Coil Model Research Articles

Radiofrequency Coil Tuning Using Matching Circuit Co-Simulation with Magnetic Resonance Integral Equations

Abstract The proposed extension to the conventional circuit co-simulation (CCS) method reliably and efficiently introduces arbitrary matching networks into CCS routines and is here dubbed as matching circuit co-simulation (MCCS). It further achieves coil tuning for resonance and an optimum scattering parameters condition that resembles a fully matched coil. Combined with magnetic resonance integral equations (MARIE), the proposed MCCS further accurately produces a full EM simulation of the coils. We first validated MARIE with the MCCS routine to use it to model simple single-channel coils and parallel transmit (pTx) head arrays coupled with Duke, a digital human body model. Having successfully validated the MCCS routine, we swept through both tuning and matching network parameters to optimize the coil. While optimizing for all parameters simultaneously is a viably efficient option for coil models of low complexity, these models are not realistic, and we found that it becomes a highly computationally expensive problem to solve for more complex coil geometries, such as birdcage coils and pTx coils with higher number of channels, especially when shielding is included. Consequently, we separated tuning and matching into two steps, by first tuning the coil to the right frequency, and then introducing matching networks to enhance the power transmission into the body. We observed lower on-diagonal S-parameters after matching in all pTx coils, but 1 coil still had strong cross-coupling. Finally, electromagnetic fields obtained via MARIE for separate port excitation were successfully combined using MCCS.

Double-pancake superconducting coil integrated with DFIG-based wind power systems under voltage-dip events: Design and performance analysis study

The doubly fed induction generator (DFIG)-based wind turbine provides massive development in power generation. Uncertain power oscillations and voltage-dip events affect the stability of the DFIG. To mitigate the effect of voltage-dips in short period, superconducting magnetic energy storage (SMES), which possess rapid energy exchange and high power density, is integrated with large-scale renewable power systems. SMES is integrated at the DC link of the DFIG to ensure the power balance and fault ride-through (FRT) capability. During this operation, frequent current changes occur in the high-temperature superconducting (HTS) coil, which leads to an increase in AC losses. As a remedy, an additional power converter structure controlled with a model-predictive controller (MPC) is proposed. Firstly, a scale-down HTS double-pancake coil model is designed using a finite element model by which transport current loss and magnetic field formulation are studied. Additionally, the critical coil current is also verified through experimental studies. The effectiveness of the proposed MPC-based SMES integrated DFIG on DC link voltage and grid current under IEC-61000-4-11 standard, symmetrical and asymmetrical voltage-dip cases are investigated. The obtained results demonstrate that the proposed system effectively reduces transients in DC link voltage and improves the FRT capabilities of the grid.

Unconventional coil shape design of eddy current sensors and the effect of shape parameters on the micro/nano-scale metal film thickness measurement performance

Abstract The thickness of metal film is a critical parameter, especially in micro/nano-manufacturing, where high-precision measurement is essential. The eddy current method, a non-destructive testing technique, is well-suited for in-situ measurement of micro/nano-scale metal film thickness due to its superior performance. However, enhancing the measurement capabilities of eddy current sensors remains a significant challenge. In practical applications, thickness sensitivity and spatial resolution are two key performance indicators of eddy current sensors, and improving both simultaneously is difficult. While the sensitive element (coil) of an eddy current sensor has a substantial impact on thickness sensitivity, its effect on spatial resolution has received less attention.
This study establishes an eddy current coil model based on electromagnetic field theory, defining both thickness sensitivity and spatial resolution in the context of micro/nano-scale metal film thickness measurement. Two unconventional coil shapes are introduced, contrasting with the traditional cylindrical design, to investigate the influence of coil shape parameters, specifically the spatial distribution of the coil turns, on the key performance indicators. Simulation results are corroborated through experimental validation. Based on a series of calculations and analyses, an optimization method for coil shape parameters is proposed using a defined comparison factor that balances both thickness sensitivity and spatial resolution, which offers a promising approach for improving coil shape design.

