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To facilitate the active magnetic bearing (AMB) design and analysis, an accurate and fast model that considers both rotor eccentricity and the saturation effect is necessary. In this article, a novel hybrid analytical model (HAM) for effective calculation of the magnetic field of the AMB is proposed. Eccentricity and local saturation are considered in the proposed HAM. In the proposed HAM, the stator and rotor are modeled by elementary subdomains (ESDs) and the air-gap is modeled by magnetic equivalent circuit (MEC). Direct coupling between the solutions in the ESD regions with MEC completes the whole model matrices. Compared to the existing literature, the proposed model considers both the rotor eccentricity and material nonlinearity. The effectiveness and accuracy of the proposed HAM are validated by both the finite element model and experimental results. The results show that the proposed HAM can accurately predict the magnetic quantities of the AMB. [ABSTRACT FROM AUTHOR]

This article presents a new rotor design to reduce rotor eddy current loss of a high-speed permanent magnet synchronous machine for flywheel energy storage system. Instead of using common nonmagnetic sleeves, the new rotor incorporates permeable retaining sleeves (PRSs) to fix permanent magnets on the rotor hub. The PRSs are made of permalloy that features high permeability and high electrical conductivity. Thus, skin depths for asynchronous harmonics are extremely small. On the other hand, the PRSs are electrically insulated along the circumferential direction. Owing to these two reasons, rotor eddy current loss at open circuit decreases by 64.2% without sacrificing torque output, compared with an original rotor with nonmagnetic retaining sleeve. In addition, thermal and structural finite element analyses are performed to calculate rotor temperature distribution and evaluate the structural integrity of the new rotor. Rotor eddy current loss reduction benefits lowering rotor temperature rise. Prototype machine with the new rotor is fabricated, and preliminary tests are carried out to confirm the analysis results. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical model for the prediction of air gap magnetic field distribution for axial flux permanent magnet (AFPM) machine with various types of misalignments. The AFPM machine geometry is first transformed to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then the stator coordinate system is chosen as reference coordinate to consider both static/dynamic angular and axis misalignments. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the proposed approach agrees with the finite-element method. The model is further validated by experiments under healthy, dynamic angular and axis misalignment conditions, which can validate the proposed approach. It turns out that the proposed approach can predict the performance of AFPM machines with types of misalignment quickly and effectively, which is greatly significant for further fault detection. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical model for the prediction of airgap magnetic field distribution for axial flux permanent magnet (AFPM) machine with partial magnet demagnetization. The AFPM machine geometry is first converted to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then current sheet representation of PM is derived to consider the partial demagnetization using superposition principle. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the results of proposed approach agrees with that of finite-element method. The model is further validated by experiments under both healthy and demagnetized conditions, which can validate the proposed approach. Main contribution of the work is to consider the partial irreversible demagnetization. Moreover, the proposed method is applicable for both AFPM and radial flux permanent magnet machine. [ABSTRACT FROM AUTHOR]

In this paper, a new hybrid model is proposed for the prediction of air gap magnetic field distribution (MFD) in interior permanent magnet machines with any rotor configuration. The slotless magnetic field is first predicted by finite-element method (FEM) with automatic scripting in MATLAB to consider saturation in the rotor iron. Afterward, the conformal mapping viz., Schwarz–Christoffel mapping is introduced to take the slotting effect into account. Consequently, the MFD could be calculated. The back electromagnetic forces, cogging torque, and output torque are obtained accordingly. Then a subdomain model is developed to consider the armature reaction. The results show that the proposed hybrid approach agrees well with the FEM. The model is further verified by experiments. The main contribution of this paper is to reduce the computation time remarkably while maintaining the calculation accuracy. [ABSTRACT FROM AUTHOR]

In this paper, novel dual-stator switched-flux hybrid magnet machines (DS-SF-HMMMs) are proposed. Two sets of armature winding are employed so as to improve the space utilization and torque density. Meanwhile, two kinds of permanent magnets (PMs), i.e., neodymium–iron–boron and low-coercive-force magnets, are placed on either a common stator or separate stators. The proposed machines can provide the merits of high torque density in DS machines, and excellent flux adjusting capability in memory machines. The topologies and operating principle of the DS-SF-HMMMs having different PM arrangements are introduced and highlighted, respectively. In order to overcome the drawbacks of the original “U”-shaped PM type, two alternate designs are presented to increase the copper area in the inner stator and facilitate the manufacturability. In addition, the equivalent magnetic circuits for various machine models are formulated to reveal the field regulation principle. Then, the electromagnetic characteristics of various available DS-SF-HMMMs are evaluated and compared by the finite-element (FE) method. The stator/rotor pole combinations of the selected machine are analytically optimized in order to maximize the torque density. Finally, two prototypes are manufactured and tested to verify the FE analyses. [ABSTRACT FROM PUBLISHER]

