FLUX FOCUSING WITH POLE PIECE 4

[Todd619]

I'm working on a design for a magnetic dipole with a steel yoke, most likely using permanent neodymium magnets. My goal is to achieve the highest field possible across a gap over a certain minimum area, with an emphasis on uniformity of the field over this area.
My question is if I use a cone shaped pole piece to focus the flux to a smaller area over the gap can I pretty much divide the larger area by the new smaller area to get a value >1 and multiply that by the value I would have gotten across the same size gap with the larger area to find my new Bg?
Also, how much, if any, will the pole piece help with uniformity?

Hope this is clear
Thanks for any help
-Todd Massure

 

[UKpete]

Todd, it is possible to increase the flux density by flux focusing as you describe, and were it not for flux leakage it would be linear with the ratio of the larger area over the smaller area.

The reason for the flux leakage is because of saturation of the pole piece material. With steel or iron pole pieces you will get a flux density above the remanent flux density of neodymium, but the best material to use is cobalt. Manufacturers of hysteresisgraphs, e.g. see:

http://www.walkerscientific.com/Pro...alysis/Hysteresisgraphs/hysteresisgraphs.html

- use cobalt pole pieces to get maximum flux density in the sample that is being tested for its B-H characteristic.

Unfortunately cobalt is expensive, and fairly soft, but it does have about the highest saturation flux density for any material.

You can only expect to get a linear field in the central area of the pole, not towards the edges, so you may have to make the pole area larger than you planned.

 

[nbucska]

The saturation of the poles limit the flux density --
if you need more, you may use superconductive magnet.

<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032

 

[IRstuff]

From what I've briefly read, flux concentration cannot be done through the magnets themselves:

http://www.sentron.ch/support/downloads/TP005_Integrated Hall sensors with flux concentrators.pdf

TTFN

 

[nbucska]

Todd:
Looks like this problem persiststs since Jan. please
read the referred FAQ !!!

<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032

 

[Todd619]

OK, to use specific values as requested by nbucska, I am planning use (2) N45 grade neodymium magnets 15cm dia. x 5cm thick. I will use a square steel yoke to complete the circuit and also to create a 1cm gap.

using Bg=Br/(1+(g/h))
I get Br=13500/(1+(1/10))=12272.72G
(this number is probably a little high(?))

The area of the 15cm surface is:
pi(7.5^2)=176.71 cm^2

then use a pole piece to reduce to a 10cm dia surface of:
78.54 cm^2

with a perfect pole piece material I would have
(176.71/78.54)*(12272.72G)=27612.83G

Any estimates on what kind of percentage loss I could expect using annealed soft iron pole pieces?

Thanks again
-Todd Massure

 

[UKpete]

Todd, you have got a small mistake in your equation for the working point of the magnet - from your figures at the top it should be:
Bm=13500/(1+(1/5))=11250 Gauss
Also this equation assumes that all the mmf drop in the magnetic circuit appears across the airgap when in reality there will be some (say 20%) dropped across the iron part of the circuit especially when it is operating near saturation. So your working point is most likely down near 10000G (1 Tesla).

Using this value then the first approximation for gap flux density would be 23400G, but the saturation flux density for pure annealed iron is I think about 21500G so you are not going to exceed this figure by very much in the gap (to any additional flux above this level the saturated iron is effectively air as its relative permeability falls towards 1.0). Note that cobalt has a saturation flux density of about 23500G so you will get higher flux density in the gap.

http://crswnew.cartech.com/wnew/techarticles/TA00005.html

(see table at the bottom of the article).

One other point, you are using a large chunk of magnet material. I know NdFeB is coming down in price but your piece of magnet is about 6.6kg so it will cost a few hundred dollars (the bulk price for Chinese i.e. Magnequench NdFeB is about $60/kg including processing I think). It will also be very difficult to handle, you will need special jigs and tooling to stop it colliding violently with the iron pieces when you assemble it. It is more common to use large electrical coils to provide the mmf (e.g. it is used in hysterisigraphs as per my earlier link) - even water cooled if necessary. This is easier to assemble and it is controllable.

