How do Integrated Programs Handle Nonlinear (irreversible) Magnetic Materials?

Magnetic materials generally have a nonlinear and history dependent B-H magnetization characteristic, as illustrated in the generic hysteresis curve to the right. However, for practical purposes magnetic materials can usually be considered as one of two types:

  • Red curve: ferromagnets (e.g. steels), paramagnets, and diamagnets
  • Blue curve: permanent magnets

The Material Editor screen capture to the left shows the material types for “Parameter: Permeability” corresponding to the descriptions above. Ferromagnets can be Linear (permeability only) or Nonlinear (B-H magnetization curve). Paramagnets and diamagnets are linear. They are specified by relative permeability or susceptibility. The input boxes are linked by formula as:
χ = µr – 1 and µr = χ + 1

Many materials cross the second quadrant reversibly along a straight line. These can be modeled as shown to the right by inputting the axis points Br and Hc.

In some other cases the behavior is linear and reversible enough over the range of operation that the option shown to the right still works.

In other cases the B-H characteristic may show significant curvature, but the behavior is still essentially reversible. Then the Nonlinear Permanent Magnet type works in a straightforward way.

For some materials and applications, irreversibility is a significant consideration. For example, for Alnico 5 shown below:

Over a small range of operation near H=0 the curve will retrace as H is increased and decreased. However, by the curve of the knee the magnet is changing material properties. If H becomes so negative that the blue point is reached, then as H changes between this value and zero the magnet operates along the blue line shown. Likewise if H becomes so low that the green dot is reached, then the magnet operates along the green line.

With such materials, the analysis necessarily involves several steps because the range over which the magnet is used will affect the appropriate material curve.

Step 1:
Using the supplied data (pink shown below) analyze the model over the range of operation to determine the largest (negative) values for H.

Step 2:
Replace the data curve, or define a new material, with the red curve shown below, corresponding to the correct characteristic for the material after a cycle through the range of operation for the device.

Note the data to the left of the operating range is irrelevant. Hence, it is common to define the material as linear with a selected Br , Hc which produce the correct behavior over the range of operation.

A supplied magnet will generally have been transported in an open circuit (no ferromagnetic return path) condition. This should be modeled as one of the scenarios for determining the true operating state.

A supplied magnet may have been “stabilized”. That is, it may have been deliberately demagnetized to a state which will be reversible under a large range of operation. In this case the B-H data entered should not be the general data for the material, but should be provided by the supplier to specify the state after stabilization.

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