A method includes positioning a linear cutting edge inclined at an angle greater than 0 and smaller than 90 with respect to a Z axis at a cutting start position displaced from a position on an X axis along a direction of a Y axis in a three-dimensional orthogonal coordinate system in which an axial line of rotation of a rotation symmetry plane is defined as the Z axis, an axis in a radial direction of the rotation symmetry plane is defined as the X axis, and an axis orthogonal to both of the Z axis and the X axis is defined as the Y axis and machining the rotation symmetry plane by feeding the cutting edge from the cutting start position along a track having an X axis component, a Y axis component, and a Z axis component while the cutting edge is in contact with a rotating machine component.

A method includes positioning a linear cutting edge inclined at an angle greater than 0 and smaller than 90 with respect to a Z axis at a cutting start position displaced from a position on an X axis along a direction of a Y axis in a three-dimensional orthogonal coordinate system in which an axial line of rotation of a rotation symmetry plane is defined as the Z axis, an axis in a radial direction of the rotation symmetry plane is defined as the X axis, and an axis orthogonal to both of the Z axis and the X axis is defined as the Y axis and machining the rotation symmetry plane by feeding the cutting edge from the cutting start position along a track having an X axis component, a Y axis component, and a Z axis component while the cutting edge is in contact with a rotating machine component.

A machine tool cuts a workpiece having an inclined or curved surface and includes a main spindle that holds and rotates the workpiece, a moving device that moves a cutting tool relative to the workpiece in a direction obtained by combining a Z direction parallel or substantially parallel with the axis of the main spindle, an X direction that is perpendicular or substantially perpendicular to the Z direction and determines the amount of cutting of the workpiece, and a Y direction perpendicular or substantially perpendicular to the Z direction and the X direction, and an angle setting mechanism that causes the direction of an edge of the cutting tool to match the inclined surface of the workpiece by inclining the direction of the edge with respect to the Z direction when seen from the Y direction in a state in which the direction of the edge is inclined with respect to the Z direction when seen from the X direction.

A machine tool cuts a workpiece having an inclined or curved surface and includes a main spindle that holds and rotates the workpiece, a moving device that moves a cutting tool relative to the workpiece in a direction obtained by combining a Z direction parallel or substantially parallel with the axis of the main spindle, an X direction that is perpendicular or substantially perpendicular to the Z direction and determines the amount of cutting of the workpiece, and a Y direction perpendicular or substantially perpendicular to the Z direction and the X direction, and an angle setting mechanism that causes the direction of an edge of the cutting tool to match the inclined surface of the workpiece by inclining the direction of the edge with respect to the Z direction when seen from the Y direction in a state in which the direction of the edge is inclined with respect to the Z direction when seen from the X direction.

A cutting method for an inner circumferential face or an outer circumferential face of a work using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein a table that supports the work is set in a rotating central axis that is coaxial with a turning central axis of the main shaft, and the table is rotated in a direction opposite to a turning direction of the main shaft to increase a cutting velocity. The cutting method allows an increase to the cutting velocity under simple control.

A cutting method for an inner circumferential face or an outer circumferential face of a work using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein a table that supports the work is set in a rotating central axis that is coaxial with a turning central axis of the main shaft, and the table is rotated in a direction opposite to a turning direction of the main shaft to increase a cutting velocity. The cutting method allows an increase to the cutting velocity under simple control.

A cutting method in which, in cutting a circumferential face of a work, control is enabled to make a cutting velocity constant accurately by using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that 0 changes in association with a change in the distance R so that
=(C.sup.2{dot over (R)}.sup.2).sup.1/2/R
is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.

A cutting method in which, in cutting a circumferential face of a work, control is enabled to make a cutting velocity constant accurately by using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that 0 changes in association with a change in the distance R so that
=(C.sup.2{dot over (R)}.sup.2).sup.1/2/R
is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.

A cutting method in which, in cutting a circumferential face of a work, control is enabled to make a cutting velocity constant accurately by using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that 0 changes in association with a change in the distance R so that

=(C.sup.2{dot over (R)}.sup.2).sup.1/2/R

is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.

A cutting method in which, in cutting a circumferential face of a work, control is enabled to make a cutting velocity constant accurately by using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that 0 changes in association with a change in the distance R so that

=(C.sup.2{dot over (R)}.sup.2).sup.1/2/R

is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.