Electromagnet lifting capability increasing unexpectedly

[aloman]

Hello,
I have been performing an experiment in which I am observing the lifting capacity of DC electromagnets while changing variables including current, number of turns, and length of the core. It is a fairly basic experiment as all the theoretical values can be obtained using the formula F=N²I²μ²A/2μ₀L²

However I am getting results that do not satisfy this equation and I am not sure why this may be.
Testing an electromagnet with a carbon steel core of length 6.5cm and 77 turns in the solenoid with currents of 5.04 A , 3.77 A and, 2.51 A I get average maximum lifting mass results of 0.7447 kg, 0.4179 kg, and 0.1875 kg respectively. However when I test the magnet with a core length of 12.25cm, 154 turns and the same currents, (which according to the theory should yield results of 1.126 times that of the first magnet) I get the following results of 1.7027 kg, 0.8407 kg, and 0.4036 kg respectively. The results of the second magnet are approximately two times greater than they should be according to the first magnet and the theory.

Could it be that I am missing something obvious, and if so what? Any input would be valued.

 

[Baluncore]

If there are other magnetic materials nearby, they may distort the field differently because the other pole is in a different position, depending on the length of your test core.

 

[aloman]

I don't think the effects would be so extreme if that were the only reason. I am thinking it could be caused by the mass I'm lifting and its addition to the length of the system. If this is the cause than there is far to much complexity in the field path for my ability level and understanding of magnetic flux to make any creditable claims. Though Believe if I were to change my setup so the magnet was only ever in contact with a piece metal that remains constant and a variable non-magnetic mass suspended from the constant piece.

as follows:

 

[OmCheeto]

I don't think the effects would be so extreme if that were the only reason. I am thinking it could be caused by the mass I'm lifting and its addition to the length of the system. If this is the cause than there is far to much complexity in the field path for my ability level and understanding of magnetic flux to make any creditable claims. Though Believe if I were to change my setup so the magnet was only ever in contact with a piece metal that remains constant and a variable non-magnetic mass suspended from the constant piece.

as follows:
View attachment 65793

It looks as though you've used the wrong equation. According to wiki, that equation is good for a horseshoe type magnet:

Closed magnetic circuit
...
For a closed magnetic circuit (no air gap), such as would be found in an electromagnet lifting a piece of iron bridged across its poles, equation becomes: F=N²I²μ²A/2μ₀L²

Bolding mine

 

[aloman]

That is true, I have an "i" magnet. What equation would I use then?

 

[OmCheeto]

That is true, I have an "i" magnet. What equation would I use then?

I'm not sure. I've been working on your problem on and off since you first posted, and the only answer I have is; "It's complicated".

I've never experimented with electromagnets, nor have I studied them since university, 30 years ago.

It might be possible for us to derive an equation for your system, if you were to provide us with the cross sectional area of your core.

 

[aloman]

the cross-sectional area is 1.2668x10^-4 m

I have also been wondering how direct the relationship between the magnetic force and lifting capacity is, If a electromagnetic force of 16 N is able to lift approximately 1.63 kg of steel then it becomes possible to estimate the relative permeability of my core.

 

[aloman]

It does seem rather complicated.
http://www.goudsmit-magnetics.nl/EN/Background-information/About-magnetic-lifting

I believe that the lift capacity of my set-up would be about 90-95% of the lifting force.

 

[OmCheeto]

It does seem rather complicated.
http://www.goudsmit-magnetics.nl/EN/Background-information/About-magnetic-lifting

I believe that the lift capacity of my set-up would be about 90-95% of the lifting force.

I was about to give up, but I ran across the equation for the pull force of a single magnet:

m=(B²A)/(2μ_og_n)

From which you can derive "k", and subsequently μ, for the first phase of your experiment.

The following statement tells me that this is not a "plug and chug" problem, and is therefore not within my abilities to solve:

This is a nonlinear equation, because the permeability of the core, μ, varies with the magnetic field B. For an exact solution, the value of μ at the B value used must be obtained from the core material hysteresis curve.

ref

Hysteresis curves always hurt my brain, as I recall.

And this:

in magnetic circuits with an air gap, the strength of the magnetic field B depends strongly on the length of the air gap, and the length of the flux path in the core doesn't matter much.

indicates that although you doubled the length of your core, it really didn't matter.

 

[aloman]

Thank you very much I think I have a fairly reliable approximation now. I was able to get a formula that seems simple enough.
lucky for me I'm not planing on going into electrical engineering.