多级行星齿轮机构的图形符号表示及同构判别

Graphic Symbol Representation and Isomorphism Identification of Multistage Planetary Gear Trains

针对多级行星齿轮机构的构型综合过程中,其拓扑模型元素符号的不确定性及同构判别困难的问题。基于图论理论,首先根据行星齿轮传动机构的结构特点,提出了更加完善的拓扑图表示方法和演化规则,建立了行星齿轮机构与邻接矩阵的一一对应关系;然后以单级行星齿轮机构为基础,将多个单级行星齿轮机构的邻接矩阵经过一系列运算转化为多级行星齿轮机构的邻接矩阵,通过拓扑反演得到多级行星齿轮机构的构型方案;最后将多级行星齿轮机构的邻接矩阵转化为Hamming矩阵,利用Hamming矩阵的性质判断多级行星齿轮机构的拓扑构型方案之间是否同构。新拓扑模型的优点在于能够使行星齿轮机构的结构特征信息、各构件的区分度更加明确,易于在计算机上实现多级行星齿轮机构的构型设计与同构判别,为多级行星齿轮传动机构的创新和优化设计奠定了基础。

Aiming at the uncertainty of topological element symbols and the difficulty of isomorphism identification during the configuration synthesis of the multistage planetary gear trains.Based on graph theory,according to the structural characteristics of the planetary gear transmission mechanism,a more perfect topology symbols expression method and evolutionary rules are proposed,and the one-to-one correspondence between the planetary gear trains and the adjacency matrix is established.Then,the configuration synthesis of the multistage planetary gear trains is transformed into the operation of the adjacency matrix,and the configuration scheme of the multistage planetary gear trains is deduced through topology inversion.Finally,the adjacency matrix of configuration scheme of multistage planetary gear trains is transformed into Hamming matrix,and the isomorphism identification of configuration scheme of multistage planetary gear trains are carried out by using the Hamming matrix method.The advantage of the novel topology model is that it can make the structure information of the planetary gear trains and the differentiation of each component more clear,and it is easy to realize the configuration design and isomorphism discrimination of the multistage planetary gear trains on computer.It lays a foundation for the innovation and design optimization of multistage planetary gear trains.