## 5 Calculation Method for Torsional Fatigue Life of Titanium Alloy Turning Surface
### Comparison and Analysis of Experimental Methods and Measurement Results  
The measurement method shown in Figure 5 of Section 2.2 was used to detect the five characteristic points of Scheme 1 and Scheme 2 separately. In surface morphology analysis, measurements were conducted within a 1 mm radius of the titanium alloy workpiece's characteristic points. Figure 27 presents the test results for Scheme 1, revealing uniform and smooth surface morphology at positions \(a_{1}\) and \(a_{2}\). Figure 27 demonstrates that the characteristic parameters of surface morphology exhibit greater heterogeneity at positions \(a_{3}\) and \(a_{4}\) compared to other measurement points in Scheme 1. From \(a_{3}\), surface roughness and irregular texture increase significantly, while surface defects become more pronounced at \(a_{4}\), suggesting the presence of micro-defects or stress concentration zones. These material imperfections promote fatigue stress accumulation between \(a_{3}\) and \(a_{4}\), initiating crack propagation that ultimately leads to fracture in this region. The results of Scheme 2 are shown in Figure 28. The surface morphology at points \(a_{1}\) and \(a_{2}\) is relatively smooth and regular, while the surface morphology at point \(a_{3}\) exhibits more obvious roughness and an increase in microdefects. Due to pre-existing defects or stress concentration within the material, stress tends to accumulate and propagate cracks between points \(a_{2}\) and \(a_{3}\) during fatigue testing, resulting in fractures occurring in this region. The surface topography of the processed cross-sections at different characteristic points for Scheme 2 is shown as illustrated. The normalized comparison results of the characteristic parameter standard deviations between Scheme 1 and Scheme 2 are shown in Figure 29. As can be seen from the figure, Scheme 2 generally performs better than Scheme 1 under most parameters. In particular, the standardized values of parameters x and z are close to 1, indicating Scheme 2's advantage in processing accuracy. In comparisons of spacing \(\Delta\)x and \(\Delta\)z in different directions, Scheme 2 also demonstrates significantly more consistent performance at most feature points. Figure 27: Test results of surface morphology of characteristic points in Scheme 1 (**a**) \(a_{1}\), (**b**) \(a_{2}\), (**c**) \(a_{3}\), (**d**) \(a_{4}\), (**e**) \(a_{5}\). Figure 28: Test results of surface morphology of feature points in Scheme 2 (**a**) \(a_{1}\), (**b**) \(a_{2}\), (**c**) \(a_{3}\), (**d**) \(a_{4}\), (**e**) \(a_{5}\). The change in element content reflects the difference in surface characteristic parameters directly, which can effectively reveal the performance difference of the machined surface in different regions. Element composition and content ratio of the titanium alloy turning surface were obtained by SU5000 scanning electron microscope and energy spectrum analyzer, and element content of different machined surfaces and different positions of the same machined surface were analyzed and compared. The SEM scanning results of Scheme 1 and Scheme 2 and their area scanning element distributions are shown in Figure 30.  
Figure 30 reveals that Scheme 1 exhibits inferior surface quality relative to Scheme 2, displaying increased surface defects, localized microcracks, and porosity. The results of scanning electron microscope testing show that there is obvious plastic deformation on the surface of the titanium alloy turned parts. These observations suggest localized stress concentration during machining. In contrast, Scheme 2 demonstrates a smooth, dense surface morphology, achieved through optimized machining parameters that enhance titanium alloy surface integrity. Figure 31 comparatively presents the elemental composition of machined surfaces from both Schemes.