螺旋傘齒輪的製造方式分為面銑式加工(Face milling)與面滾式(Face hobbing)加工，這兩種製造方式分別使用五軸與六軸的CNC機台，加工運動較傳統三軸加工複雜，加上刀具不是一般CNC銑床加工使用的刀具需要經過幾何的設計來特別訂製，為了防止機台在加工過程中發生撞機，通常會在進行加工前驗證NC加工路徑的正確性。現有的切削模擬軟體只有VERICUT有提供滾切功能(Gear hobbing)，但在模擬加工時無法直接使用電子齒輪箱(Electric gear box)，NC程式需要改寫。本研究的目標是開發一套可以滿足螺旋傘齒輪各種切製法的切削模擬軟體。
本研究使用Visual C# 2019與C++/CLI為開發平台，以Open CASCADE程式庫做為幾何核心，以及使用其可視化應用服務功能(Application interactive services, AIS)在OpenGL的渲染環境。論文的主要貢獻在整合Open CASCADE和Visual C#程式，運用座標轉換實現各種齒輪切削模擬。首先建立刀具與齒胚的數學模型，藉由Open CASCADE程式建立刀具與齒胚的三維模型，並依據NC程式加工路徑進行座標轉換，產生刀具與齒胚的相對運動，利用Open CASCADE的布林運算類別進行切削模擬，最後進行切削齒面與理論齒面的齒面誤差分析。另外，開發之軟體亦能用於其它齒輪的切削模擬。

The popular mass production methods of spiral bevel gears are face milling and face hobbing. The two methods are performed on the five-axis and six-axis CNC machines, respectively. Compared to traditional machining, cutting movements of CNC machines are more complicated, and some special tools are required for cutting bevel gears. To prevent the machine from colliding, the correctness of the NC tool paths must be ensured before machining. Among commercial cutting simulation softwares, only VERICUT provides simulation of gear hobbing. However, VERICUT cannot directly invoke the function of electric gear box to simulating gear hobbing. The NC codes needs to be further modified. This paper aims to develop a cutting simulation software to satisfy various cutting methods for bevel gears.
An open-source platform, Open Cascade, is here adopted as a geometry kernel for 3D surface and solid modeling, and Visual C# 2019 is the development tool to invoke a C++ 3D modeling library of Open Cascade through C++/CLI. This open-source platform also supports a visualization module called as application interactive service to link OpenGL for displaying geometry in 3D Viewer. The main contribution of this paper is the integration of Visual C# and Open CASCADE to calculate coordinate transformations and to implement various gear cutting movements. At the first step, the tool and the workpiece are modeled using Open CASCADE. The coordinates of tool and workpiece are then transformed to cutting positions according to the given NC codes. Finally, cut boolean operator of Open CASCADE algorithms is performed for cutting simulation. A numerical example of cutting face-milled spiral bevel gear is shown and a flank deviation analysis between the simulated and theoretical tooth surfaces is done to verify the correctness of proposed method. Moreover, this developed software can also simulate the cutting situations of other different kind gears.

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