## 1 Introduction  
Featuring high specific strength, high creep corrosion resistance, and high wear resistance, titanium alloy has been extensively used in the fields of aviation, aerospace, energy, and biomedical science [1]. Nevertheless, small tool-chip contact area, large unit cutting force, and high cutting temperature might be caused in the cutting process due to the physical properties of titanium alloy, like low thermal conductivity, small elastic modulus, and large friction coefficient. In general, a ball end milling cutter is utilized to produce the surface finish of titanium alloy. In that case, the forming of the helix angle and the rake angle of the end tooth is limited by the tool manufacturing method and fails to achieve the same design parameters as its cylindrical tooth [2; 3; 4; 5; 6; 7; 8]. The machining quality and application of titanium alloy parts are severely restricted by the physical characteristics of titanium alloy and the shortcomings of the existing tool. A variety of research concerning the cutting technology of titanium alloy has been conducted by scholars at home and abroad. [PERSON] et al. [9] studied the tool wear mechanism when TC4 was cut at a speed of 150 m/min using an uncoated tool made of hard alloy under dry cutting conditions. In the experiment, crater wear, bond wear, and diffusion wear occurred on the rake face of the tool. Moreover, certain plastic deformation could also be observed on the rake face of the tool. [PERSON] et al. [10] put forward a segmented monitoring method based on cutting vibration signals. Tests showed that the proposed method can achieve a satisfactory detection result with different cutting parameters. By studying the wear pattern of the blade on a coated tool continuously cutting titanium alloy, [PERSON] et al. [11] determined that the wear pattern of the rake face of the coated blade is broken without plastic deformation. Further, coating damage was also affected by the interface strength between adhesive materials and coatings, as well as the strength of adhesive materials at high temperatures. [PERSON] et al. [12] studied the influence of workpiece inclination on surface integrity during the machining of titanium alloys. The findings showed that the average compressive stress decreases with increasing angle of the workpiece for avoiding tool center cutting and tool deflection. The best surface roughness was provided when the workpiece inclination was 15\({}^{\circ}\). [PERSON] et al. [13] carried out a test study on titanium alloy milling with respect to the inclination angle of the ball end milling cutter and obtained the influence law of milling method on the cutting force, tool wear, and its surface integrity. By observing from the test, the cutting force generated by upwards milling along the angle, the best surface quality, and the longest service life of the tool milling downwards along the angle could be obtained. [PERSON] et al. [14] detected that the cutting depth has maximum influence on the cutting force, while the cutting speed has a significant influence on temperature, after conducting a study on a high-speed TC4 cutting test using a carbide-tipped milling cutter. [PERSON] et al. [15] studied the tool wear and corresponding surface morphology in the processing of fine-grained tools machining TC4 at a high speed. First of all, wear on the rake face and the flank face of the tool was studied in detail from the aspects of wear morphology and chemical elements. This indicated that the wear on the rake face is associated with the combined effect of adhesion, diffusion, and wear, while the major wear mechanism of the flank face is adhesive wear. Next, the influence of tool wear on the corresponding surface morphology was evaluated in regard to surface roughness and defects. [PERSON] et al. [16] solved the problem of chip accumulation by proposing a tool featuring coordinated chip flow with variable strengthening edge.