Modeling non-linear magnetic materials may be intimidating to new users of PerMag and Magnum. This is the first of a series of articles where I will try to remove some of the mysteries.
To begin, we need a few definitions. I use the quantity B0 to represent the applied magnetic flux density at a point in space. This is the component of flux density created by coils with specified currents. It is related to the magnetic field by B = μ0*H. The quantity B is the total flux density with contributions from both applied currents and the effective currents resulting from alignment of domains in magnetic materials. At a point inside a magnetic material, the relative magnetic permeability is defined in PerMag and Magnum as μr = B/B0. In a soft magnetic material (like transformer steel), the relative magnetic permeability can be represented as a single-valued function of either B0 or B. We shall call the function the magnetization curve. Because the programs use different solution methods, we enter the curve as μr(B) in PerMag and μr(B0) in Magnum. For iron-like materials, the magnetization curve has μr values much greater than unity at low field and drops off when B approaches the saturation value Bs for the material (where magnetic domains are completely aligned). We say the material is unsaturated when B < Bs and saturated when B > Bs.
Here are some tips for using PerMag and Magnum for unsaturated iron. We'll talk about saturated iron in a future note.
- In many applications (e.g., bending magnets), the prime concern is the field outside the iron. Details of the field inside the iron are of secondary concern.
- You needn't worry about details of the magnetization curve in the range where μr is much greater than unity. Remember that the effect of a high value of μr is to cause external lines of B to be approximately normal to the iron surface. Therefore, a piece of unsaturated iron acts like an internal Neumann boundary. The deviation from 90 degrees is about tan(?) = 1/μr. With regard to the external field distribution, a piece of iron with μr = 3000 is indistinguishable from one with μr = 1800.
- If you are creating a μr table for a new material, the saturated range is important but the unsaturated range is not. Don't worry about modeling detailed variations of μr at low B or B0. In fact, if you replace the variations with a fixed, high value of μr the calculation will probably be more accurate. The codes won't have to expend effort to ensure convergence in a regime that has no effect on the external fields.
- If the field level in the calculation is such that all iron regions are unsaturated (B < 0.5 tesla), then don't use the nonlinear code capability. If the relative magnetic permeability is much larger than unity throughout the iron volume, simply use a fixed value of μr to represent the average. The results will be the same, and you can save hours of run time in a Magnum calculation.
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