Structural optimization of the cross-beam of a gantry machine tool based on grey relational analysis

Crossbeam structural design of gantry machine tool is a multi-level, multi-index and multi-scheme decision-making problem. In order to solve the above problem, the optimum seeking model of crossbeam structure was built through using the grey relational analysis and Analytic Hierarchy Process. The finite element analysis of the static and dynamic performance parameters for four kinds of crossbeam structural schemes designed had been done, and the optimal design scheme was selected by using the optimum seeking model. After conducting sensitivity analysis for the optimal crossbeam selected, the reasonable design variables were obtained, and the dynamic optimization design model of crossbeam was established. Six groups of non-inferior solutions were obtained after solving the optimization design model. The optimal solution was selected from the non-inferior solution set through using the crossbeam structural optimization method based on grey relational analysis again, which makes the crossbeam’s dynamic performance improving greatly. The dynamic experiments on the crossbeams before and after optimization design were conducted, then the experimental results show that the first four order natural frequencies of the crossbeam increase 17.56 %, 19.36 %, 17.04 % and 19.58 % respectively, which proves that the structural optimization design method based on grey relational analysis proposed in this paper is reasonable and practicable.