Model Of Magnetic Bearing Research Articles

Nonlinear vibration control of magnetic bearing system considering positive and negative stiffness

The nonlinear dynamics are studied for an active magnetic bearing (AMB) system under the low-frequency sinusoidal excitation, which can affect the operational stability of a high-speed magnetic bearing. A single-degree-of-freedom nonlinear dynamics model of magnetic bearing was developed with a c-type active magnetic bearing as the research target. The characteristics of the magnetic bearing system show positive and negative stiffness for different feedback gains. The amplitude–frequency response curves of the vibration characteristics of the positive stiffness magnetic bearing system were obtained by using the method of multiple scales. The influence of each parameter on the resonance amplitude and nonlinearity of the magnetic bearing system is understood by analyzing the amplitude–frequency response curve. The bifurcation diagram for the rotor with rotor mass, and control parameters is derived from the numerical simulation of the negative stiffness magnetic bearing system. The parameter intervals that cause single-cycle vibration, double-cycle vibration, and chaotic state of the magnetic bearing rotor are discovered by analyzing the bifurcation diagrams of each parameter. The simulation results show that the magnetic bearing system exhibits complex nonlinear dynamic characteristics when it is a negative stiffness system.

Modeling of a Digital Twin for Magnetic Bearings

As an essential enabling technology to realize advanced concepts such as digitization, intelligence, and service, information technology plays a critical role in shaping modern society and driving innovation across various industries and domains. The concept of the digital twin is attracting attention from academics and industry, and how to apply it in various fields. In this paper, the performance of the magnetic bearing system may be simulated in real-time using a digital twin, especially the resulting vibration from the unbalanced rotor mass, which caused a drop in performance and a high risk of system instability and potential safety accidents. It is suggested to use a model-data combination driven digital twin model to examine its dynamic characteristics and vibration mechanism. The vibration data of the magnetic bearing was collected through experiments and compared with the data derived from the simulation results. The efficiency of the suggested strategy is demonstrated by confirming that digitally anticipated vibration signals are consistent with physical space measurements. The result shows that the fine digital twin geometric model of magnetic bearing is more consistent with the actual operation. By allowing the identification of problems before they become critical, using a digital twin may increase the dependability of magnetic bearings while reducing the possibility of unexpected downtime or failures.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

Displacement Control and Simulation Based on A Hybrid Magnetic Bearing Model

The mechanical structure of a hybrid magnetic bearing contains both a permanent magnet and electromagnet, besides, its magnetic force form is relatively complex. The installation deviation of the sensor, processing quality, and other factors will make the actual working position of the magnetic bearing deviate from the rated balance position when it is stably suspended. This situation affects the working efficiency of magnetic bearings. This paper takes a magnetic levitation structure as the research object, and obtains the single-end magnetic force of the structure from electromagnetics-related knowledge. From the mechanical point of view, the detailed force formula of the system is obtained. The control system is designed by combining fuzzy control with PID control, and the performance of the two control methods is compared. In this paper, based on a hybrid magnetic bearing model, its mathematical model is obtained through electromagnetics and other related formulas, and PID and fuzzy PID algorithms are designed and simulated

Novel Magnetic Suspension Platform with Three Types of Magnetic Bearings for Mass Transfer

For ultra-precision, large stroke, and high start/stop acceleration, a novel magnetic suspension platform with three types of magnetic bearings is proposed. The structure and working principle of the novel platform are introduced. The passive magnetic bearings are used to compensate for the weight of the actuator. The repulsive force of the passive magnetic bearing model is established and analyzed. The Lorentz force-type magnetic bearings are used to provide driving force and rotational torque in the XY-plane. The driving force model and rotational torque model are established. The electromagnetic suspension bearing is used to provide driving force in the Z-axis and rotational torque along the X-axis and Y-axis. A novel Halbach magnetic array is designed to improve the magnetic flux density in the air gap. The finite element method is used to validate the force model, torque model, and magnetic flux density in the air gap. The results show that the maximum force of the passive magnetic bearing is 79 N, and the rotational torque stiffness is 35 N/A in the XY-plane and 78 N/A along the Z-axis. The driving force stiffness is 91 N/A in the XY-plane and 45 N/A along Z-axis.

