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Orthogonal Optimization of Geometric Parameters of Spherical End Mills for Titanium Alloy Slotted

**I. Introduction** Fan wheels and diagonal wheels are essential components of an engine, and their machining quality directly impacts the engine’s thrust and efficiency. These complex surfaces can be machined using multi-axis CNC machining centers with 3D CAD/CAM technology. However, due to the difficulty in machining TC6 titanium alloy—a material known for its high strength and low thermal conductivity—the performance of the CNC milling cutter plays a critical role in determining the workpiece's geometric accuracy, surface finish, and overall processing efficiency. To address these challenges, five-axis CNC grinding technology is used to customize ball-end mills for titanium alloy surfaces. By applying orthogonal experimental design, the geometric parameters of the milling tool can be optimized, significantly improving machining efficiency and reducing production costs. **II. Characteristics of Titanium Alloy Surface CNC Milling** 1. **Surface Formation in CNC Milling** In NC milling, two main methods are used: wire forming and surface forming. The surface forming method utilizes the side edges of the milling cutter as cutting edges, making it suitable for curved surfaces like inclined, cylindrical, conical, and toroidal shapes. The wire forming method treats the surface as a set of lines, with each point on the cutter’s edge creating a single profile line. This allows for the machining of highly complex curved surfaces. Key features include: - Ball-end mills are commonly used for complex surfaces, sometimes replaced by cone-end ball-end mills for increased rigidity. - Surface roughness tends to be relatively poor. - In curved surface machining, the contact between the chip and the tool changes dynamically due to multi-axis movement and uneven cutting conditions. 2. **Cutting Characteristics of TC6 Titanium Alloy** TC6 (Ti-6Al-2.5Mo-2.0Cr-0.3Si-0.5Fe) is a heat-resistant titanium alloy, capable of operating at temperatures between 350°C and 450°C. Its mechanical properties at room and high temperatures are listed in Table 1. **Table 1: Specified Properties of TC6 Titanium Alloy** | Property | Value | |----------|--------| | Room Temperature | High Temperature | | δb (MPa) | 931 | 588 | | δ (%) | 10 | 539 | | ψ (%) | 23 | – | | αK (MJ·m⁻²) | 0.3 | – | | Temperature (°C) | – | 450 | The cutting characteristics of TC6 titanium alloy include: - **High Cutting Edge Load**: Despite lower cutting force compared to steel, the load is concentrated near the cutting edge, leading to chipping. - **High Cutting Temperatures**: Due to poor thermal conductivity, cutting temperatures can be twice as high as when machining 45 steel. - **Tool Wear**: The alloy reacts with oxygen and nitrogen, forming a hard brittle layer that increases abrasive wear. Additionally, strong chemical affinity between titanium and tool materials leads to adhesive wear. These factors contribute to difficulties in cutting, reduced tool life, and lower machining efficiency. **III. Orthogonal Optimization of Ball-End Mill Geometry Parameters** To meet the requirements of machining fan wheel and diagonal wheel surfaces, a five-axis CNC grinding center is used to manufacture customized ball-end mills for titanium alloy. An orthogonal test method was employed to optimize several sets of geometric parameters for the end mill. The parameter combinations are shown in Table 2. **Table 2: Tool Geometry Parameter Combinations** | Tool No. | Rake Angle γ₀ (°) | Relief Angle α₀ (°) | Blade Width br₁ (mm) | Helix Angle β (°) | |----------|------------------|--------------------|----------------------|-------------------| | 1 | 8 | 8 | 0.2 | 36 | | 2 | 8 | 10 | 0.3 | 38 | | 3 | 8 | 12 | 0.4 | 40 | | 4 | 10 | 8 | 0.3 | 40 | | 5 | 10 | 10 | 0.4 | 36 | | 6 | 10 | 12 | 0.2 | 38 | | 7 | 12 | 8 | 0.4 | 38 | | 8 | 12 | 10 | 0.2 | 40 | | 9 | 12 | 12 | 0.3 | 36 | Test conditions included a spindle speed of 540 rpm, feed rate of 140 mm/min, and a depth of cut of 4 mm. The evaluation criteria were based on flank wear after specific time intervals. The results are presented in Table 3 and Table 4. **Table 3: Test Results** | Tool No. | Workpiece No. | Test Result (Flank Wear) | |----------|---------------|--------------------------| | 1 | 1# groove, second layer | 0.15mm after 30 mins, broke at 33 mins | | 2 | 2# groove, second layer | 0.05mm after 30 mins, broke at 33 mins | | 3 | 3# groove, second layer | 0.12mm after 6 mins, damaged | | 4 | 4# groove, second layer | 0.1mm after 30 mins, broke at 32 mins | | 5 | 5# groove, second layer | Broke at 15 mins | | 6 | 6# groove, second layer | Damaged at 6 mins, 0.05mm | | 7 | 7# groove, second layer | 0.05mm after 32 mins | | 8 | 8# groove, second layer | 0.05mm after 30 mins | | 9 | 9# groove, second layer | Broke at 6 mins | **Table 4: Analysis of Test Results** | Tool No. | Rake Angle γ₀ (°) | Relief Angle α₀ (°) | Blade Width br₁ (mm) | Helix Angle β (°) | Test Score | |----------|------------------|--------------------|----------------------|-------------------|------------| | 1 | 8 | 8 | 0.2 | 36 | 1 | | 2 | 8 | 10 | 0.3 | 38 | 3 | | 3 | 8 | 12 | 0.4 | 40 | 0 | | 4 | 10 | 8 | 0.3 | 40 | 2 | | 5 | 10 | 10 | 0.4 | 36 | 0 | | 6 | 10 | 12 | 0.2 | 38 | 0 | | 7 | 12 | 8 | 0.4 | 38 | 3 | | 8 | 12 | 10 | 0.2 | 40 | 1 | | 9 | 12 | 12 | 0.3 | 36 | 0 | From the analysis, the best wear resistance was achieved when the tool had γ₀ = 12°, α₀ = 8°, br₁ = 0.4 mm, and β = 38°. This combination represents the optimal geometry for ball-end mills used in machining fan wheel surfaces. Additionally, the tests showed that tools must be re-sharpened after 30 minutes of use to prevent excessive wear and maintain efficiency. **IV. Conclusion** By employing whole CNC grinding technology and orthogonal test design, custom CNC tools can be developed for titanium alloy surfaces. Even with standard tool materials, optimizing the geometric parameters can lead to improved cutting performance. The test results demonstrated that the slotted ball-end mill, after orthogonal optimization, had more than double the lifespan of a similar-sized tool from Swiss Mikron, achieving international standards in cutting performance. This approach not only enhances machining efficiency but also reduces costs, making it a valuable strategy for advanced manufacturing processes.

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