Wavelet Coefficient Characteristics During Rotor/Auxiliary Bearing Contact in Active Magnetic Bearing Systems

Auxiliary bearings are present in active magnetic bearing systems to prevent rotor/stator contact. If rotor/bearing contact occurs, significant impact forces may arise. Furthermore, linear control strategies may become ineffective due to the non-linear dynamics introduced by the auxiliary bearing. Rotor/auxiliary bearing contact is therefore an important consideration for the continued safe operation of an active magnetic bearing system. This work utilizes the localized nature of wavelets coefficients in characterising rotor/bearing contact responses. An experimental approach is adopted using a flexible rotor/active magnetic bearing test rig. Different disturbances resulting in periodic rotor contact and rotor/bearing rub were applied using a single active magnetic bearing. Rotor displacements were measured and the radial component and associated wavelet coefficients identified from off-line data processing. Variations of the wavelet coefficients characteristics corresponding to the periodic contact and rotor/bearing rub are assessed. The choice of mother wavelet is seen to have only a small effect on wavelet coefficient values. Wavelet analysis is shown as a feasible method for identifying time-frequency characteristics of rotor/bearing contact.

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On the Use of Actively Controlled Auxiliary Bearings in Magnetic Bearing Systems

Volume 5: Structures and Dynamics, Parts A and B ◽

10.1115/gt2008-50831 ◽

2008 ◽

Cited By ~ 2

Author(s):

Iain S. Cade ◽

M. Necip Sahinkaya ◽

Clifford R. Burrows ◽

Patrick S. Keogh

Keyword(s):

Controller Design ◽

Control Strategies ◽

Frictional Heating ◽

Magnetic Bearing ◽

Contact Forces ◽

Active Magnetic Bearing ◽

Physical Limit ◽

Drop Tests ◽

Auxiliary Bearing ◽

And Control

Auxiliary bearings are used to prevent rotor/stator contact in active magnetic bearing systems. They are sacrificial components providing a physical limit on the rotor displacement. During rotor/auxiliary bearing contact significant forces normal to the contact zone may occur. Furthermore, rotor slip and rub can lead to localized frictional heating. Linear control strategies may also become ineffective or induce instability due to changes in rotordynamic characteristics during contact periods. This work considers the concept of using actively controlled auxiliary bearings in magnetic bearing systems. Auxiliary bearing controller design is focused on attenuating bearing vibration resulting from contact and reducing the contact forces. Controller optimization is based on the H∞ norm with appropriate weighting functions applied to the error and control signals. The controller is assessed using a simulated rotor/magnetic bearing system. Comparison of the performance of an actively controlled auxiliary bearing is made with that of a resiliently mounted auxiliary bearing. Rotor drop tests, repeated contact tests, and sudden rotor unbalance resulting in trapped contact modes, are considered.

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Effects of some design parameters on bifurcation behavior of a magnetically supported coaxial rotor in auxiliary bearings

Engineering Computations ◽

10.1108/ec-04-2017-0141 ◽

2017 ◽

Vol 34 (7) ◽

pp. 2379-2395 ◽

Cited By ~ 2

Author(s):

Reza Ebrahimi ◽

Mostafa Ghayour ◽

Heshmatallah Mohammad Khanlo

Keyword(s):

Magnetic Bearing ◽

Active Magnetic Bearing ◽

Design Parameters ◽

Maximum Lyapunov Exponent ◽

Content Type ◽

Coaxial Rotor ◽

Rotor Bearing ◽

Auxiliary Bearing ◽

Bearing Stiffness ◽

Bifurcation Behavior

Purpose This paper aims to present bifurcation analysis of a magnetically supported coaxial rotor model in auxiliary bearings, which includes gyroscopic moments of disks and geometric coupling of the magnetic actuators. Design/methodology/approach Ten nonlinear equations of motion were solved using the Runge–Kutta method. The vibration responses were analyzed using dynamic trajectories, power spectra, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent. The analysis was carried out for different system parameters, namely, the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position. Findings It was shown that dynamics of the system could be significantly affected by varying these parameters, so that the system responses displayed a rich variety of nonlinear dynamical phenomena, including quasi-periodicity, chaos and jump. Next, some threshold values were provided with regard to the design of appropriate parameters for this system. Therefore, the proposed work can provide an effective means of gaining insights into the nonlinear dynamics of coaxial rotor–active magnetic bearing systems with auxiliary bearings in the future. Originality/value This paper considered the influences of the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position on the bifurcation behavior of a magnetically supported coaxial rotor system in auxiliary bearings.

