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姓名	曹文昌(Wen-chang Tsao)  查詢紙本館藏	畢業系所	機械工程學系
論文名稱	適當本質模態函數篩選應用於滾珠軸承故障診斷 (Fault Diagnosis of Ball Bearings Using Appropriate Intrinsic Mode Functions)
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摘要(中)	傳統包絡譜分析須檢測所有結構共振頻帶於軸承缺陷故障診斷，分析過程中帶通濾波頻率選取範圍易受主觀影響。為了改善上述問題，本研究提出一新概念基於經驗模態分解法(Empirical Mode Decomposition, EMD)選擇合適的本質模態函數(Intrinsic Mode Function, IMF)應用於後續包絡譜分析(Envelope Analysis)及倒頻譜分析(Cepstrum Analysis)，以凸顯軸承缺陷特徵頻率。經由EMD方法的帶通濾波特性，結構共振頻帶位於特定IMF分量內。當滾珠通過缺陷所引發脈衝訊號會與結構系統共振產生幅值調變，選擇合適IMFs分量能夠有效偵測軸承缺陷特徵，代替過去學術研究中所見總是選用第一個IMF分量於診斷。實驗方面，探討雙面轉子平台的滾珠軸承於單缺陷、雙缺陷及三缺陷不同故障型式，以放電加工製作不同軸承缺陷，診斷結果與傳統包絡譜方法結果相互比較。實驗及分析結果顯示，本研究提出方法能有效及正確地診斷出軸承缺陷型式。
摘要(英)	Traditional envelope analysis must examine all the resonant frequency bands during the process of bearing fault detection. To eliminate the above deficiency, this research presents an insight concept based on the empirical mode decomposition (EMD) to choose an appropriate resonant frequency band for characterizing feature frequencies of bearing faults by using the envelope analysis and cepstrum analysis subsequently. By the band-pass filtering nature of the empirical mode decomposition, the resonant frequency bands are allocated in a specific intrinsic mode function (IMF). As impulses arising from rolling elements striking bearing faults modulate with structure resonance, appropriate IMFs are potentially able to characterize fault signatures, instead of always using the first IMF. In the study, the single, dual- and triple-fault bearings are used to justify the proposed method and comparisons with the traditional envelope analysis are made. The experimental results show that the proposed insight concept can efficiently and correctly diagnose the bearing fault types.
