1. Introduction Pipelines used in the petrochemical industries are an essential means of transporting materials economically, efficiently and safely. However, ferromagnetism can lead to cracking, corrosion and other defects due to operation, wear, stress and accidental damage. Moreover, because the pipelines work under the condition of high pressure and for long periods of time, if these defects cannot be discovered and repaired quickly, it will cause problems leading to lower transport efficiency, leaks and other issues. Most pipelines are built under the sea or underground, in the event there are some troubles, the repair cost will be very high. Magnetic flux leakage (MFL) is the most common technique used in pipeline inspection at present [1] . In this technique [2] , the wall of the pipelines is magnetised axially to near saturation flux density. If, at some point, the thickness of the wall is reduced by a defect, a higher fraction of the magnetic flux will ‘leak’ from the wall into the air inside and outside the pipe. The magnetic leakage field measured on the near side of the pipe contains information about the pipe condition. Then the identification of the defect can be implemented based on MFL signals by analysing the correlation between MFL signals and the defect geometry parameter [3] . Therefore, the analysis of MFL signals is the basis for MFL testing, and the finite element method (FEM) is used widely in MFL signals analysis. More recently, 2-D finite element methods have been used to study MFL signals under different defects shapes, materials, magnetising situation and so forth, and it is also proved to be an effective method [4-8] . However, in 2-D FEM defects are also treated as a 2-D profile rather than actual 3-D geometry, and the resulting MFL signal is single channel whereas the actual signals are multi- channel. In this paper, 3-D FEM is adopted to analyse the MFL signals, accurate 3-D defects are modelled and detailed MFL signal in the test surface are calculated by the method. The relationship MFL between defect geometry and MFL signals is discussed in detail; the influence of lift-off value and intensity of magnetisation is also studied. It is the basis for optimising the design of the magnetic detecting equipment and the quantitative testing of MFL. 2. Building and solving of the finite element model 2.1 3-D finite element computation of MFL numerical models Because the electromagnetic phenomena underlying the MFL systems still comply with the well-established electromagnetism, Maxwell’s equations are applicable to the analysis of the electric as well as the magnetic field within MFL systems. Since, in our work, permanent magnets are used for generation of the magnetic field, the electric field has not been taken into account and accordingly the magnetostatic analysis applies to our simulation study [9] . Therefore, electromagnetic phenomena in MFL are governed by the simplified Maxwell’s equation along with one constitutive relationship. Based on Maxwell’s equations [10] : !" ( 1 μ !" A) = J .................................(1) B= !" A .......................................(2) where µ, A, J, B represent magnetic permeability constant, magnetic vector potential, equivalent current density of permanent magnet and magnetic flux density vector, respectively. By the finite element method, from the above formula we can obtain [11] : K [ ] A { } = S { } ....................................(3) where [K] is a global stiff matrix, {S} is a column vector which contains the excitation source, {A} is an unknown column vector about magnetic vector potential. Using the boundary condition, the magnetic potential vector can be solved from formula (3), and then the distribution of the magnetic field can be obtained. 3-D FEM is applied to analyse oil-gas pipeline by ANSYS finite element software in this paper. 2.2 Building a solid model Calculations are made for a simple MFL detector, and Figure 1 shows the 3-D finite element solid model (air model is not given). The magnetic circuit is constituted by yoke, magnets, brushes and specimen, and a rectangular defect located at the centre of the Application of 3-D FEM in the simulation analysis for MFL signals Fengzhu Ji, Changlong Wang, Shiyu Sun and Weiguo Wang are with the Department of Electrical Engineering, Mechanical Engineering College, Hebei Shijiazhuang 050005, People’s Republic of China. Corresponding author: Fengzhu Ji. Tel: +86 31187994734; Fax: +86 3118794731; E-mail: [email protected]Fengzhu Ji, Changlong Wang, Shiyu Sun and Weiguo Wang Paper submitted 23 July 2008 Accepted 01 September 2008 The analysis of the magnetic flux leakage (MFL) signals is the basis of MFL testing. The magnetic flux leakage (MFL) of defects in pipes is simulated by using a three-dimensional (3-D) finite element method (FEM). The 3-D FEM model is built on the principle of magnetic flux leakage (MFL) testing. The distribution of magnetic flux density is obtained. The relationship between defect geometry parameter and MFL signals is discussed in detail; the influence of path station lift-off value and intensity of magnetisation is also studied in this paper. It is the basis for optimising the design of the magnetic detecting equipment and the quantitative testing of MFL. Keywords: Magnetic flux leakage testing, magnetic flux density, 3-D finite element, simulation analysis. Figure 1. 3-D finite element solid model DOI: 10.1784/insi.2009.51.1.32 32 Insight Vol 51 No 1 January 2009
Transcript
1. IntroductionPipelines used in the petrochemical industries are an essential means of transporting materials economically, efficiently and safely. However, ferromagnetism can lead to cracking, corrosion and other defects due to operation, wear, stress and accidental damage. Moreover, because the pipelines work under the condition of high pressure and for long periods of time, if these defects cannot be discovered and repaired quickly, it will cause problems leading to lower transport efficiency, leaks and other issues. Most pipelines are built under the sea or underground, in the event there are some troubles, the repair cost will be very high. Magnetic flux leakage (MFL) is the most common technique used in pipeline inspection at present[1]. In this technique[2], the wall of the pipelines is magnetised axially to near saturation flux density. If, at some point, the thickness of the wall is reduced by a defect, a higher fraction of the magnetic flux will ‘leak’ from the wall into the air inside and outside the pipe. The magnetic leakage field measured on the near side of the pipe contains information about the pipe condition. Then the identification of the defect can be implemented based on MFL signals by analysing the correlation between MFL signals and the defect geometry parameter[3]. Therefore, the analysis of MFL signals is the basis for MFL testing, and the finite element method (FEM) is used widely in MFL signals analysis.
