Kinematic Analysis of Planetary Gear Trains Based on Topology

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Ming-Fei Gao ◽  
Ji-Bin Hu
Keyword(s):  
Automatic Transmission ◽  
Planetary Gear ◽  
Graph Representation ◽  
Speed Ratio ◽  
Topological Graph ◽  
Planetary Gear Trains ◽  
And Topology ◽  
Conceptual Design Phase ◽  
Gear Trains ◽  
The Relationship

Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

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.

scholarly journals The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879410 ◽  
Author(s):  
Yahui Cui ◽  
Jing Gao ◽  
Xiaomin Ji ◽  
Xintao Zhou ◽  
Haitao Yan
Keyword(s):  
Power Flow ◽  
Flow Analysis ◽  
Planetary Gear ◽  
Topological Graph ◽  
Template Model ◽  
Power Flow Analysis ◽  
Analysis Process ◽  
Planetary Gear Trains ◽  
Graphical View ◽  
Gear Trains

The concept of multi-attribute topological graph is proposed in this article to represent the characteristics of both structure and state for typical one-degree-of-freedom planar spur closed planetary gear trains. This method is well applied in power flow analysis and provides a graphical view for the types, values, directions, and transmission relationship of power flow, especially for the recirculation power representation. Furthermore, a template model of multi-attribute topological graph for closed planetary gear trains is also presented, which would be helpful to the multi-attribute topological graph generation for some certain types of closed planetary gear trains just by changing symbols in the template model. A corresponding software is also developed to make the analysis process more convenient. By inputting different parameters, the different visual results can be obtained automatically, thus benefiting engineers in conceptual design.

Study on the Method of Planetary Gear Trains Based on Topological Theory

2013 ◽  
Vol 568 ◽  
pp. 169-175 ◽  
Author(s):  
Ya Feng He ◽  
You Ming Wang
Keyword(s):  
Planetary Gear ◽  
Basic Structure ◽  
Graph Representation ◽  
Topological Graphs ◽  
Topological Theory ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
New System

The method research of planetary gear trains (PGTs) by applying topological theory is very significance in searching for innovative planetary trains. A new graph representation and stratification standard are introduced firstly. Then three topological graphs of basic structure of PGTs are established as the basis of synthesis theory. Next several kinds of planetary trains with small teeth difference and method of isomorphic determination are presented, thus built up the procedure of PGTs by graphs and example. Finally a new system of classification and synthesis for PGTs is put forward according to the feature of loops in topological theory.

New Graph Representation for Planetary Gear Trains

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding ◽  
Bin Zi ◽  
Dan Zhang
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Planetary Gear ◽  
Graph Representation ◽  
Synthesis Process ◽  
Planetary Gear Trains ◽  
Computer Aided ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Canonical Rotation

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

The Research and Design on the Electric Vehicles’ Centrifugal Automatic Transmission

2014 ◽  
Vol 721 ◽  
pp. 12-15
Author(s):  
Yi Fan
Keyword(s):  
Electric Vehicles ◽  
Optimization Design ◽  
Simple Structure ◽  
Automatic Transmission ◽  
Planetary Gear ◽  
Design Concepts ◽  
Transmission Parameters ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Research And Design

Aiming at the deficiencies of the commonly used AMT and DSG structure in the electric vehicles’ transmission, a kind of three-speed automatic transmission structured by the planetary gear trains is designed. It uses the centrifugal components to realize the gear shifting, while using the electromagnetic brake and the motor reversal to realize the reversing. Based on the design concepts proposed, we did some matching calculations on the transmission system of a three-wheel pure electric vehicle, and finally made the optimization design on the driving motor’s selection and transmission parameters. The designed electric vehicle’s centrifugal automatic transmission has the characteristics of simple structure, small size and shifting smoothness, which can not only meet the requirements of the automobile power, but also improve the efficiency of the driving motor.

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.

scholarly journals A new method for isomorphism identification of planetary gear trains

2021 ◽  
Vol 12 (1) ◽  
pp. 193-202
Author(s):  
Wei Sun ◽  
Ronghe Li ◽  
Jianyi Kong ◽  
Anming Li
Keyword(s):  
Detection Method ◽  
Planetary Gear ◽  
Distance Matrix ◽  
New Method ◽  
Topological Graph ◽  
Weighted Distance ◽  
Planetary Gear Trains ◽  
The Matrix ◽  
Gear Trains ◽  
Isomorphism Identification

Abstract. Planetary gear trains (PGTs) are widely used in machinery such as vehicles, pulley blocks, wrist watches, machine tools, and robots. During the process of structural synthesis of PGTs using graph theory, isomorphism identification of graphs is an important and complicated problem. The reliability of the isomorphism detection method directly determines the accuracy of the synthesis result. In this paper, a novel isomorphism identification method for PGTs is proposed. First, a new weighted adjacent matrix is presented to describe the topological graph of PGTs, which has is unique in describing the structure of PGTs. Then, the weighted distance matrix is proposed and the sum of the matrix is obtained, which can determine whether the planetary gear trains is isomorphic or not. Eventually, the examples demonstrate that this new method can be accurately and effectively performed.

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