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標題: 含剛體運動效應旋轉軸動態響應之探討
Studies of Dynamic Responses of Spinning Shafts Including Rigid Body Motion Effect
作者: 王偉帆
Wang, Wei-Fan
關鍵字: Rigid-Body Motion;剛體運動;Spinning Shaft;旋轉軸
出版社: 機械工程學系所
引用: [1] M. Lalanne, G. Ferrarris, Rotordynamics Prediction in Engineering, John Wiley And Sons, Chichester/New York/Brisbane/Singapore (1990). [2] C.W. Lee,Vibration Analysis of Rotor, Kluwer Acdemic Publishers, Dordrecht/Boston/London(1993) [3] F.F. Ehrich, Handbook of Rotordynamics, McGraw-Hill, New York(1992) [4] M. A . Hill, T.Frkhfakh, M. Hadder, “Vibration Analysis of Rotating Flexible Shaft-Disk System, ” Journal of Engineering Mathematics, Vol. 57, n 4, p 351-363, April 2007 [5] Z.Yuan, F.Chu, Y.Lin, “External and Internal Coupling Effects of Rotor’s Bending and Torsional Vibration under Unblances, ” Journal of Sound and Vibration, Vol. 299, n 1-2, p 339-347, 2007 [6] S. M. Yang, “Vibration of a Spinning Annular Disk with Coupled Rigid-Body Motion, ” Journal of vibration, acoustics, stress, and reliability in design, Vol.115, n 2, p 159-164, Apr 1993 [7] K. Hu, Z. P. Mourelatos, N. Vlahopoulos, “Computational analysis for dynamic response of a rotation shaft on flexible support structure with clearances, ” Journal of Sound and Vibration, Vol 267, n 1, p 1-28, October 9, 2003 [8] C. O. Chang, J. W. Cheng, “Non-Linear Dynamics and Instability of a Rotating Shaft-Disk System, ” Journal of Sound and Vibration, Vol.160, n 3, p 433-454, Jan 22, 1993 [9] H. A. DeSmidt, K. W. Wang, E. C. Smith, “Coupled Torsion-Lateral Stability of a Shaft-Disk System Driven Through a Universal Joint, ” Journal of Applied Mechanics, Transactions ASME, Vol.69, n 3, p 261-273, May 2002 [10] B. O. Al-Bedoor, “Transient Torsional and Lateral Vibrations of Unbalanced Rotors With Rotor-To-Stator Rubbing, ” Journal of Sound and Vibration, Vol. 229, n 3, p 627-645, January 20, 2000 [11] 魏瑞宏, “旋轉軸系統之振動與控制-兩種數學模式之比較, ”碩士論文, 中興大學機械系研究所, 2001 [12] 詹政川, “承受持續外激力旋轉軸振動之主動控制, ”碩士論文,中興大學機械系研究所,1996 [13] 凌玉揚, “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, ”碩士論文,中興大學機械系研究所,2008 [14] J. N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York (1984). [15] H. Baruh, Analytical Dynamics, McGraw-Hill, Boston(1999) [16] A. D. Dimarogonas and S. A. Paipetis, Analytical Methods in Rotor Dynamics, Applied Science Publishers, London and New York( 1983).
本文主要目的是探討剛體運動效應對撓性旋轉軸系統的動態響應的影響。所分析系統為含剛性轉盤之撓性軸,並以黏滯阻尼器與彈簧模擬軸承支撐。首先,推導系統的運動方程式,在推導的過程中,同時考慮旋轉軸的剛體運動及旋轉軸的撓性變形。運動方程式推導時,考慮旋轉軸動能、旋轉軸應變能、轉盤動能、軸承支撐作用力與圓盤質心偏移所造成的離心力對軸所做的功等,採用漢米爾頓定理(Hamilton’s principle)配合有限元素法,推導出含剛體運動效應的旋轉軸系統動態運動方程式。
在數值分析中,採用Matlab中利用高階Runge-Kutta法解微分方程式的ODE45函數來求解旋轉軸做剛體運動時的運動方程式,再將所得到的解代入含剛體運動之撓性軸系統的運動方程式利用 法分析。利用上述運動方程式,本文藉由改變系統相關參數,如旋轉黏滯係數、軸承支撐位置、剛盤位置、馬達加速的快慢等,探討這些參數之改變對於系統響應的影響,並且與不考慮剛體運動效應之撓性旋轉軸系統進行比較。

The objective of this thesis is to study the dynamic responses of the flexible spinning-shaft system including the rigid-body motion effect. The spinning-shaft system being considered include the rigid disk, the flexible shaft, and bearing supports which are modeled as springs and viscous dampers. To derive, the equations of motion of the spinning-shaft system. First, the kinetic energy and the strain energy of the spinning shaft, the kinetic energy of the rigid disk, and the work done by support forces of the bearings and centrifugal force of the disk are found. Then by employing the Hamilton's principle together with the finite element method, the equations of motion of the spinning-shaft system including both the rigid-body motion and flexible deformation effects of the shaft are obtained.
In the study of dynamic responses, in order to simplify the analysis, the influence of the flexible deformation of the shaft on the rigid-body motion of system is neglected. The equations of motion then can be divided into two groups corresponding to that of rigid-body motion and that of flexible motion affected by the rigid-body motion. The nonlinear equations for rigid-body motion is further simplified to linear ones for comparison.
In the numerical analysis, a higher-order Runge-Kutta method is used to solve the equations of motion describing the rigid-body motion of the system. With above obtained results equations of flexible motion affected by rigid-body motion are then analyzed by the Newmark's method. The influences of the parameters such as rotational viscous damping coefficient, the locations of bearings and the disk, and the motor's acceleration on the dynamic responses are investigated. Comparisons are also made with those of the spinning shaft system without considering the rigid-body motion effect.
其他識別: U0005-1808201016153800
Appears in Collections:機械工程學系所

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