Synthesis Of Epicyclic Gear Trains Research Articles

Patent Analysis and Structural Synthesis of Epicyclic Gear Trains Used in Automatic Transmissions

A patent survey is conducted to investigate the application status of epicyclic gear trains (EGTs) used in automatic transmissions (ATs). In this regard, 673 AT patents are investigated firstly, and 274 different EGTs are obtained after the patent processing. EGTs are presented by corresponding double bicolor graphs (DBGs) and they are sorted into 13 groups in accordance with the degree of freedom (DOF) of DBGs and the degree of hollow vertices. Then, structural characteristics of obtained EGTs, which are used to detect whether the EGTs obtained in the future can be used in ATs, are analyzed and summarized. Finally, a new approach is proposed to obtain new configurations of the EGTs with one main shaft based on the transformation relation between DBG and the basic graph. Several examples are presented to illustrate the validity of the proposed approach.

Enumeration of displacement graphs of epicyclic gear train from a given rotation graph using concept of building of kinematic units

Use of graph theory for enumeration of Epicyclic gear trains (EGTs) is common during conceptual stage. According to theory of structural synthesis of EGTs, two kinds of graphs are defined namely rotation and displacement graphs, for a given number of links and one degree of freedom. In case, all the non-isomorphic rotation graphs are enumerated, then the next stage of synthesis involves the generation of displacement graphs for each rotation graph. To this end, given a rotation graph, the present work proposes an algorithm for generation of all the displacement graphs. Firstly, the rotation graph is decomposed into modules called kinematic units (KUs). Then, for each KU, all the edge-labeling possibilities of turning pairs are evaluated. Finally, displacement graphs are obtained by building the edge labeled KUs in all possible ways. Acyclic graph based representation is employed and displacement graphs with and up to 7 links are enumerated. The enumeration of displacement graphs is treated as two different cases corresponding to rotation graphs enumerated using recursive and non-recursive schemes and the results are in agreement with C.H. Hsu and others.

Synthesis of epicyclic gear trains with one and two degrees of freedom from kinematic chains belonging to minimal sets

The enumeration of kinematic chains for epicyclic gear trains allows obtaining all the possible configurations from specified structural characteristics. However, the more complex becomes the desired structure, the greater the number of options to analyse in order to select the most suitable one, therefore, it is necessary a criterion to reduce this range of choices. The variety of kinematic chains and the concept of minimal sets can be used for this purpose. This paper enumerates the kinematic chains with zero variety for epicyclic gear trains with one and two degrees of freedom, and with up to four independent loops. Some epicyclic gear trains generated from the chains belonging to minimal sets are presented afterward, and the advantages of using zero variety chains are discussed.

Synthesis of epicyclic gear trains with one and two degrees of freedom from kinematic chains belonging to minimal sets

The enumeration of kinematic chains for epicyclic gear trains allows obtaining all the possible configurations from specified structural characteristics. However, the more complex becomes the desired structure, the greater the number of options to analyse in order to select the most suitable one, therefore, it is necessary a criterion to reduce this range of choices. The variety of kinematic chains and the concept of minimal sets can be used for this purpose. This paper enumerates the kinematic chains with zero variety for epicyclic gear trains with one and two degrees of freedom, and with up to four independent loops. Some epicyclic gear trains generated from the chains belonging to minimal sets are presented afterward, and the advantages of using zero variety chains are discussed.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Innovation Synthesis of Basic Configurationof Epicyclic Gear Trains with Three-Degrees of Freedom

Epicyclical gear trains with three-degrees of freedom have found its wide application as the development of new technique. Currently, nearly all domestic researches on epicyclical gear trains with three or more degrees of freedom are aimed at the practical application, and scare works systematically investigate basic configuration and synthesis of the train system. An innovation synthesis method is proposed based on the compound joint kinematic chain and the substitution of low pair with high pair for epicyclical gear trains with three-degrees of freedom, and the possible independent basic configurations of epicyclical gear trains with three-degrees of freedom are obtained by applying the proposed method and the utilization of the method is also discussed. The method provides not only a new approach for innovation synthesis of epicyclical gear trains but also a few basic configurations of epicyclical gear trains with three-degrees of freedom for practice design.

