## 1 Introduction
[9] took Ti-6 Al-4V titanium alloy as experimental material, based on the single variable control strategy, and used the research method of combining the circumferential milling process with the durability evaluation of the specimen, systematically exploring the correlation mechanism between the multi-dimensional characteristics of machined surface and the fatigue resistance of materials by cutting parameter optimization. [PERSON] et al. [10] studied the effect of feed rate on fatigue life in titanium alloy machining. By changing the feed rate, titanium alloy (Ti-6 Al-4V) was machined with a single-factor Scheme, and the morphological characteristics of the machined surface under different feed rate conditions were observed. High-cycle fatigue tests were carried out for samples machined with different feed rates, and the effect of feed rates on high-cycle fatigue life was discussed. [PERSON] et al. [11] found that in FGH96 superalloy turning, the fatigue life of the tool wear VB \(\leq\) 0.15 mm decreased slightly, and it decreased sharply after exceeding it, so it was necessary to control the wear amount. [PERSON] [12] pointed out that in turning, increasing the thickness of the TiAlN coating can reduce the surface tensile residual stress and improve the low-cycle fatigue life. The 3 \(\upmu\)m coating can increase the life linearly by 15.6%. Comparing turning with grinding, [PERSON] [13] found that the surface compressive residual stress, microhardness, and fatigue life of finish turning samples were higher than those of grinding samples. [PERSON] et al. [14] study of TC17 titanium alloy shows that feed rate has the greatest effect on surface residual compressive stress and roughness, the former improves fatigue life, and the latter linearly decreases it. [PERSON] [15] further reveals that feed has the most significant effect on fatigue life in TC17 turning, and cracks mostly originate from the surface, so it is necessary to optimize turning parameters to improve surface integrity. [PERSON] [16] found that large tip radius, sharp cutting edge, and low feed speed can make polycrystalline copper amorphous and lattice transformation in diamond turning and obtain an ultra-smooth and ultra-hard surface. [PERSON] [17] found that the surface quality of low carbon steel can be improved with the increase in cutting speed, deteriorated with the increase in feed rate and cutting depth, and the surface quality is the worst in the late stage of tool wear. [PERSON] [18] pointed out that the tool flank wear and cutting speed increase will reduce the EN31 steel hard turning subsurface stress distribution compressibility, residual stress, and tool wear, where white layer thickness is highly correlated. [PERSON] et al. [19; 20] pointed out that residual stress is caused by surface thermal gradient or plastic deformation difference, which directly affects the service performance of materials. [PERSON] et al. [21] found that the non-uniform distribution of surface integrity significantly accelerates stress corrosion cracking initiation. [PERSON] et al. [22] further showed that the dynamic state parameters, such as residual stress and strain in the surface layer/subsurface layer, showed significant variability in multiple cutting strategies. In essence, both national and international researchers have conducted comprehensive investigations on the surface integrity and fatigue characteristics of titanium alloy turning surfaces. These studies have focused on regulating processing parameters and examining the effects of vibration and interface conditions, thereby establishing a groundwork for assessing the fatigue properties of such surfaces. Nevertheless, ensuring the precise identification of fatigue properties for titanium alloy turning surfaces proves challenging due to intricate factors like surface morphology and the non-uniform distribution of subsurface property parameters.