More recently, 2-D finite element methods have been used to study MFL signals under different defects shapes, materials, magnetising situation and so forth, and it is also proved to be an effective method[4-8]. However, in 2-D FEM defects are also treated as a 2-D profile rather than actual 3-D geometry, and the resulting MFL signal is single channel whereas the actual signals are multi-channel. In this paper, 3-D FEM is adopted to analyse the MFL signals, accurate 3-D defects are modelled and detailed MFL signal in the test surface are calculated by the method. The relationship
MFL
between defect geometry and MFL signals is discussed in detail; the influence of lift-off value and intensity of magnetisation is also studied. It is the basis for optimising the design of the magnetic detecting equipment and the quantitative testing of MFL.
2. Building and solving of the finite element model
Because the electromagnetic phenomena underlying the MFL systems still comply with the well-established electromagnetism, Maxwell’s equations are applicable to the analysis of the electric as well as the magnetic field within MFL systems.
Since, in our work, permanent magnets are used for generation of the magnetic field, the electric field has not been taken into account and accordingly the magnetostatic analysis applies to our simulation study[9]. Therefore, electromagnetic phenomena in MFL are governed by the simplified Maxwell’s equation along with one constitutive relationship. Based on Maxwell’s equations[10]:
! " (1
µ! " A) = J .................................(1)
B = ! " A .......................................(2)
where µ, A, J, B represent magnetic permeability constant, magnetic vector potential, equivalent current density of permanent magnet and magnetic flux density vector, respectively.
By the finite element method, from the above formula we can obtain[11]:
where [K] is a global stiff matrix, {S} is a column vector which contains the excitation source, {A} is an unknown column vector about magnetic vector potential. Using the boundary condition, the magnetic potential vector can be solved from formula (3), and then the distribution of the magnetic field can be obtained. 3-D FEM is applied to analyse oil-gas pipeline by ANSYS finite element software in this paper.
2.2BuildingasolidmodelCalculations are made for a simple MFL detector, and Figure 1 shows the 3-D finite element solid model (air model is not given).The magnetic circuit is constituted by yoke, magnets, brushes and specimen, and a rectangular defect located at the centre of the
Application of 3-D FEM in the simulation analysis for MFL signals
Fengzhu Ji, Changlong Wang, Shiyu Sun and Weiguo Wang are with the Department of Electrical Engineering, Mechanical Engineering College, Hebei Shijiazhuang 050005, People’s Republic of China.
Fengzhu Ji, Changlong Wang, Shiyu Sun and Weiguo WangPapersubmitted23July2008 Accepted01September2008
The analysis of the magnetic flux leakage (MFL) signals is the basis of MFL testing. The magnetic flux leakage (MFL) of defects in pipes is simulated by using a three-dimensional (3-D) finite element method (FEM). The 3-D FEM model is built on the principle of magnetic flux leakage (MFL) testing. The distribution of magnetic flux density is obtained. The relationship between defect geometry parameter and MFL signals is discussed in detail; the influence of path station lift-off value and intensity of magnetisation is also studied in this paper. It is the basis for optimising the design of the magnetic detecting equipment and the quantitative testing of MFL.
Keywords: Magnetic flux leakage testing, magnetic flux density, 3-D finite element, simulation analysis.
