I MAGNETGUIDELINES

I. Basic physics of permanent magnet materials ._

II. Design relationships, figures of merit and optimizing techniques

Ill. Measuring

IV. Magnetizing

V. Stabilizing and handling

VI. Specifications, standards and communications

VII. Bibliography

INTRODUCTION

This guide is a supplement to our MMPA Standard No. 0100. It relates theinformation in the Standard to permanent magnet circuit problems. The guide isa bridge between unit property data and a permanent magnet component havinga specific size and geometry in order to establish a magnetic field in a givenmagnetic circuit environment. The MMPA 0100 defines magnetic, thermal,physical and mechanical properties. The properties given are descriptive innature and not intended as a basis of acceptance or rejection. Magnetic measure-ments are difficult to make and less accurate than corresponding electrical mea-surements. A considerable amount of detailed information must be exchangedbetween producer and user if magnetic quantities are to be compared at twolocations. MMPA member companies feel that this publication will be helpful inallowing both user and producer to arrive at a realistic and meaningful specifica-tion framework.

AcknowledgmentThe Magnetic Materials Producers Association acknowledges the out-standing contribution of Rollin J. Parker to this industry and designersand manufacturers of products usingpermanent magnet materials. MrParker the Technical Consultant to MMPA compiled and wrote thisdocument. We also wish to thank the Standards and Engineering Com-mittee of MMPA which reviewed and edited this document.

December 1987 3MJuly 1988 5MAugust 1996 1MDecember 1998 1 M

CONTENTS

The guide is divided into the following sections:

Glossary of terms and conversion tables-A very important starting point since the whole basis ofcommunication in the magnetic material industry involvesmeasurement of defined unit properties. . . . . . . . . . . . .l

I. Basic physics of permanent magnet materials-An overview of the physics of permanent magnetism is felt tobe an important part of learning about permanent magnets. . . . . . .4

II. Design relationships, figures of meritand optimizing techniques-Relationships are developed that allow materials to becompared. The figures of merit are a guide to the best choiceof unit properties for effectively using the energy conversionprocess in electromagnetic devices and systems. . . . . . . . . . . . .7

III. Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...12

IV. Magnetizing . . . . . ~ , . . . . . . . . . . . . . . .18

V. Stabilizing and handling. . . . . . . . . . . . . . .22

VI. Specifications, standards and communications . . . . . . . . . . .25

VII. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

The sections on measuring, magnetizing and stabilizing contain the basicconsiderations that allow the user to choose the techniques most suitable fora specific permanent magnet component and operating environment.

GLOSSARY OF TERMS

As Area of the air gap, or the cross sectional area of thean gap perpendicular to the flux path, is the averagecross sectional area of that portion of the air gap withinwhich the application interaction occurs. Area is mea-sured in sq. cm. in a plane normal to the central flux lineof the air gap.

A,,, Area of the magnet, is the cross sectional area ofthe magnet perpendicular to the central flux line, mea-sured in sq. cm. at any point along its length. In design,A,,, is usually considered the area at the neutral sectionof the magnet.

B Magnetic induction, is the magnetic field induced bya field strength, H, at a given point. It is the vector sum,at each point within the substance, of the magnetic fieldstrength and resultant intrinsic induction. Magnetic in-duction is the flux per unit area normal to the directionof the magnetic path.

B, Remanent induction, is any magnetic inductionthat remains in a magnetic material after removal of anapplied saturating magnetic field, H,. (Bd is the mag-netic induction at any point on the demagnetizationcurve: measured in gauss.)

B,/H, Slope of the operating line, is the ratio of theremanent induction, Bd, to a demagnetizing force, H,.It is also referred to as the permeance coefficient, shearline, load line and unit permeance.

B,H, Energy product, indicates the energy that a mag-netic material can supply to an external magnetic circuitwhen operating at any point on its demagnetizationcurve; measured in megagauss-oersteds.

vw?lax Maximum energy product, is the maximumproduct of (BtlHtt) which can be obtained on the demag-netization curve.

Bi, (or J) Saturation intrinsic induction, is the maxi-mum intrinsic induction possible in a material.

B, Magnetic induction in the air gap, is the averagevalue of magnetic induction over the area of the air gap,A,; or it is the magnetic induction measured at a spe-cific point within the air gap; measured in gauss.

Bi (or J) Intrinsic induction, is the contribution of themagnetic material to the total magnetic induction, B. Itis the vector difference between the magnetic inductionin the material and the magnetic induction that wouldexist in a vacuum under the same field strength, H. Thisrelation is expressed by the equation:

Bi=B-H

where: Bi = intrinsic induction in gauss; B = magneticinduction in gauss; H = field strength in oersteds.

B, Recoil induction, is the magnetic induction thatremains in a magnetic material after magnetizing andconditioning for final use; measured in gauss.

B, Magnetic induction, at the point of the maximumenerajr product (BH),,,,; measured in gauss.

B, Residual induction (or flux density), is the magneticinduction corresponding to zero magnetizing force in amagnetic material after saturation in a closed circuit;measured in gauss.

f Reluctance factor, accounts for the apparent mag-netic circuit reluctance. This factor is required due tothe treatment of H, and H, as constants.

F Leakage factor, accounts for flux leakage from themagnetic circuit. It is the ratio between the magneticflux at the magnet neutral section and the average fluxpresent in the air gap. F = (B, A,,)/(B, Ag).

F Magnetomotive force, (magnetic potential differ-ence), is the line integral of the field strength, H, be-tween any two points, p1 and pz.

I;=;‘Hdl

Pl

F = magnetomotive force in gilbertsH = field strength in oerstedsdl = an element of length between the two points, incentimeters.

H Magnetic field strength, (magnetizing or demagne-tizing force), is the measure of the vector magneticquantity that determines the ability of an electric cur-rent, or a magnetic body, to induce a magnetic field at agiven point; measured in oersteds.

H, Coercive force of a material, is equal to the demag-netizing force required to reduce residual induction, B,,to zero in a magnetic field after magnetizing to satura-tion; measured in oersteds.

H,i Intrinsic coercive force of a material indicates itsresistance to demagnetization. It is equal to the demag-netizing force which reduces the intrinsic induction, Bitin the material to zero after magnetizing to saturation;measured in oersteds.

1

H, is that value of H corresponding to the remanentinduction, Bd; on the demagnetization curve, measuredi n o e r s t e d s .

H, is that value of H corresponding to the recoil induc-tion, B,; measured in oersteds.

H, is the magnetic field strength at the point of themaximum energy product (BH)maX; measured inoersteds.

pre recoil permeability, is the average slope of the re-coil hysteresis loop. Also known as a minor loop.

4 magnetic flux, is a contrived but measurable conceptthat has evolved in an attempt to describe the “flow” of amagnetic field. Mathematically, it is the surface integralof the normal component of the magnetic induction, B,over an area. A.

+=ijB*dA

H, Net effective magnetizing force, is the magnetiz-ing force required in the material, to magnetize to satu-ration measured in oersteds.

J, see Bi Intrinsic induction.

where:C$ = magnetic flux, in maxwellsB = magnetic induction, in gaussdA = an element of area, in sauare centimetersWhen the magnetic induction, B, is uniformly distrib-uted and is normal to the area, A, the flux, 4 = BA.

J, see Bi, Saturation intrinsic induction.

Es Length of the air gap, is the length of the path of thecentral flux line of the air gap; measured in centimeters.

A closed circuit condition exists when the externalflux path of a permanent magnet is confined with highpermeability material.

U,,., Length of the magnet, is the total length of magnetmaterial traversed in one complete revolution of thecenter-line of the magnetic circuit; measured in centi-meters.

P,.,,ID Dimension ratio, is the ratio of the length of amagnet to its diameter, or the diameter of a circle ofequivalent cross-sectional area. For simple geometries,such as bars and rods, the dimension ratio is related tothe slope of the operating line of the magnet, BdH,.

The demagnetization curve is the second (or fourth)quadrant of a major hysteresis loop. Points on this curveare designated by the coordinates Bd and Hd.

A fluxmeter is an instrument that measures the changeof flux linkage with a search coil.

The gauss is the unit of magnetic induction, B, in thecgs electromagnetic system. One gauss is equal to onemaxwell per square centimeter.

P Permeance, is the reciprocal of the reluctance, R,measured in maxwells per gilbert.

R Reluctance, is somewhat analogous to electrical re-sistance. It is the quantity that determines the magneticflux, 4, resulting from a given magnetomotive force, F.

A gaussmeter is an instrument that measures the in-stantaneous value of magnetic induction, B. Its prin-ciple of operation is usually based on one of the follow-ing: the Hall-effect, nuclear magnetic resonance(NMR), or the rotating coil principle.

where:R = F/qb

The gilbert is the unit of magnetomotive force, F, in thecgs electromagnetic system.

R = reluctance, in gilberts per maxwellF = magnetomotive force, in gilberts4 = flux, in maxwells

T, Curie temperature !, is the transition temperatureabove which a material loses its magnet properties.

T max Maximum service temperature, is the maximumtemperature to which the magnet may be exposed withno significant long range instability or structuralchanges.

Vg Air gap volume, is the useful volume of air or non-magnetic material between magnetic poles; measuredin cubic centimeters.

p permeability, is the general term used to express vari-ous relationships between magnetic induction, B, andthe field strength, H.

A hysteresis loop is a closed curve obtained for a mate-rial by plotting (usually to rectangular coordinates) cor-responding values of magnetic induction, B, for ordi-nates and magnetizing force, H, for abscissa when thematerial is passing through a complete cycle betweendefinite limits of either magnetizing force, H, or mag-netic induction. B.

Irreversible losses are defined as partial demagnetiza-tion of the magnet, caused by exposure to high or lowtemperatures external fields or other factors. Theselosses are recoverable by remagnetization.Magnets can be stabilized against irreversible losses bypartial demagnetization induced by temperature cyclesor by external magnetic fields

A keeper is a piece (or pieces) of soft iron that is placedon or between the pole faces of a permanent magnet to

decrease the reluctance of the air gap and thereby re-duce the flux leakage from the magnet. It also makesthe magnet less susceptible to demagnetizing influ-ences.

nates (Bd,Hd) or that point within the demagnetizationcurve defined by the coordinates (B,,H,).

Leakage flux is flux, 4, whose path is outside the usefulor intended magnetic circuit; measured in maxwells.

An oriented (anisotropic) material is one that has bet-ter magnetic properties in a given direction.

The major hysteresis loop of a material is the closedloop obtained when the material is cycled between posi-tive and negative saturation.

A permeameter is an instrument that can measure, andoften record, the magnetic characteristics of a speci-men.

The maxwell is the unit of magnetic flux in the cgselectromagnetic system. One maxwell is one line ofmagnetic flux.

Reversible temperature coefficients are changes influx which occur with temperature change. These arespontaneously regained when the temperature is re-turned to its original point.

The neutral section of a permanent magnet is definedby a plane passing through the magnet perpendicular toits central flux line at the point of maximum flux.

The oersted is the unit of magnetic field strength, H, inthe cgs electromagnetic system. One oersted equals amagnetomotive force of one gilbert per centimeter offlux path.

Magnetic saturation of a material exists when an in-crease in magnetizing force, H, does not cause an in-crease in the intrinsic magnetic induction, B, of the ma-terial.

An open circuit condition exists when a magnetizedmagnet is by! itself with no external flux path of highpermeability~~material.

