Ring-shaped tool for processing a work piece

Ring-shaped tool for processing a work piece, comprising:

• a fastening area for fastening onto a rotatable drive shaft, wherein the fastening area is centered with relation to the ring-shape of the tool;
• and
• a plurality of sprockets arranged around the circumference of the tool, wherein the plurality of sprockets are arranged on the head end of the tool and have an arc-shape seen in axial direction of the ring, the arc-shape having a summit, wherein the sprockets are formed in a mirror-symmetric manner relative to the ring surface of the tool which is cutting through the summit, wherein the arc-shape is given by two circles which tangentially merge into each other in a contour-less way, the circles having a first radius of gyration and a second radius of gyration, wherein the center of circle for the first radius of gyration is located below the summit and wherein the center of circle for the second radius of gyration is located below the center of the circle having the first radius of gyration seen in radial direction, wherein the first radius of gyration is smaller than the second radius of gyration, and wherein the ratio between the second and the first radius of gyration is between 14 and 17.