Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

Karin Mora, Christopher Budd, Paul Glendinning, Patrick Keogh

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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.
Original languageEnglish
Pages (from-to)20140490
Number of pages23
JournalProceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
Issue number2171
Early online date17 Sept 2014
Publication statusPublished - 8 Nov 2014


  • non-smooth bifurcation,
  • rotordynamics
  • impact with friction,
  • magnetic bearing system
  • ,Hopf-type bifurcation


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