Epicyclic gear trains for automotive automatic transmissions

2000 ◽  
Vol 214 (5) ◽  
pp. 523-532 ◽  
Author(s):  
C-H Hsu ◽  
J-J Hsu
Keyword(s):  
Adjacency Matrix ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Systematic Methodology ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Admissible Graph

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.

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

2019 ◽  
Vol 10 (1) ◽  
pp. 82 ◽  
Author(s):  
Huafeng Ding ◽  
Changwang Cai
Keyword(s):  
Structural Characteristics ◽  
Main Shaft ◽  
Structural Synthesis ◽  
New Approach ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Transformation Relation ◽  
Gear Trains ◽  
Basic Graph ◽  
Patent Survey

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.

Automatic Detection of Embedded Structure in Planetary Gear Trains

1997 ◽  
Vol 119 (2) ◽  
pp. 315-318 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Automatic Detection ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of a planetary gear train is used to clarify the kinematic structure. Next, the concept of fundamental circuit is applied to derive an algorithm for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

The Detection of Embedded Structure in Planetary Gear Trains

1996 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Jin-Juh Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

Abstract The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of planetary gear trains are used to clarify the kinematic structure. Next, a method which is based on the concept of fundamental circuits for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains

2002 ◽  
Vol 124 (4) ◽  
pp. 662-675 ◽  
Author(s):  
V. V. N. R. Prasad Raju Pathapati ◽  
A. C. Rao
Keyword(s):  
Graph Isomorphism ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Graph Representations ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
A New Technique

The most important step in the structural synthesis of planetary gear trains (PGTs) requires the identification of isomorphism (rotational as well as displacement) between the graphs which represent the kinematic structure of planetary gear train. Previously used methods for identifying graph isomorphism yielded incorrect results. Literature review in this area shows there is inconsistency in results from six link, one degree-of-freedom onwards. The purpose of this paper is to present an efficient methodology through the use of Loop concept and Hamming number concept to detect displacement and rotational isomorphism in PGTs in an unambiguous way. New invariants for rotational graphs and displacement graphs called geared chain hamming strings and geared chain loop hamming strings are developed respectively to identify rotational and displacement isomorphism. This paper also presents a procedure to redraw conventional graph representation that not only clarifies the kinematic structure of a PGT but also averts the problem of pseudo isomorphism. Finally a thorough analysis of existing methods is carried out using the proposed technique and the results in the category of six links one degree-of-freedom are established and an Atlas comprises of graph representations in conventional form as well as in new form is presented.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

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.

Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Reference Frame ◽  
Power Efficiency ◽  
Power Flow ◽  
Flow Direction ◽  
Efficiency Analysis ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Two Degree Of Freedom

The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.

Applying Rigidity Theory Methods for Topological Decomposition and Synthesis of Gear Train Systems

2012 ◽  
Author(s):  
Maria Terushkin ◽  
Offer Shai
Keyword(s):  
Synthesis Method ◽  
Building Blocks ◽  
The Body ◽  
Computational Method ◽  
Gear Train ◽  
Graph Representation ◽  
Rigidity Theory ◽  
Graph Representations ◽  
Machine Theory ◽  
Gear Trains

This paper introduces a novel way to augment the knowledge and methods of rigidity theory to the topological decomposition and synthesis of gear train systems. A graph of gear trains, widely reported in the literature of machine theory, is treated as a graph representation from rigidity theory—the Body-Bar graph. Once we have this Body-Bar graph, methods and theorems from rigidity theory can be employed for analysis and synthesis. In this paper we employ the pebble-game algorithm, a computational method which allows determination of the topological mobility of mechanisms and the decomposition of gear trains into basic building blocks—Body-Bar Assur Graphs. Once we gain the ability to decompose any gear train into standalone components (Body-Bar Assur Graphs), this paper suggests inverting the process and applying the same method for synthesis. Relying on rigidity theory operations (Body-Bar extension, in this case), it is possible to construct all of the Body-Bar Assur Graphs, meaning the building blocks of gear trains. Once we have these building blocks at hand, it is possible to recombine them in various ways, providing us with a topological synthesis method for constructing gear trains. This paper also introduces a transformation between the Body-Bar graph and other graph representations used in mechanisms, thus leaving room for the application of the proposed synthesis and decomposition method directly to known graph representations already used in machine theory.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

A Study of the Duality Between Epicyclic Gear Trains and Beam Systems

2006 ◽  
Author(s):  
Gordon P. Pennock ◽  
Jeremiah J. Alwerdt
Keyword(s):  
Gear Train ◽  
Specific Design ◽  
Beam System ◽  
Dual Beam ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Design Requirements ◽  
Primary Contribution ◽  
Insight Into

This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.

Automatic Structural Synthesis of Epicyclic Gear Trains With One Main Shaft

2015 ◽  
Author(s):  
Huafeng Ding ◽  
Shuai Liu ◽  
Peng Huang ◽  
Changwang Cai ◽  
Zhen Huang
Keyword(s):  
Automobile Industry ◽  
Structural Characteristics ◽  
Graph Representation ◽  
Synthesis Process ◽  
Automatic Method ◽  
Main Shaft ◽  
Topological Graphs ◽  
Epicyclic Gear ◽  
Adjacency Matrices ◽  
Gear Trains

Design of automatic gear boxes with better performance is a pursuit goal of the modern automobile industry. In order to develop CAD method for the creative design of automatic gear boxes, this paper proposes an automatic method for the structure synthesis of one degree of freedom (DOF) epicyclic gear trains (EGTs) with one main shaft which serve as the key mechanisms in automatic gear boxes. First, based on the graph representation of EGTs, the canonical perimeter graphs and the corresponding canonical adjacency matrices are obtained. Then, based on the canonical adjacency matrices, the characteristic number strings are obtained and used to identify isomorphism in the synthesis process. Third, an automatic method is proposed to generate the basic graphs of the topological graphs of EGTs, and the basic graphs up to 9 links are synthesized. After that, based on the structural characteristics for the graphs of EGTs, an automatic method is proposed to synthesize the topological graphs of EGTs from the basic graphs, and an algorithm for the detection of rigid subchains in EGTs is also presented. Finally, a program is developed, and 1-DOF EGTs having one main shaft with up to 9 links are synthesized.

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