Hi smudge and thank you! I really appreciate constructive criticism like this rather than "You are wrong."
And it is via these dialogues that we all learn. Your replies here help me understand where you are coming from and I will do my best to clarify my perception of the problem. What I find strange is how using magnetic energy over the elements gives such a different results. Here is a FEMM example where they talk about the different way to calculate inductance and how they are pretty much similar. One utilizes the magnetic energy while the other would then be your current method:
https://www.femm.info/wiki/InductanceExample
And as they state the former is indeed more accurate but the latter should be plenty accurate when most of the energy is confined and not in open air. Note that they clearly state the integration should encompass the whole area of the problem, whereas you were only doing the core. Now I have two remarks for you.
- 1) I find it very peculiar that your calculated energy values are in the ball park of 2x of mine? In the attached sim images I changed the magnets to be air to eliminate their contribution. I then Energized the coil to 50A and calculated the magnetic energy in the region both with and without the surrounding air. As you see the difference does not account for the 2x. I find it strange that FEMM itself demonstrates that both of these values can yield the same results when used in the correct situation yet ours are very different.
When you eliminated the magnets the field is then almost entirely contained in the core, but there is some in the air as you can see some field contours. So you would expect your two values to be slightly different as you found. Your two values are to be expected, and to check this I modified your sim so that the coil is wound around the whole core, not just the RH limb. Then the field in the air disappears and the two values are virtually the same. With the magnets present the field in the air has contribution both from the magnets and from the coil current, so the air contribution is even higher. - 2) Then what is also important in your analysis is to consider how this summation calculation of energy behaves depending on mesh refinement. Something I often do as a sanity check to validate the values on super fine meshes. where I do most of the quick checks with medium fine meshes and then the final with a superfine refinement that takes much longer to process but gives more accurate results. Does your energy delta change much with finer meshing?
If so then this should be considered as an stastical error and accounted for especially when dealing with summations where errors tend to add up.
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I understand what you are implying but your findings with finer mesh showing that your mesh size is adequate will also apply in my case since the fields are the same. To expand on the latter I believe for flux linkage, FEMM is using a clever contouring technique to calculate the area encased by the coil terminals. You even see such contours when you work with very refined meshes and calculate forces in such regions. It draws little red contours around the magnets for instance and uses them to calculates the force. The more "smooth" these lines (aka more triangles) the more accurate the calculated values. Thus in your analysis this "enclosing area" should be more refined to increase the accuracy of this value. Whereas right now the core region of the coil does not have that fine of a refinement as you see in the attached image. That "contouring technique" is the Maxwell stress tensor mask and only applies to the force and torque measurements. It is not used in the magnetic energy integration, that is done in the area you select where the BH product is evaluated for a finite number or area elements within the material boundary. Also as an another example I compared the flux linkage difference between the current mesh and a more refined mesh at 50A current (again with no magnets). And as you see attached the difference cannot be underestimated. And following the rule of error propagation in statistics, and by assuming that the error value (sigma) is the same over every sample point. This simplifies to sigma*squareroot(n) where n is the amount of sample points (current values) you took. This means the error value grows by the square root of the amount of sample points. Whereas using the magnetic energy you dont need to worry about such propagation as you dont need multiple summations to approximate the energy. You just get it in one shot and thus focus all the processing power on the final run. Whereas with flux linkage you need to consider the error of each samplepoint which depends on the the mesh refinement. Thus to consider this cumulative error I suggest you do one run with the current mesh and then one with a super fine one and take the difference. This difference can be your "fixed" error and used as the error for any subsequent run with a more coarse mesh to improve simulation times. From this you can determine the total error of the final result by multiply it to the squareroot of the amount of samples taken. I see flux linkage presented to three significant figures as 0.0595, 0.0595 and 0.0595 for the three meshes you used. That tells me even the coarsest mesh is OK to use and your argument on the statistics does not apply. Of course this is a simplistic approach. A more thorough one would be to do the entire analysis with a fine mesh and more sample points.
Can you perform this suggestion at perhaps 100 amps with 10 sample points and consider the errror value? I can do the 100A but I don't see a significant error value in my method. Using Simpson's rule takes care of the small number of current data points. EDIT: Forgot to ask, did you move the magnets 1mm away or towards the core/coil in your analysis? As in the previously shared file the magnet was already moved away 1mm and thus the analysis should be done by comparing the current magnet location vs 1mm TOWARDS the core.
I used the two magnet positions that you used as shown by the agreement of my force values with yours. From your next post Can you elaborate how you have come to this value please? It is simple. The flux change that takes place during the 1mm magnet movement with the coil current at 50A was 0.03987 at the outer position minus 0.037457 at the inner position yielding a difference of 0.002413 that when multiplied by 50A gives 0.12065 Joules energy. Smudge
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Topic: FEMM shows interesting OU effect, the airgap is everything. (Read 6802 times)