關鍵字(中)	★ 包絡譜分析 ★ 經驗模態分解 ★ 本質模態函數 ★ 倒頻譜分析 ★ 軸承多缺陷診斷	關鍵字(英)	★ Envelope analysis ★ Intrinsic mode function ★ Empirical mode decomposition ★ Cepstrum analysis ★ Multiple bearing-fault detection
論文目次	摘　要 I Abstract II 致　謝 III 目　錄 IV 圖目錄 VII 表目錄 XI 第一章 緒論 1 1.1 研究動機 1 1.2 文獻回顧 2 1.3 研究範疇 6 1.4 全文概述 7 第二章 行星齒輪運動分析與滾珠軸承缺陷特徵頻率 8 2.1 行星齒輪運動分析 9 2.2 滾珠軸承缺陷型態與缺陷特徵頻率 13 2.2.1 列表法 14 2.2.2 切線速度法 17 第三章 缺陷診斷之訊號分析演算法 23 3.1 傳統包絡譜分析方法 24 3.1.1 解析訊號 24 3.1.2 缺陷訊號之調變與解調 26 3.2 經驗模態分解法 30 3.2.1 時間尺度介紹 30 3.2.2 瞬時頻率 31 3.2.3 本質模態函數 34 3.2.4 經驗模態分解法 35 3.3 經驗模態分解法特性 39 3.3.1自適應性(adaptive) 39 3.3.2完整性(complete) 41 3.3.3 IMF分量調制特性 41 3.4 倒頻譜分析 42 3.5 軸承缺陷診斷方法 45 第四章 軸承缺陷模擬訊號驗證 48 4.1 軸承缺陷模擬訊號製作 49 4.2 軸承缺陷模擬訊號分析結果 51 4.2.1 模擬軸承外環缺陷 52 4.2.2 模擬軸承內環缺陷 62 4.2.3 模擬軸承雙缺陷 72 第五章 實驗架構與實驗方法 82 5.1 訊號量測系統 83 5.2 雙面轉子平台 86 5.3 實驗參數與設計 89 第六章 軸承缺陷診斷結果與討論 91 6.1 良好軸承 92 6.1.1 傳統包絡譜分析法結果 92 6.1.2 EMD結合Envelope結果 94 6.1.3 EMD結合Cepstrum結果 96 6.2 外環單缺陷軸承 97 6.2.1 傳統包絡譜分析法結果 98 6.2.2 EMD結合Envelope結果 100 6.2.3 EMD結合Cepstrum結果 103 6.3 內環單缺陷軸承 104 6.3.1 傳統包絡譜分析法結果 105 6.3.2 EMD結合Envelope結果 106 6.3.3 EMD結合Cepstrum結果 108 6.4 雙缺陷軸承 110 6.4.1 傳統包絡譜分析法結果 111 6.4.2 EMD結合Envelope結果 112 6.4.3 EMD結合Cepstrum結果 115 6.5 三缺陷軸承 118 6.5.1 傳統包絡譜分析法結果 119 6.5.2 EMD結合Envelope結果 121 6.5.3 EMD結合Cepstrum結果 123 6.6 結果與討論 125 6.5.1 在軸承單缺陷診斷方面 125 6.5.2 在軸承雙缺陷診斷方面 129 6.5.3 在軸承三缺陷診斷方面 130 第七章 結論及未來展望 131 7.1 結論 131 7.2 未來展望 133 參考文獻 134 附錄A 傳統包絡譜分析其餘共振頻帶診斷結果_良好軸承 139 附錄B 傳統包絡譜分析其餘共振頻帶診斷結果_外環單缺陷軸承 141 附錄C 傳統包絡譜分析其餘共振頻帶診斷結果_內環單缺陷軸承 144 附錄D 傳統包絡譜分析其餘共振頻帶診斷結果_雙缺陷軸承 147 附錄E 傳統包絡譜分析其餘共振頻帶診斷結果_三缺陷軸承 149 圖目錄 圖2.1 行星齒輪構造 9 圖2.2 列表法求解流程示意圖 10 圖2.3 滾珠軸承幾何尺寸 14 圖2.4 滾珠軸承基本特徵頻率 17 圖2.5 滾珠軸承幾何參數定義 18 圖3.1 振幅調變及解調流程圖 27 圖3.2 軸承缺陷振幅調變現象 28 圖3.3 軸承缺陷振動模擬訊號 29 圖3.4 瞬時頻率物理解釋圖 33 圖3.5 EMD訊號分解流程圖 38 圖3.6 訊號x(t)及EMD分解前五個IMF分量 40 圖3.7 訊號x(t)及前五個IMF分量頻譜圖 40 圖3.8 EMD完整性驗證 41 圖3.9 倒頻譜流程示意圖 44 圖3.10 傳統包絡譜分析流程圖 47 圖3.11 適當IMF分量選擇流程圖 47 圖4.1方波函數模擬低頻振動 49 圖4.2 隨機雜訊高斯分佈形式 49 圖4.3 模擬軸承缺陷脈衝訊號 50 圖4.4 模擬訊號時域波形 50 