GEOMETRY DESIGN OF A NOVEL ELEMENTARY PLANETARY GEAR TRAIN WITH HYPERBOLIC TOOTH-PROFILES

Abstract

This work presents a novel concept of elementary planetary gear trains such that the tooth-profiles of the pinion are hyperbolic. The pitch radius is kinematically replaced by the distance between the gear center and the tooth center. The triple vector product of differential geometry is used to derive the equation of meshing. A program is developed to solve the conjugate surface equations, and to show the solid modeling of proposed elementary planetary gear trains. This approach can be applied to design the elementary planetary gear trains in which the pinion is with hyperbolic tooth-profiles. The proposed novel elementary planetary gear trains can operate smoothly, can transmit more precision, can endure higher torque, and are more compact than traditional planetary gear trains.