雙螺桿壓縮機因穩定、高轉速及連續運轉可靠性，廣泛應用於工業壓縮空氣系統。變導程轉子相較固定導程設計，具有更高壓力比、更大排氣流量及高壓區低洩漏等優勢，但其連續變化的螺旋幾何使齒間間隙評估更為困難。本研究建立以CMM為基礎之量測、表面重建與齒間間隙評估。採用Leitz Reference CMM量測六個截面齒形輪廓及各螺旋跡線導程數據，並沿每一齒兩側齒面量測導程點資料；經相位展開與分段三次Hermite插值（Piecewise Cubic Hermite Interpolating Polynomial， PCHIP）推導各齒面之連續旋轉角函數，再以旋轉矩陣將參考截面逐層掃掠，建立完整3D點雲。重建曲面與CMM實測輪廓比對，各截面法向偏差之均方根誤差小於10 ，並輔以螺旋軌跡檢驗確認幾何連續性。3D點雲一方面擬合成三次B-spline曲面，另一方面轉換為二進位STL表面網格。間隙計算採用兩套幾何表示相互獨立之方法進行交叉驗證：B-spline曲面法於擬合曲面上以兩階段最近點搜尋計算各截面最小間隙；STL截面多邊形法則直接對STL截面多邊形求取精確平面距離。以一根公轉子與兩根母轉子組成之兩組配對進行驗證，無干涉之組合I於全部三十組齒對配置之平均絕對誤差皆低於17 μm，證實兩法互為一致；組合II則於靜態組裝姿態下偵測出幾何干涉。無干涉之轉子組合將經驗證之間隙分布沿螺旋洩漏路徑之弧長積分，得到接觸帶面積作為量化洩漏的指標，據以比較各嚙合配置並識別各齒加工偏差分布；對於干涉之轉子組合而言，靜態幾何計算並不具物理意義，故以相同重建曲面於RecurDyn建立多體動力學模型，評估其實際嚙合之動態響應。本研究所建立之流程可為變導程轉子之精密製造檢測與轉子對最佳組配選擇提供系統化之依據。;Twin-screw compressors are widely used in industrial compressed-air systems for their stable， high-speed， and reliable continuous operation. Variable-lead rotors offer a higher pressure ratio， greater discharge flow， and reduced high-pressure-side leakage compared with fixed-lead designs， but their continuously varying helical geometry makes interlobe clearance difficult to evaluate with conventional feeler-gauge or analytical methods. This study establishes a complete coordinate-measuring-machine (CMM)-based methodology for measuring， reconstructing， and evaluating the interlobe clearance of variable-lead twin-screw compressor rotor pairs， and for selecting the optimal rotor-pair assembly. The rotors form a 5/6 lobe pair with a three-segment (variable–constant–variable) lead design. Using a Leitz Reference CMM， cross-sectional tooth profiles were measured at six axial positions， and lead-point data were acquired along both flanks of every tooth. piecewise cubic Hermite interpolation (PCHIP) yielded a continuous rotation-angle function for each flank， and the reference cross-section was swept through 236 axial layers to reconstruct a complete three-dimensional point cloud， validated against CMM measurements with a normal deviation below 10 μm. Each point cloud was fitted with a cubic B-spline surface and independently converted into an STL surface mesh. Two geometrically independent clearance-calculation pipelines， a B-spline surface method and an STL polygon method， were cross-validated for clearance calculation. Applied to two rotor combinations of 30 lobe pairs each， the interference-free Combination I showed a mean absolute error below 17 μm between the two pipelines， confirming their consistency， while Combination II exhibited geometric interference in the static assembly. This procedure can complete the full axial clearance evaluation and interference prediction for all 30 rotor combinations before real rotor assembly. For the interference-free pairing， clearance distributions were integrated along the helical leakage path to yield a contact band area as a leakage indicator， revealing that leakage is dominated by individual lobe manufacturing deviation rather than the mating slot， and identifying the pairing with minimum contact band area as optimal. For the interfering Combination II， a multibody dynamic model was established in RecurDyn using the same reconstructed surfaces and Hertzian contact settings， with theoretical rotor profiles serving as a reference baseline. The theoretical penetration envelope remained nearly constant between -0.13 and -0.15 mm， whereas the envelope of Combination II fluctuated between -0.15 and -0.29 mm， reaching a maximum penetration depth of -0.2944 mm， approximately 1.91 times that of the theoretical rotor. The pairings exhibiting the deepest dynamic penetration coincided exactly with the lobe pairs identified as interfering in the static evaluation， and the most severe contact events concentrated near the two rotor ends， providing direct manufacturing feedback on the axial regions of the female rotor that require correction. These results confirm the pairing-by-pairing consistency between the static interference evaluation and the dynamic meshing response， demonstrating that the two analyses are mutually complementary. The integrated framework， including CMM measurement， surface reconstruction， cross-validated clearance calculation， contact band area evaluation， and multibody dynamic analysis， thus provides a systematic and practical basis for the precision inspection of variable-lead rotors and the selection of the optimal rotor-pair assembly.
