Hybrid Magnetic Bearing Research Articles

A Novel Three-Degree-of-Freedom Hybrid Magnetic Bearing for Air Compressors

A Novel Three-Degree-of-Freedom Hybrid Magnetic Bearing for Air Compressors

Fuzzy gain scheduled adaptive sliding mode control of a vertical shaft hybrid magnetic bearing under variable rotor speeds

Fuzzy gain scheduled adaptive sliding mode control of a vertical shaft hybrid magnetic bearing under variable rotor speeds

Design and Analysis of an Axial Hybrid Magnetic Bearing With the Slice Stator for the Magnetically Suspended Centrifugal Compressor

Design and Analysis of an Axial Hybrid Magnetic Bearing With the Slice Stator for the Magnetically Suspended Centrifugal Compressor

Decoupling Control of Six-Pole Radial Hybrid Magnetic Bearing Based on Least Square Support Vector Machine Inverse System

Decoupling Control of Six-Pole Radial Hybrid Magnetic Bearing Based on Least Square Support Vector Machine Inverse System

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

AbstractA backstepping controller based on a non‐linear disturbance observer (NDOB) was created to enhance the dynamic performance and reliability of three‐degree‐of‐freedom hybrid magnetic bearings. After the structure of three‐degree‐of‐freedom hybrid magnetic bearings is introduced, the mathematical model is established, and the equation of the state is derived by the equivalent magnetic circuit technique. Based on the mathematical model, non‐linear disturbance observer (NDOB) is designed and is used to predict the system disturbance, and the backstepping control algorithm is compensated. To verify the effectiveness of the proposed controller, the backstepping controller, proportion integration differentiation controller, and backstepping controller based on a NDOB were compared by simulation and experiment. Results show that the backstepping controller based on a NDOB has better dynamic performance and robustness.

Decoupling Control of Six-Pole Hybrid Magnetic Bearing Based on LM Neural Network Inverse System Optimized by Improved Differential Evolution Algorithm

In order to solve the problems of strong coupling and nonlinearity of the hybrid magnetic bearings for flywheel energy storage, a novel decoupling control combining Levenberg Marquardt neural network inverse system (LMNNIS) with improved differential evolution (IDE) algorithm is proposed for the six-pole radial-axial hybrid magnetic bearing (HMB). Firstly, the structure and principle of the HMB are introduced, and the mathematical model of its radial-axial suspension forces is deduced. The IDE algorithm is used to optimize the initial model parameters of LMNNIS, and the displacement and current data are collected and normalized to input into LMNNIS for training, so as to realize the decoupling control between the suspension forces of the HMB. Then, the simulation system is constructed, and the simulation experiments of the rotor floating and anti-interference are carried out, which show the convergence speed and anti-interference performance of IDE algorithm optimized LMNNIS are better than the traditional neural network inverse system. Finally, the verification experiments are carried out on the basis of the experimental platform, which prove the feasibility and reliability of the proposed method.

Control Study for Compensating Rotor Vibration of Four-DOF Six-Pole Hybrid Magnetic Bearings Based on Variable Step Size LMS Algorithm

In order to solve the problem that the unbalance vibration caused by rotor mass eccentricity of the four-degree-of-freedom (four-DOF) six-pole hybrid magnetic bearings (HMBs), a feed-forward compensation control strategy based on variable step size least-mean-square (LMS) adaptive filter is proposed. First, the structure, operation principle and mathematical model of the four-DOF six-pole HMBs are introduced, the motion law of rotor vibration is analyzed, and the dynamic equation is derived. Second, the variable step size LMS adaptive filter is improved by using the Versoria function. The step size of LMS algorithm is adjusted adaptively by using Versoria function model and Takagi–Sugeno (TS) fuzzy inference machine. The LMS adaptive filter can generate a signal with the same frequency, amplitude, and phase as the rotating speed to offset the vibration signal, so as to realize the vibration compensation control of the four-DOF six-pole HMB rotor. Finally, the simulations and experiments not only prove the effectiveness of this method but also show that the method has good compensation accuracy. The result shows that the Versoria function used in variable step size LMS adaptive filter for vibration compensation is better than the traditional variable step size filtering algorithm based on Sigmoid function.

