PERMANENT MAGNETS WITH CONVERGENT ANISOTROPIC STRUCTURE

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PERMANENT MAGNETS WITH CONVERGENT ANISOTROPIC STRUCTURE

Z. Blazek, V. Landa, P. Novák

To cite this version:

Z. Blazek, V. Landa, P. Novák. PERMANENT MAGNETS WITH CONVERGENT ANISOTROPIC STRUCTURE. Journal de Physique Colloques, 1985, 46 (C6), pp.C6-295-C6-298.

�10.1051/jphyscol:1985652�. �jpa-00224907�

PERMANENT MAGNETS WITH CONVERGENT ANISOTROPIC STRUCTURE

Z. Blazek, V. Landa and P. Nov5k

National Research I n s t i t u t e for MateriaZs, GpZetaZova 25, CS-113 12 Praha 1, CzechosZovakia

Rbsumc - De nouveaux aimants permanents prbsentent une orientation converpente des axes de facile aimantation des cristaux, ce qui concentre le flux

magngtique sur une section infbrieure 1 celle de l'aimant. Des aimants avec une structure convergente peuvent Gtre fabriqugs a partir de la plupart des matkriaux durs modernes qui prbsentent un champ coercitif et une aniso tropie magndtocristalline importants. Dans ce papier, les rbsultats obtenus avec des aimants ferrites et 2 base de terres rares sont prbsentgs et les densitgs de flux externe d'aimants prbsentant respectivement des orientations

convergentes et homogSnes sont comparbes.

Abstract - New permanent magnets have a convergent anisotropic crystal orientation of the axes of easy magnetization which concentrates the magnetic flux into a smaller cross-section than that of the magnet. Magnets with convergent structure can be manufactured from most modern hard magnetic material with high coercive force and magnetocrystalline anlsotropy. In this paper, the results obtained on ferrite and rare earth hard materials are presented and the external flux density of convergently and homogeneously oriented magnets made of the same materials compared.

INTRODUCTION

With a view to enhance air gap flux density we worked on magnets having an

anisotropic magnetic structure wherein the orientation of the axes of easy magneti- zatlon 1s convergent (Fig.

1

a). The convergent structure can have a linear,

curvilinear, continuous or discrete, two or three-dimensional configuration. Magnets of this type enable the value of flux density in the vicinlty of the pole to be substantially increased in comparison with conventional homogeneously oriented magnets. Raising the flux density supplied to the exterior is reached in a smaller cross-section than the cross-section of the magnet where the convergent orientation concentrates magnetic flux.

THEORY

The effect of convergent magnetic orientation on the external flux density was studied by means of a theoretical model. For calculations of flux density produced by continuously convergent magnets the polarization vector J was determined by a vector function of place which is constant in magnitude and varies only in direction The flux density was calculated from magnetic scalar potentlal

( 1 ) .

The flux

density components were found by differentiating under the integral in the equation for scalar potential and than numerical integrating the result.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985652

JOURNAL DE PHYSIQUE

F i g . 1 - S c h e m a t i c v i e w o f m a g n e t s w i t h v a r i o u s s t r u c t u r e s o f p o l a r i - z a t i o n v e c t o r s . S .

+ +

3

S p e c i a l l i n e a r form o f J ( r ) i l l u s t r a t e d i n F i g . 1 b / 2 / shows J b e i n g d i r e c t e d t o t n e f o c u s z on t h e z-axis o u t s i d e a c y l i n d r i c a l magnet.

It

can be s e e n i n F i g . 2 t h a t s u c h aOmapnet h a v i n g t h e dimension r a t i o V / R = I s u p p l i e s c o n s i d e r a b l y h i g h e r f l u x d e n s i t y component B Z i n t o a r e s t r i c t e d r e g i o n n e a r t h e s u r f a c e o f t h e magnet i n comparison w i t h homogeneously o r i e n t e d s a m ~ l e of t h e same dimensions. The n e a r e r zo t o t h e magnet s u r f a c e t h e h i g h e r B v a l u e i s o b t a i n e d i n t h e p r o x i m i t y of t h e s u r f a c e . A s i m p l e e x p r e s s i o n h a s beenzfound f o r t h e f l u x d e n s i t y produced by t h i s magnet i n t h e o o i n t zo

:

J ( p + I ) ~ .

( p 2 + 1) z

Bz(O,O,p)

=

- I n where p

=

-P

4 p21(p

+

1 ) 2

+

11 R

It s h o u l d be n o t e d t h a t t h e maximum f l u x d e n s i t y o c c u r s j u s t a t t h e s u r f a c e of t h e magnet, n o t i n t h e f o c u s .

I n c a s e o f d i s c r e t e l y c o n v e r p e n t magnets t h e assumption

-f

J

=

c o n s t . was u s e d f o r c a l c u l a t i o n . F l u x d e n s i t y was found by l i n e a r s u p e r p o s i t i o n of t e r m s a r i s i n p from each p a r t i c u l a r segment o f t h e c o n v e r g e n t magnet. These s i m o l i f y i n g assumptions a r e o f t e n made when c a l c u l a t i n g f l u x d e n s i t y produced by permanent magnets w i t h h i g h c o e r c i v e f o r c e and h i g h v a l u e o f t h e r e l a t i o n K / J ~ . High u n i a x i a l a n i s o t r o p y d e p r e s s e s f l u c t u a t i o n o f t h e p o l a r i z a t i o n v e c t o r J caused by nonuniform

d e m a p n e t i s a t i o n f i e l d s . YcCaig / 3 / g i v e s formulae f o r c a l c u l a t i o n of t h e magnetic

f i e l d produced by r e c t a n g u l a r p l a n e s w i t h uniform magnetic c h a r g e d e n s i t y .

