Okay, very promising results from my new FEMM modeling technique and this afternoon's simulation run. Even better, I don't have to turbocharge the mesh density to make this method work so the simulation runs 2x faster or better.
I'll take the time to explain what I'm doing more thoroughly a little later, after I've tested it a little more thoroughly, collected more data, and rung out any bugs. For now, suffice it to say that I'm not bothering with any actual force calculations within FEMM, everything is based off the flux and BEMF. I expect this to be a little less accurate, but should be valid within appropriate bounds. Then again, given how much trouble I was having getting results which passed the sniff test before...
One thing I still need to do is a little bit of reading on what the usual conventions are for defining Kv, Kt, and such in terms of the waveforms. I may have been a little sloppy about this when reporting previous results, and it's difficult to make an apples-to-apples comparison against a commercial product unless I'm using the same definition, but I can at least be precise about what I'm calculating here and how it's specified.
Without further ado...
These are the simulated phase BEMF waveforms (phase-to-neutral). Note that the shape of the A and C waveforms are slightly distorted - this is due to the approximate nature of the model (only half of the stator). All of my other calculations rely on the phase B waveform which should be correct. Peak phase-to-neutral voltage is 7.004 mV/RPM. I had previously been using the inverse of this number as Kv, which would be 142 RPM/V (this version of the model is 18 turns/tooth). However, I think using the line-to-line number is more correct which is below.
In this initial simulation run, I ran the model for a handful of currents in the range 0 - 100 A. The above plot shows the flux linkage waveforms and the BEMF waveforms for phase B over this range of currents. Note that for a current of 100 A the flux linkage is nearly constant (cores heavily saturated), which results in a very small BEMF and as will be shown later, significantly reduced torque. For very small currents (5 A here), the flux waveform is shifted slightly but the shape is not significantly altered, which results in a BEMF waveform almost identical to the zero-current case. These results make sense.
This is the plot that I think is more useful for talking about Kv. This plot shows the line-to-line BEMF waveforms, accounting for the commutation changes every 60 degrees. The vertical red dashed lines indicate the commutation changes (I have aligned the model and the commutation so this happens at the correct instants). The peak line-line voltage is 11.44 mV/RPM, which equates to a Kv of 87 RPM/V. I believe this is the correct number for comparison. This also happens to be pretty close to 7.004*sqrt(3) = 12.13, which is what we'd expect from theory. Based on this definition, I obviously need to back the turns count way down to get back to the 150 Kv range. Note also that the voltages drop off significantly for the higher currents.
Here's the plot we've all been waiting for, torque calculations for various current levels. The instantaneous torque curves are shown, and on the left side the shorter lines show the average torque value across the active portions (note that I'm only exciting the B phase here, over 240 degrees of rotation) and the resulting Kt values. If we convert the above Kv into the appropriate units (11.44 mV/RPM * 60/2/pi) we get a theoretical Kt of 0.109 N-m/A, which is pretty close to the value we get from the lowest current. Kt drops off as the current rises, which we should expect as saturation kicks in. I didn't run enough different currents to get a really good picture, but the peak torque here is 1.75 N-m at 40 A. Now that this model seems to be working, it's pretty obvious that some design tweaks will be in order to get to the specs Miles wants.
Finally, curves of torque and Kt versus current. There will obviously be a peak torque, probably somewhere above 40 A, then it drops off again. Kt is roughly level at low currents and then drops off at higher currents. I'm a little bit torn about the phenomena that this model shows where the torque peaks, and then
decreases for really high currents. My intuition was expecting it to level off, but remain more or less flat into saturation. However, despite the fact that this is sort of a back-door approach to the calculations the theory should be valid. The power output of a motor should be a function of the product of current and BEMF (rate of change of flux), and as the second plot shows, the BEMF flattens out as the stator gets heavily saturated, so this does seem to imply that the results might be correct. In the end I don't think it really matters because 1) we should consider this a region of operation where the model becomes suspect, and 2) the motor would never be operated in this regime anyhow. Mostly for the second reason, I think the question of validity is mostly academic.
Tonight I'm going to leave my computer running the model again for a broader range of currents. Assuming that everything still looks good, it should then be time to update the model for Miles' latest design tweaks and then start twiddling parameters. I also need to go over the model and my calculations one more time. I'm confident that the basic technique is correct, but I need to make sure that I didn't slip a factor of 2 or something in there somewhere where it shouldn't be.
Where are all the losses coming from? Eddy currents in the copper?
