Method for machining three dimensional contours utilizing a numerically controlled lathe

Claim 1

A method for machining a workpiece comprising the steps of: (a) providing a rotatable lathe spindle including means for mounting the workpiece thereto such that the workpiece may be rotated about a rotational axis; (b) providing a cutting tool; (c) positioning said cutting tool in response to control signals with respect to both a first axis perpendicular to the axis of rotation of the spindle mounted workpiece and a second axis parallel to the axis of rotation of the spindle mounted workpiece; and (d) producing a predetermined set of control signals x, z, i and k for each predetermined segment of rotation of the workpiece, wherein each x control signal defines the position of the cutting tool in said first axis, each z control signal defines the position of the cutting tool in said second axis, each i control signal defines the distance traveled by the cutting tool in said first axis for each revolution of the workpiece and each k control signal defines the distance traveled by the cutting tool in said second axis for each revolution of the workpiece, said step (d) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system using mutually orthogonal axes having corresponding coordinates X, Y and Z; (ii) compensating said X, Y and Z coordinates for offsets produced by the cutting tool to produce coordinates x', y' and z; (iii) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (iv) defining a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (v) calculating a set of i coordinates, each i coordinate being a predetermined function of said R and θ coordinates; (vi) calculating a set of k coordinates, each k coordinate being a predetermined function of said z and θ coordinates; and (vii) producing said x, z, i and k control signals in response to said x, z, i and k coordinates, respectively.

Claim 2

A method for machining a workpiece comprising the steps of: (a) providing a rotatable lathe spindle including means for mounting the workpiece thereto such that the workpiece may be rotated about a rotational axis; (b) providing a cutting tool; (c) positioning said cutting tool in response to control signals with respect to both a first axis perpendicular to the axis of rotation of the spindle mounted workpiece and a second axis parallel to the axis of rotation of the spindle mounted workpiece; and (d) producing a predetermined set of control signals x, z, i and k for each predetermined segment of rotation of the workpiece, wherein each x control signal defines the position of the cutting tool in said first axis, each z control signal defines the position of the cutting tool in said second axis, each i control signal defines the distance traveled by the cutting tool in said first axis for each revolution of the workpiece and each k control signal defines the distance traveled by the cutting tool in said second axis for each revolution of the workpiece, said step (d) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system using mutually orthogonal axes having corresponding coordinates X, Y and Z; (ii) compensating said X, Y and Z coordinates for offsets produced by the cutting tool to produce coordinates x', y' and z; (iii) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (iv) defining a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (v) calculating a set of i coordinates, each i coordinate being a predetermined function of said R and θ coordinates; (vi) calculating a set of k coordinates, each k coordinate being a predetermined function of said z and θ coordinates; and (vii) producing said x, z, i and k control signals in response to said x, z, i and k coordinates, respectively.

Claim 5

The method of either one of claims 2 or 3 wherein step (vi) comprises the step of calculating each k coordinate in accordance with: ##EQU4## where the subscript n denotes the nth coordinate, with n varying in integer values from 1 to N.

Claim 6

The method of any one of claims 1 or 3 comprising the further steps of: (e) comparing successive i, k control signals to the immediately preceding i, k control signals; and (f) deleting those x, z, i and k control signals whose i, k values are predeterminedly related to the i, k values of the immediately preceding control signal.

Claim 8

A method for machining a workpiece comprising the steps of: (a) providing a rotatable lathe spindle including means for mounting the workpiece thereto such that the workpiece may be rotated about a rotational axis; (b) providing a cutting tool; (c) positioning said cutting tool in response to control signals with respect to both a first axis perpendicular to the axis of rotation of the spindle mounted workpiece and a second axis parallel to the axis of rotation of the spindle mounted workpiece; and (d) producing a predetermined set of control signals x, z, i and k for each predetermined segment of rotation of the workpiece, wherein each x control signal defines the position of the cutting tool in said first axis, each z control signal defines the position of the cutting tool in said second axis, each i control signal defines the distance traveled by the cutting tool in said first axis for each revolution of the workpiece, and each k control signal defines the distance traveled by the cutting tool in said second axis for each revolution of the workpiece, said step (d) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system having mutually orthogonal axes with corresponding coordinates X, Y and Z, the Z coordinate axis being parallel to the axis of rotation of the workpiece; (ii) selecting a total of N, X, Y data pairs to define each desired contour of the workpiece at a corresponding Z coordinate, where N is a predetermined integer; (iii) compensating said X, Y and Z coordinates for offsets produced by the cutting tool to produce coordinates x', y' and z; (iv) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (v) producing a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (vi) calculating a set of i coordinates, each i coordinate being produced in accordance with: ##EQU5## where the subscript n denotes at the nth coordinate, with n varying in integer values from 1 to N; (vii) calculating a set of k coordinates, each k coordinate being produced in accordance with: ##EQU6## where the subscript n denotes the nth coordinate, with n varying in integer values from 1 to N; and (viii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.

