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A numerical-control (NC) method and system for machining a desired three-dimensional contour in a workpiece with an axial tool, e.g. a rotary milling cutter or electroerosion electrode, formed at its axial end with an active machining surface which is spherical about a center intersected by the axis

A numerical-control (NC) method and system for machining a desired three-dimensional contour in a workpiece with an axial tool, e.g. a rotary milling cutter or electroerosion electrode, formed at its axial end with an active machining surface which is spherical about a center intersected by the axis of the tool. According to the invention, numerical coordinate values for the positions of this center of the tool to be displaced relative to the workpiece need not to be preprogrammed and stored on a record medium. Rather, the numerical coordinate values for a series of prescribed points on the desired contour, together with the angular values defining an imaginary line normal to the contour at each of these points are simply programmed and stored on such an NC tape or like medium, and a numerical datum for a constant value substantially equal to the radius of the sphere is keyed in into a computing device arranged between a tape reader and drive units for computing from the data reproduced from the NC tape and the keyed-in datum, for each of the prescribed points, the three-dimensional coordinate values of the position of the center of the sphere. The computing device is associated with a drive control unit for producing from the computed numerical coordinate values, command signals to operate the drive units so that the workpiece and the tool are relatively displaced to allow the desired contour to be progressively developed in the workpiece.

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1. A numerically controlled method of machining a desired three-dimensional contour in a workpiece, comprising the steps of: (a) preparing an axial tool formed at its axial end with an effective machining surface which is substantially spherical about a center intersected by a axis of said tool;

1. A numerically controlled method of machining a desired three-dimensional contour in a workpiece, comprising the steps of: (a) preparing an axial tool formed at its axial end with an effective machining surface which is substantially spherical about a center intersected by a axis of said tool; (b) prescribing a series of points on said desired contour to be machined in said workpiece; (c) identifying each of said prescribed points in terms of its coordinate values in a predetermined three-dimensional coordinate system and of angular values defining the orientation of a normal thereat to said desired contour; (d) storing on a record medium data for said identified coordinate values and angluar values sequentially for said successive prescribed points; (e) supporting said tool and said workpiece so that they can be translationally displaced relative to each other by drive means along the three axes of said predetermined three-dimensional coordinate system; (f) electrically connecting said drive means with data processing means so that the former can be controlledly operated by the latter; (g) inputting into said data processing means a numerical datum for a constant value substantially equal to the radius of a sphere at least a portion of which constitutes said effective machining surface; (h) reproducing from said stored record medium, data for said three-dimensional coordinate values and angular values of each of said successive prescribed points on the desired contour by means of read-out means operatively connected with said data processing means; (i) in said data processing means, computing from said reproduced data and said inputted datum, for each of said prescribed points, the three-dimensional coordinate values of the position of said center of said sphere; and (j) producing from said computed numerical coordinate values, command signals to operate said drive means whereby said workpiece and said center in said tool are relatively displaced translationally along a path defined be a series of said positions to allow said desired contour to be progressively developed in said workpiece. 2. The method defined in claim 1 wherein said effective machining surface is substantially semi-spherical in shape. 3. The method defined in claim 1 or claim 2 wherein said tool is a rotary tool. 4. The method defined in claim 3 wherein said effective machining surface is formed upon rotation of said tool about said axis. 5. The method defined in claim 1 wherein in step (g), said constant value is equal to the radius of said sphere. 6. The method defined in claim 1 wherein said tool is an electroerosion electrode tool to be displaced relative to said workpiece while maintaining a small electroerosion gap spacing therebetween, and in step (g) said constant value is equal to the sum of said radius of the sphere and said gap spacing. 7. The method defined in claim 1 wherein said tool is a finish-machining tool for use to remove a layer of stock of a prescribed thickness from the workpiece to produce the desired contour therein, the method further comprising, prior to step (g), the step of rough-machining the workpiece with a rough-machining tool having an effective spherical machining surface which is similar in shape to that of said finish-machining tool but has a radius of sphere greater than that of the finish-machining tool, the step of rough-machining comprising: (go) inputting into said data processing means a numerical datum for a constant value which is substantially equal to the sum of said greater radius and said thickness; (ho) the same as step (h); (io) in said data processing means, computing from said data reproduced in step (ho) and said datum inputted in step (go), for each of said prescribed points, the three-dimensional coordinate values of the position of the center of the sphere of said greater radius; and (jo) producing from said numerical coordinate values computed in step (io), command signals to operate said drive means whereby said workpiece and said center in said rough-machining tool are relatively displaced translationally along a path defined by a series of such positions as mentioned in step (io) to allow a rough-machined contour which is similar to said desired contour to be progressively developed in the workpiece. 8. The method defined in claim 7 wherein said rough-machining tool is an electroerosion electrode tool to be displaced relative to said workpiece while maintaining an electroerosion gap spacing therebetween, and in step (g) said constant value is equal to the sum of said greater radius, said gap spacing and said thickness. 9. The method defined in claim 1 or claim 7 wherein in step (i), said three-dimensional coordinate values of the position of said center corresponding to any of said successive prescribed points are computed from said three-dimensional coordinate values of the position of said center corresponding to, and said reproduced data for, the immediately preceding prescribed point, and said inputted datum. 10. A numerical-control system for machining a desired three-dimensional contour in a workpiece, comprising: (a) an axial tool formed at its axial end with an effective machining surface which is substantially spherical about a center intersected by an axis of said tool; (b) datum sheet means for identifying a series of points prescribed on said desired contour to be machined in said workpiece, each of said prescribed points being identified in terms of its coordinate values in a predetermined three-dimensional coordinate system and of angular values defining the orientation of a normal thereat to said desired contour; (c) programming means for storing from said datum sheet on a record medium, data for said identified coordinate values and angular values sequentially for said successive prescribed points; (d) means for supporting said tool and said workpiece so that they can be translationally displaced relative to each other by drive means along the three axes of said predetermined three-diemsional coordinate system; (e) data processing means operably connected with said drive means via drive control means; (f) means for inputting into said data processing means a numerical datum for a constant value substantially equal to a radius of the sphere at least a portion of which constitutes said effective machining surface; (g) read-out means for reading out said stored record medium to reproduce data for said three-dimensional values and angular values of each of said successive prescribed points on the desired contour; (h) means in said data processing means for computing from said reproduced data and said inputted data, for each of said prescribed points, the three-dimensional coordinate values of the position of the center of said sphere; and (i) said drive control means for producing from said computed numerical coordinate values, command signals to operate said drive means whereby said workpiece and said center in said tool are relatively displaced translationally along a path defined by a series of said positions to allow said desired contour to be progressively developed in said workpiece.