## 5 Calculation Method for Torsional Fatigue Life of Titanium Alloy Turning Surface
### Titanium Alloy Torsional Strength Solution Results  
Groups 1-3 are simulation experiments with different machined surface topographies under the same surface and subsurface performance parameter conditions. Their initial states, torsional stress fields, and torsional fracture points are shown in Figure 17. When the machined surface topography is an ideal smooth surface and the surface/subsurface  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Group**} & \multirow{3}{*}{ \begin{tabular}{c} **Machined** \\ **Surface** \\ **Topography** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Residual Stress Distribution** \\ **Surface** \\ **Topography** \\ \end{tabular}  } & \multicolumn{3}{c}{ \begin{tabular}{c} **Hardening Rate** \\ **Distribution** \\ \end{tabular}  } & \multicolumn{3}{c}{\ \begin{tabular}{c} **Plastic Strain** \\ **Distribution** \\ \end{tabular}  } & \multicolumn{3}{c}{ \begin{tabular}{c} **Elastic Modulus** \\ **Distribution** \\ \end{tabular}  } \\ \cline{3-10}  & & & \(\sigma_{\mathbf{r}1}\) & \(\sigma_{\mathbf{r}2}\) & \(h_{\mathbf{r}}\) (\(\mathbf{\mu}\)m) & \(\eta\) (GPa) & \(h_{\mathbf{\eta}}\) (\(\mathbf{\mu}\)m) & \(\varepsilon_{\mathbf{p}}\) & \(h_{\mathbf{\varepsilon}}\) (\(\mathbf{\mu}\)m) & \(E\) (GPa) & \(h_{\mathbf{E}}\) (\(\mathbf{\mu}\)m) \\ \hline
1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 109.80 & 0 \\
2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 109.80 & 0 \\
3 & 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0  
performance parameters are all zero, the torsional strength of the titanium alloy workpiece reaches a maximum of 1170 MPa, with the corresponding maximum torque being 630 N m, The torsional fracture position is any point on the central section where a\({}_{3}\) is located. When the machined surface topography is a surface with uniform wave crests, wave troughs, and their spacing, and the surface/subsurface performance parameters are all zero, the maximum torque of the titanium alloy workpiece decreases to 340 N m, with a large decline. The torsional fracture point is still any point on the central section where a\({}_{3}\) is located. When the machined surface topography is a modified surface and the surface/subsurface performance parameters are all zero, the maximum torque continues to decrease to 300 N m. However, the position of the torsional fracture point is between the sections corresponding to a\({}_{3}\) and a\({}_{4}\), and the fracture point is unique. It can be seen from the calculation results that when the machined surface topographies are different, the maximum torque, fatigue life, and fracture position of the titanium alloy workpieces are different. Groups 4-6 are the simulation calculation results of single-factor analysis on the mean values of plastic strain, work hardening rate, and residual stress, as shown in Figure 18. The fracture positions are all arbitrary points on the central section where a\({}_{3}\) is located. When plastic strain acts alone, the maximum torque decreases compared to Group 3, indicating that plastic strain has a negative effect on the maximum torque; when residual stress acts alone, the maximum torque increases by 30.00% compared to Group 3, rising to 390 N m, showing a significant improvement; when the work hardening rate acts alone, the maximum torque increases by 16.67% compared to Group 3, rising to 350 N m, with the improvement range smaller than that of residual stress. Figure 17: Maximum torque and torsional fracture points of Groups 1–3. Figure 18: Maximum torque and torsional fracture points of Groups 4–6. The maximum torque and fracture location corresponding to Groups 7-10 are shown in Figure 19. They are the results of solving the minimum, average, and maximum values of the three surface sub-surface performance parameters under the same machined surface morphology conditions and the inhomogeneous distribution, respectively.