STUDY ON TOPOLOGICAL SYNTHESIS OF EPICYCLIC GEAR TRAINS BASED ON FUNCTIONAL FRACTIONATION

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.

Epicyclic gear trains for automotive automatic transmissions

Epicyclic gear trains, which contain at least four coaxial links, are widely used in automatic transmissions. This paper presents a systematic methodology for the synthesis of epicyclic gear trains for automotive automatic transmissions. The graph representation of epicyclic gear trains is applied to develop an approach for the structural synthesis of the graphs of admissible epicyclic gear trains. Next, for each admissible graph the adjacency matrix of an epicyclic gear train is defined to develop an algorithm for the configuration synthesis of epicyclic gear trains. Using the proposed algorithm, all possible epicyclic gear trains for automotive automatic transmissions are systematically synthesized. In this paper, admissible epicyclic gear trains with up to ten links have been successfully synthesized. The results of work will lead to the creation of new multispeed automotive automatic transmissions.

A Graph Grammar Approach for Structure Synthesis of Mechanisms

This paper presents a general graph grammar methodology for structure synthesis of mechanisms. Much of current mechanism design is based on a systematic method popularized by Freudenstein, Mruthyunjaya, and Tsai (among others). A graph grammar is a more natural expression for a method that relies on algebraic abstractions of graph theoretic principles. Our proposed grammar rules add vertices and loops to a start graph to obtain desired structural requirements. A grammar adaptation of an existing linear time algorithm for the detection of isomorphism is presented. Also presented is a specialized grammar for the structure synthesis of Epicyclic Gear Trains. A valid graph grammar for structure synthesis of mechanisms enables both the eventual automation of general atlas construction and atlas construction for customized mechanism classes. [S1050-0472(00)01904-8]

Application of edge permutation group to structural synthesis of epicyclic gear trains

A method of selecting nonisomorphic graphs is introduced with the aid of graph enumeration theory. Edge permutations which are induced from the symmetric group of vertex permutations are used as mapping functions to identify nonisomorphic graphs. This method is applied to the enumeration of nonisomorphic graphs of epicyclic gear trains. The results with 7 elements are presented in detail.

Closure to “Discussion of ‘An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains’” (1987, ASME J. Mech. Transm. Autom. Des., 109, p. 337)

Closure to “Discussion of ‘An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains’” (1987, ASME J. Mech. Transm. Autom. Des., 109, p. 337)

An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains

In this paper, a random number technique for computing the value of a linkage characteristic polynomial is shown to be an effective method for identifying isomorphic graphs. The technique has been applied to the topological synthesis of one-degree-of-freedon, epicyclic gear trains with up to six links. All the permissible graphs of epicyclic gear trains were generated by a systematic procedure, and the isomorphic graphs were identified by comparing the values of their corresponding linkage characteristic polynomials. It is shown that there are 26 nonisomorphic rotation graphs and 80 displacement nonisomorphic graphs from which all the six-link, one-degree-of-freedom, epicyclic gear trains can be derived.

Erratum: “Synthesis of Epicyclic Gear Trains Using the Velocity Ratio Spectrum” (Journal of Engineering for Industry, 1960, 82, pp. 173–178)

Errata Erratum: “Synthesis of Epicyclic Gear Trains Using the Velocity Ratio Spectrum” (Journal of Engineering for Industry, 1960, 82, pp. 173–178) R. C. Brewer R. C. Brewer Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information J. Eng. Ind. Nov 1960, 82(4): 444 https://doi.org/10.1115/1.3664275 Published Online: November 1, 1960 Article history Online: December 9, 2011

Synthesis of Epicyclic Gear Trains Using the Velocity Ratio Spectrum

For a simple epicyclic train, the controlling element is almost invariably fixed, i.e., prevented from rotating by being connected, in some way, to the frame. Such trains are easy to synthesize because there are a limited number of variations of the three basic elements and, normally, six equations will define all possible velocity ratios. For a compound epicyclic train, the number of equations is considerably increased. A method of synthesizing compound epicyclic trains is developed using the concept of a velocity ratio spectrum. To facilitate the application of this concept, only one train in a compound epicyclic train is regarded as basic; all others are considered as merely serving the purpose of modifying the motion of the controlling element in the basic train.