IE needs help understanding magnetic forces involved in product... 1

[wilmar13]

OK, so my company makes a product where a blade is attached to a backing with a series of neodymium magnets. The backing is zinc plated cast iron, and the blade is steel. The backing has "pockets" that are bored just over the OD of the magnet (.0001-.004”), and just slightly deeper than the magnet so that it sits snugly in the pocket and is just below the surface of the backing. Then the blade is installed and the magnets provide a “clamp force” to hold the blade on in lieu of bolts.

The issue lies in the fact that someone recently noticed the magnets are easily spin-able when placed in the pocket. I mean you can rotate them in the pocket with your finger. When placed on the same backing face (where the blade locates) rather than in the pocket, it takes quite a lot of force to even move the magnet, let alone spin it (they are N45 25mm x 3mm discs). I have done quite an exhaustive study of all part parameters and to my surprise it seems the more perfect the pocket is (bore roundness, bottom flatness, etc.) the more likely the magnet is to spin. The only thing I can think of is that there is some kind of balance of forces when the disc is perfectly surrounded on one face and the circumference so that is “floats” in the pocket. Is this possible? If so can someone explain how this works? Thanks in advance for any help you can provide.

 

[wilmar13]

Oh, I forgot to mention that the force to remove the magnet from the pocket is the same whether it spins freely or if it appears "fixed".

 

[sreid]

With a magnet in a cast iron hole, the magnetic flux from the open end of the magnet is effectively magnetically short circuited, i.e., the flux wants to jump from the magnet end to the surronding iron. With a tight fit in the hole, the shorting is even more effective.

One way to minimize this would be to make the hole bigger and install a nonmagnetic cylinder around the magnet.

 

[prex]

It would be better if you post a sketch of the situation, representing both the magnet in the pocket (where it spins freely) and out of it (where it doesn't). Can you also confirm that, as I expect, the disc is magnetized through its thickness?
The explanation by sreid doesn't convince me: if it was true, there would be no attractive force left for the blade. Also, as this is a disc 25 mm in diameter and only 3 mm deep, there is not much diffence in behavior to be expected when the magnet sits in the pocket with respect to it sitting on a flat surface.
The only idea that comes to my mind is that the bottom of the pocket is not flat, so that the disc sits with more pressure near its center. A similar condition could come from an uneven thickness of the zinc coating (non magnetic).
Anyway I'm not convincing myself. More information is needed.

prex

http://www.xcalcs.com

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[MagMike]

wilmar13: I'm also having trouble visualizing your setup. However, it is unlikely that you've acheived a "balance of forces" that will allow a magnet to freely spin. It's impossible to achieve a perfect balance of force in a permanent magnet-only system.

It's generally pretty easy to spin/rotate a cylindrical magnet (no matter how large it is) on a piece of steel. It takes a bit more effort slide the same magnet across the surface of the steel. Neither of these situations involve a change in the magnetic circuit, it's just friction forces working against you. It takes a lot more effort to pull that same magnet directly away from the steel because now there is a significant change in the circuit.

sreid's suggestion has good merit if you want to increase the holding power of your magnets.

 

[wilmar13]

Ahhh I have to post a Cad sketch to a webserver to show on this forum… I can’t do that from work. Is there a way to attach a file that I don’t see? I don’t want to go into too much product detail, but the application is for replacement of fastening hardware… so it is probably an unconventional use of magnets. Basically we have a product here that is usually bolted in place, but needs to be removed occasionally for sharpening and/or replacement. It is in a harsh environment so the fasteners quickly become corroded and need to be destroyed (blow torch, chisel, etc.) for removal in the field when maintenance of the blade is required. The magnets are used (in conjunction with locating pins) to hold the blade in place of hardware (bolt and nut), and require no tooling to change, just to make it easier for the end user in the field. Again the “backing” is the frame to which the “blade” is mounted. The interface is just a flat machined and ground surface on the backing. We have machined pockets in this mating surface on the backing (where the magnets are placed) to provide sufficient clamp force to hold the blade secure… it requires a lot of clamp force thus the use of multiple neodymium magnets. The magnets are not glued or pressed in the holes, only the magnetic force holds the magnet in the pocket, and draws the blade against the backing. We did have a larger pocket initially (.010” over magnet OD), but found that sometimes on removal of the blade, the magnet stuck to the blade rather than staying in the pocket. The bore was reduced to just over a press fit to eliminate this (it didn’t affect functionality, but the customer views it as “the magnet wasn’t holding the blade!”). It is worth repeating, the magnetic force is the only thing used to hold the assembly together and does not seem to be reduced with a spinning magnet and one that is fixed.

