Radial Hybrid Magnetic Bearing Research Articles

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

Design, optimization and test of RHMB considering dynamic characteristics

The coil inductance, stiffness and losses of the magnetic bearing (MB) have great influence on the dynamic performance for the magnetically suspended control moment gyro (MSCMG) application. Based on the equivalent magnetic circuits considering flux leakage effects, a design, optimization and test method is proposed to enhance the dynamic response ability for the radial hybrid MB (RHMB). The optimization design objectives including bearing force, stiffness, coil current, mass, inductance and loss estimation are discussed under the multiple constraints. Compared with the original design, the dynamic characteristics including frequency responses of current and rotor displacements for the RHMB-rotor system are significantly improved after optimization. A prototype of MSCMG is fabricated to verify the dynamic response characteristic of the RHMB.

Structure and Levitation Force Characteristics Analysis for Novel Radial Hybrid Magnetic Bearing

A new three-pole AC radial hybrid magnetic bearing (RHMB) is proposed. It has three characteristics of the levitation windings installed in the axial space, the permanent magnet mounted on the rotor and each stator core isolated by nonmagnetic materials. The structure and working principle are firstly introduced. Next, the force-current relationship is derived. According to the design requirement, the electromagnetic parameters are designed. Finally, the magnetic circuits, force-current curves and force coupling performance are calculated and analyzed. Furthermore, the maximum levitation forces are measured. The results show that the structure, magnetic circuit and working principle are correct, and the force-current relationship is further verified.

Structural optimization and dynamic characteristics of the new type 3-degrees of freedom axial and radial hybrid magnetic bearing

A new type of three degrees of freedom axial-radial hybrid magnetic bearing (3-DOF ARHMB) with compact structure, shorter axial length and smaller volume is proposed for the flywheel energy storage system. The axial direction adopts the permanent magnet biased thrust bearing (PMB) made of soft magnetic composite materials (SMCs). In the radial direction, the laminated structure is used to reduce the eddy current, and the Halbach array is introduced to strengthen the magnetic density of the radial air gap. Firstly, the dynamic magnetic flux distribution of the 3-DOF ARHMB is analyzed by the finite element method (FEM). Based on the equivalent magnetic circuit method, the equivalent reluctance model with comprehensive consideration of eddy current effect and magnetic leakage effect is established, and then the frequency responses are analyzed. Secondly, a constraint model coupled with structural parameters, equivalent reluctance and magnetic leakage coefficient is established, and an adaptive particle swarm optimization algorithm (APSO) is used to optimize the bearing parameters. Finally, based on the equivalent reluctance model, the axial and radial force-current factor and force-displacement factor are derived, and the dynamic characteristics of bearings with different structures and materials are compared and analyzed. The results show that the new 3-DOF ARHMB made of SMCs can provide much larger and more stable magnetic force and larger bandwidth than that made of carbon steel materials, and has better dynamic characteristics under higher-frequency conditions, which can meet the industrial requirements of flywheel energy storage system.

Design and Cosimulation of Twelve-Pole Heteropolar Radial Hybrid Magnetic Bearing

This paper presents a twelve-pole heteropolar radial hybrid magnetic bearing (HRHMB) structure. Firstly, the structure and equivalent magnetic circuit (EMC) are designed. And the radial electromagnetic force characteristics are calculated by the EMC model. At the same time, the rationality of EMC model is verified by the finite-element method (FEM) of Magnet software. Then, the 2-D model of the twelve-pole HRHMB is established in Magnet software. The flux density variations of twelve-pole HRHMB and eight-pole HRHMB under different currents are compared by using the FEM. Finally, a method of Magnet-Simulink cosimulation is proposed to analyze the suspension characteristics of the twelve-pole HRHMB and compared with the eight-pole HRHMB. Thus, the effective combination of theoretical analysis, FEM analysis, and Magnet-Simulink cosimulation analysis is realized in the design of HRHMB. The results of Magnet-Simulink cosimulation show that the twelve-pole HRHMB has the advantages of low power consumption, small coupling, large construction dynamic stiffness, and better suspension characteristics than the eight-pole HRHMB.