A search coil is a coiled conductor, usually of knownarea and number of turns, that is used with a fluxmeterto measure the change of flux linkage with the coil.

The operating line for a given permanent magnet cir-cuit is a straight line passing through the origin of thedemagnetization curve with a slope of negative B,/Hd.(Also known as permeance coefficient line.)

The temperature coefficient is a factor which de-scribes the reversible change in a magnetic propertywith a change in temperature. The magnetic propertyspontaneously returns when the temperature is cycledto its original point. It usually is expressed as the per-centage change per unit of temperature.

The operating point of a permanent magnet is thatpoint on a demagnetization curve defined by the coordi-

An unoriented (i,sotropic) material has equal mag-netic properties in all directions.

QUANTITIES, SYMBOLS, UNITS AND CONVERSION FACTORS

Quantity Unit, C.G.S. Unit, S.I.(S.I.)/(C.G.S.)

Ratio*

Length 1 centimeter, cmMass gram, gTime t second , sElectric current I abampereTemperature T degree Celsius, “CForce dyne, dyn

Work or energy erg = dyn.cmPower erg/sMagnetic flux @ maxwellFlux density B g a u s s , GMagnetic constant p.

(permeability of space) (unity)Intensity of magnetization J* * e.m.u. = Gl4a

= dyn/cm20eMagnetic dipole moment j e.m.u. = dyn.cm/Oe

Magnetic pole strength p e.m.u.Magnetic field strength H oersted, OeMagnetomotive force F gilbert, GbPermeability (abs.) b = B/H -Permeability (rel.) p = BIpoHReluctance, Rnz gilbert/maxwellPermeance (inverse of reluctance) maxwelligilbertSusceptibility (rel. vol.) % = lIpoH e.m.u.

‘A quantity in S.I. units must he multiplied by this I-atio to convert it to C.G.S. Lmits**Also referred to zis magnetic polarization in the S.I. approach.

3

meter, mkilogram, kgsecond, sampere, Akelvin, Knewton , Njoule, J = Nmwatt, W = J/sweber, Wbtesla, T = Wb/m2

henry/meter, H/mtesla, T = N/Am

Wb m = Nm”/A

W bampere/meter, Aimampere, A

henry/meter, H/m

l/henry, H-l

henry , Hratio

102103110-l(K = “C + 273.16)105

10:107

108

10”

lOi,’lO”l47r

_’ 10’@/4?r

lO”l4ir47rilO”47rllO

107147r147r110”

lO”137rl/-I*

PART I. BASIC PHYSICS AND ORlGlN OFPERMANENT MAGNET BEHAVIOR

GUIDELINES

About 60 years ago French physicist Pierre Weiss pos-tulated that a ferromagnetic body must be composed ofsome regions or domains, each of which is magnetizedto saturation level, but the direction of the magnetiza-tion from domain to domain need not be parallel. Thus amagnet, when demagnetized, was only demagnetizedfrom the viewpoint of an observer outside the material.Man-made fields only serve as a control in changing thebalance of potential energy within a magnet. This the-ory still provides the basis of our highly sophisticatedbody of knowledge that explains quite satisfactorily theobserved properties of ferromagnetic mate, ials and pro-vides an intelligent guide for the search for improvedmaterials.

The inherent atomic magnetic moment associated withsuch elements as iron, cobalt, nickel and many com-pounds is believed to originate from a net unbalance ofelectron spins in certain electron shells. For example, iniron in the third shell there are more electrons spinningin one direction than in the opposite direction. Havingan inherent atomic magnetic moment is a necessary butnot a sufficient condition for ferromagnetism to be ex-hibited. Additionally, there must be cooperative inter-atomic exchange forces that rnaintain neighboring at-oms parallel. Little is known of the exact nature ormagnitude of these forces but observations suggestthey are electrostatic. It has been pointed out that inferromagnetic materials the ratio of interatomic dis-tance to the diameter of the shell in which the unbalanceexists is unusually large compared to this ratio in mate-rials which do not exhibit ferromagnetism.

In Figure I-l an exploded view of a ferromagnetic vol-ume is shown. The relative dimensions of the atom,domain, crystal and a measurable volume are noted inthe figure.

102 CRYSTALS

ATOM

UNiT CRYSTAL

106 DOMAINS

ATOMS

Figure I-l. Exploded assembly of ferromagnetic volume. Figure I-3. Bloch wall between ferromagnetic domains.

The atomic exchange force also produces magnetostric-tive effects and is associated with the crystalline struc-ture of magnetic materials in a way that exhibits anisot-ropy or directional dependence with respect to thecrystal axis.

In Figure I-2 the directional dependence is shown foriron. The easy axis of magnetization is the cube (100)

25K

20K

15K

IOK 1

5K

0 2 0 0 400 6 0 0 6 0 0-H- (oersteds)

Figure I-2. Directional dependence (iron).

We can view the magnetic domain as a region in whichthe atomic moments cooperate to allow a common mag-netic moment which may be rotated by externally ap-plied fields. Domain size, not a fundamental constant ofphysics, varies widely depending on composition, pu-rity and state of strain of the material as well as somevery important energy relationships. Figure I-3 shows aboundary region between two domains. This boundaryregion and its significance was first proposed by Bloch.

4

The Bloch wall is a transition region containing manyatomic planes. The 180 degree change in magnetizationmust occur over a considerable distance to minimize thepotential energy in the wall. However, the width of thewall will be restricted because of the restraining influ-ence of crystal anisotropy (directional dependence ofmagnetism with respect to crystalline axis). Figure I-4illustrates an additional energy relationship which influ-ences the size of the domain and involves the magneto-static or field energy surrounding a magnetized volume.A magnetized volume tends to subdivide itself. It will beenergetically possible for subdivision to occur as shownin Figure I-4 until the decrease in magnetostatic energyis less than the potential energy associated with theBloc11 wall foundation. At this point we might say thatthe magnetization vector arrangement associated withdomain volumes in a ferromagnetic material resultsfrom a complex energy balance so arranged that thetotal potential energy of the system is a minimum. Ex-ternally applied fields to magnetize or demagnetize onlydisturb the balance of the potential energies involvedand our familiar S-shaped magnetization curves are re-cords of the change in balance with respect to the exter-nal influence. Figure I-5 shows the action pictorially as abar of ferromagnetic material is magnetized.

(4 (WFigure I-4. Domain subdivision.

atMAGNETIZED

:A,,,,, MAGNETIZATION

SUDDEN REVERSALS COMPLETE% -Hd

H

A

:ATURATED. DOMAINS ROTATED INHIGH FIELD

Figure I-5. Pictorial explanation of magnetization curve ina ferromagnetic bar.

The demagnetized condition (A) results from an inter-nal arrangement with mutually cancelling directions ofmagnetization vectors. In region (B) with low values ofexternal field the action is primarily one of domainboundary stretching, usually around imperfections.

This is a reversible process (reversible magnetizationprocess is one in which the magnetization vectors re-orient to their original position after the field (H) is re-moved). As the field is increased, region (C) domainboundaries break away and move through the material.The more favorably oriented regions grow at the ex-pense of their less favorably oriented neighbors. As aresult, a large increase in magnetic induction occurs.This is an irreversible process in which the magnetiza-tion vectors tend to keep their new position after a field(H) is removed.

In region (D) at still higher values of magnetizing force,the magnetization vectors are rotated against the forcesof strain and crystalline anisotropy into alignment withthe direction of the applied field, and saturation occurs.Remo-ving the magnetizing force causes some relaxa-tion; the domains rotate back to the easy direction ofmagnetization (a reversible process). This relaxationcan be minimized by making the direction of easy mag-netization coincident with the desired direction of mag-netization.

Subjecting the magnet to a demagnetizing force returnsthe domain boundaries to a condition similar to theiroriginal positions in (A) and hence the magnet is demag-netized. In normal use a permanent magnet operates inthe second quadrant of the hysteresis loop. The magnetwill operate at some point such as(d) in Figure I-5 wherea magnetic potential -H, per unit length and induction+ B, per unit area will be established. For outstandingpermanent magnets, domain wall motion and rotationof the magnetization vectors should be made difficult.‘The more external energy required to magnetize thesystem, the more will be required to demagnetize thesystem and hence a better permanent magnet.

Figure I-5 describes the magnetizing process satisfacto-rily for magnetic materials having coercive force (H,)values up to approximately 300 oersteds. The coerciveforce of the early carbon, tungsten and cobalt steel per-manent magnets is believed to be a result of impedingdomain wall motion. These quench hardened magnetshave nonmagnetic inclusions building up at the domainboundaries, obstructing wall motion. This mechanismis believed to be of significance only at relatively lowfield strength.

Today’s modern permanent magnets exhibit coerciveforces well above the level explained by domain wallmotion. One therefore must look for magnetizationmechanisms requiring greater, energy input. A signifi-cant milestone in understanding permanent magnetproperties occurred with the suggestion of Frenkel andDorfman that, if small particles were prepared with di-mensions less than the width of a domain boundary,such particles would contain no boundaries. This expla-nation forms the central concept in fine particle magnettheory and provides a satisfactory explanation of mod-ern high coercive force magnets such as alnico, ferrite,rare earth cobalt and rare earth iron magnets.

5

The dimensions of a single domain volume are predicta-ble from a consideration of the wall energy and magne-tostatic energy. For a sphere the wall energy is propor-tional to the cross section or to the square of the radius.The magnetostatic energy is proportional to the spherevolume or to the radius cubed. A critical radius existswhere the two energies are balanced. For this value andbelow, it is energetically impossible for a boundary toexist. Without domain boundaries the magnetization ofa permanent magnet can be changed only by rotation ofthe magnetic moments associated with each domainvolume. This process requires higher energy input thandomain wall movement. The degree of difficulty in ro-tating the magnetic moments depends on the anisot-ropy, or the forces that give direction to a domain’s mag-netization.

In alnico magnets, during precipitation, elongated do-main regions are formed in a less magnetic matrixphase. The major axis is the easy axis of magnetizationand the elongated regions exhibit greater coercive forcethan spherical regions. Today most research in perma-nent magnets is in the area of materials exhibiting crys-talline anisotropy. Ferrite magnets, rare earth cobaltand rare earth iron magnets all exhibit high coerciveforce because of the strong attachment of the magneti-zation to a crystal axis.

The two principle types of anisotropy and the propertyinterrelationships which result are shown in Figure I-6.With particles having shape anisotropy it is necessary toretain spacing between adjacent particles so that theelongated regions will not short each other. Maximumenergy density occurs with packing fractions of about0.6. With a system relying on crystal anisotropy theproperties continue to increase as the packing fractionincreases. Real permanent magnets often have coerciveforces due to several kinds of anisotropy.

CRYSTAL

PACKING FRACTION

S H A P E

5,P%ax

HC,

,:-.:

0 2 .4 .6 .a 1.0

Figure I-6. Two kinds of anisotropy.

PACKING FRACTION

associated with the permanent magnet is independentof time unless the magnet is subjected to some form ofadditional energy input such as heat or demagnetizationenergy.

The permanent magnet is a unique component in theenergy conversion process. A permanent magnet in astabilized condition is a reversible medium for energytransformation. Potential energy is stored both in themagnet volume and in the external field associated withthe magnet. Permanent magnets often operate over adynamic cycle where energy is converted from electri-cal or mechanical form to field energy and then returnedto the original form.

