Working Surface Calculation of Teeth Bevel Gear Helical-Bevel Gearing at Milling with Hob

摘要

The paper considers an internal gearing of a bevel gear and a spur gear, shaped according to a conventional technology. There is a technological problem of obtaining the working profile of the bevel gear teeth in the internal spur-bevel gearing when the working profiles are being shaped. Obtaining a theoretically accurate surface of the gear teeth is troublesome due to the difficulty of making cutters with internal teeth and practical realization of machine gearing with the axis inclination of the workpiece or the cutter axis. This is related to the need of producing a shaping cutter with internal teeth for each gear train so that its geometry would be identical to that of the spur gear in the gear train. The paper describes a method for shaping an approximate teeth profile of a bevel gear in a spur-bevel gearing with a rack-type tool. The proposed method provides a sufficient degree of approximation of the shaped surface to the theoretically accurate one, which makes it applicable. In the paper, the equations are presented describing the teeth surface, as a result of a two-parameter bending with a hob of the surface with conical billet for evaluation. This makes it possible to evaluate the degree of approximation received for the working surface of the teeth to the theoretically accurate surface.