Structural Optimization for Column of Gantry Machine Tool Using Response Surface Method

Abstract

As the first part of an ongoing integrated project for developing a desktop gantry grinding machine tool, the structural optimization of column part is taken as the focus of the study. The thickness, height, and width of column are the design variables. The objective of optimization is to minimize volume while keeping the deformation of spindle tip smaller than the desired maximum value and the 2nd natural frequency below the given limit. Based on results of static and dynamic analyses obtained from finite element method, the response surface method with factorial design was utilized to create the metamodel for optimization. Two kinds of response surface model with two kinds of factorial design were used for comparison. The gradient search method was applied to the response surface model for optimization. The optimal structure of machine tool made the volume and the second natural frequency both decreasing 13% while the y-displacement of spindle tip were confined to required range. The result shows the successful application of response surface method with carefully chosen factorial design on structural optimization problem. Keywords-structural optimization; gantry machine tool; response surface method; finite element analysis