Asynchronous Partial Contact Motion due to Internal Resonance in Multiple Degree-of-Freedom Rotordynamics

AD Shaw (Swansea University), AR Champneys (University of Bristol) & MI Friswell (Swansea University)

Royal Society Proceedings Part A, Vol. 472, No. 2192, August 2016, paper 20160303

Abstract

Sudden onset of violent chattering or whirling rotor- stator 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 damping is 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.

Paper Availability

This material has been published in the Royal Society Proceedings Part A as open access under a Creative Commons Attribution License. The paper can be downloaded from the Royal Society website - link below.


Link to paper using doi: 10.1098/rspa.2016.0303

Link to paper on the Royal Society website

Royal Society Proceedings Part A