Novel methods of chaos detection of active magnetic bearing (AMB) system by signal analysis

2013 ◽  
Author(s):  
Alireza Fakhrizadeh Esfahani ◽  
Rafal P. Jastrzebski ◽  
Tuomo Kauranne ◽  
Heikki Haario ◽  
Olli Pyrhonen
Keyword(s):  
Signal Analysis ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Chaos Detection ◽  
Novel Methods ◽  
Amb System

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.

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.

scholarly journals Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

2020 ◽  
Vol 2020 ◽  
pp. 1-29 ◽  
Author(s):  
W. Zhang ◽  
R. Q. Wu ◽  
B. Siriguleng
Keyword(s):  
Perturbation Method ◽  
Electromagnetic Force ◽  
Nonlinear Vibrations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation ◽  
Quadratic And Cubic Nonlinearities

The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

scholarly journals Nonlinear Control of an Active Magnetic Bearing System Achieved Using a Fuzzy Control with Radial Basis Function Neural Network

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Seng-Chi Chen ◽  
Van-Sum Nguyen ◽  
Dinh-Kha Le ◽  
Nguyen Thi Hoai Nam
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Fuzzy Logic Controller ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Highly Nonlinear ◽  
Radial Basis ◽  
Amb System

Studies on active magnetic bearing (AMB) systems are increasing in popularity and practical applications. Magnetic bearings cause less noise, friction, and vibration than the conventional mechanical bearings; however, the control of AMB systems requires further investigation. The magnetic force has a highly nonlinear relation to the control current and the air gap. This paper proposes an intelligent control method for positioning an AMB system that uses a neural fuzzy controller (NFC). The mathematical model of an AMB system comprises identification followed by collection of information from this system. A fuzzy logic controller (FLC), the parameters of which are adjusted using a radial basis function neural network (RBFNN), is applied to the unbalanced vibration in an AMB system. The AMB system exhibited a satisfactory control performance, with low overshoot, and produced improved transient and steady-state responses under various operating conditions. The NFC has been verified on a prototype AMB system. The proposed controller can be feasibly applied to AMB systems exposed to various external disturbances; demonstrating the effectiveness of the NFC with self-learning and self-improving capacities is proven.

scholarly journals Transient Response Technique Applied to Active Magnetic Bearing Machinery During Rotor Drop

1996 ◽  
Vol 118 (2) ◽  
pp. 154-163 ◽  
Author(s):  
T. Ishii ◽  
R. Gordon Kirk
Keyword(s):  
Transient Response ◽  
New Technology ◽  
Contact Point ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Theoretical Formulation ◽  
Rolling Element ◽  
Bearing Design ◽  
Amb System

The active magnetic bearing (AMB) is a relatively new technology which has many advantages compared with conventional bearing design. In an AMB system, the rolling-element back-up bearings are indispensable to protect the magnetic bearing rotor and stator, and other stationary seals along the rotor shaft. In this paper, a theoretical formulation is proposed and solved numerically to examine the transient response of the flexible rotor, from the time just previous to when the AMB shuts down and including the rotor drop onto the back-up bearing. The backward whirl of the rotor, which may lead to the destructive damage of the machinery, has been analytically predicted at very light support damping and very high support damping. Also, the vibration due to the nonlinearity of the contact point geometry has been included in the analysis. The influence of the support damping on the displacement of the disk and also the contact force between the journal and the inner-race of the back-up bearing have been computed for various rotor system parameters. By comparing these results with the optimum support damping for the simple flexible rotor model, it is shown that this support damping optimization can be applicable for specifying the required optimum range of support damping for the back-up bearings of AMB systems.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Dynamic responses of the rotor supported by a new type zero-clearance catcher bearing

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740014
Author(s):  
Yi-Li Zhu ◽  
Zhong-Qiao Zheng
Keyword(s):  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Dynamic Responses ◽  
Failure Event ◽  
Long Time ◽  
New Type ◽  
Amb System ◽  
Rotor Dynamic

Catcher bearings (CB) are required to support the rotor rotating for some time when a failure event of active magnetic bearing (AMB) system occurs. For this purpose, a new type zero-clearance catcher bearing (NTZCB) is proposed. The influences of different parameters of NTZCB on the rotor dynamic responses are theoretically and experimentally analyzed. The results indicate that choosing relatively soft spring and heavy moveable supporting pedestal can effectively buffer the rotor vibrations, which makes it possible for the rotor to keep rotating with the support of the CB system for a long time.

Dynamics of a Radial Active Magnetic Bearing System during Maneuvering Flight

2014 ◽  
Vol 536-537 ◽  
pp. 1321-1325
Author(s):  
Kai Zheng
Keyword(s):  
Research Result ◽  
Great Influence ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Regional Stability ◽  
Model Stability ◽  
Maneuvering Flight ◽  
Electric Aircraft ◽  
Amb System ◽  
More Electric Aircraft

Active magnetic bearing (AMB) is a prime component of the more electric aircraft technology that aims at reducing weight and emissions, and augmenting reliability and efficiency for future aircraft. The effect of maneuvering flight on performance of AMB system is investigated. A mathematical model considering maneuver equivalent force is presented and based on the model stability analysis is presented in terms of asymptotical and regional stability. The research result indicts that maneuvering flight has a great influence on system dynamics and stability.

Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations

2003 ◽  
Author(s):  
Wei Zhang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Steady State ◽  
Transient State ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Quasiperiodic Solutions ◽  
Local Bifurcations ◽  
Averaged Equations ◽  
Amb System

In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.

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.

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