## 1 Introduction
Through static analysis, modal analysis, and harmonic analysis of the machine tool structures for both open-frame and closed-frame bench-top machines, the static and dynamic loop stiffness of the machine structure was predicted and the effectiveness and feasibility of the proposed approach were validated. Preliminary cutting experiments also confirmed that this approach can ensure the right operation of the machine tool during its initial setup [5]. [PERSON] et al. (2011) proposed an approach to ensure the minimization of the mass of the moving structural components of a large milling machine tool while maximizing material removal (targeted productivity). This design method involved an iterative design process that translated the productivity target requirements of the milling process into design optimization criteria, which guided the conceptualization of a large milling machine tool with the minimum possible mass of moving structural components while ensuring a stable cutting productive performance. A modeling approach was employed that used a stability model of the milling process in modal coordinates to model the interaction between the milling process and the machine tool structure. This model allowed for the identification of mechanical design parameters that limited the productivity and the threshold values required to meet the targeted productivity. These critical values were reached through an iterative procedure aimed at minimizing the mass of critical structural components in the machine tool. This methodology was applied to redesign an actual milling machine tool and machining tests were conducted. It resulted in a productivity increase of over 100% and a reduction in energy consumption by more than 20% due to the mass reduction of the moving structural components [6]. [PERSON] et al. (2012) developed a simple and practical method for the optimal design of a machine tool bed structure. First, establish a simplified fiber model composed of a shell and matrix elements to handle the numerical simulations of the complex mechanical structures and boundary conditions. Next, identify the load bearing path topology of the bed structure to represent the optimal layout of the internal stiffener ribs. Subsequently, utilize innovative optimization criteria that describe the best weight distribution for both the external support panels and internal stiffener ribs to produce a detailed sizing optimization design. The results demonstrated the effectiveness of the proposed method when using the example of a grinding machine tool bed as a design case [7]. [PERSON] et al. (2021) focused on the structural analysis of the hollow square column of three-sided and four-sided CNC machine tools. Various parameters were considered, such as a bionic design, total number of ribs and apertures, type of aperture, and tapering angles. The analysis concentrated on the stability, static structural analysis, and load effects of the CNC machine tool. The results of finite element analysis were compared with those in the literature. An optimization method using the derivative parameter approach was employed to determine the optimized ranking of the tested columns. With the assistance of software, successful static structural analysis was conducted. These research findings will contribute to the development of CNC machine tool structures. Based on the literature and finite element analysis results, the following conclusions can be drawn: based on the optimization criterion, which is the minimum value of the derivative parameter, a four-sided column with four horizontal plate ribs featuring rotated square-shaped apertures provides the best choice and is the optimal option among 14 competing cases. For the most rigid structure, i.e., the one with the minimum displacement, the best choice among the 14 competing cases was a four-sided column with an optimized wall thickness and four horizontal plate ribs without any apertures.