Electromagnetic Characteristics and Capacity Analysis of a Radial–Axial Hybrid Magnetic Bearing with Two Different Radial Stators

Compared with the widely used four-pole magnetic bearings, three-pole magnetic bearings are driven by a three-phase power inverter and have advantages pertaining to their small volume, low costs, and low power losses. However, the asymmetric structure of the three-pole bearings presents disadvantages in terms of their strong nonlinearity and couplings among the suspension forces of the control currents and displacements. The radial–axial hybrid magnetic bearing (RAHMB) with six-pole bearings is proposed to solve this problem. Firstly, the structure and working principle of the RAHMB are introduced. Secondly, the mathematical models of the RAHMB are established, and in order to obtain the radial capacity, the maximum suspension forces of the three-pole and six-pole RAHMBs are theoretically analyzed. Thirdly, the nonlinearity and couplings of the suspension forces with the control currents and displacements are analyzed. The radial capacity of the three-pole and six-pole RAHMB is 74.6 N and 83.6 N, respectively, which is an increase of 12.0%. Finally, the experiment results prove that the nonlinearity and couplings of the six-pole RAHMB are smaller than the nonlinearity and couplings of the three-pole RAHMB, and the maximum radial capacity of the three-pole and six-pole RAHMB is 84.1 N and 94.8 N, respectively, which is an increase of 12.7%. The simulation results are basically consistent with the experimental results, indicating the correctness of the theoretical analysis.

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

Modeling, Design and Suspension Force Analysis of a Novel AC Six-Pole Heteropolar Hybrid Magnetic Bearing

To improve the radial suspension force of heteropolar hybrid magnetic bearing (HMB), a novel AC six-pole heteropolar HMB is proposed. Firstly, the structure, magnetic circuit, and suspension force generation principle are introduced and analyzed. Secondly, the equivalent magnetic circuits are established. The mathematical models of magnetic resistances, air gap magnetic fluxes, and levitation force are derived by node magnetomotive force (MMF) method. The main parameters of prototype heteropolar HMB, such as outer and inner air-gap length, winding turns, and permanent magnets, are designed. Then, the analysis model is established by MagNet 3D. The magnetic circuit, air-gap flux density, suspension mechanism, force-current relationships, force-displacement relationships, and force coupling characteristics are analyzed and calculated. Finally, the experimental system was built to test the levitation force and levitation displacement waveforms. The research results have shown that the proposed novel six-pole heteropolar HMB has a reasonable structure and magnetic circuit. The design method is also proven to be correct. Furthermore, it is compared with the traditional heteropolar six-pole HMB, the maximum suspension forces in the X and Y directions are increased by 1.96 and 2.02 times, respectively.

Modeling and Multilevel Design Optimization of an AC–DC Three-Degree-of-Freedom Hybrid Magnetic Bearing

In this article, in order to improve the bearing capacity per unit area and reduce the nonlinearity and couplings of three-pole magnetic bearing, which is driven by a three-phase power inverter, a three-degree-of-freedom (3-DOF) six-pole hybrid magnetic bearing (HMB) is proposed. To realize the larger bearing capacity and smaller volume, a multilevel design optimization is proposed to conduct multiobjective optimization. At first, the structure and working principle of the ac–dc 3-DOF six-pole HMB are introduced. Then, the suspension force mathematical models of the 3-DOF HMB based on the Maxwell tensor method are established. Next, the design variables and optimization objectives are selected, and the comprehensive sensitivity analysis is adopted to divide the design variables into three levels; the response surface method and multiobjective particle swarm optimization algorithm are applied to realize a compromise among the three optimization objectives. Finally, the results of the simulation and experiment verify the validity and correctness of the modeling and optimization design.

