To execute optimum deburring in accordance with position dispersion of a work surface while automatically absorbing dispersion, by movement of a grinding wheel with shaft itself.

A tool has a shank 1 connected to a spindle of machine tool or the like, cylinder part 2 formed in a tip end of the shank 2, tilt support surface 3a line contact supported by an internal peripheral edge 2a of the cylinder part 2, and a collet 3 mounting a grinding wheel 4 with a shaft in a tip end part. So that the tilt support surface 3a of the collet 3 is brought into contact with the internal peripheral edge 2a of the cylinder part 2 by a prescribed pressure, a tensile spring 5 pulling a rear end part of the collet 3 in the spindle direction is provided in the cylinder part 2.