Flux Path Research Articles

Mechanical Characterization of Low-Carbon Steels for High-Field Accelerator Magnets: Application to Nb$_{3}$Sn Low-$\beta$ Quadrupole MQXF

In the quest for higher field accelerator superconducting magnets, essential parts of their design are the so called yokes, which are traditionally made of low – carbon magnetic steel. In currently used magnets, they are typically found in the form of fine – blanked laminations, or machined from laminated heavy plates. The material’s choice is made based on a compromise between the high saturation field, providing a return path for the magnetic flux, and the mechanical robustness conferred to the magnets’ cold masses. This paper describes the mechanical characterization of low – carbon steel, and applies several approaches for the design and validation of the material from the structural point of view, applicable to a Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> Sn quadrupole: MQXF. Tensile tests at room and cryogenic temperatures, together with fatigue and fracture toughness at cryogenic temperature have been performed. Calculations based on the obtained material properties and results of extensive non-destructive examination (ultrasonic testing) have been implemented in order to ascertain the structural limits of low – carbon steel for its use in the fabrication of high field accelerator superconducting magnets.

Study of a Modular Toothed Linear Hybrid Reluctance Motor With Permanent Magnets in Translator Slots

This article introduces an innovative modular and split-tooth linear hybrid reluctance motor (MLHRM) with embedded permanent magnets (PMs) to achieve improved performance of linear switched reluctance motors (LSRMs). First, three new motor structures are introduced, including two, three, and four teeth per pole MLHRMs (MLHRM2, MLHRM3, and MLHRM4). Then, the operating principles of the proposed motors are studied through the flux path of windings and PMs, and the impact of the PMs on the MLHRM’s performance is investigated via a magnetic equivalent circuit (MEC). Third, using the extracted relations among the motors’ parameters, classic design equations of the SRM, and the genetic algorithm (GA), the proposed motors are optimized and compared through the finite-element analysis (FEA). The results indicate the superior performance of the MLHRM2 over MLHRM3 and MLHRM4. The static and dynamic performance of MLHRM2 is compared with the modular and split-tooth LSRM (MLSRM2) and the conventional modular LSRM (MLSRM1) in the fourth step. The simulation results show the superior performance of MLHRM2 over MLSRM2 and MLSRM1. Finally, the proposed MLHRM2 is prototyped, and the experimental results are obtained in both the presence and absence of the PMs. The experimental results verify the simulation results with an acceptable agreement.

Magnetothermal Coupling Analysis of Permanent Magnet Claw Pole Machine Using Combined 3D Magnetic and Thermal Network Method

The permanent magnet claw pole machine (PMCPM) is a special kind of transverse flux machine, different from conventional electrical machines the main magnetic flux path of PMCPM is 3D. Therefore, for accurate performance analysis,the 3D finite element method (FEM) is required to calculate both the electromagnetic characteristics and thermal distribution. However, it is time consuming especially when the coupling effect needs to be considered. In this paper, a combined 3D magnetic and thermal network method is proposed to obtain the performance of PMCPM. As the developed thermal network shares the same structure as the magnetic network, the calculated core loss can be regarded as the heat source in the thermal analysis easily, in which 3D rotational core loss is calculated as the 3D network is adopted. The proposed method holds the advantages of close magnetothermal coupling and fast calculating speed.For the calculation results verification, 3D FEM is used.

Design and Performance Analysis of a Staggered Vernier Generator for Wave Power Generation

In this paper, a staggered vernier generator suitable for a counter-rotating self-adaptable WEC is proposed to meet the energy demand of the small-scale engineering equipment in the deep sea. According to the vernier effect of the magnetic gear, the generator modulates the low-order rotating magnetic field generated by the rotation of the low-speed permanent magnet rotor into a high-order magnetic field rotating at a high speed, thereby realizing the acceleration of the generator magnetic field. A staggered structure permanent magnet vernier generator with 18 teeth/28 poles is designed. The main magnetic flux path on the staggered structure in the staggered vernier generator is analyzed, and the air-gap magnetic field distribution of the generator is analyzed with the help of numerical simulation software. The influence of different design parameters on the vernier generator is discussed. The staggered vernier structure can improve the main magnetic flux of the generator, reduce the magnetic flux leakage, and improve the performance of the generator without adding additional structures and materials.

