Morse taper

A machine taper is a system for securing cutting tools or toolholders in the spindle of a machine tool or power tool. A male member of conical form (that is, with a ) fits into the female socket, which has a matching taper of equal angle.

Almost all machine tool spindles, and many power tool spindles, have a taper as their primary method of attachment for tools. Even on many drill presses, handheld drills, and lathes, which have chucks (such as a drill chuck or collet chuck), the chuck is attached by a taper. On drills, drill presses, and milling machines, the male member is the tool shank or toolholder shank, and the female socket is integral with the spindle. On lathes, the male may belong to the tool or to the spindle; spindle noses may have male tapers, female tapers, or both.

Machine tool operators must be able to install or remove tool bits quickly and easily. A lathe, for example, has a rotating spindle in its headstock, to which one may want to mount a spur drive or work in a collet. Another example is a drill press, to which an operator may want to mount a bit directly, or using a drill chuck.

Virtually all milling machines, from the oldest manual machines up to the most modern CNC machines, utilize tooling that is piloted on a tapered surface.

The machine taper is a simple, low-cost, highly repeatable, and versatile tool mounting system. It provides indexability, as tools can be quickly changed but are precisely located both concentrically and axially by the taper. It also allows high power transmission across the interface, which is needed for milling.

...
Wikipedia