Calculation Method of Planetary Gear Train Transmission Ratio based on Adjacency Matrix

Zhao Wang; Xinping Wang; Jiexin Zhang

doi:10.16578/j.issn.1004.2539.2019.05.010

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Calculation Method of Planetary Gear Train Transmission Ratio based on Adjacency Matrix

Design· Calculation | 更新时间：2022-10-03

- Calculation Method of Planetary Gear Train Transmission Ratio based on Adjacency Matrix
- Journal of Mechanical Transmission Vol. 43, Issue 5, Pages: 47-51(2019)
- 作者机构：
  
  1.长安大学工程机械学院，陕西西安 710001
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2019.05.010
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王昭,王馨萍,张接信.基于邻接矩阵的行星轮系传动比计算方法[J].机械传动,2019,43(05):47-51.

Wang Zhao,Wang Xinping,Zhang Jiexin.Calculation Method of Planetary Gear Train Transmission Ratio based on Adjacency Matrix[J].Journal of Mechanical Transmission,2019,43(05):47-51.
王昭,王馨萍,张接信.基于邻接矩阵的行星轮系传动比计算方法[J].机械传动,2019,43(05):47-51. DOI： 10.16578/j.issn.1004.2539.2019.05.010.

Wang Zhao,Wang Xinping,Zhang Jiexin.Calculation Method of Planetary Gear Train Transmission Ratio based on Adjacency Matrix[J].Journal of Mechanical Transmission,2019,43(05):47-51. DOI： 10.16578/j.issn.1004.2539.2019.05.010.

摘要

行星轮系的种类有很多，而且每一种对应一个传动比计算公式，对行星轮系的综合研究以及通用的设计软件开发造成了很大困难。为解决这一问题，根据行星轮系的结构图写出其对应的邻接矩阵，再从邻接矩阵中搜寻出该轮系的基本回路，构建基本回路矩阵，最后，将基本回路矩阵转化为运动方程的系数矩阵，利用MATLAB软件将此算法自动化并求解运动方程，得到行星轮系的传动比。

Abstract

There are many types of planetary gear trains， and each one corresponds to a transmission ratio calculation formula， which makes great difficulties in the comprehensive research of planetary gear trains and the development of general design software. According to the structural diagram of the planetary gear train， the corresponding adjacency matrix is written. Then， the basic loop of the train is searched from the adjacency matrix to construct the basic loop matrix. Finally， the basic loop matrix is transformed into the coefficient matrix of the equation of motion. And use MATLAB to automate this algorithm and solve the equation of motion to obtain the gear ratio of the planetary gear train.

关键词

行星轮系图论模型邻接矩阵基本回路传动比

Keywords

Planetary gear trainGraph modelAdjacency matrixFundamental circuitTransmission ratio

references

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TSAI L W. An application of the linkage characteristic polynomical to the topological synthesis of epicyclic gear trains［J］. Journal of Mechanisms， Transmission and Automation in Design， 1987， 109：329-336.

林建德，李润方. 一种齿轮系的图画表示法及其在齿轮系运动分析上的应用［J］. 机械科学与技术， 2004， 23（1）：60-62.

史晓影，陈良钰，薛隆泉. 行星轮系的图论模型及其应用［J］. 机械传动，2008， 32（5）：49-52.

俞庆，毛旭东. 基于拓扑学的行星轮系综合与研究［J］. 机械传动， 2012， 36（5）：33-36.

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