At any rate, the convex shape of the hole was my initial theory as the endmill used to interpolate around the hole does leave a small rise in the middle (as much as .002” from outside edge). Unfortunately after running extensive CMM inspections over 100’s of holes, there is actually a correlation between the rise in the middle and NOT SPINNING… in other words the flatter the bottom surface of the pocket, the more likely the magnet is to spin, so it was totally counter intuitive. The magnets are perfectly (within .0005”) flat with no taper and I assume it is magnetized through its thickness (neodymium magnets are incredibly powerful… dangerous to handle even!). It is important to note that this condition does not affect the functionality of the assembly, the spinning magnets hold the blade to the backing with equal force compared to a fixed magnet.

I disagree WRT the spinning magnet on a flat surface. These magnets are so powerful that the surface friction will not allow the magnet to spin on a flat surface with equal surface finish and plating (zinc). You can place them on the blade mating surface and it takes quite a lot of force to slide them off (spinning is impossible). This is a very strange phenomenon and I would love it if someone could figure out what is going on. Thanks for the ideas so far and keep them coming.

 

[prex]

Can you visually determine the direction of flow lines in the magnet?
It's easy to do so with some iron particles that are easy to find in any workshop.
First test a magnet alone. If it's magnetized through thickness you should see the particles staying upright like soldiers all over the surface, with some crowdy zones near the corner.
Then test it when it's in the pocket to see what happens : you can use a piece of white paper before throwing the particle to see better (though I understand it will be difficult to explain the result here...)
Can you also check whether there is any difference in behavior when you turn a magnet upside down in the same pocket where it was already before?

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[wilmar13]

No difference in placement orientation of magnet in pocket. It is magnetized through its thickness, but I will try your test to see if there are crowdy zones... I assume steel chips will work? I dont think I have iron particles handy ;-)

 

[electricpete]

I haven't read all the responses.

I agree with the relevant factor keeping a magnet from spinning is the force pulling the magnet toward the metal underneath... provides normal force that increases sliding friction.

Now how do we compute force? F = - dW/dx

energy density is 0.5 * B^2/mu

Energy density is negligible in the iron (where mu is high), and very large in the air.

Due to the B^2 term, a disproportionate amount of energy is stored in the small volumes of highest energy density.

So bottom line simplified model for predicting force: everything is pushed in a direction that minimizes the volume of high-density flux paths in air and the magnitude is dW/dx.

Let's consider the two cases, magnet sitting on top of flat surface and magnet sitting in hole. In both cases, the relevant force to prevent spinning is the downward force.

First look at the magnet sitting on a flat surface. The flux that comes out the top vertically goes up and then goes back down vertically. If we move the magnet out a small distance dx, we increase the length of those flux lines by dx or perhaps 2*dx, resulting in increase in energy... dW/dx fairly large.

Now look at magnet sitting in a hole perhaps even slightly recessed. The relevant flux goes out the top and flows primarily horizontally to complete the circuit. If I move the magnet up by small distance dx, does the flux path in air increase by dx? No, it is much less than dx. The flux is still flowing primarily horizontally and the horizontal distance in air barely changes. The stored energy barely changes so the force = -dW/dx is small.

The ideas of flux flowing vertically and horizontally are of course an approximation (the actual shape is curves and more comlex). But I think it captures the relevant aspects. In quick summary, when the flux in air flows primarily vertically (for magnet on top of flat sheet), then moving the magnet vertically small distance dx causes increase in length of flux path within air of dx (or 2*dx), which causes high dW, high dW/dx, high F = -dW/dx. In contrast, when the flux in air flows primarily vertically from top of magnet to the top of the adjacent hole (for magnet within a hole), then moving the magnet a small distance vertically barely changes the length the flux travels in air, barely causes any dW/dx, and barely causes any force. The downward force in the latter case is very small.

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[electricpete]

I should mention that the description above used the "virtual work method" of imagining a small movement of the magnet upward and examining resulting change in energy... from which we estimate downward force.

The force exists whether the actual problem involves any upward movement or not. The imagined upward movement is just a tool to compute the downward force.

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