Radial Magnetic Bearing Research Articles

Analytical method for levitation force calculation of radial HTS magnetic bearings

Introducing high-temperature superconductors (HTS) and their outstanding properties stimulates scientists and engineers in various fields to modernise the products with this new technology. Electric power industry also was affected by this finding in different branches including bearings. The idea of HTS bearings was rapidly developed due to its two main features, i.e. self-stability and contactless operation which leads to save remarkable amount of energy. However, a successful implementation of HTS bearing undoubtedly requires an accurate modelling in the beginning. The contribution of this study is an analytical method for simulating the electromagnetic behaviour of a radial HTS magnetic bearing. The governing non-linear system of partial differential equations in the HTS bulks deduced from the H-formulation along with the E–J power law and is efficiently solved using variational iteration method (VIM). The validity of VIM is ascertained by comparing the results with numerical two-dimensional axisymmetric finite-element method simulations.

A Generalized Unbiased Control Strategy for Radial Magnetic Bearings

The present work extends a method of unbiased control originally developed for three-pole radial magnetic bearings into a generalized unbiased control strategy that encompasses bearings with an arbitrary number of poles. By allowing the control of bearings with more than three poles, the applicability of the approach is broadened to the case of large rotors. Other ramifications of this generalized unbiased control strategy are fault tolerant unbiased bearings, control of bearings with more than three poles using 3-phase drives, and a novel approach to the unbiased control of eight-pole magnetic bearings.

Radial magnetic bearings: An overview

Radial magnetic bearings (RMBs) are one of the most commonly usedmagnetic bearings. They are used widely in the field ofultra-high speed and ultra-precise numerical control machine tools, bearingless motors, high speed flywheels, artificial heart pumps, and molecular pumps, and they are being strengthened and extended in various important areas. In this paper, a comprehensive overview is given of different bearing topologies of RMBs with different stator poles that differ in their construction, the driving mode of electromagnets, power consumption, cost, magnetic circuits, and symmetry. RMBs with different poles and couplings between the two bearing axes in the radial direction responsible for cross-coupling generation are compared. In addition, different shaped rotors are compared, as the performances of magnetic bearing-rotor systems are of great concern to rotor constructions. Furthermore, the parameter design methods, the mathematical models and control strategies of the RMBs are described in detail. From the comparison of topologies, models and control methods for RMBs, the advantages, disadvantages and utilizable perspectives are also analyzed. Moreover, several possible development trends of the RMBs are discussed.

Magnetic Suspension with Motorization to Measure the Speed of Gravity

This work aims to design a magnetic suspension for an experiment to measure gravitys velocity. Such device must rotate two objects symmetrically with the greatest mass and largest radius as possible, at the speed of [Formula: see text], which means this device falls into the high-speed machines category. The guidelines and solutions proposed in this paper constitute a contribution to this class of engineering problems and were based on an extensive literature search, contacts with experts, the tutors and author’s experience, as well as on experimental results. The main solution proposed is a hybrid bearing that combines a radial passive magnetic bearing with an axial sliding bearing, here called MPS (Magnetic Passive and Sliding) bearing.

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.

Analytical Model of Radial Permanent Magnet Biased Magnetic Bearing With Assist Poles

In this paper, an analytical model is established to predict the performance of a novel permanent magnet (PM) biased heteropolar radial magnetic bearing, which has some merits of volume and axial length. Due to the symmetrical structure, the periodic boundary condition is applied to the Laplace's equation. To simplify the computational process of the PM biased field, the region of air-gap is divided into pieces to acquire the similar boundary condition with the leakage area and the two magnetic fields are solved in the same way. Meanwhile, the effect of the slotting and the rotor eccentricity are taken into consideration and the linear mathematics model is built. Consequently, the analytical model is validated by two-dimensional finite-element analysis. The present work paves a fast way to precise prediction of the magnetic-bearing's performance.

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.

Novel Structure of Three-Axis Active-Control-Type Magnetic Bearing for Reducing Rotor Iron Loss

Magnetic bearings (MBs) are useful for suspending the rotor shaft of a high-speed, high-output motor because they can do so without mechanical contact. In [2] , we have proposed a three-axis active-control-type MB (3-axis AMB) with a cylindrical rotor whose diameter is equal to that of the rotor of a radial MB (RMB) or a motor. The proposed 3-axis AMB integrates an RMB and a thrust MB in one unit. However, the assembly of the conventional 3-axis AMB is complex, and the rotor iron loss is large. Thus, in order to simplify the assembly of the 3-axis AMB and to reduce rotor iron loss, this paper discusses a novel structure for the 3-axis AMB in which small auxiliary permanent magnets (PMs) are inserted in the radial winding slots. The suspension force and the rotor iron loss of the proposed device are evaluated by 3-D finite-element analysis in comparison with a 3-axis AMB without small auxiliary PMs.

Subdomain Method for Permanent Magnet Biased Homo-Polar Radial Magnetic Bearing

This paper presents an analytical model based on the subdomain method and conformal mapping method for predicting the performance of the permanent magnet (PM) biased homo-polar radial magnetic bearing (HRMB). Due to the homo-polar PM flux field of HRMB, the subdomain method combined with the periodic boundary condition is applied to obtain PM flux field distribution. The saddle winding is treated as a current sheet, while the rotor eccentricity is taken into account with a simple relative permeance model. The conformal mapping method is employed to obtain ending field distribution of HRMB. The developed analytical model is validated by 3-D finite element analysis. It is shown that the coupling effect between two radial freedoms is negligible. Ultimately, the parameters of HRMB are analytically optimized, while the predicted result from proposed analytical model is compared with prototype’s experiment results.

