多級魯氏轉子具有複雜的葉形幾何，不僅程式編寫成本高昂，且加工極具挑戰性。本論文提出一套整合式流程，利用錐形刀具在立式四軸平台上進行側銑加工。首先建立幾何嚙合模型，並由離散掃描點資料經樣條曲線重建生成的轉子輪廓，求得刀具與工件之間的接觸線、嚙合角與刀具姿態。接著利用避碰邏輯，對刀具背平面半徑、半錐角與錐體長度加以限制，以防止過切與軸干涉，特別是在軸向間距緊密的級數中。所得的刀具定位點透過 Mathematica 模組自動轉換為 NC 程式，並使用WELE AA-1880 機台的運動學精確模型在 VERICUT 中驗證生成的刀具路徑。實驗與模擬結果顯示：(i) 忽略碰撞約束會在高曲率區域產生局部過切；(ii) 對葉片側面進行平滑處理並選擇可行的錐角能有效避免過切；(iii) 在加工過程中強制轉子以單一且單調遞增的旋轉方向運動，可大幅降低因改變旋轉方向而產生的最大法向偏差。總體而言，本研究所提出的方法縮短了程式撰寫時間，提高了幾何吻合度，並實現了多級魯式轉子的可重複且無碰撞加工。;Multi-stage Roots rotors exhibit complex lobe geometries that are expensive to program and challenging to machine. This thesis presents an integrated workflow for side milling such rotors on a vertical four-axis platform using a conical cutter. A geometric meshing model is first formulated to determine the contact line, meshing angle, and tool pose between the cutter and a spline-reconstructed rotor profile derived from discrete scan data. Collision-avoidance logic then constrains the cutter back-plane radius, semi-vertex angle, and conical length to prevent undercutting and shaft interference, particularly in stages with tight axial spacing. The resulting contact points (driven points) are automatically translated into NC code (Numerical Control code) through a Mathematica module, and the generated toolpaths are validated in VERICUT software using a kinematically accurate model of the WELE AA-1880 machine. Experimental and simulation results indicate that (i) neglecting collision constraints produces localized undercutting in high-curvature regions; (ii) smoothing lobe flanks and selecting a feasible conical angle effectively eliminates gouging; and (iii) enforcing a single, monotonic rotor rotation (without reversals) during processing substantially reduces peak normal deviations arising from rotation reversals. Overall, the proposed approach shortens programming time, improves geometric conformity, and enables repeatable, collision-free machining of multi-stage Roots rotors.
