Non-smooth Hopf-type bifurcations arising from impact-friction contact events in rotating machinery.
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.
Department of Mathematical Sciences , University of Bath , Claverton Down, Bath BA2 7AY, UK.
Karin
K
Mora
Department of Mathematical Sciences , University of Bath , Claverton Down, Bath BA2 7AY, UK.
Chris
C
Budd
Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) and School of Mathematics , University of Manchester , Manchester M13 9PL, UK.
Paul
P
Glendinning
Department of Mechanical Engineering , University of Bath , Claverton Down, Bath BA2 7AY, UK.
Patrick
P
Keogh
Hopf-type bifurcation; impact with friction; magnetic bearing systems; non-smooth bifurcation; rotor dynamics