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It's called a "self locking taper". There are several types and sizes of them. A old tool maker trick to make the fit lock up even tighter is to use a dusting of chalk.
A follow up on Jims idea of the drill pulling off. In soft metals where the drill trys to pull in it is a good idea to grind a 0 or slight negative rake at the tip. Then the drill press drives the bit into the material.
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