Magnetic Theory and Design

1. Can you explain the difference between coercive force and intrinsic coercive force?
The intrinsic coercive force is the coercivity of a magnet material in a closed circuit configuration. A closed circuit configuration means the magnet does not have any exposed poles. Some examples of a closed circuit configuration are a ring shape magnetized circumferentially, or a block or disc squeezed between the pole pieces of an electromagnet.

2. Generally, as an Nd-Fe-B material’s maximum energy product goes up, Hci goes down. When and why should I care?
If a magnet is in a closed circuit configuration and doesn’t have any exposed poles, it will not generate an external magnetic field. If it isn’t generating a magnetic field, it often serves no useful purpose.
The normal coercive force, just called coercivity, describes the magnet in the open circuit configuration, which is typical for most applications.

Magnetic Theory and Design

Magnetic Theory and Design

3. Generally, as an Nd-Fe-B material’s maximum energy product goes up, Hci goes down. When and why should I care?
You should care if the magnet is going to be exposed to elevated temperature(above 150 °F/ 65 °C), if the magnets will be in repulsion, or if the magnets will go into quadrature or Halbach assemblies.
You should care because low Hci magnets will irreversibly lose a lot of magnetic strength. Usually this can be recovered by remagnetizing, but if they are in a complicated assembly, you might have to take it apart.

4. In a dipole, why do we sometimes want to generate Oersteds in the gap and sometimes generate flux in the gap? What’s the difference, if any?
We generally measure magnetic field intensity in Gauss, but if that field is used to magnetize something else, it becomes a magnetizing force in Oersteds. Since permeability (U) equals B/H, anywhere that U=1, B will be equal to H. In the cgs system, the permeability of air is 1, the unit of magnetizing force (H) is the Oersted, and the unit of flux density is the Gauss, so Oersteds are numerically equivalent to Gauss (B=H). Note that “flux in the gap” must be divided by the area of the gap, in centimeters, to get a value in Gauss, or Oersteds.

5. The magnet I ordered has a Br spec of 12.4 kG – why is the flux density only measuring 3.0 kG?
This is best explained through referencing the permanent magnet characteristic of permeance coefficient, which is strictly determined by geometry. In general, longer magnets have greater permeance coefficients. Additionally, a magnet with a higher permeance coefficient functions at a higher operating point. Now, imagine stretching a magnet so that its magnetic length is infinite. Per the previous few sentences, this would result in a magnet with the largest possible permeance coefficient and, consequently, the highest possible operating point. This is the only configuration where a magnet operates at Br.
Any other geometric configuration will operate at some point less than this. Since practical magnets have discrete lengths less than infinity, they fall victim to this geometric constraint and operate at levels lower than the Br value. Further, a magnet’s Br value is not an indication of the field density seen outside of the magnet. It is the induced field, inside of the magnet, which remains when the magnetizing force is removed and the permeance coefficient is infinte.
To perform work, the magnetic flux must leave the magnet and induce a field in space. This induced field will vary with position outside of the magnet. Numerous images show plots of magnetic flux lines in space, (e.g. the iron filings experiment in school). A Gauss reading measures the density, or how closely packed, these lines are in any given space. The surface of a magnet will produce the highest gauss reading because (very nearly) all of the flux generated by the magnet is exiting from the pole face. This reading is still, however, not equal to Br. This is due to the geometric constraints mentioned in the preceding paragraph. As the flux lines enter the outside world, they become less densely packed as they wend their way to the nearest permeable material (often the opposite pole of the same magnet). Consequently, when designing a magnet, not only must the magnetic characteristics of the material be considered, but also the geometric effects of the proposed shape.

