crazy loud minilathe VFD (??) whine - HELP!

Yep. Ceramic capacitors made with certain dielectrics are notorious for being piezoelectric. No only can they act as miniature (unwanted) speakers, they also can become microphones. Capacitors made with so-called "high K" dielectrics (like X7R and X5R) are worst and they also have really large voltage coefficients -- their capacitance can go down to 50% or less of their rated capacitance when they have a voltage across them!

However, that source of noise isn't consistent with your observation about it coming from the pulley end of the motor. But higher frequency noise can be difficult to localize by ear, unless you use something like what was shown in the video.
 
Ok, I’ll admit I did not read this entire thread but I did want to chime in. I work on Variable Frequency motor drives (VFDs) all the time at work. Usually pretty big ones but the principles are usually the same.

The high pitched whine or chirping is caused by the way the VFD controls the motor. The VFD rapidly switches the outputs on and off swinging the voltage from rail to rail of the DC bus (~170VDC on a 120V drive, 325V on a 240V drive). This occurs many times per second at the carrier frequency. This is almost always 4kHz. The pulse width is modulated to generate the desired waveform to the motor. This high change in voltage (dV/dt) generates electrical and mechanical stress in the system. On the control board, the actual switching elements (IGBTs) might make noise, but commonly it is the windings in the motor mechanically vibrating at the carrier frequency. Better quality motors whine less.

Most drives allow you to select higher carrier frequencies (8 and 12kHz are common) to reduce audible noise at the expense of increased motor and drive heating. This is done especially in elevators and HVAC since the noise would be bothersome in an office setting.

Your lathe sounds particularly bad, could be a cheap drive or something else. Hope you get it fixed.
 
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