Research Of Designing And Optimization Method Of Planetary Gear Train Based On Graph Theory

With the continuous development of the machinery industry,people have higher requirements on the performance of the transmission part of the mechanical system,requiring a larger and more precise transmission ratio,higher transmission efficiency,and smaller volume.In this context,the planetary gear train(PGT)has been widely used due to its own advantages,and plays an increasingly important role in the modern industry.However,the mismatch between its status is the design method of the existing PGTs,which only achieves partial intelligence,which completely does not match the requirements of China Manufacturing 2050 for industrial intelligence.The fundamental reason is that there are many kinds of PGTs,and the design methods of different types are not the same,which causes great interference to realize the intelligent design of the PGT.In order to realize the intelligent design of PGTs,firstly,based on a large number of planetary wheel train mechanism synthesis methods and design algorithms,based on graph theory,a new planetary wheel train graph theory model is proposed.It can accurately express its structural topology and motion topology.Secondly,the mathematical expression method of the planetary wheel system graph theory model is established.The adjacency matrix method is proposed.The basic circuit matrix of the PGT is used to express the motion topological relationship among the components inside the PGT,and a kind of adjacency matrix is proposed.A method of searching for a basic loop matrix.Then,based on the basic circuit matrix,the kinematics analysis,static analysis and efficiency analysis of the PGT are studied.The general kinematics,statics and efficiency analysis algorithms of various PGTs are proposed.Next,on the basis of previous studies,the constraint formula of the number of teeth of the PGT is proposed,and the algorithm for calculating the constraint coefficient matrix is proposed.On the basis of the second,a general PGT intelligent matching algorithm and design method are proposed.Finally,based on the standard particle swarm optimization algorithm,an improved and dedicated PGT structure optimization algorithm is proposed to solve the multi-objective and multi-constrained problems in PGT optimization.All of the above proposed algorithms are programmed using MATLAB software and verified by examples,as well as the results of traditional design methods.The results show that all methods can be implemented by programming,and the calculation results are correct.Through the optimization of the optimized PGT,the transmission efficiency has been greatly improved and the volume has been significantly reduced.It has laid a solid foundation for the intelligent design and green manufacturing of PGTs.