Design and Optimization Method with Independent Radial and Axial Capacity for 3-DOF Magnetic Bearings in Flywheel

The six-pole radial–axial hybrid magnetic bearing (RAHMB) has the advantages of small space and low power consumption, making it suitable for flywheel batteries. The bearing capacity and the volume are the main specifications of magnetic bearings that should be considered comprehensively. In this work, the six-pole RAHMB was used in a horizontal flywheel battery. As the axial bearing capacity is relatively smaller than the radial bearing capacity, a design method with independent radial and axial bearing capacity is proposed, and the parameters are optimized to minimize the volume. The mathematical model of six-pole RAHMB was derived from the equivalent magnetic circuit method. The relationships between bearing capacity, biased flux density, saturation flux density and the section area of magnetic poles were analyzed. The basic principle of the design method with independent radial and axial bearing capacity is to determine which five of the variables are preferred. According to the design method, one radial or axial biased flux density should be optimized to minimize the volume, and the genetic algorithm (GA) was adopted to search for the optimal value. The structural parameters were designed based on the optimized value of biased flux density. The total volume of the six-pole RAHMB was reduced by 24%. A 3D finite element (FE) model was built. The analysis results and experimental results show that the proposed design and the optimization method are feasible and valid.

Modeling and Control Strategies of a Novel Axial Hybrid Magnetic Bearing for Flywheel Energy Storage System

This article presents modeling and control strategies of a novel axial hybrid magnetic bearing (AHMB) for household flywheel energy storage system (FESS). The AHMB combines a passive permanent magnet (PM) magnetic bearing (MB) and an axial active MB in one unit, thus can offer benefits such as compactness of the structure, high load capacity, and low power consumption. A coupled magnetic field-circuit method is proposed for modeling this bearing. Compared with the regular equivalent magnetic-circuit (EMC) method, it introduces special concerns of the complex air-gap field, calculated from the conformal transformation of the air-gap geometry, to take into account the effect of flux fringing and leakage. A low-cost Hall sensor is used to replace the expensive Eddy-current position sensor to measure the changes in air gap flux density caused by the rotor axial displacement. Therefore, a novel flux density feedback control is adopted instead of the traditional position feedback control to directly stabilize the magnetically suspended flywheel. A prototype of this bearing is designed and fabricated, which is tested in a small-scale FESS. The simulation results and the experimental results demonstrate that the proposed model provides better accuracy than the traditional EMC and the flux-density feedback control strategy based on a low-cost Hall sensor can achieve a consistent performance with the traditional position feedback control strategy.

Modeling and Design of a Novel 5-DOF AC–DC Hybrid Magnetic Bearing

This paper investigates a novel integrated AC–DC hybrid magnetic bearing (HMB) to reduce the volume, weight, manufacturing, and operation cost of magnetic suspension motors. Two radial MBs and an axial MB are integrated with the proposed HMB. The five-degree-of-freedom (5-DOF) suspension is realized in one unit. Two axially polarized permanent magnets provide the radial and axial bias fluxes. First, the HMB structure and the suspension mechanism are introduced. Second, based on the method of equivalent magnetic circuits, magnetic circuits are calculated. The mathematical models of suspension force are discussed. Third, the main parameters of the 5-DOF AC–DC HMB are given. The 3D finite element method (FEM) is adopted to analyze the proposed system’s electromagnetic characteristics, and the suspension mechanism of the 5-DOF is verified. The radial suspension forces versus the radial control current, the axial suspension forces versus the axial control current, the relationship between the axial suspension force and the axial control current with the X direction offset, and the relationship between the radial suspension force in the X direction and the axial control current with the Z direction offset are calculated. Based on the research results, it is shown that the HMB structure is compact and reasonable, and the mathematical models and suspension mechanism are correct.

Optimization for vibration analysis in rotating machines

A not stable mechanical movement transmission between systems produces equilibrium losses, such as a rotor of motors that are coupled in rotating machines. This can be studied as a disturbance “vibration” either as characteristic of the movement transmission due to controlled displacement over rotors, which transmits the movement. Therefore, in this research is presented an analysis for an optimal control of the rotor axis displacement that includes “vibration” as the part of the movement transmission. It implies mathematical modelling and specific sensors selections to correlate the vibration in this control task. Furthermore, in order to verify the proposed analysis, it was simulated and tested in a hybrid magnetic bearing system.

