Theory & Practice of Electromagnetic Design of DC Motors & Actuators
George P. Gogue & Joseph J. Stupak, Jr.
2.1 Magnetically hard (permanent magnet) materials:
Before the 1930's, the only available magnet material other than lodestone was hardened steel. Since steel with a high carbon content hardened by heat-treatment would retain its magnetism, whereas soft or mild steel with a low carbon content would not, magnetic materials came to be called "hard" or "soft" depending on whether they would retain a permanent magnetic field or not. The names "hard" and "soft" as a description of magnetic properties have remained, even though some modern magnetically soft materials are very hard mechanically, and some relatively soft materials are magnetically hard.
Hardened steel has a very high (high flux) but very little coercivity (), as shown in Figure 1.9. Reluctance to flux flow (in the surrounding space) is less for a long, thin rod which is axially magnetized than for a shorter, thicker part. In order to avoid self-demagnetization owing to shape, i.e. a B/H slope line behind the knee of the curve, magnets had to be long and thin, like the traditional compass needle. In the early 1930's, various magnetic materials were found which had lower , but far greater coercivity and maximum energy product than steel. The most successful of these were the alnico magnets. The name "alnico" is derived from the constituent metals aluminum, nickel and cobalt. Whereas a steel magnet might need to have an aspect ratio (length to width) of 50:1 to avoid losing its field in air, an alnico magnet might be safe at somewhere between 3:1 and 10:1, depending on the type used and its intended service. By comparison, newer materials such as ferrites, samarium-cobalt, and neodymium-iron have such high resistance to demagnetization from shape effects in air that sometimes persons experienced in only these materials have never encountered the effect and do not realize that the hazard exists. It is nonetheless possible to partially demagnetize some of these materials by shape effect, e.g. by using large, thin magnets magnetized through the thickness, or by radially magnetizing a long, thin-walled tube with few poles. The B/H slopes resulting in magnets as a function of several shapes and length:width ratio are shown in Figure 2.1 (Ref. 41). If the slope results in the operating point being behind the knee of the curve for the particular material intended, then that magnet may work well in a magnetic circuit (with the magnet magnetized in place, or transferred into the circuit with the aid of "keeper" flux shunts); however, if the magnet is taken out for even an instant and then replaced, the field in the gap will be less than before.
Alnico is a hard, brittle material, which has to be ground to shape if close tolerances on dimensions are required. Ceramic (ferrite) magnets are extremely hard, so much so that they are cut only very slowly by tungsten-carbide or silicon-carbide. They must be ground or cut to shape with diamond tools.
Samarium-cobalt magnets are also difficult to cut and can be made only in limited sizes and shapes (in solid form). Neodymium-iron when cut, produces a powder which is easily ignited by the heat caused by the tool, which makes the process hazardous.
Ferrite, samarium-cobalt and neodymium-iron are also available in powder form, which is either pressed to shape with a binder, or molded with a carrier plastic. Bonded magnets made by either process are less powerful than the solid forms of the same material but can be made into a much wider range of shapes at lower cost. The final part may be relatively rigid, bonded with materials like nylon 6-6, or relatively flexible, bonded with rubber.
Some of the bonded materials are isotropic (having the same magnetic properties in all directions) and are machineable. Some bonded products and most solid magnet materials have a preferred direction of magnetization (but with either N-S or S-N alignment allowed). Resistance to magnetization in other directions may be extremely high. For example, the coercive force required to completely magnetize a particular ferrite in the preferred direction is about 10,000 G. The same material was not affected at all when exposed to a field of 20,000 G in a transverse direction and it reportedly requires 100,000 G to magnetize it in that direction.
The properties of permanent magnet materials are given in Table 2.1. These are typical values only, since the actual properties vary between manufacturers.
Notes on the above table:
1. All materials have a preferred direction of magnetization unless noted as isotropic.
2. Thermal expansion for some materials is non-isotropic. If two figures are given, "P" data is for direction parallel to preferred direction of magnetization and "T" data is for directions transverse to the preferred direction of magnetization.
