Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Absolute Wall Thickness Measurement of Conducting Plates Using Pulsed Eddy Currents

The method using pulsed eddy currents to determine the thickness of a conduction plate is extended to enable the simultaneous measurement of the plate thickness and material properties. For optimal performance, a probe must be designed depending on the thickness range that should be accessible. The need for a calibration of the material properties of a conducting plate to enable the measurement of its thickness has been removed. All that is needed is a probe with known dimensions and suitable hardware to create a current pulse and measure a transient magnetic induction.

High-sensitivity phase imaging eddy current magneto-optical system for carbon fiber reinforced polymers detection

This paper proposed a high-sensitivity phase imaging eddy current magneto-optical (PI-ECMO) system for carbon fiber reinforced polymer (CFRP) defect detection. In contrast to other eddy current-based detection systems, the proposed system employs a fixed position excitation coil while enabling the detection point to move within the detection region. This configuration effectively mitigates the interference caused by the lift-off effect, which is commonly observed in systems with moving excitation coils. Correspondingly, the relationship between the defect characteristics (orientation and position) and the surface vertical magnetic field distribution (amplitude and phase) is studied in detail by theoretical analysis and numerical simulations. Experiments conducted on woven CFRP plates demonstrate that the designed PI-ECMO system is capable of effectively detecting both surface and internal cracks, as well as impact defects. The excitation current is significantly reduced compared with traditional eddy current magneto-optical (ECMO) systems.

Model Predictive Control Coupled with Artificial Intelligence for Eddy Current Dynamometers

The recent studies on Artificial Intelligence(AI)accompanied by enhanced computing capabilities supports increasing attention into traditional control methods coupled with AI learning methods in an attempt to bringing adap-tiveness and fast responding features.The Model Predictive Control(MPC)tech-nique is a widely used,safe and reliable control method based on constraints.On the other hand,the Eddy Current dynamometers are highly nonlinear braking sys-tems whose performance parameters are related to many processes related vari-ables.This study is based on an adaptive model predictive control that utilizes selected AI methods.The presented approach presents an updated the mathema-tical model of an Eddy Current Dynamometer based on experimentally obtained system operational data.Finally,the comparison of AI methods and related learn-ing performances based on the assessment technique of mean absolute percentage error(MAPE)issues are discussed.The results indicate that Single Hidden Layer Neural Network(SHLNN),General Regression Neural Network(GRNN),Radial Basis Network(RBNN),Neuro Fuzzy Network(ANFIS)coupled MPC have quite satisfying performances.The presented results indicate that,amongst them,GRNN appears to provide the best performance.

Design Optimization of Permanent Magnet Eddy Current Coupler Based on an Intelligence Algorithm

The permanent magnet eddy current coupler(PMEC)solves the problem of flexible connection and speed regulation between the motor and the load and is widely used in electrical transmission systems.It provides torque to the load and generates heat and losses,reducing its energy transfer efficiency.This issue has become an obstacle for PMEC to develop toward a higher power.This paper aims to improve the overall performance of PMEC through multi-objective optimization methods.Firstly,a PMEC modeling method based on the Levenberg-Marquardt back propagation(LMBP)neural network is proposed,aiming at the characteristics of the complex input-output relationship and the strong nonlinearity of PMEC.Then,a novel competition mechanism-based multi-objective particle swarm optimization algorithm(NCMOPSO)is proposed to find the optimal structural parameters of PMEC.Chaotic search and mutation strategies are used to improve the original algorithm,which improves the shortcomings of multi-objective particle swarm optimization(MOPSO),which is too fast to converge into a global optimum,and balances the convergence and diversity of the algorithm.In order to verify the superiority and applicability of the proposed algorithm,it is compared with several popular multi-objective optimization algorithms.Applying them to the optimization model of PMEC,the results show that the proposed algorithm has better comprehensive performance.Finally,a finite element simulation model is established using the optimal structural parameters obtained by the proposed algorithm to verify the optimization results.Compared with the prototype,the optimized PMEC has reduced eddy current losses by 1.7812 kW,increased output torque by 658.5 N·m,and decreased costs by 13%,improving energy transfer efficiency.

