The Complete Set of One-Degree-of-Freedom Planetary Gear Trains With Up to Nine Links

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Exact Results ◽  
Planetary Gear Trains ◽  
Past Half Century ◽  
Gear Trains ◽  
Complete Set ◽  
Fully Automatic ◽  
First Time

The structural synthesis of planetary gear trains (PGTs) is helpful for innovating transmission systems in machinery. A great deal of research has been devoted to the synthesis of one-degree-of-freedom (1-DOF) PGTs over the past half century. However, most synthesis methods are limited to PGTs with no more than eight links. Moreover, the synthesis results are not consistent with each other. Until now, the inconsistency of synthesis results is still unresolved and exact synthesis results remain elusive. This paper presents a systematic and fully automatic method based on parent graphs to synthesize 1-DOF PGTs. The complete database of rotation graphs (r-graphs) and displacement graphs (d-graphs) of 1-DOF PGTs with up to nine links is established for the first time. All possible reasons for the contradictory synthesis results in the literature are analyzed and the controversy in the existing synthesis results which has lasted for nearly half a century is completely resolved. The exact results of the 6-, 7-, and 8-link r-graphs are confirmed to be 27, 152, and 1070, respectively. The exact results of the 6-, 7-, and 8-link d-graphs are confirmed to be 81, 647, and 6360, respectively. Additionally, the new results of 8654 r-graphs and 71,837 d-graphs of 9-link PGTs are provided for the first time.

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.

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.

Conditions for Self-Locking in Planetary Gear Trains

2006 ◽  
Vol 129 (9) ◽  
pp. 960-968 ◽  
Author(s):  
David R. Salgado ◽  
J. M. del Castillo
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
The Self ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Analytical Expression ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Approximate Relationship ◽  
Gear Trains

The objective of the present work is to determine the conditions that have to be satisfied for a planetary gear train of one degree of freedom to be self-locking. All planetary gear trains of up to six members are considered. As a result, we show the constructional solutions of planetary gear trains exhibiting self-locking. Unlike other studies, the self-locking conditions are obtained systematically from the analytical expression for the product of the efficiency of a given train by the efficiency of the train resulting from interchanging its input and output axes. Finally, a proof is given of an approximate relationship between these two efficiencies.

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.

Influence of the Operating Conditions of Two-Degree-of-Freedom Planetary Gear Trains on Tooth Friction Losses

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Power Loss ◽  
Power Flow ◽  
Planetary Gear ◽  
Operating Conditions ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Friction Loss ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Two Degree Of Freedom

In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application.

Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains

1991 ◽  
Vol 113 (1) ◽  
pp. 10-16 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Topological Analysis ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Graph Representation ◽  
Straightforward Manner ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Gear Trains

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.

Detection of Degenerate Structure in Single Degree-of-Freedom Planetary Gear Trains

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
Graph Theory ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Structural Synthesis ◽  
Drastic Reduction ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Planetary Gear Trains ◽  
Gear Trains

Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

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.

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