Morton Effect Induced Synchronous Instability in Mid-Span Rotor–Bearing Systems—Part I: Mechanism Study

The Morton Effect in rotor-bearing systems may lead to an unstable operation. In Part I, the mechanism of the Morton Effect–induced thermal instability in the mid-span rotor systems is studied. First, the equivalent thermal induced imbalance is introduced and its magnitude and directions are assumed, to represent the viscous thermal effect on the rotor systems. Then, the simplified rotor and bearing models are adopted for the derivation of analytical expressions. The results show that there exists a threshold of instability due to the Morton Effect in the mid-span rotors. Based on the assumptions of linear isotopic bearing supports, this threshold speed takes a simple form, which is determined by the support stiffness and the introduced equivalent coefficient of thermal effect, for the rigid or elastic rotors, with the thermal imbalance acting in the same direction as the response displacement. The threshold of instability is also obtained for the system with the thermal imbalance acting perpendicular to the response displacement, where the supporting damping plays a role. For a perspective view of the system stability, a stability map for the damped rigid mid-span rotors with the thermal imbalance having arbitrary phase difference is generated. It shows that the stable operating regions of the system are bounded by two curves of threshold of instability, named the first and second threshold speeds of instability, respectively. The Morton Effect–induced instability thresholds are actually affected by both the magnitude and relative phase of the thermal imbalance. The mechanism of the Morton Effect–induced thermal instability of mid-span rotors supported by linear isotropic bearings can be explained through the fact that the Morton Effect introduces either negative stiffness or negative cross-coupled stiffness. In addition, the Morton Effect also has a comprehensive impact on both the amplitude and phase lag of the steady-state unbalance response. It may shift both curves in a manner dependent on the relative magnitude and direction of the thermal imbalance.