A Novel Mesh‐Based Equivalent Magnetic Network for Deep Saturation Region of Permanent Magnet Machine

AbstractPartial deep saturation of magnetic circuit is common in short‐term working permanent magnet (PM) machines in aviation, aerospace, new energy power generation and other fields. In order to accurately calculate the electromagnetic characteristics of the short‐term working machine, a novel mesh‐based equivalent magnetic network for the deep saturation region is proposed. Firstly, the deep saturation mechanism of the magnetic circuit of short‐term working motor is analyzed, and the deep saturation region is determined; Secondly, a Pointy topped hexagonal segmentation approach (PT‐HSA) grid generation method is proposed to effectively simulate complex magnetic flux paths. The PT‐HSA grid division and node compilation rules were analyzed in detail. In addition, a nonlinear magnetic network model based on reluctance grid model and equivalent magnetic circuit model is established. Compared with the quadrilateral segmentation approach (QSA) model, the calculation results of PT‐HSA model are closer to the finite element simulation results in the loading and instantaneous compensation conditions. Finally, an experimental platform is built, and the accuracy of the PT‐HSA magnetic network model is verified by the experimental results. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Design Optimization of a Switched Reluctance Machine with an Improved Segmental Rotor for Electric Vehicle Applications

In this article, a switched reluctance machine (SRM) with six phases and a misaligned segmental rotor is proposed. The segmental rotor has an internal 15-degree misalignment, allowing the SRM structure to be a one-layer 2D structure with a short flux path structure. The proposed SRM produces a relatively low torque ripple by exciting two phases simultaneously. Additionally, an optimization method is applied, allowing for the maximum torque position of one phase to be aligned with the zero-torque position of the adjacent phase. The finite element method (FEM) is used to analyze and design the proposed SRM and to simulate the proposed liquid cooling system. The static torque waveforms are analyzed, and the dynamic torque waveforms are simulated with a drive using SiC MOSFETs. Finally, a prototype is manufactured, and the experiment is performed to validate the design and simulation results.

A Novel Analysis Method for Flatted Single-Layer Interior Permanent Magnet Machines Having Overhang Structure

This study describes a novel analysis method for interior permanent magnet (IPM) machines with an overhang, in which the rotor axial length exceeds that of the stator. Adopting an overhang structure facilitates the achievement of a high torque density per machine volume without increasing the stator size due to the additional magnetic flux of the rotor. However, the use of the three-dimensional (3-D) finite-element method (FEM) is inevitable, which requires substantial computation time and large computer memory to accommodate the overhang effect. Therefore, a new analysis method combined with a lumped magnetic equivalent circuit (MEC) is proposed to overcome the inefficient conventional approach. A new residual flux density can be derived by considering the magnetic flux paths in the overhang structure. Two-dimensional FEM combined with the residual accurately considers the IPM with overhang. The validity of the proposed concept is verified via 3-D FEM using several test models.

Thermal transport in porous graphene with coupling effect of nanopore shape and defect concentration

Thermal conductivity of porous graphene can be affected by defect concentration, nanopore shape and distribution, and it is hard to clarify the effects due to the correlation of those factors. In this work, molecular dynamics simulation is used to compare the thermal conductivity of graphene with three shapes of regularly arranged nanopores. The results prove the dominant role of defect concentration under certain circumstances in reducing thermal conductivity, while the coupling effect of nanopore shape should be noticed. When the atoms at the local phonon scattering area around each nanopore are properly removed, the abnormal increment of thermal conductivity can be detected with the increase of defect concentration. Heat flux vector angles can effectively characterize the local phonon scattering area, which can be used to describe the effect of nanopore shape. The coupling effect of defect concentration and pore shape with similar heat flux path is clarified according to this process. By adjusting vertex angle of triangle defect, there is a balanced state of the effect factors between the variation of defect concentration and the same phonon scattering area. It provides a possible way to describe the weighing factors of the coupling effect. The results suggest a feasible approach to optimize and regulate thermal properties of porous graphene in nanodevice.

