石化廠中的管線檢查是很重要的，一般非破壞檢測法如傳統超音波點對點的量測，雖可檢測出管壁厚度的變化，但要使用此方法檢查工廠內動輒綿延幾公里的管線幾乎不可行。導波檢測法克服了上述問題，此技術運用萊姆波收發合置系統，不僅可做長距離大範圍的管線檢測，還可根據回波訊號判別出缺陷位置所在。
但由於頻散現象與波式轉換等複雜問題，造成此技術於實際檢測中的不易，本文探討焊接管鞋對導波波傳的影響，包含實際量測6吋碳鋼管的回波訊號與使用有限元素法模擬波傳現象，研究頻率範圍為18~ 32 kHz，並且使用萃取模態法分析波式轉換模態，研究發現T(0,1)模態傳經管鞋時其能量會洩漏至管鞋中，此洩漏能量最後導致回波訊號的複雜與判讀困難。

The detection of corrosion in pipes is of major importance to the oil and chemical industries. Current methods involving point-by-point inspection are available for the detection of general wall loss associated with corrosion, but unfortunately the current methods tend to be very slow, limited to single positions, thus make the inspection of the kilometers of pipeline typically found in industrial plants virtually impossible. Ultrasonic guided waves provide an attractive solution to this problem because they can be excited at one location on the pipe and will propagate many meters along the pipe, returning echoes indicating the presence of corrosion or other pipe features.
Nevertheless such techniques still have many practical difficulties in application due to the complex characteristics of guided waves such as dispersion and mode conversion. This thesis studies guided waves influenced by the welded supports, a.k.a. pipe shoe. A research of the reflection of mode-converted guided waves from pipe shoes on pipes in the frequency range 18-32 kHz has been carried out. Measurements are made on a 6 inch bore diameter, 7.1mm wall thickness pipe. The axisymmetric symmetric T(0,1) mode is incident on the pipe shoes and the mode-converted guided waves are received in reflection. In parallel, a finite element model is used to simulate the experiments by using Ansys. Received signals are separated into single-mode with a mode extraction technique. This research reveals that when T(0,1) propagates through the pipe shoe, the energy of T(0,1) passes into the pipe shoe. The leakage phenomenon results in the complexity and misinterpretation of the echo.

目錄
目錄 i
表目錄 v
圖目錄 vi
中文摘要 xi
英文摘要 xii
第一章 緒論 1
1.1前言 1
1.2文獻回顧 3
1.3研究方法 7
第二章 基本理論 9
2.1導波在圓管中傳播的波動方程式 9
2.1.1縱向模態 11
2.1.2扭矩模態 12
2.1.3撓曲模態 12
2.2頻散曲線 13
2.3波形結構 16
2.4波式轉換 17
2.5有限元素法 18
2.5.1應力平衡方程式 18
2.5.2邊界條件 18
2.5.3應變-位移關係 19
2.5.4應力-應變關係 19
2.5.5位能平衡方程式 20
2.5.6三度空間的應力分析 20
2.5.7元素的徑度 22
2.6動態分析 23
第三章 實驗架構與量測 35
3.1實驗儀器設備 35
3.2實驗步驟 38
3.3實驗結果與討論 39
3.3.1實驗一 39
3.3.2實驗二 41
第四章 模擬分析 58
4.1 Ansys有限元素軟體 58
4.2激發L(0,2)模態 60
4.2.1建構有限元素模型 61
4.2.2負載與求解 62
4.2.3提取與分析結果 63
4.3模擬L(0,2)模態經缺陷之波傳情形 66
4.3.1建構有限元素模型(25 %周向缺陷) 66
4.3.2提取與分析結果 66
4.3.3模擬L(0,2)模態傳經50 %周向缺陷 69
4.3.4各模態的反射係數 69
4.4激發T(0,1)模態 71
4.4.1建構有限元素模型 71
4.4.2負載與求解 71
4.4.3提取與分析結果 71
4.4.4模擬T(0,1)模態傳經25 %周向缺陷 73
4.4.5模擬T(0,1)模態傳經50 %周向缺陷 75
4.4.6各模態的反射係數 76
第五章 焊接管鞋之模擬分析 110
5.1模擬T(0,1)傳經焊接管鞋之波傳情形 110
5.2探究異常回波群 112
5.3管鞋內之波傳現象 113
5.3.1管鞋內的板波模態 113
5.3.2管鞋內的波傳路徑 115
5.4焊接管鞋對缺陷訊號的影響 116
5.4.1缺陷位於管鞋後方之訊號判讀 116
5.4.2缺陷位於管鞋前方與上方之訊號判讀 117
第六章 結論與建議 148
6.1結論 148
6.2未來展望 149
參考文獻 150
附錄A：實驗一實驗結果 156
附錄B：實驗二實驗結果 164
附錄C：焊接管鞋管模擬結果(6吋管) 172
附錄D：焊接管鞋管模擬結果(3吋管與8吋管) 184
附錄E：焊接管鞋管模擬結果(10吋管與12吋管) 194




