A 3-D Magnetic Charge Finite-Element Model of an Electrodynamic Wheel

When a magnetic rotor is both rotated and translationally moved above a conductive, nonmagnetic, guideway eddy currents are induced that can simultaneously create lift, thrust, and lateral forces. In order to model these forces, a 3D finite-element model with a magnetic charge boundary has been created. The modeling of the rotational motion of magnets by using a fictitious complex magnetic charge boundary enables fast and accurate steady-state techniques to be used. The conductive regions have been modeled using the magnetic vector potential and nonconducting with the magnetic scalar potential. The steady-state model has been validated by comparing it with a Magsoft Flux 3D transient model (without translational velocity) and with experimental results. The 3D model is also compared with a previously presented 2D steady-state complex current sheet model.     

Modeling the 3-D Rotational and Translational Motion of a Halbach Rotor Above a Split-Sheet Guideway

When a Halbach rotor is simultaneously rotated and translationally moved above a split-sheet aluminum guideway a traveling time-varying magnetic field is created in the air gap. This field induces eddy currents in the guideway that can simultaneously create suspension and propulsion forces. If the rotor is offset from the center then a re-centering guidance force can also be created. As the forces are created in a highly inductive way the use of magnets circumvents any low power factor issues and enables a relatively high lift-to-weight ratio to be attained in comparison to using windings. The conductive and nonconductive regions are modeled by using a steady-state convective A- $phi$ formulation. The Halbach rotor is modeled using a 3-D analytic based model and is coupled to the conductive guideway region using boundary conditions. The steady-state rotation of the Halbach rotor is modeled by incorporating complex terms in the analytic model. The accuracy of the steady-state model is confirmed by comparing it with a 3-D transient finite-element Magsoft Flux model (with no translation) and with experimental results (with both rotation and translation). The effect of the rotor width on performance is also investigated.      

Magnetically induced vibration in a permanent-magnet brushless DC motor with symmetric pole-slot configuration

The paper reports a numerical and experimental study of magnetically induced vibration associated with rotor/stator eccentricity and imperfect magnetization for 8-pole 6-slot symmetric brushless dc (BLDC) motors. Magnetic forces and cogging torque are calculated for various slot angles by using the finite-element method (FEM). The results show that there is an optimal slot angle for minimum cogging torque, but this slot angle is not optimal for reducing magnetic forces. In the idle acoustics test, the motors with reduced magnetic forces show clear reduction at the expected frequencies while the motors with minimum cogging torque show no change at the cogging torque frequency, which implies unbalanced magnetic forces have greater effect on actual vibration of the spindle motor than cogging torque. The results show that the proper direction in motor design is to reduce unbalanced magnetic forces when both cogging torque and unbalanced magnetic forces are not achievable simultaneously.     

Force characteristics and gain determination for a slotless self-bearing motor

In this paper, we use the Maxwell stress tensor method to derive the analytical force and torque expressions for a large-scale slotless permanent-magnet (PM) self-bearing motor actuator that uses common coils to produce both the torque and radial forces, in order to include all the possible interactions among the PMs, currents, and stator/rotor back iron. We solve the radial and angular components of the two-dimensional instantaneous magnetic field distribution in the low-permeability region induced from the rotor PMs and stator windings separately, using the unwrapped geometry, and then superimpose them. Instead of being incorporated into the boundary conditions, the general winding current and PM magnetization distributions are expanded into the Fourier series in the separate source layers, with respect to one motor revolution and one PM pole pair, respectively. For each source, we first solve one homogenous Laplace's equation in the planar layer without source and one nonhomogenous Laplace's equation in the planar layer with source simultaneously in Cartesian coordinates for a centered rotor and then add the rotor eccentricity. We compare the analytical solutions for the individual magnetic field distributions, as well as the total force and torque production, to those from the finite-element analysis (FEA), and find excellent agreement between the two. We characterize the open loop current and negative stiffness gains of the SBM from the linearized force-current-displacement relationship, which forms the basis for the linear system modeling and controller design, and validate our results by comparison with the FEA results.     

Dynamical Electromechanical Model for Magnetic Bearings

Magnetic bearings are electromechanical systems. From a mechanical point of view, their modeling is plainly related to general rotor dynamics modeling. But the forces acting between the rotor and the stator are of an electromagnetic nature. This paper presents the analysis of the potentially unstable dynamical behavior of magnetic bearings. It adopts an electromechanical point of view and represents the forces acting on the system by dampers, springs, and an electrical phase shift. The coefficients of the model are found by parameter identification with a finite-element model of the system.     