Experimental Study on Magnetic Resonant Coupling AC Magnetic Suspension Considering Electrical Power Transmission

A three-degree-of-freedom AC magnetic suspension system using magnetic resonant coupling was fabricated. The AC magnetic suspension system can produce restoring force without active control. This system is dynamically stabilized by adding indirect damping, which is produced by suspending to the stator with viscoelastic support mechanisms. A non-contact electrical power transmission is achieved simultaneously by magnetic resonant coupling. The structure of magnetic resonant coupling is similar to the structure of the transformer. The magnetic flux path for suspension is combined with that of electrical power transmission. The electric characteristics of the transformer depend on the resistance of a load connecting the secondary circuit. The measured results indicate that the driving frequency needs to be adjusted to achieve stable suspension in relation to the resistance of the load. These characteristics are confirmed experimentally.

Fault‐Tolerant Characteristics Analysis of U‐Shaped Rotor Stator Excitation Generator for Vehicle Applications

In order to improve the reliability of the traditional doubly salient electro‐magnetic generators (DSEG) and realize the isolation of interphase magnetic circuit, a U‐shaped rotor stator excitation generator (UR‐SEG) for vehicle applications is proposed in this paper. The machine has the interphase physical isolation and short flux path structure because of the U‐shaped rotors. According to the theoretical analysis of the fault‐tolerant characteristics of this UR‐SEG, the characteristic of the phase electromotive force (EMF) of the UR‐SEG completely overlaps with the EMF of front and rear phase in the entire power generation stage is revealed. Then the flux linkage, EMF, output voltage of both normal and faulty states are comparative investigated using the two‐dimensional finite element method (FEM). The output characteristics of the normal state and four faulty states of the machine with different exciting currents are researched, and the influence rules of fault on output characteristics are obtained. Finally, the outstanding fault‐tolerant characteristics of the UR‐SEG were verified by the experimental results. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Practical loss prediction in soft magnetic composite components

Soft magnetic composites offer an alternative material to iron laminations for forming the active components of electrical machines. They have the advantages of being able to suppress eddy currents for three dimensional flux paths and can be pressed into complex components – facilitating the use of new and novel topologies. Most electrical machine designers, and the software they use, are familiar with working with laminations, where iron loss is described by a the two term Steinmetz equation. There is less experience in predicting iron loss in soft magnetic composite components, where a third loss term to describe bulk eddy currents is often employed. This paper describes a project which set out to use experimental loss data to improve the accuracy of loss prediction of complex soft magnetic composite components using industry standard finite element analysis software.

Permanent Maglev Platform Using a Variable Flux Path Mechanism: Stable Levitation and Motion Control

This article presents a three degrees of freedom (3-DOF) permanent maglev platform for a cleanroom conveyor system supported by four magnetic poles that utilize a variable flux path mechanism. Since the magnetic force of poles is generated and controlled entirely by the rotation of disk-type permanent magnets (PMs), the system exhibits a quasi-zero power consumption and anti-adsorption capability. First, the system mechanism is illustrated, and the magnetic force of the variable flux path pole is measured. Then the mathematical model and state-space of the maglev platform are established based on dynamic analysis. Afterward, a double closed-loop controller is designed for stable levitation and motion control, and the coordinate transformation matrix is used to decouple the control system. Finally, the simulations and experiments were implemented, and stable levitation and 3-DOF motion control were realized with a remarkable positioning precision. The results indicate that the controller and decoupling strategy are effective.

