## 5 Calculation Method for Torsional Fatigue Life of Titanium Alloy Turning Surface
### Comparison and Analysis of Calculation Results for Different Turning Process Solutions  
To validate the effectiveness of the method for identifying surface torsional fatigue performance parameters in titanium alloy turning, turning simulations and experimental tests were conducted using the same cutting tool, workpiece, mounting method, cutting method, and testing method as in Section 3.4, Scheme 1. The feed rate per revolution\(f\) was 0.1 mm, the spindle speed \(n\) was 1081 r/min, and the cutting depth \(a_{p}\) was 0.1 mm.  
The surface morphology of Scheme 2 was calculated and corrected for comparison, as shown in Figure 24.  
Grey relational analysis was employed to evaluate the correlation between section profiles and experimental data. The pre-correction relational grade measured 0.88, increasing to 0.97 post-correction, demonstrating strong correlation characteristics. This optimized correlation significantly exceeds the performance observed in Scheme 1.  
Figure 23: Parameter identification method of torsional fatigue performance of titanium alloy turning surface.  
Figure 24: Comparison of characteristic points between the simulated surface and corrected surfaces in Scheme 2.  
The titanium alloy turning process under the Scheme 2 parameters was simulated using ABAQUS finite element analysis. Five identical characteristic points corresponding to Scheme 1 were selected for comparative analysis. Material properties were initialized using the same definition methodology as Scheme 1, with consistent torsional loading application procedures. The resulting torsional response characteristics are depicted in Figure 25.  
Finite element (FE) simulation results from the torsional fracture analysis were subsequently processed in FE-SAFE for fatigue life prediction. Scheme 2 demonstrates a fatigue life of 3.72 \(\times\) 10\({}^{5}\) cycles under cyclic loading conditions. Comparative performance metrics, including peak torque, fatigue life expectancy, and fracture locations for both experimental Schemes, are systematically presented in Table 8.  
Table 8 reveals that Scheme 2 exhibits a 19.44% increase in peak torque and a 45.88% enhancement in fatigue life compared to Scheme 1. Furthermore, the torsional fracture location demonstrates closer proximity to the titanium alloy specimen's axial midpoint, suggesting improved uniformity in both material performance parameters and surface morphology characteristics.  
Calculate the maximum torque and fatigue life of each point \(a_{1}\)\(\sim\)\(a_{5}\) in Scheme 2, and the calculation results are shown in Figure 26. Compared with the first Scheme, the overall consistency of the second Scheme is improved after the optimization of process parameters. The radial maximum torque and fatigue life of the turning surface are more uniform, and the maximum torque and fatigue life of each feature point are improved.  
By analyzing the fatigue life of different feature points corresponding to the angle to obtain their uneven degree, the results are shown in Figure 26. Through analysis, the error of characteristic point \(a_{3}\) at all angles is relatively high, indicating that fatigue fracture is more likely to occur near \(a_{3}\).