Thick Coils Research Articles

Novel Multiphysics Design Methodology for Coreless Axial Flux Permanent Magnet Machines

This work is devoted to multiphysics design of coreless axial flux permanent magnet machines with concentrated coils. Recently, these machines have been proposed for the propulsion of civil miniature electric unmanned aerial vehicles, which need very high torque and power densities. Such requirements tend to be in contrast with other important features such as high efficiency and resilience, making the design quite challenging. Among the various geometrical parameters, the rotor poles to stator coils ratio plays a key role in their performance. The main contribution of this paper is the development of an original design method hinging upon the said ratio. The 2D electromagnetic model at the heart of the approach is derived at the average radius and accounts for multi-layer and axially thick stator coils. Additional contributions include the concurrent use of thermal modelling in the preliminary design stage and mechanical analyses in the design refinement stage aimed at optimizing torque density and guaranteeing rotor integrity at maximum speed. Comprehensive experimental tests on a full-scale prototype are reported and help build confidence in the proposed methodology.

Optimization of hot rolling parameters of CRNO steel with the aid of hot compression test and deformation map

Abstract Cold-rolled non-oriented (CRNO) electrical steels find a wide variety of applications in the core of electrical machines due to low core loss and high magnetic permeability. Stringent market conditions not only require CRNO steel with superior magnetic properties but also demand excellent surface conditions. CRNO steel is cold rolled to 0.5 mm in reversing mill. High hot rolled input thickness (>2.6 mm) increases the number of passes during cold rolling and adversely affects the mill productivity. It also results in surface defects such as buckling and coil break. The flow stress of this steel varies differently compared to conventional rolled steel. Thus, it becomes difficult to optimize the reduction schedule and hence safe hot rolling practice is adopted to restrict roll force within permissible limit resulting in higher thickness. A hot compression test was carried out in a Gleeble–3500 to evaluate the flow stress behaviour of this steel and a deformation map was developed to optimize the hot rolling window. The input from the hot compression test and deformation map was used to develop a mill setup model to accurately predict the roll force and optimize the reduction schedule of CRNO steel in the finishing stands of HSM. The final thickness of hot-rolled coils during industrial trials with an optimized reduction schedule was found to be in the range of 2.4–2.6 mm compared to 2.7–3.0 mm during conventional rolling. These coils were further cold rolled and finished in 4–5 passes compared to 6–7 passes with conventional rolling. Reduction in the number of passes has resulted in increased productivity during cold rolling as well as improved surface finish.

Development of a 7 T NbTi solenoidal magnet with 72 mm aperture

A close-packed coil with a 72 mm aperture is developed using the formvar-insulated NbTi wire made from the WST company. The micrometer-level inter-turn spaces are filled with CTD-101 K utilizing a vacuum pressure impregnation method with a controllable flow speed of the epoxy resin. The cryogenic excitation results indicate that the coil inter-turn spaces are well filled, so that it can generate a 7.35 T central magnetic field at an operation current of 176 A with no coil quench. The maximum loadline of the coil is proved to be 98.96%. The maximum hoop-stress is approximately 64.1 MPa at the center of the inner most coil layer. The VPI method is applicable to the close-packed coils (tcoil ≤ 28 mm) wound from the formvar-insulated NbTi wire.Differ from the fiberglass-insulated Nb3Sn wire, the formvar insulated NbTi provide a relative smooth wire surface, which does not absorb the epoxy resin. This significantly increases the difficulties of vacuum pressure impregnation (VPI) for a thick close-packed NbTi coil. With the purpose of understanding the applicable of current VPI procedure on formvar insulated NbTi coils, a close-packed solenoidal magnet wound from the formvar insulated NbTi is wound, vacuum pressure impregnated and cryogenic measured at the Institute of Plasma Physics (ASIPP), Chinese Academy of Sciences (CAS). The design aperture of the magnet is 72 mm, with coil thickness of 28.75 mm and coil height of 180.5 mm, the magnet is expected to generate a 7.04 T central magnetic field with an operation current of 170 A at 4.2 K. The excitation results show that the central magnetic field of the NbTi coil impregnated with current VPI procedure is able to reach 7.35 T with no quench under an operation current of 176 A. The loadline is close to 98.96% of the NbTi wire.

