Method for machining a workpiece and adapter for use when machining a workpiece

A method for machining a workpiece with a machine tool, the method comprises the steps:

• receiving the workpiece by an adaptor which is arranged in a clamping mechanism of the machine tool, in particular a chuck;
• wherein the adaptor has a main body with a hole extending along an axial direction through the main body, and an inner support surface for receiving the elongated workpiece and an outer support surface which is an outer circumferential surface of the main body,
• wherein the main body is coupled to the clamping mechanism via a friction and/or form-fitting connection at the outer support surface and a shape of the cross-sections orthogonal to the axial direction of the outer support surface and the inner support surface are different;
• the method further including the step of fixing, by applying a friction connection, a position of the workpiece by applying a clamping force to the adaptor.