[SOLVED] Core effective permeability and gapping

Core effective permiability and gapping

Hi

I'm looking to gap a set of RM5 cores and am going through the calculations.

My understanding is that assuming the initial permeability of the core material is high then the new effective permeability is given by:

ueff = le / g

Where le is the effective length and g is the gap.

Now taking an RM5 core https://ferroxcube.home.pl/prod/assets/rm5i.pdf and looking at 3C94 material, 680u gap if I work out ueff I get...

23.8 / 0.68 = 35, which is quite a bit different to their quoted 47.

Am I missing something here? Is there some other factor that needs to be accounted for?

Re: Core effective permiability and gapping

The calculation is wrong, either for ideal magnetic circuit model or for real circuit (considering fringing field). As for the ideal calculation, where is core µr in your formula?

Your calculated value gives a correct estimation if µr >> le/g

Re: Core effective permiability and gapping

I think I've already tried that one too, or at least something that boils down to the same thing.

N49 material µr = 1500 (from material datasheet)

So using
µe = le * µr / (le + g*µr)

µe = 23.8 * 1500 / (23.8 + 0.35*1500) = 65.05

Which is still nowhere near the quoted value of 47. I must admit I assumed that the fringing effect would be insignificant - would it be the cause of this discrepancy? Is there a formula that takes that into account?

Re: Core effective permiability and gapping

Don't see where 0.35 comes from. Problem with the relative large gap is in fact fringing field, the ideal reluctance calculation is too inaccurate.

Re: Core effective permiability and gapping

The problem with all this is fringing, and unless the gap is incredibly small, the error can be large enough to cause you some real grief.

Its not just the fringing itself distorting Ae, but with most equal core half geometries, the gap is right in the main guts of the winding, causing some pretty extreme effects on the few turns wound right over the gap.

So regardless of some theoretical formula from a reference book, there can be some real surprises when you actually fabricate it and finally test it.

Re: Core effective permiability and gapping

Hi,

I understand there will be some inaccuracy due to the fringe effect.

Sorry FvM regarding the 0.35, I don't know where I got that from either.

I have now put the values into a spreadsheet attached.
Interestingly my ueff = le / g effort (labeled approx. method) appears to be closer to the datasheet values than the µe = le * µr / (le + g*µr) (I labeled this full method)

Interestingly, both methods produce values closer to the datasheet with a smaller gap (consistent with the fringe effect).

I assume that the datasheet values are closer to reality and take into account fringe effect.
So this means that in the real world the effect causes a higher ue (and therefore Al) value for a given gap. Or in other words the fringe effect makes the gap "look" smaller than it actually is? Correct?

Re: Core effective permiability and gapping

in other words the fringe effect makes the gap "look" smaller than it actually is?

Click to expand...

Yes, because it creates reluctance in parallel to the air gap. Basically, the datasheet µeff specification is for the real gapped core, including fringing effects.

As Warpspeed mentioned, things are more complicated, most of the fringing field is inside the coil volume and you need to know the exact coil geometry to find µeff.

Re: Core effective permiability and gapping

Some time ago I built a reasonably high powered flyback mode converter that had two interleaved 1:1 ratio copper foil windings.

This was a quick one off project for myself, and I wanted to use ferrite pieces that I already had on hand, and the choice was between a large UI combination, and an EE core pair.

I started out with the EE pair which required a 3 mm gap. This obviously produces a lot of fringing, and much ringing on the waveforms which seemed pretty normal, and generally a very poor result.
The peak flyback voltages on each of these two windings were supposed to generate equal +ve and -ve supply rails. But I could only regulate one side. The very poor cross regulation caused by this ringing was its most objectional feature.

I then placed the exact same windings onto the U core, and this had the effect of moving the air gap well away from the windings. The change was dramatic.
I could pull 2Kw from one supply rail (either one) and zero from the other, and the voltage cross regulation was an astonishing 0.5% difference. The voltage waveforms were text book clean too.

Ever since that I have treated placing large air gaps between identical core halves with great doubt and suspicion. Its a really bad concept, although everyone seems to do it.

Re: Core effective permiability and gapping

Still convinced there is something not right with my calculations, can't see how though. Something doesn't make sense.

Comparing Ferroxcube with TDK gives completely different results also.
https://www.farnell.com/datasheets/528677.pdf?_ga=1.152503034.2102527688.1483035350
**broken link removed**

For ferroxcube my calculated ue values are way under the datasheet values, for TDK they are way over.
For ferroxcube the error between calculated and datasheet gets smaller with smaller gaps but the reverse happens with TDK.

Re: Core effective permiability and gapping

Are those cores factory gapped with a short centre leg, or are you gapping standard core halves ?
In theory it should not make any difference, but as mentioned above, the relationship between gap and winding can be important.

Re: Core effective permiability and gapping

I'm purely talking about datasheet Ue (for their stated gap) v my calculated values for their gap using µe = le * µr / (le + g*µr).
I haven't even got to real cores get purely calculation here.

Re: Core effective permiability and gapping

Magnetic effects can be very non linear, a quick look at a BH curve will tell you that.

The inductance is going to change significantly with excitation level and ratio of dc to ac.
What a very neat formula tells you to expect, and what you actually measure with a real inductor in actual dynamic operation can be significantly different.

In theory, a larger air gap should stabilise the inductance, in practice you will find the exact opposite.

The most reliable theoretical estimates will be for non gapped low permeability material where there is no fringing.
You are given an Al value and a dc magnetising curve, and the results are usually fairly close to expectations.
Gapped ferrite is far more unpredictable, especially where identical core halves are involved, and the gap is large.

Re: Core effective permiability and gapping

I'm purely talking about datasheet Ue (for their stated gap) v my calculated values for their gap using µe = le * µr / (le + g*µr).
I haven't even got to real cores get purely calculation here.

Click to expand...

Perhaps you should pay attention to the fact that the cores are specified for AL value rather than gap size. The gap size is qualified as approximate. You may be jumping in conclusions by relying on exactness of gap sizes in datasheets.

Re: Core effective permiability and gapping

FvM maybe you are right. To give you a better idea of what I'm trying to achieve I have picked up a pre-existing design (from an ex colleague) where I have an air gap measurement and Al/inductance value.

We are small volume and use a small but knowledgeable assembly house for magnetics. The guy there was quickly able to calculate the Al value (which pretty much matched our in house information) when only given the core and gap details. When I try to do the same calculations my answer is way off. Hence the whole process of scratching around to try to make sense of what's going on.