While it is unlikely that an occasionally-used motor will burn out if connected to the wrong frequency, one which runs continuously will not last long. I think this applies to induction motors only. Universal motors are safe.
Here is a better
explanation than I could come up with.
I can recall connecting 50Hz induction motors in industrial situations here in the US. They always had transformers due to the difference in design voltage, but I wonder if the voltage was tweaked to compensate for the difference in current as well? That was so long ago I don't remember.
Has anybody ever monitored the output of a VFD with a voltmeter? Clearly an induction motor can be run at a variety of frequencies without harm, since VFDs are widely used.
