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and
Machine Theory
Mechanism and Machine Theory 43 (2008) 791–811
ate/mechmt
Research on basic principle of moulding-surface conjugation
HouJun Chen a,*, ZhenYun Duan b, Jian Liu a, HongJi Wu a
a School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, PR China
b School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110023, PR China
Received 14 April 2006; received in revised form 8 April 2007; accepted 3 July 2007
Available online 4 September 2007
Abstract
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 mon generator, this case is termed as moulding-surface conjugation. In this paper, the basic prin-
ciples 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 con-
jugation 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 con-
tact between the design and manufacture of tooth surface. These researches lay the foundation for transforming the prin-
ciple of moulding-surface conjugation into the practical application.
Ó 2007 Elsevier Ltd.