Abstract: An adaptor is inserted between a cutting tool and a clamping section of a tool machine. The adaptor comprises a tool clamping part holding the tool, and an adaptor clamping part which is held by the machine. Between the two parts there is a bearing which controls the relative movement between the two parts in such a manner that this movements does not influence machined geometry, dimension or surface of the work piece machined by the tool, to any significant degree, and an elastic damping member which ensures that a possible relative movement between two parts is damped down to a desired degree. Possible vibrations in the tool are thereby kept down on a level where they do not contribute to amplify the normal sound pressure from the machining operation, and an efficient noise suppression is achieved.