Hello,
I have tried the nonlinear core model by Mark C. Williams, R. S. Vogelsong, and K. S. Kundert in Simulation and Modeling of Nonlinear Magnetics.

Pittingly, I cannot exactly reproduce the simulation results given on pages 10 and 11 of this paper.
But the results from my simulation look rather good.
The model shows in core c1 the hysteresis loop from Figure 4 with the limits from Figure 6.

I'm also wondering about the names of the result curves in the given diagram of Figure 5.
The label 'n4' of curve vnn(i,'n4') appears nowhere in the test circuit.

Can anybody of you acknowledge the results presented in Figures 5 and 6 of the paper?

With thanks in advance and best regards,
Tobias Nähring

Hello,
the state equation for the irreversible magnetization in [1]  is

dMirr = (Manh - M)/(sign(Hdot)*k - alpha*(Manh-M)) * Hdot

while the formula suggested in [2] is  

dMirr = (Manh - Mirr)/(sign(Hdot)*k - alpha*(Manh - Mirr)) * Hdot.

I assume that this difference results from a modification of the power balance equation from

Mirr * d Beff / dt = Man * d Beff / dt - k* d Mirr / dt * sign(Hdot)

to

M * d Beff / dt = Man * d Beff / dt - k* d Mirr / dt * sign(Hdot).

(Note, that the first version of the power balance is not contained in [2] in this form. But one has to apply the proposed modifications from section "3.4. Domain wall motion of flexible domain walls" to equation (17) or (19) from the paper).
To me it seems that the first version (used by Jiles-Atherton) has a better physical justification since the second version tries to balance the power losses of the irreversible Bloch wall motions with the overall magnetization power which also includes the elastic Bloch wall deformations. But I'm not too much experienced with magnetics. So maybe I am wrong.

Is there some other physical justification for the version from [1]?

I am asking because there are practical cases where the two different formulations deliver significantly different results.

Bibliography:

[1] www.designers-guide.org/Modeling/mag.pdf

[2] D. C. Jiles and D. L. Atherton: Theory of ferromagnetic hysteresis. Journal of Magnetism and Magnetic Materials, Vol 61 (1986), pp. 48-60.

With best regards,
Tobias Naehring