Nonlinear Dynamics of a Simplified Model of an Overhung Rotor Subjected to Intermittent Annular Rubs

The dynamic forced response of a two-degrees-of-freedom model of an unbalanced overhung rotor with clearance and symmetric piecewise-linear stiffness is examined in the time domain. The stiffness nonlinearity is representative of the contact between the rotor and a concentric stator ring. This rubbing interaction comes as a result of the rotor transient motion initiated by the sudden application of a static unbalance, such as in a blade loss scenario. The focus of this study is on the range of rotor speeds above resonance, where the contact between rotor and stator is characterized by a “bouncing” or intermittent type of behavior. Brute-force numerical bifurcation analysis on the long-term forced response revealed ranges of rotation frequency for which there is bistability between nonimpacting synchronous equilibrium and impacting subsynchronous motion. It is found that, for sufficiently high levels of transient energy in the rotor, there exists the possibility for the solution to jump into a stable limit cycle characterized by three nonharmonically related frequencies, namely, the synchronous response frequency and the forward and backward whirl frequencies. A simple relationship defining the point of synchronization between these three components is proposed as an explanation to the region of bistability detected. The stiffening effect induced by the contact nonlinearity enables this synchronization to be maintained over a range of forcing frequencies rather than just at the single condition determined from the nominal whirl mode frequencies.