Calculating Flux from a Permanent Magnet

In summary, the conversation discusses the use of permanent magnets and magnetic circuits in designing an alternator. The speaker wants someone to confirm their theory on sizing a permanent magnet for the alternator and determining the minimum thickness of Neodymium magnet needed for the desired voltage at a specific RPM. The conversation also touches on the properties of permanent magnets, such as the Br and Hc ratings, and how they relate to the B-H curve. There is a question about the equivalency of using an air gap or a coil to oppose the permanent magnet flux. Finally, the conversation mentions the use of Kirchhoff's loop law and magnetomotive force in calculating the magnetic circuit.
  • #1
nickw1881
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I am hoping someone here has experience with permanent magnets. 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 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.
 
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  • #2
In magnetic circuits, the conserved quantity corresponding to electric current is magnetic flux. Where B is measured in Tesla, or Webers per square meter, then the flux, Phi is in units of Webers. [itex]\Phi = \int B \cdot dA_e[/itex] The flux passing through any cross section of the magnetic circuit is the same when leakage flux is taken into consideration.

Another useful quantity, akin to Kirchhoff's voltage law is the integral of H around the loop. Magnetomotive force, NI = [itex]NI = \oint H \cdot dl_e[/itex]. dl_e is an element of the magnetic path. NI is current times number of turns of wire. It is the equivalent of a voltage source. Unfortunately, I'm unclear how permanent magnets or magnetic reluctance might modify this equation.
 
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What is flux?

Flux is a measure of the amount of magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of Weber (Wb).

How is flux calculated from a permanent magnet?

Flux from a permanent magnet can be calculated using the formula Φ = BA, where B is the magnetic field strength in Tesla (T) and A is the area perpendicular to the magnetic field in square meters (m²).

What factors affect the flux from a permanent magnet?

The strength of the magnetic field, the size and shape of the magnet, and the material it is made of can all affect the flux from a permanent magnet.

Can flux be negative?

Yes, flux can be negative if the magnetic field is directed in the opposite direction to the area being measured. This can happen if the magnet is flipped or rotated.

Why is calculating flux important?

Calculating flux is important because it allows us to understand and measure the strength of magnetic fields, which has many practical applications in fields such as engineering, physics, and materials science.

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