6. What does magnetizing to saturation mean in terms of magnetic properties?
All “magnetizable” materials are at all times as fully magnetized as their thermal state permits. This is because orbiting unpaired electron spins are the source of atomic magnetic moments. These fully magnetized atomic magnets assemble themselves into clumps, or domains, with the same orientation. The domains then orient themselves to cancel each other so there is no measurable external magnetic field. Magnetizing is the process of turning all domains to a common alignment so the magnet exhibits an external magnetic field.
The energy required to magnetize a material depends on a number of factors, and the amount of energy retained is related to the geometry and coercivity of the magnet material. Magnetizing to saturation implies that all domains are to be rotated into common alignment. This is impossible because the energy required increases asymptotically as the level of magnetization increases. In the past, the generally accepted criteria for “full saturation” was that there should be no measurable increase in induction when twice the magnetizing energy is applied. For large, high-energy magnets this would be impossible today, or impractical, but this can be done with small-scale samples. Test data from the small sample can then be used to establish the magnetizing field required for larger parts in larger coils.
Material manufacturers usually state the field required to magnetize a part having a geometry that yields the maximum energy product. Since this is seldom the case, and measurable magnetic properties are shape dependent, MPCO establishes test limits for individual parts using boundary element analysis models, which takes into account the geometry of the part and the properties of the material.

7. What is a polar surface?
For a part with a uniform cross section normal to the direction of magnetization, and homogenous magnetic properties, a polar surface is comprised of approximately one half of the magnet’s total surface area. That includes not only one end of a magnet, but half of the side area as well. If one polar end of a magnet is larger than the other, or magnetic properties are not uniform, then the flux density at one polar end will be different from that at the other polar end, and the polar surface area will adjust to compensate until pole strengths are equal. The neutral zone, when observed with viewing paper, would be offset toward the pole displaying a higher flux density.

8. What is pole strength?
Pole strength is defined as the total magnetic flux passing through a magnetic pole, and because each line of flux passes continuously from one polar surface to the other, both internally and externally, both poles of a magnet have equal pole strengths.

9. What is the definition of the North pole? Why is the North pole more properly called the “North-SEEKING” pole? How do I find it?
We use the definition from the Magnetic Materials Producers Association (MMPA) which states “the North pole of a magnet is that pole which is attracted to the geographical North Pole. Therefore, the North Pole of a magnet will repel the north seeking pole of a magnetic compass”. In other words, if you want to use a compass, remember that the South pole of the compass will indicate the North Pole of our magnet.
The North pole of a compass is more properly called the North-seeking pole because it “seeks out” the geographical North Pole. But few people take the time to say “North seeking pole”.
If you were to use a compass to determine polarity, the South pole of the compass will point towards the North pole of the magnet. Don’t let the compass get too close to the magnet though, or you’ll risk remagnetizing the compass the wrong way!
If you were to use a gaussmeter, you’ll have to use an axial probe. The side of a magnet that gives you a positive reading will be the North pole.
The simplest method is to have a magnet with the North pole marked on it and see which side attracts and repels the other magnet. Unlike poles attract, like poles repel.

10. What is the difference between flux density and field strength? Which should a magnetic circuit designer be more concerned with and why?
Flux density is a measure of flux lines PER UNIT AREA. The unit for the value of flux lines per square centimeter is the Gauss, as read by a Gaussmeter. Field strength generally refers to the total flux available in the area of interest, and units are Maxwells or Webers; as when making a fluxmeter measurement using a search coil.
A magnet will only generate a certain amount of flux, depending on its material, size and geometry. The magnetic circuit designer must utilize the available flux in the most efficient manner to achieve the desired results. That usually translates to producing some value of flux density in a defined area.

