Abstract
We focus on the hysteretic characteristics of the varying compliance (VC) principal resonance in a ball bearing. The branches of the periodic VC response are traced by the harmonic balance method and the alternating frequency/time domain technique (HB-AFT) embedding Arc-length continuation, and the stability of these solutions is investigated by using Floquet theory. We find that the resonant response displays a swallow-tail structure due to the coupling nonlinearities between the Hertzian contact and the bearing clearance, which differs from the soft hysteresis of the non-loss Hertzian contact resonances. Furthermore, we find that period-1 VC branch cannot completely characterize the response of the system for a large bearing clearance, because multiple instability regions may occur from the cyclic fold, the secondary Hopf bifurcations, supercritical and subcritical period doubling bifurcations, in which case co-existences of period-1, period-2, and even quasi-periodic VC motions emerge in the hysteretic resonant range.
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