## 4 Conclusions  
In this study, a multiple physical coupling simulation analysis was performed for the cooling channel design of a built-in spindle, and the DOE method was adopted to optimize the critical dimension of the cooling channel. A comparison of the theoretical calculation and experimental results indicates that the heat generation of the front bearing and rear bearing was higher than the built-in motor at a spindle rotating speed of 12,500 rpm. Therefore, the front bearing cooling channel of a spindle was changed from the original single-turn design to the paralleling design to enhance the cooling efficiency by simulation. Based on the simulation results, the spindle cooling channel wall temperature was improved effectively when the cooling oil type was changed from VG10 to VG5, reducing the temperature of the front bearing by 18.8 \({}^{\circ}\)C (30.7%) and of the motor by 7.5 \({}^{\circ}\)C (14.7%). In the cooling channel optimization design, the Design of Experiments (DOE) method and Central Composite Design (CCD) method were employed for analysis to obtain the critical dimension and related composite list. The optimal dimensions of the cooling channel in simulation were derived from the sensitivity analysis table, correlation matrix, and response surface diagram, and the channel wall temperature of the front bearing was reduced by 7.1 \({}^{\circ}\)C. The thermal deformation and temperature variation experiments were conducted to investigate the optimal cooling channel design with the thermal deformations. For the comparison of the cooling channel dimension optimization and original cooling channel design, the spindle bearing temperature of the cooling channel with dimension optimization was lower than the temperature of the original cooling channel design temperature by at most 6.7 \({}^{\circ}\)C, and the thermal deformation was reduced from 53.8 \(\upmu\)m to 30.9 \(\upmu\)m. In addition, the required steady-state time of the machine tool was shortened from 185.3 min to 132.6 min as the cooling efficiency of the spindle was enhanced. Because the heat generation of the spindle can be removed at a rapid rate, the spindle can rapidly reach thermal equilibrium. In terms of machining verification, the flatness accuracy and the surface roughness \(R_{a}\) of the cooling channel dimension optimization were improved by 61.3% and 52%, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline
**Workpiece** & **Cooling Channel Type** & **Flatness** & \(R_{a}\) & \(R_{max}\) & \(R_{z}\) \\ \hline
1 & Original design & 9.3 & 0.5 & 8.94 & 1.97 \\
2 & Dimension optimization & 3.6 & 0.24 & 6.11 & 1.25 \\  & Accuracy improvement (\%) & 61.3 & 52 & 31.7 & 36.5 \\ \hline \end{tabular}
\end{table} 
Table 9: Machining accuracy results in the machining verification. In the past, the cooling channel dimensions were designed mostly based on the experience without systematic design procedures. In this study, the cooling channel optimization design by the DOE method was adopted to enhance the cooling efficiency. The cooling efficiency of a cooling channel can be greatly improved, the machining accuracy can be enhanced, and the required steady state time can be shortened. In future machining applications, because the machining load is positively correlated with spindle temperature, which is positively correlated with thermal deformation, the spindle temperature can be directly controlled to decrease the thermal deformation by the cooling system with the optimal supply conditions of cooling oil flow rate or temperature. Only if the relation between spindle temperature and thermal deformation is known, the required build-up time for coolant flow rate control modeling can be reduced, which can satisfy the application requirements of a machine tool in the heavy machining process. [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] contributed reagents/materials/analysis tools; [PERSON] wrote the paper.