On stability of rotordynamic systems with rotor–stator contact interaction

In machine systems where a rotor spins within a finite clearance space supported by bearings, contact between the rotor and its surround can result in persistent coupled vibration of the rotor and stator. When the vibration response is driven predominantly by friction forces, rotordynamic stability becomes a serious issue. This paper introduces a theory for model-based verification of dynamic stability in rotor systems with stator contact and rub. Generalized multi-degree-of-freedom linear models of rotor and stator lateral vibration are considered, combined with contact models that account for finite clearance and Coulomb friction. State-space conditions for global stability as well as stability of contact-free synchronous whirl responses are derived using Lyapunov’s direct method. This leads to feasibility problems involving matrix inequalities that can be quickly verified using numerical routines for convex optimization. Parametric studies involving flexible rotor models indicate that tight bounds on regions of stability can be obtained. A case study involving a realistic machine model illustrates how design optimization based on the theory might be used to overcome instability problems in real machines.