When a permanent magnet is magnetized energy is dis-sipated in changing the internal potential energy bal-ance. For a magnet to establish external field energyadditional input energy is required to set up the freepoles and establish the magnet’s magnetomotive force.Energy is only involved in changing a magnetic field,not in maintaining the field. Hence the field energy

6

PART II. DESIGN RELATIONSHIPS,FIGURES OF MERIT AND OPTIMIZING

TECHNIQUES

Permanent magnets are characterized and compared interms of defined unit properties which are obtainedfrom the hysteresis loop of the magnet material. Thehysteresis loops for a typical permanent magnet mate-rial are shown in Figure II-l. These relationships aredetermined by measurements as detailed in section IIIof this guide. The relationship between B, the magneticinduction, and H is known as the normal curve. Therelationship between J, the intrinsic magnetization, andH is known as the intrinsic curve. The curves are relatedat every point by the equation B = J + H in absolutevalues. *

(+t

I V

Figure 11-l. Magnet hysteresis loop.

*Note: 1st Quadrant: B = J+( +H) = J+H2nd Quadrant: B = J+(-H) = J-H

The permanent magnet is uniquely different from anelectromagnet. An electromagnet establishes a field Hby having a current in a winding. If a ferromagneticbody is placed in the coil, magnetic induction (B) isborn. H and B vectors are parallel to each other andadditive. When a field is applied to a permanent magnetintrinsic induction (J) is born. Again J and H are paral-lel. If the permanent magnet is removed from the mag-

netizer free poles are established and a field potential-Hd exists between the free poles. The field potential inthis case is due to some of the magnetization J returninginternally. The field potential -Hd associated with a per-manent magnet is a product of the magnetization J andis 180” opposed to J. The magnitude of -Hd depends onthe geometry of the magnet and thus the spacing of thepoles. These relationships are shown pictorially in Fig-ure 11-2.

B = J-t-id

Figure II-Z. BH relationships in a permanent magnet.

Generally, the second quadrant of the hysteresis loop isused in analysis of permanent magnet behavior. Boththe intrinsic curve and the normal curve are used. Thenormal B curve is used for designing since it representsthe net output of the magnet n-hen the magnet’s use is toestablish energy in an air gap. M-hen the magnet isplaced in an external field. the intrinsic curve is used todetermine how the external field changes the intrinsicproperties. The change in normal properties can be con-structed from the equation relating the two curves.While it is true that having one cuI1p allows construc-tion of the other, everything is due to the intrinsic mag-netization. In the development of permanent magnetmaterials, intrinsic values are universally used to reportprogress.

Figure II-3 shows the second q!iadrant demagnetizationcurves. B,, the residual induction, is defined as the fluxdensity of the magnet in a closed magnetic circuit afterremoval of the magnetizing force. H, is that demagne-tizing force which will reduce B to zero. (BH),,,, proba-bly the most important single criterion of magnet per-formance, is obtained by constructing the energyproduct curve, i.e., the product of abscissa and ordinateplotted against the value of B or sometimes H at appro-priate points on the demagnetization curve. The energyproduct curve starts at the origin, rises to a maximum

7

point, (BW,,, and then falls again to zero. An alternateand more widely used display is also shown in Figure II-3 where energy product contours are constructed on thedemagnetization curves and allows one to compare theenergy product of a family of demagnetization curvesby inspection.

;-- ENERGYCONTOURS

I I I/’HCl HC 0 (BH MAX)

Figure 11-3. Second quadrant demagnetization curves.

An important characteristic of a permanent magnet istermed its recoil permeability (CL&. If at any point, suchas P in Figure 11-3, the cycle in H is reversed in direc-tion, then the flux density changes along an interiorcurve PR. If, from R the field H retraces its values, theflux density traverses the upper half of the loop RP untilit again reaches P, after which the major hysteresis loopis followed. Such a minor loop is known as a recoil loopand the slope of the loop is the recoil permeability orreversible permeability. In many materials the slope isfairly constant whatever the point of origin and is veryclosely approximated by the slope of the major hystere-sis loop at point H = 0 where B = B,.

Demagnetization Factors-Loadlines and CircuitConcepts

The field H inside the magnet at any point is the resultof the applied field H,, and the self demagnetizing fieldH,. As we have seen Hd is a result of pole formation andis proportional to the magnetization J. ThereforeH = H, + Hd = H, - NJ where N is termed the demag-netization factor. If the magnet is in a closed magneticcircuit Hd will be zero since the free poles do not exist.For a magnet in an open circuit condition or for a mag-net circuit containing an air gap the effect of Hd will beto lower the magnetization J. The factor N is dependenton magnet geometry. Joseph15 has derived both ballisticand magnetometric values for N for cylinders as shownin Figure 11-4. Nl,, the ballistic value must be used indetermining properties for the central or neutral sectionof the cylinder. The magnetometric value N, is usedwhen the average properties of the entire cylinder arebeing determined. If the demagnetizing field is ex-pressed as Hd = -NJ and (Bd, Hd) is substituted for J,rearranging one has:

H,=B, Bdand also - = 1 - &1 1 Hdl - -

NThis is an important relationship relating the demagne-tizing factor to the load line.

Figure 11-4. Ballistic (.Nb) and magnetometric (N,) demag-netizing factors for cylindrical rods.

F%iY R

4

E R

Figure 11-5. Interrelationships between magnetic and elec-trical circuits.

To establish the relationship between the unit proper-ties of the magnet material and the physical dimen-sions, consider the magnetic circuit of Figure 11-5. Thefollowing equations are based on the CGS system. Themagnetic circuit analogy of Ohms law is:

flux = Magnetomotive ForceReluctance

or 4 = F/R (1)

In Figure II-5 the Magnetomotive Force (F) is suppliedby electromagnetic ampere turns. In Figure II-6 a per-manent magnet is substituted to supply F. By applyingthe well known line integral theorem to magnet and gap,a basic equation involving magnetomotive forces in themagnet and air gap can be written. The small magneto-motive force drop associated with the steel pole piecescan be neglected for the moment.

8

F=@R E = If?

Bd/Hd

A4

‘\‘\

‘\(BVmax , , Bd

; ‘\‘\I X<

HC Hd 0

Figure 11-6. Magnetic circuit analysis.

where P”, =H, =

Pg =H, =

magnet lengthmagnetic potential of magnet per unitlengthlength of air gapair gap magnetic potential per unitlength

Another fundamental equation involving magnetdimensions and unit properties results from the premisethat flux lines are continuous and may be equated at anytwo points in a magnetic circuit. Choosing a point in thecenter of the gap and a point in the center of the magnetone may write:

A, Bd = A, B,

where A, = magnet areaBd = magnet flux densityA, = area of air gapB, = air gap flux density

from equations (2) and (3)

A In = A,B,Bd

V, = tn, A, = ‘g Hk’2 AgBd Hd

(4)

where V, = magnet volume and B, = H, numericallyin the cgs system.

Now using the magnetic analogy of Ohms law, we have:

(7)

Where p = permeability of gap and will be consideredas unity for air, therefore the gap reluctance is PglAg.Rewriting equation (7)

Equation (8) is in terms of B and H and can be plotted asa straight line with a negative slope on a magnet dema.g-netization curve. The intersection of this line with thedemagnetization curve represents the operating pointof the magnet. In terms of the demagnetization curvethe flux density has decreased from B, to Bd and a nega-tive potential &, H, has developed which is equal to thepotential drop in the air gap $ H,. The slope repre-sented by equation (8) may be expressed as:

Bd _ ‘rn A, _ ‘m-----=p, p

Hd Arn $ AlnR 40(9)

The reciprocal of l/R is permeance (P), and is widelyused in actual calculations. The concept of permeancereduced to a unit volume of magnet material is simplythe slope of the load line.

Usually the designer will select the dimensions so as tooperate at given Bd/Hd ratio. Often it is the point

@mllax where the product Bd Hd is at a maximum andconsequently the V, used will be a minimum. [Refer toequation (@.I For the case of the magnet by itself out-side of its return path the Bd/Hd will be set entirely bythe geometry of the magnet and Bd/Hd must be deter-mined from the demagnetization factor N as previouslydeveloped. The total permeance is usually broken upinto a value for each region. For example our simplecircuit could be analyzed by breaking total permeance Pinto PI + P, + P, where Pp is the magnet limb per-meance obtained from N. P, is the permeance of thepole pieces and P, is the air gap permeance A,IP,. Equa-tion (10) can be rewritten as follows:

Rc! = 5L Pp + P, + PHd Arn

g (11)

The design equations were developed under the idealbut unobtainable assumption that all of the magnet po-tential was used across the air gap and all of the magnetflux was confined in the circuit. In practice it is difficultto determine the true permeance. For example, for ashort air gap of large area the permeance will be A,&.In practice the true permeance will be more than thisvalue since part of the flux is leakage. This is equivalentto a proportionate increase in gap area which may beconsidered as a leakage factor F. Similarly it is oftenadvisable to apply a correction factor to the gap lengthto allow for losses introduced by joints in the magneticcircuit and potential loss in the pole piece material.

The reluctance factor f is convenient to use. Conse-quently the corrected permeance would be:

(12)

F can vary widely from 1.5 to 10 in typical magnet de-signs. Usually f is much smaller and would have a typi-cal range of 1.1 to 1.3 in most magnetic circuits.

In using permanent magnets the influence of externalfields in changing the flux level is an important consid-eration. The geometry of the magnet and return pathsets the self demagnetization (Bd/H, ratio) and has con-siderable effect on the interaction of a magnet and anexternal field. To predict the change in flux density of amagnet in the presence of an external field, both thenormal and intrinsic curves of the magnet material arerequired. Refer to Figure 11-7. If the unit permeance Bd/Hd is known, a line with a slope Bd/Hd + 1 will intersectthe intrinsic curve and give the correct level of intrinsicmagnetization. Now the magnitude of an external field-H, is laid off parallel to BJHd + 1 slope. The intersec-tion with the intrinsic curve is projected down to thenormal curve to yield the new level of fll1.x density in thepresence of this external field influence. In Figure II-7AB is the loss of flux density for -H, applied externalfield influence.

Hci Hc -Ha 0 + H

Figure 11-7. AB is the loss of flux density for-H, externalapplied field influence.

Use of Flux Conducting Materials in PermanentMagnet Circuits

Flux conducting members in a permanent magnet cir-cuit are used to 1) complete a return path for the flux, 2)change the flux density in a circuit, or 3) form multiplemagnet poles. Figure II-8 shows the circuits involved.In Figure II-9 some widely used high permeability ma-terials are shown. Usually cost is an important factor inthe choice of material. A high percentage of permanentmagnet circuit elements are ordinary cold rolled steel.Cobalt-iron alloy is used in some high performance cir-cuits. It is well to operate these materials near theirmaximum permeability. This will tend to minimize thecross sectional area and at the same time keep the mag-netic potential loss to a low level. If the cross section istoo small then the H drop in the material will tend to behigh. This will cause an appreciable part of the

magnet’s potential to be dropped in the circuit memberand be unavailable as potential to use across the air gap.The longer the circuit member the more serious theproblem.

M A G N E T

*STEEL(W

Figure II-S. The use of high permeability steel in perma-nent magnet circuits.

MAGNETIZING FORCE (H), OERSTEDS

Figure 11-9. Magnetization curves for some high permea-bility materials.

