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.

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.

Compound Topological Invariant Based Method for Detecting Isomorphism in Planar Kinematic Chains

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Rongjiang Cui ◽  
Wenjian Yang ◽  
Chuanyu Wu
Keyword(s):  
Detection Method ◽  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Fourth Power ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Simple Detection ◽  
Gear Trains

Abstract An important step in the structural synthesis of kinematic chains (KCs) or mechanisms is the detection of isomorphic structures. Although many detection methods have been proposed, most of them require complex computations and have poor versatility. In this study, a simple detection method is proposed based on a compound topological invariant (CTI), which comprises the fourth power of adjacency matrix and eigenvalues. Besides two complex 15- and 28-link planar simple-joint KCs (PSKCs), the method is tested on the complete atlas of contracted graphs with up to six independent loops, PSKCs with up to 13 links, 8-link 1-degree-of-freedom (DOF) planar multiple-joint KCs (PMKCs), and 6-link 1-DOF planetary gear trains (PGTs). All the results are in agreement with the reported results in the literature. Our method possesses good versatility and has been verified as being reliable and efficient.

Topological invariant and definition method for detecting isomorphism in planar kinematic chains

2020 ◽  
pp. 095440622096078
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Liang Sun ◽  
Chuanyu Wu
Keyword(s):  
Planetary Gear ◽  
Topological Invariant ◽  
Detection Methods ◽  
Kinematic Chains ◽  
Essential Step ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Isomorphism Identification

Isomorphism identification is an essential step in mechanism configuration synthesis. Although various detection methods have been proposed, some of them can only effectively identify kinematic chains (KCs) within 10 links or complex programs that are needed to identify multilink KCs. In this study, a new isomorphism identification method is proposed based on the distance concept of graphs and the graph theory definition of isomorphism. In addition to two complex 21- and 28-link planar simple-joint KCs (PSKCs), the proposed algorithm is tested on the complete atlas of 8-link 1-DOF, 9-link 2-DOF, 10-link 1-DOF, 12-link 1-DOF, and 13-link 2-DOF PSKCs. The algorithm is also tested on 6-link 1-DOF and 7-link 1-DOF planetary gear trains (PGTs) to detect isomorphism. All results are in agreement with those of the existing literature. The method is fully automated via a computer program and has been verified to be reliable and efficient.

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.

Synthesis method for planetary gear trains without using rotation graphs

2021 ◽  
pp. 095440622199839
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Liang Sun ◽  
Guanghui Zheng ◽  
Chuanyu Wu
Keyword(s):  
Synthesis Method ◽  
Planetary Gear ◽  
Synthesis Methods ◽  
Intermediate Step ◽  
Automatic Method ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Fully Automatic ◽  
Configuration Synthesis ◽  
Isomorphism Identification

The displacement graphs (d-graphs) are the final form of planetary gear trains (PGTs) synthesis. The existing configuration synthesis methods for the d-graphs of PGTs need rotation graphs (r-graphs) as the intermediate step and produce a large amount of isomorphic KCs. This paper proposes a method to obtain d-graphs directly from the geared graph. Meanwhile, a uniform isomorphism identification method suitable for parent graphs, geared graphs, and d-graphs is presented. Finally, a fully automatic method based on parent graphs is tested on synthesizing 1-DOF PGTs with up to nine links. Our synthesis results and those in the literature are comparatively analyzed, and the reasons for contradictory synthesis results are analyzed.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

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.

Dynamic Modeling of the Torsional Vibration of the Slewing Mechanism of a Hydraulic Excavator

2012 ◽  
Vol 253-255 ◽  
pp. 2102-2106 ◽  
Author(s):  
Xu Juan Yang ◽  
Zong Hua Wu ◽  
Zhao Jun Li ◽  
Gan Wei Cai
Keyword(s):  
Torsional Vibration ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Moment Of Inertia ◽  
Hydraulic Excavator ◽  
Planetary Gear Trains ◽  
Vibration Model ◽  
Gear Trains ◽  
The Moment ◽  
Relationship Of

A torsional vibration model of the slewing mechanism of a hydraulic excavator is developed to predict its free vibration characteristics with consideration of many fundamental factors, such as the mesh stiffness of gear pairs, the coupling relationship of a two stage planetary gear trains and the variety of moment of inertia of the input end caused by the motion of work equipment. The natural frequencies are solved using the corresponding eigenvalue problem. Taking the moment of inertia of the input end for example to illustrate the relationship between the natural frequencies of the slewing mechanism and its parameters, based on the simulation results, just the first order frequency varies significantly with the moment of inertia of the input end of the slewing mechanism.

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