Development of An Analytical Method for Design of Electromagnetic Energy Harvesters with Planar Magnetic Arrays

In this paper, an analytical method is proposed for the modeling of electromagnetic energy harvesters (EMEH) with planar arrays of permanent magnets. It is shown that the proposed method can accurately simulate the generation of electrical power in an EMEH from the vibration of a bridge subjected to traffic loading. The EMEH consists of two parallel planar arrays of 5 by 5 small cubic permanent magnets (PMs) that are firmly attached to a solid aluminum base plate, and a thick rectangular copper coil that is connected to the base plate through a set of four springs. The coil can move relative to the two magnetic arrays when the base plate is subjected to an external excitation caused by the vehicles passing over the bridge. The proposed analytical model is used to formulize the magnetic interaction between the magnetic arrays and the moving coil and the electromechanical coupling between both the electrical and mechanical domains of the EMEH. A finite element model is developed to verify the accuracy of the proposed analytical model to compute the magnetic force acting on the coil. The analytical model is then used to conduct a parametric study on the magnetic arrays to optimize the arrangement of the PM poles, thereby maximize the electrical power outputted from the EMEH. The results of parametric analysis using the proposed analytical method show that the EMEH, under the resonant condition, can deliver an average electrical power as large as 500 mW when the PM poles are arranged alternately along the direction of vibration for a peak base acceleration of 0.1 g. A proof-of-concept prototype of the EMEH is fabricated to test its performance for a given arrangement of PMs subjected to vibration in both the lab and field environments.

Experimental and computational study of the equivalent thermal conductivity coefficient when heating a strip coil

Heating of layered metal cages in bell furnaces, for example, stops from strip coils, due to the presence of gas gaps between the layers in them, leads to an increase in the temperature drop in the radial direction with a simultaneous temperature drop along the height of the charge. An accurate calculation of the heating time of the charges of strip coils requires knowledge of the temperature field in them, and, consequently, the radial equivalent coefficient of thermal conductivity and the end coefficient of thermal conductivity, on which the consumption of electricity, fuel and the performance of the furnace will depend. The formula and method for calculating the equivalent coefficient of thermal conductivity in the radial and end directions of ta strip coil are proposed, based on the numerical solution of the differential equation of thermal conductivity using an explicit difference scheme, a constant coefficient of thermal conductivity and boundary conditions of the first kind, suggesting the useof its experimental values as the tem perature of the roll surface at various points in time. The values of the thermal conductivity coefficients calculated according to the proposed formula and methodology were confirmed by experimental laboratory heating of a 0,3 mm thick steel strip coil made of electrical steel E3412; height, inner and outer diameters of the coil, respectively: 52,0; 51,882; 79,667 mm; with the number of tape layers per side equal to 46; with a filling coefficient of 0,86 and the degree of contact of layers – 2,9%. The strip coil was heated both together with the furnace to a temperature of 920 °C, and when it was loaded into a preheated furnace to a temperature of 620 °C, followed by heating to 920 °C and holding. When forming the charges, two heating options were carried out: radial and end heating.

A Three-Coil Setup for Controlled Divergence in Magnetic Nozzle

Magnetic nozzles with their contactless feature have opened new grounds for long-distance space travels. For quicker mission completions along with improving system reliability, it becomes necessary to design robust systems that exhibit the ability to confine thrust. A semianalytical numerical method is proposed for rapid and assumption-less calculations of the magnetic field because of a thick coil with rectangular cross section. The method is extended for the proposal of a three-coil setup, where divergence angle of the magnetic field lines is readily controlled in-flight to provide the flexibility to modify the output magnetic thrust and the nozzle's efficiency.

Design of Heating Coils Based on Space-Filling Fractal Curves for Highly Uniform Temperature Distribution

Heating coils utilize the concept of resistive heating to convert electrical energy into thermal energy. Uniform heating of the target area is the key performance indicator for heating coil design. Highly uniform distribution of temperature can be achieved by using a dense metal distribution in the area under consideration, however, this increases the cost of production significantly. A low-cost and efficient heating coil should have excellent temperature uniformity while having minimum metal consumption. In this work, space-filling fractal curves, such as Peano curve, Hilbert curve and Moore curve of various orders, have been studied as geometries for heating coils. In order to compare them in an effective way, the area of the geometries has been held constant at 30 mm × 30 mm and a constant power of 2 W has been maintained across all the geometries. Further, the thickness of the metal coils and their widths have been kept constant for all geometries. Finite Element Analysis (FEA) results show Hilbert and Moore curves of order-4, and Peano curve of order-3 outperform the typical double-spiral heater in terms of temperature uniformity and metal coil length.

