## 5 Turning Experiment
### Actual Temperature of the Cutting Area
#### 5.1.2 Derivation of Tool Nose Temperature  
Because the thermocouple temperature measurement can only measure the temperature at a certain point the certain distance from the rake face, in order to eliminate this limitation of thermocouple temperature measurement, the inverse heat conduction method was used to find out the relationship between the temperature measured by the thermocouple and the actual temperature of the tool nose. The specific flow chart of the inverse heat conduction method is shown in Figure 8.  
Figure 6: Enlarged views of micro-texture shapes of five tool noses.  
Figure 7: Position of the temperature measurement point: (**a**) hole of the thermocouple; (**b**) the hole machined by EDM of the tool.  
The heat transfer model was established in ANSYS. As shown in Figure 9, only the tool nose and its adjacent area participated in the whole cutting process, and the cube of 0.7 mm \(\times\) 0.7 mm \(\times\) 1 mm was divided at the tool nose. The upper surface of the cube was used as the cutting area, the lower surface was used as the measurement area of the thermocouple, and the temperature obtained in the cutting area was the cutting temperature.  
In the analysis of the heat-transfer process, the main step was the temperature transfer of the small cube cut from the tool nose. Then, the meshes of the small cube part were refined to improve the accuracy of the calculation. The properties of the carbide material are shown in Table 6. After applying the cutting temperatures of 200 \({}^{\circ}\)C, 250 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, and 350 \({}^{\circ}\)C in the cutting area, the temperatures in the thermocouple measurement area can be obtained, respectively. Table 7 shows the comparison between the measured temperatures of the thermocouple and the actual cutting temperatures.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Materials** & **Carbide** \\ \hline Thermal Conductivity (W/M\({}^{\circ}\)C) & 71 \\ Density (Kg/m\({}^{3}\)) & 15,600 \\ Specific Heat(J/Kg\({}^{\circ}\)C) & 452 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Properties of cemented carbide.  
Figure 8: Flow chart of heat conduction inverse method.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Number** & **Tool Nose Temperature \(Y\)** & **Measuring Temperature \(X\)** \\ \hline
1 & 200 & 123.98 \\
2 & 250 & 167.47 \\
3 & 300 & 214.97 \\
4 & 350 & 256.90 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Heat transfer results.  
Figure 9: Heat-transfer model.  
The data in Table 7 were fitted by MATLAB, and the final equation of the relationship between the actual temperature of the tool nose and the measured temperature is as follows:  
\[Y=0.00021873X^{2}+1.0366X+68.6841 \tag{2}\]  
where \(X\) was the temperature of the measurement area of the thermocouple, and \(Y\) was the temperature of the tool nose in the cutting area. Experiments showed that the temperature measured by the thermocouple in dry cutting was 136 \({}^{\circ}\)C; substituting this into the above formula, \(X\) obtained that \(Y\) was equal to 213.71 \({}^{\circ}\)C, which was the temperature of the tool nose. Under the same cutting parameters, the cutting temperature of the simulation was 197 \({}^{\circ}\)C by using DEFORM. Compared with the results of DEFORM, the results obtained by substituting the temperature measured by the thermocouple into the formula and the error of the simulation results relative to the experimental results is 7.51%, which was within the acceptable range. In conclusion, the fitted quadratic function is more accurate.