lines/in²

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 tradeoffs.

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. The Design Engineering team at Hegao Magtech has extensive experience in many types of magnetic designs and is able to assist in the design and execution of FEA models.

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_r - the residual induction - and H_c - the coercive force - respectively), and the point at which the product of B and H are at a maximum (BH_max - the maximum energy product). B_r represents the maximum flux the magnet is able to produce under closed circuit conditions. In actual useful operation permanent magnets can only approach this point. H_c represents the point at which the magnet becomes demagnetized under the influence of an externally applied magnetic field. BH_max 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 need be the volume of the magnet. 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".

When plotting a B-H curve, the value of B is obtained by measuring the total flux in the magnet (?/font>)and then dividing this by the magnet pole area (A) to obtain the flux density (B=?/font>/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 B_i where total flux B = H + B_i, or, B_i = 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_i = 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 H_ci. High H_ci 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.

4.3 Magnet Calculations

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

   Equation 1

and

    Equation 2

where B_m = the flux density at the operating point,
H_m = the magnetizing force at the operating point,
A_g, = the air-gap area,
L_g = the air-gap length,
B_g = the gap flux density,
A_m = the magnet pole area,
and L_m = the magnet length. 

Combining the two equations, the permeance coefficient P_c may be determined as follows:

where ?is the permeability of the medium, and k is a factor which takes account of leakage and reluctance that are functions of the geometry and composition of the magnetic circuit.

Click here to calculate Permeance Coefficients of Disc, Rectangle, Ring

(The intrinsic permeance coefficient P_ci = B _i/H. Since the normal permeance coefficient P_c = B/H, and B = H + B _i, P_c = (H + B _i)/H or P_c = 1 + B _i /H. Even though the value of H in the second quadrant is actually negative, H is conventionally referred to as a positive number. Taking account of this convention, P_c = 1 - B _i /H, or B _i /H = P_ci = P_c + 1. In other words, the intrinsic permeance coefficient is equal to the normal permeance coefficient plus 1. This is a useful relationship when working on magnet systems that involve the presence of external fields.)

The permeance coefficient is a useful first order relationship, helpful in pointing towards the appropriate magnet material, and to the approximate dimensions of the magnet. The objective of good magnet design is usually to minimize the required volume of magnet material by operating the magnet at BH_max. The permeance coefficient at which BH_max occurs is given in the material properties tables .

We can compare the varios magnet materials for general characteristics using equation 3 above.

Consider that a particular field is required in a given air-gap, so that the parameters B_g, H_g (air-gap magnetizing force), A_g, and L_g are known.

The permeance coefficient method using the demagnetization curves allows for initial selection of magnet material, based upon the space available in the device, this determining allowable magnet dimensions.

4.3.1 Calculation Of Flux Density On A Magnet's Central Line

Click here to calculate flux density of rectangular or cylindrical magnets in various configurations (equations 4 through 8).

For magnet materials with straight-line normal demagnetization curves such as Rare Earths and Ceramics, it is possible to calculate with reasonable accuracy the flux density at a distance X from the pole surface (where X>0) on the magnet centerline under a variety of conditions.

a. Cylindrical Magnets

c. For a Magnet on a Steel Back plate

Equation 6 Substitute 2L for L in the above formulae.

 d. For Identical Magnets Facing Each Other in Attracting Positions

Equation 7 The value of B_x at the gap center is double the value of B_x in case 3. At a point P, B_p is the sum of B_(x-p) and B_(x-p), where (X+P) and (X-P) substitute for X in case 3.

 e. For Identical, Yoked Magnets Facing Each Other in Attracting Positions

Equation 8 Substitute 2L for L in case 4, and adopt the same procedure to calculate B_p.

 4.3.2 Force Calculations

The attractive force exerted by a magnet to a ferromagnetic material may be calculated by:

   Equation 9

where F is the force in pounds, B is the flux density in Kilogauss, and A is the pole area in square inches. Calculating B is a complicated task if it is to be done in a rigorous manner. However, it is possible to approximate the holding force of certain magnets in contact with a piece of steel using the relationship:

The ability of a permanent magnet to support an external magnetic field results from small magnetic domains "locked" in position by crystal anisotropy within the magnet material. Once established by initial magnetization, these positions are held until acted upon by forces exceeding those that lock the domains. The energy required to disturb the magnetic field produced by a magnet varies for each type of material. Permanent magnets can be produced with extremely high coercive forces (H_c) that will maintain domain alignment in the presence of high external magnetic fields. Stability can be described as the repeated magnetic performance of a material under specific conditions over the life of the magnet.

