螺旋傘齒輪和戟齒輪的製造方式主要分為兩種，分別為面銑式切製法以及面滾式切製法，由於面銑式切製法能夠用於切齒以及研磨，面銑式較面滾式擁有較佳的加工精度，且其刀具設定和磨銳相對簡單，故工業界大多採用此切製法。為做齒面誤差修正和磨齒，需要給齒輪預留量，進行第二次加工或磨齒，因此必須執行自動對齒找到齒空位置。
本研究改善了以往使用的傘齒輪面銑式切削模擬方法，因此可以模擬出所有的面銑式加工工序，此方法是基於三維環線法，可進一步用於建立未變形切屑數學模式，計算出未變形切屑體積，並且還可以透過未變形切屑體積和切削進給速率推導出體積移除率(MRR)，以優化切削效率，而其中的未變形切屑體積透過SOLIDWORKS 3D設計軟體對數學模式進行驗證。
此外，本研究建立了探頭量測座標系統，以推導傘齒輪凸面和凹面的接觸量測位置，再以此編程NC程式達到自動對齒的功能，並透過VERICUT模擬軟體驗證其NC程式的正確性。最後在傘齒輪CNC切齒機進行切削實驗，透過實驗找出體積移除率與主軸扭矩之間的關聯性，以此優化切削速度，從而降低加工時間，在大齒輪成形法粗加工節省約18%的加工時間，小齒輪創成法粗加工節省約44%的加工時間。

There are two main manufacturing methods of spiral bevel gears and hypoid gear: face milling and face hobbing. Since face milling can perform cutting and grinding processes, it has better machining accuracy than face hobbing. And its tool setting and re-sharpening system are simpler than face hobbing. Therefore, the gear industry mainly adopts this method. The new six-axis CNC bevel gear cutting machine can adopt both cutting systems. To enhance the machine’s competitiveness, cutting speed optimization is demanded to increase productivity. Moreover, second machining is necessary to correct the flank errors and finish grinding. Thus, the machine must perform automatic tooth-gap alignment to find a tooth gap.
This research improves the previous cutting simulation method for producing bevel gear using face milling. Therefore, it can simulate all face-milling processes. This simulation is based on the three-dimensional loop method. It can be further adopted to establish the mathematical model of undeformed cutting chips. And we also can use chip volume and cutting feed rate to derive the material removal rate (MRR) for optimization of cutting feed rate. Here, SolidWorks 3D design software is adopted to prove the mathematical models. Moreover, the research establishes the measuring coordinate system of the probe. It is adopted to derive the touch positions of convex and concave flanks. These positions can be used to program an NC program for automatic tooth-gap alignment. And VERICUT CNC simulation software is performed to verify its correctness. Finally, we conduct cutting experiments on the CNC bevel gear cutting machine to find the correlation between the MRR and the cutting torques of the spindle. That is then used to optimize the cutting feed rates. The processing times of rough cuttings for the gear and the pinion are reduced by 18% and 44%, respectively.

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