Optimal pole arrangement of air gapped pull assy?

[jstewart]

Hello all,

I'm working on a new design (for my company, that is) of a small wheeled carriage that rolls along the bottom of a 1018 steel bar. I would like to use magnets to hold the carriage to the bar.

The bar is 1" wide, .1875" thick, and several feet long.

I need to maintain an air gap of approximately .200" between the bar and the face of the magnets.

I'm thinking of using N42 Nd-Fe-B blocks, but am wondering about the best way to arrange them for maximum pull. After some perusing of Moskowitz, I thought of using a linear array of magnets with alternating N, S, N, S... faces exposed on a steel back plate. That seems to give it some reach. I can make the array as long as I need it to achieve the desired force. (of course, I'd like to minimize it...)

The charts in the book seem to show that better reach can be achieved with fewer poles on a surface. (His example was 2 poles vs. 3 poles, although I'm not limited to 3 poles.) Also, the diagrams show a gap between magnets in an assembly.

So, not seeing any more detail in Moskowitz (or perhaps being too ignorant), I'm left with the following questions:

1. Is there an optimum pole width for the array in my application?

2. Does the magnet thickness play an important role?

3. And finally, is the space between magnets important?

I apologize for the lengthy post, but I didn't want to leave out any important details.

 

[prex]

You didn't tell us what kind of force the magnets should develop. Also, need that force be always present?
I hope you are aware that some braking due to eddy currents (additive to friction) will be present. This will depend on the speed of the carriage on the rail.
The short answers to your questions are:
1)No optimum, use square blocks. The holding force will be higher with larger blocks.
2)Yes. You can simplify your reasoning by assuming that more magnet volume you use, more force you get.
3)Put the magnets in contact on their sides, except that you'll need some plastic or wooden spacer to avoid the magnets slamming together: a small spacing may be beneficial, but not that much.

prex

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[MJR2]

We assume you want to hang the carraige from the steel strip magnetically.

An airgap of 0.20 inches would at first seem to be rather extreme for a holding application.

How about magnetic casters? That way you could maintain contact.

Mike

 

[jstewart]

Thanks for your quick replies!

Here are some more particulars:
A. You didn't tell us what kind of force the magnets should develop.
That's because I'm not 100% sure of the exact value. I'm hoping to optimize the force generated per unit length of array. I suppose for estimation purposes, 35-40 pounds wouldn't be too far out.

B. Need that force be always present?
Yes, this is an "always on" application.

C. I hope you are aware that some braking due to eddy currents (additive to friction) will be present.
Yes, and this is a desired feature. In fact, a large portion of the "air gap" is actually aluminum to increase the eddy current braking effect. I didn't want to cloud the issue of holding, however, which is my biggest concern. The eddy braking feature is one that I've tested and used before. The holding portion is new.

D. An airgap of 0.20 inches would at first seem to be rather extreme for a holding application.
I agree, but the holding works hand-in-hand with the eddy-current braking, which requires the "air gap." I was not aware of magnetic casters, although they wouldn't work so well for this application because of the desire for eddy braking. (that, and I'd like to use urethane wheels to keep the rolling noise to a minimum.)

prex, you made some statements that I'm still curious about. (not to sound ungrateful for your answers, I'm just confused. Maybe I need coffee?)
No optimum, use square blocks. The holding force will be higher with larger blocks.
Are you saying that there isn't a difference between 3 1x1 blocks and 6 1x0.5 blocks? (of equivalent thickness, say .125") Certainly the total magnet pole area is the same for each (3 in^2) but the fields generated appear different (NNSSNN vs NSNSNS) It didn't seem to me that they would perform the same, especially in view of the charts shown in Moskowitz.

2)Yes. You can simplify your reasoning by assuming that more magnet volume you use, more force you get.
Okay, that's fair. But is it a better use of material to increase the pole area instead of the magnet thickness? (longer/thinner vs. shorter/thicker) Or does the answer change depending on the particular dimensions?

3)Put the magnets in contact on their sides, except that you'll need some plastic or wooden spacer to avoid the magnets slamming together: a small spacing may be beneficial, but not that much.
Since my last post, I've assembled a first prototype using 1" x 0.5" x .125" magnets (N42) that didn't need any spacers (the magnets are quite stable against their steel back plate (.25" thick). The magnets pull each other together against the back plate, but that got me to wondering whether they were partially short-circuiting some flux? I did play a bit with some small spacers (~.060") but wasn't able to discern any change in the holding force. I may need a better spring scale. Or perhaps some larger spacers.

Again, thanks to both of you for your replies!

p.s. Happy New Year!