Thermal quench modeling of REBCO racetrack coils under either alternating current or short-circuit voltage

Abstract Racetrack coils in REBCO High-Temperature Superconductor (HTS) motors help to increase the power-over-weight ratio by raising the magnetic flux density and output power. Nevertheless, HTS motors face thermal quench due to self-heating effects when subjected to alternating or short-circuit onset DC voltage. Additionally, thermal events have been observed due to screening currents when motors operate at high frequencies. Therefore, for the safe operation of HTS motors, quench research is crucial. To accurately simulate and analyze quench events in different scenarios, it is imperative to employ fast and precise software to numerically model the electrothermal behavior in racetrack coils. Our contribution involves the development of a novel and efficient model implemented in C++ that takes screening currents into account. This model is designed to conduct coupled electromagnetic and electrothermal analyses, utilizing variational methods. Specifically, the model incorporates both Minimum Electro-Magnetic Entropy Production and the Finite Difference Method. In this article, we explore the phenomenon of temperature rise within a racetrack coil subjected to either alternating or DC voltages of magnitudes ranging from 0.1 V to 1000 V. The study encompasses conditions of adiabatic operation and heat exchange with liquid nitrogen (LN2). Among other results, we found that in moderate DC voltages like 10 V, non-uniformity in the AC loss causes highly localized quench at the central turns. Then, screening currents play a key role also for DC voltages. The developed model exhibits the potential to comprehensively and swiftly analyze the electromagnetic and electrothermal characteristics of real-world superconducting applications, including high-field rotating machines, such as motors for aviation.

Safety and efficacy of targeting the supplementary motor area with double-cone deep transcranial magnetic stimulation vs figure-eight coil in treatment of obsessive-compulsive disorder with comorbid major depressive disorder

Background and objectiveThe Supplementary Motor Area (SMA), a relatively large brain structure predominantly located along the interhemispheric fissure, is an established target for repetitive Transcranial Magnetic Stimulation (rTMS) treatment of Obsessive-Compulsive Disorder (OCD). We investigated the feasibility, safety, and efficacy of targeting SMA using a double-cone “deep” TMS coil compared to conventional figure-eight coil for treatment of OCD with comorbid Major Depressive Disorder (MDD). MethodsSixty-two patients with treatment-resistant OCD and comorbid MDD participated in the study. All patients received high-frequency rTMS over the left dorsolateral prefrontal cortex (DLPFC) with a figure-eight coil (MagVenture B70), followed by 1 Hz rTMS over the bilateral SMA using either the B70 (N = 25) or double-cone deep coil (MagVenture DB80) (n = 23) for 36 treatment sessions. Weekly clinical assessments were conducted. ResultsSubjects overall had significant reductions in OCD and depressive symptom severity at the primary endpoint. Subjects stimulated at SMA with the double-cone deep coil had statistically significantly lesser reductions in overall OCD and depression symptom severity compared to the figure-eight group. The intensity of stimulation at SMA was significantly greater with the double-cone deep than figure-eight coil and e-field modeling showed that it affected broader regions beyond SMA (off-target stimulation). There was no significant difference in reported tolerability between groups. ConclusionsSMA stimulation using either a double-cone deep or conventional figure-of-eight coil was safe and was associated with a significant reduction in comorbid OCD and depression symptoms, but the higher intensities of stimulation with the double-cone deep coil used in this study were significantly less clinically beneficial than figure-eight coil stimulation.

Analysis of the Temperature Field Characteristics and Thermal-Induced Errors of Miniature Interferometric Fiber Optic Gyroscopes in a Vacuum Environment