Reconfiguration rules for loosely-coupled redundant supporting structure in radial magnetic bearings

Targeting at the radial magnetic bearings of loosely-coupled redundant supporting structure, we classify the failure conditions of electromagnetic coil or power amplifier, and propose the reconfiguration rules for different failure conditions. Selection and configuration methods of redundant supporting structure are described towards the failure characteristics. With the restriction of minimum compensation current, the flux compensation strategy within one pole pair and the magnetic force compensation strategy between adjacent magnetic poles are combined to compensate the loss of electromagnetic force in different failure conditions, which realizes the reconfiguration of the residual supporting structures. The current distribution according to variable electromagnetic force output after the reconfiguration has been discussed under specific fault conditions and current safety factor of the coils. The influence of the current safety factor to the supporting ability of radial magnetic bearings has been analyzed. The application proves the effectiveness of the reconfiguration rules discussed.

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.

Optimization-based radial active magnetic bearing controller design and verification for flexible rotors

Engineering costs, especially cost for controller design, are substantial and obstruct active magnetic bearings for broader industrial applications. An optimization-based active magnetic bearing controller design method is developed to solve this problem. Optimization criteria are selected to describe active magnetic bearing practical performance. Controller components are chosen considering that the parameters can be manually interpreted and modified on-site for commissioning. A multi-objective optimization toolbox can be used to tune the controller parameters automatically by minimizing the optimization criteria. The method has been verified within a controller design process for an active magnetic bearing levitated machine. With this method, engineering effort for controller design can be reduced significantly.

Controllability of Radial Magnetic Bearing

The magnetic bearing works on the principle of magnetic levitation. Integration of the geometric and control designs is the current trend in mechatronic products. Conventionally, in control of rotors in the vertical direction, it must be supported at two places by radial magnetic bearings. A thrust magnetic bearing is also provided to prevent axial movement of the shaft. In the present work, control design methodology of four pole pair active magnetic bearings has been proposed. This work is dealing with the modeling, investigations and controlling of radial magnetic bearing system. Considerations based on the four pole pair's model with switched mode power supply. Investigations of radial forces in two axes model and performance response are carried out through the PID controller system. The response is presented for standstill and dynamic conditions using the implemented Simulink software. Simulation results showed that rotor is in standstill position with constant air gap of 1mm. This validates bearing design dimensions and system parameters designed for control of four pole pair radial magnetic bearing considering 1mm air gap length.

Linear and nonlinear control of a three pole combined radial and axial active magnetic bearing - a comparison

Linear and nonlinear control of a three pole combined radial and axial active magnetic bearing - a comparison

Design and Analysis of a Radial Active Magnetic Bearing for Vibration Control

Vibration caused by rotor unbalance is one of the most pertinent problems facing the rotating machines, including electrical motors and turbo machinery among others. Thus vibration attenuation has become very essential in improving the overall performance of such machines. In this paper, a 12-pole radial Active Magnetic Bearing (AMB), using AC excitation has been proposed to counteract the unbalance. Here a switching variation of AMB teeth excitation currents is implemented to generate a rotating force, synchronous with the rotor unbalance but in opposite direction.

К теории расчета радиального активного магнитного подшипника

К теории расчета радиального активного магнитного подшипника

The Identification of Multivariable Radial Magnetic Bearing System Based on RLS-DE Algorithm

The Identification of Multivariable Radial Magnetic Bearing System Based on RLS-DE Algorithm

200 마력급 터보 블로워 적용을 위한 자기베어링 설계

Recently, the development trend of turbomachinery is high capacity and high efficiency. Most of turbomachinery in the market are adopting ball bearings or air foil bearings. However, ball bearings have a limit for high speed product over 2.0×10SUP6/SUP DN(product of the inner diameter of the bearing in mm (D) and the maximum speed in rpm (N)). Air foil bearings have a limit for high axial load for high power products over 200~300 HP(horse power). Magnetic bearing is one of the solutions to overcome the limits of high speed and high axial load. Because magnetic bearings have no friction between the rotor and the bearings, they can reduce the load of the motor and make it possible to increase the rotating speed up to 5.0×10SUP6/SUP DN. Moreover, they can have high axial load capacity, because the axial load capacity of magnetic bearing depends on the capacity of the designed electromagnet. In this study, the radial and thrust magnetic bearings are designed to be applied to the 200 HP class turbo blower, and their performance was evaluated by the experiment. Based on the tests up to 26,400 rpm and 21,000 rpm under the no-load and load condition, respectively, it was verified that the magnetic bearings are stably support the rotor of the turbo blower.

Enhancing working performance of active magnetic bearings using improved fuzzy control and Kalman-LMS filter

This paper develops a novel control approach to enhance working performance of eight-pole radial active magnetic bearings (AMB). In the proposed method, the improved fuzzy proportional-integral-derivative (PID) control based on variable universes of proportional scaling is designed firstly to obtain better identification performance and flexibility of AMB control. Then, a Kalman filter is implemented to estimate the rotor displacement to reduce the noise disturbance and undesirable parameter adjustments caused by fuzzy control scheme. Finally, the least mean square (LMS) filter is connected with fuzzy control to compensate the unknown mass unbalance which might induce serious vibrations of AMB facilities. The simulation results show that the improved fuzzy PID control plays better performance than PID control in overshoot control, and the transient time of improved fuzzy PID is much shorter compared to conventional fuzzy PID. Meanwhile, the impacts of noise disturbance can be significantly limited by connecting with Kalman filter, and the maximum steady-state error can be decreased to about 85%. It is also shown that the LMS filter algorithm can effectively compensate the unknown mass unbalance in relatively short time without affecting the stability of AMB system.