Multi-Objective Parameter Optimization-Based Design of Six-Pole Radial Hybrid Magnetic Bearing

To reduce the couplings between the radial suspension forces and control currents caused by the asymmetry structure of the three-pole hybrid magnetic bearing (HMB) which is driven by an inverter, a six-pole radial HMB is proposed. To improve the bearing capacity and reduce the eddy current loss and volume of the six-pole radial HMB, an improved multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters. At first, the structure and working principle of the six-pole radial HMB are introduced based on the equivalent magnetic circuit method. Then, the optimization objectives and optimization variables are determined and the number of multi-objective optimization parameters is reduced by sensitivity analysis. Next, the fitting function of the suspension force is obtained by the response surface method (RSM). Based on the theoretical analysis of the MOPSO, the linear decreasing inertia weight and the concept of hybridization are introduced to improve the diversity and convergence of the MOPSO to get Pareto optimal sets. Finally, simulation analysis and prototype experiment are carried out on the optimized six-pole radial HMB. The feasibility of the optimization method is verified by the results of simulation and experiment.

Multiobjective optimization of 3-DOF magnetic bearing considering eddy current effects and saturation

The multiobjective optimization method of three-degrees-of-freedom hybrid magnetic bearings (3-DOF HMBs) is crucial compared to time-consuming finite element calculation due to their three dimensional magnetic field. Solid rotors are the first choice for high-speed applications because the yield strength of laminated rotors is lower. However, solid materials may induce eddy current effects and saturation problems. In addition, a 3-DOF HMB has solid and laminated materials and permanent magnet materials, and the material price presents a risk for the structure. In view of the above mentioned problems, a dynamic magnetic circuit model of the 3-DOF HMB with eddy current and saturation effects is initial given. Subsequently, a multiobjective optimization design method for maximum axial and radial bearing capacity and the lowest cost is proposed. Finally, the optimized parameters are given, and a prototype is manufactured. The range of all optimal solutions considering saturation is less than that without saturation, and the maximum reduction is 99%. The experimental results demonstrate the effectiveness of the optimized design results.

Gimbal Angular Velocity Feedforward Method for Magnetically Suspended Control Moment Gyro with Hybrid Magnetic Bearing#

Control moment gyro(CMG) has the advantages of high precision and large output moment. It is the key actuator of agile spacecraft attitude control system. Magnetically suspended CMG(MSCMG) supports high-speed rotor through magnetic bearing, which has the advantages of no friction, no wear, high precision and long life. Hybrid magnetic bearing(HMB) generates bias magnetic field by replacing bias current with permanent magnet, which greatly reduces the power consumption. However, when MSCMG output moment, moving-gimbal effect makes the control current of HMB increase sharply, which result in the rapid increase of power consumption. To solve this problem, gimbal angular velocity feedforward(GAVF) method is proposed in this paper. Firstly, the model of HMB-rotor system containing moving-gimbal effect is established. Secondly, GAVF method is introduced to make the rotor deflect by designing a feedforward matrix with gimbal angular velocity and stiffness of HMB which is determined with rotor deflection angle and rotation speed. Thus, the gyroscopic moment is mainly offset by the bias magnetic field of HMB. Finally, an adaptive compensation method based on GAVF is proposed to maintain the system performance under parameter perturbation. By the above, the power consumption of control current during moment output process is reduced. Simulation and experiment results show the effectiveness of the proposed method.

Displacement Estimation of Six-Pole Hybrid Magnetic Bearing Using Modified Particle Swarm Optimization Support Vector Machine

In order to solve the problems of the large volume and high cost of a six-pole hybrid magnetic bearing (SHMB) with displacement sensors, a displacement estimation method using a modified particle swarm optimization (MPSO) least-squares support vector machine (LS-SVM) is proposed. Firstly, the inertial weight of the MPSO is changed to achieve faster iterations, and the prediction model of an LS-SVM-based MPSO is built. Secondly, the prediction model is simulated and verified according to the parameters optimized by the MPSO, and the predicted values of MPSO and PSO are compared. Finally, static and dynamic suspension experiments and a disturbance experiment are carried out, which verify the robustness and stability of the displacement estimation method.

Two Models for Time-Domain Simulation of Hybrid Magnetic Bearing's Characteristics.

A comparison of two developed simulation models for a hybrid magnetic bearing (HMB) transient states is presented. This applies to analyses using the flux-circuit directly coupled magnetic equivalent circuit and field-circuit indirectly coupled finite element analysis. The required control system was implemented for both models. The results obtained from the simulations were compared with those obtained from measurement tests.