Numerically efficient steady-state finite-element analysis of magnetically saturated electromechanical devices

We present a numerically efficient steady-state finite-element solver for electromechanical devices incorporating magnetic saturation in which the magnetization of ferromagnetic materials is modeled as a field-dependent equivalent current density. We use a Lagrangian representation of continuum variables, thereby removing numerical instabilities due to the Peclet effect but precluding the use of standard harmonic balance methods. The shooting-Newton method is therefore used to calculate the steady-state behavior. A matrix-free Krylov-subspace linear solver, the generalized minimum residuals method (GMRES), dramatically reduces the computational burden by eliminating the need to calculate the shooting-Newton Jacobian. Simulation results from a synchronous reluctance motor model with 10 288 nodes and 4935 elements confirm that the proposed method requires much less computation time than running transient analysis until convergence.     

Influence on the stability of generator rotors due to radial and tangential magnetic pull force

Forces due to nonuniform airgaps in rotating electrical machines have been a research topic for over 100 years. However, most research in the area of rotating electrical machines has been performed on motors. Large forces in hydropower generators can lead to expensive damage and failures. Therefore, it is of interest to calculate the forces that arise in a large synchronous generator with an eccentric rotor and study the influence these forces have on the stability of the generator rotor. A 74 MVA synchronous hydropower generator was simulated with an eccentric rotor, using a time-stepping finite-element technique. The forces were calculated using Coulomb's virtual-work method and simulations were performed for no-load and load cases. The resulting force was found to be reduced significantly when a damper winding was taken into account. An interesting effect of the rotor damper winding was that it reduced the eccentricity force and introduced a force component perpendicular to the direction of eccentricity. The results from the finite-element simulations were used to determine how the forces affect the stability of the generator rotor. Damped natural eigenfrequencies and damping ratio for load and no-load conditions are presented. When applying the forces computed in the time-dependent model, the damped natural eigenfrequencies were found to increase and the stability of the generator rotor was found to be reduced compared with when the forces were computed in a stationary model.     

Bridge configured winding for polyphase self-bearing machines

The self-bearing or bearingless machine is an electromagnetic device that supports its own rotor by way of magnetic forces generated by windings on its stator. Various winding configurations have been used to accomplish the task of force production. This paper proposes a winding based on a bridge connection for polyphase self-bearing rotating electrical machines with advantages such as: 1) requiring only one power supply for torque production; 2) lateral forces are produced using auxiliary power supplies of relatively low current and voltage ratings; 3) relatively low power loss; and 4) preserving the flexibility for extensions to other polyphase machines. The bridge connection has been verified to exhibit the characteristics of a self-bearing motor via an electrically coupled finite-element analysis. A comparison of power loss with conventional winding schemes and general applications of such a proposed scheme are also presented.     

Modeling switched-reluctance Machines by decomposition of double magnetic saliencies

This paper presents a novel analytical model for a switched-reluctance machine (SRM) based on decomposition of its inherent double joint magnetic saliencies due to rotor and stator salient poles and saturation of magnetic field at high stator currents. With this method, the magnetic characteristics of the motor, such as flux linkage and incremental inductance, are decomposed to vector functions of rotor position and phase current. Dynamic state and torque equations for the SRM are derived on the basis of this representation. The proposed model is appropriate for online identification and for sensorless position control algorithms. It is easy to implement and computationally efficient. Comparison of the predicted motor magnetic characteristics to machine data from finite-element analysis verifies the accuracy of the model.     

Numerical Studies of Axial and Radial Magnetic Forces Between High Temperature Superconductors and a Magnetic Rotor

The magnetic bearing is considered as one of the most prospective applications of high temperature superconductors (HTSs) which can realize stable levitation in a magnetic field generated by permanent magnet devices or coils. The exploration of this kind of HTS bearing through numerical investigation is usually made by assuming the induced current circulates only within the ab-plane and thus simplifying the actual three-dimensional problem to a two-dimensional one. In this paper, on the basis of the three-dimensional model of the HTS bulk established before, we further introduce the developed finite-element software to calculate the magnetic field generated by a magnetic rotor which is composed of permanent magnet (PM) rings and ferromagnet (FM) shims, and in this way, we can investigate the magnetic forces (radial force and axial force) of a simplified HTS bearing model, i.e., two symmetric HTS bulks and a magnetic rotor, at a three-dimensional level. The investigations performed in this paper lead to the observations: the favorable configuration to construct the HTS bearing is that the axial height of each HTS element should be equivalent to the axial heights of PM ring plus FM shim; the increase of the radial thickness of PM ring will improve both the radial force and the axial force considerably, but its margin decreases; the enhancement of critical current density of HTSs due to the decrease of operating temperature can result in a higher increase of both the radial and axial force with a lower nominal gap between the HTSs and the magnetic rotor.     