This paper presents the simple analytical modeling for switched flux memory machine to provide in-depth insight into its working mechanism. The analytical approach is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations for a doubly salient structure. In addition, due to low coercivity and highly nonlinear hysteresis curve at the second quadrant, the piecewise and virtual-linear hysteresis models of AlNiCo permanent magnet (PM) are presented to determine the PM working point. This combined analytical solution allows rapid calculation of several electromagnetic characteristics, e.g., air-gap flux density and back electromotive force. The effectiveness of the analytical method is validated by both finite-element results and measurements. [ABSTRACT FROM AUTHOR]

In this paper, a general analytical model is proposed to calculate the back electromotive forces of various manufacturing imperfections in the double-rotor axial flux permanent magnet machine. First, the axial and circumferential flux density in the air gap under healthy condition is developed by Maxwell’s equations and Schwarz–Christoffel mapping. Second, the equations of air gap length and radii are introduced to calculate the flux density with manufacturing imperfections. The back EMFs of each case are calculated. For each case, finite-element (FE) method models are developed to validate the analytical model, and the results show that the analytical model predictions match well with the FE results. Finally, the analytical model is verified by experimental results. [ABSTRACT FROM AUTHOR]

The memory machine concept is recently extended to switched-flux (SF) machines, forming a series of SF hybrid magnet memory machines (SF-HMMMs). They exhibit the merits of good demagnetization withstand capability and effective flux adjustability. Nevertheless, the torque density is inevitably compromised due to the geometric conflict within the stationary part. Meanwhile, the inactivated dc coil, excluding online magnetization transients, results in system redundancy. Hence, in this paper, a new hybrid-excited (HE) concept is developed and implemented in a partitioned-stator SF-HPMM (PS-SF-HMMM). Thereby, the distinct synergies of a dual-magnet memory machine and an HE machine are achieved. With slight compensated field excitation, the torque can be improved at low-speed operation. Meanwhile, the high-speed constant-power region can be further extended without sacrificing high efficiency. The stator/rotor pole numbers are optimized first. The operating mechanism and optimal stepwise HE implementation over a whole operating envelop are then addressed. In addition, a comparison between PS-SF-HMMM with hybrid-excitation and its pure HE counterpart is established. Finally, both the finite-element simulation and experiments are carried out to verify the utility of the proposed HE concept. [ABSTRACT FROM AUTHOR]

This paper deals with a sizing optimization approach to reducing the cogging torque and maximizing the flux linkage of a transverse flux permanent magnet generator with double C-hoop stator and flux-concentrated rotor. The previous investigations demonstrated that the cogging torque is significantly influenced by ks and kr , which denote the ratios of circumferential widths of stator hoop and rotor core to pole pitch, respectively. The 3-D finite-element method (FEM) is employed to investigate the relationship between the abovementioned ratios and the cogging torques of both single-phase and three-phase prototypes. The optimal ratios of ks and kr , which comply with the equation, i.e., $(k_{{ r}} >1-k_{{ s}} )\cap (k_{{ r}} >1-0.788~*~k_{{ s}} )=k_{r} >1-0.788~*~ k_{{ s}} $ , are selected, and the procedures are described. The FEM results show that the amplitude of the cogging torque can be reduced significantly due to the reshaped rotor core. Besides, two additional zero-crossing points can be observed with the increase in kr and the decrease in ks . The cogging torque can be decreased by 20% with a skewed rotor core. A three-phase prototype is optimally designed and manufactured to verify the optimization approach. [ABSTRACT FROM AUTHOR]

Transverse flux permanent magnet (TFPM) machine possesses the characteristic feature of decoupled electric load and magnetic load to obtain high power density. A novel TFPM generator (TFPMG) with double C-hoop stator and flux-concentrated rotor is proposed for low-speed applications, such as direct-drive power generation, which has larger torque capability and more poles than traditional double-side TFPMGs. The structure and operation principles of the generator are described in detail. The 3-D finite-element method (3-D FEM) is employed to compute the no-load magnetic field distributions. The analytical results, including flux density waveform, electromotive force (EMF) waveform, and inductance waveform of the armature winding, are obtained to verify the principle and feasibility of the proposed generator. The cogging torque is also analyzed and optimized by the 3-D FEM. A prototype is fabricated, and some experiments are conducted. The experimental results of back EMF and waveforms of current and voltage with different loads verify the FEM analysis previews well. [ABSTRACT FROM AUTHOR]

