Beam structure design of CNC vertical milling machine based on topology and size optimization

Abstract

To address the coupled determination of initial topology and size parameters in structural optimization, a combined topology and size optimization method is applied to the beam of a CNC vertical milling machine. With a 40% mass retention constraint, topology optimization based on the variable density method was performed, reducing the beam wall thickness and removing redundant mass. Under a constant mass condition, the wall thickness was further reduced and a number of stiffeners were added. Size optimization based on the response surface method was then conducted, with stiffener thickness and spacing selected as design variables. Optimal parameters were determined by minimizing the maximum deformation and maximizing the first natural frequency. Optimization results show that, compared with the post-topology optimization configuration, the maximum deformation of the beam after size optimization is reduced to 8.43×10-2 mm, a reduction of 6.01%, and the first natural frequency increases to 40.782 Hz, an increase of 25.21%, indicating a significant enhancement in static and dynamic performance. This method provides a systematic and reproducible technical pathway for lightweight design and performance enhancement of machine tool structural components, offering valuable engineering guidance.