以面銑式切製法(Face-milling cutting system)為製造螺旋傘齒輪的主要加工方式，其刀具分為多刀刃所組成之面銑刀型與砂輪型，分別用於切齒和磨齒加工，而多刀刃刀具設計較為複雜，所以目前切削模擬大都使用砂輪作為切削模擬刀具。此切製法必須使用五軸工具機加工，由於加工時運動複雜，為了避免發生撞機意外，須預先模擬切削路徑來驗證NC加工路徑的正確性。基於上述兩點，本論文開發出一套以面銑刀具加工螺旋傘齒輪之切削模擬軟體，來模擬齒輪加工，且提出不同於以往的多刀刃型銑刀切削模擬方法，不再僅限於使用砂輪刀具模擬。
模擬切削的演算核心是使用體素法(Voxel)，首先將齒胚實體模型用適應性體素建立，並產生多刀刃型銑刀的曲面數學模式。上述兩者建立完成後，將NC碼五軸位置，帶入刀具至工件座標系統之座標轉換矩陣，可得出在工件座標系統下觀察的刀具位置。以方向性邊界盒(Oriented bounding box)包圍之齒胚與各個刀刃來做碰撞干涉檢查，達到多刀刃切削效果。並使用移動立方體(Marching Cube)演算法來優化齒面顯示精度，將切削結果以STL格式儲存。最後比較切削齒面與理論齒面之法向量誤差，驗證模擬切削數學模式的正確性，同時也計算出單位時間之體積移除率，以做為後續NC路徑規劃最佳化的參考。

Face milling is a mainstream mass production method for spiral bevel gears. Two types of tools were adopted in face milling method, including a milling cutter and a wheel. Because of difficulty in building a mathematical model of a milling cutter, the commercialized cutting simulation softwares apply an axisymmetric wheel instead of a milling cutter. This cutting method must be applied on a five-axis machine, however, five-axis movement is quite complex in processing. In order to remove the NC errors and avoid the collision between the cutting tool and machine axes or fixtures. A cutting simulation is required to verify the correctness of NC tool paths before cutting. To address the above issues, this study aims to develop a dedicated cutting simulation software for spiral bevel gears using a face-milling cutter.
A voxel-based method is adopted as a calculation core for the presented cutting simulation. The solid model of work gear is constructed using adaptive voxels, and the mathematical models of cutting blade surfaces are established. According to NC codes, the cutter positon relative to the workpiece is then determined use coordinate transformation matrix from the cutter coordinate system to the workpiece coordinate system. First, an interference detection between each cutting blade and the workpiece is made using oriented bounding box method. After limiting search scope for possible collision voxels, all vertices of candidate voxels are checked whether they are inside or outside the blade to implement cutting simulation. In order to improve the display resolution of produced tooth surface, the marching cube algorithm is adopted. Tooth surfaces of bevel gear are save as STL format for further investigation. Finally, an evaluation method for tooth surfaces deviations is applied to verify the correctness of the cutting simulation. And the material removal rate is examined for further NC programming optimization.

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