Abstract: Topological graph using functional fractionation methods is presented to describe epicyclic gear trains (EGTs). Three levels of topological units are established. It is summarized that three basic units compose complex EGTs. Based on the combinational characteristics of basic units, four combination modes are put forward. Micro-transformation is performed on topological graph and stratified adjacency matrix is established, approaches of isomorphism criterion are given that provide theoretical basis for topological synthesis of EGTs. According to the characteristics of loops in topological graphs, common EGTs are divided into four kinds of gear trains. By taking EGTs containing six gears for instance, statistical methods for four sorts of EGTs are derived. For each combination of basic units, topological atlases are synthesized by evolution rules and various possible EGTs are deduced by inversion rules. The results show that topological synthesis method is a convenient and effective method for constructing innovative planetary mechanisms. The method may be universally applied to the topological synthesis of multimember EGTs.

Key words: Epicyclic gear train, Functional fractionation, Topological synthesis, Cutting loads, Hob spindle system, Vibration response, High-speed dry bobbing