## 3 Results and Discussion
Notably, all interaction effects are insignificant because the contribution values of two-way interaction are too small, as shown in Table 8. These results are consistent with the analysis of tool geometry in hard turning, which demonstrated that the inclination angle has the most significant influence on the local rake angle. The quadratic model for cutting temperature (1) with R\({}^{2}\)= 95.2% indicates a high degree of concordance between the predicted and experimental values, as shown in Figure 8. The regression equation for the cutting temperature be presented as follows:  
\[ \begin{array}{l}\text{T\_exp}=510.9+9.07\text{ Kr}-10.87\text{ }\gamma-3.74\text{ }\lambda-0.0619\text{ Kr}\times\text{Kr}-0.246\text{ }\gamma\times\gamma-0.340\\ \text{ }\lambda\times\lambda+0.0752\text{ Kr}\times\gamma-0.0405\text{ Kr}\times\lambda+0.195\text{ }\gamma\times\lambda\end{array}  \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**No. **} & **Cutting-Edge** & **Rake Angle** & **Inclination** & **Average Local** & **Simulated** & **Experimental** \\  & **Angle** \(K_{r}\) (\({}^{\circ}\)) & \(\gamma\) (\({}^{\circ}\)) & **Angle** & **Make Angle** & **Temperature** & **Temperature** \\  & **Angle** \(K_{r}\) (\({}^{\circ}\)) & \(\gamma\) (\({}^{\circ}\)) & **\(\gamma\)\_ave (\({}^{\circ}\))** & **\(T\_{\text{sim}}\) (\({}^{\circ}\)C)** & **\(T\_{\text{exp}}\) (\({}^{\circ}\)C)** \\ \hline
1 & 84 & \(-\)3.6 & \(-\)3.6 & \(-\)29.7 & 888 & 868 \\
2  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Source** & **DF** & **Seq SS** & **Contribution** & **Adj SS** & **Adj MS** & **F-Value** & _p-Value_ \\ \hline Model & 9 & 73.7959 & 99.98\% & 73.7959 & 8.1995 & 6783.94 & 0.000 \\ Linear & 3 & 72.5213 & 98.26\% & 72.5213 & 24.1738 & 20,000.32 & 0.000 \\ Kr & 1 & 0.7243 & 0.98\% & 0.7243 & 0.7243 & 599.22 & 0.000 \\ \(\gamma\) & 1 & 23.1987 & 31.43\% & 23.1987 & 23.1987 & 19,193.58 & 0.000 \\ \(\lambda\) & 1 & 48.5984 & 65.84\% & 48.5984 & 48.5984 & 40,208.15 & 0.000 \\ Square & 3 & 0.1496 & 0.20\% & 0.1496 & 0.0499 & 41.26 & 0.000 \\ Kr \(\times\) Kr & 1 & 0.1483 & 0.20\% & 0.1426 & 0.1426 & 118.01 & 0.000 \\ \(\gamma\times\)\(\gamma\) & 1 & 0.0006 & 0.00\% & 0.0007 & 0.0007 & 0.60 & 0.458 \\ \(\lambda\times\)\(\lambda\) & 1 & 0.0007 & 0.00\% & 0.0007 & 0.0007 & 0.60 & 0.458 \\
2-Way & 3 & 1.1250 & 1.52\% & 1.1250 & 0.3750 & 310.26 & 0.000 \\ Interaction & 1 & 0.7200 & 0.98\% & 0.7200 & 0.7200 & 595.70 & 0.000 \\ Kr \(\times\)\(\lambda\) & 1 & 0.4050 & 0.55\% & 0.4050 & 0.4050 & 335.08 & 0.000 \\ \(\gamma\times\)\(\lambda\) & 1 & 0.0000 & 0.00\% & 0.0000 & 0.0000 &Figure 5: The cutting process at the tool-nose radius in hard turning as determined from (**a**) simulation and (**b**) experimental results. Figure 6: Main effect plots for average local rake angle. Figure 7: Temperature distributions at the chip–tool interface, as determined through 3D finite element modeling (FEM). The main effect plots for the simulation and experimental cutting temperature are shown in Figures 9 and 10. They both indicate that increasing the negative rake angle and negative inclination angle leads to a rise in cutting temperature. The reason is when the negative inclination angle and rake angle are increased, the local rake angle becomes more negative. This results in increased friction at the contact surface between the chip and the chamfered face of the tool, as well as greater material deformation in the primary and secondary shear zones, thereby raising the cutting temperature. Figure 11 presents the relationship between the rake angle, inclination angle, and cutting temperature, which is consistent with the results in Figures 9 and 10. This figure also reveals that increasing the negative rake angle and negative inclination angle raises the cutting temperature. Interestingly, Figure 8 presents the comparison of measured and predicted temperatures of the hard-turning process. The results from the FEM simulation are