Calculating flux in a permanent magnet circuit

[nickw1881]

I am hoping someone here has experience with permanent magnets. Since I haven't been able to find any published techniques (that arent really expensive FEA sim programs) I have a theory on how to size a permanent magnet for an alternator I am designing, and I want someone to confirm that my technique will yield a result that is useful enough to go through the expense of building a prototype. My goal is to find the minimum thickness of Neodymium magnet that will produce the needed voltage in an alternator at the RPM I plan to run.

First, permanent magnets as I understand them: Permanent magnets have a 'Br' rating, which is the amount of flux that would flow if this magnet were part of a magnetic circuit with 0 Reluctance. They also have an Hc rating, which defines the opposing magnetic field intensity that would result in 0 flux in that same magnetic circuit. If Br is plotted as a point on the vertical axis, and Hc as a point on the negative horizontal axis, then the curve between them is the B-H curve.

The B-H curve (most of it) is drawn by reducing the net flux in the circuit by A) Adding an air gap that will store potential energy as a magnetic field, or B) Using an electromagnet to create an H-field that opposes the one from the magnet. It is my understanding that a magnetic circuit is roughly analogous to an electric circuit, in that Kirchoff's loop law can be applied to both.

****If I add an air gap that has a reluctance of 10 Ampturn/Tesla, and there is 1 Tesla flowing through the circuit from the permanent magnet, then is that air gap the equivalent to using a coil to supply 10 amp turns opposing the permanent magnet flux? If the air gap and coil were swapped, would the total flux in the circuit remain the same: 1 Tesla?****

By choosing my air gap and core material, I can know the reluctance of my magnetic circuit. I will take that reluctance, multiply it with the chosen flux density (flux needed to produce rated voltage@rpm) to get H opposing. Br is constant, no matter how thick or thin the magnet is, and since Hc is rated per unit length, I should be able to scale the H axis of the B-H curve to find the correct magnet thickness. It should be similar to how I would do per-unit calculations or normalized filter design in other EE calculations.

 

[electricpete]

A few thoughts:
1 - There are probably a lot more answerers hiding in another forum:
forum340
2 - Strictly speaking, the units of reluctance would not be Amp-turn per Tesla, it would be Amp-turn per (Tesla-meter^2) or Amp-turn per Weber. But I gather you are assuming constant cross section of the path so the distinction might not be important if you account for the area correctly in your calculations.
3 - The equivalence between the 10*Amp-turn/Wb reluctance, creating 10amp-turns MMF drop at 1Wb and the 10 Amp-turn opposing coil (presumed to have negligible reluctance) holds only at that single operating point. i.e. the 10 Amp-turn opposing coil will remain 10 Amp-turn regardless of other changes in the circuit while the 10*Amp-turn/Wb reluctance will not create 10 Amp-turn mmf drop for any operating point other than 1 Weber.

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(2B)+(2B)' ?

 

[electricpete]

If the air gap and coil were swapped, would the total flux in the circuit remain the same: 1 Tesla?

Yes. I'll assume for simplicity area of 1m^2. If the operating point of the original circuit had average flux density 1T in a cross section 1m^2 = 1Wb flowing through series elements including a reluctance of 10 Amp-turn/Wb, and if you could replace that single reluctance with 10 Amp-turn negligible-reluctance coil of polarity opposing the PM, the flux and flux density would remain 1Wb and 1T.

=====================================
(2B)+(2B)' ?