## 1 Introduction
The harmonic response analysis can determine whether or not the designs will be able to overcome resonance and the negative impacts of forced vibrations [12]. The micro machine tool has been the subject of much research, development, and production. When designing a five-axis ultra-precision micro milling machine tool, [PERSON] et al. [13] took a comprehensive dynamic approach to conceptualizing and designing the machine. [PERSON] et al. [14] studied an electromechanical-hydraulic design method based on co-simulation and showed that it could accurately reflect the actual situation. [PERSON] et al. [15] established a finite element analysis model of the car body, calculated its bending and torsional strength according to the actual situation, and finally optimized its structure. [PERSON] et al. [16] redesigned the rib of the column based on the principles of bones and plant stems to improve the static and dynamic performance of the column. [PERSON] et al. [17] achieved energy savings by reducing the weight of the machine worktable and conducting studies on a three-axis vertical milling machine. [PERSON] [18] studied a multi-objective optimization design method for machine tool structural parts, which also had strong reference values for the multi-objective optimization designs of other mechanical parts. [PERSON] et al. [19] established a new dynamic design optimization method by using both structural topology design optimization techniques and dynamic sensitivity analysis, while considering both members and contact parts. The proposed design method was beneficial to the machine tool's product upgrade design and contributed to the effective improvement of the machine's dynamic performance. [PERSON] et al. [20] developed a completely new structure for surface profile grinders by violating basic design rules and using topology and shape-optimization methods to pursue the ideal structure. [PERSON] et al. [21] improved the optimization efficiency by using the orthogonal experiment method. [PERSON] et al. [22] investigated the machining stability by using the integrating spindle unit model [23; 24; 25], while considering the machine frame's structure [26; 27]. [PERSON] et al. [28] investigated and the recorded three small five-axis machine tools' temperature, spindle current, and vibration real-time signals. Unfortunately, the previous publications are insufficient and mostly concerned with the principle of conventional equipment; few studies have concerned themselves with the design of a micro machine tool. Therefore, the progress of micro machine tools depends on their systematic design and dynamic optimization. The abovementioned literature review shows that the finite element analysis is widely used for structural analysis. The static and dynamic analyses of the model can be performed using the finite element analysis, and the natural frequency of the machine can be obtained. In a few cases of topology optimization for structure optimization, the weight of the model was reduced, and the natural frequency increased. The primary goal of the current study was to create an experimental technique for measuring the effect of machine-tool stiffness. To ensure that the analysis results were consistent with the experimental results, the analysis model and conditions were modified. The force of each component and casting of the machine tools, as well as the load of the motor during the cutting stroke, were examined using multi-body dynamics analyses. The finite element analysis of the existing machines was mainly conducted using the ANSYS FEA package, and the results were verified using modal experiments. The machine was optimized using topology optimization to reduce both the quality of the machine and production cost and, finally, to improve the quality of the surfaces of the parts machined. Detailed steps of the development process are shown in a flowchart in Figure 1.  
Figure 1: _Cont._