Motor: current vs forces

Posted on December 15, 2007


One of the things I wanted to get a better idea about is the relationship between electric current and the resulting magnetic field and mechanical forces.

This will help in determining an electrical operating point for the motor (current and voltage for a desired torque).

Using my old lua script and FEMM, I made another brute-force run of snapshots, this time with the rotor standing still at the most powerful position for torque (32,5mm offset) and setting the current from 0 to 100 Amps in 1 Amp steps. As before, I set 2 coils on, just like a regular step of an LRK motor. Click on the picture to get a better idea. It shows the flux at its maximum (100 A), so you can see more clearly the two coils that cause it.


The movie shows it well. In the beginning, there is only the magnetic flux caused by the magnets. Then there is an increase of flux caused by coils 1 and 3.

After cooking the values of the forces that come out of this, we get the following graph:


You know, I wasn’t expecting exactly this. I expected the relationship to be a bit less linear… at least for the tangential force & torque. Instead, I got a non-linear ratio for the radial force, and a pretty linear ratio for the tangential force and torque. Strange… but quite nice to use! 🙂 But lets not forget I’m still modelling this in “steady-state”, without consideration of switching frequencies or transients… The truth may be quite different!

One thing I’ve been noticing is that it feels very wasteful to only use 2 coils energized in each step. I see a lot of lost opportunities to use the whole set of stator teeth to pull the rotor… here’s some modifications I’m considering to do:

– wind all the stator teeth with coils, not just half of them. This will provide double the opportunities to use torque-creating force, although the current switching scheme (i.e. the number of phases) will probably have to change.

– experiment with a higher number of stator teeth (twice the current ones?); the higher granularity of switching that this provides should guarantee a nicer, fuller, more continuous torque under tough conditions (such as vehicle start).

Having more coils in the stator (and therefore reducing the coil current for the same total torque) has the beneficial effect of:

– distributing the local forces (which permits a lighter structure);

– reducing the local losses at each tooth (due to saturation, hysteresis, and induced currents) and therefore lowering the thermal losses and even increasing thermal stability (easier cooling).

These enhancement studies will depend on the difficulty of getting this show on the road in the first place (so to speak). 😉

As to the motor operating point, I think I will have to find a way to determine the losses first. That way I can chose the point based on motor efficiency, and aim for the best compromise.

Posted in: Motorfemmulator