螺旋傘齒輪和戟傘齒輪的加工方式有面銑式切製法以及面滾式切製法，而面銑式加工可再分為切齒加工以及磨削加工，且面銑式磨削加工較面滾式切製法與面銑式切製法擁有較佳的加工精度，能夠應用於高精度的需求，因此工業上高精度需求的齒輪多以研磨加工來對齒輪提高精度。本研究改善了以往模擬加工時使用三維環線法與刀具刃口線數學模式求解交點，嘗試改善了以往加工模擬時刀具刃口線為直邊，對砂輪刃口線進行修整(Relief)，使砂輪刃口由多段曲線所組成，以滿足磨齒需求。改善了以往模擬加工時，先前齒底模擬不完整的問題，在齒底部分進行補點，藉由增加齒底齒面點數量，來提高齒底的解析度。利用砂輪刃口線數學模式與三維環線解出交點後，使用向量法判斷砂輪刃口線所解出之交點是否為新舊齒面點，以及利用邊界盒法判斷倒圓處是否為新舊齒面點，並將齒面點與齒頂圓進行三角網格鋪面形成封閉的3D網格體。計算出每一步齒輪齒空的體積，利用磨削體積變化量計算出磨削體積。再透過三角網格鋪面來建構出研磨後的齒輪產出STL檔，並對模擬出的齒輪STL進行齒面誤差分析，驗證模擬面銑式加工的正確性。最後利用磨削體積與時間的關係，算出體積移除率(Material Remove Rates)，並透過提高體積移除率較低的區間，達到平均化體積移除率的效果，來提高進給速率，減少加工的時間，由單齒加工18.6秒減至13.8秒，縮短約26.4%加工時間。改良的模擬方法亦可以用於切齒加工。

The processing methods for spiral bevel gears and hypoid gears include face milling and face hobbing. Face milling can be further categorized into gear cutting and gear grinding. Face milling grinding offers superior machining accuracy compared to face hobbing and face milling, making it suitable for high-precision requirements. Therefore, in the industrial sector, gears with high precision demands are mostly processed using grinding to enhance accuracy. This study has improved upon previous simulation processes by employing a ring-Dexel method and a mathematical model for tool edge profiles to calculate intersection points. It attempts to enhance the previous machining simulations where tool edge profiles were straight by refining them through relief. This modification transforms the grinding wheel's tool edge into a series of curved segments to meet the gear profile requirements. Additionally, it has addressed issues with simulating the gear root that were present in previous simulations. It rectifies the problem of incomplete gear root simulations by adding points to the gear root, thereby increasing the number of gear root surface points to enhance the resolution of the gear root. The boundary box method is employed to determine whether the fillet region is a new or existing tooth surface point. Subsequently, tooth surface and fillet points are used to create a closed 3D mesh structure with triangular mesh surfaces. The volume of the tooth space is calculated for each step of the gear teeth, and the grinding volume is determined based on the variation in volume. Subsequently, the post-grinding gear is constructed by utilizing the triangulated mesh to generate an STL file. The simulated gear's STL file is analyzed for tooth surface errors, validating the accuracy of the simulated face milling grinding process. Finally, the material removal rate (MRR) is calculated based on the relationship between grinding volume and time. By averaging the feed rate in intervals with lower MRR, the efficiency of the grinding process is enhanced, leading to a reduction in processing time. This improvement results in a reduction of processing time from 18.6 seconds per tooth to 13.8 seconds per tooth, a reduction of approximately 26.4%. The improved simulation method can also be applied to gear cutting processes.

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