Permeability of rare earth magnets 1

[mapponfish]

My understanding is that the relative permeability of rare earth magnets is almost unity. This would mean that, in simple permanent magnetic circuit analysis, you would need to consider the thickness of the magnet as well as the thickness of the air-gap when calculating the circuit flux.

Is this correct ?

Thanks for any corrections.

 

[gphatch]

Hello mapponfish - you do indeed need to consider the thickness for such magnets - in fact all dimensions. The flux density of a permanent magnet is significantly dependent on the geometry of the magnet. A long thin magnet will produce a very different flux profile than a short "tile" like magnet.

Magnet design engineers use some reasonably good approximations of the flux generated by a magnet, by taking into account the ratio of the surface area of one pole of the magnet [basically half the surface area for a rare earth rectangle, for example], to the cross-section of the magnet through which flux is flowing. See the web site in my signature file for more details - we have a free permanent magnet reference and design manual available for download.

Gareth P. Hatch, Ph.D.
Director of Technology
Dexter Magnetic Technologies

http://www.dextermag.com

 

[prex]

Your statement is incorrect, mapponfish.
The permeability of a permanent magnet is very high, just like that of iron, up to saturation. However, unlike iron, the magnet can saturate itself only in a closed circuit (unless it is used in a circuit with a larger magnet, a quite odd situation).

prex

http://www.xcalcs.com

Online tools for structural design

 

[hacksaw]

of course it depends on which permeability definition you are interested in, but the differential permeability of permanent magnets is usually taken as unity. Why? Firmly fixed permanent magnets do not respond to small changes in the applied field, and so are relatively "impermeable"...

 

[mapponfish]

Thanks to the respondents for their replies. There does seem to be a conflict between the comment by PREX and others however.

My limited understanding was that, in a simple magnetic circuit (say a C-core with one air gap and one ferritic, permanent magnet), the permeability of the magnet and iron core were so high (compared to the air gap) that a first order estimate of the air-gap flux density could be made by considering the air gap reluctance only.

Thus, the MMF of the magnet is essential dropped over the air gap only.

With the same circuit using a rare earth magnet, I understood that the MMF of the magnet would be dropped across the air gap plus the magnet - necessitating a consideration of the magnet thickness as well as that of the air gap.

I hope I'm not labouring the point but it's not totally clear to me whether this is what's going on !

 

[hacksaw]

you are looking for the operating point for the magnet. you might refer to the following site:

http://www.magnetweb.com/Sect4A.htm

 

[sreid]

Here are some equations I use for permanent magnet magnetic field strength.

PC=(Lm/Lg)(Ag/Am)

Bm=(Br)(PC/[PC+1])

Bg=Bm(Am/Ag)

PC = Permeance Coefficient

Lm = Length of the Magnet

Am = Area of the Magnet

Lg = Length of the Gap

Ag = Area of the Gap

Br = Magnet flux density remnance

Bm = Flux density in the magnet

Bg = Flux density in the gap

Assumes recoil permeability is one. The magnet and the gap are connected with iron.

 

[mapponfish]

Many thanks to all respondents for their helpful advice. Magnetweb is especially good !

 

[UKpete]

Just for the record, I think prex is thinking about Alnico or steel magnets (old technology), these do have a high value of relative or recoil permeability unlike all rare earth (NdFeB and SmCo) and ferrite magnets, including all polymer-bonded types of rare earth and ferrite, which have relative permeability values of near unity as you correctly state.

This low value of relative permeability doesn't give an effective airgap of physical airgap + magnet thickness (in direction of flux) BUT it is additive for inductance calculations e.g. a linear actuator with a rare-earth magnet will have low coil inductance compared with a design with an Alnico magnet. This is generally considered an advantage.

So the near unity value of relative permeability in the rare earth magnet only affects the magnetic circuit of some secondary source of flux.

 

[prex]

UKpete, you didn't explain why, at unit relative permeability, the magnet thickness is not accounted for in the air gap, and also in what respect Alnico magnets behave differently from RE from the point of view of the magnetic circuit (that is not considering the very different demagnetization curves).
mapponfish, you could make an experiment: take a rare earth unmagnetized magnet and put it close to another (magnetized) magnet: they will attract themselves, and I think we can agree on the fact that this means the relative permeability of the RE magnetic material is not one.

prex

http://www.xcalcs.com

Online tools for structural design

 

[hacksaw]

prex you have to include the dipolar interaction not just the permeability of the magnets.

 

[UKpete]

prex, I'm not an expert on magnet physics and I'll rely on hacksaw's comment.

But the facts in my original post were intended as a practical aid to understanding magnetic circuit design and are correct.

The value of permeability is given by the slope of the B-H curve around the magnet operating point, and with reference to Peter Campbell's diagram (see hacksaw's link) showing the magnet second quadrant, you will find from manufacturer's data that this has a value very close to mu0 (permeability of free space). The significance of this fact is not worth worrying about.

If you look at the B-H curve for Alnico at around the operating point, you will see that the slope, i.e. the permeability, is very much greater.

Incidentally what IS desireable is that the magnet characteristic is linear e.g. if external excitation is applied (moving the load line to the left or right, depending on the direction of current, so that it no longer passes through the origin) or the airgap changes (altering the slope of the load line), there is no irreversible demagnetization i.e. removing the excitation (or restoring the airgap) restores the original operating point - not the case if the magnet characteristic is non-linear or you take the working point into a non-linear region.

 

[hacksaw]

my cryptic comment about dipoles meant to imply that when you replace your permanent magnet by an arragement of permanent dipoles one producing the same mmf, you only need to consider the external circuit. no physics intended.

this is already covered (i see) in Ukpetes commentary.