A Morse taper drill does grip well in the tailstock or the drill press for that matter, however it can and is likely to slip if overloaded, particularly with larger size drills. The result is not a pretty site. Nasty galling and scoring marks on the drill and the tailstock taper.
Blunt or badly ground drills are a common cause of overloading. Excessive feed pressure is another.
Also watch out for second hand drills with scored shanks, they don't grip well and will damage your machine sockets. Best to avoid them, if you must use one clean the shank with a file and check the fit with bluing in a good known taper socket. go easy on the feed.
I don't oil Morse tapers, before I use one I wipe it out with a cloth or a finger for the larger sizes, the same applies to the drill I wipe the taper shank off with my hand. The hand is very sensitive to any grit of fine chips that might interfere with the grip. On larger sizes I give them a solid wrap when inserting them. I guess the hand transfers a small amount of oil that may be on the skin, that is enough.
Regards
John
Edited By John McNamara on 15/11/2015 15:05:07