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

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.

scholarly journals Dynamic Behavior Analysis of Touchdown Process in Active Magnetic Bearing System Based on a Machine Learning Method

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Zhe Sun ◽  
Xunshi Yan ◽  
Jingjing Zhao ◽  
Xiao Kang ◽  
Guojun Yang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Machine Learning Method ◽  
Learning Method ◽  
Auxiliary Bearing ◽  
Filtering Technique ◽  
Amb System

Magnetic bearings are widely applied in High Temperature Gas-cooled Reactor (HTGR) and auxiliary bearings are important backup and safety components in AMB systems. The performance of auxiliary bearings significantly affects the reliability, safety, and serviceability of the AMB system, the rotating equipment, and the whole reactor. Research on the dynamic behavior during the touchdown process is crucial for analyzing the severity of the touchdown. In this paper, a data-based dynamic analysis method of the touchdown process is proposed. The dynamic model of the touchdown process is firstly established. In this model, some specific mechanical parameters are regarded as functions of deformation of auxiliary bearing and velocity of rotor firstly; furthermore, a machine learning method is utilized to model these function relationships. Based on the dynamic model and the Kalman filtering technique, the proposed method can offer estimation of the rotor motion state from noisy observations. In addition, the estimation precision is significantly improved compared with the method without learning. The proposed method is validated by the experimental data from touchdown experiments.

Thermal Analysis and Simulation of Auxiliary Bearings and Its Application in the High Temperature Reactor-10

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Yulan Zhao ◽  
Guojun Yang ◽  
Zhengang Shi ◽  
Lei Zhao
Keyword(s):  
High Temperature ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Hertzian Contact ◽  
Thermal Growth ◽  
Study Results ◽  
New Energy ◽  
Huge Impact ◽  
Auxiliary Bearing ◽  
Amb System

The auxiliary bearing is applied to provide mechanical uphold for the rotational dropping rotor when contact event happens due to the active magnetic bearing (AMB) failure emergencies. During the rotor drop process, the auxiliary bearing will endure huge impact force and friction heat generation. The thermal behavior will affect the mechanical interaction and dynamic behavior of the auxiliary bearing and even induce rapid failure especially when excessive temperature growth occurs. The Institute of Nuclear and New Energy Technology (INET) of Tsinghua University in China has proposed the 10 MW high-temperature gas-cooled reactor (HTR-10). It is designed to guarantee the inherent safety and economic competitiveness. The dry-lubricated ceramic auxiliary bearing is utilized to protect the AMB and aims to ensure the safety of the AMB system in the HTR-10 in the case of the special operational requirements in the reactor. This paper simulates the process of the rotor drop on the auxiliary bearings in the AMB system of the helium blower of the HTR-10, including the analysis of thermal growth based on the Hertzian contact model and a one-dimensional (1D) thermal heat transfer network model. The study results demonstrate the validation of the bearing models and elucidate different responses between mechanical and ceramic auxiliary bearings during contact events. The research in this paper offers important theoretical bases for the auxiliary bearing design to guarantee the safety of the whole system.

Preliminary Research of Auxiliary Bearing in HTR-10GT Project

2008 ◽  
Author(s):  
Qingquan Qin ◽  
Guojun Yang ◽  
Zhengang Shi ◽  
Suyuan Yu
Keyword(s):  
Reference Value ◽  
Free Fall ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Main Function ◽  
Test Results ◽  
Test Rig ◽  
Advantages And Disadvantages ◽  
Auxiliary Bearing ◽  
Amb System

Active Magnetic Bearing (AMB) was used in the project of 10MW high temperature gas-cooled reactor (HTR-10GT) for the advantages over conventional mechanical bearings: without any mechanical friction and lubrication, etc. Auxiliary Bearings (ABs) is one of the most important parts in the AMB system, and its main function is to support the rotor at rest and provide protection for the rotor system during an overload or magnetic bearings failure situation. This paper introduced auxiliary bearings used in the HTR-10GT project and compared its advantages and disadvantages with other types of auxiliary bearings. The dynamic behaviors and temperature variation are the most important factors that may affect the performance of auxiliary bearings in a rotor drop event, this paper also analyzed the touching down course and dynamics in detail, divided the drop down process into four distinct stages of motion: free fall, impact, sliding-whirling and rolling. Finally, a test rig built up for the following rotor drop test is presented in the article. Test results at lower drop down speed were discussed. The result of the theory and experiment research has important reference value for the auxiliary bearings design of HTR-10GT.

