本文主要是利用雙測點振模測定法，測定高速轉子於不同轉速下的共振頻率與操作模態變化，並討論不同配重模式對其操作模態的可能影響。雙測點振模測定法，主要是以機器或結構上兩測點所測得的位移或加速度訊號，配合傳遞函數的定義，就其主操作頻率分析其操作模態響應。為驗證此雙測點法用於轉軸之可行性，首先在轉子靜態下，分別使用傳統頻譜響應函數敲擊法與本文所使用之雙測點法進行結果比對工作。由模態確認指標（modal assurance criterion；MAC）與模態圖形比對，結果顯示在低阻尼或無阻尼系統下，兩法所得模態有良好的吻合，此亦驗證此雙測點法可成功用於靜態下之轉子測試；結果亦顯示，在高阻尼系統下，兩法測得之模態將具一定的差異性。為驗證雙測點法可克服旋轉效應，並成功應用於高速運轉下轉子之振動量測，乃利用此雙測點法量測不同轉速下之操作模態，並將此高轉速下之轉子模態測得結果，與敲擊法所求得之模態進行MAC及模態圖形比對，結果亦顯示出其轉速對模態之影響。分析結果，顯示此雙測點法可成功應用於高速運轉下轉子動態量測之可行性。文中亦利用不同的配重故意造成轉盤質量不平衡，由實驗結果顯示，雙測點法仍可求得不同配重模式對其操作模態之影響。

This paper adopts a dual-point measurement technique to predict the resonance frequency and operation modes of a high speed rotor at different operating speed. The effect of balance policy on the operating mode shapes of a rotor has also been investigated. Displacement signals measured at two different points of a rotating shaft are used to estimate the operation mode shapes at the main operating frequency based on the definition of transmissibility function. To verify the feasibility of this technique, the dynamic parameters, i.e. natural frequencies, damping ratio and normal modes of a stationary rotor are measured in advance by applying the traditional frequency response method for comparison. The values of modal assurance criterion (MAC) and mode shape diagrams indicate that both methods are in a good agreement on the normal modes when the system is undamped or lightly damped. However, a significant difference is observed for highly damped modes. The dual-point measurement technique is applicable to investigate the effect of rotating speed on measured operation modes at different speed. Results indicate that the rotating speed may affect the dynamic parameters of a rotating shaft significantly.
Furthermore, the dynamic unbalance effect on the response of a rotating shaft has also been studied in this thesis. Results indicate that the position of the unbalance is quite sensitive to the response of a rotating shaft. The sensitivity of unbalance and its position is dependent on the operation mode correspondence to the driving speed. The measured results indicate the dual-point measurement is quite available to study the dynamic responses of a rotating shaft or rotor.

目錄 i
圖目錄 iii
表目錄 vi
符號說明 vii
摘要 x
Abstract xii
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 組織與章節 5
第二章 雙測點振模測定法之理論導引 6
2.1 線性無阻尼系統 6
2.1.1 傳遞函數與振模之關係 6
2.1.2 兩測點交互能譜與自然頻率之關係 10
2.1.3 兩測點訊號�雜訊比與自然頻率之相互關係 13
2.2 非比例線性黏滯阻尼系統 15
第三章 實驗驗證 21
3.1 高速轉子靜止下之實驗驗證 21
3.1.1 傳統敲擊法測試 21
3.1.2 雙測點振模測定法於靜態下測試 44
3.2 高速轉子運轉下之實驗驗證 61
3.2.1 掃頻法測試 61
3.2.2 雙測點振模測定法於運轉下測試 71
3.3 不同配重模式對操作模態之影響 84
第四章 結論 90
參考文獻 91
附錄A 線性無阻尼系統在 基頻趨近自然頻率 之傳遞函數值 96
附錄B 交互能譜之計算 98
附錄C 模態確認指標（MAC） 100

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