Analytical model of a T-core coil above a multi-layer conductor with hidden hole using the TREE method for nondestructive evaluation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Siquan Zhang
Keyword(s):  
Analytical Model ◽  
Expansion Method ◽  
Probe Design ◽  
Magnetic Vector Potential ◽  
Impedance Change ◽  
Ferrite Core ◽  
Content Type ◽  
Eigenfunction Expansion Method ◽  
Cylindrical Coordinate ◽  
Impedance Calculation

Purpose In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive material. However, the E-core coil has some disadvantages, such as large volume and difficulty in the process of winding the coils. This paper aims to present a novel T-core probe and its analytical model used for evaluating hidden holes in a multi- layer conductor. Design/methodology/approach By using a cylindrical coordinate system, the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived, and the expansion coefficients of the solutions are obtained by matching the boundary and interface conditions between the regions. By using the truncated region eigenfunction expansion method, the final expression in closed form for the impedance of the multi-turn coil is worked out, and the impedance calculation is performed in Mathematica. For frequencies ranging from 100 Hz to 100 kHz, both the impedance changes of the T-core coil above the multi-layer conductor without a hidden hole and in the absence of the layered conductor were calculated, and the influence of a hidden hole in the multi-layer conducting structure on the impedance change was investigated. Findings The correctness of the analytical model of the T-core coil was verified by the finite element method and experiments. The proposed T-core coil has higher sensitivity than an air-core coil, and similar sensitivity and smaller size than an E-core coil. Originality/value A new T-core coil probe and its accurate theoretical model for defect evaluation of conductor were presented; probe and analytical model can be used in probe design, detection process simulation or can be directly used in defect evaluation of multi-layer conductor.

3-D Eddy Currents Analysis in Orthotropic Materials Using Truncated Region Eigenfunction Expansion Method

2012 ◽  
Vol 239-240 ◽  
pp. 258-263 ◽  
Author(s):  
Yu Jie Bai ◽  
Xiao Zhang Zhang ◽  
Lei Jiang ◽  
Chang Liang Tang
Keyword(s):  
Eigenfunction Expansion ◽  
Eddy Currents ◽  
Separation Of Variables ◽  
Expansion Method ◽  
Orthotropic Materials ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Eigenfunction Expansion Method ◽  
Vector Differential Equation ◽  
Good Agreement

A model for 3-D eddy currents analysis in orthotropic materials such as CFRPs is proposed. With artificial magnetic insulation boundary conditions, we solved a vector differential equation which describes the magnetic vector potential in the CFRPs materials with a delta coil near it using the method of separation of variables. As a result of the truncated region eigenfunction expansion method, a series solution was obtained, from which we got the eddy currents distribution. The distribution shows a good agreement with the work by others.

scholarly journals Analytical Model of an I-core Coil for Nondestructive Evaluation of a Conducting Cylinder below an Infinite Plane Conductor

2021 ◽  
Vol 21 (4) ◽  
pp. 99-105
Author(s):  
Siquan Zhang
Keyword(s):  
Analytical Model ◽  
Rectangular Cross Section ◽  
Analytical Calculation ◽  
Bottom Layer ◽  
Closed Form Expression ◽  
Magnetic Vector Potential ◽  
Infinite Plane ◽  
Impedance Change ◽  
Principle Of Superposition ◽  
Conducting Cylinder

Abstract An analytical model for eddy current testing of an I-core coil located above a two-layer conductive material is presented. The upper layer is an infinite plane conductor, and the bottom layer is a conductive cylinder. The method of truncated region eigenfunction expansion (TREE) is used to solve this axisymmetric problem. First the magnetic vector potential of a filamentary coil coaxial with the I-core over the two-layer conductor is considered. Then the closed form expression for the impedance of the multi-turn coil with rectangular cross section is derived by using the principle of superposition from the filamentary coil field. For frequencies ranging from 0.1 kHz to 10 kHz, both the impedance changes of the I-core coil located above the infinite plane conductor without the conducting cylinder, and in the absence of the two-layer conductor are calculated using Mathematica, respectively. The influence of the conducting cylinder below the infinite plane conductor on the impedance change is analyzed. The analytical calculation results are verified by the finite element method and experiment, the results agree very well, which verifies the correctness of the analytical model.

scholarly journals I-cored Coil Probe Located Above a Conductive Plate with a Surface Hole

2018 ◽  
Vol 18 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Grzegorz Tytko ◽  
Leszek Dziczkowski
Keyword(s):  
Expansion Method ◽  
Magnetic Vector Potential ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Conductive Material ◽  
Conductive Plate ◽  
Eigenfunction Expansion Method ◽  
Final Formula ◽  
Good Consistency ◽  
Made In

Abstract This work presents an axially symmetric mathematical model of an I-cored coil placed over a two-layered conductive material with a cylindrical surface hole. The problem was divided into regions for which the magnetic vector potential of a filamentary coil was established applying the truncated region eigenfunction expansion method. Then the final formula was developed to calculate impedance changes for a cylindrical coil with reference to both the air and to a material with no hole. The influence of a surface flaw in the conductive material on the components of coil impedance was examined. Calculations were made in Matlab for a hole with various radii and the results thereof were verified with the finite element method in COMSOL Multiphysics package. Very good consistency was achieved in all cases.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

How firms' performance mediates the relationship between corporate governance quality and earnings quality?

