Coil Cross-section Research Articles

Optimal design of thick-walled circular coils for uniform magnetic field generation

Abstract Uniform magnetic field coils are widely used as electromagnetic equipment in industrial, medical, and research applications, with Helmholtz coils being a common configuration. For applications requiring a relatively high magnetic field (∼mT), Helmholtz coils typically feature a large coil cross-section. However, this characteristic makes them unsuitable for describing the magnetic field generated by a current loop model during the design process. In this work, we model the magnetic field of a large cross-section Helmholtz coil system, often referred to as a thick-walled Helmholtz coil. By employing a genetic algorithm, we transform the design problem of a Helmholtz coil into a constrained optimization problem. Subsequently, we propose a method for reverse designing a Helmholtz coil based on constraints on the target magnetic field. Finite element simulations verify the accuracy of the established magnetic field calculation model in describing the magnetic field generated by the thick-walled Helmholtz coil. Moreover, the designed Helmholtz coil effectively meets the design constraints and objectives. This method addresses the issue of significant errors in calculating the magnetic field and its uniformity resulting from the cross-sectional effect during the design of thick-walled Helmholtz coils. Furthermore, it satisfies the constraints for coil operating time and lightweight design.

Miniaturized S-shaped flexible magnetic pulse welding coil design for engineering applications

Magnetic pulse welding (MPW) as a new solid-phase welding technology in the manufacturing field has vast application prospects. However, the application of MPW in engineering is severely limited by the large working area required for existing coils resulting in poor flexibility of the process. In this paper, a highly flexible, miniaturized S-shaped stereoscopic coil was proposed to reduce the working area required for the MPW process. The required working area was reduced to 32 × 30 mm. Numerical simulations were performed to determine the most suitable coil cross-section size. In addition, the feasibility of the coils was verified by welding AA5052 aluminum alloy and 316 L stainless steel through the new stereoscopic coils. Quasi-static tensile testing, laser microscopy, Scanning Electron Microscopy (SEM) and Energy Dispersive Spectrometer (EDS) were used to characterize the mechanical properties of the joints, weld interface morphology and element diffusion, respectively. It was revealed through simulation that the impact velocity of the new stereoscopic coil during MPW (342 m/s) was slightly higher than that of the conventional flat coil (327 m/s) at the same discharge energy. This indicated that the coil could achieve reliable welding. The AA5052-316 L joint welded by the new stereoscopic coil was demonstrated to be reliable by experiments. Furthermore, microscopic observation revealed that two effective bonding regions were formed at the interface. In addition, continuous interfacial waves and element diffusion were observed at the welding interface. Finally, the typical parts of AlFe double-cap beam structure were successfully welded by using a new stereoscopic coil. The coil is beneficial to broaden the application field of MPW.

Model of Ferrite-cored Driver-pickup Coil Probe Application of TREE Method for Eddy Current Nondestructive Evaluation

An analytical model of a driver-pickup coil probe, consists of a cylindrical ferrite core, located above a layered conductor is presented. The truncated region eigenfunction expansion (TREE) method is used and the solution region is truncated with a certain radius around markedasmathitalicz axis. First, the magnetic vector potential of each region of filamentary coil problem is derived and solved with variables separation method using boundary and interface conditions, and then the rectangular cross-section coil problem is solved with superposition method. The expression of induced voltage in pickup coil is obtained and can be calculated with software such as Matlab or Mathematica. Using the proposed analytical model, the influence of the excitation frequency and excitation current in the driver coil on the responses of the pickup coil is examined. Experiments are performed, and the changes of voltage induced in the pickup coil due to the conductor are measured at different excitation frequencies and excitation currents. The analytical calculation results agree with the experimental results very well, verifying the correctness of the proposed analyticalmodel.

