Method for reducing the eccentricity of the inner and outer surface of a hollow workpiece rotatably clamped in a machine tool

Method for reducing the eccentricity of the inner surface relative to the outer surface (7, 9) of a hollow work piece (1) rotatably clamped into a machine tool (2), for example of a hollow shaft, in which method multiple measurement data dependent on the contour of the inner surface (7) of the hollow work piece (1) are recorded in one clamped position, for example using ultrasound, a reference surface (13) for at least a part of the outer surface (9) having a reduced eccentricity relative to the inner surface (7) is calculated using the recorded measurement data, and, in a further step, the rotating work piece (1) is machined, at least partially in chip-removing manner, on its outer surface (9), in accordance with the reference surface (13), wherein at least one partial surface (14, 15) corresponding to the calculated reference surface (13) is produced on the outer surface (9) of the work piece (1), using chip-removing machining, and wherein the work piece (1) is newly clamped using at least the produced partial surface (14, 15), by way of clamping means (3, 4), for example a clamping chuck (3′) and/or steady rest (17), after which, in this new clamped position, at least the remaining outer surface (9) of the rotating work piece (1) is machined in chip-removing manner, at least in part, in order to thereby at least partially reduce the eccentricity of the inner surface relative to the outer surface (7, 9).