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Finding a Crack and Determining Depth in a Material

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The purpose of this paper is to find geometry of a crack (length and depth) in a conductive plate, on the basis of non-destructive testing with eddy currents. The position of a crack can be determined by taking into consideration the change in the magnetic density between the measured points. The depth is determined with the use of FEM model. The calculated test case points to an accurate determination. Streszczenie. W artykule opisano metodę wyznaczania rozmiarów pęknięć w płytkach przewodzących, na podstawie testów z wykorzystaniem prądów wirowych, nieniszczących elementu. Metoda wykorzystuje wpływ pęknięć na zmianę gęstości pola w badanym rejonie. W analizie posłużono się metodą elementów skończonych. Otrzymane wyniki potwierdzają skuteczność działania. (Lokalizacja i analiza rozmiarów pęknięć w materiale przewodzącym). Keywords: Measurements, finite element method, non-destructive testing. Słowa kluczowe: pomiary, metoda elementów skończonych, próba nieniszcząca. Introduction The method of identifying and searching for a crack, with a non-destructive testing, is all more widespread and important [1,2,3,4]. Non-destructive testing is often used, based on considering the impact of eddy currents and the usage of different excitation coils and sensors for measuring magnetic flux density [5,6,7]. Several devices for non-destructive testing have additional programs for displaying measurement results, within which a graphical display of the measured results helps to determine the position of a crack within a material [8]. This paper describes a procedure that determines a crack’s position on the basis of measurements. The input data is represented by the measured values for magnetic flux density at the centre of an excitation coil, supplied with an alternating current. Our intention was to also determine a crack’s depth. This meant dealing with an inverse problem. Some authors use analytical methods that help to solve th[...]

The advantages of the finite line elements application for the analysis of the grounding systems

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In this paper, the new numerical model is presented to analyze the electromagnetic field around the grounding rod and grounding wire. In contrast to recently existent procedure based on the "classical" finite element method (FEM), in this new methodology the soil and the air domain of the problem are discretized by the 3-D finite elements and the conductors of the grounding electrodes are discretized by 1-D finite line elements. The results of calculations have been verified by comparison with the results of measurements found in the literature. Streszczenie. W artykule prezentowane jest analiza pola elektromagnetycznego wokół pręta uziemiającego i obwodu uziemiającego. W przeciwieństwie do istniejących metod analizy, bazujących na metodzie elementów skończonych (MES) wprowadzono nową metodę, w której gleba i obszar powietrzny są dyskretyzowane siatką elementów skończonych 3-D a przewodniki uziemiających elektrod przez sieć elementów skończonych 1-D. Wyniki obliczeń skonfrontowano z wynikami pomiarów z literatury. (Zalety zastosowania liniowych elementów skończonychdo analizy systemów uziemiających) Keywords: electromagnetic transient analysis, finite element methods, grounding electrodes . Słowa kluczowe: analiza elektromagnetycznych stanów przejściowych, metoda elementów skończonych, uziemiające elektrody Introduction The primary goal of grounding systems is to provide conductive paths to dissipate electrical currents into the ground, in order to ensure the safety of personnel and prevent damage of electrical installations, while their secondary goal is to provide common reference voltage for all interconnected electrical and electronic systems. To optimize the design of grounding systems, as well as to minimize the disturbance level in the protected area, the program tool able to analyze the transient performance of grounding systems is fundamental. For that very reason, the goal of this work was to develop the methodology (the pr[...]

