A method for cutting a thread on a rotating workpiece by means of a cutting tool having a cutting edge. The method includes sequentially performing a number of passes, each pass includes simultaneously moving the cutting tool and/or the workpiece relative to each other along and oscillating the cutting tool towards and away from workpiece rotational such that the cutting edge exits and enters the workpiece forming an air cut. The air cuts performed in a final pass are longer than all the other passes.

A cutting tool for thread cutting has a thread turning cutting insert releasably retained in an insert pocket by a fastening member. The thread turning cutting insert has a thread cutting portion having three spaced apart cutting teeth. and a chip forming groove recessed in an insert upper surface. The chip forming groove includes a near-flank groove surface close to the cutting teeth and far-flank grove surface further away from the cutting teeth. The thread cutting portion includes three cutting edges formed at the intersection of the insert upper surface and an insert peripheral surface. Each cutting edge is located on a respective cutting tooth. The thread cutting portion includes three planar land surfaces located on the insert upper surface. Each land surface extends from an entire length of a respective cutting edge to the near-flank groove surface.

What is provided is a modular cutting tool (1; 40) with a base body (2) extending along a tool axis and a tool head (3) connected via a positive coupling to the base body (2), wherein the positive coupling is formed from front toothings (4), which are engaged with one another, on the base body (2) and tool head (3), which each have a plurality of radially running teeth (5), which are distributed equidistantly around the tool axis. For each front toothing (4) the tip surfaces (7) of the teeth (5) lie on a virtual inner conical surface in the tool head (3) or base body (2) with the tool axis as cone axis, and the tip surfaces (7) of the teeth (5) are rounded concavely.