Are you sure about that? My electrician buddy who is also a hack knife maker told me that they are not in the sense that you cannot use a single phase/leg (?) AC motor with a VFD.
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Both are right.
Your buddy is right that you can't use a single phase AC motor and dc vfd controller.
Bruno's right that a fixed or variable speed AC motor is basically the same. Usually, only three phase motors are variable, not single phase units,, and you vary the phase or hertz to change speed on AC motors, not the voltage like in a dc setup.
Hope that helps.
Single phase motors can be used with a single phase VFD. It's not ideal and it is not really common.
3 phase motors can be used with or without VFD. Now, most VFDs hae some intelligence built in, like current protection etc. You can compare it with an amplifier and a sound speaker. it makes no sense to put a 10 watt speaker on a 100 watt amp. In that sense, your friend is right. However, from the motor's perspective, it's all the same. A 3 phase motor is a 3 phase motor no matter how you drive it.