Forces between perpendicular permanent magnets

[morganj2003]

I'm desperately trying to verify a FEM analysis done on a system of two permanent magnets. I'm trying to analytically find the force between two large neodymium magnets spaced 1/8 inch apart. This problem would be easier if the magnets were oriented such that their magnetized planes were parallel with each other, but this analysis requires that the magnets be PERPENDICULAR to each other. Since the magnets are close to each other, considering the dimensions of the magnets themselves, I cannot make the magnets into dipoles.

 

The question is, then: HOW DO I ANALYTICALLY (NO FEA OR ONLINE CALCULATORS) determine the force (normal and transverse) between these two perpendicular magnets?

 

THANKS!

[Externet]

If "-" is one magnet and "|" the other, they can be perpendicular in these ways :

 

-|

 

and

_|

 

Which one are you talking about ?

[morganj2003]

The magnets are perpendicular in the following way:

 

|-

 

where the left magnet has poles S-N (from left to right) and the right magnet has poles N-S (from top to bottom).

 

I am willing to assume that the magnets are sufficiently long into the page such that the end effects of the magnets are perhaps negligible.

 

Thanks!

[InigoMontoya]

Would a composite 6-DOF load cell work? Granted, given the rest of what you said I suspect it's beyond your budget, but I'd think it is a technically feasible solution (if not economically feasible).

[morganj2003]

A load cell would work if I as trying to determine forces experimentally, but I need to determine the forces ANALYTICALLY.

[ajb]

I am wondering if we could use electromagnetic duality. What is the corresponding situation for electrostatics?

 

Though it maybe the case that an analytical solution does not exist.

 

Is this of any help?

http://instruct.tri-c.edu/fgram/web/Mdipole.htm

[InigoMontoya]

I'm confused... You're trying to verify a model by just using another model? What guarentees that both models aren't crap?

[ajb]

I'm confused... You're trying to verify a model by just using another model? What guarentees that both models aren't crap?

 

There is a fundamental duality between electric and magnetic field in vacua. Thus, if we know the corresponding problem and solution in electrostatics we know the solution to the magnetic problem.

 

One thought was to treat the poles of the magnets like "magnetic charges"* and relate the problem to the forces between electric charges. There is of course going to be some questions of how reliable such an approximation will be. But, it is a possible mathematical approach.

 

I expect anything more "realistic" is going to be very difficult.

 

 

----------------------------

* I am not suggesting magnetic monopoles exist in nature by doing this.

[morganj2003]

Inigo,

 

I'm verifying a FEM analysis with an analytical analysis. This is common practice in FEA. In fact, a FEA without an analytical verification is not respected at all.

 

ajb,

 

Yes I considered, as I mentioned in my first post, the idea of using an electrostatic equivalent (making the permanent magnets into dipoles). This is not acceptable, though, as such an approach is not a sufficient approximation when magnets are so close to each other.

 

No more ideas?

[ajb]

That's all I can think of. For complicated problems sometimes all you can do is solve them numerically. To test the numerical methods you need to find situations that you know how to solve analytically.

 

Anyway, I did a multipole expansion so a situation like that you describe and get this picture (all charges are of equal magnitude). The arrows are the field and the contours are the potential. It may be qualitative use to someone.

[morganj2003]

So, I found an answer to my previous question about finding the force between perpendicular magnets, but I still have a problem.

 

The following paper uses the variables t and g on the bottom left side of page 163:

 

http://hal.archives-ouvertes.fr/docs/00/42/23/19/PDF/OS5.1.pdf

 

The t and g do not seem to be defined previously. I've looked into the possibility of t and g being some kind of common values used in magnetics, but my research hasn't turned up anything. Maybe you have some thoughts?

 

Thanks,

Jon

[InigoMontoya]

I'm verifying a FEM analysis with an analytical analysis. This is common practice in FEA. In fact, a FEA without an analytical verification is not respected at all.

I guess we just live in different worlds. In my world, a FEA without *experimental* verification is not respected at all.

[morganj2003]

So, I found an answer to my previous question about finding the force between perpendicular magnets, but I still have a problem.

 

The following paper uses the variables t and g on the bottom left side of page 163:

 

http://hal.archives-ouvertes.fr/docs.../PDF/OS5.1.pdf

 

The t and g do not seem to be defined previously. I've looked into the possibility of t and g being some kind of common values used in magnetics, but my research hasn't turned up anything. Maybe you have some thoughts?

 

Thanks,

Jon