| 摘要: | 螺桿轉子技術持續進步，尤其是在線型設計與螺距分佈方面。研究顯示，變螺距轉子可降低功耗並改善散熱；然而，螺桿轉子結合了變螺距與基於擺線的共軛齒型這兩大幾何複雜性，因此在製造方面難度依然很高。錐形螺桿轉子可用以克服傳統變螺距螺桿轉子的問題，但目前大多數的平行軸錐形轉子仍依賴非對稱擺線曲線，這進一步增加了加工難度。為改善既有設計在可製造性上的不足，本研究提出一種以可製造性為導向的錐形轉子設計，採用對稱的非共軛線型，並避免凹曲線（擺線）。此對稱特性使左右切削刃相同，進而降低刀具複雜度並提升經濟可行性。此外，本研究藉由建立完整的多軸加工機運動學模型，提出適用於錐形螺桿轉子的通用製造方法；此議題迄今尚未被系統性地深入探討。本研究所提出的方法包含：轉子生成、加工間隙評估、多軸 CNC (Computer Numerical Control) 運動學，以及切削加工過程模擬之數學模型，其中加工精度是以法向偏差分佈 (normal deviation distribution) 進行量化。此外，也探討了使用 Levenberg-Marquardt (L-M) 演算法進行刀具位置補償對精度提升的影響。數值算例證實，在 (a) 固定螺距與變螺距錐形轉子，以及 (b) 模擬這兩類轉子對應的多軸刀具運動方面的靈活性。生成的轉子對在所提出的評估方法下滿足嚙合間隙標準，且加工模擬證實切削過程可以由所建立之運動學模型一致且可靠地描述。此外，所提出的對稱線型簡化了可製造性：轉子表面可以使用直刃標準刀具加工，而無需專用的成形刀具。由於刀具與生成的轉子表面之間的接觸區域會發生變化，利用 (L-M) 演算法在加工過程中修正切削刀具位置的補償方法，並未能持續提供穩健的改善效果。;Screw rotor technology continues to advance, particularly in profile design and pitch distribution. Variable-pitch rotors have been shown to reduce power consumption and heat dissipation; however, they remain difficult to manufacture because they combine two major geometric complexities: variable-pitch and cycloid-based conjugate profiles. Conical screw rotors can overcome the problem of variable-pitch screw rotors, but most parallel-shaft conical rotors currently available still rely on asymmetric cycloidal curves, which further increase machining difficulties. To address this gap, this study proposes a manufacturability-oriented conical rotor design featuring a symmetric non-conjugate profile that avoids concave (cycloidal) curves. The symmetry allows identical left-right cutting-edges, reducing tooling complexity and improving economic feasibility. In addition, this study describes general manufacturing strategies for conical screw rotors, a topic that has not been systematically studied, by formulating a complete kinematic model of the machine for multi-axis machining. The proposed methodology builds mathematical models for rotor generation, meshing clearance evaluation, multi-axis CNC (Computer Numerical Control) kinematics, and cutting process simulation, where machining accuracy is measured using normal deviation distribution. Furthermore, the effect of tool position compensation using the Levenberg-Marquardt (L-M) algorithm on accuracy improvement is also investigated. Numerical examples demonstrate the flexibility of the framework in (a) designing fixed- and variable-pitch conical rotors and (b) simulating the corresponding multi-axis tool motions for machining both rotor types. The generated rotor pairs satisfy meshing-clearance criteria under the proposed evaluation approach, and the machining simulations confirm that the cutting process can be consistently described by the developed kinematic model. Moreover, the proposed symmetric profile simplifies manufacturability: the rotor surfaces can be machined using a Straight, standard cutting-edge tool, rather than requiring specialized Form cutting-edge tools. The compensation method for correcting the cutting tool position during the machining process using the L-M algorithm did not consistently provide robust improvement because the contact area changes between the cutter and the generated rotor surface. |