表目錄
表3.1 警戒訊號離管鞋距離 44
表4.1 3吋碳鋼管之材料參數 77
表4.2 L(0,2)經缺陷之反射係數 77
表4.3 T(0,1)經缺陷之反射係數 77
表5.1 各頻率之模擬結果 119


圖目錄
圖1.1 傳統超音波與導波檢測法比較 8
圖2.1 應用導波技術檢測管路缺陷示意圖 26
圖2.2 無限長圓管（內徑為a，外徑為b） 26
圖2.3 不同n值之節點位移分佈 26
圖2.4 圓管上縱向模態波傳模式 27
圖2.5 圓管上扭矩模態波傳模式 27
圖2.6 圓管上撓曲模態波傳模式 27
圖2.7 6吋管中不同頻率的L(0,2)模態傳遞1.5公尺訊號圖 32
圖2.8 六吋碳鋼管之相位速度頻散曲線 33
圖2.9 六吋碳鋼管之群波速度頻散曲線 33
圖2.10 70 kHz L(0,2)模態之波形結構 34
圖2.11 T(0,1)模態之波形結構 .34
圖2.12 缺陷引發波式轉換示意圖 35
圖2.13 體積V，表面積S，單位體積重f的物體 35
圖2.14 元素體積平衡圖 36
圖2.15 一表面之元素體積 36
圖2.16 元素的表面變形 .37
圖2.17 四面體元素 37
圖2.18 四面體元素的Shape Function 38
圖3.1 GUL公司環狀陣列探頭（6吋管及8吋管） 44
圖3.2 訊號處理器（Wavemaker SE16） 45
圖3.3 Wave Pro 45
圖3.4 Wave Pro回波訊號示意圖 46
圖3.5 法蘭之回波訊號圖 .46
圖3.6 焊道之回波訊號圖 47
圖3.7 彎管之回波訊號圖 47
圖3.8 缺陷之回波訊號圖 47
圖3.9 管件特徵配置圖 48
圖3.10 管鞋尺寸 48
圖3.11 安裝探頭 49
圖3.12 探頭安裝完成圖 49
圖3.13 32 kHz 實驗一結果 .50
圖3.14 28 kHz 實驗一結果 51
圖3.15 25 kHz 實驗一結果 52
圖3.16 20 kHz 實驗一結果 53
圖3.17 32 kHz 實驗二結果 54
圖3.18 28 kHz 實驗二結果 .55
圖3.19 25 kHz 實驗二結果 56
圖3.20 20 kHz 實驗二結果 57
圖4.1 3吋碳鋼管群波速度圖 .78
圖4.2 3吋探鋼管波型結構：(a) 70 kHz L(0,2)及(b)55 kHz T(0,1) 78
圖4.3 1.8公尺3英吋碳鋼管薄膜模型 79
圖4.4 網格劃分完成圖 79
圖4.5 70 kHz 5cycles toneburst .80
圖4.6 施加負載 .80
圖4.7 70 kHz 5cycles toneburst與位移為0之負載 81
圖4.8 邊界條件完成圖 .81
圖4.9 時間參數設定 82
圖4.10 70 kHz L(0,2)模態變形時間關係圖 83
圖4.11 POST26處理器分析之節點 84
圖4.12 C處節點各方向之位移量 85
圖4.13 D處節點各方向之位移量 .86
圖4.14 缺陷薄膜模型完成圖 .87
圖4.15 25%周向缺陷 87
圖4.16 L(0,2)模態傳經25%周向缺陷之變形時間關係圖 88
圖4.17 C處節點之軸向時域訊號 89
圖4.18 萃取0階模態時域圖 90
