A method for quantifying a magnetic flux leakage signal characteristic

Abstract

The application discloses a kind of quantitative methods of magnetic flux leakage signal characteristics, including based on the step of establishing subarea magnetic charge distribution density model, the step of establishing subarea magnetic charge received coulomb force model and the step of establishing the magnetic charge amount equation group of defect area, obtain the magnetic charge amount equation group of defect area, in the step of establishing magnetic charge density model, obtain the magnetic charge density model of defect area first sidewall, based on the step of establishing improved effective field model to obtain improved effective field model, and in the step of establishing the relationship model between improved magnetization intensity and stress to obtain the relationship model between improved magnetization intensity and stress, again based on improved magnetic charge density model to obtain composite magnetic charge analytical model, again through experimental verification step, improved magnetic charge density model and composite magnetic charge analytical model are verified.The non-uniform distribution of magnetic charge and stress of stress concentration area are introduced into composite magnetic charge analytical model in the application, so that the calculation and measurement result of magnetic flux leakage signal characteristics is more accurate.

Description

Technical Field

[0001] This invention belongs to the field of nondestructive testing technology, and in particular relates to a method for quantifying the characteristics of magnetic leakage signals. Background Technology

[0002] With the rapid development of industry, the production and use of ferromagnetic materials are becoming increasingly widespread, and they are now applied in various fields of life. Ferromagnetic materials are prone to aging and corrosion during long-term service, leading to defects. Therefore, regular inspection and maintenance of ferromagnetic materials are particularly important. Because ferromagnetic materials have large stress concentration zones at defects, when these zones reach the yield point, the defects continue to expand, potentially causing accidents.

[0003] In existing technologies, the theory of magnetic flux leakage detection does not take into account the effects of non-uniform magnetic charge distribution and stress concentration areas, which leads to large errors in the calculation and measurement results of magnetic flux leakage signal characteristics, posing significant challenges to the quantitative evaluation of ferromagnetic materials.

[0004] To address the aforementioned shortcomings, it is necessary to study a quantification method for leakage magnetic signal characteristics. Summary of the Invention

[0005] The purpose of this invention is to provide a method for quantifying the characteristics of magnetic leakage signals. Based on the magnetic effect, and combined with the non-uniform distribution of magnetic charge and the stress concentration area at the defect, a composite magnetic charge analytical model is obtained. This solves the technical problem that the calculation and measurement results of magnetic leakage signals are greatly erroneous due to the influence of the non-uniform distribution of magnetic charge and the stress concentration area during the quantification process, and that it is difficult to quantify and evaluate the characteristics of magnetic leakage signals at defects in ferromagnetic materials.

[0006] This invention provides a method for quantifying the characteristics of magnetic flux leakage signals, comprising: based on the step of establishing a sub-region magnetic charge distribution density model, obtaining m×n sub-regions of the defect region and a sub-region magnetic charge distribution density model; then, in the step of establishing a Coulomb force model of the magnetic charge in the sub-regions, obtaining the Coulomb force model of the magnetic charge in the m×n sub-regions; then, in the step of establishing a set of magnetic charge equations for the defect region, simultaneously solving the Coulomb force models of the magnetic charge in the m×n sub-regions to obtain a set of magnetic charge equations for the defect region; in the step of establishing a magnetic charge density model, calculating the magnetic charge of each sub-region according to the set of magnetic charge equations for the defect region; and substituting the magnetic charge of each sub-region into the sub-region magnetic charge distribution density model to obtain the magnetic charge density model of the first sidewall of the defect region.

[0007] Based on the step of establishing an improved effective field model, the elastic effective field model and the plastic effective field model are substituted into the effective field model to obtain an improved effective field model. In the step of establishing an improved relationship model between magnetization intensity and stress, the improved effective field model is substituted into the relationship model between magnetization intensity and stress to obtain an improved relationship model between magnetization intensity and stress. The improved relationship model between magnetization intensity and stress is combined with the magnetic charge density model of the first sidewall of the defect region to obtain an improved magnetic charge density model. Based on the step of establishing a composite magnetic charge analytical model, the improved magnetic charge density model is substituted into the magnetic charge model to obtain a composite magnetic charge analytical model.

