An efficient analysis method is suggested to investigate the frequency characteristics and stability of asymmetric anisotropic rotor-bearing systems. Modifications are made to incorporate the effect of stator asymmetry into an existing three-dimensional (3D) solid finite element procedure developed for rotors with symmetric supports. The reduced ordered linear differential equations with periodic coefficients of the asymmetric anisotropic rotor model are established in the rotating frame. The frequency characteristics and stability of the obtained periodic time-varying coefficient differential equations are investigated based on Floquet theory and Hill's method. Numerical examples and experimental studies are presented to validate the effectiveness of the presented method.
Issue Section:
Gas Turbines: Structures and Dynamics
References
1.
Lee
, C. W.
, 1991
, “A Complex Modal Testing Theory for Rotating Machinery
,” Mech. Syst. Signal Process.
, 5
(2
), pp. 119
–137
.10.1016/0888-3270(91)90019-22.
Floquet
, G.
, 1883
, “Sur les equations lineaires a coefficients periodiques
,” Ann. Sci. Ec. Norm. Super.
, 12
, pp. 47
–88
.http://eudml.org/doc/808953.
Hill
, G. W.
, 1886
, “On the Part of the Motion of the Lunar Perigee Which is a Function of the Mean Motions of the Sun and Moon
,” Acta Math.
, 8
(1
), pp. 1
–36
.10.1007/BF024170814.
Black
, H. F.
, 1969
, “Parametrically Excited Lateral Vibrations of an Asymmetric Slender Shaft in Asymmetrically Flexible Bearings
,” Proc. Inst. Mech. Eng., Part C
, 11
(1
), pp. 57
–67
.10.1243/JMES_JOUR_1969_011_008_025.
Yamamoto
, T.
, Ota
, H.
, and Kono
, K.
, 1968
, “On the Unstable Vibrations of a Shaft With Unsymmetrical Stiffness Carrying an Unsymmetrical Rotor
,” ASME J. Appl. Mech.
, 35
(2
), pp. 313
–321
.10.1115/1.36011976.
Gladwell
, G. M. L.
, and Stammers
, C. W.
, 1966
, “On the Stability of an Unsymmetrical Rigid Rotor Supported in Unsymmetrical Bearings
,” J. Sound Vib.
, 3
(3
), pp. 221
–232
.10.1016/0022-460X(66)90091-57.
Han
, Q. K.
, and Chu
, F. L.
, 2012
, “Parametric Instability of Two-Disk Rotor With Two Inertia Asymmetries
,” Int. J. Struct. Stab. Dyn.
, 12
(2
), pp. 251
–284
.10.1142/S02194554125000348.
Han
, Q.
, and Chu
, F.
, 2013
, “Parametric Instability of a Jeffcott Rotor With Rotationally Asymmetric Inertia and Transverse Crack
,” Nonlinear Dyn.
, 73
(1–2
), pp. 827
–842
.10.1007/s11071-013-0835-69.
Genta
, G.
, 1988
, “Whirling of Unsymmetrical Rotors: A Finite Element Approach Based on Complex Coordinates
,” J. Sound Vib.
, 124
(1
), pp. 27
–53
.10.1016/S0022-460X(88)81404-410.
Nandi
, A.
, and Neogy
, S.
, 2005
, “An Efficient Scheme for Stability Analysis of Finite Element Asymmetric Rotor Models in a Rotating Frame
,” Finite Elem. Anal. Des.
, 41
(14
), pp. 1343
–1364
.10.1016/j.finel.2005.03.00111.
Lee
, C. W.
, Han
, D. J.
, Suh
, J. H.
, and Hong
, S. W.
, 2007
, “Modal Analysis of Periodically Time-Varying Linear Rotor Systems
,” J. Sound Vib.
, 303
(3–5
), pp. 553
–574
.10.1016/j.jsv.2007.01.04112.
Lee
, C. W.
, Han
, D. J.
, and Hong
, S. W.
, 2006
, “Modal Analysis of Periodically Time-Varying Linear Rotor Systems Using Floquet Theory
,” 7th IFToMM Conference on Rotor Dynamics
, Vienna, Austria, Sept. 25–28, Paper No. 78.13.
Lee
, C. W.
, Suh
, J. H.
, and Hong
, S. W.
, 2004
, “Modal Analysis of Rotor System Using Modulated Coordinates for Asymmetric Rotor System With Anisotropic Stator
,” 8th International Conference on Vibrations in Rotating Machinery
, Swansea, UK, Sept. 7–9, pp. 575
–584
.14.
Lazarus
, A.
, Prabel
, B.
, and Combescure
, D.
, 2010
, “A 3D Finite Element Model for the Vibration Analysis of Asymmetric Rotating Machines
,” J. Sound Vib.
, 329
(18
), pp. 3780
–3797
.10.1016/j.jsv.2010.03.02915.
Geradin
, M.
, and Kill
, N.
, 1984
, “A New Approach to Finite Element Modelling of Flexible Rotors
,” Eng. Comput.
, 1
(1
), pp. 52
–64
.10.1108/eb02356016.
Stephenson
, R. W.
, and Rouch
, K. E.
, 1993
, “Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements With Matrix Reduction
,” ASME J. Vib. Acoust.
, 115
(4
), pp. 484
–489
.10.1115/1.293037617.
Geradin
, M.
, and Kill
, N.
, 1986
, “A Three Dimensional Approach to Dynamic Analysis of Rotating Shaft Disc Flexible Systems
,” 2nd International Conference on Rotordynamics IFToMM
, Tokyo, Sept. 14–17, pp. 87
–93
.18.
Irretier
, H.
, Jacquet-Richardet
, G.
, and Reuter
, F.
, 1999
, “Numerical and Experimental Investigations of Coupling Effects in Anisotropic Elastic Rotors
,” Int. J. Rotating Mach.
, 5
(4
), pp. 263
–271
.10.1155/S1023621X9900023819.
Kim
, K. T.
, and Lee
, C. W.
, 2012
, “Dynamic Analysis of Asymmetric Bladed-Rotors Supported by Anisotropic Stator
,” J. Sound Vib.
, 331
(24
), pp. 5224
–5246
.10.1016/j.jsv.2012.06.01420.
Nandi
, A.
, 2004
, “Reduction of Finite Element Equations for a Rotor Model on Non-Isotropic Spring Support in a Rotating Frame
,” Finite Elem. Anal. Des.
, 40
(9
), pp. 935
–952
.10.1016/S0168-874X(03)00121-521.
Genta
, G.
, 2005
, Dynamics of Rotating Systems
, Springer
, New York
, Chap. 9.22.
Jacquet-Richardet
, G.
, Ferraris
, G.
, and Rieutord
, P.
, 1996
, “Frequencies and Modes of Rotating Flexible Bladed Disc-Shaft Assemblies: A Global Cyclic Symmetry Approach
,” J. Sound Vib.
, 191
(5
), pp. 901
–915
.10.1006/jsvi.1996.016223.
Chatelet
, E.
, D'Ambrosio
, F.
, and Jacquet-Richardet
, G.
, 2005
, “Toward Global Modelling Approaches for Dynamic Analyses of Rotating Assemblies of Turbomachines
,” J. Sound Vib.
, 282
(1–2
), pp. 163
–178
.10.1016/j.jsv.2004.02.03524.
Boru
, F. E.
, 2010
, “Numerical and Experimental Response and Stability Investigations of Anisotropic Rotor-Bearing Systems
,” Ph.D., thesis, Kassel University, Kassel, Germany.Copyright © 2015 by ASME
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