 

[Todd619]

I actually meant Bg=13500/(1+(1/10))=12272.72G Not Br=....
Am I still incorrect?
It's my understanding that one uses the total magnet length in series when figuring for the flux density at the gap i.e. 5cm + 5cm=10, but your figue tends to agree more closely with what I get from the online calculator at:

http://www.dextermag.com/Calculations/Calculation.aspx?mode=input&id=FieldCalcDipole

You are also much more knowledgeable than I am about magnetic circuits, so I'm sure you're right.
Also, does the length of the steel yoke in the circuit matter much? I'm sure there is additional loss for additional length, but it seems to be something that no one worries about too much.
I was wondering if the pole pieces are completely saturated, does that help with uniformity of flux density?
I've been trying to find a good supplier for small amounts of pure Iron and Iron-cobalt material, but haven't really found anything yet, any reccomendations anyone? (plug your company!)
I don't think I want to go with electromagnets after researching them for a while, this project is to reside in my garage and there's not a lot of power available or extra space for that matter. I think I have a good jig system worked out where I can slide the magnets from a flush surface onto the steel etc., but I'll probably experiment with smaller neodymium magnets first...I am scared of these magnets, and I know I should be!

Thank you for the valuable help!
-Todd

 

[UKpete]

Sorry Todd it was my mistake, I didn't notice that you intend to use two magnets in series, so your original equation is correct. Strictly speaking it should be Bm= ... (the magnet flux density) because the gap flux density Bg is later found from the ratio of the areas.

The length of the magnetic circuit does matter to a certain extent, you might drop say 10-20% of the mmf across it (the rest across the airgap) - it all depends on the relative permeability of the iron (which in turn depends on the level of saturation in the iron) and the ratio of the path lengths (iron/airgap). This is allowed for by increasing g in your equation (10-20%).

I'm in the UK by the way so I can't really recommend any particular supplier; I work for a US-owned company (Waukesha Magnetic Bearings) but we only use electrical steel laminations.

Unfortunately you will have to pay a high price for cobalt, e.g.:

http://www.goodfellow.com/scripts/web.wl?MGWLPN=MNT&PROG=SEARTOW&LAN=E&HEAD=CO15&SPAGE=CO15

Could you settle for 10% lower flux density and use steel?

 

[MJR2]

I put together a model using N45H material. I also checked it with another program we have for this type of circuit. You'll be getting about 12,200 gauss across the center of the air gap. I used 1010 low carbon steel. The losses in the steel I used were very low. I used much more steel than I would build the circuit with. But not so much that it would not be economic to do so.

Be careful.

An electromagnet would be much easier to deal with.

 

[Todd619]

Thanks once again to UKPete, and yes the cobalt material is almost as expensive as the magnets themselves!
Well MJR2, thanks for modeling this design, but I must say that that figure is dissapointing to me. I was sure I could get at least 20,000G. by concentrating the flux from an area of 15cm. dia. to about 10cm.
Any idea why it seems so lossy?

 

[nbucska]

Todd:
There are many ways to skin a cat.
My experiece is that if something is difficult, perhaps you can approach the problem from different side. I suggest
to step back and try somethin else...

What do you use the field for? does it have to be
constant or can it be pulsed? etc.


<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032

 

[mac2]

Todd,

If you wish to persue the tapered pole approach, there is a good section in the book "Electromagnets" by D.J.Kroon that deals with (Stray flux and flux density). It covers both low and high fields (i.e. saturation). While principally dealing with electromagnets, the section dealing with pole shape is helpful for either electro or permanent magnets once you establish the primary flux.

 

[Todd619]

This magnetic circuit is for what is basically a cyclotron, and is just for my own experiments / hobbyist satisfaction. I have a goal of attaining certain energies of particles so I am definitely trying hard to maximize the field across the gap.
Basically increasing the B field by using tapering pole pieces reduces the overall dia. of the rotating particles. Since area changes at a greater than the respective dia. so does the flux density, and the diameter of the rotating particles should reduce faster than the diameter of the pole face, but I am restricted by the saturation limit of the pole pieces.
Sorry I don't have the formulas in front of me to list here.
So to answer the other question, it does need to be a continuous / non pulsing design, and also fairly small and light. The whole apparatus is also going to be put inside of a vacuum vessel, this is not the traditional way of constructing a cyclotron, but it keeps the gap much smaller.

I will probably order the book mentioned in the last post, thank you!

