In a method of producing a toothed workpiece having a modified surface geometry by a diagonal generating method by means of a modified tool, a tool may be used whose surface geometry comprises a modification which can be described at least approximately in the generating pattern at least locally in a first direction of the tool by a linear and/or quadratic function, with the specific modification of the tool producing a corresponding modification on the surface of the workpiece by the diagonal generating method, with the modification of the workpiece produced by the specific modification of the tool having a profile modification and/or a modification caused by a change of the machine kinematics during the machining process of the workpiece superposed on it.

A toothed workpiece having a modified surface geometry may be produced by a diagonal machining method by means of a modified tool. The modification of the tool can be described at least approximately at least locally in the generating pattern in a first direction of the tool by a linear and/or quadratic function; the coefficients of this linear and/or quadratic function are formed in a second direction of the tool which extends perpendicular to the first direction. A pitch and/or crowning of the modification varies in dependence on the angle of rotation of the tool and/or on the tool width position, and a tooth thickness of the modified tool varies in a non-linear manner in dependence on the angle of rotation of the tool and/or on the tool width position.

A method of producing a tooth profile surface on a workpiece. The method comprises providing a gear cutting tool and rotating the gear cutting tool about an axis of rotation. The cutting tool and workpiece are engaged with one another and rolled together in accordance with a generating roll to generate a profile surface of a tooth. The generating roll comprises a first ratio-of roll and a second ratio-of-roll with the first and second ratios-of-roll being different from one another and with one of the first ratio-of-roll and the second ratio-of-roll resulting in a relief section being formed on the tooth profile surface.