Monitoring the Effect of Vibrations in Rotating Shafts and Controlling Using Active Magnetic Bearings (AMBS)

Vibrations in rotating shafts have been studied because of their great importance in engineering applications and ways to reduce these vibrations using modern techniques such as magnetic bearings and traditional bearings.A representative model of magnetic bearings was built using COMSOL program, and the effect of adding these bearings on amplitude, vibration reduction, and frequency behavior was calculated. When active magnetic bearings were added to the rotating systems, the level of vibrations was greatly reduced to about 60%, giving them a more stable and firm character. The changes that occur to the vibrations in the rotating shafts when changing the coil current and the distance of air gap in magnetic bearings, as well as the effect of a change in the amplitude of forces entering magnetic bearings on the value of the natural frequencies in magnetic bearings, were also monitored.Using SigView software, the Fast Fourier Transform (FFT) was employed to evaluate system vibrations and detect the frequency domain of the system supported by active magnetic bearings.

Analytical modeling and experimental validation of the six pole axial active magnetic bearing

The article presents a novel design of the axial active magnetic bearing with six poles. An analytical magnetic bearing model was developed to provide the axial magnetic induction distribution in 3D. The model utilizes magnetic vector potential formulation and Schwarz-Christoffel mapping. The paper covers in-depth deliberations on the end effect influence and the conjugate complex permeance function. Numerical model and simulations were provided in 3D mode with support of COMSOL Multiphysics software. The six pole axial active magnetic bearing was manufactured and investigated experimentally. Identification of the magnetic field distribution was carried out with a single axis magnetic induction sensor using custom automatic field scanner. High convergence of the modeling results and experimental research was demonstrated. The main advantage of the proposed analytical method is significantly shorter computation time compared to the numerical one that is useful from the modeling and controller study point of view. The configuration, modeling, simulation and experimental investigation results are well illustrated for the better overview.

Displacement Estimation of Self-Sensing Magnetic Bearings Based on Biorthogonal Spline Wavelet

By collecting the ripple current in the control coil, the self-sensing magnetic bearings can obtain rotor displacement information without a displacement sensor, which has the advantages of low cost and high integration. According to the problems of incomplete and inaccurate displacement information extraction caused by the traditional displacement estimation method using Fourier method to analyze the ripple current with non-stationary characteristics to estimate the rotor displacement with the Gibbs effect. Therefore, this paper proposes a rotor displacement estimation algorithm based on multiresolution filter bank biorthogonal spline wavelet for a magnetic bearing motor based on two-level switching power amplifier. This algorithm utilizes the biorthogonal spline wavelet with the characteristics of generalized linear phase and tight support, which can accurately demodulate the ripple current in the coil and extract the displacement information in the ripple current. Therefore, it is able to overcome the Gibbs effect in the traditional Fourier analysis estimation algorithm, to reduce the influence of ripple on rotor displacement estimation, and to improve the accuracy and stability of displacement estimation. In order to verify the correctness and effectiveness of the proposed algorithm, this paper establishes a simulation model of magnetic bearing in MATLAB Simulink and designs the proposed displacement estimator. Simulation results demonstrate that the proposed algorithm has higher accuracy and better stability than traditional displacement estimation algorithms. Experimental results show that the maximum deviation rate of the displacement estimation method proposed in this paper does not exceed 1% when the radial magnetic bearing gap is 0.5 mm, which can effectively estimate the rotor displacement.