-Todd Massure

 

[MJR2]

Todd,
I case you're interested here is an electromagnet. It does not fit your spec of light weight. And it does require force cooling since you have it in a vacuum.
The specs are
20000 gauss in air gap
1 cm air gap
15.25 cm square pole face
taper angle back from pole face to core of 45
Pole length 5 cm
Core (and C-Frame circuit cross section) 25.4 cm
Core length 7.6 cm
1010 steel
Coil Specs (2 in series)they go same place as your PM's.
#15 copper wire 82.1 pounds each
1000 watts at 230 VDC
Coil 16.5 x 16.5 ID's x 7.6 height 1.3 cm corner radius
2805 turns
4.35 amps DC 26.45 ohms per coil 24,394 ampturns
Cooling
Immersed in transformer oil temperature in at 70F out at 110F
Continuous duty if force cooled. It will drop off to about 3.26 amps when hot.

It will start off cold at about 22000 gauss. It will not stay there long due to heating. Field should be pretty uniform given the pole taper.

This design is based on equations from the above mentioned book. Really impressive amount of force between these poles.

 

[Todd619]

Thanks a lot for that electromagnet design, it gives me a really good idea of what kind of an electromagnet it would take and I could pretty much use that design exactly, except for changing the poles to round.
I think that by using an electromagnet it might be possible to design it so that the pole pieces are built into a vacuum chamber that could slip between the pole faces.....but that's another story.
On the permanent magnet circuit you described the flux was a lot lower than I expected, and no one has disputed it (I was kind of hoping someone would...anyone, anyone?), so maybe I do need to use and electromagnet design. The book you listed is out of print, so I ordered another one that looks good called:
The Magnetic Circuit - Electromagnetic Engineering
By: V. Karapetoff
but I'll still look out for that one, once I get a book I can hopefully stop bugging you guys!

 

[UKpete]

Todd, I agree with MJR2's estimate of gap flux density - I have a student copy of Maxwell from Ansoft and I ran it with the dimensions you provided using an axisymmetric model. With a sintered NdFeB material with Br=1.23T and Hc=8.9e5A/m, and steel grade 1008 (saturation flux density a little over 2.0T, magnetically identical to 1010) I get a flux density in the airgap of between 1.19 and 1.21T (multiply by 10,000 to get gauss).

Finite element analysis will give accurate results with this geometry. The problem with the simple equations we used are the leakage and saturation factors, which are obviously a source of inaccuracy, my mention of 10-20% was a gross underestimate as it turns out.

I would consider the wound coil version as proposed by MJR2; you can get a higher gap density, although of course you will have the expense of the power supply and cooling (if required).

 

[UKpete]

One other point, I reran my FE model with cobalt pole pieces and it doesn't give any improvement. To get any benefit from cobalt you will have to be aiming to get more magnetizing force i.e. the wound coil version rather than the PM version.

 

[Todd619]

Thanks for confirming MJR2's model (MJR2, how could I ever have doubted you?) I was still working on a PM design, but I really think I will hve to abandon it now. Maybe the electromagnet will really be easier to deal with, and possibly cheaper anyway, safer to construct I'm sure. My little microwave pulls 1350 Watts so ~ 1000 Watts is totally doable and I can run it for just seconds at a time so cooling may not be an issue. Hopefully I can modify the design so I can use 110, but if not, I know a place I can set it up that has 220.
The program you mentioned from Ansoft, I see some free downloads available for 2D electromagnet modeling, is that what you used? I'm going to download it anyway, but I wondered if you used a 3D model.
Hopefully when I'm done some trusting soul (sucker) here around San Diego will lend me a Gaussmeter to qualify my Bg!
Thanks again for all your help, you guys have really gone above and beyond with the computer modeling & everything!

-Todd Massure

 

[UKpete]

Yes it was the 2D download from Ansoft which I obtained a couple of years ago. It will also do axisymmetric i.e. a cylinderical type model which has a single axis about which the model is symmetrical if you rotate around this axis e.g. a loudspeaker voice-coil (hope that makes sense). If a model is axisymmetric you get a full 3D solution. Your pole piece arrangement can be modelled as axisymmetric.

The Ansoft program will do permanent magnets and coils, but the copy I have doesn't let you put in additional materials; however there is a good variety of materials already entered. It is a relatively easy way into electromagnetic FE modelling because it has fully automatic (adaptive) meshing, avoiding the hours of fun you can have with manual meshing. The only problem I have had with it is trying to get accurate answers for forces; also I haven't managed to sort out how to get point values of flux density in the post processor but there is a work-around by manually setting the colour bands.