Multi-objective Optimization Design on Gear Train of Planetary Reducer in Shield Tunneling Machine Based on Reliably Grey Particle Swarm Optimization

Abstract

The sigma is introduced into grey relational degree,the notion of reliably grey relational degree is creatively put forward to be used as mutation strategy to control the basic particle swarm optimization(PSO),which may avoid the problem that the algorithm prematurely falls into local optimum.For those variables called for integers,their initial position and speed of each flight are taken as integers,to ensure that the obtained solutions are integral.Meanwhile,to understand easily and operate conveniently,the mechanism and processes of the algorithm are illustrated,thus,a practical and convenient method is provided for multi-objective mixed integer programming problems subject to complex non-linear conditions.The mathematical models are constructed for planetary gear reducer in shield tunneling machine(STM) with 4 objective functions,that is to make its volume smallest,its efficiency highest and the reliability of its contacting and bending strength highest,which are subject to the conditions such as teeth,modification coefficient,interference,strength,equal strength and equal life on the basis of the 4 assumptions,which are solved by means of Matlab programming language compiled by using the reliably grey PSO.The research results show that generalization ability not only resolves the strength problem which is a little weak in the original 3rd grade of the planetary gear reducer,but also decreases the volume by 11.55% and increases the efficiency by 0.56% and the transmission ratio by 3.67%,and the strength and life in every grade are basically equal under the condition of ensuring high reliability.