Another fundamental principle in permanent magnetcircuits is illustrated in Figure 11-10. Here the locationof the magnet in the circuit is of importance. The mag-net should be as close to the gap as possible, otherwisethe magnet’s full potential will lead to excessive fluxleakage between the circuit elements or pole pieces.

H I G H L E A K A G E MEDIUM LEAKAGE L O W L E A K A G E

Figure 11-10. Circuit element location.

Some Important Figures of Merit

In developing the design relationships, mention wasmade of a magnet’s volumetric efficiency. For a fixedstatic air gap it is desirable to operate at a particularB,/H, slope where the product of Bd and Hd is a maxi-mum. This particular point on the normal demagnetiza-tion curve is defined at (BH),,,. Refer to Figure II-11(a). Depending on how the magnet is used there aresome other important figures of merit to consider. If themagnet is used in an application that converts field

10

energy to mechanical work such as a holding or liftingmagnet, it is a dynamic load situation. The cycle ofevents is shown in Figure 11-11(b). In the design processwe must control both P, and P3. Area 0 P2 B, repre-sents the magnetic energy per unit that can be con-verted to mechanical work. This value, multiplied bymagnet volume, would be the total area under a force-distance curve for a holding magnet. At a particular airgap between magnet and armature, or load representedby P,, the product of force and distance would be amaximum. We define the shaded rectangular area as(BH), or useful energy. It will be less than (BH),,,which is the total available energy per unit volume.

09 B,

(Cl (4Figure H-11. Permanent magnet figures of merit.

Another type of permanent magnet use involves theexposure to a very high external field for a short timeduration followed by a much lower self demagnetizationfield during continuous operation. The typical d.c. mo-tor application subjects a magnet to the above describedevents. At start or stall the armature draws many timesthe normal running current. The figure of merit undersuch conditions is approximated by (JH),,, as shown inFigure 11-11(c). This is the largest rectangle which canbe drawn under the J vs H demagnetization curve. Thelength of the magnet in a d.c. motor is inversely propor-tional to coercive force and the magnet area inverselyproportional to B,. Consequently the magnet volumewill be inversely proportional to the rectangular area. Asimilar figure of merit B, Hk is shown in Figure 11-11(d).Here we define Hk as the demagnetization field thatreduces the intrinsic magnetization by 10%. In this casethe knockdown is arbitrarily specified: in the case of thelargest rectangular area a somewhat more intrinsicquantity as shown in Figure II-1 l(c) is involved.

Optimizing Permanent MagnetCircuits-Estimating Permeance and FiniteElement Modeling

problems. In the simplest cases the analytical solutioncan be exact, but in any practical problem analyticalsolutions are approximate and a large error betweencalculation and measurement can exist. In practice wehave lumped circuit constants and electrical analogmethods. For two dimensional analysis flux plotting onconducting paper has been useful. A simple modelingtechnique uses three dimensional foam and aluminum-wrap scale models to simulate the capacitance betweencircuit elements. Since capacitance is the analog ofmagnetic permeance one can easily arrive at accuratepermeance values. Zoning can be used to improve theaccuracy. Today most designs are optimized by mea-surement and reference to experiences with similarmagnetic circuits.

Now the availability of digital computers means thatvery accurate numerical techniques such as finite ele-ment modeling can be used to study circuits, devicesand systems. The timing is fortunate because rare earthpermanent magnets are expensive. They tend to beused in sophisticated and costly systems. Accurate solu-tions are rather imperative if one is to fully exploit thepotential of these new magnets and to arrive at costeffective solutions. The permanent magnet is a veryinteractive component and digital techniques allow us toexplore many alternatives that can minimize materialcost and the manufacturing events to arrive at a high-performance energy-conversion system. r2s the cost ofcomputerized solutions improve and as the ease of get-ting the problem on to the computer improves. numeri-cal analysis of magnetic circuits will be estensivel!used.

Over the years several analytical techniques have beenused to give approximate solutions to magnetic iicld

11

PART III. MEASURING

Some Basic Systems for Measuring Flux or FluxDensity

Man’s early attempts to express a magnetic field inquantitative terms involved force relationships betweenmagnetic bodies. One early system used the force re-sulting from the magnet under test reacting with a mov-ing magnet free to rotate to indicate relative strength.Figure III-1 shows the elements of a permanent magnetgaussmeter that is sometimes used to measure fieldstrength.

- --N-

Figure III-l. Permanent magnet gaussmeter or magne-tomete r

A second system, based on Faraday’s law, is the inducedvoltage method. An e.m.f. is induced in a coil when themagnetic flux within the coil changes.

e = n? 10-s voltsdt

Where n is turns of the coil. Since the voltage changeswith the rate of change of flux, the practice is not tomeasure voltage but to measure the time integral ofvoltage je dt. The above expression can be rewritten togive:

d+ = F j e dt by integration

n4 = 1:; d4 = !!? jbe dt = maxwellsn

Knowing the number of turns, one is able to calculatethe total flux change from the j e dt measurement. Theelectronic integrating fluxmeter shown in Figure III-2 isan example of the induced voltage method.

Figure 111-2. B signal integration circuit (fluxmeter).

An interesting variation of the mduced voltage methodis to use a Helmholtz coil pair instead of a tight fittingcoil around a magnet. A magnet being measured underopen circuit conditions may be considered to be a mag-netic dipole with orientation parallel to the axis of thecoil set. The magnetic moment is Bi/V, where V, issample volume. The coil arrangement and sample rela-tionship is shown in Figure 111-3. As the magnet ismoved from the center of the coil set to a point welloutside the coils the time integrated voltage je dt ismeasured with a fluxmeter or electronic integrator. Thewave form is shown at the bottom of the figure. Thevalue of je dt is proportional to the magnetic moment of

ilL3i

co

T O F L U X M E T E R

TII k-D-- COIL 2

(A) SCHEMATIC TEST SETUP

TIME t, 21

(B) TIME VS. VOLTAGE PLOT

Figure 111-3. Measurement of magnetization in aHelmholtz co i l .

the sample. Since Bi is the magnetic moment per unitvolume it follows that,

Bi =&jedtm

where c is a proportionality constant for the coil pair.This constant is independent of sample volume andshape if the sample is small with respect to coil diam-eter. The Helmholtz pair is a very convenient detectorfor use with high coercive force magnets where the typi-cal sample is short. This technique frees one from tightfitting coils and corrections for high self demagnetizingfields. One coil set can measure a wide range of magnetvolumes and shapes. However, one must know the loadline rather accurately since it is necessary to subtractHd from Bi to obtain Bd.

12

A third widely used system involves the Hall effect. Theuse of Hall generators in measurements has found wideacceptance. The small size of the field sensor elementand the static characteristic (no relative motion is re-quired) enables the Hall probe to be used in areas wheremeasurements with the induced voltage method wouldnot be feasible. Figure III-4 shows the principle ele-ments of the measuring system using the Hall effect.The Hall output voltage (e) is given by the followingequation:

e =RHi-

d

Where R = Hall constant (material constant)H = field strengthi = current across Hall elementd = thickness of Hall element

Figure 1114. The Hall effect, with a thin plate of materialsuch as indium arsenide, placed in a magnetic field with itsplane perpendicular to the field, a coincidental longitudi-nal current i, through the material produces a propor-tional transverse voltage e, between surfaces A and B.

When a thin plate of material exhibiting the Hall effectis placed in a magnetic field with its plane perpendicularto the field, a longitudinal current (i) through the mate-rial produces a proportional transverse voltage (e) be-tween surfaces (A) and (B). The Hall elements can mea-sure D.C. fields or A.C. fields. The output voltage is afunction of the current and field characteristics. Be-cause of its small size a Hall probe is ideally suited tocheck field homogeneity and is useful in flux plotting.The Hall output voltage is a sine function of the anglebetween the lines of force and the plane of the Hallelement. At any point in a field where the output is zero,it follows that the lines are parallel to the Hall element.When the element is oriented for maximum output, thelines are perpendicular to the element.

Direct and continuous reading of field strength coupledwith relatively low equipment investment cost havemade the Hall system widely used in production mea-surements.

To measure magnetic potential (F) between two points, The following information is intended to help users ob-a special coil known as the Chattock magnetic potential tain accurate unit property measurements on perma-coil is used. Physically the Chattock coil consists of a nent magnets. Lack of accepted magnetization refer-flexible strip of non-metallic material of uniform cross ences and non-uniform techniques and procedures havesection, uniformly wound with fine wire. The coil is long been severe problems in industry. At present weconnected to an integrating instrument such as an elec- have the technology to permit both producer and user totronic flux meter. The Chattock coil is essentially the measure magnetic properties based on length, area and

magnetic equivalent of a voltmeter. Referring to FigureIII-5 the magnetic potential between two points x1 andx2 is defined as the work done in moving a unit polebetween the two points. We can express the potentialdifference between x1 and x2 as:

j;;HcosBdx

Measurement of Magnetic Potential Between TwoPoints

Xl x2

Figure 111-5. A Chattock coil to measure the magnetic po-tential difference between points x1 and x2 of a bar mag-net.

Where dx is a small increment of the path and 0 is theangular displacement between the directions of H anddx. If the Chattock coil has an area A and nU turns perunit length, the flux linkages in length dx are equal toA nU H cos 13 dx and the total interlinkages from x1 to x2are:

or:

n0 = A nU jzf H cos 0 dx

0 n = A nU (potential between points)

potential between x1 and x2 = -A “u

Unit Property Measurements

The basis of information exchange in the permanentmagnet industry is the relationships between B,, B andH and the unit property intercepts B,, H,, H,i and(BH),,,. To determine this data the demagnetizationcurves or second and third quadrants of the hysteresisloop must be plotted.

The procedure outlined in the following section on unitproperty measurement focuses on a uniform set of pro-cedures regarding sample selection, field uniformityconditions and arrangement of sensors and instrumen-tation.

Introduction.’

13

volume unit dimensions within a very narrow error bandprovided due attention is paid to several sensitive is-sues, which can introduce errors. The procedures dis-cussed call attention to these issues while providingtechniques flexible enough to permit use of a wide rangeof equipment.

The focus is on obtaining the demagnetization curve(second quadrant of the hysteresis loop) of a specimen.The relationships between the magnetic induction (B),the field strength (H) and the intrinsic induction (Bi) areshown by the demagnetization characteristic (Figure111-6). Important unit property values for residual induc-tion B,, coercive force H,, intrinsic coercive force H,iand maximum energy product (BH),,, can be obtainedfrom the demagnetization curves.

4+Bml

i,/- -Whax

-Ii Hc, Hc Hd‘J=B,=B-H

Figure M-6. Property relationships (second quadrant).

1. Electromagnetic Yoke

The measurements are carried out in a closed circuitconsisting of the test specimen and a yoke or returnpath made of soft magnetic material. The yokeshould be of symmetrical construction and at leastone pole should be movable to accommodate variousspecimen lengths and ensure minimum air gap be-tween specimen and pole pieces (Figure 111-7). Thecoercivity of the yoke and pole pieces should not bemore than 2 oersteds.

FIXED’POLE POLE PIECE

Figure 111-7. Electromagnet and specimen arrangement.

2.

3.

Field Uniformity Requirements

To obtain uniform magnetization in the region occu-pied by the specimen, certain geometric relation-ships linking specimen dimensions and electromag-net gap dimensions must be maintained. See Figure111-7.

