No Cover Image

Journal article 67 views

Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis / Karin Mora; Alan R. Champneys; Alexander Shaw; 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

Full text not available from this repository: check for access using links below.

Check full text

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...

Full description

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1364-5021 1471-2946
Published: The Royal Society 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa54468
Tags: Add Tag
No Tags, Be the first to tag this record!
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.
Keywords: rotordynamics, resonance, bouncing, grazing, bifurcation
College: College of Engineering
Issue: 2237
Start Page: 20190549