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Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics

Alexander Shaw Orcid Logo, A. R. Champneys, Michael Friswell

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Volume: 472, Issue: 2192, Start page: 20160303

Swansea University Authors: Alexander Shaw Orcid Logo, Michael Friswell

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DOI (Published version): 10.1098/rspa.2016.0303

Abstract

Sudden onset of violent chattering or whirling rotorstator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial...

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Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
ISSN: 1364-5021 1471-2946
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa29380
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spelling 2020-07-17T15:47:14.4298201 v2 29380 2016-08-01 Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2016-08-01 AERO Sudden onset of violent chattering or whirling rotorstator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronisation condition previously reported for a single disc system. The synchronisation formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the dampingis sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further secondary bifurcations can also occur within each family, altering the nature of the response, and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice. Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 472 2192 20160303 1364-5021 1471-2946 rotordynamics, whirl, impact, nonlinear dynamics 31 8 2016 2016-08-31 10.1098/rspa.2016.0303 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University RCUK, EPSRC, EP/G036772/1 2020-07-17T15:47:14.4298201 2016-08-01T14:47:56.8784318 Alexander Shaw 0000-0002-7521-827X 1 A. R. Champneys 2 Michael Friswell 3 0029380-31082016114242.pdf asynchronousrotorcontactorbits.pdf 2016-08-31T11:42:42.4430000 Output 1845089 application/pdf Version of Record true 2016-08-31T00:00:00.0000000 Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited. true http://creativecommons.org/licenses/ by/4.0/
title Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
spellingShingle Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
Alexander Shaw
Michael Friswell
title_short Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
title_full Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
title_fullStr Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
title_full_unstemmed Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
title_sort Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics
author_id_str_mv 10cb5f545bc146fba9a542a1d85f2dea
5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Alexander Shaw
Michael Friswell
author2 Alexander Shaw
A. R. Champneys
Michael Friswell
format Journal article
container_title Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
container_volume 472
container_issue 2192
container_start_page 20160303
publishDate 2016
institution Swansea University
issn 1364-5021
1471-2946
doi_str_mv 10.1098/rspa.2016.0303
document_store_str 1
active_str 0
description Sudden onset of violent chattering or whirling rotorstator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronisation condition previously reported for a single disc system. The synchronisation formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the dampingis sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further secondary bifurcations can also occur within each family, altering the nature of the response, and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice.
published_date 2016-08-31T03:40:54Z
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