Magneto-Mechanical Optimization of Cross-Sections for $ \text{cos}(\theta)$Accelerator Magnets

The cross-sectiondesign of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cos (\theta)$</tex-math></inline-formula> superconducting magnets is historically developed in a two-step process: initially, the coil geometry is defined on the basis of magnetic optimizations; then, the structure is designed around the coil. The first step searches for the best coil cross-section maximizing the magnetic field, margin, field quality and conductor efficiency. The latter step aims at limiting the coil stresses and deformations. However, the coil design, defined with the initial magnetic optimization, can influence the mechanical behaviour of the magnet, altering, for example, the peak stress during operation. As the critical current is a function of the applied strain, the mechanical implications of the coil cross-section design can limit the achievable performance. In this paper we propose an integrated optimization process that targets the peak stress on the conductor in addition to the magnetic objectives. The results are presented for a sample high-field 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 dipole: a 4-layer design aiming at ultimate conductor performance.

A novel understanding of circular four-coil configuration for uniform magnetic field generation

The uniform magnetic field is widely used in sensors and other laboratory devices. The four-coil configuration has the advantage of open space and good uniformity. Traditional schemes include Lee-Whiting, Tetracoil, Braunbeck, etc. The first two schemes have rounding errors of coil turns. The Braunbeck configuration avoids rounding errors, but the structure is solidified and cannot meet the requirements of flexible sensors. In this study, we derive a general constraint equation that fits various four-coil configurations and show that the constraint parameter uniquely defines the configuration. Moreover, we develop a simple optimization approach that allows building the optimized configuration that lacks rounding errors of coil turns. We analyzed system performance for different coil cross sections and configurations. The comparison of the original Lee-Whiting and optimized coils revealed that the normalized maximum radius Rmax increased by 7.67%. Finally, the increase in cross-section resulted in performance that was principally different from classical models. The proposed approach makes both scientific and educational contributions for future studies.

Improvement of Transverse-Flux Machine Characteristics by Finding an Optimal Air-Gap Diameter and Coil Cross-Section at the Given Magneto-Motive Force of the PMs

This paper presents analysis and study of the single-phase transverse-flux machine. The finite element method results of the machine are compared with the laboratory measurements to confirm the accuracy of the computer model. This computer model is then used to investigate the effect of the machine’s geometry on its output characteristics. Parametric analysis of the machine is carried out to find the optimal air-gap diameter at which the cogging torque of the machine is minimal. In addition, the influence of the coil cross-section on the torque and output power characteristics of the machine is investigated and discussed.

Thermally induced bias error due to strain inhomogeneity through the fiber optic gyroscope coil.

One of the performance limits of a navigation grade fiber optic gyroscope is the bias error due to the thermal sensitivity of the fiber coil. Thermal stress inside the fiber coil is an important source of the bias error. The reduction of the total stress inside the fiber coil can be limited. In this paper, it is shown that further improvement can be achieved by controlling the strain inhomogeneity through the fiber coil. A validated simulation environment is presented for strain distribution analysis. Thermally induced bias error formation mechanisms are compared. The effect of the strain inhomogeneity is reduced by presenting a different coil cross section and spool material. Experiments utilizing a coil design with better performance are presented for the verification of the approach.

Numerical study on turbulent heat transfer performance of twisted oval tube with different cross sectioned wire coil

This work numerically explores the thermal-hydraulic performance of twisted oval tube with three cross sectioned wire coils including circular, equilateral and square cross sectioned wire coils in turbulent regime. The effects of geometric shape, direction of rotation and the orientations of wire coil's cross section were also investigated. Polyhedral mesh is adopted and water is used as working fluid. The obtained results are compared with those of the twisted oval tube without wire coils. Our results show that using twisted tube and wire coil together can further enhance heat transfer rate and pump consumption while the PEC decreased. Compared with twisted oval tube only, the equilateral cross sectioned wire coil has the best thermal-hydraulic performance. The averaged increase ratio of Nu is 45.92% and the averaged f is 674.86%.