11. What is the permeance coefficient and how it is used in magnetic design?
In its broadest sense, the permeance coefficient is a figure of merit for a magnet, or magnetic circuit, which indicates the ease with which flux travels from the North Pole to the South Pole (of course, magnetic flux does not actually travel, or flow. However, it is conceptually beneficial to describe the system in this manner).
After magnetization, a magnet, or magnetic circuit, will operate at some point on the demagnetization curve for that magnet. Certain shapes of magnetic circuit will operate lower down on the demagnetization curve than others. The permeance coefficient, calculated by using values based purely on the geometrical parameters of the magnetic circuit, allows the magnetic design engineer to determine this operating point of the magnet on the demagnetization curve.
A good example to indicate the qualitative difference between magnets of low and high permeance coefficient would be to consider a long, pencil shaped magnet (magnetized through its length) and a flat, coin shaped magnet magnetized through its thickness. In the case of the pencil shaped magnet, it is clear that the distance the flux has to travel from North to South poles is roughly the same if the flux has to travel back through the magnet itself, or if the flux has to travel outside of the magnet through the surrounding air. As we know, magnetic flux (like all physical systems) takes the easiest path presented to it (the path of least reluctance, in magnetic terms). Therefore, in the pencil shaped magnet, the vast majority of the magnetic flux will travel to the South Pole of the magnet by flowing outside of the magnet itself. Because of this, the amount of self demagnetization the magnet sees, (Hd), is very low. In such a situation, the magnet operates very close to Br, high up on the demagnetization curve.
Considering the flat, coin shaped magnet, one can imagine a line of magnetic flux emerging from the centre of the North Pole surface. This line of magnetic flux will again seek out the path of least reluctance. However, in a coin shaped magnet, the path to the opposite pole through the surrounding air is quite long. In fact, in some cases the magnetic flux would prefer to travel back through the magnet itself, (against its direction of magnetization), in order to get to the South Pole. In this instance, the amount of self demagnetization that the magnet sees can be quite significant. In this case, Hd has quite a high value and the magnet will operate much further down the demagnetization curve, closer to Hc.
The permeance coefficient is mathematically equal to Bd/Hd. Calculation of the permeance coefficient allows the magnetic design engineer to determine the operating point of a magnet by construction of a load line from the origin of the BH curve at a gradient equal to the permeance coefficient. The intersection of this load line and the demagnetization curve (at the point (Hd, Bd)), is the operating point of the magnet.

12. What is the relationship between field shape and magnet proportions and does the material type make a difference?
Flux lines take the easiest (lowest reluctance) route they can from one polar surface to the other. This means that all flux lines passing through an isolated magnet will bend to the side as soon as they can. Because flux crowds toward the edges on polar ends, radial flux density increases. Using iron filings to see the field shape, this gives the appearance of bowed flux lines passing from pole to pole, with a higher concentration toward the magnet ends, and some flux lines bowing from the sides of the magnet. If the off-axis flux vector amplitude is greater than the coercivity of domains in that portion of the magnet, weaker domains will align with the vector.
Field shape is also dictated by magnet geometry, or permeance coefficient (PC), which is related to the magnet’s effective l/d (equivalent length / diameter ratio). Total resistance to demagnetization is proportional to the product of length and coercivity (Hc), so longer magnets have a higher PC and less self demagnetizing effect (Hd). The greater pole spacing in longer magnets results in greater magnetic field “reach”, and field lines that emerge from the side surfaces of the magnet. The earth’s magnetic field is an example.
All high coercivity materials (those where the value of Hc in Oersteds approaches that of Br in Gauss), like rare earth and ceramic, have similar external field shapes. With a resistance to demagnetization (Hc) almost equal to the residual magnetization (Br), the external magnetic field strength (Bd) has less effect on internal domain alignment, so the effective poles appear to be at the polar ends of the magnets in field line plots.
Low coercivity materials, like Alnico 5, have a different external field shape because Hc is much lower than Br. Hc for Alnico 5 is about 5% of Br, so a magnet’s own external field, Bd, affects internal domain alignment toward the polar ends. Thus, domains at the ends and corners of an open circuit Alnico rod magnet do not remain aligned after magnetization in an air core coil (unless keepered), and plotted external field lines appear to have a focal point below the polar surfaces of the magnet. A length factor of 0.7 is often used in calculations to account for this effect (poles offset 15% from each polar end). However, 0.85 is a more realistic length factor for Alnico magnets with a geometry that causes them to operate above the knee in their second quadrant curve.

13. What is the relationship between the dimension and shape of a magnet’s keeper and the shape and strength of the field?
As an example, for a “U” magnet lying on a table, the keeper should be as “deep” as the magnet depth (toward the table) and the keeper thickness should be about 2/3 of the magnet pole width. This is based on the fact that the Br value of the best magnet materials is about 2/3 of the Bs of the best steel. For lower grades of material (lower Br) the keeper thickness should be (Br / 18000) x Wp (magnet pole width). For Alnico 2 this would be 7500 / 18000 x Wp, or 0.42″ for a Wp of 1.0″.

