Device for machining by turning

A device (1) for machining by turning of rotationally symmetrical surfaces of a workpiece (10), comprising a rotating drive for the workpiece chucked thereto, rotation of the workpiece (10) creates a cutting speed of a cutting operation, a tool (12) having a cutting edge and with a feed for the tool, a feed speed of which is substantially lower than the cutting speed and by which the cutting edge (16) comes into engagement with the workpiece (10) at an active location travelling along the cutting edge (16), the tool (12) with the cutting edge (16) being arranged pivotably about a tool rotation axis (A1), and the cutting edge (16) being oriented on the tool (12) such that the cutting edge (16) obliquely intersects an axial plane containing a tool rotation axis (A1), the tool (12) having a second cutting edge (17) which is arranged and oriented so as to be offset to the first cutting edge (16) by an amount of a rotary angle about the tool rotation axis (A1) and can be moved together with the first cutting edge (16) along a feed path (f), the first cutting edge (16), which is in front as seen in the feed direction of the tool (12), being a roughing cutting edge (17) and the second cutting edge being a smoothing cutting edge, an axial width (b) of the cutting edges (16, 17) is equal to a width (1) of a surface (18, 20, 22) machined by the cutting edges (16, 17), and the feed of the tool (12) is set up for executing a compensating movement of the tool (12), superposed on the pivoting movement of the tool (12) about the tool rotation axis (A1) and oriented radially to the tool rotation axis (A1) or to a workpiece rotation axis (A2), for turning free of turning marks.