## 1 Introduction  
In recent years, titanium alloy materials have been widely used in aerospace, shipbuilding, metallurgy, light industry, chemical industry, biomedical and other industries due to their excellent physical and chemical properties. However, the low thermal conductivity and high chemical activity of titanium alloys lead to severe tool wear and low cutting efficiency, which are the main factors limiting the development of titanium alloys. In the field of tribology, uneven surfaces have the function of reducing friction, and have received unprecedented attention. Therefore, the basic concept of surface texture is proposed. Preparing regularly arranged micro pits or grooves on smooth and susceptible surfaces can greatly reduce the friction and surface abrasion [1; 2; 3]. Micro-textures also play an active role in the field of modern cutting tools. Milling titanium alloys is intermittent, and cutting process of the cutter is very complicated. The cutting force on the cutter is unevenly distributed during the milling process, and its size and direction change with time. The distribution of the milling force directly affects the stress distribution inside the milling insert. Therefore, it is necessary to study the stress field of the cutter during the cutting process in order to obtain the worst conditions of the cutter. [PERSON] and [PERSON] studied the stress density function and stress field of the corrugated edge milling cutter and concluded that, during the cutting process of the corrugated edge milling cutters, the stress on the cutter is mainly distributed on the main cutting edge near the tip, and the stress is concentrated near the tip [4,5]. [PERSON] et al. studied the cutting stress field of ceramic tools with a gradient function by finite element analysis and obtained the optimal gradient distribution index by modeling the cutting stress field under the same cutting load [6,7]. [PERSON] et al. carried out milling force prediction experiments on the titanium alloy TC21. The results show that, in the process of high-speed milling TC21 titanium alloy, the cutting depth and feed per tooth have a greater impact on the cutting force, while the cutting speed and radial cutting depth have no significant effect on the cutting force [8,9]. [PERSON] and [PERSON] simulated the static and dynamic milling force in the face milling process. Based on the machine tool structure and fixture design, a mathematical model of the scattered force components of the face milling cutter was established. Consistent results were obtained from cutting experiments on different milling cutters and workpiece materials [10]. [PERSON] et al. studied the performance of spiral and serrated edge milling inserts in the cutting process. They believed that curved-edge milling inserts can improve the stability of machining, reduce milling forces and improve chip flow [11]. [PERSON] et al. numerically modeled and experimentally studied the micro-milling force of titanium alloy based on tool runout. The micro-milling force model was validated by analyzing the width of the steps on the edge of the groove [12,13]. [PERSON] simulated the stress field of a flat-faced milling cutter and a 3D complex groove milling cutter using the density function of the milling force as a boundary condition. It was found that a milling cutter with a rake angle and an edge inclination can fundamentally change the stress at the tool tip [14,15]. [PERSON] et al. fabricated micro-grooves and micro-pits on the rake face of WC/Co tools, and then studied the cutting performance of the tools. The results show that the composite texture with micro-pits and micro-slots can be used as a micro-reservoir to continuously supplement lubricating oil, thus improving the cutting performance of the mixed micro-textured cutter [16, 17, 18]. [PERSON] et al. conducted tribological and cutting experiments on aluminum alloy workpieces by sandblasting micro-materials and machining micro-geometric features of the rake face of the sapphire tools.