Manifold Conjugation and Discrete Gear Design

This paper presents a new conjugation theory and a new design methodology for the advanced conjugation design based on CAD (computer aided design) and CAE (computer aided engineering). A general conjugation theory called manifold conjugation is established based on the classic conjugation theory and manifold theory. It leads to both smooth conjugation modeling and discrete conjugation modeling. The former one has been studied in the previous work for design optimization of analytical conjugation properties. The latter one is a desirable methodology for the conjugation design based on CAE simulation. The paper brings up a new perspective towards conjugation representation theory, leading to a new design process. Contrary to the traditional idea that CAD has to be known before and separated from CAE, the new theory suggests using discrete manifold to bridge CAD and CAE. Furthermore, discrete modeling techniques from CG (computer graphics) such as subdivision can be employed for conjugation modeling and design. Two planar examples that minimize gear PPTE (peak to peak transmission error) show that the methodology is capable of and effective in conjugation optimization.