M agnetic bearing systems incorporate auxiliary bearings to prevent physical interaction between rotor and stator laminations. R otor/auxiliary bearing contacts may occur when a magnetic bearing still retains a full control capability. To actively return the rotor to a non-contacting state it is essential to determine the manner in which contact events affect the rotor vibration signals used for position control. An analytical procedure is used to assess the nature of rotor contact modes under idealized contacts. N on-linearities arising from contact and magnetic bearing forces are then included in simulation studies involving rigid and exible rotors to predict rotor response and evaluate rotor synchronous vibration components. An experimental exible rotor/magnetic bearing facility is also used to validate the predictions. It is shown that changes in synchronous vibration amplitude and phase induced by contact events causes existing controllers to be ineffective in attenuating rotor displacements. These ndings are used in Part 2 of the paper as a foundation for the design of new controllers that are able to recover rotor position control under a range of contact cases.

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a b s t r a c tThis paper presents a novel topology for enhanced vibration sensing in which wireless MEMS accelerometers embedded within a hollow rotor measure vibration in a synchronously rotating frame of reference. Theoretical relations between rotor-embedded accelerometer signals and the vibration of the rotor in an inertial reference frame are derived. It is thereby shown that functionality as a virtual stator-mounted displacement transducer can be achieved through appropriate signal processing. Experimental tests on a prototype rotor confirm that both magnitude and phase information of synchronous vibration can be measured directly without additional stator-mounted key-phasor sensors. Displacement amplitudes calculated from accelerometer signals will become erroneous at low rotational speeds due to accelerometer zero-g offsets, hence a corrective procedure is introduced. Impact tests are also undertaken to examine the ability of the internal accelerometers to measure transient vibration. A further capability is demonstrated, whereby the accelerometer signals are used to measure rotational speed of the rotor by analysing the signal component due to gravity. The study highlights the extended functionality afforded by internal accelerometers and demonstrates the feasibility of internal sensor topologies, which can provide improved observability of rotor vibration at externally inaccessible rotor locations.

The dynamics of a multimode rotor-bearing system are analysed when the rotor contacts with a stator having annular clearance. By transforming to a rotating frame, all possible steady state rotor vibration modes that involve periodic contact with the surround may be predicted. Using a harmonic decomposition with generalized fundamental frequency, periodic solutions are obtained for rotor motions that involve asynchronous periodic contact. The analytical solutions are compared with previously published experimental results, which are predicted with considerable accuracy thus confirming the efficacy of the approach. Solutions are obtained for different test cases, which show how the amplitude and stability of the periodic contact modes are dependent on system parameters and operating conditions. In particular, for increased unbalance levels, the amplitude of the contact mode vibration is increased and the response of the rotor progresses from a bouncing forward whirl to a backward whirl-type motion. The nature of the identified rotor responses and implications for machine operation and reliability are discussed.

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.

The dynamic behavior of a rolling element bearing under auxiliary operation in rotor/magnetic bearing systems is analyzed. When contact with the rotor occurs, the inner race experiences high impact forces and rapid angular acceleration. A finite element model is used to account for flexibility of the inner race in series with non-linear ball stiffnesses arising from the ball-race contact zones. The dynamic conditions during rotor/inner race contact, including ball/race creep, are deduced from a non-linear matrix equation. The influences of bearing parameters are considered together with implications for energy dissipation in the bearing.

A number of conditions or events may produce rotor motion that involves contact with auxiliary bearings. Standard adaptive and closed-loop control strategies based on linear dynamics can cause instability when contact occurs, resulting in increased contact forces and vibration compared with the uncontrolled case. This paper introduces a method for robust control of synchronous vibration components that can maintain dynamic stability during interaction between the rotor and auxiliary bearings. The controllers are designed to minimize the severity and duration of contact and ensure that the rotor vibration returns to optimal levels, provided that sufficient control force capacity is available. Synthesis of controller gain matrices is based on a linear time-varying system model, which can be derived from either on-line identification routines or theoretical modelling and simulation. The controllers are tested experimentally on a flexible rotor system with magnetic bearings and are shown to restore rotor position control to optimal levels without further contact.

During operation, a rotor/magnetic bearing system may be subject to various sources of vibration, either directly applied to the rotor or transmitted through the bearings owing to base motion. This paper considers controller designs that are capable of attenuating vibration arising from either source. It advances the current state of research in the area since other controller designs have considered only the direct forcing case. If base motion is not considered in the design of the controller then this disturbance may cause the bearing clearance limits to be reached. Controller design is formulated as an H∞ optimization problem, with mixed design objectives. A new controller is derived that can simultaneously reduce vibration and minimize the effect of base motion on relative rotor to bearing displacement. Account is taken of the fact that the bearings can apply only limited control force. The design study was complemented by a programme of experimental work. The base of a rig was subjected to impulse inputs and the results show the effectiveness of the new controller design. It is demonstrated that proportional, integral and derivative (PID) controllers, or controllers designed for unbalance vibration attenuation only, may result in rotor contact with retainer bushes, while the new controller may prevent contact. The potential now exists for continuing safe operation of flexible rotor/magnetic bearing systems such as compressors, gas turbines, generators, etc., in transport applications, during seismic events or in environments with expected base input disturbances.