Hysteresis37

[HansOlsson]

This clears up the unit-issues in the Hysteresis models.

Facts about the PR:

• Unit-consistent
• Without unit-casts
• Are the new unit strings correct? I don't know; it's possible - even likely, but I haven't seen the original model.

It requires more than Modelica Language 3.6, due to the odd units.

[HansOlsson]

See: modelica/ModelicaSpecification#3439 for this new unit-string, added after Modelica Language 3.6.

[christiankral]

I understand that the proposed change of units somehow leads to a consistent set of units:

• I do not understand the physical meaning of the parameters P1...P4 with their unit $\sqrt{\mathrm T}$ and of the parameter r with its unit $\sqrt{\frac{1}{\mathrm T}}$. Parameters with such weird units are usually related with emperic "numeric value equations".
• Yet, if unit consistency requires such weird units, it shall be fine with me.
• The term (1-mat.r), however, does not make sense to me at all, as the 1 has to have the same unit as r to make this calculation unit consistent.

[HansOlsson]

• The term (1-mat.r), however, does not make sense to me at all, as the 1 has to have the same unit as r to make this calculation unit consistent.

True, that would imply mat.r.unit="1".

The derivation of the unit for P1...P4 was independent of that; so then the conclusion is then that P1.unit="T(1/2)", mat.r.unit="1", and mat.M.unit="T(1/2)" (since P1=mat.M*mat.r); and the eps-binding in GenericHystTellinenEverett is just broken.
Note that this complete fixes Modelica.Magnetic.FluxTubes.Shapes.HysteresisAndMagnets.GenericHystPreisachEverett; where eps is just a fixed constant.

Someone really need to look up the original models - to me the most likely way to solve that is that the eps-binding equation is wrong in some way; likely that it seemed logical to relate the eps to mat.M and it wasn't considered in detail.

Also note that (1-mat.r) will change sign if mat.r passes through 1, and Modelica.Magnetic.FluxTubes.Material.HysteresisEverettParameter.Vacodur50 has mat.r>1; I don't know the significance of that.

[christiankral]

Someone really need to look up the original models - to me the most likely way to solve that is that the eps-binding equation is wrong in some way; likely that it seemed logical to relate the eps to mat.M and it wasn't considered in detail.

I would guess the quantity eps is solely used to numericall stabilize the model. Most likely, there is no physical reason to have it.

[HansOlsson]

Someone really need to look up the original models - to me the most likely way to solve that is that the eps-binding equation is wrong in some way; likely that it seemed logical to relate the eps to mat.M and it wasn't considered in detail.

I would guess the quantity eps is solely used to numericall stabilize the model. Most likely, there is no physical reason to have it.

Seems that way; I tried some simple experiment, and it seemed the result was fairly unchanged even if eps was changed by an order of magnitude.

[HansOlsson]

I have now updated to mat.r.unit="1" and changed eps to a unit-consistent value.

[christiankral]

In order to somehow understand the physics behind the equations

  hystR = -Js + (P1*P2-P3*P4) + mu0*Hstat - eps/2;
  hystF =  Js + (P4*P2-P3*P1) + mu0*Hstat + eps/2;

we need know the literature source. From what ist listed in Modelica.Magnetic.FluxTubes.UsersGuide.Literature I cannot find any source which uses the variables P1, P2, P3, P4.

I guess the first step where to identify the literature reference, on which the implemented equations are based.

So far I could only identify the variable P1 in [Ma03]:

This does not indicate what unit P1 is as it is not clear what unit $v_1$ has:

[christiankral]

I wonder if @ThomasBoedrich could give some input here.

[AHaumer]

This solution is weird: Units like T^(-1/2) bare physical meaning.
I think the only way to cure this part of Modelica.Magnetic is a major redesign:

• Search for all relevant pubilcations and formulas. If necessary, ask @ThomasBoedrich .
• Formulate the equations with dimensionless variables, i.e.
  r=(B/Bref)^(-1/2)
  This is the clean solution for such equations. However, this is a considerable amount of work.
  But we should stop curing single occurences of variables and parameters with weird units.
  @casella @christiankral What is your opinion?