[0008] The improved magnetic charge density model and the composite magnetic charge analytical model were then verified through experimental steps.

[0009] Optionally, in the step of establishing the magnetic charge distribution density model of the sub-region, the magnetic charge in the steady state under the action of Coulomb force exhibits a non-uniform distribution. The sidewall length at the defect location of the ferromagnetic material is set to D. y ×D z The defective region is divided into m×n sub-regions, each with a side length of m. The resulting model for the magnetic charge distribution density in the sub-region is:

[0010]

[0011] Where i equals 1, 2, 3…n; j equals 1, 2, 3…m; ρ ij Q represents the magnetic charge density of the subregion. ij s represents the magnetic charge of the sub-region; s represents the area of ​​the sidewall of the defect region.

[0012] Optionally, in the step of establishing the Coulomb force model of the magnetic charge in the sub-region, based on m×n sub-regions, when the magnetic charge on the sidewall of the defect region is in a stable state, the sum of the magnetic force vectors on the magnetic charge on the sidewall of the defect region is 0, thus obtaining the Coulomb force model of the magnetic charge in the sub-region:

[0013]

[0014]

[0015]

[0016] Among them, Q (i，j)+ Q represents the magnetic charge of each sub-region of the first sidewall of the defect region. (i，j)- q represents the magnetic charge of each sub-region of the second sidewall of the defect region. (a,b)Let r be the unit point magnetic charge within the sidewall of the defect region; a equals 1, 2, 3…n-1, b equals 1, 2, 3…m-1, and a is not equal to b; r3 is the distance between magnetic charges within the same sidewall of the defect region; r4 is the distance between magnetic charges between the first and second sidewalls of the defect region; K is the Coulomb constant.

[0017] Optionally, in the step of establishing the magnetic charge equations for the defect region, since there are m×n magnetic charge sub-regions within both the first and second sidewalls of the defect region, the Coulomb force models of the sub-regions within the m×n sub-regions are combined according to the Coulomb force model of the magnetic charge in the sub-regions to obtain the magnetic charge equations for the defect region as follows:

[0018]

[0019]

[0020]

[0021] Where i equals 1, 2, 3…n, j equals 1, 2, 3…m; Q (i，j)+ Q represents the magnetic charge of the m×n sub-regions of the first sidewall of the defect region; (i，j)- q represents the magnetic charge of m×n sub-regions on the second sidewall of the defect region; (a,b) R is the unit point magnetic charge within the sidewall of the defect region; a and b are both constants; r3 is the distance between magnetic charges within the same sidewall of the defect region; r4 is the distance between magnetic charges between the first and second sidewalls of the defect region; K is the Coulomb constant.

[0022] Optionally, in the step of establishing the magnetic charge density model, Q for each sub-region is calculated using the set of magnetic charge equations for the defect region. (n,m)+ The magnetic charge quantity, and Q of each sub-region (n,m)+ Substituting the magnetic charge quantity into the sub-region magnetic charge distribution density model, the magnetic charge density model of the first sidewall of the defect region is obtained as follows:

[0023]

[0024] Among them, D y D represents the width of the defect area. z D represents the depth of the defect area. x The length of the defective region.

[0025] Optionally, in the step of establishing the improved effective field model, based on the effective field model and combined with the influence of stress in the stress concentration zone of the defect region on the magnetic charge density distribution, the effective field model for the elastic stage is obtained as follows:

[0026]

[0027] in, The effective elastic field is represented by θ, the angle between the magnetization direction and the stress direction, ν, Poisson's ratio, σ, and λ. s M is the magnetostriction coefficient; s μ is the saturation magnetization; μ0 is the free permeability;

[0028] The effective field model for the plastic stage is obtained as follows:

[0029]

[0030] in, For the plastic effective field; k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume; ε p λ represents the amount of plastic deformation. s ρ is the magnetostriction coefficient; μ0 is the free permeability; E is Young's modulus; M s The saturation magnetization;

[0031] Substituting the elastic and plastic effective field models into the effective field model, we obtain the improved effective field model as follows:

[0032]

[0033] Where H is the excitation magnetic field; θ is the angle between the magnetization direction and the stress direction; ν is Poisson's ratio; σ is the stress; λ s M is the magnetostriction coefficient; s ε is the saturation magnetization; μ0 is the free permeability; k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume in the defect region; ε p E represents the amount of plastic deformation; E represents Young's modulus.