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammed Adel Elzahaby
Keyword(s):  
Corporate Governance ◽  
Analytical Model ◽  
Performance Measures ◽  
Earnings Quality ◽  
Direct Path ◽  
Content Type ◽  
Indirect Path ◽  
Governance Quality ◽  
Financial Performance Measures ◽  
Corporate Governance Quality

PurposeThe purpose of this study is to propose an analytical model that investigates both a direct path between corporate governance quality and earnings quality and an indirect path, in which firms' performance is a mediating variable that is influenced by corporate governance quality and that, in turn, influences earnings quality.Design/methodology/approachThe study employs a structural equation modelling (SEM), to a sample of Egyptian listed firms during 2011–2017, to test the proposed analytical model and to determine the relative importance of both the direct and indirect paths.FindingsThe findings show a statistically significant evidence of both a direct path from corporate governance quality to earnings quality, and an indirect path that is mediated by firms' performance, suggesting that both corporate governance quality and performance have a complementary effect on earnings quality. However, the weight of the evidence favouring the direct path is more important in case of accounting-based performance measures; and the weight of the evidence favouring the indirect path is more important in case of market-based performance measures.Research limitations/implicationsThe current study has some limitations. First, the study focuses specifically on one proxy for measuring earnings quality which is the absolute value of discretionary accruals. Other proxies of earnings quality could be examined in future research, such as income smoothing, earnings persistence and timely loss recognition. Another limitation is that only financial performance measures were examined, namely, return on assets, return on equity, price-to-earnings ratio and market-to-book value. Notwithstanding, non-financial performance measures could be investigated in future studies, such as balanced scorecard (BSC). Furthermore, considering cultural, political and legislative differences among countries, the results may not be generalised outside the scope of the current sample (i.e. Egyptian listed firms).Practical implicationsThe implications of the findings for both theory and practice are discussed.Originality/valueThis study is distinguished by validating an analytical model that has been overlooked by prior studies. Moreover, it provides a new constructed index for measuring corporate governance quality. Furthermore, it uses a new sophisticated statistical technique, which is SEM, for testing the proposed model.

Study on Dynamic Stability of Single Floating Pier Under Waves

2021 ◽  
Author(s):  
Yikuan He ◽  
Bing Han ◽  
Wenyu Ji
Keyword(s):  
Dynamic Stability ◽  
Expansion Method ◽  
Diffraction Effect ◽  
Exterior Region ◽  
Factors Affecting ◽  
Eigenfunction Expansion Method ◽  
Floating Bridge ◽  
Response Equation ◽  
Floating Pier ◽  
Wave Excitation Force

Abstract Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

Effect of unbalanced magnetic pull on the thermal characteristics of traction motor bearing

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tingting Wang ◽  
Dongli Song ◽  
Weihua Zhang ◽  
Shiqi Jiang ◽  
Zhiwei Wang
Keyword(s):  
Thermal Analysis ◽  
High Speed ◽  
Thermal Characteristics ◽  
Expansion Method ◽  
Fourier Series Expansion ◽  
High Speed Train ◽  
Traction Motor ◽  
Content Type ◽  
Unbalanced Magnetic Pull ◽  
Motor Bearing

Purpose The purpose of this paper is to analyze the unbalanced magnetic pull (UMP) of the rotor of traction motor and the influence of the UMP on thermal characteristics of traction motor bearing. Design/methodology/approach The unbalanced magnetic pull on the rotor with different eccentricity was calculated by Fourier series expansion method. A bearing thermal analysis finite element model considering both the vibration of high-speed train caused by track irregularity and the UMP of traction motor rotor was established. The validity of the model is verified by experimental data obtained from a service high-speed train. Findings The results show that thermal failure of bearing subassemblies most likely occurs at contact area between the inner ring and rollers. The UMP of rotor of traction motor has a significant effect on the temperature of the inner ring and roller of the bearing. When the eccentricity is 10%, the temperature can even be increased by about 12°C. Therefore, the UMP of rotor of traction motor must be considered in thermal analysis of traction motor bearing. Originality/value In the thermal analysis of the bearing of the traction motor of high-speed train, the UMP of the rotor of the traction motor is considered for the first time

Effective Estimation of Water Waves Scattering by Double-Row Pile Breakwaters

2012 ◽  
Author(s):  
Omid Nejadkazem ◽  
Ahmad Reza Mostafa Gharabaghi
Keyword(s):  
Water Waves ◽  
Wave Length ◽  
Expansion Method ◽  
Optimum Number ◽  
Intermediate Water ◽  
Double Row ◽  
Eigenfunction Expansion Method ◽  
Efficient Performance ◽  
Efficient Calculation ◽  
Efficient Prediction

This paper describes various hydraulic characteristic of double-row pile breakwaters (DPB). Applying an eigenfunction expansion method, a numerical method have been developed that can compute wave transmission, reflection, and other hydraulic characteristics. To verify the validity of developed prediction, laboratory experiments of Isaascson et al. (1999) have been utilized. Then for an efficient calculation, optimum number of necessary evanescent waves for an effective and efficient prediction is discussed for various hydraulic quantities of interest. In a nutshell, for an effective and efficient performance of the DPB, intermediate water wave and porosity range of [0.2 0.3] are recommended. Relative distance between two barriers must be set depending on significant wave length of design.

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