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 珩齒(gear honing)是目前齒輪精加工方法之一，已證實可用於改善齒面接觸特性並減少齒輪嚙合噪音及振動。為了掌握及開發珩齒加工之關鍵技術，本論文創新地提出適用於圓柱齒輪與螺桿轉子之內嚙合珩齒加工方法。首先，針對具長齒面螺旋齒輪同時與另外兩個齒輪嚙合之特殊應用，提出一種利用CNC內嚙合珩齒機進行雙導程鼓型齒面修整(dual lead-crowning)之創新方法，通過控制珩磨輪傾角(swivel angle)及珩磨輪轉角，達成在同一長齒面具有兩個導程鼓型修整之圓柱齒輪齒面。其次，更提出應用CNC內嚙合珩齒機進行閉迴路圓柱齒輪齒面拓撲修整之數學模型，通過施予多項式形式之附加運動於珩磨輪傾角、珩磨輪徑向運動及工件齒輪轉角，並建立多項式係數與齒面法向誤差之敏感度矩陣(sensitivity matrix)，研究中採用 Levenberg-Marquardt（LM）演算法進行閉迴路疊代計算，以得到最終所需之機台各軸運動方程式，並加工出具有抗扭曲(anti-twisted)、雙鼓型(double-crowned)之圓柱齒輪齒面。最後，提出了一種可用於精磨雙螺桿壓縮機轉子之內嚙合珩齒加工方法，在珩磨過程中，螺桿轉子和珩磨輪間的嚙合類似於一對少齒差、低齒數之交錯軸內嚙合螺旋齒輪，此一創新應用預期具有大幅縮短精磨螺桿加工時間之發展潛力。
 Internal-meshing gear honing process is currently one of the economical finishing methods to localize and stabilize the tooth contact pattern and reduce noise and vibration of gear systems. This dissertation proposes novel honing methods for cylindrical gears and screw rotors. For improving the gear contact performance, gears with tooth modification can effectively avoid the edge contact and improve the contact load distribution. The mathematical models are proposed for two novel tooth modification methods of helical gears with internal-meshing gear honing. In the first model, for the special case of a long face-width helical gear meshing with two gears simultaneously, a novel method is proposed for dual lead-crowning for helical gears with long face-widths using a CNC internal gear honing machine. The anti-twist tooth modification is carried out by controlling the swivel angle and the rotation angle of the honing wheel. In the second model, a mathematical procedure is proposed to apply the closed-loop topology modification on helical gears to achieve the double-crowned and anti-twisted tooth flanks on a CNC internal-meshing gear honing machine. Additional motions are added in the radial movement of the honing wheel, the swivel angle of honing wheel and the rotation angle of the work gear in the forms of polynomials. A sensitivity matrix is constructed and Levenberg-Marquardt (LM) algorithm is employed to obtain the polynomial coefficients of additional motions for desired tooth flank topologies. In addition, a novel manufacturing process for screw rotors is proposed using the internal-meshing CNC honing machine. During the honing process, the meshing between the screw rotor and the honing wheel is similar to that for a pair of crossed-axis internal-meshing helical gears with few teeth. This novel application has development potential to significantly reduce the machining time.