Passive Magnetic Bearings Research Articles

Magneto-aerostatic bearing for miniature air turbine

Under the circumstance of pursuing high speed and miniaturization, mini-type air turbines have been widely applied to high-speed dental handpieces in recent years. Among all the components of a mini-type air turbine, bearing is the most important part which significantly affects its efficiency. Friction, collision, and wear are the main causes to make the ball bearing unable to reach higher efficiency. Though very small sliding friction can be realized by the aerostatic bearing, its poor bearing capacity limits the application. This research combines the magnetic and aerostatic levitation principle to develop a magneto-aerostatic hybrid bearing for miniature air turbine. The aerostatic bearing undertakes the main function of the radial and the axial bearings. However, the air bearing also possesses a drawback, which is pneumatic hammer effect induced by the air compressibility. In order to eliminate the pneumatic instability, an axial passive magnetic bearing is integrated into the aerostatic bearing. With the magnetic bearing, not only the bearing capacity can be improved, but also the pneumatic hammer effect can be significantly damped. Both theoretical calculation and finite element method (FEM) are used to study the cause and elimination solution of the pneumatic instability. Through experimental testing, the performance of our developed magneto-aerostatic bearing is also verified. The magneto-aerostatic bearing suppresses the axial vibration over 57%, and also enhances its axial bearing capacity by 50%.

Development of Analytical Equations for Design and Optimization of Axially Polarized Radial Passive Magnetic Bearing

In the present research work, analytical equations have been developed for design and optimization of radial axial polarized passive magnetic bearing (PMB) with single layer for facilitating easy and quick solution, obviating the need of costly software. Seven design variables: eccentricity, rotor width, stator width, rotor length, stator length, clearance, and mean radius were identified as the main factors affecting the design and were thus considered in the development of analytical equations. The results obtained from the developed analytical equations have been validated with the published results. The optimization of the bearing design, with minimization of magnet volume as the objective function, was carried out to demonstrate the accuracy and usefulness of the developed equations.

Static mass imbalance identification and vibration control for rotor of magnetically suspended control moment gyro with active-passive magnetic bearings

Identification of the static mass imbalance is critical to the control of magnetically suspended rotors. A static mass imbalance identification method without using the closed-loop transfer function is proposed in this paper. Then the null displacement control of the magnetically suspended rotor is realized by using the identified static mass imbalance. Because null vibration is the control target for the rotor of a magnetically suspended control moment gyro (MSCMG) with active-passive magnetic bearings, a null vibration control method depending on the displacement stiffness is introduced. However, the displacement stiffness of the passive magnetic bearing is hard to obtain accurately. Therefore, the least mean square method is utilized to adjust the uncertain displacement stiffness adaptively according to the centroid acceleration. Simulation results show that adaptive null vibration control based on the static mass imbalance identification can remove the synchronous magnetic bearing force effectively, thus enabling the rotor of the MSCMG with active-passive magnetic bearings to rotate about its initial axis.

Design of a Brushless Permanent-Magnet Synchronous Drive With a Purely Passively Suspended Rotor

This paper deals with the design and optimization of a permanent-magnet synchronous machine as a means of propulsion for a passively levitated rotation system. The strict conditions in terms of axial and radial stiffness and the limited construction space particularly affect the design process. Three-dimensional finite-element simulations were performed to obtain the most efficient drive that fulfills the constraints. Additionally, a passive magnetic bearing was designed, which is capable of compensating for gravitational and load forces in the axial direction and of stabilizing the rotor in the radial direction. The optimization process and the constructed prototype system are described, and the work concludes with measurements validating the accuracy of the simulations.

Analytical Stiffness Calculation for Permanent Magnetic Bearings With Soft Magnetic Materials

According to Earnshaw's theorem, the ratio between axial and radial stiffness is always -2 for pure permanent magnetic configurations with rotational symmetry. Using highly permeable material increases the force and stiffness of permanent magnetic bearings. However, the stiffness in the unstable direction increases more than the stiffness in the stable direction. This paper presents an analytical approach to calculating the axial force and the axial and radial stiffnesses of attractive passive magnetic bearings (PMBs) with back iron. The investigations are based on the method of image charges and show in which magnet geometries lead to reasonable axial to radial stiffness ratios. Furthermore, the magnet dimensions achieving maximum force and stiffness per magnet volume are outlined. Finally, the calculation method was applied to the PMB of a magnetically levitated fan, and the analytical results were compared with a finite element analysis.

