| 摘要: | 蝸桿蝸輪組為兩軸交錯配置之齒輪機構，依其設計方法可區分為圓柱型與雙包絡型蝸桿蝸輪組。其中，雙包絡蝸桿蝸輪組相較於圓柱型具備較高的接觸率、優異的傳動效率及較強的承載能力等優勢。
本論文針對ZI 型雙包絡蝸桿之加工技術，提出採用動力刮削（Power Skiving）方法進行切削加工。首先，基於齒輪原理，推導螺旋齒輪及ZI 型雙包絡蝸桿之齒面數學模式，並進一步建立動力刮削刀具的數學模式。為驗證刀具設計之合理性，本文利用Bspline曲線進行輪廓擬合，並透過數值模擬比較理論齒形與實際切削結果，以確認加工精度及誤差分布情形。
接著，進行齒面接觸分析（Tooth Contact Analysis, TCA），模擬不同修整策略對嚙合行為之影響，包括螺旋齒輪齒形修整、動力刮削刀具齒數增加，以及兩者結合之綜合方案。分析結果顯示，單一修整方式易受組裝誤差影響，導致接觸型態不穩定，接觸率不足或傳動誤差呈現不連續現象；然而，結合螺旋齒輪齒形修整與刀具增齒後，能有效將線接觸轉化為穩定之點接觸，接觸齒數維持約五齒對，且傳動誤差曲線呈現連續函數，顯著提升嚙合穩定性。;A worm gear drive constitutes a skew-axis gear mechanism that can be categorized, according to its design methodology, into cylindrical and double-enveloping variants. Relative to the cylindrical type, the double-enveloping worm–wheel configuration exhibits a higher
contact ratio, enhanced transmission efficiency, and an increased load-bearing capacity.
This dissertation focuses on the manufacturing of a ZI-type double-enveloping worm utilizing a power-skiving (PS) cutting technique. Initially, grounded in gear theory,
mathematical models of the tooth surfaces for both the helical gear and the ZI-type doubleenveloping worm are developed, alongside the formulation of the corresponding PS cutter geometry model. To validate the accuracy of the cutter design, B-spline curve fitting is applied for profile reconstruction, and numerical simulations are conducted to compare the theoretical
tooth surface with the simulated machined surface, thereby evaluating machining precision and the spatial distribution of profile deviations.
Subsequently, tooth contact analysis (TCA) is performed to examine the effects of various modification strategies on meshing behavior. These strategies include helical-gear profile modification, augmentation of the PS cutter’s tooth count, and a combined approach. The findings indicate that individual modifications are vulnerable to assembly inaccuracies, potentially resulting in unstable contact patterns, reduced contact ratios, or discontinuities in
transmission error. In contrast, the integration of helical-gear profile modification with an increased number of cutter teeth effectively transforms line contact into a stable point-contact pattern, sustains approximately five pairs of teeth in mesh (effective contact ratio ≈ 5), and produces a continuous transmission error curve, thereby significantly enhancing meshing stability. |