Claim 9

A method for machining a workpiece comprising the steps of: (a) providing a rotatable lathe spindle including means for mounting the workpiece thereto such that the workpiece may be rotated about a rotational axis; (b) providing a cutting tool; (c) positioning said cutting tool in response to control signals with respect to both a first axis perpendicular to the axis of rotation of the spindle mounted workpiece and a second axis parallel to the axis of rotation of the spindle mounted workpiece; and (d) producing a predetermined set of control signals x, z, i and k for each predetermined segment of rotation of the workpiece, wherein each x control signal defines the position of the cutting tool in said first axis, each z control signal defines the position of the cutting tool in said second axis, each i control signal defines the distance traveled by the cutting tool in said first axis for each revolution of the workpiece, and each k control signal defines the distance traveled by the cutting tool in said second axis for each revolution of the workpiece, said step (d) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system having mutually orthogonal axes with corresponding coordinates X, Y and Z, the Z coordinate axis being parallel to the axis of rotation of the workpiece; (ii) selecting a total of N, X, Y data pairs to define each desired contour of the workpiece at a corresponding Z coordinate, where N is a predetermined integer; (iii) compensating said X, Y and Z coordinates for offsets produced by the cutting tool to produce coordinates x', y' and z; (iv) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (v) producing a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (vi) calculating a set of i coordinates, each i coordinate being produced in accordance with: ##EQU5## where the subscript n denotes at the nth coordinate, with n varying in integer values from 1 to N; (vii) calculating a set of k coordinates, each k coordinate being produced in accordance with: ##EQU6## where the subscript n denotes the nth coordinate, with n varying in integer values from 1 to N; and (viii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.

Claim 11

A method for machining three dimensional contours in a workpiece comprising the steps of: (a) providing a numerically controlled lathe, the lathe having a rotatable spindle and mounting means for mounting the workpiece to the spindle for rotation therewith about a workpiece rotational axis, the lathe further including a cutting tool mounted to positioning means, the positioning means being responsive to: (i) an x control signal to define the position of the cutting tool with respect to the radial axis of the workpiece, (ii) a z control signal to define the position of the cutting tool with respect to the rotational axis of the workpiece; p2 (iii) an i control signal to define the distance traveled by the cutting tool in the radial axis of the workpiece for each revolution thereof, and (iv) a k control signal to define the distance traveled by the cutting tool with respect to the rotational axis of the workpiece for each revolution thereof; and (b) producing a succession of predetermined x, z i and k control signals, each control signal being produced for a predetermined segment of rotation of the workpiece, the x, z, i and k control signals being suitable for control of said positioning means such that a contour predeterminedly varying in three dimensions is cut by the cutting tool in the workpiece, step (b) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system using three mutually orthogonal axes having X, Y and Z coordinates; (ii) compensating said X, Y and Z coordinates for offsets produced by the radius of the cutting tool to produce coordinates x', y', and z; (iii) converting said compensated x' and y' coordinates to polar coordinates of radius R and angle θ; (iv) producing a set of x coordinates, each x coordinate being predeterminedly related to a corresponding R coordinate; (v) calculating a set of i coordinates, each i coordinate being a predetermined function of each of said R and θ coordinates; (vi) calculating a set of k coordinates, each k coordinate being a predetermined function of each of said z and θ coordinates; and (vii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.

Claim 12

A method for machining three dimensional contours in a workpiece comprising the steps of: (a) providing a numerically controlled lathe, the lathe having a rotatable spindle and mounting means for mounting the workpiece to the spindle for rotation therewith about a workpiece rotational axis, the lathe further including a cutting tool mounted to positioning means, the positioning means being responsive to: (i) an x control signal to define the position of the cutting tool with respect to the radial axis of the workpiece, (ii) a z control signal to define the position of the cutting tool with respect to the rotational axis of the workpiece; p2 (iii) an i control signal to define the distance traveled by the cutting tool in the radial axis of the workpiece for each revolution thereof, and (iv) a k control signal to define the distance traveled by the cutting tool with respect to the rotational axis of the workpiece for each revolution thereof; and (b) producing a succession of predetermined x, z i and k control signals, each control signal being produced for a predetermined segment of rotation of the workpiece, the x, z, i and k control signals being suitable for control of said positioning means such that a contour predeterminedly varying in three dimensions is cut by the cutting tool in the workpiece, step (b) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system using three mutually orthogonal axes having X, Y and Z coordinates; (ii) compensating said X, Y and Z coordinates for offsets produced by the radius of the cutting tool to produce coordinates x', y', and z; (iii) converting said compensated x' and y' coordinates to polar coordinates of radius R and angle θ; (iv) producing a set of x coordinates, each x coordinate being predeterminedly related to a corresponding R coordinate; (v) calculating a set of i coordinates, each i coordinate being a predetermined function of each of said R and θ coordinates; (vi) calculating a set of k coordinates, each k coordinate being a predetermined function of each of said z and θ coordinates; and (vii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.

