TY - JOUR
T1 - Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery
AU - Mora, Karin
AU - Budd, Christopher
AU - Glendinning, Paul
AU - Keogh, Patrick
N1 - The research undertaken involved collaboration between the Departments of Mechanical Engineering and Mathematical Sciences (Bath) and the Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) and School of Mathematics (Manchester). The cross-disciplinary nature was necessary to reveal the complex dynamics associated with rotor-stator contact events in magnetic bearing systems. This forms a critical step in the ability to control the system dynamics.
PY - 2014/11/8
Y1 - 2014/11/8
N2 - We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact–friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewise-smooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action.
AB - We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact–friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewise-smooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action.
KW - non-smooth bifurcation,
KW - rotordynamics
KW - impact with friction,
KW - magnetic bearing system
KW - ,Hopf-type bifurcation
UR - http://rspa.royalsocietypublishing.org/content/royprsa/470/2171/20140490.full.pdf
UR - http://dx.doi.org/10.1098/rspa.2014.0490
U2 - 10.1098/rspa.2014.0490
DO - 10.1098/rspa.2014.0490
M3 - Article
SN - 1364-503X
VL - 470
SP - 20140490
JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
IS - 2171
ER -
