目前，魯氏轉子使用特定的CNC機台製造，基於成形銑削法加工之轉子溝槽必須使用分度盤單獨銑削，導致加工時間較長。因此本研究提出一種新型CNC機台之數學模型，使用環狀内旋刮齒刀具製造魯氏轉子以提高加工精度和效率，切削刃由刀具平面及沙漏型内輪表面之相交曲線決定，藉此建立出新型機台切削數學模型。由本研究數學模型生成的轉子表面法向偏差接近於零，以證明本研究所提出數學模型之可行性，數值範例也驗證了進給量對轉子表面精度的影響。因此本研究為進一步高效魯氏轉子切削機台建立理論基礎。;Currently, the form milling method is often used to manufacture Roots pump rotors in a specific CNC machine. However, it is time-consuming since rotor grooves must be milled individually using an indexing table. Therefore, this study proposes a mathematical model for manufacturing Roots rotors using a Ring-shaped internal-meshing skiving cutter based on new CNC machine schematics to enhance the machining precision and efficiency. The cutting edge of the skiving cutter tooth is determined by the intersecting curve between an hourglass-shaped internal wheel surface and a rake plane. Additionally, a general mathematical model of the skiving process has been established. The results indicate that the normal deviation of the skived rotor surface approaches zero, demonstrating the practicality of the proposed model. Furthermore, numerical experiments also verify the impact of the feed rate on the surface quality of the rotor. This study provides a theoretical basis for further developing an efficient Roots rotor cutting machine.