Factors affecting magnet stability include time, temperature, reluctance changes, adverse fields, radiation, shock, stress, and vibration.

5.1 Time

The effect of time on modern permanent magnets is minimal. Studies have shown that permanent magnets will see changes immediately after magnetization. These changes, known as "magnetic creep", occur as less stable domains are affected by fluctuations in thermal or magnetic energy, even in a thermally stable environment. This variation is reduced as the number of unstable domains decreases. Rare Earth magnets are not as likely to experience this effect because of their extremely high coercivities. Long-term time versus flux studies have shown that a newly magnetized magnet will lose a minor percent of its flux as a function of age. Over 100,000 hours, these losses are in the range of essentially zero for Samarium Cobalt materials to less than 3% for Alnico 5 materials at low permeance coefficients.

5.2 Temperature

Temperature effects fall into three categories:

5.2.1. Reversible losses.

These are losses that are recovered when the magnet returns to its original temperature. Reversible losses cannot be eliminated by magnet stabilization. Reversible losses are described by the Reversible Temperature Coefficients (T_c), shown in table 5.1. T_c is expressed as % per degree Centigrade. These figures vary for specific grades of each material but are representative of the class of material as a whole. It is because the temperature coefficients of B_r and H_c are significantly different that the demagnetization curve develops a "knee" at elevated temperatures.

These losses are defined as partial demagnetization of the magnet from exposure to high or low temperatures. These losses are only recoverable by remagnetization, and are not recovered when the temperature returns to its original value. These losses occur when the operating point of the magnet falls below the knee of the demagnetization curve. An efficient permanent magnet design should have a magnetic circuit in which the magnet operates at a permeance coefficient above the knee of the demagnetization curve at expected elevated temperatures. This will prevent performance variations at elevated temperatures.

5.2.3. Irreversible and unrecoverable losses.

Metallurgical changes occur in magnets exposed to very high temperatures and are not recoverable by remagnetization. Table 5.2 shows critical temperatures for the various materials, where

*Note that the maximum practical operating temperature is dependent on the operating point of the magnet in the circuit. The higher the operating point on the Demagnetization Curve, the higher the temperature at which the magnet may operate.

Flexible materials are not included in this table since the binders that are used to render the magnet flexible break down before metallurgical changes occur in the magnetic ferrite powder that provides flexible magnets with their magnetic properties.

Partially demagnetizing a magnet by exposure to elevated temperatures in a controlled manner stabilizes the magnet with respect to temperature. The slight reduction in flux density improves a magnetís stability because domains with low commitment to orientation are the first to lose their orientation. A magnet thus stabilized will exhibit constant flux when exposed to equivalent or lesser temperatures. Moreover, a batch of stabilized magnets will exhibit lower variation of flux when compared to each other since the high end of the bell curve which characterizes normal variation will be brought in closer to the rest of the batch.

5.3 Reluctance Changes

These changes occur when a magnet is subjected to permeance changes such as changes in air gap dimensions during operation. These changes will change the reluctance of the circuit, and may cause the magnet's operating point to fall below the knee of the curve, causing partial and/or irreversible losses. The extents of these losses depend upon the material properties and the extent of the permeance change. Stabilization may be achieved by pre-exposure of the magnet to the expected reluctance changes.

5.4 Adverse Fields

External magnetic fields in repulsion modes will produce a demagnetizing effect on permanent magnets. Rare Earth magnets with coercive forces exceeding 15 KOe are difficult to affect in this manner. However, Alnico 5, with a coercive force of 640 Oe will encounter magnetic losses in the presence of any magnetic repelling force, including similar magnets. Applications involving Ceramic magnets with coercive forces of approximately 4KOe should be carefully evaluated in order to assess the effect of external magnetic fields.