D, LD~ + 1.2 L (1)

Also D, ~2.0 L (2)

Where D1 = diameter of a circular pole piece or theshortest dimension of a rectangular pole piece.

L = Distance between pole pieces.

D, = Maximum diameter of the cylindrical volumewith a uniform field.

It is necessary that the flux density in the pole piecesbe well below the saturation level of the poles, so thatthe pole faces shall be near equipotential conditions.The recommended practice is to limit the flux den-sity to 10 kilogauss in iron and 12 kilogauss in ironcobalt (Permendur) pole pieces. If the foregoing con-ditions are met, the field in the specified volume isuniform to within 2% in both radial and axial direc-tions. However, these recommended kilogauss lev-els are often unreasonably low at the pole tips forhigh coercive force materials. Consequently, fielddistortion must be considered when higher flux den-sity levels are used.

Field Strength Requirements

The value of the field strength varies according tothe nature of the permanent magnet material and itsprior history. Generally saturation is achieved withfields of the order of 3-5 times the intrinsic coerciveforce (H,i). With SmCo5 and many other rare earthPM materials this ratio is less when magnetizingspecimens that have had no prior exposure to a mag-netic field. A practical way to determine saturationis to expose a specimen to a value of field HI and notethe level of magnetic induction, then apply a field Hz25% greater than H1. If the magnetic induction in-creases less than l%, one can conclude that level HIwas adequate to saturate the material. For extremelyhigh field requirements an alternative procedure isto magnetize the specimen by impulse in a solenoidand transfer it to the electromagnetic yoke. In thissituation it is imperative that the specimen geome-try be such that an irreversible loss of magnetizationdoes not occur due to self demagnetizing influenceof the free poles. This is of great concern if the mate-rial has a non-linear shaped demagnetization curve.However, most of this loss can be recovered by re-magnetizing the sample (in the closed yoke struc-ture) before generating the demagnetization curve.

1 4

4. Test Specimen Considerations

The test specimen should have a simple configura-tion (cylinder or parallelepiped) whose dimensionsare chosen according to equations (1) and (2). Thelength L should not be less than 5 mm. The facesshould be ground parallel to each other and perpen-dicular to the specimen axis to reduce air gap be-tween specimen and poles. The cross sectional areashould be uniform over the length of the specimen.

5. Integration of the Flux Density

The change in flux density in the specimen is deter-mined by integration of the induced voltage in asearch coil around the specimen. The coil should bewound as closely as possible on the magnet andshould be symmetrical with respect to the polepieces. The leads must be tightly twisted to avoidvoltage being induced in the lead loops. It is possibleto minimize error in the flux density measurementby following the above. Acceptable error in the fluxdensity measurement is of the order of + 1%. Thevariation of flux density B in the specimen betweentime tl and tZ is given by:

AB = B,-B1 = g ,:fedt (3)

Where B2 = the flux density in gauss at time tz.B, = the flux density in gauss at time tl.A = cross section of specimen in sq. cm.N = number of coil turns.edt = the induced voltage in volt seconds.

It is necessary to correct the change in flux den-sity by taking into account the flux included in thesearch coil. The corrected change is given by:

Where AH = the change in field strength inoersteds.

A, = effective cross section area of coil insq. cm. based on mean coil diameter.

6. Measurement of Field Strength

The field strength at the specimen surface is equalto the field strength inside the specimen only in thatpart of space where the field strength vector is paral-lel to the side surface of the specimen. Therefore thefield sensor must be placed in the homogeneousfield zone as near the specimen as possible and sym-metrical with respect to the poles. The field strengthcan be determined by using a search coil, a magneticpotentiometer, or a Hall probe. A suitable readoutinstrument must be used. The dimensions of thefield sensor and its location must be within the arealimited by diameter D2 [refer to equations (1) and(2)]. The field sensor or transducer must be cali-brated so that the total error is within f 1%.

When using Hall probes, non-linearity must be con-sidered, especially above 10,000 gauss.

7. Determination of Demagnetization Curve

For the measurements described below a low-driftfluxmeter or a ballistic galvanometer is used to mea-sure the voltage integral. The test specimen is as-sembled in the electromagnet and saturated at ahigh. magnetic field strength H,,,. At this fieldstrength, the induction in the specimen is equal toBmax, Figure III-g(a). Then the current is switchedoff and the change of magnetic flux density AB, =Bmax - B’, can be measured. The magnetic fieldstrength in the absence of the magnetizing current isnot zero (H’,#O) due to the permanent magnetiza-tion of the poles and yoke. Consequently, B’, f B,.The value H’r, like any other value of magnetic fieldstrength, may be measured with the magnetic fieldstrength sensor inserted into the space between thepole pieces. By increasing the negative magnetizing

IO I

-4ll,, Hc % H’r H mm

A B2

I (4

H

LIB

- I cH, H,

-hll,, (W

Figure 111-8. Principal points on the hysteresis loop.

H

15

current to obtain the value -H,,,, the change of fluxdensity aB2 = B’, + B,,, can be measured. Thevalue of the magnetic flux density B’r is calculatedfrom:

B’ = AB2 - ABlr 2 (5)

The test specimen is again magnetized to the pointB %mlnaxt and after switching off the magnetizingcurrent the magnetic flux density returns to thepoint B’r, H’,. After a negative magnetic field hasbeen applied, the magnetic flux density at any pointBd, Hd can be calculated from the flux densitychange AB according to the equation:

Bd = B’r-AB (6)

The determination of any pair of associated values Band H on the demagnetization curve shall start fromthe point B’r, H’, and necessitates magnetizing thespecimen to B,,,, H,,,. The actual value of theresidual flux density B, may be obtained by the lin-ear interpolation of the nearest points. To avoid therepetition of magnetizing to Bmax, H,,, severalpoints B, H can be determined by successivechanges AB, AH between the points, but thismethod increases the measuring error.

Together with the above mentioned procedures, thefollowing measurement order is recommended:

The value of B,,, corresponding to the maximummagnetizing current, is determined by reversing themaximum magnetizing current without changing itsvalue:

B AB3max = -2[Figure 111-8(b)] (7)

To determine value of the magnetic flux density B at anypoint on the demagnetization curve, the value of thedemagnetizing current should be such as to produce thefield strength H corresponding to this point on thecurve. Then the cyclic remagnetization of the specimenis repeated. After that the change of the magnetic fluxdensity AB is determined by changing the magnetizingcurrent from the value corresponding to the requiredvalue up to its maximum value.

The magnetic flux density is calculated from the equa-tion:

Bd = B,,, - GB (8)

An alternative method for determining the demagnet-ization curve is the use of an electronic integrator. Theintegrator is connected to the search coil and is adjustedto zero. Then the demagnetized test specimen is putinto the search coil and the assembly mounted in theelectromagnet. After magnetizing to the required mag-netic field strength the magnetizing current is switchedoff. However, the values of the magnetic flux density B’,and the magnetic field strength H’r may still be in the

first quadrant because of the permanent magnetizationof the poles and the yoke. The current is then reversedand increased until the magnetic field has passed thecoercivity H, or H,i. The speed of the variation of themagnetic field strength shall be sufficiently slow toavoid producing a phase difference between H and B.With some materials there is a considerable delay be-tween the change in the magnetic flux density and themagnetic field strength. In this case, the time constantof the flux integrator should be long enough to ensureaccurate integration. Although the procedure detailedis for obtaining the B(H) demagnetization curve, onecan easily obtain the Bi(H) by arranging to add H to theB value at every point. (In the second quadrant Bi = B +H.) Measuring Bi(H) demagnetization characteristic isof major importance when a permanent magnet is sub-jected to external demagnetization influences in serv-ice.

8. Calibration Techniques and Standards

The calibration of the integrating flux meter or gal-vanometer can be achieved by one of the following:

(1) Use of a calibrated volt-second source. A verystable voltage source and an accurate timer arecombined into a calibration device. An accuracyof f 0.1% is achievable with a volt-second refer-ence.

(2) Use of a mutual inductance standard with theswitching on and off of the primary current,which can be read with good precision. A knownflux change is produced in the inductor second-ary which can be used for calibration purposes.An accuracy of ~0.1% is achievable with themutual inductor.

(3) Use of search coil of known area turns in aknown homogenous magnetic field that is mea-sured with nuclear resonance technique. An ac-curacy of &1).01% is possible with this ap-proach.

(4) For convenience a secondary standard referenceis often used in calibration of magnetic testequipment. A specimen of pure nickel makes avery good reference. The saturation magnetiza-tion of nickel is quite invariant and if the area isdetermined accurately there will be a knownlevel of flux for calibration. Additionally, a per-manent magnet that has been stabilized andtemperature cycled makes a very good flux ref-erence. An error of iO.5% in the calibrationprocedure is to be expected with secondary ref-erences.

9. Reference Documents

ASTM A-34, Testing Magnetic MaterialsASTM A-340, Standard Terminology of Symbols

and Definitions Relating toMagnetic Testing

16

ASTM A-341, Standard Test Method forDirect-Current Magnetic Propertiesof Materials

International Electrotechnical Commission, IECStd. 404-5

Acceptance Testing of Production Quantities

Unit properties determined by obtaining demagnetiza-tion curves are generally not used in acceptance testing.Obtaining the complete demagnetization curves is timeconsuming and costly. Often the closed circuit test doesnot identify the range of operating field conditions in adevice. Samples for unit property testing must be of acritical size and shape. If the actual magnet componentinvolved is large or non-uniform in cross section sam-ples must be cut from it which are suitable for the unitproperty tests. This obviously leads to destructive test-ing. In acceptance testing a test is required that willclassify magnets into acceptable or unacceptable cate-gories for a specific application. This kind of test isuseful for quality control in the magnet producing plantand also as an incoming inspection test in the user’splant. A satisfactory acceptance test must simulate themagnetic circuit conditions and the field environmentof the actual device or system in which the magnet isused. In some applications a magnet must be subjectedto demagnetizing conditions set up by the end device.Often a magnet is used in a circuit where it is magnet-ized in place and its load line is higher than the opencircuit load line. In such a situation it may be necessaryto remagnetize the magnet if for any reason it is re-moved from its magnetic circuit. This situation is de-pendent on the H,i of the material. Often high H,i mate-rials are specified when open circuit conditions and lowload lines are involved.

Acceptance testing generally requires a fixture that canbe adjusted so the magnet under test is working at thesame load conditions as in the actual device.

R e f e r e n c e M a g n e t s

It is suggested that a reference magnet be used in ac-ceptance testing rather than exchanging and using ab-solute magnetic quantities. Reference magnets aremagnets selected and approved by the producer anduser to allow satisfactory function of the end device.

In addition to magnetic measurements it is at timesdesirable to test for related variables-for example,force or torque between magnets or between a magnetand a soft iron armature. A generated voltage test is attimes useful for testing magnets and magnet assembliesused in motors, generators and tachometers. In multi-pole structures the average flux is measured. At con-stant speed and load conditions the generated voltage isproportional to average magnetic flux.

