Numerical and experimental analysis of stable, unstable, and limit cycle spiral vibrations

In rotating machinery, non-uniform temperature distribution or hot spots on the rotor surface can induce spiral vibrations. In this paper, a novel experimental apparatus is used to analyze the influence of a hot spot on the dynamic behavior of a flexible rotor supported by oil journal bearings. The hot spot is generated using an induction system with controlled amplitude and phase shift with respect to the vibration vector. Hence, it was possible to mimic phenomena like the Morton effect or the Newkirk effect. Different types of spiral vibrations were experimentally reproduced: stable, unstable and limit cycle. In the latter case, the vibration vector describes a closed loop when plotted in a polar plot. Therefore, the present work isolates the phenomenon of spiral vibrations from the complexity of the physics behind the generation of hot spot whether this source is the viscous shearing, rotor rubbing, or eddy current losses in magnetic bearings. Moreover, a theoretical model is derived to gain insight on the mechanisms driving spiral vibrations especially the role that the phase shift between the hot spot and the vibration vector plays in the stability of the system. Theoretical and experimental stability maps obtained for sub-synchronous and super-synchronous angular speeds are in excellent agreement. Additionally, the notion of thermal period, i.e., the period that govern the oscillation of the vibration vector is introduced. A concept never addressed before. It was found that this thermal period depends not only on the thermal inertia of the rotor, but also on the amplitude and phase shift of the hot spot, the distance to the critical speed and the damping ratio.