a machining apparatus for making a plasticizing barrel includes a clamping device for securing the plasticizing barrel , with the clamping device constructed for rotation about a rotation axis and for off - center acceptance of the plasticizing barrel to thereby cause the plasticizing barrel to wobble about its symmetry axis , when the clamping device rotates . the clamping device interacts with a machining unit to provide the plasticizing barrel with an internal conical bore for receiving a screw . the machining unit has a turning tool which is movable linearly back - and - forth in a direction of an axis which extends in relation to the rotation axis at an incline of about half a cone angle of the conical bore , wherein the conical bore being produced has a center line which coincides with the rotation axis .