Electrical Design Considerations for a Bearingless Axial-Force/Torque Motor

A axial-force/torque motor (AFTM) establishes a completely new bearingless drive concept. The presented Lorentz-force-type actuator features a compact and integrated design using a very specific permanent-magnet excitation system and a concentric nonoverlapping air-gap stator winding. The end windings of the bent air-core coils, which are shaped in a circumferential rotor direction, provide active axial suspension forces. Thus, no additional (bearing) coils are needed for stable axial levitation. The four remaining degrees of freedom of the rotor are stabilized by passive magnetic ring bearings. This paper concentrates on the determination of the lumped parameters for the dynamic system modeling of the AFTM. After introducing a coordinate transformation for the decoupling of the control variables, the axial suspension force, and the drive torque, the relations for coil dimensioning are developed, followed by a discussion of the coil turn number selection process. Active levitation forces and drive torque specifications both must be concurrently fulfilled at a nominal rotor speed with only one common winding system, respecting several electrical, thermal, and mechanical boundaries likewise. Provided that the stator winding topology is designed properly, a simple closed-loop control strategy permits the autonomous manipulation of both control variables. A short presentation of the first experimental setup highlights the possible fields of application for the compact drive concept.

Research on Dynamic Characteristic of Rotor System for Small Maglev Wind Turbine Generator

Aiming at the small magnetic wind turbine, finite element software ANSYS is used to establish the model of rotor system with passive magnetic bearing, and obtain the vibration mode and critical speed of rotor system in situations: free-free, rigid bearing, hybrid combination of elastic and rigid bearing. Experimental analysis of critical speed of the rotor system can be conducted with the testing platform built by the B&K Vibration Measuring System.The result shows that the simulation analysis are approximately agreed with the experiment result. The simulation analysis has instructive significance in the structure optimization of magnetic bearing and rotor system and provides basis for vibration characteristic analysis of permanent maglev wind turbine generator and dynamic characteristics of structure.

Development of a high-speed motor at extremely low temperatures with an axial self-bearing motor and a superconducting magnetic bearing

Superconducting technology has been significantly improved since the superconductor Y-Ba-Cu-O was discovered. This technology has been applied to many medical image-processing applications such as magnetoencephalogram (MEG) and magnetic resonance imaging (MRI). Because the superconducting phenomenon occurs at extremely low temperatures, liquid helium or liquid hydrogen is essential to obtain a low-temperature environment. In addition, it is well known that the decom- pression of the liquid helium creates superfluid helium. This phenomenon improves the performance of the superconducting devices. For that reason, a vacuum pump, which can be used at a cryostat, is required. In this paper, we propose a motor that has a small size and simple structure for use in the cryostat. The proposed motor con- sists of an axial self-bearing motor, superconducting magnetic bearings, and permanent-magnet repulsive-type passive magnetic bearings. The design of the motor and control method is introduced. The experimental results show that the proposed motor has a high possibility for high-speed rotation at extremely low temperatures.

A 2-D-Based Analytical Method for Calculating Permanent Magnetic Ring Bearings With Arbitrary Magnetization and Its Application to Optimal Bearing Design

This paper investigates the optimal design of passive permanent magnetic bearings in terms of maximum stiffness per magnet volume ratio. Examining the influence of design parameters on maximum material utilization, we present general conclusions regarding cross section dimension, type of magnetization, and magnetic pole number. Furthermore, we provide generalized design plots for selected configurations, which can be used for rapid dimensioning of bearings with adequate raw material utilization. The analytical computation method used for all calculations is based on the interaction energy of elementary magnetic dipoles and thus supports any kind of magnetization, including when strength and direction may vary within the cross section of the magnetic rings. Although the design problem is 3-D and the analytical method 2-D, the resulting error is negligible for most of the practical applications.

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor.

Design and analysis of a non-hysteretic passive magnetic linear bearing for cryogenic environments

In this study, the mechanical design and analysis of a magnetic levitating linear bearing suitable for working in the non-hysteretic range of forces is presented. The semi-cylindrical design of the superconductor provides stable equilibrium positioning and restoring forces in all degrees of freedom except for two with a cylindrical magnet floating along the axis of revolution/displacement. Using finite element analysis, it has been proven that the magnet can float stably and passively in a complete non-hysteretic Meissner state. This non-hysteretic passive linear bearing could be suitable for long-stroke precision positioning. The high translational symmetry of the magnetic field seen by the superconductor assures a usable long stroke of around ±90 mm with full performance and ±150 mm with reduced performance. This linear bearing in combination with an actuating system for only one degree of freedom could be used for accurate precision positioning systems for cryogenic environments with zero hysteresis in the movement.

