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Sensitivity Analysis of a Magnetic Circuit for Non-Destructive Testing by the Magnetic Flux Leakage Technique

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Sensitivity Analysis of a Magnetic Circuit for Non-Destructive Testing by the Magnetic Flux Leakage Technique Sensitivity analysis of a magnetic circuit for non-destructive testing by the magnetic flux leakage technique Sensitivity analysis of a magnetic circuit for non-destructive testing by the magnetic flux leakage technique Análisis de sensibilidad de un circuito magnético para ensayos no destructivos por la técnica de fuga de flujo magnético Cristian Fabian Jaimes Saavedra1, Sebastián Roa Prada2 1Estudiante de Ingeniería Mecatrónica, Universidad Autónoma de Bucaramanga, Semillero de Investigación en Modelado y Simulación, Bucaramanga, Colombia. 2Ph.D. en Ingeniería Mecánica, Profesor Titular, Universidad Autónoma de Bucaramanga, Grupo de Investigación en Control y Mecatrónica, Bucaramanga, Colombia. E-mail: [email protected] Recibido 30/04/2015, Cite this article as: C. Jaimes, S.Roa, “Sensitivity analysis of a magnetic circuit for Aceptado 10/05/2016 non-destructive testing by the magnetic flux leakage technique”, Prospect, Vol 14, N° 2, 22-30, 2016. ABSTRACT Monitoring the integrity of structures in the oil and gas industry is a mandatory task to prevent both natural disasters and economical losses. This paper presents the optimization of the geometry of a magnetic circuit for the detection of defects in pipelines by the magnetic flux leakage method. The main goal is to perform a sensitivity analysis on the geometrical parameters of the circuit to find configurations that improve the performance of the defect searching tool. The sensitivity analysis of the design parameters of the magnetic circuit is based on numerical evaluations of the performance of the tool using the finite element method. The commercial finite elements software utilized for this analysis is COMSOL Multiphysics®. The results obtained in this investigation serve to identify the geometrical configurations that provide better performance, with respect to other configurations, for the detection of the same defect. Also, by using the analytical model of the magnetic flux leakage, the results obtained by means of the analytical model can be compared to the results from the finite elements model. The findings of this investigation can be utilized as guidelines for the design of magnetic circuits for non-destructive testing using the magnetic flux leakage technique. Key words: Magnetic flux leakage; Non-destructive testing; Magnetic circuit; Sensitivity analysis; Finite elements. RESUMEN El monitoreo de integridad estructural en la industria petrolera es una tarea muy importante para prevenir desastres tanto ambientales como económicos. Este artículo presenta la optimización de la geometría del circuito magnético para la detección de fallas en oleoductos por la técnica de fuga de flujo magnético. El objetivo principal es realizar un análisis de los parámetros geométricos del circuito para encontrar la configuración que incremente el desempeño del sistema para la detección de fallas. El análisis de la sensibilidad de los parámetros del circuito se basa en una evaluación numérica del desempeño del sistema usando el análisis por el método de los elementos finitos. El software comercial utilizado para este análisis fue COMSOL Multiphysics®. Los resultados obtenidos en esta investigación sirven para identificar la configuración geométrica adecuada para la mejora del desempeño del sistema, con respecto a otras configuraciones, para la detección de la misma falla. También haciendo uso del modelo matemático del fenómeno, se pretende comparar los resultados obtenidos por el modelo matemático y el modelo por elementos finitos. Los descubrimientos en esta investigación pueden ser usados como guías para el diseño de circuitos magnéticos para ensayos no destructivos por la técnica de fuga de flujo magnético. Palabras claves: Fuga de flujo magnético; Ensayos no destructivos; Circuito magnético; Análisis de sensibilidad; Elementos finitos. Doi: http://dx.doi.org/10.15665/rp.v14i2.678 22 Prospect. Vol. 14, No. 2, Julio - Diciembre de 2016, págs. 22-30 1. INTRODUCTION create a flux density in the material under study near its saturation point. These permanent magnets are Magnetism, or magnetic force, is a physical made of compounds that include rare earth materials phenomenon in which some objects exert an attraction such as the combination of Iron-Boron-Neodymium. or repulsion force against others. Some known The magnetic circuits must be properly sized so that materials which have magnetic properties such as the distance between the magnetic circuit and the wall Nickel, Iron (magnetite), Cobalt and their respective of the pipeline remains as constant as possible as the alloys, are commonly known as permanent magnets. PIG travels along the pipeline [3]. However, all materials can be influenced by magnetic fields in a larger or smaller scale. Each material Figure 1, also shows how the magnetic field lines has unique features that can strength its magnetic behave in the