Speed Measurement Feasibility by Eddy Current Effect in the High-Speed MFL Testing

It is known that eddy current effect has a great influence on magnetic flux leakage testing(MFL).Usually,contacttype encoder wheels are used to measure MFL testing speed to evaluate the effect and further compensate testing signals.This speed measurement method is complicated,and inevitable abrasion and occasional slippage will reduce the measurement accuracy.In order to solve this problem,based on eddy current effect due to the relative movement,a speed measurement method is proposed,which is contactless and simple.In the high-speed MFL testing,eddy current induced in the specimen will cause an obvious modification to the applied field.This modified field,which is measured by Hall sensor,can be utilized to reflect the moving speed.Firstly,the measurement principle is illustrated based on Faraday’s law.Then,dynamic finite element simulations are conducted to investigate the modified magnetic field distribution.Finally,laboratory experiments are performed to validate the feasibility of the proposed method.The results show that Bmz(r1)and Bmx(r2)have a linear relation with moving speed,which could be used as an alternative measurement parameter.

Characteristics of Eddy Current Attenuation and Thickness Measurement of Metallic Plate

In eddy current testing, the law of attenuation of eddy current(EC) is of great concern. In conductive half space under the excitation of uniform magnetic field, the EC density decreases exponentially in the depth direction. However, in conductor with finite thickness tested by coil, the distribution of EC in the depth direction is more complicated. This paper studies the characteristics of EC attenuation in metallic plate of finite thickness. Simulation results show that there is an EC reflection at the bottom of plate, which changes the law of EC attenuation. A new concept, namely the equivalent attenuation coefficient, is proposed to quantify the speed of EC attenuation. The characteristics of EC attenuation are utilized to explain the nonmonotonic relation between coil voltage and plate thickness. Procedure of selecting frequency is discussed. Thereafter, measurement of plate thickness is carried out and accurate result is obtained.

Feasibility study of a large-scale tuned mass damper with eddy current damping mechanism

Tuned mass dampers （TMDs） have been widely used in recent years to mitigate structural vibration. However, the damping mechanisms employed in the TMDs are mostly based on viscous dampers, which have several well-known disadvantages, such as oil leakage and difficult adjustment of damping ratio for an operating TMD. Alternatively, eddy current damping （ECD） that does not require any contact with the main structure is a potential solution. This paper discusses the design, analysis, manufacture and testing of a large-scale horizontal TMD based on ECD. First, the theoretical model of ECD is formulated, then one large-scale horizontal TMD using ECD is constructed, and finally performance tests of the TMD are conducted. The test results show that the proposed TMD has a very low intrinsic damping ratio, while the damping ratio due to ECD is the dominant damping source, which can be as large as 15% in a proper configuration. In addition, the damping ratios estimated with the theoretical model are roughly consistent with those identified from the test results, and the source of this error is investigated. Moreover, it is demonstrated that the damping ratio in the proposed TMD can be easily adjusted by varying the air gap between permanent magnets and conductive plates. In view of practical applications, possible improvements and feasibility considerations for the proposed TMD are then discussed. It is confirmed that the proposed TMD with ECD is reliable and feasible for use in structural vibration control.

ARRAY PULSED EDDY CURRENT IMAGING SYSTEM USED TO DETECT CORROSION

A theory model is established to describe the voltage-current responsefunction. The peak amplitude and the zero-crossing time of the transient signal is extracted as theimaging features, array pulsed eddy current (PEC) imaging is proposed to detect corrosion. The testresults show that this system has the advantage of fast scanning speed, different imaging mode andquantitative detection, it has a broad application in the aviation nondestructive testing.

