
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:
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 (general composition Nd_{2}Fe_{14}B, 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 is manufactured in two compositions: Sm_{1}Co_{5} and Sm_{2}Co_{17}  often referred to as the SmCo 1:5 or SmCo 2:17 types. 2:17 types, with higher H_{ci} values, offer greater inherent stability than the 1:5 types. Ceramic, also known as Ferrite, magnets (general composition BaFe_{2}O_{3 }or SrFe_{2}O_{3}) 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 AlNiCo) were commercialized in the 1930s and are still extensively used today. These 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 detail in the following sections.



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.



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.
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 Magnet Sales & Manufacturing has extensive experience in many types of magnetic designs and is able to assist in the design and execution of FEA models.
The basis of magnet design is the BH 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 BH 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 airgap 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 BH 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 BH curve with temperature. This effect is more closely examined in the section entitled "Permanent Magnet Stability".
When plotting a BH curve, the value of B is obtained by measuring the total flux in the magnet (ø)and then dividing this by the magnet pole area (A) to obtain the flux density (B=ø/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 BH 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.
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
H_{m} = the magnetizing force at the operating point, A_{g}, = the airgap area, L_{g} = the airgap 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: _{ } Equation 3
Strictly, _{}
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 airgap, so that the parameters B_{g}, H_{g} (airgap 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.
For magnet materials with straightline 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's centerline under a variety of conditions. a. Cylindrical Magnets _{
}
Table 4.1 shows flux density calculations for a magnet 0.500" in diameter by 0.250" long at a distance of 0.050" from the pole surface, for various materials. Note that you may use any unit of measure for dimensions; since the equation is a ratio of dimensions, the result is the same using any unit system. The resultant flux density is in units of gauss.



b. Rectangular Magnets 



d. For a Magnet on a Steel Back plate Equation 7 Substitute 2L for L in the above formulae.
e. For Identical Magnets Facing Each Other in Attracting Positions Equation 8 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_{(xp) }and B_{(xp)}, where (X+P) and (XP) substitute for X in case 3.
f. For Identical, Yoked Magnets Facing Each Other in Attracting Positions Equation 9 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 10
_{ }Equation 11
where B_{r} is the residual flux density of the material, A is the pole area in square inches, and L_{m} is the magnetic length (also in inches).
Click here to go to the next section of the Design Guide, Permanent Magnet Stability.


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Sales & Manufacturing Company, Inc. 