Conditions for numerically accurate TMS electric field simulation

BackgroundComputational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking. ObjectiveTo ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup. MethodWe benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods. ResultsTo achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled. ConclusionBEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

Seismic response control of multi-story base-isolated buildings using a smart electromagnetic friction damper with smooth hysteretic behavior

Abstract This paper studies the use of a smart/semi-active electromagnetic friction damper (SEMFD) for the control of seismic response of multi-story base-isolated buildings. The SEMFD consists of a ferromagnetic plate and two similar arrays of thick rectangular ferromagnetic-core coils (FCs) connected in series. The FCs are attached to the two sides of the ferromagnetic plate through two non-magnetic friction pads. The force in the damper is developed because of the friction between the friction pads and the ferromagnetic plate when the FCs moves relative to ferromagnetic plate. The normal force between the friction pad and the ferromagnetic plate is caused by the attractive magnetic interactions between the FCs arrays and the ferromagnetic plate. The magnitude of this force is controlled by a proposed semi-active controller that is capable of varying the current flowing through the FCs in such a way that it is able to avoid stick-slip motion by smoothing the nonlinear hysteretic behavior of the SEMFD. The capability of the SEMFD and the proposed semi-active controller to control the seismic response of base-isolated buildings is demonstrated by implementing them into the dynamic model of a six-story base-isolated building supported on lead-rubber bearings (LRBs). The numerical results show that the SEMFD and its semi-active controller are capable of limiting the displacement of the base floor without noticeably increasing the inter-story drifts and absolute accelerations of the floors. It is demonstrated that the parallel actions of the LRBs and the SEMFD in the base floor create a smart base isolation system that is capable of fully protecting a multi-story building from ground motions with intensities at a level as that of the ASCE 7–10 Maximum Considered Earthquake (MCE).

Miniaturized 3-D Cross-Type Receiver for Wirelessly Powered Capsule Endoscopy

This paper presents the modeling, implementation, and testing of a cross-type receiver (RX) used for wireless power transfer (WPT) into an endoscopic capsule. A 3-D configuration for the receiver is proposed to increase the wireless link power transfer efficiency (WL-PTE) and enhance its robustness to angular variations of the capsule. The diameter and thickness of the flexible transmitter coils are 200 mm and $185~\mu \text{m}$ , respectively. The diameter of the miniaturized RX is 8 mm, which is appropriate for integration within current commercially available capsules. Experimental results demonstrate a WL-PTE of 1.3% and complete system efficiency of 0.9% inside a suitable tissue phantom of the relative permittivity of 300 at 5 MHz. A maximum variation of only 8.4% of the WL-PTE across 90° orientation of the RX was also measured. The minimum WL-PTE of 1% is the recorder for 7-cm translational displacement inside the phantom. A simulated specific absorption rate of 0.86 W/Kg was calculated, which is well below the limit allowed for medical applications. A maximum temperature variation of 2.2 °C was also measured for an operating duration of 10 h, which is typical of a capsule journey inside the gastrointestinal tract. The proposed system represents a viable proposition for WPT in capsule endoscopy.

Note: Parametric tuning of the Helmholtz coil and its optimal designs with thick winding pairs

Thick winding pairs are generally utilized in high-power Helmholtz coil systems, where the coil-heating and insulation are usually of concern for their field uniformity. Beyond the ideal thin model, we discuss the field uniformity of thick Helmholtz coils and their optimal designs based on the numerical and experimental analysis. Furthermore, the design tuning parameters, i.e., ampere-turn configurations, are introduced to the numerical models to investigate their influence on the magnets’ field uniformity. The results show that different ampere-turn realizations of one ideal Helmholtz coil could induce up to ∼30% uniformity variation within the central region. Regardless of whether it is the conventional Helmholtz coil or its optimal designs, the increase in layer number and axial insulation gaps tends to improve the field uniformity. However, the increase in turns per layer results in a great reduction in their field uniformity. By optimizing the ampere-turn arrangement, it is possible to further improve the performance of a Helmholtz-coil-based magnet.

