Hypoid Gear Line Contact Meshing using Third-Order Surface and Tooth Contact Pattern

摘要

Hypoid gears are the most general form of gearing, and their theoretical solution have been long in coming. Many guesses or theorems about the gearing have been proposed, but some of them correct and many of them wrong. The tooth surfaces are parts of general curved surface and they must have principal directions and principal curvatures on every contact point. But there have been no discussion on such fundamental elements of the surface and they are still based on a contact analysis of second-order tooth surface. In this report, the tooth surfaces of a hypoid pinion and gear meshing with each other in line contact are expressed by third-order surface, and the requirements for those two surfaces to be in line contact are discussed, and the relationships between the third-order surface coefficient and the contact pattern of the surface are investigated theoretically to analyze the tooth bearing pattern.