Measurements for Optimizing a PermanentMagnet Structure

An important category of measurements is involved inthe analysis of a permanent magnet circuit. For exam-ple in the simple circuit shown in Figure III-.9 one wouldlike to check the load line of the device. Additionallythere may be questions about the potential loss in thepole pieces and the air gap flux density H,. An indica-ting instrument such as a fluxmeter or electronic digitalintegrator and some simple coils are all that is needed tocompletely analyze the structure. As indicated in Fig-ure III-S(a) the H, of the gap can be measured with agaussmeter or a small coil and fluxmeter. Another testmethod uses a potential coil to measure total magneto-motive force F across the gap. Dividing F by Pg, the gaplength, gives a value for H,. This technique can be usedwhen the gap is very short and a thin enough Hall probeor search coil is not available. To determine the loadline, wrap a few turns of wire around the magnet andpull the magnet from the assembly and the coil [FigureIII-S(b)]. Knowing the magnet area, B, can be com-puted. Hd can be determined by moving a potential coilfrom point a to b and shown in Figure III-S(c). 15thknown values for both Hd and Bd, the slope of the oper-ating line, Bd/Hd, can be calculated. Perhaps there is aquestion about pole piece material or the magnetomo-tive force (F) loss in the pole pieces (has the designerselected the iron cross section for optimum H drop inthe iron?). In Figure III-S(d) the use of the potential coilallows one to measure the F drop between point a and band by dividing F by the length of iron the unit potentialdrop in the iron can be determined. From magnetizationcurves for various flux conducting materials one canthen make a determination regarding how reasonable isthe potential loss in the iron.

F L U X M E T E R

Measure internal field H,in magnet

Measure magneticpotential loss in iron polepiece.

Figure 1118. Measurements for design analysis.

17

PART IV. MAGNETIZING AND DEMAGNETIZING

Changing the state of magnetization is a very importantconsideration in using permanent magnets. For a per-manent magnet to exhibit full properties, it must befully magnetized or saturated. Partial magnetizationresults in reduced properties, and efficiency and stabil-ity are compromised.

The magnet producer generally ships demagnetizedmagnets to the user. The principle reason for this prac-tice is that most magnets are designed for magnetiza-tion in the environment of a completed magnetic circuit.Additionally, shipping costs of magnetized magnets aregreater and the danger of collecting small magnetic par-ticles in air gaps is reduced with a demagnetized mag-net.

Recent progress in property development has beenlargely in terms of increased coercivity. With increasedresistance to demagnetization, such materials are pro-portionately more difficult to magnetize. Successful useof the newer high coercive force magnets requires mag-netizing equipment capable of producing very high fieldlevels as well as a good understanding of the magnetiza-tion process. Early low coercive force permanent mag-nets were magnetized with rather modest levels of field.Little consideration was necessary as to how magnetiza-tion was achieved. In considering high H,i rare earthmagnets one needs to be aware of the high field require-ments and of the flux density levels the magnetizingpath must be capable of handling. The basic designoften will be influenced by how to magnetize. It is veryeasy to design structures that simply will not allow in-place magnetization.

Magnetizing Requirements

To fully magnetize the following must be considered: (a)External field magnitudes, (b) The effective net fieldseen by the permanent magnet due to self demagnetiza-tion and magnetic circuit influences, (c) Conformance ofthe shape of the field to the magnet geometry beingmagnetized, (d) The time required to magnetize and theproblem of field penetration, (e) Field distortion eventsafter magnetization that may leave the magnet partiallydemagnetized

(a) The net effective field required to saturate a givenpermanent magnet material can be determinedfrom the hysteresis loop. Figure IV-l shows a typi-cal relationship between intrinsic magnetization (J)and magnetizing force (H). As the field is increasedJ will approach some maximum value (J,) character-istic of the material. The value of saturation fieldstrength (H,) is usually of the order of 3 to 5 timesthe H,i of the material. Figure IV-l represents theconditions of a closed magnetic circuit. The influ-ence of self demagnetization will be developed later.

Figure IV-l. Magnetization curves.

The demagnetization curves of J and B versus Hsupplied by magnet producers are measured withthe material in a saturated condition. Failure toproperly saturate a magnet designed on the basis ofthe given property curve will lead to disappointingresults. In order to evaluate and compare permanentmagnet materials each must be fully magnetized.Figure IV-2 shows the sensitivity of magnet proper-ties to levels of magnetizing force for SmCo5. It isclear from this example that partial magnetizationwould be wasteful and that properties achieved arenon linear with applied field level.

2 5 2 0 15 10 5

-H [kOe)

Figure IV-Z. SmCoB magnetized at various levels of field.

Several methods can be used to determine when amagnet is saturated. It is quite easy to check theapplied field level with a gaussmeter in the case ofd.c. fields. With pulse fields, a Hall probe operatedin the d.c. mode in conjunction with an oscilloscopecan be used. Another technique.is to check for satu-ration by field reversal. This check is performed bymagnetizing and measurement in a specified man-ner and then the same field is applied in the oppositedirection. The magnet is tested again and if the

1 8

(b)

results are the same, the field level may be consid-ered adequate. It is also possible to apply an initialfield level and make a reference measurement.Then, a field level larger by perhaps 25% is used andif the magnetization does not increase it is safe toassume that the initial field level is adequate.

The field levels suggested by magnet producers arealways the actual or net field levels as seen by thepermanent magnet. In practice, the only time theapplied field is the same as the actual field is whenthe magnet is in essentially a closed low reluctancecircuit such as magnetization in an iron yoke elec-tromagnet. In this case the total F applied will bevery close to the F across the magnet. The generalproblem is one of magnetizing in a magnetic circuitwhich is designed to handle the operating flux fromthe magnet and not the higher flux level associatedwith magnetization. Air gaps are present and oftenparallel return paths must be saturated, whichmeans extra flux lines during magnetization. Con-sider the case of a short rectangular magnet beingmagnetized in an air solenoid - Figure IV-3. Thepermeance coefficient -B/H is determined from themagnet geometry as developed in the design sec-tion. If a line is drawn through the JS, H, point hav-ing a slope B/Y + 1 the intersection of this line withthe H axis will give the total field necessary to mag-netize. H,-H, is the field necessary to overcome themagnet’s self demagnetization influence and allowa net H, to be experienced by the magnet. For opencircuit conditions with low B/H values, the totalfield requirements can be reduced by magnetizingseveral magnets in series.

-Jbm+

/ / I \-H 0 +H HS ’ Hr

Figure IV-3. Analysis of self demagnetizing field.

(c) Partial magnetization may occur if the field gener-ated does not conform to the configuration of themagnet. The permeability of most permanent mag-nets is very low and hence, the presence of the mag-net does little to shape an applied field. The fieldshould always coincide with the easy axis of thepermanent magnet. When magnet configurationand field do not coincide, it is possible to have fieldsthat are too great, which in effect, leave regionsmagnetized off axis and the result appears as partialmagnetization. Figure IV-4 shows the influence of afield applied at various angles to alnico 5-7, which isa highly anisotropic material.

ENERGY PRODUCT (BH),,,. MGO,

8 0 0 6 0 0 4 0 0 2 0 0 0DEMAGNETIZING FIELD H, Oe

Figure IV-4. Influence of various angles of field application(alnico 5-7).

(4 Although the magnetization process is essentiallyinstantaneous, the time duration of the applied fieldis important because of the existence of eddy cur-rents in metallic materials. Also, with highly induc-tive electromagnets, the current rise time may be ofthe order of 1-2 seconds.

Figure IV-5 shows a relationship inter-relatingdepth of penetration with resistivity, permeabilityand frequency of wave form. In general, the fre-quency must be chosen so that the magnetizingpulse lasts longer than the eddy current. The eddycurrent path is a function of geometry and for largemetallic magnets there are problems with penetra-tion. The general experience with alnico and rareearth magnets has been to use about 10 millisecondminimum pulse width. This width of pulse allows awide range of magnet configurations and sizes to befully magnetized.

D = DEPTH OF PENETRATION

e = RESISTIVITY

p = PERMEABILITY

K = CONSTANT

f = FREQUENCY

Figure IV-5. Effects of eddy currents.

(e) After calibration it is possible to inadvertently de-magnetize a magnet with improper handling; there-fore care must be taken to preserve the original con-dition of magnetization. A magnetized magnetshould not be touched along its length with ferro-

19

magnetic objects. Such action will produce conse-quent poles nhich alters the main flux pattern andreduces the useful flus in the gap or at the polesurface of the magnet. Also magnets can be demag-netized by repeated contact with poles in repulsion.Improper handling is most serious with magnetshaving H,; appreciably less than B,..

Magnetizing Equipment

Direct current structures such as electromagnets arethe oldest and still an important equipment category toconsider in magnetizing permanent magnets. An exam-ple of the field developed as a function of current andpole spacing in an electromagnet yoke magnetizer isshown in Figure IV-6. Such a unit with a controllablepower supply can serve many laboratory measurementfunctions, including obtaining hysteresis loops and de-magnetization curves to characterize permanent mag-nets. Due to penetration problems mentioned previ-ously a d.c. magnetizer can be used advantageously tomagnetize large section metallic magnets. An electm-magnet yoke magnetizer is somewhat limited to rectan-gular or cylindrical form magnets having straight-through direction of magnetization.

Air

l/4”

I/2"

IO 20 30 40 50 60 70 75Amperes

Figure IV-6. Electromagnet gap fields.

Another widely used d.c. structure is the open solenoidoften used in production since it permits magnets tomove through in a continuous stream.

In some instances the steady state field of one permanentmagnet is used to magnetize another permanent magnet.However, there are problems in avoiding distortion as themagnet being magnetized is removed from the largermagnet supplying the field. In this case the magnetizingenergy is supplied in terms of mechanical input from theperson removing the magnetized magnet.

Since the time interval required to magnetize is ex-tremely short, magnetization can be achieved by a

current pulse, provided its magnitude is sufficient todeliver the peak H requirement. The development ofmaterials with high coercive force has led to short mag-net lengths and parallel circuits. There are also manymagnet configurations with multiple poles that cannotbe magnetized by placing them in contact with conven-tional electromagnetic structures. The use of a singleconductor or a few conductors threading through themagnetic circuit is necessary.

Impulse magnetization has become popular not only forits necessity in some circuits but generally for nearly alltypes of magnetization because of the modest invest-ment requirements. The basic components of a capaci-tor discharge magnetizer are shown in Figure IV-7. Thecapacitor is charged to voltage V at a rate determined byR,. The capacitor (C) is switched to discharge into a coilhaving inductance (L) and resistance (R). If R is greaterthan 2,/L/C, the current will be unidirectional withoutoscillations.

(1) (2)

rTc$RFigure IV-7. Basic elements of capacitor discharge mag-netizer.

Another type of impulse magnetizer is the half cyclemagnetizer shown in Figure IV-8. Such a system hasthe disadvantage of drawing the current surge directlyfrom the power line. It, however, offers a very rapidrepetition rate and is often used ‘n production. The tim-ing and phase shifting control features allow the currentlevel to be adjusted. Figure IV-9 shows voltage, currentand flux changes for various firing points in the halfcycle. Figure IV-10 shows several conductor arrange-ments used to achieve specific magnetization patternswith cur .rent pulses.

TlMlNG AND PHASE

MAGNETIZINGF I X T U R E

TRANSFCJRMER

60 CYCLE o-cFigure IV-S. Half-cycle magnetizer circuit passes half-cycle current impulses whose amplitude and duration iscontrolled by the firing of a thyratron in the ignitor circuit.For currents above 10,000 amp a transformer is used. Toprevent flux reversal, a pre-magnetizing circuit saturatesthe transformer with d-c pulses of opposite polarity to themain pulse.