This paper investigates the mechanism of thermal-induced errors in interferometric fiber optic gyroscopes (IFOGs) caused by temperature changes in a vacuum environment, proposing a method for calculating thermal-induced errors in small fiber coils. Firstly, based on the Shupe effect and the thermal stress caused by temperature changes around the fiber coil, a three-dimensional thermal-induced error model for small fiber coils is established. Secondly, a spatial fiber optic inertial measurement unit (IMU) model is designed using the Creo 3D modeling software (creo 7.0.0). The model is then imported into the Ansys finite element simulation software (ANSYS Workbench 15.0), where a temperature field is applied to the IMU based on actual temperature profiles to obtain the temperature distribution of the fiber coil at different times in a vacuum state. These data are then used in the three-dimensional thermal-induced error model to calculate the thermal-induced error of the FOG. Finally, a thermal vacuum experimental platform is set up to collect temperature variation data from the inertial measurement components. The experimental data are compared with the three-dimensional error model proposed in this paper as well as traditional error models. The root mean square error is approximately 33% lower than that of traditional error calculation methods, which also proves the theoretical accuracy.

A comprehensive numerical approach to coil placement in cerebral aneurysms: mathematical modeling and in silico occlusion classification

Endovascular coil embolization is one of the primary treatment techniques for cerebral aneurysms. Although it is a well-established and minimally invasive method, it bears the risk of suboptimal coil placement which can lead to incomplete occlusion of the aneurysm possibly causing recurrence. One of the key features of coils is that they have an imprinted natural shape supporting the fixation within the aneurysm. For the spatial discretization, our mathematical coil model is based on the discrete elastic rod model which results in a dimension-reduced 1D system of differential equations. We include bending and twisting responses to account for the coils natural curvature and allow for the placement of several coils having different material parameters. Collisions between coil segments and the aneurysm wall are handled by an efficient contact algorithm that relies on an octree based collision detection. In time, we use a standard symplectic semi-implicit Euler time stepping method. Our model can be easily incorporated into blood flow simulations of embolized aneurysms. In order to differentiate optimal from suboptimal placements, we employ a suitable in silico Raymond–Roy-type occlusion classification and measure the local packing density in the aneurysm at its neck, wall region and core. We investigate the impact of uncertainties in the coil parameters and embolization procedure. To this end, we vary the position and the angle of insertion of the micro-catheter, and approximate the local packing density distributions by evaluating sample statistics.

Thermo-hydraulic performance of parallel multi-shell and multi-helical coiled tube heat exchanger CFD model with Taguchi-grey relational analysis

This study utilized four distinct shell and helical tube heat exchanger layouts to numerically evaluate the thermal and hydraulic efficiency of each arrangement. The numerical research was conducted using ANSYS FLUENT 2022R1. Currently, there has been no research conducted on the investigation of multiple helical coiled tubes enclosed by multiple shell heat exchangers. This study aimed to optimize various tasks using the Grey Relational Analysis approach in combination with the Taguchi method to maximize thermal efficiency and minimize pressure drop.A parallel configuration was used to connect two to three concentric helical tubes, with each helical tube being enclosed by a shell to control the flow of fluid. The P–P-2M − 36 design, consisting of two helical tubes, has the highest enhancement ratio of Uo = 26.75 %, when compared to the P–P-3M − 36 configuration. Similarly, the P–P-2M − 42 configuration enhances Uo by 38.42 % in comparison to the P–P-3M − 42 configuration. These findings demonstrate that a configuration consisting of two helical tubes exhibits a higher enhancement ratio of Uo compared to a configuration consisting of three helical tubes. The P–P-3M − 36 design, which consists of three helical tubes, exhibits a minimum pressure drop of 39.19 % compared to the P–P-2M − 36 configuration. Similarly, the P–P-3M − 42 configuration reduces pressure drop by 37.76 % compared to the P–P-2M − 42 configuration. The P–P-3M − 36 configuration is designed to simultaneously reduce pressure drop and boost heat transfer rate. The model achieves the optimal values for heat transfer rate and pressure drop at a Reynolds number of 55,000.

