Optimization of Gear Ratios for Epicyclic Gear Train Transmissions

Abstract

An interactive design system has been developed for the automotive epicyclic gear trains that can provide at least three forward gears and one reverse gear. This user-friendly windowing system can access help files, display the functional representation of a mechanism, optimize the gear ratios for epicyclic gear trains and present the numerical results. The optimization procedure to find the optimum gear ratios and the corresponding number of gear teeth is the Augmented Lagranigian Multiplier Method, and can be applied to all gear trains having sets of three gears in which a ring gear is connected to a sun gear through a planetary gear. The procedure does not change for either different clutching sequences or number of clutches. The method is demonstrated for the Simpson and THM 440 gear trains. The gear teeth combinations are found such that they achieve the optimized gear ratios within less than 1% and satisfy the geometric constraints. An extension of the optimization procedure to the Ravigneaux gear train is also developed. PHIGS graphics functions are used in program routines to display the functional schematic of an epicyclic gear train on the computer screen. These routines are written in such a manner that other types of gear combinations can be displayed by simply adding additional modules to represent these new gear elements.