Calculation of some electromagnetic quantities for circular thick coil of rectangular cross‐section and pancake with inverse radial currents

Here, the new expressions for the mutual inductance and the magnetic force between two Bitter coils (thick coil and pancake) with the inverse radial current densities are presented. These types of coils are used for producing the high magnetic fields. For producing strong magnetic fields, the coils are extremely heated, so that they could be cooled to avoid this problem. During a water-cooled magnet trip, the induced current in coil changes as a function of decay time constant which is determined by the self-inductance and the resistance of the water-cooled magnet. Moreover, such high fields develop the strong magnetic forces which can cause the mechanical stress upon the supporting structure. This way the precise evaluation of these electrical quantities between coils must be calculated to optimise the support structure of Bitter coils. With the newly presented approach, these quantities are obtained in an analytical and semi-analytical form expressed over elliptical integrals and simple integrals. For validating this method, the comparative improved filament method is used.

Mutual inductance and magnetic force calculations between thick bitter circular coil of rectangular cross section with inverse radial current and filamentary circular coil with constant azimuthal current

In many engineering applications, the coils of different geometrical shapes are used. Usually, these coils (circular, right etc.) are with the constant currents in different directions. In the literature, there are many papers on the calculations of the magnetic fields of the circular coils with the constant azimuthal currents or the calculations of the mutual inductance and the magnetic force between them. In some applications, where the high intensity magnetic fields are required the circular metal plates and insulating spacers are used with the inverse radial current. Such configurations form an electromagnet named after its inventor Bitter. In this study, the authors calculate the mutual inductance and the magnetic force between the thick Bitter coil of rectangular cross-section with the inverse radial current and the circular filamentary coil with the constant azimuthal current. The semi-analytical and the analytical expressions of these quantities are obtained over complete elliptic integrals of the first and second kind as well as Heuman's lambda function. There is one simple integral which has to be solved numerically. The results of this method are compared by those obtained by the modified filament method for the presented configuration. All results are in an excellent agreement.

Experiment and Numerical Simulation on Quench Characteristics of ReBCO-Impregnated Coil

The SuperKEKB project underway at KEK will increase the KEKB luminosity by 40 times using nanobeam interaction-region focusing optics. The chromaticity correction of the collision beams is crucial to achieve the high luminosity. Sixteen special sextupole magnets, which can simultaneously produce normal and skew sextupole fields, are required in the 100-m-long straight sections around the interaction point for the chromaticity correction. As a candidate for the sextupoles, a cryocooled high-temperature superconducting (HTS) magnet was proposed and the development has started. In HTS magnets, quench protection is a major concern. Especially for accelerator magnets, reliable quench detection and protection systems are essential. In this study, we have performed heat-induced quench tests and numerical simulations on the ReBCO-impregnated double pancake coils at operating temperatures of 30, 40, and 50 K. Two test coils with different thickness of the copper stabilizer were prepared for the tests to compare the quench characteristics. The hot spot temperature was discussed with the operating conditions and quench detection criteria. The copper stabilizer thickness of the sextupole ReBCO coils was designed by using the validated numerical model.

Calculation of mutual inductance and magnetic force between two thick coaxial Bitter coils of rectangular cross section

The mutual inductance and magnetic force between coaxial Bitter coils with rectangular cross section were recently calculated by some authors using semi-analytical expressions based on two integrations (Ren et al.) and by using the Bessel function approach (Conway). In this study, these important electrical quantities are calculated using the analytical and semi-analytical expressions based on elliptical integrals of the first and second kinds, Heuman's Lambda function, and two simple integrals with their kernel functions continuous on the whole integration interval. Simple Gaussian numerical integration is used. This method can be applied to calculate the mutual inductance and magnetic force between two thin Bitter disk coils (pancakes) as well as between two Bitter coils, where one has a rectangular cross section and the other is a thin disk (pancake). The calculations of the mutual inductances and magnetic forces are validated by comparison with values already published in the literature. The presented approach has advantages of high accuracy and low computational time.