2D axisymmetric electromagnetic modeling of HTS coils based on T-A formulation with modified Newman boundary conditions

The T-A formulation based on thin film approximation has been widely used in electromagnetic modeling of high temperature superconducting (HTS) coated conductors (CCs). However, with the emergence of no-insulation (NI) HTS coils and its variant HTS coils, the electrical connection of HTS coils has become increasingly complex, and the traditional T-A formulation is challenging to handle the problems of conductors with non-negligible thickness and current sharing. This paper firstly describes the Neumann boundary condition of the T-A formulation under 2D axisymmetric symmetry in detail, as well as the conversion of different boundary conditions. And additional voltage variable is added to correct the Newman boundary condition from the perspective of circuit. Then, considering HTS CCs series or parallel stacking to carry current, the effectiveness of this method is verified by comparing with benchmark model. Finally, we extend the application range of the T-A formulation with modified Newman boundary conditions to simulate thick superconductors, and naturally process current sharing of azimuthal and radial current in circular NI HTS coils.

The role of pressure and friction forces in automated insertion of cochlear implants.

Despite the success of cochlear implant (CI) surgery for hearing restoration, reducing CI electrode insertion forces is an ongoing challenge with the goal to further reduce post-implantation hearing loss. While research in this field shows that both friction and quasistatic pressure forces occur during CI insertion, there is a lack of studies distinguishing between these origins. The present study was conducted to analyze the contribution of both force phenomena during automated CI insertion. Five MED-EL FLEX28 CI electrode arrays were inserted into both a regular and uncoiled version of the same average scala tympani (ST). Both ST models had a pressure release hole at the apical end, which was kept open or closed to quantify pressure forces. ST models were filled with different sodium dodecyl sulfate (SDS) lubricants (1, 5, and 10% SDS, water). The viscosity of lubricants was determined using a rheometer. Insertions were conducted with velocities ranging from v= 0.125 mm/s to 2.0 mm/s. Viscosity of SDS lubricants at 20°C was 1.28, 1.96, and 2.51 mPas for 1, 5, and 10% SDS, respectively, which lies within the values reported for human perilymph. In the uncoiled ST model, forces remained within the noise floor (maximum: 0.049 × 10-3 N ± 1.5 × 10-3 N), indicating minimal contribution from quasistatic pressure. Conversely, forces using the regular, coiled ST model were at least an order of magnitude larger (minimum: Fmax = 28.95 × 10-3 N, v = 1 mm/s, 10% SDS), confirming that friction forces are the main contributor to total insertion forces. An N-way ANOVA revealed that both lubricant viscosity and insertion speed significantly reduce insertion forces (p < 0.001). For the first time, this study demonstrates that at realistic perilymph viscosities, quasistatic pressure forces minimally affect the total insertion force profile during insertion. Mixed friction is the main determinant, and significantly decreases with increaseing insertion speeds. This suggests that in clinical settings with similar ST geometries and surgical preparation, quasistatic pressure plays a subordinate role. Moreover, the findings indicate that managing the hydrodynamics of the cochlear environment, possibly through pre-surgical preparation or the use of specific lubricants, could effectively reduce insertion forces.

Thermo-Hydraulic Modeling of JT-60SA TF02 Coil and Feeder for First Operation Predictions

Thermo-Hydraulic Modeling of JT-60SA TF02 Coil and Feeder for First Operation Predictions

Analytical model of an I-core coil inside a metal tube of finite length

An analytical solution is presented for the interaction of an I-core coil with a metal tube of finite length. Using the Truncated Region Eigenfunction Expansion (TREE) method, the impedance variation of the I-core coil is expressed in a closed form. Notably, the 1D finite element method (1D FEM) is adopted to calculate the complex eigenvalues and eigenfunctions of the steel tube, by which the overflow issue of complex eigenfunctions has been surmounted. And the 1D FEM also simplifies the calculation in the ferrite core region immensely. A performant algorithm is obtained due to the matrix formalization and the high speed of the sparse eigenvalue solver. The tubes made of aluminum alloy and stainless steel are investigated by the proposed method and tested in the experiment. The high reliability and efficiency of the proposed method are proved, and the results are also validated by the comparison with simulation and measurement data.