[0034] Optionally, in the step of establishing the improved relationship model between magnetization and stress, in the case of leakage magnetic field in ferromagnetic materials, the improved effective field model is substituted into the relationship model between magnetization and stress to obtain the improved relationship model between magnetization and stress:

[0035]

[0036] Where M is the magnetization; M s H represents the magnetic saturation magnetization. eff α represents the effective field; α is the shape coefficient of the magnetization curve.

[0037] Optionally, in the improved magnetic charge density model step, the improved model of the relationship between magnetization and stress is combined with the magnetic charge density model of the first sidewall of the defect region to obtain the improved magnetic charge density model as follows:

[0038]

[0039] Where, ρ (i,j) denoted as magnetic charge density; μ0 as vacuum permeability; M as magnetization intensity; and α as the shape factor of the magnetization curve.

[0040] Optionally, in the step of establishing the analytical model of the composite magnetic charge, the improved magnetic charge density model is substituted into the magnetic charge model to obtain the analytical model of the composite magnetic charge as follows:

[0041]

[0042] Where, ρ (i,j) denoted as , where μ is the magnetic charge density; μ0 is the vacuum permeability; r is the distance between the detection point and the sidewall of the defect region; m is a sub-region in the horizontal direction of the sidewall of the defect region; n is a sub-region in the vertical direction of the sidewall of the defect region; i is a sub-region in the vertical direction of the sidewall of the defect region; and j is a sub-region in the horizontal direction of the sidewall of the defect region.

[0043] Optionally, in the experimental verification step, the magnetic charge density under stress is calculated based on the improved magnetic charge density model to verify the improved magnetic charge density model; the leakage magnetic signal in the elastic stage and the leakage magnetic signal in the plastic stage are calculated based on the composite magnetic charge analytical model to verify the composite magnetic charge analytical model.

[0044] Compared with existing technologies, this invention is based on magnetomechanical effects. It introduces the non-uniform distribution of magnetic charge in a stable state under the action of Coulomb force and the influence of stress in stress concentration areas on the magnetic charge density distribution into the magnetic charge model, resulting in a composite magnetic charge analytical model. This makes the calculation and measurement results of leakage magnetic signal characteristics more accurate and facilitates the quantification of leakage magnetic signal characteristics of ferromagnetic materials. Attached Figure Description

[0045] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein:

[0046] Figure 1 This is a schematic diagram of the non-uniform distribution of magnetic charge on the defect sidewall of the present invention;

[0047] Figure 2 This is a contour map of the non-uniform magnetic charge distribution of the present invention;

[0048] Figure 3 This is a diagram showing the magnetic charge density distribution of the defect sidewall under different stress conditions according to the present invention.

[0049] Figure 4This is a graph showing the relationship between stress and magnetic charge density in this invention;

[0050] Figure 5 This is a diagram showing the axial components of the magnetic flux leakage signal under different stresses according to the present invention.

[0051] Figure 6 This is a radial component diagram of the magnetic flux leakage signal under different stresses according to the present invention.

[0052] Figure 7 This is a graph showing the relationship between stress and eigenvalues ​​and the rate of change of eigenvalues ​​in this invention;

[0053] Figure 8 This is a diagram showing the axial components of the magnetic flux leakage signal under different plastic deformations according to the present invention.

[0054] Figure 9 This is a radial component diagram of the magnetic flux leakage signal for different plastic deformations according to the present invention;

[0055] Figure 10 This is a graph showing the axial component of plastic deformation and magnetic flux leakage signal under different stresses according to the present invention.

[0056] Figure 11 This is a diagram showing the radial component of plastic deformation and magnetic flux leakage signal under different stresses according to the present invention.

[0057] Figure 12 This is a graph showing the relationship between the magnetostriction coefficient and the inflection point position of the present invention.

