## 3 Results and Discussions
### Validation of Cooling Channel Optimization Design
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 132.6 min, and the variation rate in thermal deformation was within \(\pm\)0.01 \(\upmu\)m/min. The maximum thermal deformation was 30.9 \(\upmu\)m. The optimal design of a cooling channel can shorten the required steady-state time of the machine tool by 52.7 min from 185.3 min to 132.6 min. The steady-state time of a machine tool can be reduced by 28.4%. The spindle thermal deformation decreased by 22.9 \(\upmu\)m from 53.8 \(\upmu\)m to 30.9 \(\upmu\)m, and the accuracy of the spindle was enhanced by 42.6%. The initial temperature of the front bearing before the operation of the spindle was 30.3 \({}^{\circ}\)C. During the initial operation of the spindle, due to the cooling effect of the coolant system, the front bearing temperature at 0.2 min of spindle operation decreased from 30.3 \({}^{\circ}\)C to 30.1 \({}^{\circ}\)C, which is a reduction of 0.2 \({}^{\circ}\)C (decrement of 0.7%). From 0 to 0.2 min of spindle operation, the temperature variation of the front bearing was 0.2 \({}^{\circ}\)C. The thermal deformation of the spindle increased from 0 \(\upmu\)m to 7.1 \(\upmu\)m, but the thermal deformation of the spindle was 6.9 \(\upmu\)m at 30.1 \({}^{\circ}\)C of the front bearing temperature. The thermal deformation of the spindle decreased as the front bearing temperature decreased. When the machine tool reached a steady state, the maximum temperature of the front bearing was 32.9 \({}^{\circ}\)C, and the temperature was increased by 1.8 \({}^{\circ}\)C. The initial temperature of the rear bearing before operation of the spindle was 30.7 \({}^{\circ}\)C, and the difference between this temperature and the front bearing temperature was 0.4 \({}^{\circ}\)C, which is the same as the result of the original cooling channel design (Figure 3a). Because the rear bearing was not designed with a cooling channel, during the initial operation of the spindle, the rear bearing was not cooled, the initial temperature of the rear bearing increased from 30.7 \({}^{\circ}\)C to 38.8 \({}^{\circ}\)C, and the temperature increased by 8.1 \({}^{\circ}\)C (26.4%). The rear bearing temperature rise was less than half of the original cooling channel design, and the temperature rise  
Figure 15: Thermal deformation experimental results of cooling channel with dimension optimization design. was reduced from 15.5 \({}^{\circ}\)C to 8.1 \({}^{\circ}\)C. The results indicate that the rear bearing without a cooling channel requires a longer thermal steady-state time than the front bearing, and the maximum temperature of the rear bearing occurred at 177.2 min. Based on the results, the built-in spindle with the optimal design of the cooling channel dimensions can reduce the required thermal steady-state time. The cooling efficiency inside the spindle is enough, and the heat generated by the bearing or motor can be rapidly carried away. Therefore, the heat transfer can be avoided from the internal structure of the spindle to the spindle nose and from the spindle nose to the upright column and base of the machine tool to ensure that the thermal steady state can be rapidly reached and the thermal deformation can be effectively decreased. According to the temperature variations of the front and rear bearings, the temperature of the cooling channel with dimension optimization can be reduced by more than 50%. The cooling efficiency by the cooling channel with dimension optimization can be enhanced, and the spindle thermal deformation can be reduced. In addition, the required steady-state time of the machine can be reduced, which decreases the warm-up time. The productivity of the machine tool spindle with cooling channel dimension optimization can be improved effectively.