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Frontiers of Mechanical Engineering

Front Mech Eng    2013, Vol. 8 Issue (3) : 244-251
Dynamic analysis of a rig shafting vibration based on finite element
Van Thanh NGO, Danmei XIE(), Yangheng XIONG, Hengliang ZHANG, Yi YANG
School of Power and Mechanical Engineering Wuhan University, Wuhan 430072, China
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In recently, finite elements method (FEM) has been used most popular for analysis of stress, vibration, heat flow and many other phenomena. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using FEM. The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes and unbalance responses. Then critical and mode shapes are determined. Finally, responses of unbalance force are analyzed in case of undamped and damped system, and peaks of response are compared.

Keywords Finite element method (FEM)      lateral vibration      rig shafting      rotor-bearing system      dynamic characteristics     
Corresponding Author(s): XIE Danmei,   
Issue Date: 05 September 2013
 Cite this article:   
Hengliang ZHANG,Yi YANG,Van Thanh NGO, et al. Dynamic analysis of a rig shafting vibration based on finite element[J]. Front Mech Eng, 2013, 8(3): 244-251.
Fig.1  Shaft- line modeling of a rig rotor-bearing system
Fig.2  Coordinate used in analysis of rotor
Fig.3  Coordinate in plane
Fig.4  Journal bearing model
Speed/ (rev?min-1)Root s/(rad?s-1)ωn/Hzωd/Hzξ
3500- 22.94±125.26j-23.48±127.77j-37.90±162.96j-38.03±163.81j-25.32±217.81j-25.47±223j-25.93±442.1j-27.56±457.24j20.266720.675826.628426.765134.899335.721670.475872.903919.935020.335325.936226.071834.665835.490970.354872.77180.1800.1840.2260.2260.1150.1130.0580.06
Tab.1  Eigenvalues (), natural frequencies (),damped natural frequencies () and damping ratio (ξ)
Tab.2  First fourth critical speeds (rev/min)
Fig.5  Campbell diagram, FW (forward whirl), BW (backward whirl)
Fig.6  The first four critical speeds mode shapes of the rotor
Fig.7  3D view the first four critical mode shapes of the rotor
Fig.8  Unbalance response of the rotor at node 13, 31, 46 in case of undamped system
Fig.9  Forward- whirl orbits at node 13 (blue circle), 31 (green circle), 46 (red circle). The cross denotes the start of the orbit and the diamond denotes the end. The dimensions are μm
Node 13Node 31Node 46
First peak12558.36833326152
Second peak636010829002191425480
Third peak840150606310591500260
Tab.3  Response magnitude at resonant in case of undamped and damped system (μm)
Fig.10  Unbalance response of the rotor at node 13, 31, 46 in case of damping system
Fig.11  Forward- whirl orbits at node 13 (blue circle), 31 (green circle), 46 (red circle). The cross denotes the start of the orbit and the diamond denotes the end. The dimensions are μm. (damping system)
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