目前，強力刮齒切削是齒輪制造中極高效率的加工方式。為了提高面齒輪的製
造效率，本研究提出了一種通用的方法，通過應用強力刮齒切削齒輪的方法和一種靈
活的數值方式来修正面齒輪齒面上的法線偏差。理輪上的面齒輪齒面是通過直齒型面
齒輪與直齒小齒輪之間的共軛條件推導出来的。本研究之數學模型建構是基於齒條切
割刀具的法向截面與配有強力刮齒刀之 CNC 加工機加工面齒輪的原理來定義。由於強
力刮齒刀的非對稱，本研究計算了面齒輪的表面法線偏差，並對機床上的軸進行調整，
使其作用於面齒輪齒面拓樸修型的数学模型上。然後採用基於 Levenberg-Marquardt
（ LM）的最小化算法來進行敏感度矩陣的計算，最終計算出機床各軸的加工系数，從
而實現控制面齒輪齒面上的法线偏差。

Power skiving is currently the most efficient process for gear manufacturing. To
improve the manufacturing productivity of face gears, this study proposes a general method for
geometric generation of face gears by applying the gear power skiving method and a flexible
numerical approach for correcting normal deviations on the face-gear tooth surfaces. The
theoretical face-gear tooth surfaces are derived using the conjugation relationship between the
spur face-gear and the spur pinion. Mathematical modelling is defined for the conical skiving
cutter based on a normal section of rack cutter and the machining principle of face gear on the
CNC gear skiving machine. Due to the asymmetric skiving cutter, surface normal-deviations of
the face gear are calculated, and the mathematical model of the machine-axis modification for
the face-gear tooth topology modification is studied. Finally, a sensitivity correction method
based on the Levenberg-Marquardt (LM) minimization algorithm for calculating the machine
motion coefficients is employed to achieve the desired normal deviations on the face-gear tooth
surface.

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