圖4.19 萃取1階模態時域圖 90
圖4.20 萃取2階模態時域圖 91
圖4.21 50%周向缺陷 91
圖4.22 L(0,2)模態傳經50%周向缺陷之變形時間關係圖 92
圖4.23 C處節點之軸向時域訊號 93
圖4.24 萃取0階模態時域圖 94
圖4.25 萃取1階模態時域圖 94
圖4.26 萃取2階模態時域圖 95
圖4.27 激發55 kHz T(0,1)模態之負載 95
圖4.28 邊界條件完成圖 96
圖4.29 時間參數設定 96
圖4.30 55 kHz T(0,1)模態之變形時間關係圖 97
圖4.31 POST26處理器分析之節點 98
圖4.32 C處節點各方向之位移量 99
圖4.33 D處節點各方向之位移量 100
圖4.34 缺陷薄膜模型完成圖 101
圖4.35 25%周向缺陷 101
圖4.36 T(0,1)模態傳經25%周向缺陷之變形時間關係圖 102
圖4.37 C處節點之軸向時域訊號 103
圖4.38 萃取0階時域訊號圖 104
圖4.39 萃取1階時域訊號圖 104
圖4.40 萃取2階時域訊號圖 105
圖4.41 T(0,1)模態傳經50%周向缺陷之變形時間關係圖 106
圖4.42 C處節點之軸向時域訊號 107
圖4.43 萃取0階時域訊號圖 108
圖4.44 萃取1階時域訊號圖 108
圖4.45 萃取2階時域訊號圖 109
圖5.1 焊接管鞋管模型 119
圖5.2 管鞋模型 120
圖5.3 6吋碳鋼管群波速度圖 120
圖5.4 32 kHz C處之0階時域圖 121
圖5.5 32 kHz C處之1階時域圖 122
圖5.6 32 kHz C處之2階時域圖 123
圖5.7 25 kHz C處之0階時域圖 124
圖5.8 25 kHz C處之1階時域圖 125
圖5.9 25 kHz C處之2階時域圖 126
圖5.10 實驗與模擬比較 127
圖5.11 T(0,1)模態傳經管鞋之應力分佈 128
圖5.12 T(0,1)模態傳經管鞋之應力分佈 129
圖5.13 T(0,1)模態傳經管鞋之應力分佈 130
圖5.14 板波類型 131
圖5.15 7mm碳鋼板群波速度圖 131
圖5.16 (a)S0模態撥型結構圖 (b)A0模態波型結構圖 132
圖5.17 P波、SH波與SV波波型結構 133
圖5.18 焊接方形板薄模模型 134
圖5.19 T(0,1)模態傳經方形板之應力分佈 135
圖5.20 方形板底端節點之位移訊號 136
圖5.21 管鞋內部之波傳路徑 137
圖5.22 缺陷管模型 138
圖5.23 32 kHz缺陷訊號分析 139
圖5.24 28kHz缺陷訊號分析 140
圖5.25 25 kHz缺陷訊號分析 141
圖5.26 20kHz缺陷訊號分析 142
圖5.27 5 %缺陷位於管鞋前方之薄膜模型簡圖 143
圖5.28 5 %缺陷位於管鞋上方之薄膜模型簡圖 143
圖5.29 32 kHz缺陷訊號分析 144
圖5.30 28 kHz缺陷訊號分析 145
圖5.31 25kHz缺陷訊號分析 146
圖5.32 20kHz缺陷訊號分析 147

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