面銑式的切製法為螺旋傘齒輪的主要量產製造方法，此切製法必須實施於五軸CNC機台。加工時需要用到多軸運動，並且刀具的設計比較複雜，因此為了避免碰撞發生，預先模擬刀具路徑和切削以驗證NC加工路徑的正確性。
本研究的目的是開發一套專門模擬切削面銑式螺旋傘齒輪的軟體，使用Visual C# 2010為開發平台，並以OpenGL圖形庫顯示三維模擬環境。模擬切削是使用體素法，首先建立刀具的曲面數學模式，齒胚實體模型則使用適應性的立方體(Cube)建立，並以體素(Voxel)記錄立方體節點的位置。根據NC加工路徑與坐標轉換矩陣，可得到刀具和齒胚的相對位置，並以布林運算計算切削模擬。
再者，本研究使用移動立方體(Marching cube)演算法優化顯示被切削的齒面，並且將被切削齒面儲存成STL格式。為了驗證加工NC碼是否正確，本文提出一種齒面誤差評估方法，以比較STL齒面與理論齒面的法向量誤差。開發之軟體亦可即時模擬切削時的體積變化，以做為進一步優化NC加工路徑的基礎。

Face milling is a popular cutting method in mass production of spiral bevel gears. A CNC machine with five-axis simultaneous control system is demanded to implement face milling. This cutting method needs multi-axis movement and its tool design is complex. Therefore, in order to avoid collision, the simulation of tool paths and material removal should be performed previously to verify the correctness of NC codes.
The study aims to develop a dedicated cutting simulation software for face-milled spiral bevel gears. Visual C# 2010 integrated with OpenGL is used as a foundation to develop the simulation program. Here, a voxel method for cutting simulation is employed. The mathematical model of tool surface is first established. The solid model of work gear is composed by cubes in which voxels are used to store the positions and values of those vertexes. According to the NC code, the relative positions between the tool and the work gear are determined through the coordinate transformations. And then, Boolean difference operation between the gear work and tool is made to simulate gear cutting.
Moreover, the marching cube algorithm is adopted to improve the display resolution of produced tooth surfaces which are save as STL (Stereolithography) format. In order to verify the correctness of NC codes, an evaluation method is proposed to obtain tooth surface deviations between the produced STL surfaces and theoretical surfaces. And, the volume removal is obtained in real-time cutting simulation, which can be used as a beneficial data for further reach in optimization of NC tool paths.

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