An anti-vibration device for the machining of a shaft includes a first fixed ring intended to be kept inside a shaft by a shoulder, the anti-vibration device including: at least one first external groove and at least one first external seal for forming at least one contact with the internal surface of the shaft; at least one first internal circumferential groove and at least one first internal seal for forming at least one contact with the external surface of the bar; an internal circumferential cavity that is able to cause the circulation of a fluid arriving through a first duct and leaving through a second duct, the first duct and second duct passing through the radial thickness of the anti-vibration device, the internal circumferential cavity making it possible to realize a vibration-damping function when a fluid passes through it.

A boring tool includes a clamping shaft and a boring body. Between the end face of the boring body and the clamping shaft, at least one main blade extends along a longitudinal axis of the boring body and includes a blade web with a rake face facing a groove-shaped chip space, and a free surface on the outer circumferential side, these converging at a cutting edge which runs along the boring body longitudinal axis and which removes material on an inner wall of a pre-bored workpiece core bore hole as a result of said boring tool being rotated. The main blade extending along the longitudinal axis of the boring body transitions at the end face, of the boring body into a groove blade that is aligned transversely to the longitudinal axis of the boring body. This groove blade allows the boring tool to be displaced, prior to removing the material by rotation, into the core bore hole in an axial lifting motion such that a groove is formed which extends along the longitudinal axis of the core bore hole, the main blade of the boring tool engaging in this groove.