## 4 Temperature Field Prediction Model Application
### Boundary Conditions of the Model  
One of the boundary conditions of the prediction model is the rate of heat generation, which is calculated based on losses in the motorized spindle. The motor losses and bearing friction losses could be measured by the loss experimental device shown in Figure 6. The specific steps are as follows:  
First, the loading machine and motorized spindle are connected, power supply to the motorized spindle is cut off, and it is rotated synchronously with the loading machine. At this point, the spindle exhibits only frictional loss, and the input power \(P_{J1}\) of the loading machine is tested. Second, the motorized spindle and loading machine are disconnected, where the latter has the same speed as in the first step, and the input power \(P_{J2}\) of the loading machine is determined. Figure 5: Temperature testing system of the motorized spindle. Figure 6: Loss experimental device. Third, the motorized spindle and loading machine are disconnected, where the former has zero load under the same speed as in the first step, the electrical parameter tester measures the input voltage and current of the motorized spindle, and the input power pin of the motorized spindle is obtained. At the same time, the torque/speed transducer can measure the output torque and speed of the motorized spindle, and the output power point of the motorized spindle can be measured. The loss due to friction in the motorized spindle is  
\[p_{f}=P_{I1}-P_{I2} \tag{10}\]  
and the loss in the motor is  
\[p_{e}=P_{in}-P_{out}-p_{f} \tag{11}\]  
Usually, two-thirds of the motor loss occurs at the stator and one-third at the rotor [25]. Using the above method, the bearing loss, rotor loss, and stator loss of the 170 MD30 motorized spindle (Luoyang Bearing Science & Technology Co., Ltd., Luoyang, Henan, China) were measured at 10,000 rpm and 15,000 rpm as shown in Table 3. All losses were converted into heat, and the rates of heat generation of the stator, rotor, and bearing are calculated as the boundary conditions of the finite element model. In the finite element model for the temperature field of the motorized spindle, another boundary condition is the heat transfer coefficient at the key positions. In this paper, the traditional empirical formula [26; 27; 28] was used to calculate the initial value of the heat transfer coefficient. The temperature-related test data for the optimization of the heat transfer coefficient were drawn from a temperature test system consisting of 31 temperature sensors placed on the surface of the motorized spindle. The arrangement of the temperature test is shown in Figure 7. Test position 1 was at the front bearing, position 3 at the rear bearing, position 2 was directly between the first two, and the end of the spindle formed test position 4. There were 10 thermocouples from test positions 1 to 3 that were uniformly distributed along the direction of the circumference. Moreover, an infrared thermal sensor was arranged at test position 4. To prove the validity of the model, the temperature field of the motorized spindle was predicted under the following two conditions. The test parameters when the speed of the motorized spindle was 10,000 rpm included cooling water flow of 0.25 m\({}^{3}\)/h, an initial temperature of 12 \({}^{\circ}\)C of the cooling water, compressed air inlet pressure of 0.365 MPa, a fuel supply interval of 2 min, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Speed (rpm)** & **Heat of Stator (w)** & **Heat of Rotor (w)** & **Bearing Heat (w)** \\ \hline
10,000 & 326.68 & 143.32 & 77.08 \\
15,000 & 452.67 & 226.33 & 151 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The heat rates of the motorized spindle. Figure 7: Arrangement of temperature test positions.