Active Disturbance Rejection Decoupling Control for Three-Degree-of- Freedom Six-Pole Active Magnetic Bearing Based on BP Neural Network

In order to decouple the three-degree-of-freedom six-pole active magnetic bearing (3-DOF 6-pole AMB) with strong couplings, nonlinear and unstable disturbance, an active disturbance rejection control strategy based on BP neural network (ADRC-BP) is put forward. Firstly, the configuration, magnetic circuit, working principle and mathematical model of 3-DOF 6-pole AMB are introduced and established. Then, taking the 3-DOF 6-pole AMB as the controlled object, an ADRC-BP system is designed and a method of parameter tuning is proposed. Finally, the effectiveness of the control strategy is verified by simulation and experiments. The results show that the ADRC-BP has strong robustness and adaptability to the uncertainty of magnetic bearing model and the variation of external disturbance. The decoupling control effect of ADRC-BP is better than that of conventional ADRC.

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two‐degree‐of‐freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

Field\u2013circuit model of the radial active magnetic bearing system

Paper presents a mathematical model of the radial active magnetic bearing, which is indented for the simulation of the magnetic bearing dynamic response. The circuit model of the bearing is based on differential equations. The circuit model has incorporated results of magnetic field analysis, which led to the creation of the field–circuit model. Presented model of the magnetic bearing takes into account the necessary control system. The experimental results are presented to validate the proposed model.

Asynchronous input-output finite-time filtering for switched LPV systems

The input-output finite-time filtering problem is addressed for a class of switched linear parameter-varying systems in this paper. Firstly, by constructing a parameter-dependent Lyapunov function and resorting to the average dwell time approach, sufficient conditions ensuring finite-time boundedness and input-output finite-time stability are established for the augmented filtering error system. Then, a parameter-dependent asynchronous filter is designed such that the augmented filtering error system are both finite-time bounded and input-output finite-time stable. Finally, the active magnetic bearing model is introduced and verifies the main algorithms in this paper.

Control of Active Magnetic Bearings in Turbomolecular Pumps for Rotors with Low Resonance Frequencies of the Blade Wheel

Rotors with high gyroscopic effects and low resonance frequencies caused by the blade wheel (blade frequencies) can lead to stabilization problems in the application field of turbomolecular pumps. If such a rotor is stabilized by active magnetic bearings, the control structure could be destabilized by the splitting up of the rigid body eigen-frequencies caused by the gyroscopic effect. The control structure of the magnetic bearings can also destabilize the eigen-modes caused by the blade wheel, if the gain of the control structure is too high in the range of the eigen-frequencies of the blade wheel. To deal with the problem of the gyroscopic effect, a decoupling and compensation method was developed based on the inverse dynamics of the rigid body rotor. The gain of the control structure in the range of the blade frequencies is decreased using a Kalman filter. To increase the damping of the system, the predicted states of the linear magnetic bearing model using a Kalman filter are applied instead of the sampled values of the sensors directly. For the decoupled structure, PID controllers are used for stabilization. The functionality of the control structure is verified by a measurement of the current and position signal using the Kalman states and the sensor values. The robustness and performance in the frequency range are verified using the sensitivity and compliance function.

Design, Modeling and Control of Magnetic Bearings for a Ring-Type Flywheel Energy Storage System

This study is concerned with the magnetic force models of magnetic bearing in a flywheel energy storage system (FESS). The magnetic bearing is of hybrid type, with axial passive magnetic bearing (PMB) and radial hybrid magnetic bearing (HMB). For the PMB, a pair of ring-type Halbach arrays of permanent magnets are arranged vertically to support the rotor weight. For the HMB, a set of ring-type Halbach array is placed on the rotor side, which corresponds to coil sets on the stator side. The HMB can produce both attraction and repulsion forces on the radial direction, depending on the direction of the coil currents. It is found that the ring-type configuration and the differential winding scheme for coil sets can yield linear magnetic force models for both PMB and HMB. Based on the obtained magnetic force model, an integral sliding mode controller is designed for the stable rotor levitation in the radial direction. The experimental results show that the rotor can be stabilized to the bearing center, verifying the accuracy of the magnetic force models and effectiveness of the levitation controller.

