Geometric design of a planetary gear train with non-circular gears

Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions

The synthesis of elliptical gears is formulated using envelope theory by means of a suitable shaper-cutter with involute tooth profile. A general algorithm producing the pitch curves of elliptical gears and their rack with any number of lobes is proposed. Evolutes of pitch curves can be also obtained in order to choose a suitable shaper-cutter, even for pitch curves with concave-convex profiles. The complete synthesis of both meshing elliptical gears and their rack is reported, several graphical results being shown for design and analysis purposes. Computer animations are also available.

The Synthesis of Elliptical Gears Generated by Shaper-Cutters

Linkage model and manufacturing process of shaping non-circular gears

New developments in variable radius gears using constant pressure angle teeth

Computerized tooth profile generation of elliptical gears manufactured by shaper cutters

An elliptical gear drive, whose rotation axis coincides with its geometric center, is simulated using generation with a rack cutter The mathematical model of an elliptical gear based on the theory of gearing and gear generation mechanism is also developed. Owing to its complex geometry, the profile of elliptical gears may exhibit tooth undercutting, and pointed teeth. In addition, tooth undercutting of an elliptical gear based on the developed mathematical model of the elliptical gear and the theory of gearing is also investigated. Pointed teeth usually appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent the pointed teeth appearing on elliptical gears. Furthermore, a computer simulation program is developed to generate the tooth profile of elliptical gears without tooth undercutting and pointed teeth. Various numerical examples illustrate the effectiveness of the computerized design process.

Computer Aided Design of Elliptical Gears

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

Computer aided design of elliptical gears with circular-arc teeth

A circular-arc elliptical gear drive with convex (or concave) tooth profiles, which is used in an oil pump with a larger pumping volume, was simulated by using circular-arc shaper cutters with concave (or convex) tool profiles. Mathematical models of circular-arc elliptical gears, based on the theory of gearing and the gear generation mechanism, were also developed. The generated elliptical gear drive has a convex-concave tooth profile contact. Because of its complex geometry, the profile of circular-arc elliptical gears may exhibit tooth undercutting, and pointed teeth. Pointed teeth usually appear on the major axis of the elliptical pitch curve. A geometric relation was developed and applied to prevent the pointed teeth on the elliptical gears. A larger pressure angle at major axis and circular-arc radius can eliminate tooth undercutting and increase its tooth thickness at the addendum circle for small teeth. Moreover, a computer simulation program was developed to generate the tooth profile of circular-arc elliptical gears without tooth undercutting and pointed teeth.

Biing-Wen Bair

Papers

Computerized tooth profile generation of elliptical gears manufactured by shaper cutters

Computer Aided Design of Elliptical Gears

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

Computer aided design of elliptical gears with circular-arc teeth

Mathematical Model and Characteristic Analysis of Elliptical Gears Manufactured by Circular-Arc Shaper Cutters