鼓形齒(Coniflex)直傘齒輪之特色是在齒長方向做修形為中凸狀齒形，此種齒形具有低組裝敏感度的特點，在遇上組裝誤差或製造誤差所造成的組裝位置偏差時，仍能保持良好的接觸情況。加工鼓形齒直傘齒輪時使用一對刀刃交錯的碟型刀具切削齒面，且在加工過程中不做齒長方向的移動，而是旋轉刀具使外型輪廓產生凹面，以此對齒輪加工出具齒長方向中凸狀的齒形，且可藉由控制刀具角度來調整齒輪的接觸長度。美國格里森公司為製造此種齒形提供了No.102型、No.104型、No.114型，及No.134型直傘齒輪切齒機，使用上下交錯刀具加工齒輪，以此命名為雙連鎖碟型刀具切製法，並提出此種機台的齒胚設計、刀具設計及機械設定的計算方式，但其齒面數學模式因商業理由未對外公開。
本論文主要目的是推導格里森No.104機台所切製出的鼓形齒直傘齒輪齒面數學模式，首先依格里森公司所提出的計算公式表計算鼓形齒直傘齒輪齒胚參數、刀具數學模式及機械設定數值，使用座標轉換法由刀具軌跡推導出齒面包絡線，並配合嚙合方程式即可解出齒輪齒面，再由兩接觸性能分析方法，分別是齒面相對修形及齒面接觸分析，來驗證齒面數學模式的正確性。最後，為了修正製造誤差，本論文以最佳化方法建立齒面誤差修正方法，以齒面拓樸點誤差與齒厚誤差作為目標函數，調整各軸機械設定求解目標函數最小值，由克林根貝格P40齒輪量測機台量測齒輪產生齒面誤差分析報告，根據報告結果進行齒面誤差修正以計算出各軸機械設定須如何調整以修正齒面。

The Coniflex® straight bevel gear (SBG) characteristic is the lengthwise crowning tooth flanks, and thus achieves the advantages of low assemble sensibility and high precision. When the deformation, assembly deviation or manufacturing deviation cause the displacement of assembling position, Coniflex® SBG could preserve the contact situation. This method uses two interlocking disk cutters to generate tooth flanks. The profile of the cutter can generate lengthwise crowning tooth flank. By change the cutter pressure angle, the contact length of gear can be adjusting. Gleason provides No. 102, No. 104, No. 114 and No. 134 straight bevel cutting machine for this gear. Gleason also provides the blank design, cutter design and machine setting calculating instructions. However, the detail of the Coniflex® cutting method is not provided because of commercial considerations.
The main goal of this paper is to establish a mathematical model of the tooth surfaces of Coniflex® gears produced by machine No. 104. First, using calculating instructions calculate Coniflex® straight bevel gear blank parameters and tool, mathematical model. Machine settings of the machine are determined from the formulas provided by the machine calculating instructions. The locus of the cutter can be derived using the coordinate transformation method, and their envelope constructs the tooth surface which is solved using the equation of meshing. Two evaluation methods, ease off and tooth contact analysis, are adopted to confirm the correctness of the proposed models. Lastly, to correct the manufacturing deviation. We establish the flank correction method by the optimization method. KlingelnbergP40 export flank deviation report which used for calculating correction of machine setting.

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