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# Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

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## Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

(OP)
Hello~!

I am interested in finding the force and torque exerted onto a PM by another PM within the vicinity.

So I am just wondering if I could use the same force/torque equations (e.g. for the force as shown below-sorry for the messy typeset) between two axially magentised PMs for the diametrically magnetized ones as well:

I see that most cases are calculated for axially magnetized PMs. I am working with two diametrically magnetized NdFeB magnets and got pretty confused as to how I should compute the dynamics (force and torque of one PM (primary) when another is closely present).. as well as how far should the NdFeB PMs be apart so I could ignore the effect of the other PM onto the primary PM. Also, I am not sure if the generally available equations for the axially magnetized PMs can be used in my case.

I am thinking that the magnetization, M through the diametrically and axially magnetized PMs is different in direction, thus the force and torque on either one of the two PMs might be different with different PM dimensions and positions.

Looking forward to hearing from anyone with ideas and advice =) Thank you very much!

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

No, you cannot use the same equation. I doubt there even exist such a model for a diametrically orientated magnet. A math model seems to be too complex. Diametrical is mainly for sensor applications, not for force/torque, as far as I concern. You may have to use trial and error method to figure out your forces.

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

normally the "contacting" area or the gaps of a motor are parallel to each other, more like axially oriented.
The "contacting" for diametrical is a point.

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

Oh, I was thinking the OP was contrasting between an auto A/C clutch, which I thought was axial, as opposed to a PM motor where the magnets are on a diameter inside or outside of the windings.

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### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

(OP)
Thanks alot MagBen and IRstuff for your comments.

I realised that I should include an sketch of the setup I am working on for better illustration =)

So these are the two diametrically magnetized cylindrical NdFeB PMs placed beside one another with a distance, d. Both are rotated by independent external sources (I have solenoids to independently drive the PMs). This will affect each PM in terms of the torque and force.

If the expressions for forces and torque in the case of axially magnetized PMs are not compatible in this case, is there any idea how I could find out how it differs in the diametric model? I do not have a software for this, thus I would need to model it mathematically.. (i have spent weeks trying to find a way to do it but I ran out of idea)

I kind of visualised it similar to a bar magnet but it is usually rectangular and not cylindrical. So there's this geometric aspect that I have to think about.
Besides, I could only find force analysis on bar magnets (attract/repel) but not torque as bar magnet is rarely expected to rotate the way I need my cylindrical PMs to rotate axially. Pretty perplexing..

Any ideas and comments are appreciated =) thanks again~

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

You could discretize the round magnets by dividing them into a number of flat bars having their lengths varying in order to suit the round boundary. Then you can sum up all the contributions of each bar with all the opposing ones in a spreadsheet. To account foe the bar magnets not being centered each other you can use the formula for magnetic dipoles.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

(OP)
Thanks, IRstuff and Prex =)

IRstuff, in that case, I probably should start exploring some FEA tools. FEA would need some sort of mathematic expressions (e.g. in this case, the magnetic field density computation which contributes to the force and torque) to start with too, yes?

prex, do you mean something like numerical analysis?

One of the complications I see is that these PMs will have to be positioned randomly and the arrangement will be at a distance in terms of x,y and z axes from another. I should be able to take that into account in the vector form of the magnetic field, B_x, B_y, and B_z. But then again, the force and torque onto one when both are rotation independently is a tricky problem =(

Thanks again! =)

### RE: Is the force btw 2 diametrically magnetized magnets & that of 2 axially magnetized ones the same

Yes, definitely, it's numerical analysis. However the formula for two dipoles gives the 3D force between them in closed form, so that's not so tricky. To get a reasonable accuracy you don't need to divide the magnets into thousands of dipoles (though you can).

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

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