Figure 1. 3-D finite element solid model
DOI: 10.1784/insi.2009.51.1.32
32 Insight Vol 51 No 1 January 2009
Insight Vol 51 No 1 January 2009 33
specimen. l, w and d denote, respectively, the length, width and depth of the defect. In the model, two permanent magnets, made of NdFeB material which is characteristic of smaller volume, lighter weight and higher coercive force, are used as the magnetic flux induction; the yoke and brushes use the same material, the relative permeability of which is 186,000, and the reference material is ferro-nickel alloy; there are many trademarks used in practice such as A3, X52, X60, X70 and so on. In these models X52, which is a familiar kind of steel, is adopted.
In the process of calculating for finite element model, the size of excited equipment (constituted by the yoke, magnets and brushes) and magnetisation clearance (MC, clearance between brush and specimen) hold the line. Scantling real values of the 3-D finite element solid model are shown in Table 1.
After the model is built, we should define the element type, material properties, then mesh the model based on the above analysis.
2.3LoadandsolvePermanent magnets are the excitation source of the system, and also are load, and the characteristics of magnets have been defined in material properties. When using ANSYS to treat with permanent magnets, they are translated automatically into equivalent current and apply on every element and node of the model.
Corresponding boundary conditions in this model satisfy the following relationship: q Using magnetic scalar potentials (MAG) to specify flux-normal
(homogeneous Neumann boundary condition), flux-parallel (Dirichlet boundary condition), and far-field zero, let MAG=0, which can satisfy the boundary condition.
q The outside air model of solid model adopt INFIN47 far-field element, so they are required to flag the surface of an infinite element which is pointing towards the open domain.
Then, the model can be solved and analysed.
3. Calculated results Figure 2 shows a surface plot of the amplitude of X, Y, Z direction component of magnetic flux density in the vicinity of a defect whose sizes are l=10 mm, w=10 mm, and d=5 mm. The X axial direction
of magnetic flux density is Bx the radial component of magnetic flux density, the surface plot is with positive, negative two pieces of peak value, and the midpoint of peak-peak value separation lies in defect centre, MFL signal is more intensive in peak; the Y axial direction of magnetic flux density is By the axial component of magnetic flux density, the surface plot is with one piece of peak value, and the peak value lies in defect centre, on the defect edge the MFL signal have a minimum, the signal is relatively intensive near the MFL signal peak value; The Z axial direction of magnetic flux density is Bz the circumference component of magnetic flux density, the surface plot is with two groups peak-peak value, the two groups peak-peak value are divided along the defect width direction from centre line, peak-peak value variation tendency opposite, MFL signals are intensive in peak-peak value too.
4. Various factors to influence the MFL signals
The shape of the defect is complex and diverse, usually the tested defect is equivalent to a rectangular one when analysing the defect characteristics from three shape parameters (the equivalent length, equivalent width and the biggest depth). Environmental factors, such as lift-off, intensity of magnetisation and so forth will also influence the MFL signals.
Figure 3 shows the relationship between the MFL peak-peak value (MFLpp) and the depth of defect at different lift-off values with constant width (10 mm), length (10 mm) and intensity of magnetisation. It can be seen that MFLpp is strongly related to defect depth, MFLpp following with the defect depth increasing, and the relationship between defect depth and MFLpp is nearly linear if other parameters keep constant.
Concerning with 2-D FEM, the relationship cannot be studied because the length of defect is assumed infinity. But 3-D FEM not only can analyse the influence of the depth and width of the defect, but also can study the influence of the length of the defect. Figure 4 shows the relationship between the MFL peak-peak value (MFLpp) and the length of the defect at different lift-off values with constant width (10 mm), depth (5 mm) and intensity of magnetisation. It can be seen that the defect length also plays an important part in MFLpp too. As the length increases, MFLpp will increase, and the influence is weakening while the lift-off value is increasing.
Figure 5 shows the relationship between the MFL peak-peak value (MFLpp) and the width of the defect at different lift-off values
Term size/mm
Yoke l : 400 w : 50 d : 40
Magnet l : 40 w : 50 d : 40
Specimen l : 400 w : 50 d : 10
MC 0
Table 1. 3-D finite element solid model scantling of structure
Figure 2. Surface plot of the amplitude for magnetic flux density
Figure 3. Relationship between MFLpp and the depth of defect
with constant length (10 mm), depth (5 mm) and intensity of magnetisation. It can be seen that the MFLpp originally increases following with the width of the defect, while the defect width beyond a certain value, MFLpp reduces with the width of defect. Otherwise it affects MFLpp less, mainly influences the separate of MFL peaks, which is shown in Figure 6, the separate of MFL peaks increases with defect width.
Compared with 2-D FEM using a single channel to catch information, 3-D FEM can show so much information with multi-channel that the diagnosis result is more accurate. Figure 7 shows the influence of the path station (the coordinate magnetic sensor moving path, and take the defect centre as zero point) and lift-off to MFL peak-peak value. It can be seen that the MFL peak-peak value (MFLpp) is weak off from the defect centre to two sides, the more the value of lift-off, the weaker the signals, while reaching a certain point the signals would be not tested exactly. So the lift-off value should be chosen reasonably according to the actual circumstance when designing equipment for MFL testing.
