The invention concerns a clamping element of a coupling device for releasably but axially and rotationally fixing tool components for dry machining (MMS technology) and for wet machining. The element provides a friction-type connection between the components to be coupled. A cooling tube is arranged at the center of the coupling device. The spindle is provided with an elongated hole run through which cooling tube passes. A variable contour between the base body and the clamping segment enables an increase in distribution of forces for the support of the clamping segments. The novel geometry of the clamping segments results in novel contours in the base body with smoother transitions, hence a better force distribution, thereby reducing material breakage and a more reliable and robust clamping. By virtue of their novel geometry, the clamping segments have an increased surface enabling larger clamping screws to be used.