螺旋傘齒輪跟直傘齒輪相比之下有著更佳的傳遞效能與低噪音等優點，因此在工業界上有更廣泛的使用。螺旋傘齒輪通常採用面銑式和面滾式等切製法來製造。而另一方面，模造製程擁有高效率以及低成本等優點，而且近幾年來精度則不斷提升，所以模造齒輪逐漸被採用在圓柱齒輪以及直傘齒輪上。模造是形容詞，模造齒輪是指以模具然後採用鑄造、粉末冶金等方式來生產，具有速度快以及成本低等優點。因為模造製程近十年來的這些進步，所以嘗試使用模造製程應用於製造螺旋傘齒輪上。然而到目前為止，國內廠商仍然缺乏模造螺旋傘齒輪的經驗。本論文主要的目的是在格里森公司的SGDH切製法(面铣式)上來建立螺旋傘齒輪的齒面數學模式。在推導齒面數學模式的基礎上，使用SolidWorks API (Application Programming Interface，應用程式介面)來自動產生螺旋傘齒輪的3D零件圖，因此將可以使用這零件圖來做模具設計。除此之外，在齒面相對修形的基礎上來改進傘齒輪對的接觸性能，而後這模型的正確性則用齒面相對修形以及齒面接觸分析來確認。

Compared with straight bevel gears, spiral bevel gears (SBGs) have been more widely used in industry due to their better transmission performance and lower noise. SBGs are generally produced by cutting methods, such as face-milling and face-hobbing methods. On the other hand, molding method takes the advantage of efficiency and low cost, and its precision is improved in recent years, molding method becomes more popular in fabricating gears, such as cylindrical gears and straight bevel gears. Moreover, due to the advances in molding technology over the last decade, this method is tried to be applied in manufacturing SBGs. However, until now, domestic manufacturers are lack of technology in molded SBGs. The main goal of this work is to establish a mathematical model of SBGs with the Gleason SGDH cutting system (Face Mill). Based on the derived tooth surfaces, a 3D model is automatically generated using SolidWorks API (Application Programming Interface). Therefore, the generated model of SBG can be used for mold design. Moreover, based on the ease off, a flank modification is proposed to improve the contact condition of the gear pair. The correctness of the model is confirmed using the ease-off and tooth contact analysis.

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