According to one implementation, a drill has at least one cutting edge. A projected shape of a passing area of a ridgeline of the at least one cutting edge when the at least one cutting edge is rotated around a tool axis becomes a line-symmetric and discontinuous line along a parabola, two parabolas, an ellipse or two ellipses. The projected shape is drawn on a projection plane parallel to the tool axis.

The invention describes an apparatus (1) for a cutting edge preparation of cutting tools (5), in particular of drills or milling tools or similar tools (5), in particular of hard-metal cutting tools, wherein during a relative movement the cutting tool (5) interacts in a machining fashion with a flexibly-bonded grinding body (2) that is provided with abrasive particles, the particles of the grinding body (2) influencing the edge geometry of the cutting tool (5),

wherein the grinding body (2) is adapted with its dimensions substantially to the dimensions of the respective cutting tool (5) that is to be prepared and is accommodated in an exchangeable holder (4) which is arranged in a region of a processing device, in particular of a tool grinding machine, and is held such that it is machinable by the cutting tool (5) for the cutting edge preparation. Furthermore, a corresponding method and a corresponding grinding body (2) are given.

The radial run-out tool (2), particularly a drill or a cutter, has a basic body (12) extending in an axial direction (4) and comprises at least two chip grooves (14), to which a guide chamfer (22) is connected in the rotational direction (24), with a ridge (15) being formed between them. A radial clearance is connected to the guide chamfer (22). In order to enable simple and economical production of such type of radial run-out tool (2), an unprocessed rod (30) is ground non-concentrically, in a first process step, such that a radius (R) of the unprocessed rod (30) varies, depending on the angle, between a maximum radius (R2) and a minimum radius (R1). In a second process step, the chip grooves (14) are grounded down such that the guide chamfers (22) are formed at the positions with the maximum radius (R2) and the radius (R) is subsequently reduced downstream of the respective guide chamfer (22) in order to form the radial clearance (28).