Journal article 739 views
Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
,
Michael Friswell
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume: 476, Issue: 2237, Start page: 20190549
Swansea University Authors:
Alexander Shaw , Michael Friswell
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DOI (Published version): 10.1098/rspa.2019.0549
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...
| Published in: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
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| ISSN: | 1364-5021 1471-2946 |
| Published: |
The Royal Society
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa54468 |
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| 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 Ωp:q. 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 = Ωp:q. 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 Ωp:q. 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. |
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| Keywords: |
rotordynamics, resonance, bouncing, grazing, bifurcation |
| College: |
Faculty of Science and Engineering |
| Issue: |
2237 |
| Start Page: |
20190549 |