A 3D finite element model for the vibration analysis of asymmetric rotating machines

This paper suggests a 3D finite element method based on the modal theory in order to analyse linear periodically time-varying systems. Presentation of the method is given through the particular case of asymmetric rotating machines. First, Hill governing equations of asymmetric rotating oscillators with two degrees of freedom are investigated. These differential equations with periodic coefficients are solved with classic Floquet theory leading to parametric quasimodes. These mathematical entities are found to have the same fundamental properties as classic eigenmodes, but contain several harmonics possibly responsible for parametric instabilities. Extension to the vibration analysis (stability, frequency spectrum) of asymmetric rotating machines with multiple degrees of freedom is achieved with a fully 3D finite element model including stator and rotor coupling. Due to Hill expansion, the usual degrees of freedom are duplicated and associated with the relevant harmonic of the Floquet solutions in the frequency domain. Parametric quasimodes as well as steady-state response of the whole system are ingeniously computed with a component-mode synthesis method. Finally, experimental investigations are performed on a test rig composed of an asymmetric rotor running on nonisotropic supports. Numerical and experimental results are compared to highlight the potential of the numerical method.

[1]  Henri Poincaré,et al.  Sur les déterminants d'ordre infini , 1886 .

[2]  Chong-Won Lee,et al.  Modal analysis of periodically time-varying linear rotor systems , 2006 .

[3]  Giancarlo Genta,et al.  Dynamics of Rotating Systems , 2005 .

[4]  H. Ulbrich,et al.  Rotordynamics prediction in engineering (second edition): by Michel Lalanne, Guy Ferraris (Wiley, New York; ISBN 0471972886) , 1998 .

[5]  Dong Ju Han.  Vibration analysis of periodically time-varying rotor system with transverse crack , 2007 .

[6]  S. Neogy,et al.  An efficient scheme for stability analysis of finite element asymmetric rotor models in a rotating frame , 2005 .

[7]  G. Hill.  On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon , 1886 .

[8]  J. Der Hagopian,et al.  Dynamic Behavior of a Drill-String: Experimental Investigation of Lateral Instabilities , 1996 .

[9]  Giancarlo Genta,et al.  Whirling of unsymmetrical rotors: A finite element approach based on complex co-ordinates , 1988 .

[10]  D. Combescure,et al.  Refined finite element modelling for the vibration analysis of large rotating machines: Application to the gas turbine modular helium reactor power conversion unit , 2008 .

[11]  C. Hsu.  On the Parametric Excitation of a Dynamic System Having Multiple Degrees of Freedom , 1963 .

[12]  Régis Dufour,et al.  Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions , 1998 .

[13]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[14]  Aouni A. Lakis,et al.  INVESTIGATION OF THE STABILITY AND STEADY STATE RESPONSE OF ASYMMETRIC ROTORS, USING FINITE ELEMENT FORMULATION , 2001 .

[15]  Michel Lalanne,et al.  Rotordynamics prediction in engineering , 1998 .

[16]  S. Audebert,et al.  A comprehensive theoretical, numerical and experimental approach for crack detection in power plant rotating machinery , 2008 .

[17]  G.M.L. Gladwell,et al.  On the stability of an unsymmetrical rigid rotor supported in unsymmetrical bearings , 1966 .

[18]  R. Gasch,et al.  A Survey Of The Dynamic Behaviour Of A Simple Rotating Shaft With A Transverse Crack , 1993 .

[19]  P. J. Brosens,et al.  Whirling of Unsymmetrical Rotors , 1961 .