Calculate magnetic flux density of a magnetic circuit?
Hello! Can anyone help me with the tasks?
I drew the equivalent circuit diagram
My approach for the flux density would be:
Here, the equivalent circuit doesn't change because x is still at 0. Furthermore, the flux density is the same everywhere. I would have connected the two outer legs in parallel and then the middle leg in series, but that would only produce crap.
My approach would then be via the river so phi= H*length/R,total
But I can't get 0.44 T.
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EDIT: You get 0.44 T if you include the reluctance of the magnet (center leg) in the total reluctance. However, this is almost certainly the wrong approach, because H*l for the magnet is then used again in the calculation, which is then counted twice and thus makes no sense. We're happy to discuss this.
The characteristic curve of the magnet is:
This characteristic curve must intersect the operating line, consisting of the remaining total reluctance. However, it makes no sense to calculate a reluctance here, since the characteristic curve is extremely harsh. In any case, you get the specified value of 6MA/Vs if you take the green line. That doesn't make any sense. The specified value of 0.44T is nonsense, I'm pretty sure of that now…
EDIT:
Now I know how you calculate it:
You assume the hysteresis curve like this:
while I accepted it like this:
However, for very hard magnetic materials this is a poor approximation.
With your version you actually get 0.88T in the middle section:
and so the calculation is correct.
However, a hard magnetic material actually tends to have the first form—so that's how the calculation is intended, and therefore correct. In this model, you can use the superposition theorem, but not in mine.
I was wondering…
Hmm… wie kommst du da auf 0,44 Tesla, was ist die Rechnung? Ich komme da einfach nicht drauf..
If you consider the magnet as the middle leg and use the reluctance that was given (Rm = 6MA/Vs), you get a total reluctance of
Rtot = Rm + Rli || Rre = Rm + Rli/2 = 8.8 MA/Vs
It is generally the flow
Θ = Rtotal * Φ = Rtotal * A * B
B here is of course the B in the middle leg (so basically the "total current"), the fact that it is divided left and right is already taken into account by Rges.
And now I have set
Hc*l = Θ (l is the length of the middle leg)
Hc*l = Rtotal * A * B
=> B = Hc*l /(Rtotal * A)
which gives B=0.88T.
Since the river is divided equally on the left and right, each side gets half, i.e. 0.44T.
However, this approach is almost certainly wrong. It makes no sense to assume a constant permeability for a hard magnet and calculate a reluctance from it. The magnet, after all, has hysteresis.
You have to proceed differently here, namely, intersect the characteristic curves. But I don't want to confuse you with that—in any case, you get something completely different.
Jetzt ist es mir klar wie ihr das rechnet. Siehe Ergänzung
No, that's 100% wrong. I'm assuming you're assuming the magnet is ideal, meaning it has a rectangular hysteresis curve. But then you'd get something completely different.
The point is: soft magnetic iron is described by a linear relationship (left in the image) – this results in reluctance. The magnet, on the other hand (right image), is hard magnetic and is approximated by a rectangular curve. You can't simply pretend that this is a straight line in the HB diagram.
I'll calculate it for you this evening. I have to work now.
Thanks for the detailed explanation! The professor said today that 0.44 T should be correct. 🤔