14. What’s the difference between an open circuit and a closed circuit in a magnet application?
A magnet operating by itself is referred to as an open circuit application. There are a lot of open circuit applications, like permanent magnets used to actuate Hall effect devices and reed switches. Helmholtz coil measurements are open circuit tests since no other magnetic materials are in the flux path during the test. The permeance coefficient of an open circuit magnet is determined by the magnet’s geometry alone. For example, a magnet with a length equal to its radius will have a PC close to 1.0.
A true closed magnetic circuit would have the poles joined by a high permeability material and a Bd/Hd ratio of infinity, since Hd=0. This condition is approximated when a steel magnetizing fixture is used, or when magnets are tested in a permeameter. A true closed magnetic circuit has little practical value as no external flux is available to perform a function. However, many functional magnetic circuits are more closed than open, i.e. they have a high PC value. An estimate of the PC value for a magnetic circuit is the magnetic length of the magnets in the circuit divided by the length of the working gap. For a motor, this might be a .5” thick magnet divided by a gap length of .025” for an estimated PC value of 20.

15. What’s the difference between the intrinsic curve and the normal curve? I understand that we generally use normal curve when designing the magnets, so when is the intrinsic curve used?
“Intrinsic” is defined as “belonging to the real nature of a thing”. In the case of a permanent magnet, intrinsic refers to its internal magnetic parameters, known as Bd(i) and Hc(i). Since it is impossible to measure internal values directly, we obtain them from their relationship to external parameters, Bd and Hd. The relation states that Bd(i) = Bd – Hd, so the intrinsic curve can be constructed from the normal curve. In the second quadrant, where permanent magnets operate, H is negative, so Bd(i) = Bd – (-Hd) = Bd+Hd. Under usual operating conditions, Bd is then always less than Bd(i).
In a closed circuit, where H = 0 (no gaps), Bd = Bd(i) = Br. However, there will always be a gap in a static magnetic circuit for it to be of use, so a self demagnetizing force (Hd) is always present. External flux density, Bd, referred to as “normal” flux density, is used for circuit design because it represents the amount of flux available to the circuit after the self demagnetizing field, Hd, is taken into account.
Intrinsic values become important when analyzing the effect of external applied fields, as in a motor, where the permanent magnet is subject to strong reversing fields. Measured or calculated opposing field strengths are plotted as an offset [Ha] to the intrinsic loadline [Bd(i)/Hd] to determine if any permanent “knock-down” is likely to occur by forcing the magnet over the knee in its intrinsic curve. Another place where intrinsic properties must be considered is when calculating the effect of magnet shape (permeance coefficient) on the field strength needed for magnet saturation.

16. Why are attraction forces stronger than repelling forces? Shouldn’t the magnetic forces be equal and opposite?
Magnets in attraction produce an increasing field strength in the gap between them as they approach, and therefore greater force. The reason is that the effective system permeance coefficient (PC) increases as the magnets get closer. As they approach, more flux lines flow from one magnet to the other, rather than taking a path from North to South pole of the same magnet. This causes them to act increasingly more like a single, longer magnet with a greater load line slope, increasing the value of Bd and decreasing Hd for both magnets. (PC = Bd/Hd)
Since flux lines cannot cross each other, the bucking magnetic fields of magnets in repulsion are compressed. Flux density in the radial component of the bucking fields increases in amplitude as the magnets approach each other, and more of their own external field (Bd) is pushed back into the magnets themselves, where it becomes part of the self demagnetizing field (Hd). Since Bd decreases while Hd increases, the PC value decreases as repelling magnets get closer and there is less external field available to create a repelling force. A repelling magnet arrangement can apply intense cross fields where magnetic domains have the least resistance to external influences, so some level of demagnetization may occur, depending on magnet geometry and the coercivity of the material.

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