20

Figure IV-g. Voltage, current and flux change for variousfiring points on a half-cycle magnetizer with transformer.

CONDUCTOR

“C” OR RING MAGNETS SOLENOID MAGNETIZING COILBAR MAGNET

STEEL

M A G N E T

C O N D U C T O R

MULTIPLE POLES ON ONE FACE OF DISC OR RING MAGNET

M A G N E T

STEEL RING u

P-POLE ON ID OF STATOR MAGNET OR ASSEMBLY

Figure IV-lo. Magnetizing conductor arrangements.

Demagnetization

Both producers and users of permanent magnets find itnecessary to demagnetize magnets. The producer mag-netizes magnets to check quality and must then demag-netize prior to shipping. The magnet user will often findneed to partially demagnetize to calibrate or to stabilizeagainst adverse fields or temperature variations. Themost common method of demagnetization is to subjectthe magnet to an a.c. field of a magnitude sufficient tonearly fully magnetize and then gradually reduce thisfield by pulling the magnet slowly from the field or byslowly reducing the a.c. current. It is also useful to pro-duce a damped wave form by charging a capacitor anddischarging into a coil. By proper choice of R, L and Can oscillatory wave form can be obtained, Figure IV-7.

With large metallic magnets a.c. fields are often ineffec-tive due to eddy current shielding. A d.c. supply withsome means to vary current and a reversing switch, isthe best way to demagnetize very large magnets. Thetechnique involves applying the field in alternate direc-tions at the same time the field magnitude is slowlyreduced. By experimenting with the cycles and fieldreduction per cycle, fairly complete demagnetizationcan be obtained.

With rare earth magnets some success in demagnetiza-tion has been achieved by using both thermal and fieldenergy to demagnetize. Exposing the magnet to per-haps 150”-200°C in conjunction with a.c. field of 1000oersteds has been useful. If the temperature of a mag-netized magnet is raised above its Curie temperatureand then returned to room temperature complete de-magnetization occurs. This procedure works well withceramic magnets but with metallic magnets structuralchanges may occur at the higher temperatures thatcause properties to be changed.

21

PART V. STABILIZING AND HANDLING

Introduction and Clarification of MagnetizationChanges

A compelling reason to use permanent magnets in manydevices and systems is the magnet’s ability to maintain aconstant flux output over a very long period of time. Inmost uses the magnet is subjected to influences thattend to alter the flux output to some extent. If the natureand extent of these influences is known it is possible topredict the amount of the flux change. It is also possi-ble, by exposing the magnet to the influence in advance,to render the magnet insensitive to subsequent changesduring the life span of the device. Using special stabili-zation techniques it is common to achieve field con-stancy of 1 part change in 105. To achieve this order ofstability with a regulated electromagnet would be pro-hibitively complex and costly. Today’s stability achieve-ments with modern permanent magnets are in sharpcontrast to very early permanent magnets which exhib-ited structural or metallurgical change with time.

It is helpful to classify the magnetization changes as totheir nature and cause:

(1) Reversible Changes-The reversible change influx as a function of temperature originates from thechange in spontaneous magnetization. Thesechanges obey the same temperature law as doessaturation magnetization. Reversible changes arefunctions of temperature and are not time depen-dent. They disappear completely without need forremagnetization when the magnet is returned to itsinitial temperature.

(2) Irreversible Change Resulting from a Change inThe Magnetic State-In this type of change afterremoval of the disturbing influence the magnetiza-tion does not return to the original value. Examplesof such changes are:

(A) Ambient temperature changes

(B) After-effects

(C) Magnetic field induced changes such as an ex-ternal field or change in magnetic circuit per-meance or load line

In the above changes, magnetization may be fullyrestored by remagnetization at room temperature.

(3) Permanent Irreversible Change Resulting Froma Change in the Structural or MetallurgicalState. Examples of such changes which are gener-ally time-temperature dependent are:

(A) Oxidation

(B) Phase Change

Remagnetization does not restore the original state ofmagnetization after this type of change. In the literaturethis type change is often referred to as aging since theremay be time dependence. The temperature at whichchange in properties first occur corresponds closely tothe maximum recommended service temperature.

No energy is required to maintain a magnetic field. En-ergy is only required to change a field. Thermal, me-chanical, magnetic field and radiation are energy inputforms that may change a permanent magnet field.

The magnetization in a permanent magnet is held by anet internal field (H,i - Hd). There is a dynamic energybalance which involves thermal energy and internalfield energy. The magnetic state is stable when the ther-mal energy is low compared to the internal field. We areconcerned with the coercive force mechanism and thetemperature dependence of H,i. If, for example, there isa difference between room temperature H,i and H,i atan elevated temperature, the formation of reversed do-mains will take place as soon as the temperaturechanges, until a new internal energy balance isachieved.

Time Effects at Constant Temperature

These changes are known as after effects or sometimesmagnetic viscosity. The domain regions of a freshlymagnetized magnet are in a self imposed internal field.They are also in a field that fluctuates in time. At aparticular site in the magnet small local temperatureexcursions occur. The temperature change causes afield change and an energy unbalance and hence a timeadjustment of magnetization. Because the change isthermally activated it can be accelerated with increasedtemperature. The after effect can also be anticipatedand stabilization can be achieved by subjecting the mag-net to an alternating field sufficient to demagnetize tothe extent of the loss which would occur during the timeperiod of interest. In practice demagnetizing 3-5% isusual. Table V-l shows the constant temperature (roomtemperature) adjustment with respect to time for fourwidely used permanent magnet materials. The magni-tude of the change is of little concern unless one is work-ing with a calibrated device. ,

Table V-l.Examples of property changes with time.

L O S SLoss At 100,000 Hrs

Material Per Log Cycle (11.4 years)

C e r a m i c Essentially Zero Essentially ZeroAlnico 5 (near residual) 0 . 0 1 % 0 . 0 6 %Alnico 5 (near max. energy). 0 . 1 5 % 0 . 9 %Alnico 5 (near coercive) 0 . 4 % 2 . 4 %Alnico G-no data (expected to be less than Alnico 5)SnlCOS 0 . 0 8 % 0 . 5 %

22

Structural and Metallurgical Changes

Alnico magnets are very stable and have no oxidationproblems up to about 500°C. Ferrite magnets are notsubject to oxidation but due to their lower Curie temper-ature are not used above 400°C.

Rare earth magnets have oxidation problems whichlimit their use to between 200°C and 300°C. For exam-ple with SmCos as temperature and time increase, oxy-gen diffuses into the material causing an oxidized layerto form. This oxidized layer has a changed compositionand a much lower coercive force. The internal field ofthe magnet will reverse the magnetization of the outerlayer. This leads to a compounding of flux loss since theouter layer represents a flux loss because of its volumewhich is not effective and also it acts as a shunt in reduc-ing the output of the interior magnet. For SmCo5 to beused above 200°C some kind of surface protection isneeded. An appropriate plating or coating is effective insome applications.

Irreversible Losses

Complete demagnetization curves at various tempera-tures are necessary to understand the irreversiblechanges as a function of temperature. From material tomaterial there is a wide range of behavior. For examplealnico 5 characteristics show curves at various tempera-tures crossing each other, leading to both positive andnegative coefficients.

For NdFeB magnets H,i decreases with increasing tem-perature. The relatively high positive H,i coefficientlimits the usefulness of NdFeB in high temperature ap-plications.

In the case of ferrite magnets the coercive force dimin-ishes with decreasing temperature so irreversibility atlow temperatures becomes a concern.

Table V-2 shows a general comparison of temperatureparameters for several materials. Curie temperature,maximum use temperature, reversible coefficient of B,and reversible coefficient of H,i with respect to temper-ature are compared in the table.

Table V-2. Temperature Characteristics Comparison

To form a perspective of how the various materialschange flux output with temperature variations, TableV-3 was constructed. The different materials have been

compared near their point of (BHmaX). One must re-member that irreversible loss is a strong function of B/Hsince the change is sensitive to the internal field of themagnet Hd. In the table the magnet is referenced toroom temperature and the percent irreversible lossshown is determined by exposure to the indicated tem-perature and then returning to room temperature tomeasure the percent loss. Table V-3 shows that the vari-ous materials have a wide range of behavior in responseto temperature. To predict change it is necessary to findthe change in the intrinsic magnetization J and then bygraphical construction project the change in B.

Table V-3. Comparison of Irreversible LossMate r ia l 1 -6OOC / +loo"c +200% +300% +400°c +woT

Alnico 5 1 -1.4% 1 0 . 4 j 0 . 8 1 1.1 1 1.7 1 -2.1%

The table indicates the irreversible loss of permeance measured at 20°C after exposure to theindicated temperature. B/H is near (BH),,, for all materia!s.

The ideal way to stabilize against irreversible losses is tosubject the magnet to several temperature cycles whichare to be the temperature limits expected in use. How-ever, this is time consuming and an acceptable alternateis to partially demagnetize by means of an a.c. field.Depending on the material, it may be necessary to fielddemagnetize to an extent greater than the loss due tothe temperature cycle to completely stabilize againstthe loss due to the temperature.

Reversible Losses

One cannot eliminate these reversible changes by stabi-lization. However, temperature compensation materialsmay be used as a shunt in parallel with a magnet toreduce the reversible loss to a negligible level. The watt-hour meter and the automotive speedometer are exam-ples of devices that normally use temperature compen-sation materials.

It is also possible to compensate a permanent magnetinternally, at the atomic level. Light rare earth elementssuch as Sm, Pr and Nd exhibit a negative temperaturecoefficient in the range of most interest (-40°C to+ 15O’C). Heavy rare earth elements such as Gd, Tb,Dy, Ho and Er have a positive coefficient because of adifferent mode of coupling between magnetic atoms. Bycombining both light and heavy rare earth atoms onecan produce a near zero reversible coefficient over alimited temperature range. However, since the mag-netic moments of the heavy atoms are lower, the overallproperties are lower than for the uncompensated mag-net.

Adverse Fields and Permeance Change

If a magnet is subjected to adverse magnetic fields par-tial demagnetization can result. Permeance or reluc-

23

tance change in a magnetic circuit can also result inpartial demagnetization. The extent to which thesechanges are irreversible depends on the magnitude ofthe change and the reversible permeability of the mate-rial.

Shock and Vibration

Mechanical shock and vibration add energy to a perma-nent magnet to decrease the magnetization in much thesame manner as discussed for the case of thermal after-effect. While our earliest magnets were magnetized anddemagnetized by shock in the earth’s field, today’s highenergy density magnets require much higher energyinput levels to change the level of magnetization. Foralmost all but the most closely calibrated devices, me-chanical energy input is not a magnetic problem withtodays magnets. However, magnetic material may bebrittle and subject to fracture from mechanical impacts.

Radiation

There are limited reported radiation tests for both softand hard magnetic materials. For soft magnetic materi-als the evidence is the coercivity increases. For perma-nent magnets there is little evidence that the flux loss isanything beyond that which can be attributed to temper-ature effects.

