• CN:11-2187/TH
  • ISSN:0577-6686

›› 2008, Vol. 44 ›› Issue (4): 80-86.

• 论文 • 上一篇    下一篇

周转轮系系统化的数学模型

薛隆泉;雷亚荣;宋念龙   

  1. 西安理工大学机械仪器工程学院;西安理工大学自动化与信息工程学院
  • 发布日期:2008-04-15

System Mathematic Model of Epicyclic Gear Trains

XUE Longquan;LEI Yarong;SONG Nianlong   

  1. School of Mechanical Instrumental Engineering, Xi’an University of Technology School of Automatization and Communication Engineering, Xi’an University of Technology
  • Published:2008-04-15

摘要: 在分析轮系结构特征及状态特征的基础上,完善包涵两类特征的拓扑图;认识到轮系是一个物理系统,提出网络问题是解决轮系物理特征的系统化图论模型,并发现轮系拓扑图满足基尔霍夫定律;在分析拓扑图物理特征的基础上,结合拓扑图几何特征,提出支路特性矩阵、切割特性矩阵用于构建系统化研究的数学模型,即回路方程组、切割方程组,为系统地研究周转轮系结构特性、状态特性提供新的理论基础。以实例论述这一理论的具体应用。

关键词: 基尔霍夫定律, 数学模型, 图论模型, 网络问题

Abstract: On the basis of analyzing structure character and state character of epicyclical gear trains (EGTs) , topological graph is improved. It is realized that gear trains is a physics system , and net problem is presented that is a systems graph theory model applied to solve physics character of EGTs. It is found that topological graph accords with Kirchhoff ’s law. On the basis of analyzing physics and geometry character of topological graph, branch-characteristics matrix and cut-characteristics matrix are presented, the two are applied to create a systems mathematic model, namely loop-equations and cut-equations. A new fundamental theory is presented for structure characteristics and state characteristics of EGTs based on systems research. And it is applied to velocity, torque and bifurcated power characteristics of EGTs with an example.

Key words: Graph theory model, Kirchhoff ’s law, Mathematics model, Net problem

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