TFC-PREDIM: A FE dimensioning procedure for the TF coil system of a DEMO tokamak reactor

Abstract The equatorial plane of the inner leg of a toroidal field (TF) coil is the most stressed part of the TF coil system and optimal usage of the radial space in this region is crucial for the design of the DEMO tokamak reactor. A procedure for initial dimensioning (pre-dimensioning) of this region developed earlier [ 1 ] is based on a simplified 2D geometry of the TF coil cross-section and a semi-analytical approach to estimate stresses in the TF coil case and the conductor jackets with limited capabilities for optimization. This work presents a new procedure named TFC-PREDIM which features a detailed 2D finite element (FE) generalized plane strain model. The model gives very accurate results within a short calculation time and allows additional options for layout optimization. The FE model for the cross-section is generated automatically from the input geometrical parameters of the given layout allowing any of the conductor design options currently investigated for DEMO. The post-processing of the results is also automated, consisting in the determination of the maximum values of the membrane and membrane + bending Tresca stresses for each conductor jacket and for the TF coil case. Two strategies for the optimization of the cross-section are presented: minimization of the TF coil radial build with a predefined maximal toroidal field and maximization of the maximal toroidal field for a predefined radial space.

Experimental investigation of heat transfer and pressure drop inside elliptic tube with inserted helical coils

The paper deals with an experimental study of the influence of varying helical coil cross section diameter and pitches of helical coil on heat transfer and friction characteristics in an elliptical tube. The present work studies the effects of copper helical coils of circular cross section formed with different diameters of 2 and 6 mm at varying pitches (20, 45, 135 and 225 mm) inside elliptic tube. In the experiments, cold air at ambient condition is passed through the uniform heat flux circular tube for Reynolds numbers in a range of 11000 to 37500. The experimental results demonstrate that the use of helical coil inserts in elliptic tube leads to a higher heat transfer rate than that of the plain surface tube. Also, increasing helical coil cross section diameter and decreasing pitches of the helical yield a better heat transfer than the plain tube. The enhancement efficiencies of the helical coil cross section 6 mm over wire cross section 2 mm diameter at a pitch of 20 mm is 2.3% at Re=11000. The results are also correlated in the form of Nusselt number, friction factor and enhance efficiency as a function of Reynolds number, pitches and diameter of helical coil

Reduction of AC Loss in HTS Coils of Superferric Magnets for Rapid-Cycling Synchrotrons by Changing Cross-Section of Coils and Iron Yoke Geometry

We have been studying the potential of energy consumption reduction in rapid-cycling synchrotrons (RCSs) by using superferric magnets with coils wound with high temperature superconductor (HTS). By conducting three-dimensional electromagnetic field analyses on superferric magnets with different coil cross-sections and iron yoke geometries, ac loss of each magnet design was estimated. Rough estimations of the iron loss were also conducted to obtain overall energy consumption of each magnet design. By the comparison, influence of coil cross-section and iron yoke geometry on electricity consumption of the magnet were evaluated.

Power efficiency analysis in various types of coil design

The efficiency of power produced by magnetic flux in the coil has been analysed using various forms of coil section. Magnetic flux was produced by magnets which were moved radially with a certain rotational speed. Meanwhile, a coil placed close to the magnets will produce an electromotive force (emf) according to Faraday’s law. Besides affecting the magnitude of emf, the shape of coils also affected the power loss due to partial of magnetic field radially dispersed or didn’t go through a coil cross-section. It caused only a portion of the magnetic field would be converted. Therefore, this study aims to reduce the power loss by various type of coil design i.e. round-shaped coil, square-shaped coil, and cone-shaped coil. The coil was formed by the same wire with a length of 60 m to produce the same resistance. The results showed that at a speed of 1100 rpm, the voltage which obtained using round-shaped coil, square-shaped coil, and cone-shaped coil respectively of 1.26 V and 1.01 V and 1.5 V and 1.88 V.

