An Analysis of Undercut Conditions and of Appearance of Contact Lines Envelope Conditions of Gears

Abstract

Necessary conditions of undercutting of gears, necessary and sufficient conditions of the existence of the contact lines envelope on the generating surface are found. The conditions are studied under which the contact lines envelope appears in the vicinity of the given contact point of the generating surface with beginning of undercutting simultaneously on the mating surface. The Wildhaber-Baxter problem of the limit normal location is a special case of the theory suggested. It is proved that the appearance of a contact lines envelope on the generating surface of skew worm-gears can be avoided and meshing conditions improved.