Suspension Force Analysis of Four-Pole Hybrid Magnetic Bearing With Large Radial Bearing Capacity

To make full use of the space and improve the radial bearing capacity, a new two-degree of freedom (DOF) four-pole radial hybrid magnetic bearing (RHMB) is researched in this article. This RHMB is characterized by that independent magnetic circuit is adopted, and the radial suspension winding is installed in the axial space. First, the structure and working principle are introduced. Second, the mathematical models are established and the main parameters of the prototype RHMB are designed. The 3-D finite-element analysis is carried out to analyze and calculate the magnetic circuit, suspension mechanism, and force–current relationship. Finally, the experimental system is built and the suspension force is tested. The research results have shown that the structure and magnetic circuit of the RHMB is reasonable and the mathematical model is correct.

Backstepping control of three‐pole radial hybrid magnetic bearing

To improve dynamic performance and robustness of a three-pole radial hybrid magnetic bearing (HMB), a backstepping controller is designed in this study. After introducing configuration of the three-pole radial HMB, the mathematical model is established by using the equivalent magnetic circuit method, and then the state equations are derived. Based on the state equations, the backstepping controller is designed by conducting backstepping algorithm and Lyapunov theorem which is adopted to confirm the stability of the system. Aiming at the difficulty of parameter adjustment, the adjustment factor is introduced through theoretical analysis. And the suitable value range of regulation factor is given by simulation. To identify the validity of the presented controller, the backstepping controller and the proportional–integral–derivative (PID) controller are compared by simulation and experiment. Simulation and experimental results have verified that the dynamic performance and the robustness of the backstepping controller are superior to the PID controller.

Rotor Displacement Self-Sensing Method for Six-Pole Radial Hybrid Magnetic Bearing Using Mixed-Kernel Fuzzy Support Vector Machine

In order to solve the problems of larger volume, higher cost and lower reliability caused by displacement sensors in a magnetic bearing system, a self-sensing method using mixed-kernel function fuzzy support vector machine (FSVM) displacement prediction model is proposed. Firstly, The structure and working principle of six-pole radial hybrid magnetic bearing (HMB) are introduced, and its suspension force mathematical model is deduced. Secondly, the FSVM displacement prediction model among control currents and rotor displacements is established, and the performance parameters of FSVM are optimized by genetic algorithm. Finally, a simulation test of the six-pole radial HMB system is constructed, the simulation results show that the performance of the prediction model using the mixed-kernel function FSVM is significantly better than that using other kernel functions, and the predicted values are about 93.35% and 95.5% of the actual values in the x- and y- direction. The anti-disturbance experiments are carried out and the feasibility of the method proposed is verified.

Rotor Displacement Self-Sensing Modeling of Six-Pole Radial Hybrid Magnetic Bearing Using Improved Particle Swarm Optimization Support Vector Machine

An inverter-fed six-pole radial hybrid magnetic bearing (HMB) has the characteristics of compact structure, high support speed, long service life, and so on. However, using displacement sensors to detect rotor displacements leads to the problems of large volume, high cost, and low reliability. In this article, a self-sensing method using improved particle swarm optimization (IPSO) least square support vector machine (LS-SVM) is proposed, which eliminates the influences of displacement sensors fundamentally. The structure and working principle of six-pole radial HMB are introduced, and the mathematical model of its radial suspension force is deduced according to the equivalent magnetic circuit method. Based on the regression principle of the LS-SVM, the prediction model between the currents in control coils and the rotor displacements is established. Also, the performance parameters of LS-SVM are optimized by the IPSO algorithm, which realizes self-sensing modeling of rotor displacement. The simulation system for self-sensing modeling of rotor displacement for six-pole radial HMB is constructed, and floating experiment, static suspension experiment, dynamic suspension experiment, and disturbance experiment of the rotor are carried out, which verify the robustness and stability of the self-sensing method proposed.

Principle and Performance Analysis for Heterpolar Permanent Magnet Biased Radial Hybrid Magnetic Bearing

In order to solve the nonlinear problem and strong coupling of three-pole magnetic bearings, a heterpolar permanent magnet biased radial structure is proposed. Firstly, the structure and working principle of the heterpolar permanent magnet biased radial hybrid magnetic bearing are introduced, and the mathematical models of suspension forces are established by the equivalent magnetic circuit method. Secondly, in the case of the same volume and the same ampere-turn, the force-current characteristics and maximum carrying capacity of the couple-piece type three-pole structure and the heterpolar permanent magnet biased radial structure are obtained through theoretical analysis and 3D finite element method (FEM) analysis, respectively, and the data obtained are analyzed and compared. Finally, the theory analysis and experiment results show that compared with the couple-piece type three-pole structure, the nonlinearity among the suspension forces and the control currents of the heterpolar permanent magnet biased radial structure is obviously reduced, and the maximum bearing capacity of the heterpolar permanent magnet biased radial structure is increased by 29.4%, which proves the rationality of the radial heterpolar permanent magnet biased radial structure and parameters.

