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Personally I don't like the fact that Taig continue to supply 60Hz motors to 50Hz countries. In the UK I haven't actually shipped a Taig spindle with a mill for some years. We use the Kress 240V spindle and I have customers running that 6 or 7 days a week only requiring a regular change of brushes.
The motor WILL run hot as it's not pushing enough cool air through, and an additional fan is a good move to tubbocharge the air moving through it, but the spindle itself should not get too hot, and it sounds as if it has been preloaded a little too tight. I warm the cutters on the Kress up taking bigger cuts than you indicate, but normally only when they are getting a bit blunt, so I would be looking to check how freely the bearings in the spindle are turning without the belt on ...
Lester Caine - G8HFL
http://medw.co.uk - Home of electronics for the Model Engineer