Research on basic principle of moulding-surface conjugation

The tooth surfaces of spur gear, straight bevel gear, involute helical gear, Wildhaber worm and Wildhaber–Novikov gear are generated by moving a generator (a straight-line or a circular-arc) along a directrix (a trajectory curve), and their surface normals at all points of the same generator are coplanar. In geometric terms, the surfaces with such geometric properties are called moulding surface. When a pair of conjugate surfaces is moulding surfaces and their instantaneous contact-line is the common generator, this case is termed as moulding-surface conjugation. In this paper, the basic principles of this conjugation are developed. Based on the shape of the generators, this conjugation is classified into three types, and corresponding conjugate conditions are investigated. In order to examine the existence of conjugation, the structure conditions, embodying the transmission types and the characteristics of the directrix, are discussed. Moulding-surface conjugation can be studied by means of a pair of directrixes, so that the process of discussion is simplified. This conjugation can also be studied with the generating surface by introducing the indirect generating method, which establishes direct contact between the design and manufacture of tooth surface. These researches lay the foundation for transforming the principle of moulding-surface conjugation into the practical application.