5.5 Radiation

Rare Earth materials are commonly used in charged particle beam deflection applications, and it is necessary to account for possible radiation effects on magnetic properties. Studies (A.F. Zeller and J.A. Nolen, National Superconducting Cyclotron Laboratory, 09/87, and E.W. Blackmore, TRIUMF, 1985) have shown that SmCo and especially Sm₂Co₁₇ withstand radiation 2 to 40 times better than NdFeB materials. SmCo exhibits significant demagnetization when irradiated with a proton beam of 10⁹ to 10¹⁰ rads. NdFeB test samples were shown to lose all of their magnetization at a dose of 7 x 10⁷ rads, and 50% at a dose of 4 x 10⁶ rads. In general, it is recommended that magnet materials with high H_ci values be used in radiation environments, that they be operated at high permeance coefficients, P_c, and that they be shielded from direct heavy particle irradiation. Stabilization can be achieved by pre-exposure to expected radiation levels.

5.6 Shock, Stress, and Vibration

Below destructive limits, these effects are very minor on modern magnet materials. However, rigid magnet materials are brittle in nature, and can easily be damaged or chipped by improper handling. Samarium Cobalt in particular is a fragile material and special handling precautions must be taken to avoid damage. Thermal shock when Ceramics and Samarium Cobalt magnets are exposed to high temperature gradients can cause fractures within the material and should be avoided.

6.0 Manufacturing Methods

Permanent magnets are manufactured by one of the following methods:

The sintering process involves compacting fine powders at high pressure in an aligning magnetic field, then sintering to fuse into a solid shape. After sintering, the magnet shape is rough, and will need to be machined to achieve close tolerances. The intricacy of shapes that can be thus pressed is limited.

Rare Earth magnets may be die pressed (with pressure being applied in one direction) or isostatically pressed (with equal pressure being applied in all directions). Isostatically pressed magnets achieve higher magnetic properties than die pressed magnets. The aligning magnetic field for die pressed magnets can be either parallel or perpendicular to the pressing direction. Magnets pressed with the aligning field perpendicular to the pressing direction achieve higher magnetic properties than the parallel pressed form.

Both Rare Earth and Ceramic magnets can also be manufactured by pressure bonding or injection molding the magnet powders in a carrier matrix. The density of magnet material in this form is lower than the pure sintered form, yielding lower magnetic properties. However, bonded or injection molded magnets may be made with close tolerances "off-tool" and in relatively intricate shapes.

Alnico is manufactured in a cast or sintered form. Alnicos may be cast in large or complex shapes (such as the common horseshoe), while sintered Alnico magnets are made in relatively small sizes (normally one ounce or less) and in simple shapes.

Flexible Rare Earth or Ceramic magnets are made by calendering or extruding magnet powders in a flexible carrier matrix such as vinyl. Magnet powder densities and therefore magnetic properties in this form of manufacture are even lower than the bonded or injection molded form. Flexible magnets are easily cut or punched to shape.

7.0 Physical Characteristics and Machining of Permanent Magnets

Sintered Samarium Cobalt and Ceramic magnets exhibit small cracks within the material that occur during the sintering process. Provided that cracks do not extend more than halfway through a section, they do not normally affect the operation of the magnet. This is also true for small chips that may occur during machining and handling of these magnets, especially on sharp edges. Magnets may be tumbled to break edges: this is done to avoid "feathering" of sharp edges due to the brittle nature of the materials. Tumbling can achieve edge breaks of 0.003" to 0.010". Although Neodymium Iron Boron is relatively tough as compared to Samarium Cobalt and Ceramic, it is still brittle and care must be taken in handling. Because of these inherent material characteristics, it is not advisable to use any permanent magnet material as a structural component of an assembly.

Rare Earth, Alnico, and Ceramic magnets are machined by grinding, which may considerably affect the magnet cost. Maintaining simple geometries and wide tolerances is therefore desirable from an economic point of view. Rectangular or round sections are preferable to complex shapes. Square holes (even with large radii), and very small holes are difficult to machine and should be avoided. Magnets may be ground to virtually any specified tolerance. However, to reduce costs, tolerances of less than +0.001" should be avoided if possible.

Cast Alnico materials exhibit porosity as a natural consequence of the casting process. This may become a problem with small shapes, which are machined out of larger castings. The voids occupy a small portion of the larger casting, but can account for a large portion of the smaller fabricated magnets. This may cause a problem where uniformity or low variation is critical, and it may be advisable either to use a sintered Alnico, or another material. In spite of its slightly lower magnetic properties, sintered Alnico may yield a higher or more uniform net density, resulting in equal or higher net magnetic output.

In applications where the cosmetic qualities of the magnet are of a concern, special attention should be placed on selecting the appropriate material, since cracks, chips, pores, and voids are common in rigid magnet materials.

