## 3 Results and Discussion
### Dynamic Characteristic Analysis Results and Discussion
#### 3.2.3 Harmonic Response Analysis Results and Discussion
Harmonic response analysis of the upper-surface center of the workpieceIt is found in Figure 17 that when the milling force is added to the center of the upper surface of the workpiece on the direct-drive turntable, the first peak amplitude of its X, Y, and Z directions also appears at about 600 Hz. The maximum deformation in the X direction is 1.476 \(\times\) 10\({}^{-3}\) mm, and the maximum deformation in the Y direction is 8.053 \(\times\) 10\({}^{-4}\) mm. The maximum deformation in the Z direction is 9.089 \(\times\) 10\({}^{-7}\) mm. The dynamic stiffness is calculated according to the method of calculating Kx = 4.319 \(\times\) 10\({}^{5}\) N/mm, Ky = 3.688 \(\times\) 10\({}^{5}\) N/mm, and Kz = 4.843 \(\times\) 10\({}^{11}\) N/mm; still, the Y direction has the greatest influence at about 600 Hz under the action of milling force. A comprehensive analysis of the results of the two different applied load positions in the direct-drive turntable milling condition shows that:  
The sum of static and dynamic deformation for the two loading cases reaches a maximum of about 600 Hz. Comparing Figures 16 and 17, We can find that the load addition position has almost no effect on the natural frequency distribution of the direct-drive turntable. Since each peak's frequency does not overlap the excitation frequency provided by the machine tool to the direct-drive turntable, the machine tool can easily avoid the harm caused by resonance to the structure under regular operation. Figure 17: Harmonic response curve of turntable under center loading: (**a**) X-directional harmonic response curve; (**b**) Y-directional harmonic response curve; (**c**) Z-directional harmonic response curve. By comparing the results of single-condition topology optimization and composite-condition topology optimization, it can be found that the main removed region is the C-axis part of the direct-drive turntable after increasing the percentage of removal mass under the same working condition, and the removed region of other parts has almost no increase. Therefore, the C-axis part of the direct-drive turntable has a certain mass redundancy, and we can adjust its size to a certain extent. By observing the same mass retention rate of the turning and milling topology model, we can find that the two topology models are similar. Still, the topology optimization results are somewhat different due to the constraints and stress conditions. The topology optimization model of the composite working condition of the direct-drive turntable synthesizes the topology optimization results of the two working conditions. It conforms to the stress characteristics of the two working conditions. According to the actual situation and direct-drive turntable topology optimization model, the following conclusions can be drawn by comparison:  
1. When the direct-drive turntable works, the torque motor transfers movement through the axis. The best axis optimization method is size optimization to ensure the direct-drive turntable's normal operation. The diameter was selected as the optimization parameter. 2. The maximum radius of the workpiece is determined so we cannot change the turntable surface's diameter, but the thickness of the turntable surface can be optimized. 3. Topology optimization results of the mounting sleeve are shown in light red and red. To avoid direct-drive turntable internal parts being exposed and the displacement of internal parts during sudden braking, the radius, rather than the installation sleeve's length, was considered optimized. Topology Optimization of Swing Frame  
According to the topology optimization results, the swing frame was redesigned, and two optimization schemes were obtained, as shown in Figure 21.  
Figure 20: Topology optimization results of direct-drive turntable in composite condition: (**a**) 50% mass retention rate; (**b**) 60% mass retention rate. The simulation of two swing frames with different openings was carried out.