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Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis

Karin Mora, Alan R. Champneys, Alexander Shaw Orcid Logo, 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 Orcid Logo, 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...

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Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1364-5021 1471-2946
Published: The Royal Society 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54468
first_indexed 2020-06-15T13:09:33Z
last_indexed 2020-11-07T04:13:00Z
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spelling 2020-11-06T14:34:15.0092074 v2 54468 2020-06-15 Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2020-06-15 ACEM 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. Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 2237 20190549 The Royal Society 1364-5021 1471-2946 rotordynamics, resonance, bouncing, grazing, bifurcation 27 5 2020 2020-05-27 10.1098/rspa.2019.0549 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2020-11-06T14:34:15.0092074 2020-06-15T09:50:45.8249971 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Karin Mora 1 Alan R. Champneys 2 Alexander Shaw 0000-0002-7521-827X 3 Michael Friswell 4
title Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
spellingShingle Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
Alexander Shaw
Michael Friswell
title_short Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_full Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_fullStr Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_full_unstemmed Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_sort Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
author_id_str_mv 10cb5f545bc146fba9a542a1d85f2dea
5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Alexander Shaw
Michael Friswell
author2 Karin Mora
Alan R. Champneys
Alexander Shaw
Michael Friswell
format Journal article
container_title Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
container_volume 476
container_issue 2237
container_start_page 20190549
publishDate 2020
institution Swansea University
issn 1364-5021
1471-2946
doi_str_mv 10.1098/rspa.2019.0549
publisher The Royal Society
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
active_str 0
description 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.
published_date 2020-05-27T04:48:40Z
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score 11.444314

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