## 3 Results and Discussions
### Validation of Cooling Channel Optimization Design  
From the dimension optimization of the front bearing by simulation, the cooling channel width of 7.5 mm and height of 4.5 mm have the best effect on the cooling efficiency. In this study, thermal deformation measurement experiments were performed to verify the optimized design of the front bearing cooling channel. To verify the cooling channel optimization design for the front bearing, the thermal deformation measurement was performed for the original design and optimized design of the cooling channel. The experimental conditions include: (1) the rotational speed of spindle was 12,500 rpm, and the measurement experiment was completed when the horizontal machine tool reached the thermal steady state; (2) the coolant system of the machine tool operated simultaneously with the machine tool, and the cooling method of the coolant system was temperature tracking cooling. The temperature was adjusted by the preset temperature, which was set to 2 \({}^{\circ}\)C lower than the environment temperature in this study. In the measurement experiments, the main data that were measured include the front bearing temperature, rear bearing temperature, environment temperature, cooling oil temperature, and thermal deformation of spindle. The front bearing temperature and rear bearing temperature are the data that can be obtained by the controller of the horizontal machine tool. However, the temperature sensor and thermal deformation measurement system had slight steady-state errors due to external factors. To accurately define the steady state of the horizontal machine tool, the difference was calculated every 5 min and then the average was calculated. The total experimental time was 300 min, and 60 intervals were utilized for analyzing the thermal deformation trend. The thermal stability was defined by the following equation. \[TDR=(TD^{n+1}-TD^{n})/\Delta\tau \tag{24}\]  
where \(TDR\) is the thermal deformation rate, \(TD\) is the thermal deformation, \(\Delta\tau\) is the time interval, and \(n\) indicates the \(n\)th time step. The thermal deformation rate represents the difference in thermal deformation between the (\(n+1\))-th time step and the \(n\)th time step with a time interval of \(\Delta\tau\). To determine the thermal steady state of the spindle, a criterion of 0.01 \(\upmu\)m/min was defined. While the thermal deformation rate was less than this criterion value, the spindle was considered to attain a thermal steady thermal state. The measurement results of the cooling channel before the dimension optimization was performed are shown in Figure 14. The environment temperature rose from 29.6 \({}^{\circ}\)C to 31.3 \({}^{\circ}\)C, the temperature difference was \(\pm\)0.85 \({}^{\circ}\)C, and the average rate of variation in environment temperature was 0.0055 \({}^{\circ}\)C/min. During the 300 min of experimental time, the initial cooling oil temperature of the coolant system was 28.9 \({}^{\circ}\)C, the maximum oil temperature was 31.5 \({}^{\circ}\)C, the minimum was 27.4 \({}^{\circ}\)C, and the difference was 4.1 \({}^{\circ}\)C. Because the coolant system supplied a constant oil flow rate to the cooling channel of the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Cooling Channel Wall Temperature**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Front Bearing (\({}^{\circ}\)C)**} & \multicolumn{2}{c}{**Improvement (\%)**} \\ \hline
1 & Without dimension optimization (Figure 3a) & 61.2 & – \\
2 & Cooling channel improvement & 42.4 & 30.7 \\
3 & Dimension optimization & 35.3 & 57.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of optimal dimensions of front bearing cooling channel. rotating spindle, the bearing, and motor generating heat during operation, the cooling oil flow rate of the coolant system was insufficient for effectively cooling the heating source. Therefore, a large temperature difference is probable.