## 3 Results and Discussions
### Numerical Analysis of Cooling Channel
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Comb-Nation**} & \multicolumn{2}{c}{**Cooling Channel Pattern**} & \multicolumn{2}{c}{**Average**} & \multirow{2}{*}{**Increment**} & \multirow{2}{*}{**Average**} & \multirow{2}{*}{**Increment**} & \multirow{2}{*}{**Pressure Drop**} & \multirow{2}{*}{**Increment**} & \multirow{2}{*}{**Deformation**} & \multirow{2}{*}{**Increment**} \\  & & & **Temperature of** & **(\%)** & & & & **Temperature of** \\  & & & & & & & **Max (C)** & & & \\ \hline
1 & Single-turn (VCG) & Helical type & 61.2 & - & 50.9 & - & 3.35 & - & 124.6 & - \\
2 & Single-turn (VCG 5) & Helical type & 57.6 & 5.9 & 48.4 & 4.9 & 2.13 & 36.4 & 118.3 & 5.0 \\
3 & Parallelization & Helical type & 43.3 & 29.2 & 48.3 & 5.1 & 2.33 & 30.4 & 99.8 & 27.9 \\
4 & Parallelizing (split flow) & Helical type & 42.4 & 30.7 & 43.4 & 14.7 & 1.65 & 50.7 & 86.8 & 30.3 \\
5 & Parallelizing & Single-turn paralleling & 42.4 & 30.7 & 38.9 & 23.6 & 5.1 & -52.2 & 86.2 & 30.8 \\
6 & Parallelizing & Single-turn paralleling & 43.1 & 29.6 & 49.6 & 2.6 & 2.29 & 31.6 & 89.4 & 28.3 \\
7 & Parallelizing & Double turn paralleling & 42.7 & 30.2 & 43.1 & 15.3 & 2.76 & 17.6 & 86.2 & 30.8 \\
8 & Parallelizing & Axial type & 42.6 & 30.4 & 37.3 & 28.7 & 9.25 & -76.1 & 85.7 & 31.2 \\
9 & Parallelizing & Axial type dimension up & 42.6 & 30.4 & 38.6 & 24.2 & 4.20 & -25.4 & 86.2 & 30.8 \\
10 & Parallelizing & Trappededal type & 43.6 & 28.8 & 49.3 & 3.1 & 2.49 & 26.7 & 93.0 & 25.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of simulation results of spindle thermal and cooling channel pressure drop. In terms of the design of the motor cooling channel, different cooling channel types--the helical type, paralleling type, axial type, and trapezoidal type--and different channel dimensions were analyzed. The results indicate that the design of the axial type cooling channel can reduce the motor cooling channel wall temperature by 11.1 \({}^{\circ}\)C from 48.4 \({}^{\circ}\)C to 37.3 \({}^{\circ}\)C, followed by the axial cooling channel with larger dimensions. According to the analysis results, the helical type, single-turn paralleling size, and trapezoidal type of motor cooling channel have no obvious effect on reducing the motor temperature, whereas the cooling channel design alteration of the front bearing has a better effect. Because the front bearing has a much higher heat generation rate than the motor, the cooling effect can be improved by increasing the cooling efficiency of the front bearing. According to the pressure drop results of the cooling channel designs, only if the front bearing has the paralleling type design and the motor has the helical type cooling channel split design, the pressure drop can be minimized to 1.65 bar. However, the axial type cooling channel design achieved the maximum pressure drop of 9.25 bar, followed by the helical type design. For the practical application of the machine tool spindle cooling channel, a lower pressure drop is better. Considering the cost, the larger is the pressure drop, the larger should be the supply pump of the cooling machine and the cooling capacity of the cooling system, which generates a higher cost. According to the accuracy results of the spindle, the spindle deformation of the motor cooling channel design type of the axial type size (No. 9) was 85.7 \(\upmu\)m, which was the smallest among all cooling channel design types, followed by the single-turn paralleling, double turn paralleling, and axial design types with a deformation of 86.2 \(\upmu\)m. The third smallest type was the helical type cooling channel split design of motor with a deformation of 86.8 \(\upmu\)m.  
In Table 3, the temperature, pressure drop, and deformation in the simulation results are evaluated. The front bearing and the motor adopted the paralleling type cooling channel design and helical type cooling channel design, respectively. The cooling channel temperature of the front bearing was the lowest, followed by the cooling channel wall temperature of the motor.