## 7 Conclusions  
1. To account for the influence of tool geometry parameters, cutting parameters, and cutting forces on tool-workpiece surface morphology, an instantaneous cutting behavior model was developed. Parametric equations describing the primary and secondary cutting edges, along with their transitional arc segments, were formulated. Solutions for machining transition surfaces across adjacent cutting cycles were derived. A methodology for characterizing instantaneous cutting layers and mechanical responses during titanium alloy machining was established. Furthermore, a simulation framework and surface morphology correction model were implemented to analyze machined titanium alloy surfaces.  
Figure 34: Point scan detection results of Scheme 2: (**a**) The elements are distributed along the feed direction, (**b**) Element content at different sampling points.  
To address the non-uniform distribution of surface feature parameters in titanium alloy turning, the instantaneous subsurface state during machining was characterized. A finite element model and analytical framework were developed to investigate axial and radial distributions of surface feature parameters on machined titanium alloy surfaces. Results demonstrate positional variations in both axial and radial dimensions for the size and depth of machined surface features during titanium alloy processing.
3. A torsional fatigue life prediction model for turned titanium alloys was developed, incorporating torque loading conditions and torsional strength variations induced by non-uniform initial load distributions. Fatigue life analysis of machined surfaces with heterogeneous parameter distributions was performed, accounting for surface feature parameter discrepancies across distinct regions. This investigation quantifies the influence of parameter heterogeneity on fatigue performance. Experimental results demonstrate significant variations in fatigue life distribution among titanium alloy workpieces under identical torque conditions, directly attributable to differences in surface feature parameters. Comparative analysis and experimental verification demonstrate that tool parameter optimization enables modification of titanium alloy turned surfaces' performance parameters, elemental composition, and distribution characteristics. This adjustment enhances surface mechanical properties, effectively improving torsional strength and fatigue life in titanium alloy components.
4. Comparative analysis and experimental verification results show that by adjusting the cutting tool process parameters to alter the performance parameters, element content, and distribution of the machined surface of titanium alloys, it is possible to improve the mechanical properties of the machined surface to a certain extent, thereby enhancing its torsional strength and fatigue life.  
Conceptualization, B.J.; methodology, P.Z.; software, D.W.; validation, H.S.; data curation, D.W.; writing--original draft preparation, D.W.; writing--review and editing, B.J. and P.Z.; funding acquisition, B.J. and P.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52375421, and the Key R&D Program of Heilongjiang Province, grant number JD2023 SJ12.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.