## 4 Parameter Reverse Identification Combined with Cutting Theory
### Parameter Correction  
The parameters of the equal shear zone model that were required for S32760 orthogonal cutting are shown in Table 6.  
It is observed that the strain rate increased with an increase in the cutting speed. When the strain rate increased to more than \(10^{4}\) s\({}^{-1}\), the dislocation slip velocity was controlled using the viscous resistance of dislocation, and the cutting process showed a viscous flow process similar to that of a fluid. The variation in the strain rate relative to the cutting speed is shown in Figure 12.  
From Equations (1), (2), and (5), the relationship between the flow stress and the cutting force is as follows:  
\[ \begin{cases}\sigma_{AB}=F_{c}\frac{\sin\varphi\cos\theta}{\cos(\lambda-\alpha )I_{1}w}\\ \sigma_{AB}=F_{t}\frac{\sin\varphi\cos\theta}{\sin(\lambda-\lambda)I_{1}w} \end{cases}  \tag{43}\]  
The shear angle \(\varphi\), friction angle \(\lambda\), and the included angle \(\theta\) were solved iteratively using the equal shear zone model. The parameters listed in Tables 4 and 6 were input into the equal shear zone model, and the predicted values of the equal shear zone model were obtained, which are shown in Table 7.  
The effects of the cutting speed on the shear angle, friction angle, and angle was analyzed, and the results are presented in Figures 13-15. It can be seen from Figure 13 that the shear angle decreased with an increase in the cutting speed. The plotted results in Figure 14 indicate that the friction angle increased with the increase in the cutting speed. Figure 15 shows that the included angle increased with the increase in the cutting speed. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Numerical Value** & **Unit** \\ \hline \(\rho_{w}\) & 8000 & Kg/m\({}^{3}\) \\ C\({}_{w}\) & 434.8 & J/Kg.\({}^{\circ}\)C \\ \(K_{w}\) & 17.6 & W/m\({}^{\circ}\)C \\ \(A\) & 596 & MPa \\ \(B\) & 964 & MPa \\ \(n\) & 0.138 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The parameters of the equal shear zone model required for S32760 orthogonal cutting. Figure 12: Variation in the strain rate relative to cutting speed. Therefore, from the relationship between the flow stress and the cutting component, the constitutive parameters were identified using the principle of the least-square method. The sum of the squares of the difference between the flow stress value calculated using the constitutive equation, and the flow stress value obtained using the cutting component was \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Number** & **Strain** & **Strain Rate/s\({}^{-1}\)** & **Angle of Shear \(\varphi\) /\({}^{\circ}\)** & **Angle of Friction \(\lambda\) /\({}^{\circ}\)** & **Included Angle \(\theta\) /\({}^{\circ}\)** \\ \hline
1 & 0.4548 & 10,811 & 40.97 & 3.39 & 26.36 \\
2 & 0.4551 & 18,161 & 40.91 & 3.54 & 26.45 \\
3 & 0.4555 & 25,317 & 40.85 & 3.68 & 26.53 \\
4 & 0.4558 & 36,549 & 40.79 & 3.83 & 26.63 \\
5 & 0.4545 & 7992 & 41.02 & 3.24 & 26.26 \\
6 & 0.4548 & 13,385 & 40.95 & 3.38 & 26.35 \\
7 & 0.4551 & 19,018 & 40.90 & 3.52 & 26.43 \\
8 & 0.4555 & 26,814 & 40.83 & 3.65 & 26.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Predicted values of equal shear zone model. Figure 14: Variation in the friction angle as a function of the cutting speed. Figure 13: Variation in the shear angle as a function of the cutting speed. taken as the objective function so that the objective function would be as small as possible. The objective function is expressed as follows:  
\[P(y)=\sum_{i=1}^{N}(\sigma_{i}(y)-\sigma_{AB})^{2} \tag{44}\]  
where \(y=[\overline{Y},n_{2},\sigma_{sh},\alpha,\beta,p,q]\) is the parameter to be optimized, \(N\) is the number of points taken, \(\sigma_{i}\) is the value calculated using the constitutive equation at the \(i\)-th point, and \(\sigma_{AB}\) is the value calculated using the cutting component at the \(i\)-th point. The MATLAB program was used to optimize the calculation.