 

[prex]

A. I suppose the exact value of the force should equal the weight of the carriage times a safety factor? If 40 pounds is the total force sought, this is not a challenging value, though of course it all depends on the amount of magnets you are prepared to install (and of course don't forget to count the magnets in the weight of the carriage).
C. So you want an eddy current braking. I hope this time that you aware that the holding force will be zeroed by the eddy current effect above a certain speed that depends on the amount of conductor in the gap. Of course this could be disastrous for your application, unless you are sure that the speed is always sufficiently low.
D. An airgap of 0.2" appears not too big to me with the magnets dimensions you quoted.
1. As you certainly already know, the holding force is substantially proportional to the area of the pole faces times the induction squared. So there will be not much difference between the two configurations. I expect that with your 6 blocks, the best configuration will be with the orientation NSSNNS (this is because the end magnets should be half size to use the iron section more effectively). However to join two coorientated magnets is rather difficult, you need something to hold them in place: so go on with your configuration, it doesn't matter too much whether you use square or 1:2 blocks.
2. Of course we could analyze the formulae to discover where is the optimum ratio etc., but believe me, as we are bound to commercially available sizes, it is a second order optimization and you can forget about it.
3. Your magnets are not that big, so you can handle them with your hands: just forget about spacing and put them in contact, especially if you have space constraints on the row length. It's again a second order effect to look for an optimum spacing (that will highly depend BTW on the permeability of the back iron and of the rail bar).



prex

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[sreid]

When the air gap length equals the magnet length (in your case 0.2 inch air gap, 2x0.125=0.250 inch), the magnets are operating at their maximum MgOe. This is the most cost effective arrangement. Magnets are often made longer in lenght to help avoid demagnetization from other magnetic fields(motors). This is not your case. Increasing the length of the magnets will increase the magnetic flux across the air gap (an thus the atractive force) but with ever decreasing returns (at max MgOe, the field strength is 1/2 Br. No matter how long you make the magnet, the field strength will never exceed Br (for equal areas)). From a cost standpoint it is better to increase the magnet area (where the force is proportional to area).

The NSNS magnet arrangement is usually chosen as it minimies the amount of "Back Iron" required. If a NNSS arrangement is chosen, the back iron would need to be twice as thick to avoid magnetic saturation in the iron.

 

[Clyde38]

jstewart:
Have you considered concentrated poles?
To All:
What are your thoughts?

 

[jstewart]

Who knew this discussion would be so lively?

A. The 40 lbs assumes a safety factor and includes the weight of magnets in the carriage. I'll also have a mechanical backup (for accidental overload, etc).

C. I know that the eddy current effect will tend to counter the holding force. I don't know the extent. I believe that the speed is relatively low (peak speed <40 ips).

E. When the air gap length equals the magnet length (in your case 0.2 inch air gap, 2x0.125=0.250 inch), the magnets are operating at their maximum MgOe.
That's a very helpful rule to remember. But should the air gap be 2x0.200 also (round trip through the steel bar)? Then that might indicate the use of a .250" thick magnet block instead of the .125"?

F. Have you considered concentrated poles?
I hadn't looked too closely at them because the book I was looking at showed reduced "reach" with the concentrating pole arrangement, and I was concerned about the large air gap. Also, doesn't the back iron in your illustration reduce the available flux for the working gap?

-- Jon

 

[sreid]

jstewart, you are correct, there are two air gaps so each magnet should be 0.2 inches thick minimum.

 

[prex]

OK, at 1 m/s you'll be far from the holding force being equal to the repulsive one. This should occur at about 10 m/s for a 3 mm thick Al 99,5 conductor in the gap.
Concerning the gap, there's not really an optimum: the minimum compatible with stiffness, tolerances, etc. of the system will simply give the maximum attraction. An optimization can be done by taking into account the braking effect required. At so low speeds you should use copper instead of the aluminum: with about 2/3 the thickness you would get the same braking, but you could recover the reduced thickness by reducing the gap, with an increased braking and attraction.
With your 6 magnets and gap, you should be already well above your 40 lbs (200 N) goal, but as you made a test assembly, you should already know about that.

prex

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: Air bearing pads

 

[MJR2]

Clyde38,

This circuit will have considerable shorting/shunting thru the steel backbar.

Mike

 

[jstewart]

Looks like some more good info this morning!

OK, at 1 m/s you'll be far from the holding force being equal to the repulsive one. This should occur at about 10 m/s for a 3 mm thick Al 99,5 conductor in the gap...At so low speeds you should use copper instead of the aluminum...

Thanks for the info on the speed effect. I agree with you on the performance advantage of copper, but I'll probably end up using aluminum because of the cost delta. If I need more braking, increasing the magnet count is probably more cost-effective, copper being as expensive as it is these days. (plus I can extrude the aluminum and have it perform other functions in the machine.)

The thickness of the conductor is another matter, though. IIRC, at this low speed the eddy drag is proportional to the square of B, versus linear with the conductor thickness. So it might be best to reduce the thickness to increase the drag. (and reduce material usage) Does this agree with your understanding?

