Method and apparatus for shaping the interior surfaces of bores

A honing tool for honing a workpiece having an interior bore, the tool being used in shaping the interior bore of the workpiece by means of an abrasive coating, and when rotated and reciprocated in an axial direction simultaneously, and when further energized by an ultrasonic resonant motion, the honing tool having an operative condition and an inoperative condition, and comprising:

• a shaft with a free length equal to a half wavelength of the ultrasonic motion or an integer multiple thereof;
• and
• means for introducing the ultrasonic motion onto said honing tool at one end of said honing tool, said one end being adapted to be received in a sound transmission body, wherein:
• said shaft having a free end and an abrasive coating, said abrasive coating having a contour, which, when viewed from the free end of said honing tool and in the operative condition of said honing tool when energized with the ultrasonic motion, includes a relative short conical section and adjacent thereto a relatively long cylindrical section,
• the contour of the honing tool in the inoperative condition being determined such that in the operative condition it is obtained by superposition of an amplitude of a radial oscillation component of the ultrasonic motion and the contour of the honing tool in the inoperative condition.