## 4 Results and Discussion
### Cutter Edge Temperature in One Trochoidal Cycle  
Adopting the same tool-workpiece pair as in Section 3.1, a straight slot was machined by trochoidal milling strategy, as shown in Figure 6. Cutting parameters adopted are shown in Table 4. The period for the cutter feeding one trochoidal cycle is calculated to be 15.57 s. By applied Equation (21), the immersion angles at a number of moments of the period are calculated and plotted in Figure 11. It is evident that the immersion angle gradually increases and reaches its maximum \(\theta_{max}\) = 83.82\({}^{\circ}\) at the moment \(t\) = 2.41 s. This implies that cutting edges engage with the material for a longer period. Then the immersion angle starts to decrease until the cutter leaves the material at the moment \(t_{c}\) = 8.805 s, which is calculated by Equation (19). After the moment \(t_{c}\), no cutting edge cuts the material until next trochoidal cycle. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(V\) & \(f_{z}\) & \(a_{p}\) & \(n\) & \(R\) & \(c\) & \(r\) \\
**m/min** & **mm/z** & **mm** & **rev/min** & **mm** & **mm** & **mm** \\ \hline
214 & 0.105 & 2 & 1310 & 26 & 4 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cutting parameters adopted during trochoidal machining. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth** & **Predicted Max \(T\)** & **Measured Max \(T\)** & **Difference of Max \(T\)** \\ \hline
0.1 mm & 399.7 & 407.9 & \(-\)2.05\% \\
0.2 mm & 381 & 359.7 & 5.59\% \\
0.3 mm & 358 & 296.4 & 17.21\% \\
0.4 mm & 330.6 & 231.7 & 29.92\% \\
0.5 mm & 302.5 & 211.6 & 30.5\% \\ \hline \hline \end{tabular} \(T\)—temperature (\({}^{\circ}\)C).  
\end{table} 
Table 3: Differences between the predicted and experimental results by [PERSON] et al. [35]. For the selected cutting edge, the heat flux \(q_{c}\) during the machining of one trochoidal cycle is calculated by Equation (1) and plotted in Figure 12a. Three zoom-in diagrams at the intervals of 0.2308-0.3692 s, 2.3080-2.4460 s, and 6.4620-6.600 s are presented in Figure 12b-d. In the interval of 0.2308-0.3692 s (Figure 12b), the cutter rotates three revolutions, and the cutting edge cuts the material three times. The cut-in and cut-out moments of each cut are marked with red and blue dot, respectively. From the cut-in moment to the cut-out moment of a cut, from 0.2769 to 0.2789 s for example, the heat that flows into the cutting edge is about \(2.5\times 10^{9}\) W/m\({}^{2}\), and the cutting edge is heated up for 0.0020 s. While from the cut-out moment of the cut to the cut-in moment of the next cut, from 0.2789 to 0.3231 s for example, no heat flows into the cutting edge so it is cooling down for 0.0442 s. The heat flux pattern and magnitude in Figure 12c are similar with those in Figure 12b. However, the heat-up time was extended to 0.0110 s, and the cooling-down time was reduced to 0.0350 s, in which situation a higher temperature on the cutting edge is expected. To investigate the cutting-edge temperature, a location inside the cutter, 0.1 mm under its rake face, is selected to conduct the simulation. The location coordinate is (0.1, 0.6, 1.3). By numerically solving Equation (14), the temperature of the location in a trochoidal cycle is calculated and plotted in Figure 13. A detailed zoom-in diagram is provided in the figure as well. In the interval of 6.45-6.60 s  
Figure 11: Immersion angles \(\theta_{imm}\) obtained of the trochoidal toolpath. Figure 12: Heat flux \(q_{c}\) flows into the cutter (**a**) in one trochoidal cycle, (**b**) at the interval of 0.2308–0.3692s, (**c**) at the interval of 2.3080–2.4460s and (**d**) at the interval of 6.4620–6.600s. (see zoom-in Diagram in Figure 13), the cutter rotates three revolutions and the cutting edge cuts the material three times. Three temperature waves are observed in the diagram. The temperature rises rapidly at the beginning of the wave, after reaching its maximum \(T_{max}\), the temperature drops down sharply then drops a little slower.