Analysis of the cross-coupling effect and magnetic force nonlinearity in the 6-pole radial hybrid magnetic bearing

Analysis of the cross-coupling effect and magnetic force nonlinearity in the 6-pole radial hybrid magnetic bearing

Design Optimization of a Novel Heteropolar Radial Hybrid Magnetic Bearing Using Magnetic Circuit Model

In this paper, one novel heteropolar radial hybrid magnetic bearing (HRHMB) with low-power loss is proposed for flywheel energy storage system. First, its structure and equivalent magnetic circuit (EMC) are introduced in detail. Then, some main design parameters are analyzed based on EMC, including air-gap bias flux density, magnetic pole area, permanent magnet (PM) dimensions, and control current. Furthermore, to improve the performances of the novel HRHMB, the optimizations are implemented both on its structure and some key size parameters, such as the second air-gap length, PM height, and width. Finally, the optimal scheme is verified by the 3-D finite-element analysis, which indicates the maximum control current can be reduced to only 40% that of initial design by the optimizations.

Novel Heteropolar Radial Hybrid Magnetic Bearing With Low Rotor Core Loss

In this paper, one novel heteropolar radial hybrid magnetic bearing (HRHMB) is proposed for flywheel energy storage system. First, its structure and working principle are introduced in detail. Then, its fundamental equations are derived based on magnetic circuit model, such as displacement stiffness, current stiffness, and load capacity. Furthermore, its suspension performance and magnetic coupling are analyzed based on the 2-D finite-element analysis. Finally, the comparison of main performance indexes between the proposed HRHMB and conventional one under the same constraints is made. It indicates that the displacement stiffness can be reduced by the novel structure. In addition, the rotor core loss of the novel HRHMB is just 22.53 W, which is only 41.6% of the conventional eight-pole HRHMB with the same load capacity.

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.

A novel integrated 4-DOF radial hybrid magnetic bearing for MSCMG

This paper proposes a novel integrated radial hybrid magnetic bearing (RHMB) for application with the small-sized magnetically suspended control moment gyroscope (MSCMG), which can control four degrees of freedom (4-DOFs), including two radial translational DOFs and two radial tilting DOFs, and provide the axial passive resilience. The configuration and working principle of the RHMB are introduced. Mathematical models of radial force, axial resilience and moment are established by using equivalent magnetic circuit method (EMCM), from which the radial force–radial displacement, radial force–current relationships are derived, as well as axial resilience–axial displacement, moment–tilting angle and moment–current. Finite element method (FEM) is also applied to analyze the performance and characteristics of the RHMB. The analysis results are in good agreement with that calculated by the EMCM, which is helpful in designing, optimizing and controlling the RHMB. The comparisons between the performances of the integrated 4-DOF RHMB and the traditional 4-DOF RHMB are made. The contrast results indicate that the proposed integrated 4-DOF RHMB possesses better performance compared to the traditional structure, such as copper loss, current stiffness, and tilting current stiffness.

Modeling for Three-Pole Radial Hybrid Magnetic Bearing Considering Edge Effect

In order to overcome the shortcoming of magnetic bearings whereby general mathematical models of the radial suspension forces cannot be accurately established, a mathematical model considering the edge effect is set up. The configuration, operation principle and flux distribution features of a three-pole radial hybrid magnetic bearing (HMB) are analyzed in this paper. The magnetic field division method is employed to calculate the permeance of different regions around the end portion of poles. The total permeance of a single pole is composed of the permeance of the regions. Then, an accurate mathematical model of the radial suspension forces considering the edge effect is deduced by the equivalent magnetic circuit method. From the modeling procedures, it can be seen that the edge effect calculation is only related to the configuration and parameters of the magnetic poles, and is isolated with the other configurations and parameters of the three-pole radial HMB, therefore, the mathematical model is proved universal for calculating different suspension forces of hybrid magnetic bearings. A finite element analysis (FEA) simulation and three-pole radial HMB experiments are performed. The error between the theoretical calculation values and the FEA simulation values of the suspension forces is less than 5%, and the error between theoretical calculation value and experimental value of suspension forces is less than 7%. The comparison between the results of the theoretical calculation, FEA simulation and experiments has verified that the established mathematical model can accurately calculate the suspension forces.