圖4.5 模擬訊號頻譜分析結果 50 圖4.6 模擬訊號之時域圖及譜頻圖(S＞N)_外環缺陷 53 圖4.7 模擬訊號及IMF 1分量時域圖(S＞N)_外環缺陷 53 圖4.8 IMF 1分量於包絡譜分析結果(S＞N)_外環缺陷 54 圖4.9 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S＞N)_外環缺陷 54 圖4.10 模擬訊號之時域圖及譜頻圖(S?N)_外環缺陷 56 圖4.11 模擬訊號及IMF 1分量時域圖(S?N)_外環缺陷 56 圖4.12 IMF 1分量於包絡譜分析結果(S?N)_外環缺陷 57 圖4.13 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S?N)_外環缺陷 57 圖4.14 模擬訊號之時域圖及譜頻圖(S 圖4.15 模擬訊號及IMF 1分量時域圖(S 圖4.16 IMF 1分量於包絡譜分析結果(S 圖4.17 IMF 1分量之時域圖及譜頻圖(S 圖4.18 IMF 1分量於功率譜及功率譜取對數結果(S 圖4.19 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S 圖4.20 模擬訊號之時域圖及譜頻圖(S＞N)_內環缺陷 63 圖4.21 模擬訊號及IMF 1分量時域圖(S＞N)_內環缺陷 63 圖4.22 IMF 1分量於包絡譜分析結果(S＞N)_內環缺陷 64 圖4.23 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S＞N)_內環缺陷 64 圖4.24 模擬訊號之時域圖及譜頻圖(S?N)_內環缺陷 66 圖4.25 模擬訊號及IMF 1分量時域圖(S?N)_內環缺陷 66 圖4.26 IMF 1分量於包絡譜分析結果(S?N)_內環缺陷 67 圖4.27 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S?N)_內環缺陷 67 圖4.28 模擬訊號之時域圖及譜頻圖(S 圖4.29 模擬訊號及IMF 1分量時域圖(S 圖4.30 IMF 1分量於包絡譜分析結果(S 圖4.31 IMF 1分量之時域圖及譜頻圖(S 圖4.32 IMF 1分量於功率譜及功率譜取對數結果(S 圖4.33 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S 圖4.34 模擬訊號之時域圖及譜頻圖(S＞N)_雙缺陷 73 圖4.35 模擬訊號及IMF 1分量時域圖(S＞N)_雙缺陷 73 圖4.36 IMF 1分量於包絡譜分析結果(S＞N)_雙缺陷 74 圖4.37 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S＞N)_雙缺陷 74 圖4.38 模擬訊號之時域圖及譜頻圖(S?N)_雙缺陷 76 圖4.39 模擬訊號及IMF 1分量時域圖(S?N)_雙缺陷 76 圖4.40 IMF 1分量於包絡譜分析結果(S?N)_雙缺陷 77 圖4.41 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S?N)_雙缺陷 77 圖4.42 模擬訊號之時域圖及譜頻圖(S 圖4.43 模擬訊號及IMF 1分量時域圖(S 圖4.44 IMF 1分量於包絡譜分析結果(S 圖4.45 IMF 1分量之時域圖及譜頻圖(S 圖4.46 IMF 1分量於功率譜及功率譜取對數結果(S 圖4.47 IMF 1分量於幅值倒頻譜及功率倒頻譜結果(S 圖5.1 振動訊號擷取介面 85 圖5.2 振動訊號擷取流程 85 圖5.3 雙面轉子平台架構 86 圖5.4 撓性聯軸器實體圖 87 圖5.5 ASAHI UCP-204連座軸承 88 圖6.1 軸承振動訊號時域圖與頻譜圖(1500 rpm)_良好軸承 92 圖6.2 結構共振頻率圖_良好軸承(漢寧窗長度4096、交疊比0.97) 93 圖6.3 傳統包絡譜分析結果_良好軸承(帶通濾波範圍6500~7500 Hz) 93 圖6.4 前五個IMF分量頻譜圖_良好軸承 94 圖6.5 IMF 1分量於包絡譜分析過程_良好軸承 95 圖6.6 IMF 1分量於包絡譜分析結果_良好軸承 95 