臺灣博碩士論文加值系統

本文使用有限元素方法，針對60瓩級外軸式渦輪引擎，建立轉子-軸承系統之離散模型，根據結構各部份組裝之實際狀況，將整機渦輪轉子-軸承系統劃分成若干個可分離之子結構系統，包括葉輪、轉軸、導流板、渦輪及軸承，再以各子結構連接面上節點的動態參數一致性及力平衡，整合渦輪轉子系統的運動方程式。以有限元素分析商用軟體ANSYS，探討重要零組件及渦輪機系統之模態特性，並以實驗驗證之。
為了驗證建模以及比較分析結果的準確性，本文結合模態實驗和有限元素的混合建模方法，經由實驗與分析求得之模態振形及自然頻率相互比較，以實驗值為基準，並根據有限元素模型的物理意義，修正各子結構之動態特性，以及調整連接面的動態參數，使分析結果與實驗結果相比得到很高的正確性，除了可驗証分析模型之準確性，亦可鑑別子結構連接面間接點之動態參數，以提高分析精確度，建立一個成功且可靠的渦輪轉子-軸承系統。

This study builds the discrete model of the rotor-bearing system based on finite element (FE) method for 60kw innovative micro gas turbine, The assembled system is separated into several dividable sub-structures, which including impeller, shaft, guide fan, turbine and bearings. The motion equation of whole structures is combined by the unity of the dynamic variables and force balances on connections of each substructure. Additionally, utilizing commercial software ANSYS to investigate the modal characteristics of the turbine engine systems and its key components, and furthermore verifies the results of analysis via experiments of modal testing.
Besides verifying the model and comparing with the results of analysis, this study presents the hybrid method, which combines the experiment of modal testing and FE model. The mode shapes and natural frequencies are obtained by comparing the results of experiment with analysis. Simultaneously, according to the physical signification of FE model, modify the dynamic characteristics of each sub-structure and adjust the dynamic parameters between connected interfaces based on the experimental values to arise the validity by decreasing the errors of analysis and experiment. Not only examining the accuracy of analysis module but also finding out the dynamic parameter of structures, that can increase the analysis accuracy to establish a success and dependable turbine rotor-bearing system.

目 錄
中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 導論 1
1.1 緣由與背景 1
1.2 文獻回顧 2
1.3 本文大綱 5
第二章 研究方法 7
2.1 模態分析有限元素建模 7
2.1.1 樑元素模型 7
2.1.2 剛性轉子元素建模 8
2.1.3 撓性轉子模型 9
2.1.4 軸承模型 10
2.1.5 連接面建模 12
2.1.6 實體元素模型 13
2.2 模態分析方法 13
2.3 有限元素分析 14
2.3.1 ANSYS求解 16
第三章 子結構模態分析及建模修正 18
3.1 渦輪轉子組合 18
3.2 子結構連接面之動態參數鑑別 21
3.3 連接面彈簧剛度之影響 22
3.4 自由懸吊之模態分析結果 23
3.4.1 葉輪 27
3.4.2 轉軸 28
3.4.3 導流板 29
3.4.4 渦輪 30
3.4.5 渦輪本體 31
3.4.6 渦輪轉子 32
第四章 模態測試及驗證 37
4.1 模態測試原理 37
4.1.1 架設量測儀器 37
4.1.2 規劃量測位置/激發位置 38
4.1.3 分析頻寬 40
4.1.4 模態頻率與振形求解 40
4.2 模態測試結果 41
4.2.1 轉軸 43
4.2.2 導流板 44
4.2.3 渦輪-1 46
4.2.4 渦輪-2 47
4.2.5 渦輪本體 49
4.2.6 渦輪轉子 51
4.3 模態分析與模態測試實驗之比較 57
第五章 轉子-軸承系統之臨界轉速分析 66
5.1 渦輪轉子-軸承系統 69
第六章 結論 74
參考文獻 75

