由於非線性的多軸機械設定，傘齒輪的切削方法相當複雜。因此有必要使用模擬器來驗證和分析NC刀具路徑是否正確。這可避免NC規劃錯誤並減少試機空跑的時間。傘齒輪製造方法主要有兩種，分別為面銑式和面滾式切製法。在面滾式切製法中，刀盤上帶有多個刀刃組。每個刀刃組至少由兩個刀刃構成，內和外刀刃分別產生左和右齒面。然而在現有商業軟體中，只有軸對稱的刀具，如砂輪，才可以被採用來做切削模擬。Vericut是一個著名的NC驗證模擬軟體，由於其刀具幾何限制，故無法應用於面滾式切製法的模擬。本論文主要目的是基於SolidWorks API(應用程式介面)開發NC驗證模擬器，可用於面滾式切製法模擬。從泛用型搖台傘齒輪切齒機的機械設定，虛擬的六軸直角坐標傘齒輪切齒機的六軸機械設定首先被推導出來。因此可以根據六軸機械設定規劃加工NC碼。此外，發展出FANUC 16i控制器的電子齒輪箱(EGB)功能應用於面滾傘齒輪切削。本論文採用Visual C# 2010做為軟體開發平台，來發展切削模擬器。解析FANUC系統的NC碼編譯器也被開發，以讀取NC檔產生刀具路徑。根據刀具路徑的線性插補位置，調用SolidWorks API移動刀具和工件齒輪到每一個正確的切削位置。工件齒輪和刀具之間重疊部分，則使用SolidWorks API布林運算的差集函數來刪除工件干涉的部份。最後，我們使用一對面滾式直傘齒輪當作切削模擬的數值範例，並以兩種評估方法，齒面誤差分析和體積殘留分析，分別來驗證產生NC碼的正確性和最小步長是否適當。

Cutting methods of bevel gears are quite complicated due to nonlinear machine set-tings. Hence, simulators are necessary for verifying and analyzing NC tool paths. Those can avoid NC errors and reduce dry-run time of the machine. There are two major methods for manufacturing bevel gears, face-milling and face-hobbing cutting methods. In face-hobbing method, the cutter head carries a plurality of blade groups. Every blade group is constituted by at least two finishing cutter blades – one inside and one outside – to generate left and right surfaces, respectively. However, only an axisymmetric part like a wheel can be adopted as a cutter in commercial softwares. Vericut, a famous simulator, fails in the simulation of face-hobbing cutting method due to its limitation in cutter geometry. The main goal of this work is to develop a NC verification simulator for face-hobbing method based on the Solidworks API (Application Programming Interface). The mathematical model of virtual six-axis Cartesian-type bevel gear cutting machine is first derived from the universal cradle-type bevel gear cutting machine. Therefore, the NC code can be pro-grammed according to the determined six-axis machine settings. And, the usage of electric gearbox (EGB) of Fanuc 16i CNC controller for hobbing bevel gears is revealed. Visual C# 2010 is adopted as a development platform to develop this cutting simulator. A NC compiler for Fanuc system is also developed to generate the NC tool path. According to the linear interpolation of tool path, the program invokes the Solidworks API to move the cutter and work gear to every correct cutting position. The overlap volumes between work gear and cutters are removed using the SolidWorks API substrate boolean function. Here, a face-hobbed straight bevel gear pair is used as a numerical example for cutting simulation. Two evaluations, flank topographic errors and volume residue analysis, are made to verify the correctness of the generated NC data and the minimum step size of NC interpolation, respectively.

[1]Stadtfeld, H. J., “Straight Bevel Gear Cutting and Grinding on CNC Free Form Ma-chines,” Fall Technical Meeting of the American Gear Manufactures Association 2007, Detroit, USA, pp. 172-183 (2007).
[2]Hunecke, C., “The Road Leads Straight to HypoflexR”, Klingelnberg Sigma Report No. 18 (2009).
[3]Litvin, F. L., Chaing, W. S., Kuan, C., Lundy, M., and Tsung, W. J., “Generation and Geometry of Hypoid Gear-Member with Face-Hobbed Teeth of Uniform Depth,” In-ternational Journal of Machine Tools and Manufacture, Vol. 31, No. 2, pp. 167-181 (1991).
[4]Shih, Y. P., “Mathematical Model for Face-Hobbed Straight Bevel Gears,” Journal of Mechanical Design, Transactions of the ASME, Vol. 134 (2012).
[5]Shih, Y. P., Huang, Y. C., Lee, Y. H., and Wu, J. M., “Manufacture of Face-Hobbed Straight Bevel Gears Using a Six-Axis CNC Bevel Gear Cutting Machine,” Interna-tional Journal of Advanced Manufacturing Technology, pp. 1-17 (2013).
[6]石伊蓓、林忠運，2005，「蝸線傘齒輪和戟齒輪切削刀具」，機械月刊，第三十一卷，第八期，第72-87頁。
[7]黃雅絹，2012，六軸CNC傘齒輪切齒機之面滾式直傘齒輪切製法，國立台灣科技大學碩士論文。
[8]Oerlikon Geartec Ltd.
[9]Litvin, F. L., and Fuentes A., Gear Geometry and Applied Theory, 2nd edition, Cambridge University Press, New York, NY (2004).
[10]Shih, Y. P., “Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator,” Transactions of ASME, Journal of Mechanical Design, Vol.130 /062604-1-10 (2008).
[11]吳俊霖，2006，六軸CNC加工戟齒輪之路徑規劃與電腦模擬，國立中正大學碩士論文。
[12]Gleason Works, Face Hobbing Development, Rochester, NY 14692-2970, USA, (2000).
[13]FANUC Series 16i/160i/160is-MB, FANUC Series 18i/180i/180is-MB5, FANUC Se-ries 18i/180i/180is-MB Operator’s Manual.
[14]Alfred V. Aho，2006，編譯系統設計，碁峰資訊。
[15]林秉毅，2003，車銑複合五軸工具機之 PC-based CNC 即時系統設計與實現，國立成功大學碩士論文。
[16]吳稚逸，2004，基於STEP-NC之五軸曲面加工，國立清華大學碩士論文。
[17]張欽宇，2011，五軸CNC成形砂輪磨齒機NC路徑模擬與碰撞檢測，國立台灣科技大學碩士論文。
[18]徐永源，高春林，2010，SolidWorks API二次開發-使用Visual C++，知城。
[19]http://help.solidworks.com/2013/english/api/sldworksapiprogguide/Welcome.htm
[20]黃建凱，2011，直進式刮齒刀插槽設計與切削模擬平台開發，虎尾科技大學碩士論文。
[21]林冠亨，2010，泛用型齒輪加工機切削模擬方法研究，國立中正大學碩士論文。
[22]邱述文，2007，應用CAD軟體API建立刨齒加工模擬系統，清雲科技大學碩士論文。
[23]石伊蓓，2009，基於SolidWorks API之螺旋傘齒輪三維建模方法研究，第十二屆全國機構與機器設計學術研討會。
[24]Gottschalk, S., Lin, M.C., and Manocha, D., “OBBTree: A Hierarchical Structure for Rapid Interference Detection,” Proceedings of the ACM SIGGRAPH Conference on Computer Graphics, pp. 171-180(1996).
[25]Tropp, O., Tal, A., and Shimshoni, I., “A Fast Triangle to Triangle Intersection Test for Collision Detection,” Computer Animation And Virtual Worlds, Vol.17, pp. 527-535 (2006).