Erratum to: Synthesis of a Simulation Model of Coupled Coils in an Electric Vehicle Wireless Charging System

Erratum to: Synthesis of a Simulation Model of Coupled Coils in an Electric Vehicle Wireless Charging System

Magnetic field analysis and modeling of gradient coils based on ferromagnetic coupling inside magnetically shielded cylinder

To accurately analyze the magnetic field of gradient coils inside a magnetically shielded cylinder (MSC) and enhance the precision of remanence compensation, analytical models for calculating the magnetic field of the gradient coils are proposed. First, the coupling between the high-permeability MSC and the coils is accurately analyzed based on Green’ s function method, magnetic field boundary conditions and image method. Secondly, the current density of four commonly used gradient coils is analyzed, and analytical models for the magnetic fields of these four types of gradient coils are established. Finally, the validity of the analytical models is proved through finite element simulations and experimental tests. The experimental results indicate that within the range of x,z∈−80,80mm (± 0.5R), the analytical values have good consistency with experimental values, and the maximum relative error between the two is only 0.91%. The analytical models will be beneficial to the research on the coil optimization design inside the MSC.

Human Head Transcranial Magnetic Stimulation Using Finite Element Method

Transcranial magnetic stimulation (TMS) is a wearable neuromodulation technique. It is approved for several therapies for various neurological disorders, including major depressive disorder, traumatic brain injury, Parkinson’s disease, and post-traumatic stress disorder. This method became an alternative neuromodulation technique for such brain-related disorders. However, it has shown significant improvement in this alternative approach. Studies based on this technique have shown limited efficacy. They might be associated with current levels, poor coil locality, optimal coil size, and neuromodulator settings. It has been shown in this research that coil heating is related to higher levels of current. Thus, it is required to analyze the impact of the current levels on the induced magnetic distribution to define the optimal current range for the TMS coils. It is not feasible to investigate this research with experimental tests and analytic methods. Alternatively, using an advanced computational model of the coils and accounting for different human head anatomical layers, coil current capacity can be optimized based on finite element magnetic field distribution. This paper aims to investigate the impact of the coil current levels on the induced magnetic field distribution. The current capacity of the coils can be optimized based on the required magnetic field. In this way, the overheating may be reduced and may result in increased efficacy. As a proof-of-concept, a prototype coil and multi-layered geometrical human head models were generated using geometric shapes. The fundamental human head tissue layers were generated based on their average thickness. The model was simulated based on a finite element magnetic simulation using appropriate boundary conditions and neuromodulator settings. The various coil current levels were applied to analyze the outcome. The models were simulated, and the results were recorded based on these current levels. Results showed that there is a direct relation between applied current levels and induced magnetic flux density in the region of interest.

Tension identification of bridge suspension rods based on multiple impedance parameters from self-inductive coils

ABSTRACT This study introduces a method for identifying tension in suspension rods based on impedance from self-inductive coils, grounded in electromagnetic induction and magnetic elasticity principles. The theoretical feasibility of this method was analysed through a high-frequency inductive coil model. Steel strand tensile tests, utilising self-inductive coil sensors at various frequencies, explored the relationship between resistance, inductance, and capacitance with tension. According to the experimental results, the sensitivity coefficient is used to determine the optimal prediction frequency of each impedance parameter. Within the optimal frequency range, a single impedance parameter regression prediction method based on the impedance difference ratio index was proposed. To improve the accuracy and stability of the predictions, a GA-BP neural network prediction model based on the fusion of multiple impedance parameters was proposed. The results indicate that the GA-BP neural network prediction method, which integrates multiple impedance parameters, achieves higher accuracy in identifying cable forces than the single impedance parameter regression prediction method. Specifically, at a frequency of 5 kHz, the relative error of the GA-BP neural network prediction method, which integrates multiple impedance parameters, was only 3.74%. This research offers a novel approach for future in-service tension identification in bridge suspension rods.

