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Magnet Design Guide for Technical Applications

Contents

1.0 Introduction

Magnets are an important part of our daily lives, serving as essential components in everything from electric motors, loudspeakers, computers, compact disc players, microwave ovens and the family car, to instrumentation, production equipment, and research. Their contribution is often overlooked because they are built into devices and are usually out of sight.

Magnets function as transducers, transforming energy from one form to another, without any permanent loss of their own energy. General categories of permanent magnet functions are:

  • Mechanical to mechanical - such as attraction & repulsion.
  • Mechanical to electrical - such as generators & microphones.
  • Electrical to mechanical - such as motors, loudspeakers, charged particle deflection.
  • Mechanical to heat - such as eddy current & hysteresis torque devices.
  • Special effects - such as magneto resistance, Hall effect devices, & magnetic resonance.

The following sections will provide a brief insight into the design and application of permanent magnets. The Design Engineering team at Magnet Sales & Manufacturing will be happy to assist you further in your applications. (top)

2.0 Modern Magnet Materials

There are four classes of modern commercialized magnets, each based on their material composition. Within each class is a family of grades with their own magnetic properties. These general classes are:

NdFeB and SmCo are collectively known as Rare Earth magnets because they are both composed of materials from the Rare Earth group of elements.

  • Neodymium Iron Boron magnets (general composition Nd2Fe14B, often abbreviated to NdFeB) is the most recent commercial addition to the family of modern magnet materials. At room temperatures, NdFeB magnets exhibit the highest properties of all magnet materials.
  • Samarium Cobalt magnets are manufactured in two compositions: Sm1Co5 and Sm2Co17 - often referred to as the SmCo 1:5 or SmCo 2:17 types. 2:17 types, with higher Hci values, offer greater inherent stability than the 1:5 types.
  • Ceramic magnets, also known as Ferrite, magnets (general composition BaFe2O3 or SrFe2O3) have been commercialized since the 1950s and continue to be extensively used today due to their low cost. A special form of Ceramic magnet is "Flexible" material, made by bonding Ceramic powder in a flexible binder.
  • Alnico magnets (general composition Al-Ni-Co) were commercialized in the 1930s and are still extensively used today.

These magnet materials span a range of properties that accommodate a wide variety of application requirements. The following is intended to give a broad but practical overview of factors that must be considered in selecting the proper material, grade, shape, and size of magnet for a specific application. The chart below shows typical values of the key characteristics for selected grades of various materials for comparison. These values will be discussed in more detail in the below sections. (top)

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Table 2.1 Magnet Material Comparisons

Material

Grade

Br

Hc

Hci

BHmax

Tmax (ºC)*

NdFeB

39H

12,800

12,300

21,000

40

150

SmCo

26

10,500

9,200

10,000

26

300

NdFeB

B10N

6,800

5,780

10,300

10

150

Alnico

5

12,500

640

640

5.5

540

Ferrite

8

3,900

3,200

3,250

3.5

300

Flexible

1

1,600

1,370

1,380

0.6

1000

*Tmax (maximum practical operating temperature) is for reference only. The maximum practical operating temperature of any magnet is dependent on the circuit the magnet is operating in.

3.0 Units of Measure

Three systems of units of measure are common: the cgs (centimeter, gram, second), SI (meter, kilogram, second), and English (inch, pound, second) systems. This catalog uses the cgs system for magnetic units, unless otherwise specified. (top).

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Table 3.1 Units of Measure System

Unit

Symbol

cgs
System

SI
System

English
System

Flux

%

maxwell

weber

maxwell

Flux Density

B

gauss

tesla

lines/in2

Magnetomotive
Force

F

gilbert

ampere
turn

ampere
turn

Magnetizing
Force

H

oersted

ampere
turns/m

ampere
turns/in

Length

L

cm

m

in

Permeability of a vacuum

µv

1

0.4π  x 10-6

3.192

 
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Table 3.2 Conversion Factors

Multiply

By

To Obtain

Inches

2.54

Centimeters

Lines/in2

0.155

Gauss

Lines/in2

1.55 x 10-5

Tesla

Gauss

6.45

Lines/in2

Gauss

0-4

Tesla

Gilberts

0.79577

Ampere turns

Oersteds

79.577

Ampere turns/m

Ampere turns

0.4"

Gilberts

Ampere turns/in

0.495

Oersteds

Ampere turns/in

39.37

Ampere turns/m

Mega Gauss Oersteds

7.91667

Kilo Joules/m3

Click here for an interactive version of this conversion table.

