Abstract: According to the present method and apparatus work pieces such as railroad wheels are power clamped on a cone shaped inwardly facing side. In a first clamping step clamping areas are impressed into the side or surface of the work piece said clamping areas having a suitable inclination. In a second clamping step the actual power clamping is performed at these clamping areas. For this purpose a plurality of radially moving clamping jaws are arranged to carry at least one clamping tooth. Each clamping tooth in turn is adjustable in its position in an axial direction along its respective radially moveable clamping jaw.