Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis.
Proc Math Phys Eng Sci
; 476(2237): 20190549, 2020 May.
Article
en En
| MEDLINE
| ID: mdl-32523408
ABSTRACT
The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 1 and 3 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ω pq . The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ω pq . An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ, stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O ( ζ ) beyond Ω pq . The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.
Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
Proc Math Phys Eng Sci
Año:
2020
Tipo del documento:
Article
País de afiliación:
Alemania
Pais de publicación:
ENGLAND
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ESCOCIA
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GB
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GREAT BRITAIN
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INGLATERRA
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REINO UNIDO
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SCOTLAND
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UK
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UNITED KINGDOM