Hegao Magtech has extensive experience in the machining and handling of all permanent magnet materials. In house machining facilities allow the ability to deliver prototype to production quantities with short lead times.

8.0 Coatings

Samarium Cobalt, Alnico, and Ceramic materials are corrosion resistant, and do not require to be coated against corrosion. Alnico is easily plated for cosmetic qualities, and Ceramics may be coated to seal the surface, which will otherwise be covered by a thin film of ferrite powder (although not a problem for most applications).

Neodymium Iron Boron magnets are susceptible to corrosion and consideration should be given to the operating environment to determine if coating is necessary. Nickel or tin plating may be used for Neodymium Iron Boron magnets, however, the material must be properly prepared and the plating process properly controlled for successful plating. Plating houses experienced in the plating of NdFeB materials are difficult to locate, and must be furnished with the necessary information for proper preparation and control of the process. Aluminum chromate or cadmium chromate vacuum deposition has been successfully tested, with coating thickness as low as 0.0005". Teflon and other organic coatings are relatively inexpensive and have also been successfully tested. A further option for critical applications is to apply two types of protective coatings or to encase the magnet in a stainless steel or other housing to reduce the chances of corrosion.

9.0 Assembly Considerations

Hegao Magtech Inc. has manufacturing capabilities to manufacture complex magnet pole pieces and housings to provide a complete magnet assembly. The following points should be considered when designing magnet assemblies.

9.1 Affixing Magnets to Housings

Magnets can be successfully affixed to housings using adhesives. Cyanoacrylate adhesives that are rated to temperatures up to 350F with fast cure times are most commonly used. Fast cure times avoid the need for fixtures to hold the magnets in place while the bond cures. Adhesives with higher temperature ratings are also available, but these require oven curing, and fixturing of the magnets to hold them in place. If magnet assemblies are to be used in a vacuum, potential out-gassing of the adhesives should be considered.

9.2 Housing Design

Hegao Magtech is equipped with state of the art CNC and EDM equipment allowing the manufacture of complex housings. Effective magnet locating sections should be included in housing designs to support and locate magnets precisely.

9.3 Mechanical Fastening

When arrays of magnets must be assembled, especially when the magnets must be placed in repelling positions, it is very important to consider safety issues. Modern magnet materials such as the Rare Earths are extremely powerful, and when in repulsion they can behave as projectiles if adhesives were to break down. We strongly recommend that in these situations mechanical fastening be included in the design in addition to adhesives. Potential methods of mechanical retention include encasement, pinning, or strapping the magnets in place with non-magnetic metal components. The Design Engineering team at Hegao Magtech is experienced in magnet housing and fastening designs, and we will be pleased to assist in arriving at an appropriate design.

9.4 Potting

Magnet assemblies may be potted to fill gaps or to cover entire arrays of magnets. Potting compounds cure to hard and durable finishes, and are available to resist a variety of environments, such as elevated temperatures, water flow, etc. When cured, the potting compounds may be machined to provide accurate finished parts.

9.5 Welding

Assemblies that are required to be hermetically sealed can be welded using either laser welding (which is not affected by the presence of magnetic fields) or TIG welding (using appropriate shunting elements to reduce the effect of magnetic fields on the weld arc). Special care should be taken when welding magnetic assemblies so that heat dissipation of the weld does not affect the magnets.

10.0 Magnetization

Permanent magnet materials are believed to be composed of small regions or "domains" each of which exhibit a net magnetic moment. An unmagnetized magnet will possess domains that are randomly oriented with respect to each other, providing a net magnetic moment of zero. Thus a magnet when demagnetized is only demagnetized from the observer's point of view. Magnetizing fields serve to align randomly oriented domains to give a net, externally observable field.

10.1 Objective of Magnetization

The objective of magnetization is initially to magnetize a magnet to saturation, even if it will later be slightly demagnetized for stabilization purposes. Saturating the magnet and then demagnetizing it in a controlled manner ensures that the domains with the least commitment to orientation will be the first to lose their orientation, thereby leading to a more stable magnet. Not achieving saturation, on the other hand, leads to orientation of only the most weakly committed domains, hence leading to a less stable magnet.

Anisotropic magnets must be magnetized parallel to the direction of orientation to achieve optimum magnetic properties. Isotropic magnets can be magnetized through any direction with little or no loss of magnetic properties. Slightly higher magnetic properties are obtained in the pressing direction.

