## 1 Introduction
### Design and Fabrication of Variable Density Micro-Textures  
Previous studies of micro-textured cutters used a uniform distribution method to prepare micro-textures in the areas where the cutter-chips are in close contact [25; 26]. However, from the tool wear diagram of the micro-textured cutters after cutting titanium alloy, it can be seen that the wear of the tool along the contact length and width of the cutter-chip in the compact contact area of the rake face is irregular. The wear near the cutting edge is more severe, and, as the distance from the cutting edge gets longer, the wear on the tool becomes less and less [27]. There is also some wear in the direction of chip outflow. This is because, during the outflow of chips, the cutting speed of the ball-end milling cutter along the cutting edge is different, which leads to the transverse curl of the chip. As the cutting depth increases, the flow rate at the bottom of the chip is different from flow rate at the top, and the chip curls upward. Therefore, in the process of chip deformation, \"secondary cutting\" occurs at the edges of the micro-texture, as shown in Figure 1. This phenomenon will cause secondary wear of micro-textured cutters.  
In order to solve the \"secondary cutting\" phenomenon of the micro-textured cutter, the region where the cutter-chip is in compact contact is divided into three regions according to the wear condition of the cutter, namely the first area \(X_{1}\), the second area \(X_{2}\), and the third area \(X_{3}\), as shown in Figure 2. Studies have shown that pit texture can effectively reduce friction and wear [28; 29]. Therefore, by changing the density of micro-texture in each region, the dynamic evolution of secondary cutting between micro-textured cutter and the chip was studied. Experiments have shown that a texture distribution density (the ratio of the total area of the pit texture to the total area of the micro-texture preparation is defined as the texture distribution density) between 0.05 and 0.1 can play a better role in reducing friction and wear. Therefore, the micro-texture densities in the cutter-chip contact area of the cemented carbide tool designed in this paper are 0.05, 0.07 and 0.09, respectively. By arranging and combining the three texture densities in the cutter-chip compact contact area, three uniformly distributed micro-textures and six variable density micro-textures were obtained. The distribution combination of the texture density is shown in Table 1.  
Figure 1: Diagram of “secondary cutting” for the micro-textured cutter.  
According to previous studies, when the diameter, depth and distance from the cutting edge of the micro-texture are 50 \(\upmu\)m, 35 \(\upmu\)m and 120 \(\upmu\)m, respectively, the micro-textured cutter can achieve better friction reduction and wear resistance [30]. Therefore, the diameter, depth and distance from the cutting edge of the micro-texture designed in this paper are 50 \(\upmu\)m, 35 \(\upmu\)m and 120 \(\upmu\)m, respectively. According to the three densities of 0.05, 0.07 and 0.09, the center spacing between the micro-textures are 190 \(\upmu\)m, 170 \(\upmu\)m and 150 \(\upmu\)m, respectively. The micro-textures were then prepared in three areas of the cutter-chip compact contact by using a fiber laser. After processing, the melt around the micro-texture was cleaned by sandpaper and an ultrasonic cleaner.