Bonded Terfenol-D composites with low eddy current loss and high magnetostriction

Bonded Terfenol-D composites,with high electrical resistivity and low eddy current loss,can be used in an alternating magnetic field with high frequency.However,the nonmagnetic binder impairs the magnetostriction of the composites.To achieve high magnetostriction and low eddy current loss,the mixture of the alloy powder and binder was compressed at low pressure in an oriented magnetic field.After this,the aligned samples were recompressed by cold isostatic pressing（CIP）.Besides,the effect of particle size on the magnetostriction of the bonded Terfenol-D composites was also studied.The results showed that the bonded Terfenol-D composites had excellent magnetostriction when the particle size was 50-80 μm.The oriented magnetic field and CIP could improve the magnetostriction of the bonded composites,which reaches 1020×10-6.The bonded Terfenol-D composites had good compact structure and high density（7.24 g/cm3）.The magnetic loss of the bonded Terfenol-D composites was 192 mW/cm3 at a frequency of 100 kHz in a magnetic field of 960 A/m,which was about one third of that of casting Terfenol-D alloys.

Subsurface Defect Evaluation of Selective-Laser-Melted Inconel 738LC Alloy Using Eddy Current Testing for Additive/Subtractive Hybrid Manufacturing

New materials and manufacturing technologies require applicable non-destructive techniques for quality assurance so as to achieve better performance.This study comprehensively investigated the effect of influencing factors includ-ing excitation frequency,lift-off distance,defect depth and size,residual heat,and surface roughness on the defect EC signals of an Inconel 738LC alloy produced by selective laser melting(SLM).The experimental investigations recorded the impedance amplitude and phase angle of EC signals for each defect to explore the feasibility of detecting sub-surface defects by merely analyzing these two key indicators.Overall,this study revealed preliminary qualitative and roughly quantitative relationships between influencing factors and corresponding EC signals,which provided a prac-tical reference on how to quantitively inspect subsurface defects using eddy current testing(ECT)on SLMed parts,and also made solid progress toward on-line ECT in additive/subtractive hybrid manufacturing(ASHM)for fabricating SLMed parts with enhanced quality and better performance.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows： 1） the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2） the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3） the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.

3D Eddy Current and Temperature Field Analysis of Large Hydro-generators in Leading Phase Operations

As a common practice,a large hydro-generator will operate in leading phase conditions to absorb the reactive power of the power grid.However,the accurate and precise prediction of the leading phase operation capacity of a large hydro-generator has always been a formidable challenge to engineers and academicians because it is extremely hard to compute the eddy currents and losses as well as the local overheating in the pressure plate and finger.To address this problem,a full three dimensional(3D)finite element model and method of the coupled eddy current and temperature fields in the end region of a large hydro-generator are developed.The equivalent medium parameters used in the computations are comprehensively discussed.Moreover,some numerically based solution methodologies for accurate computation of the field and armature currents under different leading phase conditions are proposed.Numerical results on the coupled eddy current and temperature fields in the end regions of a 250 MW hydro-generator confirm positively the feasibility of the present work.

Influence of eddy current on transient characteristics of common rail injector solenoid valve

Influence of eddy current on transient characteristics of common rail injector solenoid valve was studied in this paper. Experimental investigations of drive current and power source volt- age of both drive current ascending and descending process were conducted on a common rail injec- tor solenoid valve. A new discretizing calculation method of solenoid valve flux linkage was put for- ward for the first time based on the experimental results and drive circuit principle, and flux linkage of both drive current ascending and descending process were evaluated. New inductance calculation methods for drive current ascending and descending process respectively were also presented. Influ- ence of parasitic inductance was evaluated. Results indicate that the air gap, under which the transi- ent flux linkage of the solenoid valve is the biggest, varies with drive current due to eddy current. Flux linkage of drive current descending process is bigger than that of drive current ascending process under the same drive current and the same air gap width. Eddy current can reduce the delay between the time that drive current begins to descend and the time that armature begins to move downward. Inductance of drive current descending process is bigger than that of drive current as- cending process over larger scope of drive current, but the difference becomes smaller with the in- creasing of air gap width. The differences of both flux linkage and inductance between drive current ascending and descending process are caused by the eddy current in core and armature materials.

