关键词: 多目标优化, 响应面法, 优化设计, 有限元法

Abstract: In order to satisfy the performance requirement of the dynamic and static stiffness and light weight of a machining centre, a method of multi-objective optimization driven by the first natural frequency and mass is proposed. Modal parameters are identified by using a comprehensive approach based on modal test and finite element analysis. The appropriate structural finite element analysis samples in design space are selected by using the central composite design (CCD) experiment method. Quadratic polynomials are employed to construct response surface (RS) model, which reflects the relationship between design inputs and structural response outputs, according to the response outputs of these samples obtained by analyzing the dynamic and static characteristics of the machining centre at these samples with the software ANSYS. Well-distributed samples are generated in the design space by shifted Hammersley sampling method. The prominent points are selected as initial samples. The goal of getting higher first natural frequency and lighter weight is reached and the Pareto optimal solution set is obtained by the multi-objective genetic algorithm in the optimization. Through the optimization, the mass of the machining center is decreased by 6.58 % under the condition of ensuring the dynamic and static performance. The results show the high precision and strong engineering practicability of the proposed optimization method.

Key words: Finite element method, Multi-Objective optimization, Optimization design, Response surface methodology