When other parameters keep constant, the intensity of magnetisation will change following with magnet coercive force (HC) value. Figure 8 shows the variety of MFL peak-peak value (MFLpp) following the intensity of magnetisation. It can be seen that the MFLpp originally increases following with the intensity of magnetisation, and tends towards stability when the intensity reaches a certain value. When the ferromagnetic material reaches the magnetic saturated condition, the increase of magnetisation of the external magnetic field contributes little to strong the intensity of defect magnetic field. The design of the magnetic circuit should be made so that the test piece reaches as close to magnetic saturation as possible.
5. ConclusionsCompared with 2-D FEM, 3-D FEM is capable of reflecting the characteristic of MFL signals more generally and accurately. The 3-D FEM model is built on the principle of MFL testing. The distribution of local region magnetic field at length direction is obtained, which is unavailable using 2-D FEM. It makes the
Figure 4. Relationship between MFLpp and the length of defect
Figure 5. Relationship between MFLpp and the width of defect
Figure 6. Contour plot x-component of magnetic flux density
34 Insight Vol 51 No 1 January 2009
Insight Vol 51 No 1 January 2009 35
analysis result more accurate and approaching the actual condition, and lays a foundation for further analysis. The effect of geometry parameter of the defect, the lift-off and the magnetisation intensity to MFL signals are also studied. It is the basis for optimising the design of the magnetic detecting equipment.
AcknowledgementsThis research was supported in part by the Natural Science Foundation of Hebei Province (No E2008001258), PR China.
References 1. Ding Jinfeng, Kang Yihua and Wu Xinjun, ‘Tubing thread
inspection by magnetic flux leakage’, NDT&E Int, 39, 53-56, 2006.
2. Gwan Soo Park and Sang Ho Park, ‘Analysis of the velocity-induced eddy current in MFL type NDT’, IEEE Trans Magn, 4(2), 663-66, 2004.
3. Fengzhu Ji, Changlong Wang, Xianzhang Zuo, Songshan Hou and Siyang Liang, ‘LS-SVMs-based reconstruction of 3-D defect profile from magnetic flux leakage signals’, Insight, 49(9), 516-520, 2007.
4. F I Al-Naemi, J P Hall and A J Moses, ‘FEM modeling techniques of magnetic flux leakage-type NDT for ferromagnetic plate inspections’, Journal of Magnetism and Magnetic Materials, 304, e790-e793, 2006.
5. Miya Kenzo, ‘Recent advancement of electromagnetic nondestructive inspection technology in Japan’, IEEE Trans Magn, 38(2), 321-326, 2002.
6. M Katoh, K Nishio and T Yamaguchi, ‘The influence of modeled B–H curve on the density of the magnetic leakage flux due to a flaw using yoke-magnetization’, NDT&E Int, 37, 603-609, 2004.
7. M Katoh, N Masumoto and K Nishio et al, ‘Modeling of the yoke-magnetization in MFL-testing by finite elements’, NDT&E Int, 36(7), 479-86, 2003.
8. J Y Lee, S J Lee, D C Jiles et al, ‘Sensitivity analysis of simulations for magnetic particle inspection using the finite-element method [J]’, IEEE Trans Magn, 39(6), 604-06, 2003.
9. Yong Li, J Wilson and Gui Yun Tian, ‘Experiment and simulation study of 3D magnetic field sensing for magnetic flux leakage defect characterization [J]’, NDT&E Int, doi:10.1016/j.ndteint.2006.08.002, 2006.
10. Sunho Yang, ‘Finite element modeling of current perturbation method of nondestructive evaluation application [D]’, Iowa State University, 13-34, 2000.
11. Jin Jianming, ‘The Finite Element Method of the Electromagnetic [M]’, in Chinese, Wang Jianguo translation, Xi’an: Xidian University Press, 106-109, 1998.
Figure 7. Influence of the path station and lift-off to MFLpp
Figure 8. The variety of MFL signals following the intensity of magnetisation
4th European-American Workshopon Reliability of NDE
24-26 June 2009
BAM, Berlin
The workshop will be organised by the German Society for Non-Destructive Testing (DGZfP) in cooperation with the Federal Institute of Materials Testing (BAM), the American Society for
Nondestructive Testing (ASNT) and the Southwest Research Institute (SwRI).
For further information contact: Steffi Schäske, Head of Conference Department, DGZfP e.V., Max-Planck-Straße 6, 12489 Berlin.