absence and in the presence of a defect. effect. The magnetic properties of most materials are The magnetic flux is uniform if the wall does not have highly sensitive to environmental changes such as any defects (figure 1 a). If internal or external defects temperature fluctuations [1]. are present (figure 1 b), such as corrosion damage or cracks, the magnetic flux is distorted outside the wall The magnetic flux leakage (MFL) technique is an and this “leakage” is measured, typically by hall effect electromagnetic method used for nondestructive sensors [4]. testing, which helps detecting reductions in thickness, Magnetic flux leakage is not the only method to inspect cracks and other anomalies that can be found on the pipelines, other techniques that can be used include walls of oil pipelines, or metallic objects in general. As ultrasound, eddy currents [5] and Barkhausen noise a nondestructive testing method, the MFL technique [6]. Often times PIGs are equipped with both MFL does not permanently change the physical, chemical, and ultrasound sensors so that the MFL sensors detect mechanical or dimensional features of the object the superficial defects, while deeper defects are more under test. In general, the nondestructive test provides easily found by the ultrasonic sensors. The study of less exact data from the variable measured than the these techniques goes beyond the scope of this article. destructive test does. However, the nondestructive test is in general less expensive because the piece analyzed There are different approaches to model the process is not permanently damaged during the test. In some of defect detection by means of the MFL technique. cases, the nondestructive test is used to verify the The three most common approaches are analytical, homogeneity and continuity of the component, and equivalent circuit and finite elements modelling [7, these results can be complemented by destructive test. 8]. Sometimes analytical or circuit modelling are more In the oil and gas industry, these methods are used to convenient over finite element modelling since they inspect pipelines and detect cracks, corrosion damage require less computational resources. and leaks [2]. Pipelines are inspected by means of robotic tools called PIGs (Pipe Inspection Gauge), The Finite Element Method (FEM) is a powerful tool which travel on the inside, pushed by the fluid being to study the behavior of the underlying physical pumped, and are often equipped with and array of phenomena that enables defect detection by means of magnetic circuits similar to those shown in figure 1. the MFL technique [9]. The FEM method is a convenient approach for the analysis of the magnetic circuit used Figure 1. Principle of MFL, a) without defect, b) with in the MFL technique because it allows solving the defect. non-lineal equations governing the physical behavior Figura 1. Principio de MFL, a) sin defecto, b) con of the system, and allows estimating the value of defecto the magnetic field at any point in the circuit and its vicinities. The goal of this study is to improve the strength of the magnetic leakage signal in the presence of a defect. The leakage will be evaluated using the commercial software for FEM analysis COMSOL®, by changing the geometrical variables of the magnetic circuit and trying to find the best geometry of the system for the optimal leakage. The optimization of a MFL tool is a multiobjective As seen in figure 1, the main components of a magnetic optimization problem [10]. The optimization process for circuit are two magnets and a yoke that connects the the particular problem under study consists of finding magnets. The principal function of the magnets is to the optimal value for each geometrical parameter of magnetize the pipe wall. Most MFL magnetic circuits the system that maximizes the probability of detection incorporate permanent magnets, strong enough to of an anomaly. 23 Sensitivity analysis of a magnetic circuit for non-destructive testing by the magnetic flux leakage technique 1.1 Constitutive equations that govern the behaviour The defect is exposed to a magnetic field in the y-axis of a MFL magnetic circuit direction and it has a half positive magnetic charge (North Pole) and a half negative charge (South Pole). As a first approximation, the problem of pipeline inspection by MFL can be considered as a magneto- For this case study, a differential charge, dm, will be static problem in two dimensions. Maxwell equations defined as: govern the physical behavior of the magnetic field in the circuit. These equations are presented next [11]. dm=σs Rdθdz (1) •B=0 (8) where σs: Charge density. B=µ•H [T] (9) θ: The angle that r makes with the x-axis. The density charge is assumed to have a value of 1, Where H [A/m] is the intensity of the magnetic field, 2 since it does not change much the behavior of the B [T] is the density of the magnetic flux and µ [N/A ] generated magnetic field. Then the magnetic field is the permeability of the material. The first equation generated at a distance r from the charge dm is: describes the behavior of the magnetic flux in all the elements of the circuit.
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