On stability of rotordynamic systems with rotor–stator contact interaction

Abstract

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.

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

“…The condition for backward whirl, which may involve severe contact forces, is understood as the condition in which the rotor is in rolling contact with the TDB [22]. A number of authors have considered the dynamics of a rotor within a clearance space [27][28][29][30][31][32][33][34][35][36][37][38][39]. With respect to operational magnetic bearing systems, which is in contrast to complete delevitation, it is important to gain a full understanding of all nonlinear dynamic issues so that appropriate control action may be designed to recover contact-free levitation.…”

An Active Vibration Control Strategy to Prevent Nonlinearly Coupled Rotor–Stator Whirl Responses in Multimode Rotor-Dynamic Systems

“…A linear model with the form (3) can be derived theoretically using finite element techniques, which are well-covered in the rotordynamics literature (see [18] or [19]). Note that (3) and (4) may also be appropriate for an actively controlled system if linear controller dynamics are incorporated in (3).…”

Bifurcation on synchronous full annular rub of rigid-rotor elastic-support system

“…The elastic rotor-to-stator model was also widely used in rotor-auxiliary bearing interaction system. Large numbers of researches were made by Xie et al [38] , Cole [39] , Keogh and Cole [40] , and Sahinkaya et al [41] in this field.…”