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On the Use of Actively Controlled Auxiliary Bearings in Magnetic Bearing Systems

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2982159 ◽

2008 ◽

Vol 131 (2) ◽

Cited By ~ 5

Author(s):

Iain S. Cade ◽

M. Necip Sahinkaya ◽

Clifford R. Burrows ◽

Patrick S. Keogh

Keyword(s):

Controller Design ◽

Control Strategies ◽

Frictional Heating ◽

Magnetic Bearing ◽

Contact Forces ◽

Active Magnetic Bearing ◽

Physical Limit ◽

Drop Tests ◽

Auxiliary Bearing ◽

And Control

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Development and Experimental Validation of Auxiliary Rolling Bearing Models for Active Magnetic Bearings (AMBs) Applications

International Journal of Rotating Machinery ◽

10.1155/2019/4675286 ◽

2019 ◽

Vol 2019 ◽

pp. 1-19 ◽

Cited By ~ 2

Author(s):

Anna Tangredi ◽

Enrico Meli ◽

Andrea Rindi ◽

Alessandro Ridolfi ◽

Pierluca D’Adamio ◽

...

Keyword(s):

Load Capacity ◽

Critical Phenomenon ◽

Magnetic Bearing ◽

Design Tool ◽

Magnetic Bearings ◽

Active Magnetic Bearing ◽

Active Magnetic Bearings ◽

Short Period ◽

Auxiliary Bearing ◽

Bearing System

Nowadays, the search for increasing performances in turbomachinery applications has led to a growing utilization of active magnetic bearings (AMBs), which can bring a series of advantages thanks to their features: AMBs allow the machine components to reach higher peripheral speeds; in fact there are no wear and lubrication problems as the contact between bearing surfaces is absent. Furthermore, AMBs characteristic parameters can be controlled via software, optimizing machine dynamics performances. However, active magnetic bearings present some peculiarities, as they have lower load capacity than the most commonly used rolling and hydrodynamic bearings, and they need an energy source; for these reasons, in case of AMBs overload or breakdown, an auxiliary bearing system is required to support the rotor during such landing events. During the turbomachine design process, it is fundamental to appropriately choose the auxiliary bearing type and characteristics, because such components have to resist to the rotor impact; so, a supporting design tool based on accurate and efficient models of auxiliary bearings is very useful for the design integration of the Active Magnetic Bearing System into the machine. This paper presents an innovative model to accurately describe the mechanical behavior of a complete rotor-dynamic system composed of a rotor equipped with two auxiliary rolling bearings. The model, developed and experimentally validated in collaboration with Baker Hughes a GE company (providing the test case and the experimental data), is able to reproduce the key physical phenomena experimentally observed; in particular, the most critical phenomenon noted during repeated experimental combined landing tests is the rotor forward whirl, which occurs in case of high friction conditions and greatly influences the whole system behavior. In order to carefully study some special phenomena like rotor coast down on landing bearings (which requires long period of time to evolve and involves many bodies and degrees of freedom) or other particular events like impacts (which occur in a short period of time), a compromise between accuracy of the results and numerical efficiency has been pursued. Some of the elements of the proposed model have been previously introduced in literature; however the present work proposes some new features of interest. For example, the lateral and the axial models have been properly coupled in order to correctly reproduce the effects observed during the experimental tests and a very important system element, the landing bearing compliant suspension, has been properly modelled to more accurately describe its elastic and damping effects on the system. Furthermore, the model is also useful to characterize the frequencies related to the rotor forward whirl motion.

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Destabilization of Forward Rub in Rotor Magnetic Bearing Systems Using Actively Controlled Auxiliary Bearings

Volume 6: Structures and Dynamics, Parts A and B ◽

10.1115/gt2010-23028 ◽

2010 ◽

Author(s):

Iain S. Cade ◽

M. Necip Sahinkaya ◽

Clifford R. Burrows ◽

Patrick S. Keogh

Keyword(s):

Design Feature ◽

Magnetic Bearing ◽

Open Loop ◽

Active Magnetic Bearing ◽

Loop Control ◽

Bending Mode ◽

Operating Limits ◽

Auxiliary Bearing ◽

Contact Free ◽

Bearing System

During fault conditions, rotor displacements in magnetic bearing systems may potentially exceed safety/operating limits. Hence it is a common design feature to incorporate auxiliary bearings adjacent to the magnetic bearings for the prevention of rotor/stator contact. During fault conditions the rotor may come into contact with the auxiliary bearings, which may lead to continuous rub type orbit responses. In particular, forward rub responses may become persistent. This paper advances the methodology by considering an actively controlled auxiliary bearing system. An open-loop control strategy is adopted to provide auxiliary bearing displacements that destabilize established forward rub orbit responses. A theoretical approach is undertaken to identify auxiliary bearing motion limits at which forward rub responses become unstable. Experimental validation is then undertaken using a rotor/active magnetic bearing system with an actively controlled auxiliary bearing system under piezoelectric actuation. Two different operating speeds below the first bending mode of the rotor are considered and the applied harmonic displacements of the auxiliary bearing are shown to be effective in restoring contact free levitation.