Numerical scalar hysteresis model and its precision

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The calculation of magnetic fields in the electromagnetic devices is an important part of the design process. The numerical approach in consideration to the measured material hysteresis is discussed in the paper. Some precision problems of the model are pointed out. The results of the calculation are compared with the measurement results made on the magnetization set up for the characterization of semi and hard magnetic materials. Streszczenie. Obliczanie pola magnetycznego w urządzeniach elektrycznych jest istotną częścia procesu projektowania. W artykule dyskutowane jest numeryczne podejście do zmierzonej histerezy. Pewne precyzyjne problemy zostały wypunktowane. Wyniki obliczeń porównane są z wynikami pomiarów wykonanych na zestawach magnetycznych charakterystycznych dla materiałów magnetycznych twardych i półtwardych. (Numeryczny model skalarny histerezy i jego dokładność) Keywords: Finite element methods, Magnetic fields, Measurement. Słowa kluczowe: metoda elementów skończonych, pole magnetyczne, pomiary Introduction The program for the 3D finite element magnetic field calculations includes the numerical scalar hysteresis model. The description of the magnetic material is based on the measured major hysteresis loop and as many as possible measured first order reversal curves (FORCs) for the increase and for the decrease of the excitation current. In each of the finite elements, the new magnetic induction B is calculated on the basis of the nonlinear finite element method calculation made with different magnetization curves in each finite element. The magnetic induction in each of the finite elements, calculated from the previous time step, the history of the magnetic density and the excitation current, are the basis for the evaluation of the new magnetization curve, which will be used for nonlinear calculation in the current time step. Some calculations must be repeated, if the result is on the wrong magnetization curve. S[...]

Determination of a crack's size on the basis of the nondestructive testing with eddy currents using metaheuristics DOI:10.15199/48.2019.05.07

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Non-destructive testing is now used more and more often for the testing of materials [1-4]. One of nondestructive methods is testing using eddy currents. In this testing case we measure the magnetic flux density within the vicinity of the tested material which has changed because of the material damage [5-9]. Our problem is a conductive plate with a crack, and is limited to a crack of rectangular geometry having a constant depth. The crack’s position, crack’s length l, crack’s depth d and crack’s width w must be found. The first part of the research was searching for the crack’s position and length. These were found by consideration of the differences between the measured magnetic flux densities and the neighbouring measurement points. Second, the more complex part of the research was searching for the crack’s depth and width. We used differential evolution [10-13] for determining the crack’s depth and width. The Finite Element Method (FEM) [1, 3] model was used for the evaluation of cost function. Measurements Measurements were carried out for two test-cases. These were two plates, the first made of aluminium and the second of austenitic stainless steel, both of 30 mm thickness and dimensions of 330 x 285 mm. The cracks of both plates were the same and had lengths of 40 mm, depths of 10 mm, and widths of 0.5 mm. The cracks were in the middle of their respective plates. The used measuring system, together with the test plate, is shown in Fig. 1. Fig.1. Measuring system The excitation coil had an inner diameter of 36.8 mm, an outer diameter of 53 mm, and a height of 56 mm. It had 566 turns and was supplied with a sinusoidal current of 1A and a frequency of 500 Hz. An axial Hall-probe HS-AGB5-4805 was placed within a bore at the centre of the coil. The Hall probe measured the z component of the magnetic flux density. When, in the continuation of the paper, we talk about the magne[...]

Analysis of Electromagnetic Conditions Around the Conductor Clamp of a Covered Conductor DOI:10.15199/48.2019.05.08

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Electric insulators are almost indispensable parts of each electric power network. Development of materials constantly brings new insulators with better insulation and mechanical properties. In the recent years, covered conductors that have many advantages and contribute to increased security of network operation often replace bare conductors. Covered conductors also have some disadvantages, such as inefficient performance of protection systems, difficult location of faults [1], insulation damage due to corona [2], [3], danger for people in the case of a fall of conductor to the ground, if the conductor remains energized, etc. The most frequent problems with covered conductors appear at the points of fixing the conductor to insulator [4], [5]. The reasons of these problems are usually inadequate combinations of properties of materials that compose conductor clamps. In most cases, they are composed of several materials with different dielectric constants with some metal parts between them. Inadequate geometrical forms of components of conductor clamps additionally worsen the situation. The paper presents the results of analyses of electromagnetic conditions in a »D-type« pin insulator, model »VS SER-b/20«, with metal conductor clamp and the use of covered conductor [6], [7]. The numerical computations of conditions inside the insulator and its surroundings were performed using Opera Vector Fields 3D program tool [9]. Computations of electrostatic and timeharmonic electromagnetic field were performed for different materials of components of conductor clamps having the same shape [8]. The influence of various materials is evident from the differences in electric field distribution in and around the insulator and eddy currents in the nearby metal parts. An accurate analysis of electric field calculation results also enabled identification of conditions that lead to damaging of conductor clamps and conducto[...]

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