Relationship between Flux Density and air gap distance

[pirc865]

Hi all,

I was curious about how fast the flux density falls off as air gap increases.

 

[dpc]

Incredibly fast if the rest of the flux path is iron and it isn't saturated. Think of the iron as a flux superconductor and the air gap as a flux resistor.

Calculation of flux is normally done using just the air gap reluctance alone and ignoring any reluctance in the iron. The flux density in the gap is not quite the same as in the iron due to fringing effect, but this can usually be ignored and the air gap flux density considered equal to the core density.

 

[waross]

The ratio between the permeability of iron and air is so great that for small air gaps the iron can be ignored and the flux density is almost inversly proportional. I know the purists will take exception to this. Rather than a challenge, that I will admit is justified, how about working out an example and showing me how wrong I am.
Say for example a magnetic path 3" long, and enough amp turns to put the flux density in iron at a reasonable level. Now work out the flux density with a 1/16' air gap, a 1/8" air gap, a 1/4" air gap, a 1/2" air gap, and a 1" air gap. Taking 1/4" as an example of a small air gap, what is the percentage of error between the correct answer and the quick answer using the inverse proportions of the air gaps?
respectfully

 

[edison123]

waross

Iron is more permeable than air only up to the saturation point. Beyond saturation, iron will require more magnetic intensity (amp-turns) than air.

* Money doesn't grow on tress since the banks own all the branches *

 

[electricpete]

Here's my take: it depends on what you are holding constant.

If you were holding mmf constant, then flux density falls off roughly inversely proportional to gap length... shown by magnetic circuit analysis.

Is it reasonable to assume mmf constant?

If were were talking about a motor (this is a motor forum), and the only thing I change is an increase in the gap length, I would say the mmf will increase as magnetizing current increases. The result is the flux will be approximately the same since we still have to satisfy Vapplied = N * dPhi/dt and we didn't change Vapplied or number of turns. There will of course be some secondary effects to consider... mostly the effect of voltage drop accross leakage reactance which be most pronounded under locked rotor conditions.

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[pirc865]

Hi again,

I might be in the wrong forum. If I am I do apologize.

My application involves an electromagnet that will be holding something from beneath a surface (a 'gap' of about .25 inches).

Ok I have found some electromagnets that have various amount of force - with the object touching.

Since I will not be touching the object, the holding strength will decrease - but by how much is the question

Anyway, choosing a one that is too weak will not hold and choosing one to strong will hold too much. In the words of GoldiLox.... I need one that is JUST right.

The mmf will be consant once the magnet is engergized. The type of magnet that I will be using has the poles on the same side ( one in the center and then one along the outer ring - it is a circular mag.)

Their is not much in the way of actually designing the magnet. I would try but it would be cheaper for me to just by one rather than trying to wind one myself.

Ok, I'll shut up now. Please excuse any mistakes or bad assumptions as I am a non-typical engineer.

Thanks

Rodger

 

[electricpete]

No apologies necessary, I just wanted to clarify the application. There is a magnetic forum, also but the folks here are knowledgeable in these areas as well.

"The mmf will be consant once the magnet is engergized. The type of magnet that I will be using has the poles on the same side ( one in the center and then one along the outer ring - it is a circular mag.)"

If you apply a constant voltage to an iron core device and increase the airgap, I would expect the current and mmf to increase to keep the flux density roughly the same. One again flux density determined by the voltage, frequency and turns: v = n*dPhi/dt so Phi = |V|/[n*2*pi*f]

That's just my thought. Anyone else is welcome to comment.

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[electricpete]

Please ignore my last post.

The same flux will need to flow between the pole faces. But if the distance d1 from object to pole faces is not << the distance d2 between pole faces, then some significant portion of the flux will go directly between the pole faces and not flow through the object, thus reducing holding force.

I think to answer the question, anyone would need to know more about the dimensions of your electromagnet especially the distances between the two pole faces.

Even with that info I don't think I could answer it well (other than if d1 remains << d2 there is no change in force with distance). This is starting to sound like a question that does belong on the magnetic forum unless someone else here wants to add anything.

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[aolalde]

In general I disagree with the answers above.

The FLUX PER POLE (phi) in a motor depend on the series conductors per phase (N), connection, frequency (F) and voltage (E)( not the air gap).

phi = E/(4.44*N*F*Kp*Kd*Ks)

Since the flux is constant the Flux density is constant too because the cross sectional area is not a function of the air gap but the core length and lamination.

The magnetizing current is another history. Since the amper-turns or magnetizing force has to increse to provide the increased reluctance (Rg) due to a gap increase which is in series to the lamination reluctance(Rh).

AT = phi/ (Rg + Rh)

The no load current (magnetizing current) will increase as the air gap reluctance is increased.

 

[waross]

I hope we can assume that this is a DC magnet.
It makes things a lot simpler and there will be more current flow, resulting in a stronger magnet.
The holding force will depend on the flux density.
You have two different calculations for the flux density of your magnet.
One calculation is the magnetic force when the object is touching the magnet. The holding force is directly dependent on the MMF (Amp Turns) and the permeability of the iron, and inversely proportional to the length of the magnetic circuit.
The second calculation is the calculation with an air gap.
As soon as you add an air gap, the situation changes.
The magnetic permeability of air is several thousand times less than the magnetic permeability of iron. What this means is that for practical purposes you can ignore the iron in your calculations.

Calculation of flux is normally done using just the air gap reluctance alone and ignoring any reluctance in the iron.

Note; Reluctance is the reciprocal of permeability.
If the magnet is large in comparison to the air gap, most of the lines of force will still go through the magnetic object. Any air gap greatly reduces the holding force.
I would guess that your magnetic path length may be 3".
With 1/4" spacing, your total air gap will be 1/2 inch. This is a 6:1 ratio in your favour. Now let's assume that the permeability of the iron is 1500 times that of air. 1500/6 = 150
Our assumptions may be subject to errors of -50% to +100% or more. That's a range of 75 to 300. That means that a magnet with a holding force of 300 Lbs. may have a force of 1 Lb. to 4 Lbs. through a distance of 1/4"
This is NOT meant to be an accurate solution to your problem. It is an example based on assumptions to illustrate and explain the results you can expect when you buy your magnet.
I suggest that you do just that. Buy a magnet and play with it.

Hello edison123;
I'm glad to see you have taken up my challenge. A little discussion helps everyones understanding and keeps our minds sharp.

how about working out an example and showing me how wrong I am.
Say for example a magnetic path 3" long, and enough amp turns to put the flux density in iron at a reasonable level. Now work out the flux density with a 1/16' air gap, a 1/8" air gap, a 1/4" air gap, a 1/2" air gap, and a 1" air gap. Taking 1/4" as an example of a small air gap, what is the percentage of error between the correct answer and the quick answer using the inverse proportions of the air gaps?
respectfully

I'm actually quite anxious to see how far the calculations are off when you ignore the iron.

respectfully

 

[electricpete]

aolalde - you said that increasing gap in a motor causes exciting current to increase and mmf to increase and flux density to remain the same... that's the same thing I said with regard to a motor, so I'm not sure who you're disagreeing with.

Note that this is not a motor and things may be a little different depending on the geometry as discussed above.

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[waross]

I think that most of these posts are accurate. Some of them are assuming AC and some of them are assuming DC and that is creating a little confusion.
respectfully

 

[electricpete]

Yes I was assuming ac and dc would certainly act differently. (mmf would be constant and flux would decrease at least inversely proportional to gap length since reluctance is proportional to gap length... also additional decrease possible due to the geometric factor discussed above if gap length is not much less than pole distance)

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