Characterization of Early Fatigue Microstructure in AISI 321 Steel Using Eddy Current Non-destructive Methodology

Accumulative damage during early stage of fatigue in AISI 321 steel was investigated by eddy current test, atomic force microscopy, X-ray diffraction and transmission electron microscopy. Surface slip, dislocation, and strain-induced martensite were determined as the main damage types. Moreover, damage during the fatigue was found to be increased with the increasing fatigue cycles and load amplitude. The contribution of strain-induced martensite to the total eddy current amplitude （V） was enhanced with the increase in its volume fraction. Finally, a linear relationship between V I~, and the height of surface slip was established.

Numerical Simulation of the Eddy Current Effects on the Arc Splitting Process

This paper focuses on a numerical simulation of the arc plasma behavior in the arc splitting process, considering the eddy currents in the electrodes and the splitter plate. Based on three-dimensional （3D） magneto-hydrodynamic （MHD） theory, a thin layer of nonlinear electrical resistance elements is used in the model to represent the voltage drop of plasma sheath and the formation of new arc root in order to include the arc splitting process in the simulation. In the arcing process, eddy currents in metal parts are generated by a time-varying magnetic field. The arc model is calculated with the time-varying magnetic field term, so that the eddy current effects can be considered. The effect of nonlinear permeability of a ferromagnetic material is also involved in the calculation. Using the simulation results for the temperature, velocity and current density distribution, the arc splitting process is analyzed in detail. The calculated results are compared with the simulation neglecting eddy currents.

Numeral eddy current sensor modelling based on genetic neural network

This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network （GNN） according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method.

Combination of eddy current and heat treatment for crack healing and mechanical-property improvement in magnesium alloy tube

The continuous eddy current pulse treatment(ECPT)combined with heat treatment was employed to heal the microcracks in spin formed Mg alloy tubes and improve their mechanical properties in this study.The results show that all the microcracks in different tube specimens were almost healed after different continuous ECPT schemes up to 15 cycles.The schemes with less cooling intervals exhibited better healing effect and increased the strength and elongation of Mg alloy tubes more obviously.After aging treatment,the strength improvement of the specimens with ECPT was more remarkable than that of the specimens without ECPT,and the elongation decrease of the specimens with ECPT was less evident than that of specimens without ECPT due to the segregation of RE elements on the crack surface.Besides,after solution treatment,the strength reduction and ductility improvement of the specimens with ECPT were more pronounced than that of the specimens without ECPT owing to the notable decrease of dislocation density of the specimens with ECPT.Both narrowed cracks induced by ECPT and the segregation of precipitates in the vicinity of microcrack surface during aging treatment contributed to the maximum strength in the as-spun specimens with ECPT followed by aging treatment.

Analytical model of tilted driver–pickup coils for eddy current nondestructive evaluation

A driver-pickup probe possesses better sensitivity and flexibility due to individual optimization of a coil. It is fre- quently observed in an eddy current （EC） array probe. In this work, a tilted non-coaxial driver-pickup probe above a multilayered conducting plate is analytically modeled with spatial transformation for eddy current nondestructive evalua- tion. Basically, the core of the formulation is to obtain the projection of magnetic vector potential （MVP） from the driver coil onto the vector along the tilted pickup coil, which is divided into two key steps. The first step is to make a projection of MVP along the pickup coil onto a horizontal plane, and the second one is to build the relationship between the pr, ojected MVP and the MVP along the driver coil. Afterwards, an analytical model for the case of a layered plate is established with the reflection and transmission theory of electromagnetic fields. The calculated values from the resulting model indicate good agreement with those from the finite element model （FEM） and experiments, which validates the developed analytical model.