Characterization of noise and vibration sources in interior permanent-magnet brushless DC motors

This work characterizes electromagnetic excitation forces in interior permanent-magnet (IPM) brushless direct current (BLDC) motors and investigates their effects on noise and vibration. First, the electromagnetic excitations are classified into three sources: 1) so-called cogging torque, for which we propose an efficient technique of computation that takes into account saturation effects as a function of rotor position; 2) ripples of mutual and reluctance torque, for which we develop an equation to characterize the combination of space harmonics of inductances and flux linkages related to permanent magnets and time harmonics of current; and 3) fluctuation of attractive forces in the radial direction between the stator and rotor, for which we analyze contributions of electric currents as well as permanent magnets by the finite-element method. Then, the paper reports on an experimental investigation of influences of structural dynamic characteristics such as natural frequencies and mode shapes, as well as electromagnetic excitation forces, on noise and vibration in an IPM motor used in washing machines.     

Steady-state finite-element solver for rotor eddy currents in permanent-magnet machines using a shooting-Newton/GMRES approach

This paper presents a two-dimensional steady-state finite-element solver, incorporating mechanical motion, that calculates eddy-current losses in the rotors of permanent-magnet machines. A shooting-Newton method is used to determine the periodic solution of the electromagnetics. Computation of the shooting-Newton Jacobian is avoided by using a generalized minimum residual (GMRES) linear solver. This method is more computationally efficient than performing transient analysis until convergence. The solver can be used to compare the rotor losses of different design choices for a high-speed permanent-magnet machine. Results show that rotor losses can be reduced significantly by laminating the rotor backiron, segmenting the permanent-magnet poles, increasing the number of stator slots, and closing the stator slots.     

Fault-tolerant homopolar magnetic bearings

This paper summarizes the development of a novel magnetic suspension that improves reliability via fault-tolerant operation. The suspension is suitable for flywheels used in satellites and space stations for attitude control and energy storage. Specifically, we show that flux coupling between poles of a homopolar magnetic bearing can deliver desired forces even after termination of coil currents to a subset of "failed poles". Linear, coordinate-decoupled force-voltage relations are also maintained before and after failure by bias linearization. We determined current distribution matrices that adjust the currents and fluxes following a pole set failure for many faulted pole combinations. We used one-dimensional magnetic circuit models with fringe and leakage factors derived from detailed, three-dimensional finite-element field models to obtain the current distribution matrices and the system response. Reliability is based on the success criterion that catcher bearing-shaft contact does not occur after pole failures. The magnetic bearing reliability is improved by increasing the number of the radial poles. An advantage of our method over other redundant approaches is a significantly reduced requirement for backup hardware such as additional actuators or power amplifiers.     

Fast Calculation of Field Currents and Reactances for Doubly Fed Generators With Rotor Duct Pieces

Doubly fed generators have been used as adjustable-speed pumped-storage generator motors and wind turbine generators. Accurate determination of field currents and reactances is important for the design of these machines. We propose a calculation method to obtain the field currents and reactances of machines with rotor duct pieces under any steady-state balanced load condition. The method links two-dimensional static finite-element analysis (FEA) with an approximate calculation to consider three-dimensional (3-D) skin effect in the duct pieces. Its advantage is that the computational time is much smaller than 3-D transient FEA when the slip frequency is not zero. The method will contribute to improvement of the design of doubly fed generators with rotor duct pieces. It was applied to a 395 MVA machine, and the calculated field currents agreed well with the measurements. Variation in the reactances due to saturation is also discussed     

Driving Mechanism of a Superconducting Magnetic Bearing System

Driving the rotor of a superconducting magnetic bearing without mechanical contact in the optimum conditions is an important task for high operational speeds. For this reason, an alternative eddy current mechanism is proposed to drive the rotor by means of magnetism with a speed higher than that of the driver. The designed driving system provides strong and stable magnetic coupling between the relatively rotating parts. The drag and lift forces between the rotor and driver disc are discussed by considering various conditions, such as the rotor configurations and the saturation of the magnetic field within the conducting material. The overall results indicate that the designed electromechanical driving system has potential solutions for the various applications for magnetic bearings from the effective driving mechanism point of view.     