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Dynamic Analysis for the Rotor Drop Process and Its Application to a Vertically Levitated Rotor/Active Magnetic Bearing System

Journal of Tribology ◽

10.1115/1.4035343 ◽

2017 ◽

Vol 139 (4) ◽

Cited By ~ 4

Author(s):

Yulan Zhao ◽

Guojun Yang ◽

Patrick Keogh ◽

Lei Zhao

Keyword(s):

High Speed ◽

Sliding Friction ◽

Engineering Application ◽

Magnetic Bearing ◽

Contact Forces ◽

Active Magnetic Bearing ◽

Detailed Model ◽

Vertical Rotor ◽

Auxiliary Bearing ◽

Rotor Dynamic

Active magnetic bearings (AMBs) have been utilized widely to support high-speed rotors. However, in the case of AMB failure, emergencies, or overload conditions, the auxiliary bearing is chosen as the backup protector to provide mechanical supports and displacement constraints for the rotor. With lack of support, the auxiliary bearing will catch the dropping rotor. Accordingly, high contact forces and corresponding thermal generation due to mechanical rub are applied on the dynamic contact area. Rapid deterioration may be brought about by excessive dynamic and thermal shocks. Therefore, the auxiliary bearing must be sufficiently robust to guarantee the safety of the AMB system. Many approaches have been put forward in the literature to estimate the rotor dynamic motion, nonetheless most of them focus on the horizontal rotor drop and few consider the inclination around the horizontal plane for the vertical rotor. The main purpose of this paper is to predict the rotor dynamic behavior accurately for the vertical rotor drop case. A detailed model for the vertical rotor drop process with consideration of the rotating inclination around x- and y-axes is proposed in this paper. Additionally, rolling and sliding friction are distinguished in the simulation scenario. This model has been applied to estimate the rotor drop process in a helium circulator system equipped with AMBs for the 10 MW high-temperature gas-cooled reactor (HTR-10). The HTR-10 has been designed and researched by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University. The auxiliary bearing is utilized to support the rotor in the helium circulator. The validity of this model is verified by the results obtained in this paper as well. This paper also provides suggestions for the further improvement of auxiliary bearing design and engineering application.

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Rotor vibration with auxiliary bearing contact in magnetic bearing systems Part 1: Synchronous dynamics

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440603321509676 ◽

2003 ◽

Vol 217 (4) ◽

pp. 377-392 ◽

Cited By ~ 40

Author(s):

P S Keogh ◽

M O T Cole

Keyword(s):

Position Control ◽

Magnetic Bearing ◽

Physical Interaction ◽

Flexible Rotor ◽

Rotor Vibration ◽

Full Control ◽

Flexible Rotors ◽

Bearing Contact ◽

Auxiliary Bearing ◽

Control Capability

Magnetic bearing systems incorporate auxiliary bearings to prevent physical interaction between rotor and stator laminations. Rotor/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. Non-linearities arising from contact and magnetic bearing forces are then included in simulation studies involving rigid and flexible rotors to predict rotor response and evaluate rotor synchronous vibration components. An experimental flexible 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 findings 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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Dynamic Analysis of Active Magnetic Bearing Rotor Dropping on Auto-eliminating Clearance Auxiliary Bearing Devices

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4029054 ◽

2015 ◽

Vol 137 (6) ◽

Cited By ~ 10

Author(s):

Chengtao Yu ◽

Chaowu Jin ◽

Xudong Yu ◽

Longxiang Xu

Keyword(s):

