## 3 Results and Discussions
### Validation of Cooling Channel Optimization Design
The maximum temperature of the cooling oil occurred at 185 min, which was close to the steady-state time of the spindle. The minimum temperature of the cooling oil occurred at 2.6 min. During the initial operation of the spindle, the heat generation was not high. When the initial supply temperature of the cooling oil was lower than the bearing temperature by 0.5 \({}^{\circ}\)C and the coolant system continuously cooled the cooling oil, the temperature of the cooling oil dropped after the spindle was in operation for a period of time. The machine tool reached a steady state at 185.3 min, and the variation rate in the thermal deformation was within \(\pm\)0.01 \(\upmu\)m/min. The maximum thermal deformation after the steady state was 53.8 \(\upmu\)m.  
The initial temperature of the front bearing before the operation of the spindle was 29.4 \({}^{\circ}\)C. In the initial operation of the spindle, due to the cooling effect of the coolant system, the front bearing temperature at 0.4 min of spindle operation was reduced from 29.4 \({}^{\circ}\)C to 29.1 \({}^{\circ}\)C, which was reduced by 0.3 \({}^{\circ}\)C and 1.02%. From 0 to 0.4 min of spindle operation, the temperature variation of the front bearing was 0.3 \({}^{\circ}\)C, and the thermal deformation of the spindle increased from 0 \(\upmu\)m to 7.6 \(\upmu\)m. However, the thermal deformation of the spindle was 6.8 \(\upmu\)m at 29.1 \({}^{\circ}\)C of the front bearing temperature, which means that the thermal deformation of the spindle was reduced as the front bearing temperature drops. When the machine tool reached a steady state, the maximum temperature of the front bearing was 35.2 \({}^{\circ}\)C, and the temperature was increased by 5.8 \({}^{\circ}\)C. The initial temperature of the rear bearing before the operation of the spindle was 29.6 \({}^{\circ}\)C, and the difference between this temperature and the front bearing temperature was 0.2 \({}^{\circ}\)C. The rear bearing of the horizontal machine tool was sealed inside the spindle, no environmental convection occurred, and the measurement errors are summed. Because the rear bearing was not designed with a cooling channel, during the initial operation of the spindle, the rear bearing was not cooled, and the initial temperature of the rear bearing increased from 30 \({}^{\circ}\)C to 45.5 \({}^{\circ}\)C, i.e., the temperature increased by 15.5 \({}^{\circ}\)C (51.7%). Based on these results, the rear bearing without a cooling channel required a longer thermal steady-state time than the front bearing, and the maximum temperature of the rear bearing occurred at 300.5 min. In this study, the experiments were performed with the original cooling channel design (refer to Figure 3a). The required steady state time of the horizontal machine tool was approximately 3 h at a spindle rotational speed of 12,500 rpm. In addition, the thermal deformation was 53.8 \(\upmu\)m, and the maximum temperature of the front bearing was 35.2 \({}^{\circ}\)C, which is an increase of 5.8 \({}^{\circ}\)C.  
Figure 14: Experimental results of cooling of the original cooling channel design. To validate the benefit of cooling channel dimension optimization, the experiments were performed with the same spindle operating condition; the results are shown in Figure 15. The results indicate that the ambient temperature rose from an initial temperature of 30.2 \({}^{\circ}\)C to 30.9 \({}^{\circ}\)C. The temperature difference was \(\pm\)0.35 \({}^{\circ}\)C, and the average rate of change in the ambient temperature was 0.0017 \({}^{\circ}\)C/min. The maximum temperature of the cooling oil occurred at 129.4 min, which is close to the required spindle steady-state time. The minimum temperature of the cooling oil occurred at 1.9 min. In the initial operation of the spindle, the heat generation was not high.