Development of a High-Speed Permanent-Magnet Brushless DC Motor for Driving Embroidery Machines

We describe the development of a permanent-magnet (PM) brushless DC motor for driving high-speed embroidery machines by employing advanced design and analysis techniques. In the design of the motor, magnetic field finite-element analyses accurately calculate the key motor parameters such as the air-gap flux, back electromotive force (EMF), and inductance. Using the numerical magnetic field solutions, a modified incremental energy method calculates the self and mutual inductances of the stator windings. A phasor diagram is derived to compute the motor's steady-state characteristics. To predict the dynamic performance and increase the prediction accuracy, a Simulink-based model simulates the motor performance with the real waveforms of applied phase voltage, back EMF, and current. The motor prototype tested with both a dynamometer and a high-speed embroidery machine validated the theoretical calculations.     

Alford力和磁悬浮轴承对转子系统动力学特性的影响

以磁悬浮轴承支承的航空发动机高压模拟转子为对象,研究了在压气机叶尖气流激振力和磁悬浮轴承电磁力共同作用下的转子系统动力学特性。采用Timoshenko梁理论建立了模拟转子的有限元模型,在模型中引入由PID方法控制的差动磁悬浮轴承电磁力以及由Alford力表示的压气机叶尖气流激振力,利用Newmark-β法求解了转子系统的动力学响应。计算结果表明,在非线性Alford力和磁轴承电磁力共同作用下,转子系统表现出了较复杂的动力学特征;磁悬浮轴承的控制参数对转子系统特性有较大影响,不同取值可能导致转子出现单周期、多周期拟周期甚至失稳等不同动力学行为;因此,对由磁悬浮轴承支承并含轴流压气机的转子,需考虑叶尖气流激振力与电磁轴承力的相互影响进而确定轴承控制参数。     

Current Accumulation for a Self Magnetic Field Calculation in a Finite-Element Gun Code

We describe a novel current accumulation algorithm for the three-dimensional self magnetic field calculation in a charged-particle beam optics code. The current source is a charged-particle beam represented by a collection of numerically-integrated current-carrying rays. We compute the magnetic vector potential using edge basis functions and the curl–curl formulation of the finite-element method. The current accumulation algorithm takes advantage of a novel particle tracker that happens to be ideal for this application. We show that our source vector is compatible with the singular finite-element matrix, even with modest numerical integration errors. Thus, a conjugate gradient matrix solver works well, with no need for additional gauge conditions. We confirmed this behavior in a series of numerical tests on a small problem with incomplete linear and quadratic basis functions on a variety of element shapes.     

Effects of Armature Reaction on the Performance of a Claw Pole Motor With Soft Magnetic Composite Stator by Finite-Element Analysis

We investigated the effects of armature reaction on the performance of a three-phase three-stack claw pole motor with soft magnetic composite stator core by using three-dimensional finite-element analysis (FEA), which is an effective approach to accurately compute the parameters and performance such as the back electromotive force (EMF), core losses, and winding inductance at various saturation levels. The motor is rated as 500 W at 1800 rpm when the stator current is 4.1 A, driven by a sensorless brushless DC scheme. Because of the armature reaction, the back EMF produced by the rotor permanent magnets and the developed torque is reduced by about 3.3% at the rated load, and the core losses increase drastically by 41% from no-load to full-load. The winding inductance is computed with different loads at different rotor angles     

Design of a Halbach Magnet Array Based on Optimization Techniques

We have designed a Halbach magnet array by using a numerical optimization method based on finite-element analysis. The magnetization direction of each element is defined as the design variable. The optimal magnet arrays composed of two and three linear magnet layers can then be investigated to increase the attractive, repulsive, and tangential magnetic forces between magnet layers. We have applied a magnet array maximizing the tangential force to a torsional spring composed of two- and three-magnet rings. The two-dimensional finite-element analysis incorporates optimization techniques such as the sequential linear programming and the adjoint variable method.