Design and Analysis of a Doubly Salient Wound Field Starter Generator for Cost-Effective Automobile Application

Doubly salient wound field machines exhibit the advantages of robust structure and controllable flux, and hence have been utilized as generators in applications of automobiles and renewable energy. However, the inherent unbalanced phase back-electromotive force (EMF) waveform caused by the asymmetric flux path brings difficulties for precise control and smooth operation. To solve the problem caused by unbalanced back-EMF waveform in conventional doubly salient machines, this paper presents a novel doubly salient wound field machine with balanced and symmetrical back-EMF waveform as starter generator in automobile application. The robust structure and the controllable flux are inherited, while the magnetless feature makes it promising for cost-sensitive applications. The proposed machine can be operated as an assistant motor for torque boosting at start-up stage, as well as a power recycling generator for battery charging at steady state. It is revealed that the proposed wound field machine exhibits similar cost, comparable torque density, improved torque ripple, and higher efficiency than the switched reluctance machine. Finally, the proposed prototype is fabricated, and dynamic experiment is conducted to validate the feasibility for automobile starter generator application.

Dynamic modeling of stack giant magnetostrictive actuator with magnetic equivalent network considering eddy current effect

Stack giant magnetostrictive actuators (SGMAs) are widely used in various fields for its merits such as saving the space and improving the evenness of the bias magnetic field provided for the giant magnetostrictive material (GMM). In this paper, based on the flow path of the magnetic flux in SGMA, a magnetic equivalent network corresponding to quasistatic conditions is proposed taking flux leakage and fringing effect into account. Meanwhile, complex reluctances of the GMM rods are introduced to describe the decrease and phase shift of magnetic field intensities caused by eddy current under high-frequency excitation signals. Furthermore, the magnetic equivalent network, determining the relationship between excitation signals and magnetic field intensities, is combined with the Jiles–Atherton model, nonlinear constitutive theory of GMM concerning multi-field coupling, and structural dynamics of SGMA so as to derive a multi-field coupling model predicting the tracking behaviors of SGMA to the excitation signals. Moreover, a finite element method is conducted, an SGMA prototype is fabricated, and an experimental platform is set up to verify the proposed model. Comparison between results derived from the magnetic equivalent network and those calculated by the finite element method indicates that the proposed network is able to predict the magnetic field distribution inside the SGMA prototype in quasistatic conditions; further comparison between results obtained from the proposed multi-field coupling model and those from experiments indicates that the model can accurately predict tracking behaviors of the SGMA prototype to the excitation signals.

Study of Boosted Toothed Biased Flux Permanent Magnet Motors

In this article, three new toothed biased flux permanent magnet (PM) motors are introduced and studied, each of which has a specific arrangement of excitation (dc field/PM) and flux path (series/parallel). This results in three main structures, namely, hybrid excited toothed slot-PM (HETSPM), toothed biased flux PM (TBFPM) with series flux path, and, finally, toothed biased flux slot PM (TBFSPM) with hybrid flux path. The TBFSPM structure has improved the average torque, torque ripple, and efficiency compared to other stator-PM motors. The HETSPM structure has improved the average torque per PM, and the TBFPM structure features a very low-torque ripple profile compared to other stator-PM motors. All the topologies have shown a good PM demagnetization resistance and lower PM loss compared to other structures. Moreover, a new Carter’s coefficient is introduced to increase the accuracy of harmonic analysis for split-tooth structures by modeling the nonlinear effect of fringing flux with a new transition function, which has increased the accuracy by 20% compared to the traditional approach. The theoretical analyses have been checked by the 2-D finite element method (FEM), and the TBFSPM structure is prototyped and tested to validate the simulation analyses.

