I want to know if there is a manner of reducing/transforming the measured BH-loop in such a manner as to improve force calculation in an electromagnet (magnetic bearing) with superimposed DC current. I find it counterintuitive to use the virgin curve for this purpose (which is what most FEM programs provide and use). I do not want to go into the complication of using a full hysteresis model yet. I assume that if I can reproduce the bias operating point close enough to that of the actual operating condition that the force calculation will be more accurate compared to the extremes of either the outer loop or virgin curve. In other words the 'equivalent curve' should still have zero as origin as if it were a virgin curve, but the modified curve should be able to reproduce the force calculation to take into account the DC bias. Does this make sense to anyone? All of the FEM solvers' force calculation is thus wrong if it uses a non-hysteresis model/virgin curve. There has to be some transformation on the BH curve in order to obtain a better approximation of the force if we want to use a non-hysteresis model...
Thanks Ali!
The curves in figure 3 is what I had in mind. The curves in descending order gradually approximate increasing remnant flux. The smoother the transition is from (B, H) =(0, 0) to (Br, H_some_transition_point_we_choose) the easier the solver will converge. If we simply add remnant flux, i.e. (Br, 0) the solver will never converge because it is effectively a discontinuity since the non-hysteresis curve has to be symmetric, i.e. (B_r, 0^+) != (-B_r, 0^-)
Any other suggestions are still welcome!
Hi Gert,
One of the early works on the subject is:
C-C. Wong, "A dynamic hysteresis model". IEEE Trans. Magnetics, vol. 24, no. 2, 1988, pp. 1966-1968.
But frankly, that is certainly not all !
Just do a search on IEEEXplore for the string dynamic hysteresis model, and you should get many more ideas, including recent publications.
With best wishes.
-Sanjay
Not forgetting that one needs to take into account the source impedance of the DC current as this will affect the BH curve dynamic response.
Gert,
Can you give me an example where the force is not accurate. I have been doing this type of analysis for many years and the accuracy is more often associated with the method of calculating the force rather than the form of the curve. Most FEM programs today handle non-linear B-H curves quite well, even though it is the anysteretic curve , or perhaps a shifted return curve that Is used.
There are several techniques that can be used with DC bias. The choice depends a lot on what you are trying to simulate. The 2 main techniques are:
1) 2 Solution method, sometimes called frozen permeability with AC.
2) Full time domain analysis
The former uses 2 solutions. The first to determine the bias point caused by the DC field. The permeabilities are then saved and seeded for the next solution where either an AC or DC field is applied. This technique is most appropriate if the AC field has a very small amplitude and that the permeability can be approximated as a constant value.
The latter is very accurate since it considers all sources of magnetic field at all times. The user then simply has to post-process the data to obtain the forces. Again, the force calculation then becomes very important.
Gilles
Thanks for the answer's everyone.
Gilles, I can not give you an example just yet, I am currently looking into the cause of some unmodelled dynamics of the AMB, so I am still evaluating the error between different assumptions and methods of calculating the force, but thanks for the answers! You mentioned the use of a shifted return curve, what I was wondering is how to choose this shift/transformation such that the force calculation is more accurate than the anhysteretic curve. I guess one will have to parameterize such a shift and and compare to a full dynamic hysteresis model and try to find a general rule/range for which the parameter improves the force calculation error.
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