Tooth profile generation and analysis of oval gears with circular-arc teeth

An oval gear drive, which is used in an oil pump with larger pumping volume, is generated by using a rack cutter with circular-arc teeth. The generated oval gears have convex–concave tooth profile contact. The mathematical models of oval gears with circular-arc teeth are derived based on the theory of gearing and gear generation mechanism. Owing to its complex geometry, the pitch curves and tooth profiles of oval gears may exhibit convex–concave centrodes and tooth undercutting, respectively. A rack cutter with circular-arc teeth cannot be used to generate oval gears with convex–concave centrodes. Therefore, curvature analysis is utilized to design oval centrodes with convex curves. The equation of singular point is utilized to analyze tooth undercutting. In addition, a computer simulation program is developed to generate the tooth profiles of oval gears with circular-arc teeth having convex centrodes and without tooth undercutting. Various numerical examples illustrate the computerized design process.