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.