Design of Lightweight Superconducting Magnets for a Rotating Gantry With Active Shielding

In order to reduce the weight of superconducting magnets used in a rotating gantry for heavy particle radiotherapy, the design study of a cosine-theta superconducting magnet with active shielding was conducted. The superconducting magnet with active shielding was composed of a dipole coil and an active shield coil. The cross-section of each coil was designed, based on a cosine-theta current distribution made by the arrangement of a superconducting wire with NbTi filaments. The result of the design study indicated that the designed coil cross-sections can meet the requirements regarding the magnetic field distribution and the load factor for the magnet operation. Additionally, the weight of the superconducting magnet with active shielding was evaluated while comparing that of the superconducting magnet with an iron yoke. As a result, the superconducting magnet with the active shielding has a possibility to reduce the weight significantly.

Magnetic Field Design of a Full-Scale Prototype of the HL-LHC Beam Separation Dipole With Geometrical and Iron-Saturation Corrections

High Energy Research Organization (KEK) has developed three short-scale model magnets of the beam separation dipole, MBXF, which is to be installed for the High Luminosity Large Hadron Collider, HL-LHC, in CERN. We will soon undertake production of a prototype of MBXF and its magnetic design has to be finalized before the fabrication. We established a strategy for designing the new coil cross section by taking into account different error sources for its field quality. In this paper, focused on b 3 , we describe how the final b 3 integral, which should be within 2.9 units according to the acceptance criteria, is achievable.

Магнитное поле неидеальных катушек Гельмгольца

The importance of testing electronic devices for the influence of a constant magnetic field is substantiated. The magnetic field induced by Helmholtz coils having a finite rectangular cross-section is investigated. An analytical expression for the magnetic field at the axis of a finitely thick solenoid and for the magnetic field at the axis of Helmholtz coils with a rectangular cross-section is derived. In the particular case of using Helmholtz coils with a square cross-section, the condition under which the magnetic field second derivative along the system symmetry axis at the system center becomes zero is numerically analyzed, based on which the distance between the coils with a square cross-section at which the field in the system center is the most uniform is found. It is shown that consideration of coil cross-section finite dimensions results in obtaining a somewhat different optimal distance between the coils. A table of optimal distances for Helmholtz coils with a square cross-section having different thickness values has been drawn.

Flat Spiral Coil Design for Higher Riveting Force and Energy Saving in the Electromagnetic Riveting Process

AbstractElectromagnetic riveting (EMR) belongs to the green manufacturing process, which has the advantages of low noise, no pollution, and large riveting force. In this paper, the influences of structural parameters of a flat spiral coil on riveting force and energy saving were investigated, and the cross-section geometry, base angle, and height of the coil section were designed. The EMR simulation models with fully coupled electromagnetic–thermal–mechanical were built in ls-dyna software, and the riveting force was adopted to assess the performances of different types of coils. The results showed that the riveting force given by trapezoid cross-section coil was the largest compared with rectangular, pentagonal, and circular types. Moreover, the increase in the base angle and height of the coil section had a positive effect on improving the riveting force and energy saving. In addition, weights analyses showed that the contribution rates of three structural parameters (length of the bottom edge, base angle, and height) of the coil to energy saving were 0.5231, 0.2347, and 0.2422, respectively. In general, the riveting force was improved and discharge energy was saved by adjusting geometric parameters of the coil. The research could provide guidance for the coil design in the EMR process.

