Magnetic Forces in Iron 1

[meshparts]

Hello,

using Ansys I have modeled an electrical machine consisting of iron, magnets, coils and air.

I would like to compute the elastic deformation of the Iron under the influence of the static magnetic forces. By "static" I mean, that the rotor dose not move during the calculation of forces.


To accomplish that, I have defined a Maxwell surface around the Iron. But this method only compute forces on the Maxwell surface (exterior of the iron) and not on the interior of the iron.

It seems logical to me, that in reality magnetic force are also acting on the interior of magnetic materials. Is this supposition right or not?

It is very important for me to understand that, since the simulation result is depending on the correct computation of magnetic forces.

So are there also forces on the interior of the iron? And how to compute them? Are there any methods? The problems knowns are the vectors B and H on every point of the iron. I need the magnetic forces on each of these points.

Please excuse my limited knowledge on this field. I am usually doing other kinds of simulations.

Many thanks in advance!

Regards
Alex

 

[israelkk]

Are you a student? Is this a student assignmennt?

 

[EdStainless]

The magnetic forces are so small that they do not cause dimensional changes. Magnetization itself might. Look up magnetostriction.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[IRstuff]

Wouldn't you look at the field gradient in the material?

TTFN

FAQ731-376

 

[meshparts]

Hello,

@israelkk: I am not a student! You can see my profile, don't you?

Like I said, this is normally not my research field. Bu now I really must know, if the magnetic forces exists also in the inner of the iron.

Till now I have asked many people. But no one can give me a satisfying answer. Makes me wonder, how many true specialists in magnetics are really there...

Perhaps I should reformulate the question: Imagine a simple rectangular piece of iron. An also a simple rectangular piece of magnet. Magnetic forces acts on the iron. But WHERE??? Only on the surface or also on the inner of the iron???

@EdStainless: I almost agree with you. In my case (I am doing a numerical optimization) it can happen, that the structures becomes so thin, that it can largely deform under the magnetic forces.

Regards,
Alex

 

[EdStainless]

Yes, there are internal force in the iron. In order for you to be getting distortion you need to have variations in the field don't you? If the iron is in a uniform field then the effect will be volumetrically uniform.

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[BobM3]

If you cut the object and do a free body diagram on it there would have to be a reaction force on the cut section to balance the external magnetic force.

 

[meshparts]

Hello EdStainless,

thank you, this is the statement I was looking for.

Now I have one problem: the FE program I am using dose not compute the forces on the interior of the iron. All I have are forces on the exterior. That's why I am supposing, that the deformation of the iron is not quite accurate.

I have to find a way of computing the inner forces from the magnetic field. Using the programing language of Ansys, this should be possible.

As IRstuff pointed out, one should look at the gradient. If this is true, then the magnetic forces on the inner of the iron should be in an uniform magnetic field very small.

Nevertheless But what relationship exists between magnetic field (gradient of the field) and magnetic force?

Regards
Alex

 

[prex]

mihaiupb, your interesting problem is not fully clear to me, but I'll try to contribute a little.
I would say first that the way of reasoning of BobM3 doesn't prove much, as any body subject to external forces will have internal stresses equilibrating those forces, irrespective of where those forces act, on the surface or on the volume.
Continuing in the same vein, I wonder what you want to do with those deformations. If, as I suppose, you are interested in something like a beam behavior of your iron (the armature of an electromagnet as an example), then you can get it by applying the surface pressures that you already have and the support conditions.
The internal forces in the iron, apart from the stresses generated by the elastic behavior as above, are of a different nature.
As an example take a permanent magnet and break it into two parts. If you now try to join again the two parts in the original position, you will notice a strong repulsion. This is of course because of the magnetization, but what I want to say is that those repelling forces, that were present also before the break, are really of an internal nature (they do not equilibrate any external force) and so will cause only an expansion of the body similar to a thermal expansion.
The case of an iron is similar, except that the internal magnetic forces will cause generally a contraction instead of an expansion.
To visualize this take a horseshoe magnet with an iron armature joining the two poles. If you now imagine to cut the armature in the middle and try to separate the two parts, you'll notice an attractive force between them (BTW the corresponding stress should be equal to B²/2[μ]_o in a uniform field). However once again this is an internal force that will result only in a contraction of the body similar to that experienced for a temperature decrease.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[meshparts]

Hello Prex,

Thank you for your post.

I am interested in the stresses generated by the elastic behavior of the iron when deforming under the magnetic forces.

Since the elastic deformation directly depends on the magnetic forces, it is very important to know HOW and WHERE to compute these forces.

Ansys computes the forces only on the surface of the Iron. That's why I have asked my self, if this is physically correct.

I have found the post of IRstuff interesting, since a colleague told me the same thing. If this is right, then I must fin out how field gradient relates to magnetic forces. At the moment I can only imagine, that it could look like that:

Magnetic_force=Field_gradient*vacuum_permeability*iron_permeability

Regards
Alex

 

[prex]

I'm afraid that you'll need to deepen your theoretical knowledge of magnetism to solve your problem (the same would of course be valid for me, but this is not my problem ...).
I'll try to add some more considerations.
First point, on your tentative coming from IRstuff's suggestion, is that the field gradient in a piece of iron is generally very low, so it would produce small or negligible forces. Second point is that your equation cannot be OK: a force has the dimensions of ABH (A is an area), or AB²/[μ].
Possibly your forces have something to do with the change (gradient) of H (as B is nearly constant along the magnetic circuit), but we know that H changes suddenly at the surface of the iron .
Another suggestion for attacking the problem. We know that magnetic forces are generated by the interaction of B with electrical currents (ampere's law). We also know that in a magnetized piece of iron (in other words a piece of iron immersed in a magnetic field) there are the so called amperian currents that (in the absence of conduction currents generated by an external electrical circuit) are the only ones that can explain the magnetic forces acting on the iron.
Now in an iron cylinder with uniform magnetization along the axis, the only net amperian current flow circumferentially on the lateral surface of the cylinder. These currents may produce only a force stretching the surface of the cylinder.
Where the magnetization is not uniform, there are volumic amperian currents, whose density is proportional to the gradient of the vector M , that will produce forces acting on the volume of the body.
However, where, in an iron participating in a magnetic circuit, like the armature of an electromagnet, is there a non negligible gradient of M? Right near or at the surface of the iron facing the gap! (or just where there is a big change in H, that is one of the components of M=B/[μ]_o-H).
In conclusion I think that what Ansys tells you is correct, and that you might be after a no problem. Good luck!

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[meshparts]

Thank you Prex for this really professional answer. I will have to think a while on it! But if you have right then I really have no problem and that's really good to know.

Regards
Alex