Claim 15

The method of either one of claims 10 or 11 wherein step (vi) comprises the step of calculating each k coordinate in accordance with: ##EQU8## where the subscript n denotes the nth coordinates, with n varying from 1 to N.

Claim 16

The method of any of one of claims 9, 10 or 11 comprising the further steps of: (c) storing said produced x, z, i and k control signals in a memory for subsequent application to said positioning means; and (d) processing said produced x, z, i and k control signals and deleting from said memory each x, z, i, k control signal which is within a predetermined tolerance from its preceding control signal, to thereby reduce the number of control signals necessary to produce the desired machined workpiece.

Claim 20

A method for machining three dimensional contours in a workpiece comprising the steps of: p1 (a) providing a numerically controlled lathe, the lathe having a rotatable spindle and mounting means for mounting the workpiece to the spindle for rotation therewith about a workpiece rotational axis, the lathe further including a cutting tool mounted to positioning means, the positioning means being responsive to: (i) an x control signal to define the position of the cutting tool with respect to the radial axis of the workpiece, (ii) a z control signal to define the position of the cutting tool with respect to the rotational axis of the workpiece; (iii) an i control signal to define the distance traveled by the cutting tool in the radial axis of the workpiece for each revolution thereof, and (iv) a k control signal to define the distance traveled by the cutting tool with respect to the rotational axis of the workpiece for each revolution thereof; and (b) producing a succession of predetermined x, z, i and k control signals, each control signal being produced for a predetermined segment of rotation of the workpiece, the x, z, i and k control signals being suitable for control of said positioning means such that a contour predeterminedly varying in three dimensions is cut by the cutting tool in the workpiece, step (b) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system having three mutually orthogonal axes with corresponding coordinates X, Y and Z; (ii) selecting a total of N, X, Y data pairs to define each desired contour of the workpiece at a corresponding Z coordinate, where N is a predetermined integer; (iii) compensating said X, Y and Z coordinates for cutting tool offsets to produce coordinates x', y', and z; (iv) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (v) producing a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (vi) calculating a set of i coordinates in accordance with: ##EQU9## where the subscript n denotes the nth value, with n varying in integer values from 1 to N; (vii) calculating a set of k coordinates, each k coordinate being produced in accordance with: ##EQU10## where the subscript n denotes the nth value, with n varying in integer values from 1 to N; and (viii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.

Claim 21

A method for machining three dimensional contours in a workpiece comprising the steps of: p1 (a) providing a numerically controlled lathe, the lathe having a rotatable spindle and mounting means for mounting the workpiece to the spindle for rotation therewith about a workpiece rotational axis, the lathe further including a cutting tool mounted to positioning means, the positioning means being responsive to: (i) an x control signal to define the position of the cutting tool with respect to the radial axis of the workpiece, (ii) a z control signal to define the position of the cutting tool with respect to the rotational axis of the workpiece; (iii) an i control signal to define the distance traveled by the cutting tool in the radial axis of the workpiece for each revolution thereof, and (iv) a k control signal to define the distance traveled by the cutting tool with respect to the rotational axis of the workpiece for each revolution thereof; and (b) producing a succession of predetermined x, z, i and k control signals, each control signal being produced for a predetermined segment of rotation of the workpiece, the x, z, i and k control signals being suitable for control of said positioning means such that a contour predeterminedly varying in three dimensions is cut by the cutting tool in the workpiece, step (b) comprising the steps of: (i) defining the desired machined shape of the workpiece in a Cartesian coordinate system having three mutually orthogonal axes with corresponding coordinates X, Y and Z; (ii) selecting a total of N, X, Y data pairs to define each desired contour of the workpiece at a corresponding Z coordinate, where N is a predetermined integer; (iii) compensating said X, Y and Z coordinates for cutting tool offsets to produce coordinates x', y', and z; (iv) converting said compensated x', y' coordinates to corresponding polar coordinates of radius R and angle θ; (v) producing a set of x coordinates, each x coordinate being predeterminedly related to one of said R coordinates; (vi) calculating a set of i coordinates in accordance with: ##EQU9## where the subscript n denotes the nth value, with n varying in integer values from 1 to N; (vii) calculating a set of k coordinates, each k coordinate being produced in accordance with: ##EQU10## where the subscript n denotes the nth value, with n varying in integer values from 1 to N; and (viii) producing said x, z, i and k control signals responsive to said x, z, i and k coordinates, respectively.