OK, here is a quick look at your single magnet movement of 1mm for comparison with your data. The image below shows flux linkage v. current at the two magnet positions. I initially did 10A steps but then added the 5A points so as to use Simpson's rule for the integrations. I get input electrical energy when the coil is energized as 0.7383 joules and returned energy when the current is switched off as 0.7146 joules, a difference of 0.0237 joules. To this must be added the energy taken from the 50A current becaause of the flux change applying voltage to the current source during the movement, that calculates to 0.12065 joules. Thus total electrical input is 0.1443 joules, to be compared with the mechanical output of 0.1455 joules. The COP is 1.008.
Smudge
Edit. added the chart
Hi smudge and thank you! I really appreciate constructive criticism like this rather than "You are wrong." 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/InductanceExampleAnd 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. 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.
- 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.
To expand on the latter point, 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. 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. 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. 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? 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's location vs 1mm TOWARDS the core.[/list]
« Last Edit: 2024-03-01, 11:24:14 by broli »
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Topic: FEMM shows interesting OU effect, the airgap is everything. (Read 6803 times)
