PURPOSE: To increase the life of a grindstone and enable chamfering of a machining hole with a stable quality by using a chamfering tool which can rotate a grindstone with flexibility and having a spherical end, as well as swing it centering around the spherical center of said grindstone.

CONSTITUTION: An air turbine 4 holding a chamfering tool 2 is held by the holding part 6 of the robot hand 5 of an industrial robot 3. The actions of the points A, B, C of the robot and the action of the air turbine 4 are set in a sequence control circuit, to control their rotation, swinging, and movement. The chamfering tool 2 is a cylindrical grindstone in which the end of a flexible grindstone such as a rubber grindstone, etc. is formed into a spherical face, and swings at a defined angle with the center of the sphere as the swinging center. And, by moving along the circumference on the edge of a machining hole, the grindstone follows while being pressed against the circumferential part by means of a grindstone chuck having a spring mechanism, to chamfer the part into a curved face. Also, the wear of the grindstone is uniform giving a long life to the grindstone, while enabling chamfering with a stable quality at a low cost, as well as automatization.