And an update from my test model: Spacing the magnets apart has a very significant effect on the holding force. I haven't performed a rigorous study, but adding .180" spacers between 1.0" x 0.5" x .25" magnets increased the holding force by about 60% over the same magnets butted together.

My working theory is that when the magnets are close together, a lot of the flux bypasses the steel bar, crossing the (short) airgap to its neighbor instead of the (long) airgap to the bar.

Looks like I'll be doing some more experiments!

 

[sreid]

1) For a fixed magnetic field, the lower the resistance the eddy current metal has, the more the breaking force. Tis is because EMF = B x Velocity and I = EMF/R.

2) Yes if the magnets are butted together, part of the field "short circuits." With a 0.2 inch gap, a lot of the field would short circuit since the field will follow the path of least reluctance.

 

[MJR2]

I made a couple of quick circuits with N42.

First a C-frame with a steel pole/magnet/steel pole sandwich. The poles cross section were 0.25x1.0 and the magnet 0.5x0.75 for a total width of 1 inch. The force I get is about 9.5 lbs per inch of length. The poles just start to see some saturation.

Second is a circuit with magnets on a steel backbar. The cross section of each of the (2) magnets is 0.5x1.0x1.0. For the steel it is 0.25x1.0x2.5. Overall height is 0.75 inches. The gap between the magnets is 0.5 inches. As has been mentioned the gap between the magnets should be greater than the gap to the runner. Force with this design is about 29 lbs. The backbar should be thicker to reduce saturation.

A SS cover of 0.030 is included to help protect and keep the magnets in place.

The second design is a little better than 10 percent more efficient with the magnet material. The magnets are closer to the runner.

Consider a good safety factor. (2-4x) The actual pull force is likely to be 90% of these values in production.

Mike

 

[prex]

Well, if your way of reasoning was fully correct, the optimum would be with zero conductor thickness! (with of course still some braking effect, as the iron is also a conductor). In fact a maximum braking force is obtained at some finite thickness of the conductor, but this optimum also depends on the behavior of the carriage, its mass, etc.
Concerning the spacing, I'm not surprised of your results, but think of it this other way: with 6 magnets spaced .18" the overall length is about the same as with 4 square magnets in contact, and in the latter case the holding force would be probably higher. Of course more magnet material will cost more, but the cost optimization is up to you, as many more construction details will be involved in it.
And believe me, unless you plan to build hundreds of those assemblies, you don't need a sophisticated optimization analysis.

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

 

[jstewart]

Thanks, MJR2 for the analysis! It sounds like the magnet-backplate approach is the way to go. I agree that the safety factor is important, even if I do have mechanical backups. It's looking to me like this is quite feasible, even with conservative factors of safety.

Well, if your way of reasoning was fully correct, the optimum would be with zero conductor thickness!
True enough. I know that I'm making quite a few (over?)simplifying assumptions. But locally, and at the stated conditions, is it valid to say that a modest reduction in conductor thickness (say from .175" to .125") (and increase in flux due to reduced air gap) will result in a higher drag force? Or is it too much of a change to predict without analysis?

this optimum also depends on the behavior of the carriage, its mass, etc.
Hopefully I won't sound too ignorant, but how does the mass of the carriage influence the optimum thickness for the conductor? Do you refer to the thickness of the back iron?

And believe me, unless you plan to build hundreds of those assemblies, you don't need a sophisticated optimization analysis.
Actually, if the design works well, my employer will likely build thousands of them. I agree that I probably don't need a sophisticated analysis, but I can't ignore it either.

And thank you all once again for all your time and expertise in helping me with this problem!

-- Jon

 

[sreid]

You should have seen some eddy current braking from the stationary iron alone. Watch out for using too much eddy current braking; when in motion you have to supply the power to over come the braking force.

 

[prex]

I played a bit with my formulae and it turns out that, with your figures and some reasonable assumptions on other data, the optimum conductor thickness is just in between .175" and .125". However the braking force goes fast down past the optimum, whilst is relatively stable before it: so .175" seems a reasonable assumption (and the change from .175" to .125" is quite negligible in practice).
The optimum conductor thickness as intended above is the thickness that maximizes the drag force coefficient K in the equation D=Kv, v being the speed of the carriage, with v<<10 m/s.
My point is that this is not necessarily the correct optimum for your application. If your goal was to minimize the travel to stop, then the mass of the carriage and the friction coefficient would play a role in it, as the eddy current drag will never stop the carriage, it's the friction that does so. Also varying inlet speeds to the braking zone would play a role. And you could have a limit on the drag when pulling back the carriage, as, as correctly sreid reminds us, the drag force will be present all the time.
I think that you got many useful suggestions and informations from this thread: it would be difficult to go more in depth while staying in this forum. If you really need an in depth optimization including also the manufacturing options, you could ask a specialist in linear eddy current brakes.

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