## 3 Results and Discussions
### Optimization Analysis of Cooling Channel Dimension  
In this study, the optimization module of the analytical software was employed for the dimension optimization. The front bearing cooling channel dimension design was optimized with the same cooling oil conditions and heat transfer coefficient of fluid. Figure 9 shows the geometrics of the cooling channel, which were imported from Solidworks 3D drawing software into the simulation software for analysis. The optimization simulation of the critical dimensions in the front bearing cooling channel was performed. The front bearing between the flange facing and the spindle nose had the largest heat contribution to the thermal deformation. Therefore, the thermal deformation of the spindle can be reduced directly by effectively reducing the front bearing temperature. In the design of the cooling channel, direct heat removal from the heating parts is the best method, in which the temperature rise can be improved effectively, and the heat can be prevented from being transferred to other structures, which causes more unforeseeable deformation. Therefore, a front bearing cooling channel design can effectively reduce the front bearing temperature and induce structural deformation. To obtain the critical dimension of the optimal cooling channel, the optimal design method of software was adopted in this study. First, the front bearing cooling channel of the built-in spindle was drawn by Solidworks, and the model was simplified for analysis. The width and height of the cooling channel were defined as the critical design parameters. The critical dimension of the front bearing cooling channel is shown in Figure 9a, including the width (W) and height (H) definitions of the paralleling type cooling channel. In the optimized design for the front bearing cooling channel dimension in this study, the critical dimensions were the cooling channel cross-sectional width (W, denoted as P1) and cooling channel cross-sectional height (H, denoted as P2). In addition, the cooling oil flow rate (Q, set as P3) was applied. The effects of the width (W), height (H), and cooling oil flow rate (Q) on the temperature inside the front bearing cooling channel (T, denoted as P4) were analyzed. The front bearing cooling channel optimization variable settings are shown in Figure 9b. The dimension and relevant parameter ranges of the front bearing cooling channel are shown in Table 4. The width (P1) of the cooling channel was in the range 6.0 mm\(\sim\)9.0 mm; the height (P2) of the cooling channel was in the range 3.5 mm\(\sim\)5.0 mm; and the cooling oil flow rate was in the range 0.1\(\sim\)0.2 kg/s. The temperature of the front bearing is the output of the numerical simulation. Table 5 shows the results of the front bearing temperatures by the Design of Experiments (DOE) simulation. The Central Composite Design (CCD) method was adopted to automatically generate a combination, and the analytical calculation was performed according to the combination. The front bearing temperature is shown in Table 5. In the limit range of the dimension and cooling flow rate, the temperature of the front bearing was in the range 308.04-308.97 K. In the limit design space of the cooling channel, the temperature difference in the numerical results was approximately 1 K, which is not substantial. However, even a 1 K temperature difference can produce a considerable effect on structural deformation. Considering the ball-screw as an example, the thermal deformation of a 1-meter-long ball-screw is approximately 12 \(\upmu\)m for a 1 K temperature rise. The sensitivity level of the parameter variations in temperature can be obtained by numerical analysis software (ANSYS), as shown in Figure 10. The cooling oil flow rate P3 and front bearing temperature P4 have negative sensitivity levels, which means that the front bearing temperature drops obviously as the flow rate of the cooling oil increases.