摘要
周转轮系的同构识别可剔除综合过程中出现的重复结构,对于周转轮系的构型综合具有重要意义。针对周转轮系同构识别问题,提出了一种建立等效电路识别周转轮系同构的新方法。运用双色拓扑图描述周转轮系拓扑结构,避免伪同构情形。根据电路网络与周转轮系拓扑图的相似拓扑约束特性,将拓扑图转化为具有相同约束的等效电路,根据等效电路元素进行初步同构识别。应用回路电流法列出等效电路基本回路电流的齐次线性方程组,其系数矩阵保留有等效电路的结构特征。证明系数矩阵特征值相同可作为等效电路同构的充要条件。结合实例验证了该方法的简便性和可靠性。
The isomorphism identification of epicyclic gear train can eliminate the repeated structure in the process of synthesis,which is of great significance to the design and synthesis of epicyclic gear train.Aiming at the problem of isomorphism identification of epicyclic gear train,a new method to establish equivalent circuit to identify the isomorphism of epicyclic gear train is proposed.The topological structure of epicyclic gear train is described by bicolor topological graph to avoid pseudo-isomorphism.According to the similar topological constraint characteristics of the circuit network and topological graph of epicyclic gear train,the corresponding topological graph is transformed into an equivalent circuit with the same constraints,and isomorphism identification is preliminarily carried out according to the equivalent circuit elements.The homogeneous linear equations of the basic loop current of the equivalent circuit are presented by the loop current method,and the coefficient matrix retains the structural characteristics of the equivalent circuit.It is proved that the same eigenvalues of the coefficient matrix can be regarded as a necessary and sufficient condition for the isomorphism of the equivalent circuit.The simplicity and reliability of the method are verified by some examples.
作者
周明帅
孙伟
孔建益
张宇
ZHOU Mingshuai;SUN Wei;KONG Jianyi;ZHANG Yu(College of Machinery and Automation,Wuhan University of Science and Technology,Wuhan 430081)
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2021年第23期77-84,共8页
Journal of Mechanical Engineering
基金
国家自然科学基金(51875418)
湖北省教育厅基金(B2020011)
武汉科技大学国防预研基金(GF202008)资助项目
关键词
周转轮系
同构识别
双色拓扑图
等效电路
回路电流法
epicyclic gear train
isomorphism identification
bicolor topological graph
equivalent circuit
loop current method