A combined analytical and FEM technique is proposed for predicting the air-gap magnetic field distribution of a PM embedded salient pole wind generator. The influence of slotting on both radial and circumferential components of air-gap flux density is taken into account. By employing the proposed combination technique, the magnetic field distributions when the stator and rotor are at different relative positions can be calculated much faster than that by FEM. Based on the magnetic field distributions, the cogging torques are predicted and verified by the FEM, while the relationship between cogging torque and design parameters are further investigated. The proposed combination technique provides an efficient and accurate prediction method for the air-gap magnetic field distribution of large electrical machines with a complex PM pole structure. [ABSTRACT FROM AUTHOR]

Based on the linear field theory and the limiting nonlinear theory, respectively, the eddy current losses in thick iron plates and thin laminations are formulated. Two equivalent permeability calculation models are developed to take into account the saturation effects occurring in the corresponding ferromagnetic materials. By enabling the approximate treatment of the magnetic field saturation, the nonlinear eddy current problem is reduced to the linear one. The proposed approach to the linearization of the field analysis is investigated by comparing the results of the linear analysis using the equivalent permeability with those of the nonlinear finite element analysis and experimental data. [ABSTRACT FROM AUTHOR]

An improved practical two-dimensional model for the analytical calculation of the magnetic field distributions in permanent magnet (PM) eddy current couplings is presented to obtain the torque characteristics. By establishing the Cartesian coordinate reference system on the rotating conductor, the PM region is treated as a source of traveling wave magnetic field and then the multi-layer boundary value problem is solved. The formulation for the magnet blocks, the eddy current and saturation effects in the solid secondary back iron, and the equivalence relationships between typical PM shapes, are all reasonably taken into account. Calculation results produced by the proposed analytical model are compared with those from the nonlinear finite element method and experimental measurement. [ABSTRACT FROM PUBLISHER]

A three-dimensional analytical modeling of the magnetic field of the stator-ironless axial flux permanent magnet (AFPM) machine under open-circuit condition is presented in this paper. It involves the analytical solution of the governing field equations in the region between back-irons in the cylindrical coordinate, in which the magnets are assumed to be axially magnetized and have constant relative recoil permeability. The proposed modeling method is applied to a specific AFPM machine, and the analytical results are in good agreement with those of three-dimensional finite element analysis (FEA). [ABSTRACT FROM AUTHOR]

Core-loss prediction is an important issue in design and analysis of permanent-magnet (PM) motors. Because of the diverse structure, flux distribution, and rotational variation of flux, it is difficult to predict the core loss in a machine exactly. In this paper, a core-loss model for the PM motor is introduced in which flux variation loci in different parts of the motor are predicted by carrying out a finite-element transient analysis. Since the flux variation pattern is complicated, an improved equation based on the conventional three-term expression is used for core-loss calculation. The core-loss model is developed totally in ANSYS parametric design language as a parametric model and it can be used easily for different types of PM motors. Calculation and experiments on a high-speed PM motor have shown that the model can produce results that agree with the experimental ones. [ABSTRACT FROM PUBLISHER]

In a permanent magnet synchronous generator (PMSG) with modular winding, significant eddy current may be induced in the rotor magnets due to asynchronous rotating stator magneto-motive forces (MMFs), and a rectifier load may signify the situation further. The eddy-current loss prediction in the rotor magnets of a PMSG with modular winding feeding a rectifier load is described. An analytical method considering the stator current harmonics and stator MMF spatial harmonics and a time-stepping, coupled-circuit, 2-D finite-element method (FEM) are adopted. The predicted losses obtained from these two methods are compared and investigated. [ABSTRACT FROM AUTHOR]

This paper presents a method for analytically analyzing the magnetic field and predicting the cogging force and torque of a linear and rotary permanent magnet actuator (LRPMA). The tubular mover of the LRPMA is transferred into a planar one by using a proposed magnetic field curvature factor and a relative permeance function for the stator slotting so as to simplify the magnetic field calculation. Magnetic field distributions of the LRPMA when the stator slotting is neglected are analytically analyzed using the magnetic scalar potential, and validated by 3-D finite-element method. The linear cogging force and rotary cogging torque of slotted LRPMA are subsequently predicted by the Maxwell stress tensor method and verified by the experimental results on the prototype. [ABSTRACT FROM AUTHOR]

The eddy current fields in a laminated iron core and a single lamination, where the fields are considered as the 2-D and the 1-D problems, respectively, are analyzed. Then a new and simple formulation of equivalent conductivity in the direction normal to the laminations is derived by equating the eddy current loss expressions obtained from the above two problems. The validity of the formulation is verified by comparing the eddy current losses, calculated with the finite-element method using the proposed conductivity formulation and a long known formula, in an analyzed model. [ABSTRACT FROM PUBLISHER]