HIGH-TUNING RANGE FERROFLUID-BASED SOLENOID INDUCTOR FOR WIRELESS LOCAL AREA NETWORK (WLAN) APPLICATIONS

In this work, a high-tuning range ferrofluid-based liquid solenoid inductor is proposed. This project utilized the light hydrocarbon-based ferrofluids (EMG 901 660mT type) with magnetic permeability of 5.4. The liquid is injected into the channel of the designed solenoid inductor to improve the tuning range and quality factor of the device. This is achieved by several tuning methods; by changing the number of turns, the thickness and width of copper coils, the cross-sectional area of ferrofluid across the channel and the self-resonance frequency (SRF). The proposed tuning solenoid inductor is simulated using a 3D full-wave electromagnetic field tool, ANSYS HFSS. The simulation is done by injecting the ferrofluid liquid into the channel by a step of 20% until it reached 100%. The inductance values are set to be tuned at a frequency of 2.45 GHz. The simulation results show the inductance values can be tuned from 4.5 nH to 15.2 nH with a maximum quality factor of 25. On the other hand, for tuning capability, the inductor is capable to be tuned with high tuning range of up to more than 200%.

Analytical Modeling of AC Resistance in Thick Coil Integrated Spiral Inductors

In this paper, an analytical model for calculating the ac resistance due to the proximity effect in thick coil integrated spiral inductors is proposed. Based on 2-D Maxwell’s equations, the redistribution of magnetic field and current in the coils caused by the proximity effect is modeled, and the ac resistance of the inductor is extracted. The analytical model is compared with both numerical simulations and experimental results. The ac resistance calculated by the model is good (within 14.8% discrepancy) up to the frequency of the peak quality factor for thick coil integrated spiral inductors.

A new formula for calculating the magnetic force between two coaxial thick circular coils with rectangular cross-section

The magnetic force exerted by an array of two coaxial thick circular coils with rectangular cross-sections in air is important to both electrical and mechanical engineering applications. The magnetic force is typically calculated by taking the integral over the entire space defined by the array. This calculation even for this simple array is an intractable problem and numerical methods have been extensively used. In this work, the integration was subdivided into five regions, and in four of them, an analytical formula was found. The method proposed here is based on the Green’s function of the free space that leads to the elliptical integral of the first and second kind. The formula reveals new insights into how the geometry and relative positioning of the coils within the array determines the strength of the magnetic force. The thicker the coils are and the farther apart they are, the weaker the magnetic force is, and vice versa. This new formula is simpler and practically free of truncation errors, which are commonly encountered in numerical approximations. Several examples from the literature were used to corroborate the present formulation. The results show an excellent agreement with respect to the different numerical and semi-analytical approaches used by other authors.

Mutual inductance for circular coils of rectangular cross section and parallel axes shielded by two parallel screens of high permeability

The mutual inductance for the coils mentioned in the title is given in this paper, which is the generalization for the calculation method of the mutual inductance of the circular coils in the free space. Starting with the Bessel integral representation of the vector potential of a circular ring, the integral expressions of mutual inductance of the shielded circular rings with parallel axes are given by the calculation of the mutual magnetic energy, and the results are further continued analytically to the complex plane by introducing the Hankel function of the first kind, and then solved via the residue theorem. Additionally, the mutual inductance of the shielded thick coils is found based on the obtained results of the circular rings. Finally, the numerical results of the presented method are compared with those of the Finite Element Method simulations, and our method is confirmed by the good agreement between them in the numerical computations.

Optimisation Design of a Taguchi-Based Real-Code Genetic Algorithm for Thermal Reducing of Air-Core Linear Brushless Permanent Magnet Motor

This study combined the Taguchi method with the genetic algorithm (GA) to analyse the optimal design parameters of the thermal distribution in an air-core linear brushless permanent magnet motor (ALBPMM). First, this study adopted an L18(21×37) orthogonal array to determine the significant factors, including active currents, the length of magnets, pole distance of magnets, air-gap length, and thickness and width of coils. Then, the study uses response surface methodology (RSM) to construct the predictive model. Finally, the optimal combinations of design parameters that involve using real-code GA were obtained and verified by finite element modelling. The simulation results show that the thermal distribution in the optimal design of parameters is 41% more effective than that of any models in which the parameters are not optimised. Therefore, the proposed approach can be used as the basis for designing and predicting the temperature effects of the ALBPMM..