Stiffness and damping coefficients for rubber mounted hybrid bearing

ABSTRACTA non‐contact passive magnetic bearing has a low friction compared with other passive (journal or ball) bearings. But these bearings have negligible damping due to which even small rotor vibration impacts the bearing magnet. It results in breakage of brittle magnetic materials. To overcome this problem, a hybrid bearing (passive magnet + elastomer) has been proposed in the present manuscript. To select an appropriate rubber, a step‐by‐step approach, using pendulum and hysteresis tests, has been followed. A parametric study on thickness of selected rubber was carried out. Experiments were conducted on three configurations: (i) a stand‐alone magnetic bearing, (ii) magnetic bearing with a butyl rubber having a thickness of 1 mm, and (iii) magnetic bearing with a butyl rubber having a thickness of 1.5 mm. To investigate the effect of rubber Young's modulus on the damping, rubber was made softer by immersing in aromatic liquid, and the experiments were repeated using softer rubber. Copyright © 2014 John Wiley & Sons, Ltd.

Axial force calculation of passive magnetic bearing

Axial magnetic force calculation between two ring permanent magnets is presented in the paper. One magnet is magnetized in radial direction while the other one is magnetized in axial direction. Configuration like this one resembles the one passive magnetic bearing has. Force calculation is performed using semi analytical approach based on fictitious magnetization charges and discretization technique. For comparison purposes, and in order to check preciseness of the method applied, Finite Element Method (FEM) results were used.

Progress on electrodynamic passive magnetic bearings for rotor levitation

Electrodynamic suspension exploits repulsive forces due to eddy currents to produce positive stiffness by passive means, without violating the Earnshaw stability criterion. Systems employing this principle to levitate a rotor radial and/or axial degrees of freedom are called electrodynamic bearings (EDBs). Since the eddy currents can be induced either by using alternating current supplied electromagnets or by the relative motion between a conductor and a constant magnetic field, the research on EDBs has developed many different configurations. The present paper reviews the literature on electrodynamic passive magnetic bearings to analyze the evolution of this technology toward completely passive, stable, rotor levitation, and to compare the EDBs performance with other common magnetic bearing technologies. Radial and axial EDB technologies are reviewed attempting to create an organized connection between the works and to discuss some critical issues that still preclude the use of EDBs in industrial applications.

Stiffness Measurement Method of Repulsive Passive Magnetic Bearing in SGMSCMG

To measure the stiffness such as displacement stiffness and angular stiffness of repulsive passive magnetic bearing accurately, a new stiffness measurement method is proposed for the single gimbal magnetically suspended control moment gyroscope (SGMSCMG) with repulsive passive axial magnetic bearing with segmented Halbach magnetized array and active radial magnetic bearings. First, the suspension force and stiffness characteristics of the repulsive passive magnetic bearing are studied using finite element method (FEM). Second, the detailed stiffness measurement method of repulsive passive axial magnetic bearing is proposed. It includes four procedures such as measurement of the current stiffness of the active radial magnetic bearing, measurement of the displacement stiffness of the repulsive axial magnetic bearing, measurement of the displacement stiffness of the active radial magnetic bearing and measurement of the synthesis displacement stiffness and angular stiffness of SGMSCMG. A prototyped SGMSCMG with angular moments of 200 Nms is manufactured, which is of repulsive passive axial magnetic bearing with Halbach magnetized array and active radial magnetic bearings. The proposed stiffness measurement method of repulsive passive axial magnetic bearing with Halbach magnetized array is verified by prototyped experiments.

Reduced-Friction Passive Magnetic Bearing: Innovative Design and Novel Characterization Technique