An improved multi-frequency eddy current array sensor for detecting micro-defects of welding seam in metal plates

This study proposes an improved multi-frequency eddy current array sensor for the accurate detection of micro-defects (under-welding, over-welding, partial welding breakage, and minute penetration holes) of welding seam in metal plates. The primary goal is to further reduce the external and internal noise of the induced coil by optimizing the composition structure of the eddy current probe, thereby improving its sensitivity and signal-to-noise ratio in micro-defect detection. In response to the issue of external noise, this research introduces a gradient differential coil model, which can compensate for initial errors based on a geometrically balanced structure. By establishing a 3D simulation model and a physical mechanical structure, the suppression effect of this structure on excitation magnetic field and external environmental interference is verified. Furthermore, for the internal noise, a mathematical model of the direct stranded litz wire is established. Theoretical calculations and experimental validation confirm that the litz wire exhibits lower eddy current loss and higher Q value compared to traditional copper conductors, thus mitigating internal noise and improving signal-to-noise ratio. On this basis, the excitation mode of the eddy current coil probe array is set to a multi-frequency excitation method based on a center frequency, greatly reducing the electromagnetic interference between channels. Experimental results demonstrate that the improved eddy current sensor can effectively recognize as low as Φ1 mm weld penetration defect at a lift-off value of 0.5 mm, achieving a remarkably high signal-to-noise ratio of approximately 17.7 dB.

Electromagnetic field simulation modeling method and distribution characteristics of electric vehicle wireless charging system

In recent years, wireless charging technology for electric vehicles has gained significant attention. To accurately analyze the distribution characteristics of the electromagnetic field during the wireless charging process of electric vehicles, a finite element-based electromagnetic analysis method was employed. Applied in the commercial simulation software, the electromagnetic environment of the resonant coil and electric vehicle model was simulated under high-power charging conditions, resulting in an overall electromagnetic field distribution for the electric vehicle. The results indicated that within the coil region, the magnetic induction intensity in the central area of the coil was zero, and it increased as the distance from the center of the coil grew. Outside the coil region, the magnetic induction intensity gradually decreased. The electric field intensity of the resonant coil was maximum in the central area of the coil, and it weakened as the distance from the center of the coil increased. When a magnetic shielding resonant coil was used, the electromagnetic field was confined between the shielding materials, and the magnetic field rapidly attenuated on both sides of the magnetic shield. The electromagnetic field energy of the electric vehicle body was mainly concentrated at the bottom of the vehicle near the coil. When the coil was located in the front of the car body, the maximum electric field intensity distribution in the car body was 8.50 V/m, and the maximum magnetic induction intensity was 0.024 μT. When the coil was located in the middle of the car body, the maximum electric field intensity was 2.31 V/m, the maximum magnetic induction intensity was 0.019 μT. As the distance from the coil position increased, the energy weakened.

Ultra‐fast finite element analysis of coreless axial flux permanent magnet synchronous machines

AbstractLarge‐scale design optimisation techniques enable the design of high‐performance electric machines. Electromagnetic 3D finite element analysis (FEA) is typically employed in optimisation studies for accurate analysis of axial flux permanent magnet (AFPM) machines, which require extensive computational resources. To reduce the computational burden, a FEA‐based mathematical method relying on the geometric and magnetic symmetry of coreless AFPM machines is proposed to estimate the machine performance indicators using the least number of FEA solutions, thereby significantly lowering the running time. This method is generally applicable to AFPM machines with low saturation effects and cogging torque as exemplified for a printed circuit board (PCB) stator coreless AFPM machine. To further reduce the computation time, a systematically simplified equivalent 3D FEA model for planar PCB coils integrated with this machine is also proposed. The practical implementation of the introduced method is elaborated based on an example optimisation study, and an analytical method for fast design scaling is also discussed. The results of the proposed approach are compared with detailed transient FEA results, and a prototype 26‐pole PCB stator coreless AFPM machine was also used to validate the results experimentally.

Thermal design calculation method of the whole coil closed cooling tower with condensation inside the tube

In this paper, the heat exchange process of a closed cooling tower with condensation inside the tube is analyzed. Combined with the calculation method of a traditional closed cooling tower, the thermal model and mathematical model of the whole coil closed cooling tower with condensation inside the tube are established. The fourth-order Runge-Kutta (RK4) method is used to write a program to solve the differential equation. A case is calculated to solve the heat exchange area and spray water temperature. Its feasibility for design reference is verified.