Method of machining a workpiece in a turret lathe and an NC lathe for performing this method

Abstract

A method of machining a workpiece, which is rotatable about a first axis, by a tool pivotable about a second axis parallel to the first axis and drivable about a third axis perpendicular to the second axis. To allow the circumference of the workpiece to be machined off-center without the necessity of moving the first or the second axis transversely to the plane defined by these two axes, the workpiece and the tool are rotated or pivoted about the first .[.or.]. .Iadd.and .Iaddend.second .[.axis.]. .Iadd.axes.Iaddend., respectively, at the same time, in the same direction and at the same angular velocity and, simultaneously, the second axis is displaced transversely to the first axis at such a velocity that the equation X 2 =Y 2 +A 2 always applies, wherein X is the distance of the second axis from the first axis, Y is the distance of the first axis from the plane defined by the second and third axes and A is the distance of the second axis from the vertical projection of the first axis onto this plane.

What is claimed is: 
     
       1. A method of machining a circumferential portion of a rotating workpiece off-center comprising the following steps which are carried out simultaneously: (a) rotating the workpiece about a first axis in a defined direction of rotation and with a defined angular velocity dγ/dt;   (b) rotating a tool for machining a circumferential portion of said workpiece about a second axis;   (c) pivoting the second axis about a third axis in the defined direction of rotation and with said angular velocity of said first axis; said third axis being parallel to said first axis and said second axis extending radially from said third axis;     (d) displacing said third axis transversely to said first axis at a velocity dx/dt;   said velocities being the first derivatives of the following equations: ##EQU7##  wherein t, γ, X, A, Y o , and v y  denote the following: t=the time which is equal to zero when the tool touches the workpiece for the first time; γ=the angle between the second axis and a first plane defined by the first and the third axes;   X=the distance of the third axis from the first axis;   A=the distance of the third axis from the normal projection of the first axis onto a second plane defined by the third and second axes, which plane pivots about the third axis;   Y=the distance of the first axis from said second plane, with Y o  being the value of Y when t equals zero;   v y  =feed velocity (dY/dt) of the tool relative to the workpiece in the direction of diminishing values of Y.     
     
     
       2. A method of machining a circumferential portion of a rotating workpiece off-center comprising the following steps which are carried out simultaneously: (a) rotating the workpiece about a first axis in a defined direction of rotation and with a defined angular velocity dγ/dt;   (b) rotating a tool for machining a circumferential portion of said workpiece about a second axis;   (c) pivoting the second axis about a third axis in the defined direction of rotation and with said angular velocity of said first axis;   said third axis being parallel to said first axis and said second axis extending radially from said third axis;   (d) displacing said third axis transversely to said first axis at a velocity dX/dt;   said velocities being the first derivatives of the following equations: ##EQU8##  wherein t, γ, X, Y, A o , and v A  denote the following: t=the time which is equal to zero when the tool touches the workpiece for the first time; γ=the angle between the second axis and a first plane defined by the first and the third axes;   X=the distance of the third axis from the first axis;   A=the distance of the third axis from the normal projection of the first axis onto a second plane defined by the third and second axes, which plane pivots about the third axis, with A o  being the value of A when t equals zero;   Y=the distance of the first axis from said second plane.   v A  =feed velocity dA/dt of the tool relative to the workpiece in the direction of diminishing values of A. .Iadd.     
     
     
       3.  A method of machining a circumferential portion of a rotatable workpiece off-center comprising the following steps which are carried out simultaneously while performing such machining: (a) rotatively displacing the workpiece about a first axis in a defined direction of rotation;   (b) rotating a cutting tool about a second axis for machining a circumferential portion of said workpiece off-center from said first axis;   (c) rotatively displacing said second axis about a third axis in said defined direction of rotation;   said third axis of rotation being parallel to said first axis and spaced from said first axis by a variable distance;   said cutting tool being located on said second axis a predetermined tool distance from said third axis;   said second axis being positioned perpendicular to a predetermined plane of such workpiece which is parallel to said first axis; and   (d) providing relative transverse displacements between said third axis and said first axis;   the rotational displacements of said workpiece about said first axis and said tool about said third axis being simultaneously controlled to provide the same angular displacement of each in the same direction to maintain said second axis perpendicular to said predetermined plane of said workpiece while performing such machining; and   the transverse displacement of said third axis relative to said first axis being simultaneously controlled relative to said rotational displacements of said workpiece about said first axis and said tool about said third axis to effect the positioning of said cutting tool in a direction perpendicular to said plane in a predetermined manner while performing such machining. .Iaddend. .Iadd.4. The method of claim 3 wherein the radial distance between said first axis and said second axis, measured normal to said second axis, is maintained constant whereby the machining performed on said off-center circumferential portion is a boring operation. .Iaddend. .Iadd.5. The method of claim 3 wherein the distance between said third axis and said predetermined plane, measured normal to said plane, is maintained constant whereby the machining performed on said off-center circumferential portion is a planar milling operation. .Iaddend. .Iadd.6. The method of claim 3 wherein said second axis intersects said third axis and extends radially therefrom. .Iaddend. .Iadd.7. The method of claim 3 wherein said relative transverse displacements between said third axis and said first axis are provided by rectilinear movement of one of said third axis and said first axis. .Iaddend. .Iadd.8. The method of claim 7 wherein said third axis is moved toward and away from said first axis to provide said relative transverse   
     
     
        displacements therebetween. .Iaddend. .Iadd.9.  A method of machining a circumferential portion of a rotatable workpiece off-center and relative to a predetermined plane of the workpiece which is parallel to the axis of rotation of the workpiece, comprising the following steps which are carried out simultaneously while performing such machining: (a) rotating the workpiece about a first axis in a defined direction of rotation and with a defined angular velocity;   (b) rotating a tool about a second axis for machining a circumferential portion of said workpiece;   (c) rotating said second axis relative to a third axis in the defined direction of rotation and with said defined angular velocity about said third axis;   said third axis being parallel to said first axis, and said second axis lying in a plane normal to said third axis;   (d) providing relative transverse displacement between said third axis and said first axis at a displacement velocity;   said defined angular velocity and said displacement velocity being correlated such that said second axis is maintained perpendicular to said predetermined plane and said tool is positioned in a direction perpendicular to said predetermined plane in a predetermined manner during   
     
     
        such machining. .Iaddend. .Iadd.10.  A method as in claim 9 wherein said tool is a milling tool and said method comprises milling a planar surface of said workpiece parallel to said plane. .Iaddend. .Iadd.11. A method as in claim 9 wherein said tool is a boring tool and said method comprising boring an off-center hole in said workpiece. .Iaddend. .Iadd.12. A method as in claim 9 wherein said second axis intersects said third axis and extends radially therefrom. .Iaddend. .Iadd.13. The method of claim 9 wherein said relative transverse displacements between said third axis and said first axis are provided by rectilinear movement of one of said third axis and said first axis. .Iaddend. .Iadd.14. A method as in claim 13 wherein said third axis is moved toward and away from said first axis to provide said relative transverse displacement therebetween. .Iaddend.