Friction is mostly unwanted in rotating machines. In order to reduce its impact on the system, the integration of magnetic bearings is frequently regarded as a valid solution. In rotating systems like flywheel energy storage systems (FESS), mechanical losses created by mechanical bearings greatly reduce the overall performance. Magnetic bearings are thus frequently integrated in FESS to eliminate mechanical losses. The simple design of passive magnetic bearings (PMBs), their inherent security, and their very low friction make them perfect candidates for FESS. The main objective, and most important contribution of this paper, is to document an innovative PMB that minimizes energy losses induced by the axial thrust bearing, and to document the methodology used to measure its stiffness and damping. Although PMBs are fairly well documented in literature, no other PMB is designed to reduce the friction generated by the thrust bearing. In order to promote their integration, it is critical to identify their mechanical properties such as stiffness and damping. Hence, another contribution of this paper is to propose a new way to easily characterize any magnetic bearing topology to replace available techniques that only provided the properties for a precise configuration of the bearing. The new technique provides an unprecedented mapping of the forces generated by complex combinations of permanent magnets. Experimental results show that the new PMB can be configured to effectively reduce the force applied to the thrust bearing, resulting in lower friction. This friction reduction is achieved while allowing the proper operation of the bearing. Results also show that the measured stiffness is different from those obtained analytically, suggesting that a magnetic bearing should always be characterized prior to its use.

Modeling and Analysis of Coupling Performance Between Passive Magnetic Bearing and Hybrid Magnetic Radial Bearing for Magnetically Suspended Flywheel

In this paper, the design and development of a novel magnetic bearing (MB) system which consists of a passive magnetic bearing (PMB) with two pairs of passive permanent magnet rings and hybrid magnetic radial bearing (HMRB) used in magnetic bearing flywheel (MBFW) of control moment gyroscope (CMG) for agile satellite application are presented. The models of PMB and HMRB are proposed and their performances of force-current, force-position, and torque-angle are analyzed using the equivalent magnetic circuit method, finite element method (FEM), and equivalent magnetic charge method. The coupling forces between x and y position degrees of freedom (DOFs) of the HMRB, between the coil current in x-axis and y-axis, between the radial and the axial position DOF of the HMRB, and the coupling force and torque between the translating motion along the x (or y) axis and the rotary motion around x (or y) axis. These coupling problems of the novel MB system are proposed and clarified in this paper. An example is given to clarify the mathematical models and the coupling problems, and the linearized model is proposed for controller design of the MB system.

Dynamics and stability of rigid rotors levitated by passive cylinder-magnet bearings and driven/supported axially by pointwise contact clutch

A stable rotor—supported laterally by passive magnetic bearings and longitudinally by magnetic forces and a clutch—loses suddenly its contact to the clutch and executes abruptly longitudinal movements away from its original equilibrium position as a result of small increases in angular velocity. Such an abrupt unstable behaviour and its reasons are thoroughly theoretically as well as experimentally investigated in this work. In this context, this paper gives theoretical as well as experimental contributions to the problem of two dimensional passive magnetic levitation and one dimensional pointwise contact stability dictated by mechanical–magnetic interaction. Load capacity and stiffness of passive multicylinder magnetic bearings (MCMB) are thoroughly investigated using two theoretical approaches followed by experimental validation. The contact dynamics between the clutch and the rotor supported by MCMB using several configurations of magnet distribution are described based on an accurate nonlinear model able to reliably reproduce the rotor-bearing dynamic behaviour. Such investigations lead to: (a) clear physical explanation about the reasons for the rotor's unstable behaviour, losing its contact to the clutch and (b) an accurate prediction of the threshold of stability based on the nonlinear rotor-bearing model, i.e. maximum angular velocity before the rotor misses its contact to the clutch as a function of rotor, bearing and clutch design parameters.

Interaction magnetic force calculation of radial passive magnetic bearing using magnetization charges and discretization technique

Calculation of the interaction magnetic force between two ring permanent magnets with radial magnetization is presented in the paper. Such configuration corresponds to a radial passive magnetic bearing. The simple and fast analytical approach is used for this calculation based on magnetization charges and discretization technique. The results for interaction magnetic force obtained using proposed approach are compared with finite element method (FEM). The advantage of presented approach is its simplicity and time efficiency since only complete elliptic integrals of the second kind are used and other additional integrations are avoided in this calculation.

Theoretical modelling, analysis and validation of the shaft motion and dynamic forces during rotor–stator contact

This paper deals with the theoretical study of a horizontal shaft, partially levitated by a passive magnetic bearing, impacting its stator. Rigid body dynamics are utilised in order to describe the governing nonlinear equations of motion of the shaft interacting with a passive magnetic bearing and stator. Expressions for the restoring magnetic forces are derived using Biot Savart law for uniformed magnetised bar magnets and the contact forces are derived by use of a compliant contact force model. The theoretical mathematical model is verified with experimental results, and shows good agreements. However, the simulated contact forces are higher in magnitude compared to the experimental results. The cause of this disagreement is addressed and shows that the formulation of the theoretical contact force model slightly overestimates the forces acting during a full annular backward whirl motion.