臺灣博碩士論文加值系統

本論文首先依據擺線之基本幾何定義，配合齒輪原理建立擺線齒輪對之數學模式。其次利用此一數學模式進行擺線齒輪對之齒面接觸分析，藉以探討擺線齒輪對之嚙合接觸特性。依據齒面接觸分析所得之結果，針對滾圓半徑搭配錯誤與中心距誤差對擺線齒輪對傳動誤差所造成之影響進行討論。此外，並利用有限元素分析軟體ABAQUS進行擺線齒輪之接觸應力分析，探討不同滾圓半徑搭配對接觸應力之影響。本研究之結果除了可模擬擺線齒輪對之嚙合狀況外，並可作為後續包括擺線齒輪對接觸點之相對曲率、接觸點滑動率等相關研究之基礎。

In this study, the mathematical models cycloidal gears are derived based on the theorem of gearing firstly. Then, the meshing model of cycloidal gear pair is set up and tooth contact analysis (TCA) is adopted to investigate the transmission errors with different design parameters and assembly conditions. Furthermore, the general-purpose FEA software, ABAQUS, was applied to evaluate the formation of bearing contacts and stress distribution on the tooth surfaces according to different design parameters. Results in this study not only verify the contact nature of cycloidal gear pairs, but also provide the bases for upcoming research on cycloidal gear pairs such as curvature analysis and sliding ratios.

中文摘要 i
英文摘要 ii
誌 謝 iii
目 錄 iv
表目錄 vi
圖目錄 vii
符號說明 ix
第一章 緒論 1
1.1 研究之背景與動機 1
1.2 文獻回顧 1
1.3 研究內容 2
第二章 基本理論 4
2.1 位置向量轉換 4
2.2 相對運動速度 6
2.3 嚙合方程式 6
第三章 擺線齒輪之齒面數學模式 12
3.1 擺線基本定義 12
3.2 利用外擺線及內擺線基本定義推導擺線齒輪 之齒面數學模式 14
3.2.1 外擺線所構成之齒冠區域 14
3.2.2 內擺線所構成之齒根區域 16
3.3 以平擺線所構成之齒條刀創成擺線齒輪 17
3.3.1 平擺線所構成之齒條刀 刀面數學模式 18
3.3.2 擺線齒條刀創成之擺線齒輪齒面數學模式 20
第四章 擺線齒輪接觸分析 25
4.1 利用單一方程式表示由內外擺線組成之擺線齒輪 25
4.2 擺線齒輪之接觸分析模型 26
4.3 擺線齒輪對之電腦輔助繪圖 29
4.4 不同滾圓半徑對擺線齒形所造成之影響 31
4.5中心距誤差之影響 33
第五章 有限元素接觸應力分析 36
5.1 有限元素分析軟體ABAQUS簡介 36
5.2 網格種類與選用 37
5.3 有限元素分析流程 38
5.3.1 模型建立 38
5.3.2 材質選用 42
5.3.3邊界條件設定 42
5.3.4 網格分割 44
5.4 應力分析結果 46
第六章 結論與未來展望 61
6.1 結論 61
6.2 未來展望 61
參考文獻 62
個人簡歷 65

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