Eddy current theory question/femm validation

[mattg]

Sorry, I put this in the 'Other' forum, then again in here. Perhaps a moderator could delete this one?. Apologies, matt

[mattg]

Ummmm...second attempt->

Hello all.
This question is not directly related to RE, but more to magnetic circuit theory in general.

I have simulated an eddy current device in FEMM- a simple twin stator axial flux permanent magnet device with a 10mm aluminum plate passing between the stators. This is fine, the result shows around 0.7T in the air gap, which I think is reasonable. Predicting braking force using FEMM is beyond me at the minute- I am using the air gap flux density and the equation at the bottom of page 3 of this paper to calculate braking force www.thompsonrd.com/OSEE-brakes.pdf .

Qualitative results pic:


In the model, I have selected M-19 steel as the material of the stator back plates. What I would like to use is a basic mild (carbon) steel. Does anyone have a source for a BH curve for standard mild steel materials?

Not wanting to simply trust FEMM blindly, I would like to calculate the approximate air gap flux density by hand. To this end, I am attempting this by two techniques:

1. Using the magnetic equivalent of ohms law, mmf = Phi R and an equivalent magentic circuit of my device. R, the combined reluctance of each component is simple. Phi is what I am trying to find, as I can divide this by the magnet face area to get an approximate flux density.  I find mmf for a PM magnet using magnetic field intensity of a N40 NdFeB magnet, H = 900 kA/m (roughly) and the magnet's 'height', l. mmf = Hl. Eventually, this gives a fairly similar answer to FEMM of about 0.7T. Great! 

2. Following the numerical example given in Axial Flux Permanent Magnet Brushless Machines, page 19 - 20, Numerical Example 1.1 (Faraday's disc).

This can be found here http://www.scribd.com/doc/25388810/Axial-Flux-Permanent-Magnet-Brushless-Machines, by keying in '31' to the page number box in grey at the bottom of the page.

I realise this is somewhat different to the problem I am looking at, but the technique is what Im interested in. The first part of the example is the calculation of the air gap flux density, though not by method 1 mentioned above. Instead, they find the 'relative recoil permeability', the 'saturation factor', and then use these in 'Kirchhoff's magnetic voltage law'. My questions on this are as follows:

a. Is the second method more accurate? I cannot see that it takes into account fringing effects or other effects that are neglected in the first method.
b. What is recoil permeability, and why is this used rather than regular permeability?
c. Kirchhoff's magnetic voltage law- is this that the sum of mmf around a circuit = zero?
d. I realise this is a lot to ask, but perhaps other people will be interested- in the numerical example I think there is a mistake in the final line of part (a), where they have introduced incorrect terms in to the equation. This leads to a low estimate of Bg.

I hope that is understandable!
Cheers
Matt

[TomW]

Matt;

I had moved the original to Diaries  (a more appropriate board for it). I removed it when I saw this one.

Tom

[boB]

I know I have B-H curves for all the usual laminations but can't seem to find all of them now, but
I did find, in an old book, something for some  M-15 material that is probably close.

[mattg]

Thanks Bob
The back plate of the stator is not laminated- just a plain piece of sheet steel. Does this alter the BH curve? I understand the use of laminations to reduce eddy currents, but as far as I know they are not an issue in this type of application (just as in the steel magnet discs of an axial flux alternator, the discs are stationary with respect to the field).
Thanks again, and thanks TomW for sorting that out.
Matt

[boB]

Thanks Bob
The back plate of the stator is not laminated- just a plain piece of sheet steel. Does this alter the BH curve? I understand the use of laminations to reduce eddy currents, but as far as I know they are not an issue in this type of application (just as in the steel magnet discs of an axial flux alternator, the discs are stationary with respect to the field).
Thanks again, and thanks TomW for sorting that out.
Matt

I think you're correct there...  Not being laminated shouldn't alter the B-H curve....  But it will increase the Watts per pound figure.  B-H mainly shows hysteresis, permeability and saturation etc.

Fun stuff !

boB

[joestue]

http://www.consult-g2.com/papers/paper8/F4.jpg
http://www.consult-g2.com/course/chapter2/f2.2r.jpg
http://www.eng-tips.com/viewthread.cfm?qid=132964

and difference in flux density due to a generalizaion or a fea needs to be looked at if its more than a few percent, as you know its effect on machine output follows B^2..
other than that i will have to wait until i'm at work to download that book, it looks interesting.

[mattg]

Thanks chaps
Ill simulate with those curves tonight! Will be interesting to see if the difference is significant.
Cheers, matt

edit: I will also be using 4 pole pairs rather than two next time, to give a better flux path

[SparWeb]

Everything I know about modelling magnetic fields (not a lot):
A) use FEMM.  Rats you've already done that, but you want more.

B) You're using the reluctance formula okay, but what you're missing is the variation in reluctance of the varying materials in a "series-reluctance-circuit".  You also need to consider the path and the cross-section area across it.  This is very difficult!

I picture it this way:  Each field line makes a complete circuit from the magnet ("battery") across and air gap with high reluctance ("resistor") and into the plate of material which has much less reluctance ("conductor").  Through that material, next air gap, next magnet, and then through a backing plate which also has low reluctance ("conductor") to the next pole, and the cycle repeats.

If you can make a complete analogy with an electrical circuit then you can manage the calculations.

Just like the resistance of a material is determined by its resistivity, cross-section, and the length of the path the current takes through it, you can do the same for a material whose reluctance is determined by its cross-section, length of flux path, and permeability (or is the correct term "permittivity"? check that).

Looking back at your FEMM model, you can do that calculation for each and every line you see on it.

Referring to your original post:  Yeah I'm describing a Kirchoff analogy for magnetic circuits.  The "recoil" permeability is a new one on me, too, but I can suggest a possibility.  AC electric circuits depend more on impedance than just resistance.  That impedance comes from the vector sum of reactance and resistance.  The same applies to magnetic circuits.  (My brain is full at this point too).  Anyway, the effect of changing magnetic flux in a material is to cause a reactive MMF or something.  Iif you're trying to cope with static magnetic fields you can omit the reactive parts.

I refreshed my memory with Wikipedia.  I know - I'm ashamed of myself.   

[mattg]

Thanks Sparweb
Ill post the latest progress when I get home tonight.
I think I have calculated the flux density ok for a two pole pair device, using the relative permeability of each part as you suggest- that seems fine. For 4 pole pairs however, the 'equivalent electrical' circuit is more tricky and my kirchhoff analogy fails- flux into a node does not seem to equal flux out of the node. Again, this is easier to explain with pictures which ill try and get up later.
Hmmm
matt

[SparWeb]

... For 4 pole pairs however, the 'equivalent electrical' circuit is more tricky and my kirchhoff analogy fails- flux into a node does not seem to equal flux out of the node. Again, this is easier to explain with pictures which ill try and get up later.

I'm sure it is more difficult.  I wouldn't dare try!



Starting with an image like this though, you can easily see the lines form closed loops.  Since it's just a quarter-section of the whole PM generator, you can imagine the mirror image on the left and below it, for a total of 4 circuits.  Now note that the magnet at the top is cut in half - the other half has lines that go to the right instead.  So finding symmetry can make it easier to reduce the number of equations to do.

I hope you are doing your work with simultaneous equations for each circuit you can separate, then finding the vector sum of the results where the paths overlap.  By virtue of the fact that you are actually attempting this analysis I figure you know what that means.

Easy for me to say.