Nomographs and Feasibility Graphs for Enumeration of Ravigneaux-Type Automatic Transmissions

Abstract

Although there are many epicyclic-type automatic transmissions in production, the related configuration design methods are still tedious and borne to human error. A simple methodology for the systematic design of the Ravigneaux-type epicyclic gear transmissions needs to be developed. First, fundamentals and gear-shifting of four-speed and six-speed epicyclic-type automatic transmissions are illustrated to establish the design requirements. Second, based on the kinematic nomographs of the corresponding basic gear ratios, a simple clutching-sequence method is proposed and illustrated. Next, a planar-graph representation is presented to arrange the desired clutches for each possible clutching sequence into the epicyclic gear mechanism. Then, with the above methods, the systematic designs of the epicyclic gear mechanisms are given for demonstrating the feasibility of the proposed methodology. The result of this work shows that the seven-, eight-, and nine-link two-DOF Ravigneaux-type epicyclic gear mechanisms could reach four-, six-, and eight-forward speeds at most, respectively. New five-, six-, seven-, and eight-velocity automatic transmissions are enumerated from the two-ring eight-and nine-link Ravigneaux gear mechanisms. It is a major breakthrough to design completely satisfactory eight-speed automatic transmissions from the nine-link Ravigneaux gear mechanism.

Application of Complex Game-Tree Structures for the Hsu Graph in the Analysis of Automatic Transmission Gearboxes

“…The torque analysis and mechanical analysis are described, among others, in the works [26][27][28][29][30][31][32]. During the process of kinematic structure enumeration using graph theory, isomorphism identification of graphs is an important and complicated problem.…”

A universal kinematic analysis of geared mechanisms

“…The Ravigneaux gear train shown in Fig. 2a contains five GPEs: two internal GPEs (7,2,3) and (7,11,3), and three external GPEs (7, 1, 3), (7,8,3), and (8,5,3), while the simple planetary gear train shown in Fig. 2b contains three GPEs: one internal GPE (9, 4, 5) and two external GPEs (9, 1, 5) and (9,14,5).…”

“…The Humbage bevel gear train shown in Fig. 7 contains three GPEs; (1, 2, 3), (2,4,3) and (2′, 5, 3).…”

“…The following review on the kinematic of PGTs cannot be considered complete since a review of all contributions in this field is not the objective of this work. Many efforts are made to develop effective approaches to the kinematic analysis of PGTs [1][2][3][4][5][6]. Freudenstein et al [7] used efficiently the concept of fundamental circuit for the kinematic of PGTs.…”

A review of graph theory application research in gears

“…Other researches 81–83 were about topological synthesis of gear trains. Besides, some new researches about graph and gears are also presented in papers, 84–91 which introduce different analysis methods than before.…”