my experience has shown me differently, folks. it's not as black or white as hot and cold.
It's true that cold copper is less resistive than hot copper, of course, but a motor that's doing work, even at high efficiency will absolutely be warm. not hot to touch, but noticeably warm to touch (maybe 50C or about 30C above ambient on housing for BLDC, on shaft for brush PM)
why?
efficiency is powr OUT/pwr in. if you're motor isn't warm, then it is either not giving significant power out or is grossly oversized for the load. If it is oversized, you lose efficiency just moving the eccessive mass that is not needed.
look at a typical power curve (etek curve attached, I think). if this Etek is running at under 1HP, efficiency falls off fast . .. no work out. Stone cold as can be, but crummy efficiency. it's oversized for this application.
even a lowly 75% 1 hp motor does better than a mighty etek in this application.
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special note: bear in mind while 'feeling' the warmth of a brush motor, that all the heat is deep inside the motor, exiting through the shaft (and only through the housing via bearings) if it is not ventilated (or a hub motor). It may be a LOT hotter than what you feel at the surface.