表目錄
表3-1 轉子元件之材料性質與元素數目 20
表3-2 葉輪之自然頻率與振形描述 23
表3-3 轉軸之自然頻率與振形描述 24
表3-4 導流板之自然頻率與振形描述 24
表3-5 渦輪之自然頻率與振形描述 24
表3-6(a) 渦輪本體之連接面元素連接方式之影響 24
表3-6(b) 渦輪本體之連接面彈簧剛度係數之影響 25
表3-6(c) 渦輪本體之自然頻率與振形描述 25
表3-7 渦輪轉子之自然頻率及振形描述 25
表4-1 轉軸之模態實驗結果 41
表4-2 導流板之模態實驗結果 41
表4-3 渦輪之模態實驗結果 42
表4-4 渦輪本體之模態實驗結果 42
表4-5 渦輪轉子之模態實驗結果 42
表5-1 FAG-HCS71902E.T.P4S軸承參數 65
表5-2 渦輪轉子-軸承系統之振形描述 66
表5-3 轉子自由懸吊與轉子軸承系統相同模態之比較 68
表5-4 渦輪轉子-軸承系統不同轉速下之模態頻率 73

圖目錄
圖2-1 典型之軸元素 7
圖2-2 剛性轉盤之有限元素模型 9
圖2-3 撓性轉盤之有限元素模型 10
圖2-4 線性軸承之力平衡模型 10
圖3-1 渦輪轉子-軸承系統之實體模型與有限元素模型 19
圖3-2 Solid 92實體元素 20
圖3-3 Combin 14彈簧－阻尼元素 21
圖3-4 葉輪之模態分析振形及頻率 27
圖3-5 轉軸之模態分析振形及頻率 28
圖3-6 導流板之模態分析振形及頻率 29
圖3-7 渦輪之模態分析振形及頻率 30
圖3-8 渦輪本體之模態分析振形及頻率 31
圖3-9 渦輪轉子之模態分析振形及頻率 32
圖4-1 模態測試實驗儀器架設 38
圖4-2 轉軸之規劃點位置 39
圖4-3 導流板之規劃點位置 39
圖4-4 渦輪之規劃點位置 39
圖4-5 渦輪本體之規劃點位置 39
圖4-6 渦輪轉子之規劃點位置 40
圖4-7 轉軸之轉移函數頻譜 43
圖4-8 轉軸模態實驗之模態穩定指標 43
圖4-9 轉軸之模態振形及頻率 43
圖4-10 導流板之轉移函數頻譜 44
圖4-11 導流板模態實驗之模態穩定指標 44
圖4-12 導流板之模態振形及頻率 45
圖4-13 渦輪-1之轉移函數頻譜 46
圖4-14 渦輪-1模態實驗之模態穩定指標 46
圖4-15 渦輪-2之轉移函數頻譜 47
圖4-16 渦輪-2模態實驗之模態穩定指標 47
圖4-17 渦輪-1之模態振形及頻率 48
圖4-18 渦輪-2之模態振形及頻率 48
圖4-19 渦輪本體之轉移函數頻譜 49
圖4-20 渦輪本體模態實驗之模態穩定指標 49
圖4-21 渦輪本體之模態振形及頻率 50
圖4-22 渦輪轉子之轉移函數頻譜(徑向) 51
圖4-23 渦輪轉子徑向模態實驗之模態穩定指標 51
圖4-24 渦輪轉子之轉移函數頻譜(軸向) 52
圖4-25 渦輪轉子軸向模態實驗之模態穩定指標 52
圖4-26 渦輪轉子之徑向模態振形及頻率 53
圖4-27 渦輪轉子之軸向模態振形及頻率 55
圖4-28 轉軸模態分析與模態測試實驗結果之比較 58
圖4-29 導流板模態分析與模態測試實驗結果之比較 59
圖4-30 渦輪模態分析與模態測試實驗結果之比較 60
圖4-31 渦輪本體模態分析與模態測試實驗結果之比較 61
圖4-32 渦輪轉子模態分析與模態實驗徑向結果之比較 62
圖4-33 渦輪轉子模態分析與模態實驗軸向結果之比較 64
圖5-1 渦輪轉子-軸承系統轉速為0 rpm之模態分析振形及頻率 69
圖5-2 轉子-軸承系統之Campbell Diagram 73

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