3. Data are from various sources, of unknown accuracy and are given as examples only. Design data should be obtained from the manufacturer. Except for temperatures, data are at 20°C (68°F).
If magnetic materials are heated above a characteristic temperature called the Curie temperature, they suddenly lose all magnetism. If they are then cooled to room temperature, they are found to be completely demagnetized but otherwise unaffected. It may not be possible to use this method to demagnetize bonded magnets because the required temperature is high enough to destroy the bonding material but it is an excellent way to demagnetize solid magnet materials without coating or adhesives. For some materials it may be advisable to heat the parts in an inert atmosphere to prevent corrosion.
Ferrite magnets sometimes continue to lose small amounts of powder from their surfaces. They are brittle and easily chipped. Samarium-cobalt may occasionally spall off tiny bits of material. In order to avoid possible contamination and to help protect against surface and edge damage, magnets are sometimes coated. The surfacing materials used are often epoxies of polyurethane and the coatings may be as thin as a few ten-thousandths of an inch (0.0002) up to perhaps five thousandths of an inch (0.005). Ferrites may also develop cracks in manufacturing which do not affect their magnetic performance but reduce their strength and resistance to spalling. The cracks may be filled with epoxy. Some magnet materials are subject to corrosion and oxidation which a coating may prevent.
A number of other magnetic materials are known, besides the ones discussed. Some of them have been in volume production in the past but are rarely used today, because other materials are less expensive or have better properties. Among them are cunife (copper-nickel-iron), which can be machined and cold-worked; cunico (copper-nickel-cobalt); silmanal (silver-nickel-aluminum), a material with great resistance to demagnetization; and vicalloy (iron-cobalt-vanadium), which is machineable.
References 1-9 are recommended for further reading on permanent magnets and their properties.
2.2 Magnetically soft materials:
Magnetically soft materials have a very narrow B-H curve and have very little remanence, which means that after an applied magnetic field is removed, very little flux remains in the circuit. The behavior of these materials is variable and significant over such a wide range that their B-H curves are usually plotted with semi-log scales, as shown in Figure 2.2 (H plotted on the horizontal scale, logarithmically). Since the materials are reluctance rather than coercive force sources, B and H are both plotted as positive (in the first quadrant). There being very little or no difference between the rising and falling curves, the plot is a single line. Plots are normally made of B versus H; occasionally plots of permeability versus B or H are also made. Maximum permeability does not usually occur at the beginning of the curve (very low H) but somewhere in the middle. For very low-carbon steel, maximum permeability may occur at approximately 7000 G and may be 3000 or so; initial permeability (at 20 Gauss) is about 200. Permeability in this case means total B divided by total H. Differential permeability, on the other hand, is the ratio of change of B to change of H, which is the slope of the B-H curve. Differential permeability is of interest when small variations (perhaps caused electrically) are imposed over a steady magnetic field.
There is a big difference between choosing a pole material to carry a maximum amount of flux (high saturation flux-density) and in choosing one for high permeability. To specify high permeability, the maximum coercivity must also be known. For very low coercivity (to perhaps 0.005 Oersted or so) a material like Supermalloy may be best, with a permeability at this level as high as 200,000. This alloy saturates at less than 8,000 G however. For high flux-density, Vanadium Permandur is superior. Its initial permeability is only about 1,100 but it saturates at 23,000 G (compared to 20,500 G for low-carbon steel).
Figure 2.2: B-H Curves
Notes on above Figure:
1. The curves shown are intrinsic. The flux-densities shown represent the increase in field strength caused by the material, not the total field. To get the normal curve (used for design), add the value of B found from the curve to the value of (H times 1 Gauss/oersted). For example, for Vanadium-Permandur at 1000 Oe, the curve shows 22,600 G. The flux-density in an immediately adjacent gap would be 23,600 G.
2. The data shown is plotted from information from various sources, and is of unknown accuracy. It is given for illustrative purposes only. Design data should be obtained from manufacturer.
