magnetizing Frequency

F i g . 2

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Frequency dependence o f Barkhausen n o i s e e n e r g y p e r c y c l e : comparison o f measured a n d c a l c u l a t e d c u r v e s . A = 3.34 % S i S t e e l ; B = 1.85 $ S i S t e e l ;

C = 1.07 % S i S t e e l .

T h i s i n c r e a s e c a n be e x p l a i n e d by a s s u m i n g t h a t a t v e r y low f r q u e n c i e s t h e jumps behave,quasi-independently, t h e n b e g i n t o c l u s t e r as f m is i n c r e a s e d . Then c o r r e - l a t e d jumps r e s u l t i n s c a r c e r b u t s t r o n g e r v o l t a g e p u l s e s a n d , s i n c e t h e n o i s e power i s a q u a d r a t i c a v e r a g e , i n a n i n c r e a s e d BNP. An e x a c t c a l c u l a t i o n c a n n o t be p e r - formed w i t h o u t t h e e x a c t knowledge o f t h e s t a t i s t i c a l f e a t u r e s o f t h i s random pro- c e s s , which a r e summarised by t h e t r a n s i t i o n d e n s i t y M(Ar, A t ) / I / . A s t h i s p i e c e o f i n f o r m a t i o n was l a c k i n g , we t a c k l e d t h e problem i n t h e c r u d e f o l l o w i n g way. L e t N be t h e t o t a l number o f e l e m e n t a r y jumps p e r c y c l e a n d f ( t ) t h e n o r m a l i s e d p r o b a b i l i t y d i s t r i b u t i o n which would d e s c r i b e t h e i r t i m e i n t e r v a l s i f t h e y were i n d e p e n d e n t l y t r i g g e r e d . Assume t h a t , f o r a g i v e n m a g n e t i z i n g f r e q u e n c y , t h e e l e m e n t a r y jumps g e t c o r r e l a t e d i f t h e i r i n d i v i d u a l t r i g g e r i n g i n s t a n t s a r e s e p a r a t e d by a time i n t e r v a l less t h a n a g i v e n d u r a t i o n T, a n d t h a t + h e i r a m p l i t u d e s a r e t h e n j u s t a d d e d up. The number n o f c l u s t e r s is g i v e n by n = N

I

^O f ( t ) d t , a n d t h e a m p l i t u d e V o f one c l u s t e r is p r o p o r t i o n a l t o t h e number o f e l e m e n t a r y jumps i n i t , t h a t is t o N/n =

l/(To f ( t ) d t . The n o i s e e n r g y p e r c y c l e , which i s p r o p o r t i o n a l t o nVZ, c a n be f i n a l l y exp:essed a s Ef = E; n ( N / n ) 2 = E; N / ( T ~ f ( t ) d t where E0 is t h e n o i s e e n e r g y p e r c y c l e when c l u s t e r i n g d o e s n o t t a k e place: Assume f i n a l l y t % a t t h e t i m e i n t e r - v a l s t between o u l s e s s h r i n k i n p r o p o r t i o n w i t h t h e i n v e r s e o f t h e t i m e d e r i v a t i v e o f t h e f i e l d :

I

fi

I -

f,. By u s i n g t h e r e d u c e d time t f = t

I fi 1

a n d r e m a r k i n g t h a t To is much l a r g e r t h a n t h e t i m e i n t e r v a l s , Ef can be w r i t t e n a s E;

N/I:, I

f ( t f ) d t f

.

^W^e

t o o k f o r f ( t ) t h e d i s t r i b u t i o n f o u n d by Sawada /6/ a n d c o n f i r m e d by B i t t e l and W e s t e r b o e r / 7 / : f ( t ) = b 2 t e-bt. I t c a n be n o t i c e d t h a t

1

^H

I

⁼ 0.899 ~ . m - l . S - l i n S a w a d a f s e x p e r i m e n t s , w h e r e a s

I

^H

I

⁼ 1.03 ~ . m - l . ~ - l i n o u r s . Then Ef i s found e q u a l t o E; e x p ( a

I

fi

I

^{) /} ^[I ⁺ ^a

I

H

I

I ( a = r b ) . T h i s e x p r e s s i o n a g r e e s w e l l w i t h e x p e r i m e n t a t low m a g n e t i z i n g f r e q u e n c i e s ( F i g . 2 ) . t h e n d e v i a t e s from t h e e x p e r i m e n t a l d a t a . A l o g - l o g p l o t ( F i g . 3 ) shows t h a t a t h i g h e r f r e q u e n c i e s Ef i n c r e a s e s l i k e f 2 . T h i s s u g g e s t s t h a t f ( t ) d e c a y s p r o p o r t i o n a l t o t - 3 i n s t e a d o f e m b t , r e s u l t i n g i! a h i g h e r p r o b a b i l i t y o f f i n d i n g l o n g t i m e i n t e r v a l s .

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1 10 100 f r n

( X ~ O - ~ H Z )

Magnetizing Frequency

Fig. 3

-

Log-Log p l o t s of Ef vs.fm. The s l o p e s of t h e s t r a i g h t region a r e 1 .98 (A), 1.99 ( B ) , 2.07 ( C ) .

I V

-

CONCLUSIONS

The Barkhausen n o i s e power was i n v e s t i g a t e d i n non-oriented Fe-Si s h e e t s a t very low magnetizing frequencies. I n d i v i d u a l jumps t e n d t o c l u s t e r a s t h e frequencies i n c r e a s e s . A simple c l u s t e r model involving Sawadats d i s t r i b u t i o n of time i n t e r v a l p a r t i a l l y accounts f o r t h e experimental r e s u l t s . However, a c l o s e r a n a l y s i s of t h e d a t a b r i n g s t o l i g h t t h e simple physical conclusions t h a t a change i n t h e magnetizing frequency does not merely r e s u l t i n changing t h e time s c a l e of jump sequences by t h e same f a c t o r .

I t is now well e s t a b l i s h e d ( 1 ) t h a t eddy c u r r e n t l o s s e s s t r o n g l y depend on t h e c o r r e l a t i o n of magnetization jumps, because they a r e proportional t o t h e squared volumes which f e a t u r e a coherent i r r e v e r s i b l e behaviour. I t is worth t o s t r e s s t h a t t h e BNP r e f l e c t s t h e same type of second-order averaging of pulse sequences, s o t h a t both phenomena a r e expected t o be c l o s e l y linked. For i n s t a n c e t h e n o i s e energy per c y c l e a t vanishing f r e q u e n c i e s E; seems t o behave l i k e t h e square r o o t of t h e g r a i n s i z e d , which is known t o be an e s s e n t i a l parameter of eddy c u r r e n t l o s s e s .

REFERENCES

/ I / B e r t o t t i , G., J. Appl. Phys. 52 (1984) 4339.

/2/ Krumhansl, J.A. and Beyer, R.T., J . Appl. Phys. 20 (1949) 582 /3/ Haneman D . , J. Appl. Phys. 2 2 (1955) 355.

/ 4 / B i o r c i , G. and P e s c e t t i , D. , J. Appl. Phys.

28

(1957) 777.

/5/ Mazzetti, P. and Montalenti, G., P r o c . I n t : ~ o n f . on Magnetism, Nottingham (1964) 701.

1 6 1 Sawada, H., J . Phys. Soc. Japan, 1 (1952) 575

/7/ B i t t e l , H. and Westerboer, I . , Ann. Phys. Lpz., 7_ (1 959) 203