螺旋傘齒輪和戟齒輪的製造方法主要可分為兩種，分別為面滾式切製法以及面銑式切製法，不同於面銑式切製法的非連續加工，面滾式切製法乃連續切削，因此擁有加工速度較快之優點。面滾式切製法又分為刀傾全展成法(Sproflex)和半展成法(Spirac)，分別應用於，大、小齒輪齒數比小於和大於2.5的場合。面滾式切製法為連續滾切加工，其加工速度快，故廣為汽車傳動齒輪製造所採用，然而市面上傘齒輪的設計和製造必須依賴設計軟體，如Gleason的CAGE和Klingelnberg的KIMoS，每套軟體價格皆動輒百萬，本論文希望建立面滾式全展成法戟齒輪齒面數學模式，並進而推導六軸傘齒輪切齒機機械設定，應用於實際加工。
本論文首先計算面滾式刀傾全展成法戟齒輪之齒胚參數、刀具參數和奧利康S17傘齒輪切齒機的機械設定，進行轉換使其適用於泛用虛擬搖台傘齒輪切齒機，便能在泛用切齒機之座標系統上推導齒面數學模式。在推導出齒面數學模式後，對該數學模式所設計之齒輪對進行齒面接觸性能分析，檢視該齒輪對齒面接觸性能是否符合使用需求，藉此檢驗齒面數學模式的正確性。立式六軸CNC傘齒輪切齒機為最新的設計，必須求得切齒座標位置來規劃加工NC碼，以進行加工。根據六軸CNC數控型切齒機之座標系統，推導刀具到工件座標轉換矩陣，再利用泛用機和六軸機之座標轉換矩陣相同，可切出相同齒輪的條件，推導六軸切齒的座標值，藉此進行加工路徑及NC規劃，並以VERICUT模擬面滾式傘齒輪加工，計算模擬切削齒輪與理論齒輪間的齒面誤差，驗證本論文數學模式的正確性。

Face-hobbing and face-milling are two main manufacturing methods for spiral bevel gears and hypoid gears. Face-hobbing and face-milling are continuous indexing and single indexing methods, respectively. The former has faster producing rate and is further divided into Spriroflex and Spirac methods, which are respectively applied to cases where the gear ratio is less or greater than 2.5. Due to its high productivity, face-hobbing is widely used in the manufacture of automotive transmission gears. However, the design and manufacture of bevel gears must be highly dependent on design software, such as Gleason’s CAGE and Klingelnberg’s KIMoS. The prices of the commercial software are quite expensive. This paper aims to establish a mathematical model of the Spiroflex hypoid gear, and to derive machine settings of the modern six-axis CNC bevel gear cutting machine. Therefore, face-hobbing can be applied to CNC machines.
First of all, this paper calculates the gear blank parameters, tool parameters and machine settings of the Oerlikon S17 bevel gear hobbing machine using the Spiroflex method. Machine settings are then converted to those of a virtual cradle-type bevel gear generator which is a universal machine. Based on the coordinate systems of universal machine, the mathematical model of the tooth surface can be derived. Moreover, two contact performance analyses (ease off and tooth contact analysis) are applied to verify the correctness of the proposed mathematical models. The newest machine for bevel gear cutting is the vertical six-axis CNC machine. One of the key technologies of the modern machine is to determine the six-axis cutting positions, therefore, NC codes can be programed. According to the condition that coordinate transformation matrices from the tool to the workpiece must be identical for the universal machine and the six-axis CNC machine, the six-axis cutting positions can be derived. As a result, programming the NC codes for the face-hobbing process can be carried out. Finally, a commercial software VERICUT is applied to simulate the NC codes of Spiroflex face-hobbing method. The flank deviations between simulated and theoretical tooth surfaces are calculated to verify the correctness of the mathematical model.

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