Re: [femm] Torque calculation

[David Meeker <dmeeker@xxxxxxxx>]

Garmendia Azurmendi Iñaki wrote:

> Hello everybody,
>
> I am a new user of FEMM (just about one week). I am also a Mechanical 
> Engineer, with experience in Finite Element Analysis in solid 
> mechanics and heat transfer, but not in Magnetics. So I have many 
> holes in my knowledge.
>
> However, I am involved in a project whose target is to construct a 
> microengine. My task is to calculate the torque that this micromotor 
> can produce. The designers have given me the geometry, material 
> properties and have explained to me the overall functioning of the 
> microengine.
>
> I have produced a model that I attach to this e-mail. We have the 
> rotor, in the middle, which is a magnet. After this, there is a small 
> gap of air, and enclosing this, three copper sets of coils. 
> Surrounding everything, a Pure iron cilinder.
>
> My doubts come on how to model the currents that go through the coils. 
> They are the same alternate current but they are dephased 120º. I have 
> used density currents of diferent signs, but I think that I am making 
> errors. In fact, if I use no current, the same Torque is calculated by 
> the program.

I think that these tiny motors typically have 3 discrete coils with the 
conductors arranged like A+,A-,B+,B-,C+,C- going around the 
circumference of the stator. The currents would be 120 degrees apart, 
but the force that is produced is highly dependent on orientation of the 
currents relative to the magnet. For the most torque, you want the 
coils to create a field that is perpendicular to field produced by the 
magnet. (Many of these tiny motors are actively controlled, so you can 
really run them like this.)

Anyhow, I've attached a model that does just that. For the instant 
where the magnet's magnetization is pointed upwards, there should be no 
current in the top coil and equal and opposite currents in the bottom 
coil. The currents in the bottom coils are set to 8.66025 MA/m^2, which 
are the instantaneous values that correspond to a 10 MA/m^2 amplitude. 
I just picked this current level off the top of my head--I don't know 
what is the max that you can run in your machines. The maximum is 
determined by thermal considerations. Due to favorable thermal scaling 
properties, these tiny motors run current densities that would seem 
astronomical in larger machines.

Anyhow, for that particular position, I get a torque of 0.0015 N*m per 
meter of length in the into-the-page direction. This should be the max. 
torque for a 10 MA/m^2 current amplitude. This torque will scale 
linearly with the stator current amplitude, so it is easy to extrapolate 
to other current levels. In this case, you can use either stress tensor 
or the integral of "Lorentz torque" over the volume of the coils. For 
this situation, the Lorentz torque one might be more accurate.

The above analysis neglects eddy currents in the iron. The eddy 
currents will reduce the torque some, but I'd guess that your iron is 
thin enough that this would be a relatively small effect. But it still 
might be interesting to get a handle on that. This could be done by 
putting AC currents in the windings and replacing the magnetization of 
the magnet with a thin "coil" region on the outside of the magnet. 
Those "coils" would then carry AC currents. The problem would then be 
analyzed at the speed at which the shaft is turning. The proper eddy 
currents would then be induced in the stator.

Dave.

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