New Method for Isomorphism Identification of Planetary Gear Trains based on Traversing Loop

Jiawen Ding; Wei Sun

doi:10.16578/j.issn.1004.2539.2020.12.010

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New Method for Isomorphism Identification of Planetary Gear Trains based on Traversing Loop

Design· Calculation | 更新时间：2022-11-10

- New Method for Isomorphism Identification of Planetary Gear Trains based on Traversing Loop
- Journal of Mechanical Transmission Vol. 44, Issue 12, Pages: 61-67(2020)
- 作者机构：
  
  1.武汉科技大学机械自动化学院，湖北武汉 430081
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.12.010
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丁佳文,孙伟.基于遍历环路的行星轮系同构判定新方法[J].机械传动,2020,44(12):61-67.

Ding Jiawen,Sun Wei.New Method for Isomorphism Identification of Planetary Gear Trains based on Traversing Loop[J].Journal of Mechanical Transmission,2020,44(12):61-67.
丁佳文,孙伟.基于遍历环路的行星轮系同构判定新方法[J].机械传动,2020,44(12):61-67. DOI： 10.16578/j.issn.1004.2539.2020.12.010.

Ding Jiawen,Sun Wei.New Method for Isomorphism Identification of Planetary Gear Trains based on Traversing Loop[J].Journal of Mechanical Transmission,2020,44(12):61-67. DOI： 10.16578/j.issn.1004.2539.2020.12.010.

摘要

同构判定是行星轮系构型综合时必不可少的过程之一，对于设计新颖的、具有优良传输特点的行星轮系具有重要的意义。提出了一种基于遍历环路判定行星轮系同构的新方法。首先，提出了一种遍历环路的新型环路矩阵来描述行星轮系拓扑图的基本特征的新方法，该矩阵包含行星轮系拓扑结构的所有信息；然后，定义了遍历环路的规则及其优先级，确保描述的唯一性；接着，基于改进哈明数原理和行星轮系的新型环路矩阵，获得行星轮系的环路码、环路序列和环路度，通过判断环路码和环路序列和环路度3个结构特征是否相等来判断是否同构；最后，通过案例验证了该方法的有效性和可靠性。

Abstract

Isomorphism identification is one of the indispensable processes in structure synthesis of planetary gear trains. It is of great significance for the creation of novel planetary gear train with excellent transmission characteristics. A new method for identifying isomorphism of planetary gear trains based on traversing loops is proposed. Firstly，a new method for describing the topological diagram basic characteristics of planetary gear trains by the new loop matrix is proposed. This matrix contains all the information of the topological structure of planetary gear trains. Then，the rule to traverse loops and its priority is defined，to make sure that there is the uniqueness of description. Then，the loop code，the loop sequence and loop degree of planetary gear trains are obtained based on the principle of improved Hamming number and the new loop matrix. By distinguishing whether the structural constants of the loop code，the loop sequence and loop degree are equal，the isomorphism of the planetary gear trains is identified. Finally，the validity and reliability of the method are verified by many examples.

关键词

行星轮系遍历环路同构判定新型环路矩阵

Keywords

Planetary gear trainTraversing loopIsomorphism identificationImproved loop matrix

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