Magnetic and Mechanical Design of a 15-T Large Aperture Dipole Magnet for Cable Testing

A large aperture Nb3Sn dipole is proposed to replace the magnet assembly of EDIPO, which was irreversibly damaged in 2016. The goal is to generate a background field of 15 T at 4.2 K in a clear aperture of approximately 100×150 mm2 and over a uniform length of 1000 mm in order to test superconducting cables for both fusion and high-energy physics applications. The magnet features a block-type coil design wound with wide Rutherford cable (two alternative coil cross sections are considered) and supported by a mechanical structure based on keys-and-bladders technology. In the end regions, the coils tilt up (flare) through a hard-way bend of the cables to provide room for the test well, following a layout already adopted in the LBNL HD2 and CERN-CEA FRESCA2 magnets. The two considered coil design alternatives aim at minimizing the mechanical stress in the coil windings. One coil pack design makes the use of two double pancake coils per pole, whereas the other alternative features three double pancakes per pole. Both design options are presented focusing on the results of numerical computations carried out with finite-element models to investigate peak stresses in the coils during room-temperature pre-loading, cool down, and powering.

Magnetization Model and Detection Mechanism of a Microparticle in a Harmonic Magnetic Field

Inductive particle sensors are widely used in online wear condition monitoring. Understanding the behavior of a particle magnetized in an alternating current (ac) magnetic field and the associated sensing mechanism is fundamental to identifying the particle size, improving the detection precision and enhancing the sensor performance. Here, we first establish a particle magnetization model related to particle conductivity, permeability, diameter, and field frequency. Next, an expression for particle detection using inductance is derived that consists of a product of the particle volume, complex particle susceptibility, and particle sensor sensitivity. The derived formulas and experiments reveal that the output of the inductive sensor is a complex number. Therefore, a vector analysis method is proposed for inductive particle detection. The sensitivities of various sensors are discussed. Experiments are conducted using milliparticles and microparticles in various positions relative to sensors. A comparison of the calculation results with the experimental results exhibits satisfactory agreement. Consequently, an optimized rectangular cross-section of coils is proposed. This study provides a theoretical basis for the design and optimization of particle sensors based on magnetic principles.

Design optimization and experiment of a disc-type MR device considering the centrifugal effect and plug flow region

Magnetorheological (MR) technology has received tremendous attention, which is playing more and more roles in modern industry. In order to give full play to advantages of the MR devices, a good design is of great importance for a high-performance MR device. This work introduces the centrifugal effect (CE) and plug flow region (PFR) into disc-type MR devices’ design for obtaining a higher design accuracy. And, a novel structure with trapezoidal cross section coil is proposed for the design of disc-type MR devices to improve the magnetic field distribution. With this structure, a disc-type MR damper is designed and optimized with consideration of the CE and PFR. The optimal result is analyzed to demonstrate the influence of the CE and PFR. And, the advantages of the proposed structure are displayed by a contrast simulation. Finally, a prototype is manufactured and tested to verify the designed MR damper. The results show that the proposed structure can achieve a better magnetic field distribution for improving the material utilization. And, when considering the CE and PFR, the relative error between the calculated torque and the tested value is steady though the velocity changes. It is smaller than the half of the relative error between the torque of traditional calculation and the tested value. These reveal a more accurate design can be achieved for disc-type MR devices by considering the CE and PFR

Numerical study on electromagnetic crimping of tubes

Electromagnetic crimping process is a non-conventional, high energy, high-velocity, and solid state impact crimping process. In this process, high energy and high-density electromagnetic field were used to accelerate and impact the flyer tube onto the base tube. A sequential coupled electromagnetic field analysis of electromagnetic crimping was performed using finite element method and boundary element method in the LS-DYNA software. In this study, three types of actuators having cross-sections namely circular, rectangular and square were modelled and analysed for electromagnetic crimping of aluminium Al 3003 and 4340 steel tubes. For this study, the length, number of turns, the pitch and the magnitude of a cross-sectional circumference of the actuators were kept constant. Process parameters such as discharge voltage, standoff distance, and actuator cross-section were varied in this study. Properties like a magnetic field, plastic strain, current density, radial deformation, impact velocity, Lorentz force and Tresca maximum shear stress developed in the flyer tube were compared with all three types of actuators and it was found that the actuator with square cross-section gives the better results. From this study, it was observed that the use of the square cross-section coil is more efficient than that of the circular or rectangular cross-section.