A gear machining apparatus includes a machining tool having a plurality of protruding tool edges on an outer periphery of the machining tool, and driving apparatuses that form a tooth on a work piece by rotating the machining tool around a central axis thereof, rotating the work piece W around a central axis thereof, and moving the machining tool relative to the work piece. Radial outer faces of the protruding tool edges form multiple steps that are parallel to the central axis of the machining tool such that the diameter of the machining tool increases in a stepwise manner from a tool leading end toward a tool base end of the machining tool.

A gear machining apparatus causes a machining tool and a workpiece to rotate at a high speed in synchronization with each other to machine a highly accurate gear through cutting. The machining tool is manufactured such that each of pitches between tool blades of the machining tool is an integer multiple of a pitch between teeth of the gear, the integer multiple being equal to or larger than double. By using the machining tool for cutting performed by the gear machining apparatus, the number of the tool blades of the machining tool, which are brought into contact with the workpiece at the same time, is reduced. Thus, it is possible to suppress occurrence of self-excited vibrations during cutting by reducing the cutting resistance. Thus, it is possible to enhance the tooth trace accuracy of the gear.

There is provided a tool for efficiently cutting a face gear to be meshed with a helical gear. When a circular tooth thickness of a tooth tip of a cutting edge portion is represented as S.sub.atSC, a circular tooth thickness on a virtual outside diameter of a tooth profile of the helical gear in a cross-sectional view perpendicular to an axis is represented as S.sub.at, a helix angle on the virtual outside diameter of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis is represented as .sub.a, and a face width of the cutting edge portion is represented as b.sub.sc, $b_{\mathrm{SC}}\frac{s_{\mathrm{at}}-s_{\mathrm{atSC}}}{\tan {}_a}$
is satisfied.