臺灣博碩士論文加值系統

本論文主旨在探討粗糙度效應對轉子-軸承系統非線性動態之影響與分析，以數值分析去研究軸承支撐之轉子動態軌跡並考慮在非線性支撐及水平和垂直方向粗糙度之效應系統動態軌跡之影響，並同時分析轉子幾何中心和軸承幾何中心之動態行為。藉由動態軌跡圖、分岔圖、頻譜圖、龐卡萊映射圖及最大李雅普諾夫指數法分析系統的動態特性。
結果顯示不論是橫向或縱向粗糙度參數值對非線性轉子-軸承系統動態效應影響不大，但是在考慮有粗糙度和無粗糙度時動態響應的差異是非常的明顯。
此模擬結果未來將提供高速旋轉作業中，旋轉機構轉子-軸承系統研究理論的參考，特別是它考慮到軸承系統的粗糙度的效應，紊流流場和非線性支撐。

This research aims to study a numerical analysis to investigate the dynamic orbits of a rotor supported by two turbulent journal bearings considering longitudinal and transverse roughness effect under nonlinear suspension. The dynamic response of the rotor center and bearing center are studied. The dynamic trajectories of the rotor center and bearing center, bifurcation diagrams, Poincaré maps, Power Spectrum and the maximum Lyapunov exponent method are employed to analyze dynamic responses in this study.
The results show that either the longitudinal and transverse or the values of roughness parameters C1 would not affect strongly nonlinear rotor-bearing system very much but the difference of dynamic response between considering with roughness effect and without roughness effect are very obvious.
The modeling results provide some theoretical references for further researching of rotor-bearing system for rotating machinery that operate in highly rotational speed, especially it considers roughness effect, turbulent flow and nonlinear suspension of bearing system.

中文摘要Ⅰ
英文摘要Ⅱ
誌謝Ⅲ
總目錄Ⅳ
表目錄Ⅵ
圖目錄Ⅶ
符號說明Ⅸ
第一章 緒論1
1.1 前言1
1.2 文獻回顧2
1.3 研究目的與論文架構5
第二章 研究分析非線性動態與混沌的方法7
2.1 軌跡圖7
2.2 頻譜圖7
2.3 分岔圖9
2.4 龐卡萊映射圖14
2.5 最大李雅普諾夫指數19
第三章 轉子-軸承系統中混沌現象分析22
3.1 導論22
3.2 非線性油膜力23
3.2.1 雷諾方程式的建立23
3.3 粗糙度效應對轉子-軸承系統非線性動態分析29
3.3.1 運動方程式29
3.3.2 油膜力在短軸承的假設30
3.3.3 運動方程式無因次化33
第四章 結果與討論36
4.1 分岔圖分析36
4.2 動態軌跡圖分析38
4.3 頻譜圖分析39
4.4 龐卡萊暗射圖分析39
4.5 最大李雅普諾夫指數分析41
第五章 結論與未來研究方向70
參考文獻71
作者簡介77
表目錄
表4-1 不同轉速比區間內系統動態特性判續（c1=0.39/0.49）37
表4-2 不同轉速比區間內系統動態特性判續（c1=0）38
圖目錄
圖2-1 週期運動的頻譜圖8
圖2-2 非週期運動的頻譜圖8
圖2-3 誇臨界分岔圖10
圖2-4 音叉分岔圖：(a)音叉分岔圖樣(b)友音叉分岔圖12
圖2-5 邏輯疊代（Logistic）映像的倍周期分岔圖 13
圖2-6 邏輯疊代（Logistic）映像的局部3P倍周期分岔圖13
圖2-7 在3維空間的龐卡萊截面：(a)雙邊截面∑ (b)單邊截面15
圖2-8 週期解的龐卡萊截面：(a)一個交點；(b)兩個交點16
圖2-9 具時間週期項之二維非自律系統的動態軌跡與龐卡萊截面相交的情形：(a) (x1,x2,t) 空間；(b) (x1,x2,θ)空間17
圖2-10 Benettin法求最大李雅普諾夫指數示意圖21
圖3-1 滑動軸承剖面圖與座標系23
圖3-2 油膜座標系24
圖3-3 作用在油膜微元體 方向的力25
圖3-4 滑油微元體之流體流動圖27
圖3-5 一個轉子被二個橫向及縱向擾流軸承支撐之粗糙度效應系統29
圖4-1 轉子-軸承中心在水平及垂直方向的分岔圖（縱向粗糙度（C1=0.39））42
圖4-2 轉子-軸承中心在水平及垂直方向的分岔圖（縱向粗糙度（C1=0.49））43
圖4-3 轉子-軸承中心在水平及垂直方向的分岔圖（橫向粗糙度（C1=0.39））44
圖4-4 轉子-軸承中心在水平及垂直方向的分岔圖（橫向粗糙度（C1=0.49））45
圖4-5 轉子-軸承中心在水平及垂直方向的分岔圖（C1=0.0）46
圖4-6 S=0.5轉子-軸承中心軌跡圖（C1=0.39）47
圖4-7 S=1轉子-軸承中心軌跡圖（C1=0.39）48
圖4-8 S=1.2轉子-軸承中心軌跡圖（C1=0.39）49
圖4-9 S=1.6轉子-軸承中心軌跡圖（C1=0.39）50
圖4-10 S=2.2轉子-軸承中心軌跡圖（C1=0.39）51
圖4-11 S=2.4轉子-軸承中心軌跡圖（C1=0.39）52
圖4-12 S=2.8轉子-軸承中心軌跡圖（C1=0.39）53
圖4-13 S=2.9轉子-軸承中心軌跡圖（C1=0.39）54
圖4-14 S=3.0轉子-軸承中心軌跡圖（C1=0.39）55
圖4-15 S=3.2轉子-軸承中心軌跡圖（C1=0.39）56
圖4-16 S=3.4轉子-軸承中心軌跡圖（C1=0.39）57
圖4-17 S=1.0轉子-軸承中心頻譜分析圖（C1=0.39）58
圖4-18 S=1.6轉子-軸承中心頻譜分析圖（C1=0.39）59
圖4-19 S=2.9轉子-軸承中心頻譜分析圖（C1=0.39）60
圖4-20 S=3.0轉子-軸承中心頻譜分析圖（C1=0.39）61
圖4-21 S=3.2轉子-軸承中心頻譜分析圖（C1=0.39）62
圖4-22 S=0.5轉子-軸承中心龐卡萊映射圖（C1=0.39）63
圖4-23 S=1.0轉子-軸承中心龐卡萊映射圖（C1=0.39）63
圖4-24 S=1.2轉子-軸承中心龐卡萊映射圖（C1=0.39）64
圖4-25 S=1.6轉子-軸承中心龐卡萊映射圖（C1=0.39）64
圖4-26 S=2.2轉子-軸承中心龐卡萊映射圖（C1=0.39）65
圖4-27 S=2.4轉子-軸承中心龐卡萊映射圖（C1=0.39）65
圖4-28 S=2.8轉子-軸承中心龐卡萊映射圖（C1=0.39）66
圖4-39 S=2.9轉子-軸承中心龐卡萊映射圖（C1=0.39）66
圖4-30 S=3.0轉子-軸承中心龐卡萊映射圖（C1=0.39）67
圖4-31 S=3.2轉子-軸承中心龐卡萊映射圖（C1=0.39）67
圖4-32 S=3.4轉子-軸承中心龐卡萊映射圖（C1=0.39）68
圖4-33 S=1.6(a)、2.9(b)、3.0(c)時最大李雅普諾夫指數（C1=0.39）69

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