雙包絡減速機在工業上常被廣泛使用。本文藉由掃掠法(Sweeping Method)推導雙包絡蝸桿(Globoidal Worm)曲面方程式，再由螺旋理論(Screw Theory)推導雙包絡蝸輪(Globoidal Worm Gear)囓合曲面方程式。參考國際設計規範，求出蝸桿和蝸輪曲面的資料點。作為蝸桿蝸輪幾何分析，包括齒形特徵分析，蝸桿蝸輪的曲率分析，並計算雙包絡蝸桿蝸輪的傳動效率。最後藉由齒面接觸分析法(TCA)，使用電腦模擬在有裝配誤差下的傳動誤差。

Double-Enveloping Reducers are used widely in various industries. In this study, a procedure is developed to analyze the geometric and kinematic properties of such a rotational reducer. In the mechanism, the globoidal worm profile is derived by using the sweeping method and the profile of the globoidal worm wheel is obtained by employing the screw theory. Based on Standards of the American Gear Manufacturers Association (AGMA 6030-C87), the involved parameters in designing and analyzing the reducer are revealed. Finally, the transmission errors based on tooth the contact analysis (TCA) are also reported.

摘要 Ⅰ
Abstract Ⅱ
目錄 Ⅲ
圖目錄 Ⅵ
表目錄 Ⅸ
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 7
1-3研究目的與研究方法 9
1-4 論文大綱 9
第二章 雙包絡蝸桿蝸輪規範與參數計算步驟 11
2-1 雙包絡蝸桿蝸輪的特徵 11
2-2 雙包絡蝸桿蝸輪部位名稱 11
2-3 雙包絡蝸桿蝸輪參數計算步驟 15
第三章 座標轉換矩陣與接觸條件 17
3-1座標轉換矩陣 17
3-2 接觸條件 19
3-3空間曲面求法 20
第四章 雙包絡蝸桿蝸輪的曲面 22
4-1 座標設定與座標轉換矩陣 22
4-2蝸桿曲面方程式 26
4-3蝸輪曲面族方程式 28
4-4接觸條件方程式 30
4-4-1蝸桿的法向量 30
4-4-2蝸桿蝸輪的相對速度 32
4-4-3產生接觸條件方程式 33
第五章 幾何分析 35
5-1蝸輪齒形特徵 35
5-2接觸線 37
5-3壓力角、導程角、法向壓力角 40
5-4蝸輪齒厚 42
5-5囓合傳動效率 43
5-6 曲率分析 48

5-6-1蝸桿曲面的曲率分析 49
5-6-2蝸輪曲面的曲率分析 50
第六章 應用實例 52
6-1雙包絡蝸桿與蝸輪曲面應用實例 52
6-2雙包絡蝸桿與蝸輪主曲率應用實例 58
6-2-1雙包絡蝸桿的主曲率 58
6-2-2雙包絡蝸輪的主曲率 61
6-3雙包絡蝸桿蝸輪傳動效率應用實例 66
第七章 傳動誤差分析 68
7-1前言 68
7-2傳動誤差分析 68
7-3求解 和 74
第八章 結論與建議 77
參考文獻 80

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