24

PART VI. SPECIFICATIONS, STANDARDS AND COMMUNlCATlQNS

The Guide to this point has been concerned largely withthe functional aspects of understanding, designing andmeasuring a permanent magnet. Magnet volume, mag-net geometry and magnet stability in a system or deviceare influenced by the unit properties of the magnet ma-terial chosen. Figure VI-1 is an attempt to show thescope of information involved in working with a multi-disciplined subject such as permanent magnetism. Thissection focuses on how user and producer can exchangeinformation and develop a complete specification. Thespecification involves much more than choice of magnetmaterial, volume and geometry. To define acceptabilityit must include dimensional tolerances, magnetic testinformation and visual acceptance criteria. The cost ofthe magnet is greatly influenced by the level and degreespecified for the required parameters. A good specifica-tion:

(1)

(2)

(3)

(4)

Allows the magnet producer to respond to inquiriesquickly and constructively with a minimum numberof changes or exceptions.

Simplifies correspondence and improves under-standing between the user and magnet supplier.

Prevents over specification which could result inhigher than necessary costs.

Results in usable and functional magnets.

The specification is an important control vehicle as itinterrelates a wide range of events occurring in both userand producer facilities as illustrated by Figure VI-l.

Figure VI- 1. The universe of information required in speci-fy ing .

MMPA Standard Specifications for PermanentMagnet Materials-0100 is an important specificationtool. It describes:

l Definitions and terms used in the magnet industry

l Classification and designation of magnet materials

l Magnetic properties, thermal properties surfacecharacteristics and other physical properties

l Mechanical characteristics

l Dimensions and tolerances

l Inspection and testing.

lndividual sections are devoted to alnico, ceramic, rareearth and iron-chromium-cobalt magnets. Each of thesegives information on composition, manufacturing meth-ods, magnetic properties, dimensions and tolerances,mechanical characteristics, physical properties, ther-mal properties and inspection sampling plans for eachclass of material.

Manufacturing processes vary considerably for each ofthe magnet classes. What is possible to achieve in oneclass is often not possible in others. There can also beconsiderable variation between magnet suppliers due toscale, investment, knowledge and experience. It is im-possible to describe all of the tolerances, shape factorsand physical parameters covering all the classes of mag-nets in this publication.

To facilitate development of a good specification thefollowing technique and checklists are offered. Thereare three categories of information involved. The firstcategory is:

(1) General magnetic properties

(2) Nominal dimensions

(3) Direction of orientation

(4) State of magnetization

(5) Quantity and delivery

These are essential items to be initially supplied by theuser when directing,inquiries or requesting cost infor-mation. In effect they constitute the bare minimum ofinformation. The general magnetic properties and nom-inal dimensions are a result of the design process.

Reference to MMPA Standard Specifications for Per-manent Magnet Materials 0100 or producers’ literaturewill help you select the class and grade of magnet mate-rial to be used as the general magnetic properties. Adrawing covering the nominal dimensions, configura-tion and direction of orientation is required. Figure VI-2shows several examples. State of magnetization indi-cates whether the magnets are to be shipped magnet-ized or demagnetized. If magnetized, the number of

25

poles and pole positions should be indicated. Deliveryinformation should include total quantity for quotation,estimated annual requirement, date when initial partsare required and rate of delivery. This latter informationis essential to the magnet producer for determining thetype of tooling, the number of cavities and the rate atwhich the magnets must be built.

I T/J0JM

D

n-/‘/ 1 */n

Figure VI-2. Dimensions, configurations and direction oforientation (J).

The second category of information is essential infor-mation supplied by the magnet producer. It is suggestedthat the magnet producer respond with this informationas part of his quotation.

(6) Specific magnetic specification

(7) Dimensional tolerances

In some instances the user may want or need to includesome of the above in his initial inquiry. The magneticspecification may involve a defined test procedurechecking for total flux, flux density, coercive force orperformance at a specific load line. A simulated circuitand use of correlation samples may be described. Thefollowing example of a simple holding magnet showshow important it is to integrate both magnetic and di-mensional tolerances into the specification. Figure VI-3shows a rectangular magnet having dimensions of H, Wand e. The force function is proportional to @/Agwhere c&, = the total magnet flux and A, is the area ofthe gap. In turn, daB,HW, where B, is the flux densityof the magnet. The chart lists an example with individ-ual magnetic and dimensional tolerances and the accu-mulated tolerances for C& and force. Such a broad rangein flux may not be acceptable and the magnet producermay agree to hold tighter flux control than the accumu-lation indicates. The best approach is to avoid trying tocontrol magnetics through extra tight and costly groundtolerances. By looking at the total design the magnetproducer will be able to offer the most cost effectiveapproach.

A generalized summary of dimensional tolerances foreach magnet class is described in Standard Specifica-tions 0100. The recommended procedure is to allow the

EXAMPLE

B, +5%

H .20 f .Olb ( * 5%)

a

w .30 * .Ol(+3.3%)

% A 4, * 13.3%

% A F -t 26%

(4

Figure W-3. Simple holding magnet.

UPPER BOUNDARY

UPPER LIMIT

NOMINAL FLUX

LOWER LIMIT-13.3% ,

LOWER BOUNDARY

Figure VI-4. Flux specification.

magnet producer to quote and suggest the specific mag-net test and test limits along with dimensional toler-ances which represent the best overall magnet value.

The third category of information is several optionalitems that may be important enough to be included inthe specifications. The magnet user should include anyof these items that require special consideration withhis initial inquiry when requesting cost information.

(8) Visual characteristics

(9) Sampling plan, AQL levels or statistical processcontrol plan.

(10)

(11)

(12)

Identification

Protective or decorative finish

Special performance requirements

Visual characteristics and inspection sampling plans forthe various magnet classes are included in the StandardSpecification booklet 0100. If other than these are toapply they should be described and included with theinitial cost request inquiry. The use of mutually agreedupon visual standards is recommended if it is critical tothe application. Sample boards have proven effective inthis respect.

2 6

When more than one material of the same size or morethan one supplier of same part is involved some kind ofidentification may be needed. Color code or imprintfrom tooling are suggested forms of identification.

To summarize items which may pertain to the develop-ment of a magnet specification are:

(1) General magnetic properties(2) Nominal dimensions(3) Direction of orientation(4) State of magnetization(5) Quantity and delivery(6) Specific magnetic specification(7) Dimensional tolerances(8) Visual characteristics(9) Sampling plan, AQL levels or statistical process

control plan(10) Identification(11) Protective or decorative finish(12) Special performance requirements

27

Bibliography1. Permanent Magnets in Theory and Practice. Malcolm

McCaig. Halsted Press, Div. of J. Wiley and Sons, NewYork, NY (1977)

2. Permanent Magnet Design and Application Hafldbook.L. Moskowitz. Cahners Book International. Boston,Massachusetts (1976)

3. Introduction to MagneticMaterials. B. D. Cullity. Addison-Wesley Publishing Co., Reading, Massachusetts (1972)

4. Dauermagnete- Werkstoffe and Anwendungen.K. Schuler and K. Brinkman. Springer-Verlag, Berlin-Heidelberg-NY (1970)

5. Permanent Magnets and Their Applications. R. J. Parkerand R. J. Studders. J. Wiley and Sons, New York (1962)

6. Permanent Magnets and Magnetism. D. Hadfield, editor.Iliffe Books, Ltd., London and J. Wiley and Sons, NewYork (1962)

7. Permanent Magnets, F G. ,Spreadbury Pitman and SonsLtd., London, 1949

8. Proc. 2nd Intl. Workshop Rare Earth-Co Perm Msg., K. J.Strnat, Editor. Univ. of Dayton, Dayton, OH (1976)

9. Proc. 3rd Intl. Workshop Rare Earth-Co Perm Mag., K. J.Strnat, Editor. Univ. of Dayton, Dayton, OH (1978)

10. Proc. 4th Intl. Workshop Rare Earth-Co Perm Mag.,H. Kaneko and T. Kurino,, editors. The Sot. of Non-Traditional Technology, Tokyo, Japan (1979)

11. PYOC. 5th Intl. Workshop Rare Earth-Co Perez Mag., K. J.Strnat, editor. Univ. of Dayton, Dayton, OH (1981)

12. Proc. 6th Intl. Workshop Rare Earth-Co Pcrm Msg.,J. Fidler. editor. Tech. University Vienna, Austria (1982)

13. Proc. 7th Intl. Workshop Rare Earth-Co Perm Mag.,X. Pan, W. Ho and C. Yu, editors. China Academic Pub-lishers, Beijing, P.R. of China (1983). Available throughUniversity of Dayton, OH, Magnetics Laboratory.

14. Proc. 8th Intl. Workshop Rare Earth-Co Perm Msg., K. J.Strnat, editor. University of Dayton, Dayton, OH (1985)

15. R. I. Joseph, “Ballistic DemagnetizingFactorin UniformlyMagnetized Cylinders.” J. Applied Physics, vol. 37,p. 4639, (1966)

16. Evaluation of Long-Term Magnet Stability, W. L. Zingeryet. al., J. Appl. Phys., 1, March, 1966

17. Radiation Damage Thresholds for Permanent Magnets,R. S. Sery, R. H. Lundsten and D. I. Gordon, NavalOrdance Laboratory TR-61-45 Silver Springs, Md., Mayl&l961

18. Environmental Evaluation of Magnetic Materials, D. I.Gordon, Electra-Technology, 67, No. 1, January 1961,pp. 118-125

19. Irradiating Magnetic Materials, D. I. Gordon, Electro-Technology, June 1965, pp. 42-45

20. PYOC. 9th Intl. Workshop Rare Earth Permanent Magnets,Bud Soden, W. Germany (1987)

MAGNETIC MATERIALS PRODUCERS ASSOCIATION

CRUMAX MAGNETICS THE PERMANENT MAGNET COMPANY, INC.101 Magnet Drive 4437 Bragdon StreetEl izabethtown, Kentucky 42701 Ind ianapo l i s , Ind iana 46226

ELECTRON ENERGY CORPORATION SGM ARMTEK, INC.924 Links Avenue 4-6 Pheasant RunLand isv i l l e , Pennsy lvan ia 17538 Newtown, Pennsylvania 18940

GENERAL MAGNETIC COMPANY SHIN-ETSU MAGNETICS INC.5252 Investment Drive 2362 Qume Drive, Suite ADal las , Texas 75236 San Jose , Ca l i fo rn ia 95131

GROUP ARNOLD TDK CORPORATION OF AMERICA300 N. West Street 1600 Feehanvi l le Dr iveMarengo, I l l ino is 60152 Mount Prospect, Illinois 60056

HITACHI MAGNETICS CORPORATION THOMAS & SKINNER, INC.7800 Neff Road 1120 East 23rd StreetEdmore, Michigan 48829 Ind ianapo l i s , Ind iana 46205

KANE MAGNETICS INTERNATIONAL UGIMAG, INC.700 Elk Avenue 405 Elm StreetKane, Pennsy lvan ia 16735 Va lpara iso , Ind iana 46383

MAGNEQUENCH INTERNATIONAL, INC. VAC CORP.6435 Scat ter - f ie ld Road 4027 Will Rogers Pkwy.Anderson, Indiana 46013 Oklahoma City, Oklahoma 73108

NATIONAL MAGNETICS GROUP, INC.1210 Win DriveBeth lehem, Pennsy lvan ia 18017

ASSOCIATE MEMBERS

LDJ ELECTRONICS MAGNETIC INSTRUMENTATION, INC. WALKER SCIENTIFIC, INC.1280 E. B ig Beaver 8431 Castlewood Drive 17 Rockdale StreetTroy, Mich igan 48083 Ind ianapo l i s , Ind iana 46250 Worcester, MA 01606