A machine tool includes: a joint portion processing control means for controlling the processing of the joint portion in a joined workpiece such that a first workpiece is gripped by a grip section, and a predetermined region extending from a joint portion of a joined workpiece toward a second workpiece is processed over a range of not less than a predetermined width to have an outer diameter of not more than an outer diameter of the first workpiece; and a movement control means for controlling the movement of the joined workpiece so as to slidingly move the joined workpiece relative to the support section, from a state in which the first workpiece is supported by the support section, up to a state in which the second workpiece is supported by the support section.

A method to form a surface on a metal work piece includes providing a turning insert that has a nose angle formed between first and second cutting edges less than or equal to 85°; providing a turning tool having a tool body with an insert seat in which the turning insert is mountable; arranging the orientation of the second cutting edge such that it forms a back clearance angle of more than 90° in a feed direction; rotating the metal work piece around a rotational axis in a first direction; moving the turning insert in a direction parallel to or at an angle less than 45° relative to the rotational axis; and setting the longitudinal axis of the tool body at an angle greater than zero but less than or equal to 90° relative to the rotational axis of the metal work piece.

A method to form a surface on a metal work piece includes providing a turning insert that has a nose angle formed between first and second cutting edges less than or equal to 85°; providing a turning tool having a tool body with an insert seat in which the turning insert is mountable; arranging the orientation of the second cutting edge such that it forms a back clearance angle of more than 90° in a feed direction; rotating the metal work piece around a rotational axis in a first direction; moving the turning insert in a direction parallel to or at an angle less than 45° relative to the rotational axis; and setting the longitudinal axis of the tool body at an angle greater than zero but less than or equal to 90° relative to the rotational axis of the metal work piece.

A turning tool for internal turning of a metal work piece having a rear end, an opposite forward end and a longitudinal center axis extending therebetween. The first nose cutting edge includes a first radially distal point having an associated first rake face and separates and connects a first forward cutting edge and a first rearward cutting edge. A second nose cutting edge of the turning tool includes a second radially distal point having an associated second rake face and separates and connects a second forward cutting edge and a second rearward cutting edge. The second radially distal point is positioned ahead of the first radially distal point. The first forward cutting edge forms an acute first entering angle, the second forward cutting edge forms an obtuse second back clearance angle, and the second rearward cutting edge forms an acute second entering angle.

A turning tool for internal turning of a metal work piece having a rear end, an opposite forward end and a longitudinal center axis extending therebetween. The first nose cutting edge includes a first radially distal point having an associated first rake face and separates and connects a first forward cutting edge and a first rearward cutting edge. A second nose cutting edge of the turning tool includes a second radially distal point having an associated second rake face and separates and connects a second forward cutting edge and a second rearward cutting edge. The second radially distal point is positioned ahead of the first radially distal point. The first forward cutting edge forms an acute first entering angle, the second forward cutting edge forms an obtuse second back clearance angle, and the second rearward cutting edge forms an acute second entering angle.

A tool system for machining includes a tool body that has a first end for connecting to a machine tool and a second end having an end face on which a seat for an interchangeable cutting insert is formed. The cutting insert has an underside formed as an abutment surface, a top side formed as a rake face, and an encircling side face formed as a flank, and a cutting edge is formed at a transition from the top side to the encircling side face. The cutting insert is arranged on the seat such that the top side extends perpendicularly to the longitudinal axis of the tool body and the cutting edge protrudes beyond the outer circumference of the end face of the tool body in a radial direction with respect to the longitudinal axis with two usable cutting corners and cutting-corner portions adjoining the latter on both sides.

A machining apparatus machines a surface of a workpiece by feeding, relative to the workpiece, a cutting tool having a plurality of cutting edges A to D with tips of the cutting edges A to D arranged at equal intervals. The machining apparatus performs a cutting process of cutting the surface of the workpiece with the plurality of cutting edges A to D and a feeding process of feeding the cutting tool relative to the workpiece by a predetermined feed amount to form a plurality of grooves on the surface of the workpiece. The predetermined feed amount is set to a length that is not an integral multiple of the interval between the tips of cutting edges.

A machining apparatus machines a surface of a workpiece by feeding, relative to the workpiece, a cutting tool having a plurality of cutting edges A to D with tips of the cutting edges A to D arranged at equal intervals. The machining apparatus performs a cutting process of cutting the surface of the workpiece with the plurality of cutting edges A to D and a feeding process of feeding the cutting tool relative to the workpiece by a predetermined feed amount to form a plurality of grooves on the surface of the workpiece. The predetermined feed amount is set to a length that is not an integral multiple of the interval between the tips of cutting edges.

A method for performing a cutting operation on a workpiece is provided. The method comprises providing a workpiece being made of a metal characterized by a thermal conductivity of no greater than about 100 W100 .sup.W/.sub.(m.Math.K) (approximately 57.8 .sup.Btu/.sub.(hr ft ° F.)), providing a cutting device comprising an internal cooling cavity defined on one side thereof by a thin-walled structure, and performing a cutting operation on the workpiece using the cutting device. The cutting speed is no less than about 500 .sup.m/.sub.min. (approximately 1640 .sup.ft/.sub.min).

A machine tool and a control device therefor, wherein vibration cutting of a workpiece is carried out by means of a tool and wherein, after the vibration cutting, finish-cutting is carried out for cutting a finishing allowance of the workpiece by means of the tool, without relative vibration between the workpiece and the tool, by relatively rotating the workpiece and the tool and relatively moving them in the feed direction. According to the invention, before the vibration cutting, a finishing allowance calculation means calculates a finishing allowance remaining on the workpiece after vibration cutting has been completed, and a determination means determines whether or not the finishing allowance as calculated by the finishing allowance calculation means is less than, or equal to a predetermined threshold value.