Dynamic Behavior of the AMB’s Vertical Arranged Rotor During Its Drop Process

2014 ◽  
Author(s):  
Xiao Kang ◽  
Guojun Yang ◽  
Suyuan Yu
Keyword(s):  
High Temperature ◽  
Dynamic Behavior ◽  
Rotational Frequency ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Axial Stiffness ◽  
Experimental Conditions ◽  
Auxiliary Bearing ◽  
Amb System ◽  
Stiffness And Damping

The active magnetic bearing (AMB) system is a crucial part in the helium circulator system of the 10MW high temperature gas-cooled reactor (HTR-10). Though the AMB has been widely used in industrial fields, it is still limited in the research of the dynamic behavior of AMB’s vertical arranged rotor with axial magnetic load during its drop process. This paper establishes the dynamic model of such drop process by Matlab. Meanwhile using the Hertz contact theory establishes the contact model of different configurations. Analyze the axial friction between the rotor and thrust interface of the inner ring of Auxiliary Bearing System (ABS). Besides, the numerical model is verified by the drop experiment with the axial magnetic force. Moreover, this paper analyzes the influence of the rotor’s drop rotational frequency and the axial bracing features including stiffness and damping on the dynamic behavior during vertical arranged rotor’s drop process. Moreover, the paper provides the optimal axial stiffness and damping for the ABS satisfying the experimental conditions so as to reduce the contact force. Such results provide important references to the design of the ABS with a vertical arranged rotor and its application in HTR-10 and High Temperature Reactor-Pebblebed Modules (HTR-PM).

Identification of Speed-Dependent Active Magnetic Bearing Parameters and Rotor Balancing in High-Speed Rotor Systems

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Vikas Prasad ◽  
Rajiv Tiwari
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Element Model ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Flexible Rotor ◽  
Reduction Scheme ◽  
Rotor Systems

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

A Uniform Control Method for Imbalance Compensation and Automation Balancing in Active Magnetic Bearing-Rotor Systems

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Jiang Kejian ◽  
Zhu Changsheng ◽  
Tang Ming
Keyword(s):  
Delay Time ◽  
Control Algorithm ◽  
Control Method ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Identification Algorithm ◽  
Control Loop ◽  
Rotor Systems ◽  
Rotor Imbalance ◽  
Real Time Identification

The undesired synchronous vibration due to rotor mass imbalance is a main disturbance source in all rotating machinery including active magnetic bearing (AMB)-rotor systems. In the AMB-rotor system, imbalance compensation, which causes the AMB actuators to spin a rotor about its geometric axis, and automation balancing, which spins a rotor about its inertial axis, are two kinds of common control aim for the rotor imbalance control. In this study, the internal relation between the imbalance compensation and the automation balancing is analyzed and a uniform control method is proposed. With the identical control algorithm, the proposed control method can realize the automation balancing or the imbalance compensation, respectively, by switching the controller’s junction position in the original control loop. The proposed control method does not depend on the dynamic plant model, because its algorithm is based on the real-time identification for the Fourier coefficient of the rotor imbalance disturbance. In this paper, the process of identification algorithm is given in detail and all the possible junction forms of the controller are illustrated. By the simulations, the identification performances of the control algorithm are compared in the conditions with three variable factors, including the signal noise ratio (SNR), the imbalance phase and the identification delay time. The noise level has considerable influence on the identification precision, but the imbalance phase has little. To prolong the identification delay time will be of benefit to improve the identification precision but slow down the identification process. Experiments, which are carried out on an AMB-rigid rotor test rig, indicate that by switching the junction position of the controller in control loop, both kinds of rotor imbalance control can achieve the good effectiveness.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

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

2008 ◽  
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.

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

2017 ◽  
Vol 34 (7) ◽  
pp. 2379-2395 ◽  
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.

Dynamic Modeling and Analysis of Active Magnetic Bearings

2014 ◽  
Vol 494-495 ◽  
pp. 685-688
Author(s):  
Rong Gao ◽  
Gang Luo ◽  
Cong Xun Yan
Keyword(s):  
Dynamic Characteristic ◽  
Dynamic Modeling ◽  
Magnetic Bearing ◽  
Integrated System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Modeling And Analysis ◽  
Amb System ◽  
Mathematics Method

Active magnetic bearing (AMB) system is a complex integrated system including mechanics, electronic and magnetism. In order to research for the basic dynamic characteristic of rotor supported by AMB, it is necessary to present mathematics method. The dynamics formula of AMB is established using theory means of dynamics of rotator and mechanics of vibrations. At the same tine, the running stability of rotor is analyzed and the example is presented in detail.

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