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Nonlinear Analysis of the Orbital Motions of Immersed Rotors Using a Spectral/Galerkin Approach

[+] Author Affiliations
Miguel Moreira

Polytechnic Institute of Setubal, Setubal, Portugal

José Antunes

Institute of Nuclear Technology, Sacavem, Portugal

Heitor Pina

Technical Institute, Lisboa, Portugal

Paper No. IMECE2002-32414, pp. 369-376; 8 pages
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Design Engineering
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-3628-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME


We recently developed a symbolic-numerical formulation for the nonlinear planar motion of rotors under fluid confinement, based on a spectral/Galerkin approach, for gap geometries of about δ = H/R ≈ 0.1 — where H is the average annular gap and R is the rotor radius. Results showed a quite good agreement between the class of approximate models generated, the corresponding analytical exact planar model and experiments. This methodology can be almost entirely automated on a symbolic computing environment. In the present paper this symbolic-numerical spectral/Galerkin procedure is extended in order to deal with nonlinear orbital motions — X (t) and Y (t) taking place in orthogonal directions. Numerical simulations performed over a centered rotor configuration maintained by non-isotropic supports (Ky st /Kx st = 0.4, where kx st and ky st stand for the structural stiffnesses), which exhibit an interesting dynamics, show a quite good agreement between this type of approximate models and the corresponding analytical exact (but quite involved) model, developed in the past by the authors. With the proposed symbolic-numerical approach one can obtain accurate nonlinear dynamical formulations enabling the study, understanding and prediction of nonlinear orbital rotor-dynamics.

Copyright © 2002 by ASME
Topics: Motion , Rotors



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