## 3 Results and Discussions  
### Numerical Analysis of Cooling Channel  
The existing cooling channel patterns can be divided into helical type, paralleling type, axial type, and trapezoidal type. The cooling efficiencies and pressure drop of different spindle cooling channel patterns were obtained in the simulation by ANSYS software. Figure 7 shows the simulation results of different oil with original cooling channel design in the built-in spindle. Figure 7: The simulation results of different oil products by ANSYS software. (**a**) Spindle temperature distribution; (**b**) Channel pressure drop; (**c**) Spindle deformation. The measured power of the spindle motor by the power meter at 12,500 rpm was 550 W, and the generating heat could be calculated by Equations (13)-(23). In the study, the heat generated by the core loss, copper loss, front bearing and rear bearing were 48.2 W, 14.4 W, 292.4 W, and 194.9 W, respectively. The frictional torque of bearing could be obtained by Equation (13), where the frictional torque of bearing was 420 N-mm. The generating heat of the spindle can be expressed as  
\[\mathbf{W}=\frac{Mn}{9550} \tag{23}\]  
where \(\mathbf{W}\) is the heat generated, n is the rotational speed of the spindle, and \(n\) is the rotational speed of spindle. The physical properties of the different oil types applied in the study are shown in Table 1. The simulation results of the spindle temperature and deformation with different oil types are shown in Table 2.  
Figure 7 and Table 2 show a comparison of the cooling efficiency results of VG10 and VG5 oils in the built-in spindle. The average wall temperature of the front bearing cooling channel using VG5 oil was 57.6 \({}^{\circ}\)C, which is 3.6 \({}^{\circ}\)C lower than using VG10, and the cooling efficiency of the front bearing was improved by 5.9%. The average wall temperature of the motor cooling channel using VG5 oil was 48.4 \({}^{\circ}\)C, which is 2.5 \({}^{\circ}\)C lower than using VG10, and the motor cooling efficiency was improved by 4.9%. The heat transfer coefficient in the cooling channel can be improved by using the oil type, and the effect of temperature rise can be improved effectively to reduce the thermal deformation. The pressure drop of VG5 oil in the cooling channel is 2.13 bar, which is 1.22 bar lower than using VG10 at the same oil flow rate of 12 L/min, and the pressure drop is reduced by 36.4%. In terms of spindle deformation, the average deformation of the built-in spindle is 118.3 \(\upmu\)m by using VG5 oil, which is less than the average deformation 124.6 \(\upmu\)m using VG10 oil by 6.3 \(\upmu\)m at the same oil flow rate of 12 L/min. The spindle accuracy can be enhanced by 5.1%. No specification is available for existing cooling channel designs, and the cooling conditions sometimes follow the requirements of the original manufacturer of a motor. The design of a cooling channel influences not only the cooling efficiency inside the spindle but also the accuracy of the spindle and machining results. The simulation results of the cooling efficiency, channel pressure drop, and spindle axial deformation of different front bearing and motor channel designs are compiled in Figure 8 and Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Properties** & **VG5** & **VG10** \\ \hline Density \(\rho\) (kg/m\({}^{3}\)) & 828 & 840 \\ Oil viscosity \(\mu\) (kg/m-s) & \(5.7\times 10^{-3}\) & \(1.18\times 10^{-2}\) \\ Specific heat \(C_{p}\) (J/kg-K) & 2173 & 2082 \\ Heat transfer coefficient \(k\) (W/(m-K)) & 0.128 & 0.130 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of VG5 and VG10 oil products.