In textbooks of mechanical engineering, rack has been mistakenly regarded as rack cutter so that minimum teeth without undercutting have been deduced, which has made people misunderstand undercut phenomenon more than 65 years. Theoretical research and computer simulation about undercut phenomenon are presented in this paper. Firstly, the theoretical analysis and calculation on minimum teeth without undercutting have been carried out, the rack cutter is used to infer minimum teeth without undercutting of standard involute gears, and correct minimum teeth without undercutting are get; And then computer simulation is applied to verify validity results of theoretical calculations, which not only corrects the long-standing mistakes about the traditional undercut phenomenon, but also provides the correct theoretical guidance for gears’ manufacturing.

Contrast analysis of the stub tooth involute gear with 22.5 degree pressure angle, and the existing gear with standard pressure angle has been given in this study. Based on the combination of generating method, numerical calculations and simulations, reasons of undercut phenomena for stub tooth involute gear with 22.5 degree pressure angle are researched and analyzed deeply. Minimum teeth without undercutting for considering the rack cutter’s addendum c*m is given based on the traditional undercutting theory, which also illustrated the validity of theoretical derivation.

Establishing the corresponding relationship between radius at tooth tip and tooth root fillet by the curvature of conjugate flank based on the generating method to manufacture for gears. According to the Visual Basic, a 2-D mathematical model of relationship between undercutting phenomena and modulus, teeth and modification coefficient of involute gear was built, and then simulated undercutting influence level caused by modulus, teeth and modification coefficient. The generating method dynamic processes, generating profile and the root drawing obtained by the simulation will directly reflect the influences that modulus, teeth and modification coefficient with gears meshing processions, and provided a reliable basis for design gear transmission and machining involute gears.