Tool for machining

A tool for machining a workpiece, comprising:

• a cutting insert having a first side, a second side opposite the first side, and a circumferential surface extending between the first side and the second side, wherein the cutting insert comprises an opening penetrating through the first side and the second side and extending along a longitudinal axis, wherein a first cutting insert bearing section and a second cutting insert bearing section extending transversely to the first cutting insert bearing section are arranged on the circumferential surface, and a third cutting insert bearing section is arranged on the second side, wherein the cutting insert has an active cutting edge arranged on a upper side, said upper side being a part of the circumferential surface and facing away from the first cutting insert bearing section and the second cutting insert bearing section;
• a tool holder having a cutting insert receptacle comprising a recess and being configured to receive the cutting insert in such a manner that a first part of the cutting insert is arranged in the recess, and a second part of the cutting insert, on which the active cutting edge is arranged, is located outside the cutting insert receptacle and protrudes at least partially from the tool holder, wherein the cutting insert receptacle is defined by a first wall, a second wall, a third wall extending transversely to the first wall and the second wall, and a recess base extending transversely to the first wall, the second wall, and the third wall, wherein a first holder bearing section is arranged on the first wall, which first holder bearing section, in an assembled state of the cutting insert, bears against the first cutting insert bearing section, wherein a second holder bearing section is arranged on the second wall, which second holder bearing section, in the assembled state of the cutting insert, bears against the second cutting insert bearing section, wherein a third holder bearing section is arranged at the recess base, which third holder bearing section, in the assembled state of the cutting insert, bears against the third cutting insert bearing section, and wherein the tool holder further comprises an internal coolant channel that opens into a coolant outlet opening which is oriented towards the upper side of the cutting insert in the assembled state of the cutting insert;
• and
• a clamping element that is configured to be inserted, starting from the first side of the cutting insert, into the opening to fasten the cutting insert in a detachable manner to the tool holder;
• wherein in the assembled state of the cutting insert the third wall of the cutting insert receptacle faces the upper side of the cutting insert and a gap is provided between the third wall of the cutting insert receptacle and the upper side of the cutting insert, wherein a height of the gap increases along a gap depth direction that is parallel to the longitudinal axis of the opening, starting from the second side of the cutting insert towards the first side of the cutting insert, wherein the height of the gap is defined as a distance of the upper side of the cutting insert from the third wall of the cutting insert receptacle.