Multi-Objective Comprehensive Structural Optimization of the Bed for a GPC Fixed-Beam Gantry Machining Center

The static and dynamic characteristics of the fixed-beam gantry machining center bed are critical for determining machining accuracy and efficiency in precision machine tools. To address the lightweight-stiffness trade-off limitation of traditional empirical methods, this study proposes a multi-objective comprehensive structural optimization approach for the GPC bed, integrating bionic design, topology optimization, and grey relational analysis based on static-dynamic characteristic analysis. A multi-objective topology optimization model is established using the variable density method. An optimized rib design inspired by the glass sponge’s thin-walled multi-layer structure is derived, and its performance advantages are validated by finite element simulations. Combining grey relational analysis and BP neural networks, a response surface model is constructed to identify core performance-influencing parameters. The optimal rib layout and cavity-to-rib plate ratio are determined through multi-configuration experiments. Experimental verification demonstrates significant performance enhancements over the prototype: a 3.1% mass reduction, a 24.3% increase in natural frequency (improved vibration resistance), and a 17.0% reduction in maximum displacement deformation (enhanced stiffness). These improvements lead to higher machining accuracy and efficiency.