Split-Tooth Double-Rotor Permanent Magnet Switched Reluctance Motor

This article proposes a new double-rotor permanent magnet switched reluctance motor (DR-PMSRM). In the proposed topology, the rotors do not include any coils or PMs; therefore, DR-PMSRM inherits the advantages of conventional SRMs. Splitting teeth for each stator pole has resulted in a remarkable increase in the motor’s torque density. In addition, the use of small PMs between the two teeth of the stator poles has greatly improved the output characteristics of the proposed motor compared to the PMless counterpart. The operating principle of the DR-PMSRM is illustrated, and the flux paths created by the coils and PMs have been analytically obtained, which are compatible with the simulation results. The flux distributions, static and dynamic torques, flux linkage profiles, steady-state current, and torque waveforms of the DR-SRM and DR-PMSRM are obtained and compared to demonstrate the effectiveness of PMs. All the simulation results indicate that the PM-assisted structures can achieve higher torque and power than their PMless counterpart. The simulation results confirmed that there is no demagnetizing risk for the PMs used in the structure. Finally, the motor is prototyped, and the experimental results are accomplished. Both the experimental and simulation results confirm the effectiveness of the proposed DR-PMSRM.

Ultra-broadband near-field magnetic shielding realized by the Halbach-like structure

With the great developments in electronic communication technology and miniaturized electromagnetic devices, near-field magnetic shielding has attracted much attention. However, for the widely used natural magnetic shielding materials, metal and ferrite, they have the unique limitations of large Ohmic loss and heavy weight, respectively. Although a compromise solution of the shielding layer may resort to the composite structure with metal and ferrite slabs, practical magnetic shielding with broadband, high efficiency, and ultra-thinness has remained a great challenge. In this work, inspired by the effective magnetic flux path established by the Halbach array, which is constructed by stacking permanent magnet in diverse directions, we propose a physical mechanism of local magnetic moment control in artificial structures, called the “Halbach-like structure.” We demonstrate the highly efficient and ultra-broadband near-field magnetic shielding in the Halbach-like structure with patterned metal and ferrite structures. By ingeniously designing the local magnetic moment, our structure not only provides an effective method for realizing high performance magnetic shielding but also paves the way to the other near-field controls, such as the wireless power transfer, wireless communications, and magnetic resonance imaging.

Analysis and Verification of the Method of Improving Inductance by Magnetic Endcaps in Slotless Permanent Magnet Motor

The slotless permanent magnet motor (SPMM) has low phase inductance due to the larger physical air gap, which will adversely affect motor control and current harmonics. In this paper, the method of forming an extra magnetic circuit by endcap around the outer stator is proposed. The advantage of this method is that a restrained flux path is formed without increasing the motor structure and cost, and the inductance of the motor is effectively improved without causing a significant decrease in torque. The preliminary simulation analysis and corresponding experimental content are carried out. The experimental results and the simulation content showed good consistency, which verified the correctness of the theory and simulation analysis.

An Improved Equivalent Magnetic Network Model of Modular IPM Machines

This article develops an improved equivalent magnetic network (EMN) model for analysis of a modular interior permanent magnet (IPM) machine. First, focusing on the local magnetic saturation, the stator tooth crown is divided into three parts based on its structure and flux density distribution. To model the specific flux path, the tooth tips on both sides are approximated to right-angled trapezoids and the middle part is divided into isosceles trapezoid. Second, an improved air-gap model is proposed, which divides the air-gap magnetic network into three layers. The middle network uses cross-shaped mesh (CS-M) elements to represent the path of tangential and radial fluxes. The top and bottom layers are composed of parametrized nonlinear permeances between stator, rotor edge nodes, and middle network nodes, whose values are the function of angle respect to CS-M elements. In this way, as the machine rotates, the structure of the EMN model can be kept invariant, and only permeances of bottom layers should be modified. Then, the EMN model is extended to the analysis of the machine with skewed stator. The accuracy and effectiveness of the proposed EMN model are verified through comparisons with finite element analysis and experimental tests.

A Magnetic Network Model and Harmonic Analysis of a Canned Switched Reluctance Machine

This article presents a novel network model for magnetic flux and loss analysis of electrical machines. This model enables harmonic analysis and is applied on a canned switched reluctance machine, with emphasis on magnetic can-shield effect. The modeling is featured by identifying airgap flux path structure, combined with a fast calculation method of magnetic saturation and electro-magnetic field interaction due to the use of cans. Finite element (FE) method and measurement are taken as verification.