Multiobjective Optimization of Steering Mechanism for Rotary Steering System Using Modified NSGA-II and Fuzzy Set Theory

Hongtao Li,Wentie Niu,Shengli Fu,Dawei Zhang

doi:10.1155/2015/875872

Abstract

Due to the complicated design process of gear train, optimization is a significant approach to improve design efficiency. However, the design of gear train is a complex multiobjective optimization with mixed continuous-discrete variables under numerous nonlinear constraints, and conventional optimization algorithms are not suitable to deal with such optimization problems. In this paper, based on the established dynamic model of steering mechanism for rotary steering system, the key component of which is a planetary gear set with teeth number difference, the optimization problem of steering mechanism is formulated to achieve minimum dynamic responses and outer diameter by optimizing structural parameters under geometric, kinematic, and strength constraints. An optimization procedure based on modified NSGA-II by incorporating dynamic crowding distance strategies and fuzzy set theory is applied to the multiobjective optimization. For comparative purpose, NSGA-II is also employed to obtain Pareto optimal set, and dynamic responses of original and optimized designs are compared. The results show the optimized design has better dynamic responses with minimum outer diameter and the response decay decreases faster. The optimization procedure is feasible to the design of gear train, and this study can provide guidance for designer at the preliminary design phase of mechanical structures with gear train.

Highlights

Gear trains are widely used in mechanical engineering for advantages of compact structure, high reliability, and large power transmission
The optimization for gear trains has been a necessary process to solve the above problems at the preliminary design phase of gear trains, and many different optimization techniques have been reported in the literatures on gear trains
This study aims to minimize the dynamic responses and outer diameter of steering mechanism with structural parameters as design variables subject to geometric, kinematic, and strength constraints

Summary

Introduction

Gear trains are widely used in mechanical engineering for advantages of compact structure, high reliability, and large power transmission. Chong et al described a method for reduction of geometrical volume and meshing vibration of cylindrical gear pairs while satisfying strength and geometric constraints using a goal programming formulation [3]. Based on the random search method, Zarefar and Muthukrishnan investigated the optimization of helical gear design [4]. A Random-Simplex optimization algorithm was developed by Faggioni et al for gear vibration reduction by means of profile modifications [7]. Based on min-max method combined with a direct search technique, Abuid and Ameen had done the optimization problem containing seven objective functions: gear volume, center distance, and five dynamic factors of shafts and gears [8]. Selection is the first genetic operator which guarantees that individuals with excellent genes are selected from parent population, and binary tournament selection is chosen for calculation in MNSGA-II. Crossover and mutation are the genetic operators to maintain the diversity of population by producing offspring individuals, and uniform crossover and single-point mutation are, respectively, applied for mutation and mutation in this study [19]

Methods

Results

Conclusion