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Registered Member #4659
Joined: Sun Apr 29 2012, 06:14PM
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wrote ... Permeability is a factor if you are operating anywhere over ~ 60% (very rough estimate) of saturation, where the B/H curve starts to become noticeably non-linear - L becomes dependent on I as well as on geometry.
aaaaaaaaaaaaaaaahhh, that make sense. Does anyone have math for calculating the inductance based on this fact?
Registered Member #2529
Joined: Thu Dec 10 2009, 02:43AM
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IIUC there's two types of relative permeability. There's relative to mu_o, and there's differential relative permeability; basically the slope on the curve.
You can calculate the slope easily enough, even where it's non linear, but to calculate the inductance of a significantly non linear material, you pretty much just have to run FEMM on it.
Registered Member #4659
Joined: Sun Apr 29 2012, 06:14PM
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Yanom wrote ...
wrote ... Permeability is a factor if you are operating anywhere over ~ 60% (very rough estimate) of saturation, where the B/H curve starts to become noticeably non-linear - L becomes dependent on I as well as on geometry.
aaaaaaaaaaaaaaaahhh, that make sense. Does anyone have math for calculating the inductance based on this fact?
Registered Member #2939
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Modelling of non-linear inductors in SPICE circuits makes one VERY important assumption : that the core flux is uniform - i.e. an equal degree of saturation everywhere. This may or may not be the case for a core in a solenoid with a large air gap. You will see this if you play about with FEMM for a while.
Registered Member #2529
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Iron is very, very permeable so the magnetic field will even out pretty well, so it will be roughly constant saturation; side to side across the projectile at least.
But front to back will often show larger differences for geometric reasons; the flux will leak out the sides of the projectile, because it's trying to close the size of the flux loops down (as it were).
Registered Member #4659
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hmmm. in FEMM, inductance is determined by Flux/Current (in the Circuits dialog on the .ans page), right?
I used the attached FEMM file (a coil + a projectile) to test the inductance a different current levels, from 1 AmpTurn to 1,000,000,000 AmpTurns. Flux/Current is .00056 Henries at 1AT, .00056 H at 1,000AT, and .0002H at 1,000,000AT, and .0002H at 1,000,000,000AT.
Registered Member #2529
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Yeah, i reproduced that.
What I think is happening is that the iron is short circuiting half the flux loop at low gauss; the rest of the loop goes through the air.
At high gauss it saturates at 2-odd tesla, and the rest of the flux is just acting as if it's air cored; and at sufficiently high gauss that dominates the inductance; the iron does virtually nothing.
So the iron is roughly halving the reluctance and doubling the inductance at 'low' gauss; I haven't tested it, but if you close the magnetic circuit better, you'll get much higher inductance at low gauss, but the high gauss figure will be virtually unchanged.
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Forumula for calculating the force on a coilgun's projectile?