圖6.7 IMF 1分量於功率譜及功率譜取對數結果_良好軸承 96 圖6.8 IMF 1分量於幅值倒頻譜與功率倒頻譜_良好軸承 96 圖6.9 軸承振動訊號時域圖與頻譜圖(1500 rpm)_外環單缺陷 97 圖6.10 結構共振頻率圖_外環單缺陷(漢寧窗長度4096、交疊比0.97) 98 圖6.11 傳統包絡譜分析結果_外環單缺陷(帶通濾波範圍3500~4500 Hz) 99 圖6.12 前五個IMF分量頻譜圖_外環單缺陷 100 圖6.13 IMF 1分量於包絡譜分析過程_外環單缺陷 101 圖6.14 各IMF 分量於包絡譜分析結果_外環單缺陷 101 圖6.15 IMF 1分量於倒頻譜分析過程_外環缺陷 102 圖6.16 各IMF分量於功率倒頻譜結果_外環單缺陷 103 圖6.17 軸承振動訊號時域圖與頻譜圖(1500 rpm)_內環單缺陷 104 圖6.18 結構共振頻率圖_內環單缺陷(漢寧窗長度4096、交疊比0.97) 105 圖6.19 傳統包絡譜分析結果_內環單缺陷(帶通濾波範圍1300~2300 Hz) 105 圖6.20 前五個IMF分量頻譜圖_內環單缺陷 106 圖6.21 合併IMF 2 ~ IMF 4分量於包絡譜分析過程_內環缺陷 107 圖6.22 各IMF分量於包絡譜分析結果_內環缺陷 107 圖6.23 合併IMF 2 ~ IMF 4分量於倒頻譜分析結果_內環缺陷 109 圖6.24 IMF 1分量於功率倒頻譜結果_內環缺陷 109 圖6.25 軸承振動訊號時域圖與頻譜圖(1500 rpm)_雙缺陷 110 圖6.26 結構共振頻率圖_雙缺陷(漢寧窗長度4096、交疊比0.97) 111 圖6.27 傳統包絡譜分析結果_雙缺陷(帶通濾波範圍7000~8000 Hz) 111 圖6.28 前五個IMF分量頻譜圖_雙缺陷 113 圖6.29 IMF 1分量於包絡譜分析過程_雙缺陷 113 圖6.30 各IMF分量於包絡譜分析結果_雙缺陷 114 圖6.31 合併IMF 1+IMF 2分量之包絡譜分析結果 114 圖6.32 IMF 1分量於功率譜及功率譜取對數結果_雙缺陷 116 圖6.33 各IMF分量於功率倒頻譜結果_雙缺陷 117 圖6.34 軸承振動訊號時域圖與頻譜圖(1500 rpm)_三缺陷 119 圖6.35 結構共振頻率圖_三缺陷(漢寧窗長度4096、交疊比0.97) 120 圖6.36 傳統包絡譜分析結果_三缺陷(帶通濾波範圍1500~2500 Hz) 120 圖6.37 前五個IMF分量頻譜圖_三缺陷 121 圖6.38 合併IMF 2 ~ IMF 4分量於包絡譜分析過程_三缺陷 122 圖6.39 各IMF分量於包絡譜分析結果_三缺陷 122 圖6.40 合併IMF 2~IMF 4分量於倒頻譜分析結果_雙缺陷 124 圖6.41 IMF 1分量於功率倒頻譜結果_三缺陷 124 圖6.42 外環缺陷於傳統包絡譜分析診斷結果 126 圖6.43 外環缺陷於EMD結合Envelope診斷結果 127 圖6.44 外環缺陷於EMD結合Cepstrum結果(IMF 1分量) 127 圖6.45 內環缺陷軸承診斷結果 128 圖6.46 雙缺陷軸承診斷結果 129 圖6.47 三缺陷軸承診斷結果 130 圖7.1 合適IMF分量選擇流程及診斷方法 133 表目錄 表2.1 行星齒輪運動分析_列表法 12 表2.2行星齒輪運動分析正規化結果 12 表2.3 滾珠軸承與行星齒輪組成對照表 14 表2.4 滾珠軸承運轉分析結果 15 表2.5 滾珠軸承特徵頻率表 22 表3.1 倒頻譜與頻譜各相關名詞表 44 表4.1 其它機械元件故障特徵 48 表4.2 軸承幾何尺寸 51 表5.1 壓電式加速規規格表 83 表5.2 轉速計規格表 84 表5.3 資料擷取卡規格表 84 表5.4 伺服馬達規格 87 表.5.5 軸承幾何尺寸 89 表5.6 軸承各種不同缺陷型態整理 90 表6.1 三缺陷軸承之各別特徵頻率(系統轉速：1500 rpm) 118
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指導教授	潘敏俊(Min-chun Pan)	審核日期	2013-7-15
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