In theory a well designed inductor should also improve the motor efficiency.
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If only someone had a dyno setup.......
Sure...with an emphasis on "well-designed", though.
I have measured the ripple current through one of the WarP9s on our dyno and the results where somewhat surprising... there is some saturation effects as current increases, but even at 400A the AC ripple component was only 14%, or 56App. The ideal AC ripple component is usually set to 40% in a switching power supply, which would be 160App in this case! So this implies a relatively high inductance in the WarP9 - even at 400A - of over 100uH.
If the Curtis is struggling with this amount of inductance then you will need a pretty big coil of wire to make a meaningful difference - something on the order of at least 25% of the motor's inductance, but preferably more like 50% to 100%. Plugging some random numbers into my handy single-layer inductance calculator spreadsheet, it seems that a close-wound coil of 20 turns and 200mm diameter of 2/0 wire (OD: 13mm) will have an inductance of ~43uH but require 13.6M of cable!?! That's almost 50' of wire which at a current price of around $3 per foot is a pricey bit of kit, and that's not even considering the resistive losses which will assuredly greatly outweigh the iron losses in the motor housing!
Anyway, while you are technically correct that there are some iron losses in the motor housing, and that adding external inductance will reduce those particular losses, the unfortunate reality is that you will be adding far more in losses from cable resistance.
Think it could help a noisy motor?
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I have a few air core inductors and one iron core one that was made with an old transformer.
Well, Pete, if the noise is the motor "singing" at the controller's switching frequency then extra inductance might quiet it down, but most motors don't seem to act as particular good "speakers" until the frequency drops below 6kHz or so. Unfortunately, most motors do sing pretty loudly at 1.5kHz, which is the fallback frequency for Curtis.
As for making your own inductor with old transformer cores, keep in mind that the ripple frequency is the switching frequency so a 60Hz transformer isn't going to cope very well here (it's going to have extremely high losses - much higher than the motor will).