## 3 Results and Discussions
### Practical Machining Accuracy Validation  
In previous experimental results, the cooling efficiency of the cooling channel, spindle thermal deformation, and required steady-state time of the machine tool were improved by the cooling channel dimension optimization design. However, the experimental results were obtained in static experiments, which cannot represent the dynamic conditions in the actual machining process. Therefore, the actual machining verification was conducted to understand the effect of the cooling channel with optimization on the practical machining accuracy.  
The verification experiment aims to discuss the errors in the flatness and surface roughness of a workpiece after 3 h of machining time. Due to the increase in thermal deformation, the flatness and surface roughness of machining may be reduced to verify the machining effect of the cooling channel dimension optimization. The flatness and surface roughness of the machining experiment was conducted on the workpiece by a 6 mm end mill tool with a spindle rotational speed of 10,000 rpm. The dimension of the workpiece is 100 mm \(\times\) 50 mm, and the material of the workpiece is S45C steel, as shown in Figure 16.  
Figure 16: Workpiece dimension and finished workpiece.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cooling Channel** & **Original Design** & **Optimal Design** \\ \hline Front bearing temperature (\({}^{\circ}\)C) & 35.2 & 32.9 \\ Rear bearing temperature (\({}^{\circ}\)C) & 45.5 & 38.8 \\ Thermal Deformation (\(\mu\)m) & 53.8 & 30.9 \\ Warm up time (min) & 185.3 & 132.6 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Experimental results of the cooling channel with dimension optimization.  
The machining error results are shown in Table 9. The flatness machined by the original cooling channel design was 9.3 \(\upmu\)m, whereas the flatness by the cooling channel dimension optimization was 3.6 \(\upmu\)m, and the cooling channel dimension optimization can be enhanced with a flatness error of 5.7 \(\upmu\)m. The flatness of a workpiece with cooling channel dimension optimization can be improved effectively by 61.3% compared with the original cooling channel design. The centerline average roughness \(R_{a}\), maximum height roughness \(R_{max}\), and ten-point average roughness \(R_{z}\) with cooling channel dimension optimization were 0.24 \(\upmu\)m, 6.11 \(\upmu\)m, and 1.25 \(\upmu\)m, respectively. Compared with the original cooling channel design, \(R_{a}\), \(R_{max}\), and \(R_{z}\) with cooling channel dimension optimization are lower than 0.26 \(\upmu\)m, 2.83 \(\upmu\)m, and 0.72 \(\upmu\)m, respectively. \(R_{a}\), \(R_{max}\), and \(R_{z}\) can be effectively enhanced by 52%, 31.7%, and 36.5%, respectively.  
In the practical machining verification, the improved spindle cooling channel increased the cooling efficiency, reduced spindle thermal deformation, shortened the complete machine warm-up time, increased the machine operating rate, and in an actual cutting application, substantially improved the flatness and surface roughness of a workpiece. To summarize the findings, the improvement in the spindle cooling channel can improve the actual machining accuracy and shorten the required warm-up time of machine tools.