C r a i k / 4 / mentioned c a l c u l a t i o n methods a p p r o p r i a t e f o r u n i f o r m l y magnetized

c y l i n d r e s . I n t h i s way we c a l c u l a t e d f l u x d e n s i t y produced by d i s c r e t e c o n v e r g e n t

magnets which a r e p r e p a r e d by a s s e m b l i n g of homogeneously o r i e n t e d segments.

SrnCog 15xlOx5mm

Theory experiment

0.5

C o n v e r g e n t

(a

-

^45'1

^-

^{0 .}

d e n s i t y c o m p o n e n t Bz(O, 0 , z) o f h o m o g e n e o u s l y ( z ? / R +

m )

a n d c o n v e r g e n t l y o r l e n t e d c y l i n d r i c a l m a g n e t a s a f u n c t i o n o f t h e d i s t a n c e z f r o m t h e p o l e s u r f a c e .

F i g . 3 - E x a m p l e o f d i s c r e t e l y c o n v e r g e n t SmCo5 m a g n e t .

C a l c u l a t e d c u r v e s a n d e x p e r i - m e n t a l l y o b t a i n e d d a t a o f f l u x d e n s i t y c o m p o n e n t B,(O, 0, z) v e r s u s d i s t a n c e z f r o m t h e p o l e s u r f a c e .

F i g . 4 - E x a m p l e o f d i s c r e t e l y c o n v e r g e n t SmCo5 m a g n e t . C a l c u l a t e d c u r v e s a n d e x p e r i m e n t a l l y o b t a i n e d d a t a o f f l u x d e n s i t y c o m p o n e n t

~ ~ ( 0 , 0,

z )

v e r s u s y -

~ o o r d i n a t e i n d i s t a n c e

s

= 0.8 m m .

JOURNAL DE PHYSIQUE

EXPERIMENTAL RESULTS

Various t y p e s of c o n v e r g e n t magnets were p r e p a r e d from e x i s t i n g h a r d magnetic m a t e r i a l s f o r t h e o r e t i c a l s t u d y and p r a c t i c a l a p p l i c a t i o n s . These magnets have two- o r t h r e e - d i m e n s i o n a l c o n v e r g e n t o r i e n t a t i o n . I n o r d e r t o compare t h e o r e t i c a l - l y c a l c u l a t e d v a l u e s w i t h e x p e r i m e n t a l d a t a we manufactured a w e l l d e f i n e d and s i m p l e SmCo5 magnet w i t h two l i n e a r l y c o n v e r p i n p d i r e c t i o n s a s shown i n F i g . l c . A s i m i l a r approach i s r e p o r t e d t o b e used i n c o n s t r u c t i o n of m u l t i p o l e mapnet s y s t e m s f o r f o c u s i n g and g u i d i n g charged p a r t i c l e beams 15/61. I n F i g . 3 we p r e s e n t

dependence of f l u x d e n s i t y component B, on d i s t a n c e from t h e magnet s u r f a c e which shows an e x t r e m e l y h i g h f l u x d e n s i t y and i t s g r a d i e n t i n t h e v i c i n i t y o f t h e s u r f a c e . T h i s i s a t y p i c a l f e a t u r e o f s t r o n g l y c o n v e r p e n t magnets a s w e l l a s a narrow peak on t h e dependence of B, on y - c o o r d i n a t e / F i g . 41. The h i g h e s t v a l u e o f Bz

=

0 , 6 8 T measured a t a d i s t a n c e 0.25 mm from t h e s u r f a c e of t h i s magnet a p p r o x i m a t e l y d o u b l e s t h e v a l u e o b t a i n e d on homopeneously o r i e n t e d sample of t h e same m a t e r i a l and s i z e .

With c o n v e r g e n t l y o r i e n t e d magnets h i g h e r gap d e n s i t i e s t h a t a r e u n a t t a i n a b l e w i t h common permanent magnets a r e f e a s i b l e 171. Using t h e s e a d v a n t a g e s promises improvement i n e f f i c i e n c y , o u t p u t and m i n i a t u r i z a t i o n i n c e r t a i n permanent magnet systems and development of new d e v i c e s n o t p o s s i b l e w i t h c o n v e n t i o n a l a n i s o t r o p i c magnets.

REFERENCES

( 1 ) Brown, W.F.

: M a g n e t o s t a t i c P r i n c i p l e s i n Ferromagnetism.

North-Holland, Amsterdam 1962

(2) Blazek, Z . , Landa, V. and Novhk, P.

: 1984 D i g e s t s INTERMAG

Conf. Hamburg, North-Holland (1984), 75

(3) McCaig,

M. :

Proc. 3 r d Eur. Gonf. on Hard Magn. Mat. Amsterdam (1974), 33 (4) C r a i k , D . J . and H a r r i s o n , A . J .

: P r o c . 3 r d Eur. Conf. on Hard Hagn. Mat.

Amsterdam (1974), 170

(5) Halbach, K.

: P r o c . 5 t h I n t l . Workshop Rare-Earth

- Co Perm. Mag., ed. Univ. o f Dayton, Ohio (1981), 7 3

(6) P a u t h e n e t , R.

: C.R. Acad. S c i e n c e s P a r i s , t . 292, SGv.

I1 ( 1 9 8 1 ) , 1251 ( 7 ) Blazek, Z. and Landa, V.

: P r o c . Conf. " F e r i t y a n e l i n e h r n i odpory",

Sumperk, Czechoslovakia, (1980), 44