刮齒加工(gear skiving)是一種結合連續滾齒及刨齒之高效率齒輪軸向加工法，尤其可應用於多軸CNC車削加工中心(turning center)中，並可突破滾齒無法加工內齒輪之限制，然而如何設計刮齒刀並利用既有可動軸數切削出正確之齒面則需具備齒輪理論專業。本文旨在設計一具留磨量之刮齒刀具並利用立式六軸CNC工具機進行圓柱齒輪加工之數學模型，及推導各軸之運動方程式。過程中，先設計具留磨量齒條刀，藉由齒條刀創成錐型刮齒刀幾何數學模型並由前傾角及邊斜角關係求出刃口廓形。依據刮齒刀與工件齒輪之交錯軸嚙合關係得到泛用運動座標系統，再由實際機台之加工軸自由度建立出加工座標系統，比對兩個座標系統之齊次座標轉換矩陣可得到兩者運動參數之關係，進而得知實際機台各軸之運動方程式，再藉由數值程式可計算出理論工件齒面輪廓。此外，本研究利用VERICUT軟體建立加工機台模型，將各軸運動方程式轉為NC碼，進行齒面加工模擬，並將此模擬齒面與理論齒面進行誤差分析，以驗證數學模型及VERICUT模型之正確性，最後，本文更探討刀具設計角度、位置及留磨量對於加工齒面誤差之影響。

Power gear skiving is a highly-efficient axial gear-machining method which has advantages of the gear hobbing and the gear shaping. It can be applied in a multi-axis CNC turning center and break through the limitation that the hobbing cannot achieve in the internal gear cutting. However, how to manufacture exact gear tooth surfaces requires the professional gearing knowledge and technology. This study aims to apply the gear skiving on manufacturing the cylinder gears on a vertical five-axis CNC machine. Design skiving cutter with grinding allowance and solve cutting edge of skiving cutter is first and then applied in an established motion coordinate system of the CNC machine to generate the theoretical gear tooth surface. The motion equation for each machining axis is derived based on the general relative-motion relationship between the skiving cutter and the gear work-piece. In addition, the numerical examples of cutting simulation are carried out to prove the exactness of the established mathematical model through the normal deviation analysis between the simulated and standard tooth surfaces. Finally using VERICUT software to analyze the influence of rake angle and bevel angle on the normal deviation of the workpiece.

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