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研究生:凌玉揚
研究生(外文):Yung-Yang Ling
論文名稱:受碰撞限制含撓性軸承支撐剛性軸系統非線性振動響應之探討
論文名稱(外文):Studies of Nonlinear Vibration Responses of Bearing-Supported Shaft Systems Subjected to Collision Constraints
指導教授:張銘永
學位類別:碩士
校院名稱:國立中興大學
系所名稱:機械工程學系所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
畢業學年度:96
語文別:中文
論文頁數:129
中文關鍵詞:碰撞撓性軸承非線性振動
外文關鍵詞:VibrationBearingCollisionConstraint
相關次數:
  • 被引用被引用:1
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The objective of this thesis is to develop a model for studying of nonlinear vibration of bearing-supported rigid shaft systems subjected to collision constraints. The system consists of a rigid shaft and a rigid disk. The shaft is supported by bearings which are modeled as springs and dampers. The kinetic energy and the potentail energy of the system are derived. The work done by supported forces of bearings are also considered. By using the Lagrange equations, the equations of motion of the bearing-supported shaft systems are derived. Next, the geometrical constraints when the collision occurs are found. At last, the relations between the velocities of the shaft before and after impact are determind.

Analyses of transient responses of systems with and without collision are carried out, and are compared with those obtained using linearized equations of motion. Then, the individual influence of the parameters such as coefficient of restitution, bearing stiffness, the locations of bearings and collision constraints on the dynamic responses are investigated.
誌謝 i
中文摘要 ii
SUMMARY iii
章節目錄 iv
表目錄 vi
圖目錄 vii
符號索引 xx
第一章 序論 1
1.1 前言 1
1.2 文獻回顧 1
1.3 研究目的與內容 3
第二章 基礎理論推導 4
2.1 運動方程式之推導 4
2.2 線性化系統之解析解 11
2.3 系統數值解之模式 12
2.4 碰撞條件式與碰撞後速度之推導 15
2.4.1 碰撞幾何條件式之推導 15
2.4.2 桿碰撞後速度推導 17
第三章 系統無碰撞與有碰撞之響應分析 23
3.1 無碰撞之響應 23
3.2 單碰撞邊界 32
3.3 雙碰撞邊界 48
第四章 邊界條件對系統響應之影響 55
4.1恢復係數e改變對系統響應之影響 55
4.2 邊界位置改變對系統響應之影響 64
4.2.1 邊界水平位置 改變對系統響應之影響 64
4.2.2 垂直邊界位置 改變對系統響應之影響 72
4-3 系統軸承徑向勁度值改變對系統響應之影響 79
4.3.1 處軸承徑向勁度值 改變對系統響應之影響 80
4.3.2 處軸承徑向勁度值 改變對系統響應之影響 87
4-4 系統軸承 方向勁度值 改變對系統響應之影響 96
4-5 系統支撐軸承 位置改變對系統響應之影響 103
4.5.1 支撐軸承 位置 改變對系統響應之影響 103
4.5.2 改變支撐軸承 位置 改變對系統響應之影響 110
第五章 結論與未來展望 118
5.1 結論 118
5.2 未來展望 119
參考文獻 120
[1] G. Ioannou, A. Woowat and R. Gohar “Multiple Roller Bearing-Shaft Systems” Wear, Vol. 81, 1982, PP. 47-58.

[2] C.W. Lee, Y.G. Jei“Modal Analysis of Continuous Rotor-Bearing Systems” Journal of Sound and Vibration, Vol. 126, Issue 2, 1988, PP. 345-361.

[3] N. H. Shabaneh, Jean W. Zu“Dynamic Analysis of Rotor Shaft Systems with Viscoelastically Supported Bearings”Mechanism and Machine Theory, Vol. 35, 2000, PP. 1313-1330.
[4] S.P. Harsha“Nonlinear Dynamic Analysis of a High-Speed Rotor Supported by Rolling Element Bearings”Journal of Sound and Vibration, Vol. 290, 2006, PP. 65-100.

[5] M.H. Eissa, U.H. Hegazy, Y.A. Amer“Dynamic Behavior of an AMB Supported Rotor Subject to Harmonic Excitation”Applied Mathematical Modelling, Vol. 32, 2008, PP. 1370-1380.

[6] Mohammed F. Abdul Azeez, Alexander F. Vakakis,“Numerical and Experimental Analysis of a Continuous Overhung Rotor Undergoing Vibro-Impacts”International Journal of Non-Linear Mechanics, Vol. 34, 1999, PP.415-435.

[7] J.Zapomel, C.H.J.Fox, and EMalenovsky, “Numerical Investigation of a Rotor System with Disc-Housing Impact”Journal of Sound and Vibration, Vol. 2, No.243, 2001, PP.215-240.

[8] Q. -S. Lu, Q. -H. Li, E. H. Twizell“The Existence of Periodic Motions in Rub-Impact Rotor Systems”Journal of Sound and Vibration, Vol. 264, 2003, PP. 1127-1137.

[9] O. Grapis, V. Tamuzsb, N.-G. Ohlson, J. Andersonsb,“Overcritical High-Speed Rotor Systems, Full Annular Rub and Accident” Journal of Sound and Vibration, Vol. 290, 2006, PP. 910-927.

[10] S. Popprath, H. Ecker“Nonlinear Dynamics of a Rotor Contacting an Elastically Suspended Stator”Journal of Sound and Vibration, Vol. 308, 2007, PP. 767-784.

[11] S. Popprath, H. Ecker“The Effect of Bearing Cage Run-Out on the Nonlinear Dynamics of a Rotating Shaft”Journal of Sound and Vibration, Vol. 308, 2007, PP. 767-784.
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