A simulation apparatus includes: a memory to store information on the shape of a workpiece, information on a cross section of a portion of the workpiece, and information on definition points indicating the shape of an edge surface of tool edges of a machining tool; a first calculator to perform a calculation to obtain passage points in a three-dimensional coordinate system; a second calculator to cause the cross section in the three-dimensional coordinate system to be disposed parallel to a plane defined by predetermined two of the axes of the three-dimensional coordinate system, thus converting the passage points in the three-dimensional coordinate system into passage points in a two-dimensional coordinate system; and a third calculator to decide, in accordance with the passage points in the two-dimensional coordinate system, the shape of a tooth profile to be formed on the workpiece in the two-dimensional coordinate system.

A hard coating includes two first crystalline phases, and a second crystalline phase containing AlN of a wurtzite-type crystal structure disposed therebetween. The two first crystalline phases each include, independently, a laminate structure having a Ti.sub.1-x1Al.sub.x1N phase having a sodium chloride-type crystal structure, and an Al.sub.x2Ti.sub.1-x2N phase having a sodium chloride-type crystal structure that are alternately stacked. An Al composition ratio x1 satisfies a relationship 0.5x10.75, and an Al composition ratio x2 satisfies a relationship 0.75<x20.95. The laminate structure includes a region in which an Al concentration periodically changes along a stacking direction of the Ti.sub.1-x1Al.sub.x1N phase and the Al.sub.x2Ti.sub.1-x2N phase. In this region, a difference between a maximum value of the Al composition ratio x2 and a minimum value of the Al composition ratio x1 is greater than 0.25.

A skiving cutter includes a cutting edge portion in which a tooth trace extends in a direction inclined with respect to an axis of a base. The cutting edge portion is segmented into a plurality of segmented cutting edges by cutting edge grooves extending in a direction intersecting the tooth trace. One of the plurality of segmented cutting edges forms a reference cutting edge. Among the plurality of segmented cutting edges constituting the cutting edge portion, the reference cutting edge has the largest axis-cutting edge distance which is a distance from the axis to the outer circumferential cutting edge of the segmented cutting edge, and the remaining one or more segmented cutting edges have gradually smaller axis-cutting edge distances as a distance from the reference cutting edge to each of the remaining cutting edges increases. A helix angle is different according to positions of the plurality of segmented cutting edges.

A method and a device for gear cutting a work wheel includes a cutting wheel with cutting teeth, which is rotatably driven on a tool spindle about a tool spindle axis. The cutting teeth engage into the work wheel, which is rotatably driven on a workpiece spindle about a workpiece axis that intersects the tool spindle axis. In rough cuts, tooth spaces between left and right tooth flanks of teeth of the toothing are deepened via a change in axial distance of the tool spindle axis and the workpiece axis. In a first finishing cut, only the left tooth flank is precision machined with a chip removal point moving from top to base of the tooth with gear skiving movement. In a second finishing cut, only the right tooth flank is precision machined with a chip removal point moving from top to base of the tooth with gear skiving movement.

Provided is a surface-coated cutting tool including a base material and a coating including a super-multilayer-structure layer where A layers and B layers different from the A layers in composition are alternately laminated. The super-multilayer-structure layer includes an X area and a Y area those are alternately repeated. In the X area, A layers having a thickness A.sub.X and B layers having a thickness B.sub.X are alternately laminated. In the Y area, A layers having a thickness A.sub.Y and B layers having a thickness B.sub.Y are alternately laminated. The thickness A.sub.X is larger than the thickness A.sub.Y, and the thickness B.sub.X is smaller than the thickness B.sub.Y. Each of the A layers and the B layers comprising one or more elements selected from a group consisting of Ti, Al, Cr, Si, Ta, Nb, and W, and one or more elements selected from a group consisting of C and N.

A surface-coated cutting tool includes a substrate and a coating that is disposed on the substrate and formed so as to cover at least a portion of a flank face, in which the coating includes an inner layer and an outer layer formed on the inner layer, the inner layer is formed of at least one layer and includes an aluminum oxide layer as a layer in contact with the outer layer, the outer layer has a multilayer structure that includes three or more layers stacked on top of one another, and each of the layers that constitute the multilayer structure contains titanium.

A cutting tool includes a substrate and a coating film provided on the substrate, wherein the substrate is a cBN sintered material including more than or equal to 30 volume % and less than 80 volume % of cBN and a binder, the coating film includes a compound layer constituted of a composition of Ti.sub.1-xAl.sub.xC.sub.1-aN.sub.a, where 0.70X0.95 and 0<a1, and the compound layer has a NaCl type crystal structure in a whole or part of the compound layer.

A surface-coated cutting tool includes a base material and a coating formed on the base material. The base material is a cemented carbide or a cermet. A surface of the base material includes a rake face, a flank face, and a cutting edge face connecting the rake face to the flank face. The base material has an oxygen concentration of less than or equal to 1 at. % at a depth position of 0.4 m from the cutting edge face. The coating includes a hard layer. A topmost layer in the hard layer has a compressive stress of more than or equal to 1.5 GPa in absolute value.

A cutting tool includes a base material. The base material is a cemented carbide or a cermet. A surface of the base material includes a rake face, a flank face, and a cutting edge face connecting the rake face to the flank face. The base material has an oxygen concentration of less than or equal to 1 at. % at a depth position of 0.4 m from the cutting edge face.

A cutting tool includes a base material. The base material is a cemented carbide or a cermet. A surface of the base material includes a rake face, a flank face, and a cutting edge face connecting the rake face to the flank face. The base material has an oxygen concentration of less than or equal to 1 at. % at a depth position of 0.4 m from the cutting edge face.