Re: Torque calculation

["vecerkaj" <vecerkaj@xxxxxxxxx>]

> 
> 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.

Hi

I have just a note. Dave wrote, that torque will scale linearly with 
amplitude of stator current. It's correct, but only upto some value 
of stator current. After that linear torque-current characteristic 
starts to bend. (because of nonlinear material and armature 
interference)
Practicaly: The characteristic starts to bend from about 1-2 
standstill current for commercial permanent magnet motors rated to 
few Nm. For example the motor needs for torque=3 * standstill torque 
the curent=4 * standstill current. (a motor suplied by converter with 
vector control). (Of course exact value depends on construction of 
the motor).
I advice you to calculate at least few points of the characteristic 
(diferent current densities) and you will see, whether you should 
consider the bending of characteristic or not. 
Note 2:
About calculation of torque: if the stator winding is embedded in 
slots (but it is not your case), you can't use Lorentz calculation of 
torque. If you change the geometry to embedded variant, you should 
use torque calculation by stress tensor.

Jiri Vecerka