6. Magnetic materials : Soft ferromagnetic substances

SOFT FERROMAGNETIC MATERIALS (SOFT STEEL LIKE)
Mathematical modeling of the Magnetization curve

RATIONALE
These materials are very widely used in the construction of the basic electrical machinery (motors, generators, transformers) but also in many side applications such as the magnetic shielding. They are essentially composed of iron atoms and the industrial products include pure iron, the game of the Silicium-steels and Iron-Nickel alloys.

High permeability, small coercitivity and saturation under high magnetic field characterize their magnetic behavior. But their specific magnetic characteristics vary considerably depending of their composition and their fabrication processing. The material structure can be either non-oriented (isotropic behavior) or oriented (anisotropic behavior). The characteristics are expressed by their magnetization curve, which relates the magnetic response of the material under an applied magnetic field.

The magnetization curves are exhibited in different ways: B (induction), M or J (magnetization intensity, magnetic polarization), µ (permeability), X (susceptibility), R (reluctivity) as function of the applied magnetic field (Hm) and different metric units are employed depending the usage. They are presented either as table of numbers or graphics curve.

Neither of these presentations are very practical in terms of magnetic calculation or more generally in terms of information processing.
The MAGNETICA software is using a specific numerization methods with mathematical modeling of the magnetization curve through spline affine functions. The result is a reduced table of coefficients which can be used very efficiently for all magnetic data processing of the materials. That includes any numerical or graphics representation of their magnetic behavior, precise magnetic calculation of magnetic system using components made of the materials. This coefficient's table can be the element of an universal data base of ferromagnetic materials easily manageable through E-mail and the WEB.

The illustration of this approach is shown for 2 specific materials : a Silicium Steel and a Mumetal.

Example 1 : Silicium Steel
type Euronorm FeV 270 50H or M15 (USA AISI 1978)

all the curves are just the plot of the mathematical spline functions model of isotropic soft steel type material with the set of coefficients specific of this Silicium steel.
Type of curves : linear, semi-log, log-log, etc…
The units and the range of plot are free.
(N.B the mathematical model has a correct behavior in all the range of the magnetization field including the limits Hm ->0 and Hm -> infinity)

Examples shown:

1- Semi log plot M magnetization intensity f (Hm)
(M is also named J magnetic polarization),
units Hm in A/m and M (or J) in tesla

2- Log- log plot of µ permeability f (Hm),
units Hm in oersted and µ relative permeability

3- Linear plot of Xi susceptibility f(Hm), in the region of its maximum
units Hm in oersted and Xi relative susceptibility

 
Example 2 : Mu metal (alloy Nickel Iron)
in the annealed state

all the curves are just the plot of the mathematical spline functions model of a isotropic soft steel type material with the set of coefficients specific of this Mu metal.
Types of curves : linear, semi-log, log-log, etc..
The units and the range of plot are free.
(N.B the mathematical model has a correct behavior in all the range of the magnetization field including the limits Hm ->0 and Hm ->infinity)

Examples shown :

1- Semi log plot M magnetization intensity f (Hm)
(M is also named J magnetic polarization),
units Hm in A/m and M (J) in tesla

 2- Log - log plot of µ permeability f (Hm),
units Hm in oersted and µ relative permeability

3- Linear plot of X susceptibility f(Hm), in the region of its maximum
units Hm in oersted and X relative susceptibility