Dynamic Models ◽

Ball Bearing ◽

Experimental Studies ◽

Magnetic Bearing ◽

Active Magnetic Bearing ◽

Grease Lubrication ◽

Successful Operation ◽

Convex Shape ◽

Auxiliary Bearing ◽

The Impact

Auto-eliminating clearance auxiliary bearing devices (ACABD) can automatically eliminate the protective clearance between the ball bearing's outer race and the ACABD's supports, thus recenter the rotor when active magnetic bearing (AMB) system fails. This paper introduces the mechanical structure and working principles of the ACABD. When the rotor drops, numerical and experimental studies on the transient responses of the rotor and the ACABD's supports are also conducted as follows. First, we propose an equivalent clearance circle method to establish dynamic models of rotor dropping on the ACABD. Based on these models, the rotor dropping simulations are carried out to investigate the modes of lubrication and the ACABD's support shape's influences on the performance and execution time of clearance elimination. Second, various AMB rotor dropping tests are performed on our experimental setup with different ACABD supporting conditions. Indicated from the basically consistent simulation and experimental results, the correctness of the theoretical analysis and the successful operation of ACABD have been verified. Moreover, with the grease lubrication in the ball bearing and convex shape supports, the ACABD can eliminate the protective clearance within approximately 0.5 s upon the rotor drops and then sustain the rotor to operate stably around its original rotation center. Because of clearance elimination, the dramatic impact between the ball bearing and the supports is avoided and the impact forces among each part are effectively reduced. Meanwhile, the possibility of incurring full-clearance backward whirling motion is eliminated.

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Modelling, Analysis and Identification of the Parallel and Angular Misalignments in a Coupled Rotor-Bearing-AMB System

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4048352 ◽

2020 ◽

Author(s):

Siva Srinivas R ◽

Rajiv Tiwari ◽

Ch. Kanna Babu

Keyword(s):

Mathematical Model ◽

Vibration Suppression ◽

Magnetic Bearing ◽

Active Magnetic Bearing ◽

Identification Algorithm ◽

Rotor Systems ◽

Force Moment ◽

Coupling Force ◽

Auxiliary Bearing ◽

Amb System

Abstract The standard techniques used to detect the misalignment in rotor systems are loopy orbits, multiple harmonics with predominant 2X component, and high axial vibration. This paper develops a new approach for the identification of misalignment in coupled rotor systems modelled using 2-node Timoshenko beam finite elements. The coupling connecting the turbine and generator rotor systems is modelled by a stiffness matrix, which has both static and additive components. While the magnitude of static stiffness component is fixed during operation, the time varying additive stiffness component displays a multi-harmonic behaviour and exists only in the presence of misalignment. To numerically simulate the multi-harmonic nature coupling force/moment as observed in experiments, a pulse wave is used as the steering function in the mathematical model of the additive coupling stiffness (ACS). The representative TG system has two-rotor systems, each having two discs and supported on two flexible bearings - connected by coupling. An active magnetic bearing (AMB) is used as an auxiliary bearing on each rotor for the purposes of vibration suppression and fault identification. The formulation of mathematical model is followed by the development of an identification algorithm based on the model developed, which is an inverse problem. Least-squares linear regression technique is used to identify the unbalances, bearing dynamic parameters, AMB constants and importantly the coupling static and additive stiffness coefficients. The sensitivity of the identification algorithm to signal noise and bias errors in modelling parameters have been tested. The novelty of paper is the representation and identification of misalignment using the ACS matrix coefficients, which are direct indicators of both type and severity of the misalignment.

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On the Control of Synchronous Vibration in Rotor/Magnetic Bearing Systems Involving Auxiliary Bearing Contact

Volume 4: Turbo Expo 2002, Parts A and B ◽

10.1115/gt2002-30292 ◽

2002 ◽

Cited By ~ 3

Author(s):

Patrick Keogh ◽

Matthew Cole ◽

Necip Sahinkaya ◽

Clifford Burrows

Keyword(s):

Controller Design ◽

Magnetic Bearing ◽

Contact Forces ◽

Normal Operation ◽

Design Parameters ◽

Full Control ◽

Bearing Contact ◽

Vibratory Motion ◽

Auxiliary Bearing ◽

Bearing Design

During the normal operation of rotor/magnetic bearing systems, contacts with auxiliary bearings or bushes are avoided. However, auxiliary bearings are required under abnormal conditions and in malfunctions situations to prevent contact between the rotor and stator laminations. Studies in the open literature deal largely with rotor drop and the requirements of auxiliary bearing design parameters for safe run-down. Rotor drop occurs when the rotor is de-levitated and no further means of magnetic bearing control is available. This paper considers the case when full control is still available and rotor/auxiliary bearing contact has been induced by an abnormal operating condition or temporary fault. It is demonstrated that events leading to contact from a linearly stable rotor orbit can drive the rotor into a non-linear vibratory motion involving persistent contacts. Furthermore, the phase of the measured vibration response may be changed to such an extent that synchronous controllers designed to minimize rotor vibration amplitudes will worsen the rotor response, resulting in higher contact forces. A modified controller design is proposed and demonstrated to be capable of returning a rotor from a contacting to a non-contacting state.

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