Application of fuzzy entropy for the rating of epicyclic gear trains

Abstract

A Planetary gear train (PGT) is a system containing a total of three or more gears where a ring gear encircles the entire system. There are three main parts to planetary gear systems, often called sun, planet and ring gears. High power density in a lesser volume is the main advantage of a PGT. Due to high bearing loads and design complexity of planetary gear train and its inaccessibility for the operator to check, it is necessary to rate the planetary gear trains quantitatively. Planetary gear trains can be modelled as fuzzy systems, so that fuzzy logic can be applied. It is shown that fuzzy entropy can be utilised to compare many planetary gear trains in the enumeration stage from the viewpoint of rigidity and compactness. Graph theory is proved a powerful tool by many researchers in the enumeration and synthesis of planar kinematic chains and epicyclic gear trains. In the present work, fuzzy entropy is applied to estimate compactness in the rating of planetary gear trains, which is analogous to parallelism in kinematic chains. Each epicyclic gear train is represented by a graph. All the 4-, 5- and 6-link 1-DOF planetary gear trains in Appendix 1 are rated and results are presented.