以耦合離散元素法與有限元素法分析含阻尼顆粒偏心轉子的動態行為

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姓名

彭奕晨(I-CHEN PENG) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

以耦合離散元素法與有限元素法分析含阻尼顆粒偏心轉子的動態行為

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至系統瀏覽論文 (2028-10-19以後開放)

摘要(中)

本研究採用雙面平衡法，以平衡轉子系統上的偏心慣性力，同時採用顆粒阻尼技術，使用顆粒與腔體之間的碰撞及摩擦消除系統的能量，以壓制轉子轉動時帶來的振動。本研究數值模型採用耦合離散元素法(Discrete Element Method, DEM)與有限元素法(Finite Element Method, FEM)，分析含顆粒阻尼器偏心轉子的動態行為。本研究分析轉速與顆粒粒徑對偏心轉子動態行為的影響，動態反應包含中央軸心徑向位移、位移頻譜、軸承應力、轉子動能及彈性應變能。研究結果顯示：(1)偏心轉子的轉動行為均較平衡轉子更加不穩定，且偏心轉子造成的軸承應力皆大於平衡轉子的軸承應力。(2)顆粒阻尼器中阻尼顆粒與結構腔體間互相碰撞及摩擦可以降低轉子系統運轉時徑向位移、軸承應力、動能及彈性應變能。 (3)置入不同粒徑顆粒皆可達到很好的減振效果，2.0 mm顆粒體為較佳粒徑。(4)比較應力與徑向位移的關係，得知軸中央軸心的徑向位移越小則軸承應力越大。(5)加入不同顆粒粒徑於偏心轉子系統皆可以得到很好的消能效果，但顆粒粒徑對含顆粒阻尼器轉子系統的動能及彈性應變能影響甚小。

摘要(英)

This study employs a dual-sided balancing method with particle dampers to counteract the eccentric inertial forces on rotor systems. A coupled DEM and FEM model is proposed to analyze the dynamic behavior of an eccentric rotor system incorporating granular dampers. The effects of rotational speed and particle size on the dynamic behavior of the system were investigated. The dynamic responses studied here included radial displacement, displacement spectrum, bearing stresses, and kinetic energy and strain energy of the rotor systems. Numerical results indicate that the unbalanced shaft shows more unstable dynamic behavior than balanced shaft. Additionally, the bearing stresses in the unbalanced shaft are higher than those of the balanced shaft. The collisions and friction between damping particles and mechanical parts effectively reduce radial displacement, vibration frequency, bearing stresses, and kinetic energy and strain energy of the rotor system. The installation of particles dampers leads to a significant reduction in vibration, especially for 2.0 mm particle dampers exhibiting the most favorable damping effect. Comparing the relationship between stresses and radial displacements, it is observed that as the radial displacements at the central part of the shaft decrease, the bearing stresses increase. The rotor system achieves effective energy dissipation with different kinds of particle sizes. However, the particle size has minimal impact on the kinetic energy and strain energy of the rotor system with particle dampers.

關鍵字(中)

★ 偏心轉子系統
★ 顆粒阻尼器
★ 耦合離散元素法與有限元素法
★ 顆粒減振
★ 徑向位移
★ 軸承應力

關鍵字(英)

★ eccentric rotor system
★ particle damper
★ Two-way Couple DEM-FEM Approach
★ granular vibration damping
★ radial displacement
★ bearing stresses

論文目次

摘要.................................................................................................................................i
Abstract..........................................................................................................................ii
目錄...............................................................................................................................iii
附表目錄.......................................................................................................................vi
附圖目錄......................................................................................................................vii
附錄目錄......................................................................................................................xii
第一章緒論..................................................................................................................1
1-1 研究背景 .........................................................................................................1
1-2 研究動機以及研究目的 .................................................................................2
1-3 文獻回顧 .........................................................................................................3
1-3-1 轉動機械性質相關文獻.....................................................................3
1-3-2 顆粒阻尼應用相關文獻.....................................................................7
第二章研究方法........................................................................................................ 11
2-1 動平衡校正原理及雙平衡面校正法 ..........................................................11
2-2 DEM-FEM 雙向耦合建模............................................................................12
2-2-1 彈性連續體的 FEM 模型.................................................................12
2-2-2 顆粒體的 DEM 模型........................................................................15
2-2-3 DEM-FEM 雙向耦合 ........................................................................17
2-3 系統介紹 ......................................................................................................17
2-3-1 臨界時間步.......................................................................................17
2-3-2 幾何參數與邊界條件.......................................................................18
2-3-3 網格元素與材料性質.......................................................................20
iv
2-3-4 數值模擬系統與觀察點...................................................................20
第三章結果與討論....................................................................................................22
3-1 偏心轉子機構的動態分析 ..........................................................................22
3-1-1 網格品質測試...................................................................................22
3-1-1-1 轉子於軸承接觸區的網格分割尺寸測試............................22
3-1-1-2 轉子於非軸承接觸區的網格分尺寸測試............................23
3-1-1-3 圓周分割測試........................................................................23
3-1-2 時間步安全係數測試.......................................................................23
3-1-3 網格方位測試...................................................................................24
3-2 無偏心轉子機構與有偏心轉子機構的動態對比分析 ..............................25
3-2-1 轉子轉速徑向位移及頻譜分析.......................................................25
3-2-2 軸承應力分析...................................................................................27
3-3 含顆粒阻尼器的偏心轉子機構動態分析 ..................................................29
3-3-1 轉子轉速徑向位移及頻譜分析.......................................................29
3-3-2 軸承應力分析...................................................................................31
3-3-3 動能及彈性應變能分析...................................................................33
3-4 顆粒粒徑與轉子轉速影響分析 ..................................................................35
3-4-1 轉子轉速徑向位移及頻譜分析.......................................................35
3-4-2 軸承應力分析...................................................................................37
3-4-3 動能及彈性應變能分析...................................................................39
第四章結論................................................................................................................40
4-1 結論 ..............................................................................................................40
參考文獻......................................................................................................................42
附表..............................................................................................................................45

附圖..............................................................................................................................48
附錄..............................................................................................................................99

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指導教授

鍾雲吉

審核日期

2023-10-20

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