4.0 Design Considerations

Basic problems of permanent magnet design revolve around estimating the distribution of magnetic flux in a magnetic circuit, which may include permanent magnets, air gaps, high permeability conduction elements, and electrical currents. Exact solutions of magnetic fields require complex analysis of many factors, although approximate solutions are possible based on certain simplifying assumptions. Obtaining an optimum magnet design often involves experience and trade offs. (top)

4.1 Finite Element Analysis

Finite Element Analysis (FEA) modeling programs are used to analyze magnetic problems in order to arrive at more exact solutions, which can then be tested and fine tuned against a prototype of the magnet structure. Using FEA models flux densities, torques, and forces may be calculated. Results can be output in various forms, including plots of vector magnetic potentials, flux density maps, and flux path plots. Our design and engineering team at our sister company, Integrated Magnetics has extensive experience in many types of magnetic designs and is able to assist in the design and execution of FEA models. (top)

4.2 The B-H Curve

The basis of magnet design is the B-H curve, or hysteresis loop, which characterizes each magnet material. This curve describes the cycling of a magnet in a closed circuit as it is brought to saturation, demagnetized, saturated in the opposite direction, and then demagnetized again under the influence of an external magnetic field.

The second quadrant of the B-H curve, commonly referred to as the "Demagnetization Curve", describes the conditions under which permanent magnets are used in practice. A permanent magnet will have a unique, static operating point if air-gap dimensions are fixed and if any adjacent fields are held constant. Otherwise, the operating point will move about the demagnetization curve, the manner of which must be accounted for in the design of the device.

The three most important characteristics of the B-H curve are the points at which it intersects the B and H axes (at B- the residual induction - and Hc - the coercive force - respectively), and the point at which the product of B and H are at a maximum (BHmax - the maximum energy product). Brepresents the maximum flux the magnet is able to produce under closed closed circuit conditions. In actual useful operation, permanent magnets can only approach this point. Hc represents the point at which the product of B and H, and the energy density of the magnetic field into the air gap surrounding the magnet, is at a maximum. The higher this product, the smaller the volume of the magnet need be. Designs should also account for the variation of the B-H curve with temperature. This effect is more closely examined in the section entitled "Permanent Magnet Stability(top)

When plotting a B-H curve, the value of B is obtained by measuring the total flux in the magnet (φ) and then dividing this by the magnet pole area (A) to obtain the flux density (B=φ/A). The total flux is composed of the flux produced in the magnet by the magnetizing field (H), and the intrinsic ability of the magnet material to produce more flux due to the orientation of the domains. The flux density of the magnet is therefore composed of two components, one equal to the applied H, and the other created by the intrinsic ability of ferromagnetic materials to produce flux. The intrinsic flux density is given the symbol B1 where total flux B = H + B1 or B1 = B-H.

In normal operating conditions, no external magnetizing field is present, and the magnet operates in the second quadrant, where H has a negative value. Although strictly negative, H is usually referred to as a positive number, and therefore, in normal practice, B = B + H. It is possible to plot an intrinsic as well as a normal B-H curve. The point at which the intrinsic curve crosses the H axis is the intrinsic coercive force, and is given the symbol Hc1, High Hc1 values are an indicator of inherent stability of the magnet material. The normal curve can be derived from the intrinsic curve and vice versa. In practice, if a magnet is operated in a static manner with no external fields present, the normal curve is sufficient for design purposes. When external fields are present, the normal and intrinsic curves are used to determine the changes in the intrinsic properties of the material. (top)

4.3 Magnet Calculations

In absence of any coil excitation, the magnet length and pole area may be determined by the following equations:


Equation 1


Equation 2


where

  • B