A thread milling cutter having a main body which includes a shank and a cutting portion, which is cylindrical in its basic shape, an axis of rotation and a plurality of cutting teeth, which are spaced in the peripheral direction and which are arranged on the cutting portion in at least two different radial planes extending perpendicularly to the axis of rotation is provided. The thread milling cutter combines the advantages of high working efficiency of one-piece thread milling cutters having a plurality of cutting teeth and cutting lobes with the advantages of thread milling cutters having indexable cutting inserts without being restricted to large diameters. The cutting portion, respectively, has at least two seats for receiving a respective standard cutting insert in each of at least two different radial planes and the cutting teeth are formed by cutting corners of standard cutting inserts.

A thread milling cutter (1) includes an integrally formed thread milling tool (10) having a rotational axis (S), a shank portion (24) and a forward cutting portion (34). The cutting portion (34) has at least five insert pockets (42) recessed therein with at least one insert pocket (42) being devoid of an associated support protrusion (46), allowing different insert placements for different thread pitches.

A machining device threads a workpiece by relatively rotating the workpiece and a multi-blade tool and relatively moving them along a feed direction to perform cutting processes in the radial direction of the workpiece along the same cutting path in a predetermined spiral form. A controller performs a groove machining to form a threaded portion with vibration in the radial direction of the workpiece and a finish machining to form the threaded portion by bringing the multi-blade tool into contact with the grooved portion of the workpiece. The multi-blade tool has a first cutting blade and a second cutting blade arranged side by side along the feed direction. The controller sets amplitude of a vibration waveform to a value at which a cutting edge of the second cutting blade does not come into contact with the screw bottom surface of the workpiece in the finish machining.