10.2 Magnetizing Equipment

Magnetization is accomplished by exposing the magnet to an externally applied magnetic field. This magnetic field may be created by other permanent magnets, or by currents flowing in coils. Using permanent magnets for magnetization is only practical for low coercivity or thin sections of materials. Removal of the magnetized specimen from the permanent magnet magnetizer can be problematic since the field cannot be turned off, and fringing fields may adversely affect the magnetization of the specimen.

The two most common types of magnetizing equipment are the DC and capacitor discharge magnetizers.

10.2.1 DC Magnetizers

DC magnetizers employ large coils through which a current is applied for a short duration by closing a switch. The current flowing through the coil produces a magnetic field, which is usually directed by the use of iron cores and pole pieces, and magnets are placed in the gap between the pole pieces. DC magnetizers are only practical for magnetizing Alnico materials, which have a low magnetizing force requirement, or small sections of Ceramic materials.

10.2.2 Capacitor Discharge Magnetizers

Capacitor discharge magnetizers employ capacitor banks that are charged, and then discharged through a coil. Provided the coil has a resistance, R, which is greater than , where L is the inductance and C the capacitance, the current flowing though the coil will be unidirectional. Extremely high magnetizing fields (in the range of 100 KOe) can be achieved using special coils and power supplies.

10.3 Saturation Fields Required

Some Rare Earth magnets require very high magnetizing fields in the 20 to 50 KOe range. These fields are difficult to produce requiring large power supplies in conjunction with carefully designed magnetizing fixtures. Isotropic bonded Neodymium materials require fields in the high 60 KOe range to be fully saturated. However, fields in the 30 KOe range may achieve 98% of saturation. Ceramics require fields in the order of 10 KOe, while Alnicos require fields in the range of 3 KOe for saturation. Because of the ease by which Alnico 5 can become inadvertently demagnetized, it is preferable for this material to be magnetized just prior to or even after final assembly of the magnet into the device.

10.4 Multiple Pole Magnetization

In certain cases, it may be desirable to magnetize a magnet with more than one pole on a single pole surface. This may be accomplished by constructing special magnetizing fixtures. Multiple pole magnetizing fixtures are relatively simple to build for Alnico and Ceramic, but require great care in design and construction for Rare Earth materials.

Magnetizing with multiple poles will sometimes eliminate the need for several discrete magnets, reducing assembly costs, although a cost will be incurred for building an appropriate magnetizing fixture. Multiple pole fixtures for Rare Earth magnets may cost several thousand dollars to build, depending on the size of the magnet, the number of poles required, and the fields necessary to achieve saturation.

10.5 The Orientation Direction

Some applications require magnets oriented in a particular direction with a high degree of accuracy. This direction may or may not coincide with a geometrical plane of the magnet. For anisotropic materials the orientation direction can normally be held within 3° of the nominal with no special precautions. However, more precise requirements may need special measurement and testing. This is achieved by the use of Helmholtz coils, which measure the total flux in various axes, and thence calculating the resultant magnetic moment vector. Materials must be cut and machined taking into account the actual angle of orientation to achieve the required accuracy. Isotropic materials may be magnetized in any direction, and therefore pose no problem in this regard.

11.0 Measurement and Testing

It is important that incoming inspection of magnetic characteristics be clearly and properly specified. End point characteristics (such as B_r or H_c) cannot be directly observed; therefore inspection personnel should not expect to measure 8,500 Gauss on a SmCo 18 magnet even though the B_r is specified at 8,500 Gauss.

A test method or combination of test methods should be based upon the criticality of the requirement, and the cost and ease of performing tests. Ideally, the test results should be able to be directly translated into functional performance of the magnet. A sampling plan should be specified which inspects the parameters which are critical to the application. A brief description of some common test methods follows below.

11.1 B-H Curves

B-H curves may be plotted with the use of a permeameter. These curves completely characterize the magnetic properties of the material at a specific temperature. In order to plot a B-H curve, a sample of specific size must be used, then cycled through a magnetization/demagnetization cycle. This test is expensive to perform due to the length of time required to complete. The test is destructive to the sample piece in many cases, and is not practical to perform on a large sample of finished magnets. However, when magnets are machined from a larger block, the supplier may be requested to provide B-H curves for the starting raw stock of magnet material.

11.2 Total Flux

Using a test set up consisting of a Helmholtz coil pair connected to a fluxmeter, total flux measurements can b