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Research Papers

Stability and Stationary Response of a Skew Jeffcott Rotor With Geometric Uncertainty

[+] Author and Article Information
Nicolas Driot

LaMCoS, CNRS UMR 5259, INSA-Lyon, Université de Lyon, 20, rue des Sciences, F69621 Villeurbanne Cedex, France

Alain Berlioz

LGMT, INSA, UPS, Université de Toulouse, 135, Avenue de Rangueil, F 31077 Toulouse, France

Claude-Henri Lamarque1

DGCB, URA CNRS 1652, ENTPE, Université de Lyon, 3, rue Maurice Audin, F 69518 Vaulx-en-Velin, Francelamarque@entpe.fr

1

Corresponding author.

J. Comput. Nonlinear Dynam 4(2), 021003 (Mar 06, 2009) (10 pages) doi:10.1115/1.3079683 History: Received August 28, 2007; Revised July 29, 2008; Published March 06, 2009

The aim of this work is to apply stochastic methods to investigate uncertain parameters of rotating machines with constant speed of rotation subjected to a support motion. As the geometry of the skew disk is not well defined, randomness is introduced and affects the amplitude of the internal excitation in the time-variant equations of motion. This causes uncertainty in dynamical behavior, leading us to investigate its robustness. Stability under uncertainty is first studied by introducing a transformation of coordinates (feasible in this case) to make the problem simpler. Then, at a point far from the unstable area, the random forced steady state response is computed from the original equations of motion. An analytical method provides the probability of instability, whereas Taguchi’s method is used to provide statistical moments of the forced response.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

View of the rotating machine model and associated frames

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Figure 2

Campbell diagram obtained in the rotating frame (Rd) for Ida=0.029 kg m2

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Figure 3

Comparison between the spectra of x and z forced responses provided by a Newmark scheme and the spectral method; Ω=33.2 Hz and ωe=15.8 Hz

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Figure 4

Comparison between the spectra of x and z forced responses provided by a Newmark scheme and the spectral method; Ω=166.2 Hz and ωe=15.8 Hz

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Figure 5

Campbell diagram obtained in the fixed frame

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Figure 6

rms value of the x displacement (m) response versus Ω and ωe

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Figure 7

rms value of the z displacement response (m) versus Ω and ωe

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Figure 8

Points and weightings for a three point-sampled Gaussian variable

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Figure 9

g(Ida,Ω=12,250) (a), PDF hΩ(λ) computed at Ω=12,250 rpm (b), and probability PΩ to be unstable (c)

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Figure 10

Mean value (a) and standard deviation (b) of the rms forced response (m) versus ωe in the x direction provided by MC and Taguchi’s methods; Ω=1000 rpm

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Figure 11

Mean value (a) and standard deviation (b) of the rms forced response (m) versus ωe in the x direction provided by MC and Taguchi’s methods; Ω=6400 rpm

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Figure 12

Mean values of the z rms forced response (m) versus Ω and ωe provided by Taguchi’s method

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Figure 13

Standard deviation of the z rms displacement (m) versus Ω and ωe by Taguchi’s method

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