Provided is an apparatus for machining a double enveloping worm shaft, and more particularly, to an apparatus for machining a double enveloping worm shaft, which cuts threads on a workpiece having a double enveloping body having a central portion formed therein in a concave arc-shaped outer circumferential surface and in which teeth of the machined double enveloping worm shaft are cut to a uniform depth while being always directed toward a central axis of a worm wheel, machining precision of the double enveloping worm shaft is increased, and thus post-machining is not required.

A tooth shape of the first tooth-shaped die part is formed have a constant tooth width from an upper end to a lower end and to correspond to a tooth width of a part in which a desired crowning has been produced. A tooth shape of the second tooth-shaped die part is formed to have a constant tooth width from an upper end to a lower end and to correspond to a tooth width of a central part, which is a part other than the part in which the desired crowning has been produced. A crowning forming method includes the steps of: forming a tooth shape on an outer circumference of the material by the tooth shape of the first tooth-shaped die part; and pressing the central part of the tooth shape of the material against the tooth shape of the inner circumference of the second tooth-shaped die part.

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 toothed workpiece having a modified surface geometry may be produced by a diagonal generating method by means of a modified tool whose surface geometry comprises a modification. The modification may be described by a linear and/or quadratic function, with the coefficients of this linear and/or quadratic function. Pitch and/or crowning of the modification may vary in dependence on the angle of rotation of the tool and/or on the tool width position. The specific modification of the tool produces a corresponding modification on the surface of the workpiece by the diagonal generating method, with a desired modification of the surface geometry of the workpiece being specified and a modification of the surface geometry of the tool suitable for producing this desired modification being determined in combination with a diagonal ratio of the diagonal generating method suitable for producing the desired modification.

A tooth shape of the first tooth-shaped die part is formed have a constant tooth width from an upper end to a lower end and to correspond to a tooth width of a part in which a desired crowning has been produced. A tooth shape of the second tooth-shaped die part is formed to have a constant tooth width from an upper end to a lower end and to correspond to a tooth width of a central part, which is a part other than the part in which the desired crowning has been produced. A crowning forming method includes the steps of: forming a tooth shape on an outer circumference of the material by the tooth shape of the first tooth-shaped die part; and pressing the central part of the tooth shape of the material against the tooth shape of the inner circumference of the second tooth-shaped die part.

A tool which can be used for gear manufacturing machining of a workpiece may be dressed on a dressing machine, and the dressing may take place with line contact between the dresser and the tool. A specific modification of the surface geometry of the tool is produced by the suitable selection of the position of the dresser with respect to the tool during dressing. The specific modification of the surface geometry of the workpiece is specifiable with regard to various parameters.

A tool which can be used for gear manufacturing machining of a workpiece may be dressed on a dressing machine, and the dressing may take place with line contact between the dresser and the tool. A specific modification of the surface geometry of the tool is produced by the suitable selection of the position of the dresser with respect to the tool during dressing. The specific modification of the surface geometry of the workpiece is specifiable with regard to various parameters.

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.