3. The materials are shown in their highest state of permeability. Some materials require special heat-treatment to reach their best magnetic properties, and may be adversely affected if subsequent machining and forming is done. The 3% silicon-iron sheet is anisotropic, and best magnetic properties are obtained in only one direction.
In order to help suppress electrical eddy currents which slow down magnetic field strength changes and waste energy, high electrical resistance is desirable. Adding silicon to iron (up to 5%) increases the electrical resistance but reduces the flux saturation density. It also makes the material brittle and hard to form or machine. Silicon-iron is widely used in transformers, electronic chokes and electrical motors (Refs. 42 & 44).
Many of the magnetic alloys require heat-treatment (annealing) to obtain the best magnetic properties. The effect is reduced or lost by machining or forming however, so it must be repeated after these operations. Some materials require heat-treatment in a hydrogen atmosphere to obtain the best properties, a somewhat dangerous process. If this is not possible, treatment may be done in other gas mixtures, producing results which are not optimal but are greatly improved over the untreated state (Reference 11).
Besides iron, the metals nickel and cobalt are ferromagnetic and highly permeable. Pure nickel saturates at 6080 Gauss which makes it useful on occasion for calibration purposes.
Nickel plating can be either magnetic or non-magnetic, depending on the application process. Magnetic nickel is often used to protect pole steel from corrosion, with minimum added reluctance.
The 300 Series stainless steels (302, 303, 304, 316 and others) which contain significant amounts of nickel (8% to 22%), as well as chrome (14% to 24%) are usually austinitic in structure and are not considered to be magnetic. A magnet is sometimes used in machine shops to test stainless steel versus other steels. The 300 Series stainless materials may become magnetically permeable as the result of cold-working as, for example, may happen to cold-forged bolts. Certain special types (329, 355) may be either austinitic or martensitic(and therefore magnetically impermeable, or permeable) depending on heat treatment.
The 400 Series stainless steels contain chrome but little or no nickel. They are martensitic, hardenable by heat-treatment and magnetically permeable. Because they can be hardened, 400 Series stainless steels are often used for tools, instruments and bearing surfaces.
The B-H curves of magnetic materials change with temperature to varying degrees, with flux density and permeability reducing with increased temperature. Certain iron alloys containing a high percentage of nickel (around 30%) have permeabilities that are very strongly affected by temperature. For example, one material changes its permeability by about a factor of 2 between -40°F and 200°F, at 46 Oe coercive force. The variation of permeability is also a function of coercivity; this same alloy increases its permeability at an even greater rate over the same range, at a low coercivity (0.2 Oe). It is possible to use these alloys to compensate for variations in the strength of permanent magnets with temperature. The magnet is designed to produce more flux than is required in the gap and the extra flux is shunted around the gap with a section of the compensator material. If the temperature increases, the magnet output will decrease but less flux will be passed by the shunt. With proper design, the resulting flux in the gap can be made to be very nearly constant over a wide range of temperature.
Although the B-H curves of pole materials are usually drawn as a single line, there is in fact a small difference between the rising and falling curves. The area traced out in B-H space represents energy lost per cycle, which is called hysteresis loss. Although the loss per cycle is very small, the power dissipated as heat over time, in devices subjected to constant cycling (such as motors and transformers) can be significant. Eddy current losses in these materials are also important and the two added together are termed core loss. The amount of core loss, in units of watts per pound, is supplied by the manufacturers of these materials, as a function of frequency (f), lamination thickness (t) and maximum flux-density (B). An empirical formula for the core loss in pole materials is:
The first term represents the hysteresis loss and the coefficient x is called the Steinmetz coefficient (after Charles Proteus Steinmetz, who discovered the relationship). It varies from about 1.5 to 2.5, depending on the material; 1.6 is often used. The second term represents eddy current loss. The constants and depend on the material. If the power loss is known for several different conditions, the constants can be found and then the power losses at other frequencies, material thicknesses and flux-densities can be calculated.