Uncertainty and disturbance estimator-assisted control of a two-axis active magnetic bearing

In this paper, a robust nonlinear control strategy is developed for a class of second-order nonlinear uncertain systems with uncertainties and disturbances and is applied to two-axis active magnetic bearing position stabilization. The approach is based on a feedback linearization method, robustified by the uncertainty and disturbance estimator, which calculates and robustly cancels system uncertainties and disturbances via appropriate filtering. The controller uses the information regarding the known part of plant dynamics while the terms containing unknown dynamics are treated as additional system uncertainties and disturbances. The algorithm provides excellent performance in stabilizing the active magnetic bearing position and rejecting disturbances both at standstill and under movement. Simulations are given to show the effectiveness of the strategy via an application to an experimentally derived active magnetic bearing model.

Adaptive controller for stabilisation of rotational motion of a vertical shaft magnetic bearing

This paper proposes an adaptive controller to stabilise the rotational motion of a vertical shaft magnetic bearing. The gyroscopic coupling between the vertical and horizontal motion depends on rotational angular velocity and for variable speed applications, this velocity is considered an unknown parameter. Moreover, there are uncertainties in the mechanical and electrical parameters of the magnetic bearing model. This motivates the application of adaptive control to magnetic bearing system. The proposed adaptive controller is a model reference controller which uses the air gap measurement only as a feedback signal. The adaptive control system is proven to be globally asymptotically stable using Lyapunov direct method. Simulation results show the effectiveness of the proposed method.

Research on Inverse Control of Active Magnetic Bearing Based on Fuzzy Inverse Model

For magnetic bearing system with characteristics of zero damping, negative stiffness and nonlinearity, this paper put forward a method of inverse control based on the fuzzy inverse model. The fuzzy system with fuzzifier and defuzzifier was used as an interpolator to approximate the inverse model of magnetic bearing. Then we connected the fuzzy inverse model in series with the magnetic bearing system to form a generalized pseudo linear plant, and selected a PID controller to control the pseudo linear plant. The fuzzy inverse model and the PID controller together formed an inverse controller to implement the closed-loop inverse control of the system. The simulation results demonstrate that the inverse control can reduce the overshoot, shorten the settling time, and make the rotor levitate in a larger range.

Dynamical Electromechanical Model for Magnetic Bearings Subject to Eddy Currents

Eddy-current forces may play a significant role in magnetic bearings. They generate losses and unpredicted forces, which may lead to a malfunction of the bearing. But eddy currents in magnetic bearings may also be used positively, to generate desired forces, like in electrodynamic bearings. This paper presents a model able to predict, analyze, or simulate the dynamical behavior of any rotating magnetic bearing in which classical eddy-current forces arise. This model integrates the mechanical aspects linked to the rotor dynamics and the electrical aspects linked to the electromagnetic nature of the forces. This paper explains how the parameters of the model can be identified on the basis of quasi-static finite element method (FEM) or experiments. The validation of the model is done by comparison with FEM results on an electrodynamic radial bearing.

Unbalance Compensation Control in Active Magnetic Bearings Using Bias Current Excitation

The model of magnetic bearing and vibration producing mechanism were analyzed. A new adaptive law was developed to eliminate the rotor vibration. The adaptive control system for stabilization of the rotor geometric center to the origin was designed by varying magnetic stiffness through excitation of the bias currents. Finally, the simulation results validated the effectiveness of the proposed algorithm

Homopolar Magnetic Bearing Saturation Effects on Rotating Machinery Vibration

An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than their magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the - curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This paper addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of a permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with a flexible rotor is analyzed. Nonlinear effects due to power amplifier voltage and current saturation and position dependent reluctances are also included in the model. A new curve fit model of the - curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear. The modified Langmuir method, with a novel correction terms for the weak flux region, is used to form an analytical model of the experimental magnetization curve of Hiperco 50. High static and dynamic loads applied to the rotor force the magnetic bearing to operate in a flux saturated state. The response of the heavily loaded 4-DOF rotor-bearing system shows that limit cycle stability can be achieved due to the magnetic flux saturation or current saturation in the amplifier. The stable limit cycle prevents the linear model instability, creating what is experimentally observed as a “virtual catcher bearing.” To the authors' knowledge this is the first explanation of this commonly observed phenomenon.