Abstract: A cylindrical abrading tool, such as a tire rasp, has a hollow body formed from a stack of blades -- or a single helicoidally wound blade -- with toothed outer edges sandwiched between a pair of apertured end disks. The blade tiers and disks are interconnected by axially extending mounting bolts, with maintenance of generally radial air-circulation passages between adjacent tiers by means of interposed spacers which may comprise lugs bent out of the blade planes or arcuate inserts with channeled transverse faces.