Analysis and design of permanent magnet biased magnetic bearing based on hybrid factor

In this article, hybrid factor is proposed for hybrid magnetic bearing. The hybrid factor is defined as the ratio of the force produced by the permanent magnet and the forces produced by the permanent magnet and current in hybrid magnetic bearing. It is deduced from a certain radial hybrid magnetic bearing using its important parameters such as the current stiffness and displacement stiffness at first and then the dynamic model of magnetically suspended rotor system is established. The relationship between structural parameters and control system parameters is analyzed based on the hybrid factor. Some influencing factors of hybrid factor in hybrid magnetic bearing, such as the size of the permanent magnet, length of air gap, and area of the stator poles, are analyzed in this article. It can be concluded that larger hybrid factor can be caused by the smaller power loss according to the definition of hybrid factor mentioned above. Meanwhile, the hybrid factor has a maximum value, which is related to control system parameters such as proportional factor expect for structural parameters. Finally, the design steps of parameters of hybrid magnetic bearing can be concluded.

Stiffness measurement of radial hybrid magnetic bearing in MSFW

To measure the current stiffness and displacement stiffness of a radial hybrid magnetic bearing, a new stiffness measurement method is proposed for a magnetically suspended flywheel (MSFW). Firstly, the suspension force and stiffness characteristics of the radial hybrid magnetic bearing are studied using magnetic circuit method and finite element method. Secondly, a detailed stiffness measurement method for a radial hybrid magnetic bearing is proposed. It has two procedures: one is the determination of the relationship between the rotor displacement and the corresponding current when the gravity of the rotor is in the + X (or + Y) direction and − X (or − Y) direction respectively, and the other is the calculation of the current stiffness and the displacement stiffness of the radial hybrid magnetic bearing in an MSFW according to the relationship between the rotor displacement and the current. Three prototype MSFWs with angular moments of 15 Nms are manufactured, and they mainly consist of two axial hybrid magnetic bearings and one radial hybrid magnetic bearing. The proposed stiffness measurement method of the radial hybrid magnetic bearing is verified by all prototype experiments.

Dynamic circuit model of a radial magnetic bearing with permanent magnet bias and laminated cores

A hybrid radial magnetic bearing (HRMB) with permanent magnet creating bias flux is used to reduce the power consumption. Laminated cores are widely used in HRMB to reduce eddy currents. Nevertheless, when the frequencies of rotation and control currents are extremely high, eddy-current effects in laminated iron cores still have a significant influence on the behavior and performance of magnetic bearings. In order to predict performance and guide design of the HRMB system in high frequency, an analytical method based on equivalent circuit model whose parameters are frequency-dependent is used in this paper. The analytical results show that, the eddy currents induced due to rotor movement and dynamically changing control currents will result in considerable magnitude decrease and phase lag of bearing stiffness. Furthermore, the eddy current effect on HRMB can be reduced by increasing the air gap, decreasing the laminations thickness and decreasing the laminations conductivity. Finally, a prototype is designed and fabricated; the experimental results demonstrate the validity of the analysis.

Design and Optimization of a Radial Hybrid Magnetic Bearing With Separate Poles for Magnetically Suspended Inertially Stabilized Platform

To decrease the mass of the radial hybrid magnetic bearing (RHMB) when used in large journal diameter application, this paper researches the relationships of the structure parameters and presents an optimization method for an RHMB with separate poles. The designed RHMB is composed of four separate magnetic poles, with a secondary air gap constructed to help the control flux form its loop. Considering the effect of the secondary air gap to the value of both bias flux and control flux, the reluctance of the secondary air gap is optimized based on the magnetic circuit analysis, and the optimum value turns out to be determined by the reluctances of permanent magnet and the air gap only. The optimization of the whole RHMB is conducted with four constraints considered: the maximum force, copper loss, flux density of the air gap, and flux density of the secondary air gap. After a series of analyses, it is found that the copper loss of the RHMB depends mainly on the geometric size of the magnetic pole, and has no relationship with the number of coil turns or the current of the control coil. By the optimization method of sequential quadratic programming, the structure parameters have been obtained. Then the finite element method is adopted to simulate the distribution of the flux density, and the result is in accordance with that of the magnetic circuit analysis. The prototype is manufactured based on the optimal design, and the experiment carried out on the current stiffness and displacement stiffness verified the design result of the optimization.