[0058] Figure 13 This is a diagram showing the axial components of the leakage magnetic field signal under different stresses in the experiments of this invention;

[0059] Figure 14 This is a radial component diagram of the leakage magnetic field signal under different stresses in the experiment of this invention;

[0060] Figure 15 This is a graph showing the axial component fitting and eigenvalue analysis in the experiment of this invention;

[0061] Figure 16 This is a graph showing the radial component fitting and eigenvalue analysis in the experiment of this invention;

[0062] Figure 17 This is a diagram showing the axial components of the magnetic flux leakage signal under different plastic deformations in the experiments of this invention.

[0063] Figure 18 This is a radial component diagram of the magnetic flux leakage signal under different plastic deformations in the experiments of this invention;

[0064] Figure 19 This is a comparison chart of the uniform magnetic charge model and the improved magnetic charge model under different tensile forces in this invention.

[0065] Figure 20This is a schematic diagram of the experimental equipment of the present invention. Detailed Implementation

[0066] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Unless otherwise specified, the techniques used in the embodiments are conventional means well known to those skilled in the art.

[0067] It should be noted that, unless otherwise stated, the technical or scientific terms used in this invention should be understood in their ordinary sense by those skilled in the art. The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0068] This embodiment provides a method for quantifying the characteristics of magnetic leakage signals, including: based on the step of establishing a sub-region magnetic charge distribution density model, obtaining m×n sub-regions of the defect region and a sub-region magnetic charge distribution density model; then, in the step of establishing a Coulomb force model of the magnetic charge in the sub-regions, obtaining the Coulomb force model of the magnetic charge in the m×n sub-regions; then, in the step of establishing a set of magnetic charge equations for the defect region, simultaneously solving the Coulomb force models of the magnetic charge in the m×n sub-regions to obtain a set of magnetic charge equations for the defect region; in the step of establishing a magnetic charge density model, calculating the magnetic charge of each sub-region according to the set of magnetic charge equations for the defect region; and substituting the magnetic charge of each sub-region into the sub-region magnetic charge distribution density model to obtain the magnetic charge density model of the first sidewall of the defect region.

[0069] Based on the step of establishing an improved effective field model, the elastic effective field model and the plastic effective field model are substituted into the effective field model to obtain an improved effective field model. In the step of establishing an improved relationship model between magnetization intensity and stress, the improved effective field model is substituted into the relationship model between magnetization intensity and stress to obtain an improved relationship model between magnetization intensity and stress. The improved relationship model between magnetization intensity and stress is combined with the magnetic charge density model of the first sidewall of the defect region to obtain an improved magnetic charge density model. Based on the step of establishing a composite magnetic charge analytical model, the improved magnetic charge density model is substituted into the magnetic charge model to obtain a composite magnetic charge analytical model.

[0070] The improved magnetic charge density model and the composite magnetic charge analytical model were then verified through experimental steps.

[0071] This embodiment provides a method for quantifying the characteristics of magnetic flux leakage signals, wherein the finite element model is a long-distance oil and gas pipeline.

[0072] The specific steps of the quantization method for leakage magnetic signal characteristics in this embodiment are as follows:

[0073] Steps for establishing a sub-region magnetic charge distribution density model:

[0074] Currently, the magnetic charge model has been widely used in the analysis of leakage magnetic signals. The defect region generates magnetic charges, which are distributed on the sidewalls of the defect region. Therefore, the leakage magnetic field at a distance p from the infinitesimal surface dydz on the sidewall of the defect region, i.e., the magnetic charge model, is:

[0075]

[0076] Where ρ is the magnetic charge density, with units of Wb / mm². 2 μ0 is the vacuum permeability in H / m; r is the distance from the detection point to the sidewall of the defect region in the ferromagnetic material in mm.

[0077] The magnetic charge in defect regions of ferromagnetic materials is affected by the defect shape. Under the influence of Coulomb force, the magnetic charge in the steady state exhibits a non-uniform distribution, such as... Figure 1 As shown, the defect side length is D y ×D z The rectangular defect area is divided into m×n sub-regions, each with a side length of m. Therefore, we only need to determine the magnetic charge quantity of each sub-region, and then obtain the magnetic charge distribution density of each sub-region:

[0078]

[0079] Where i equals 1, 2, 3…n, j equals 1, 2, 3…m; ρ ij It is the magnetic charge density of the subregion, in Wb / mm².2 Q ij is the magnetic charge of the subregion, in Wb; s is the area of ​​the defect sidewall, in mm. 2 .

[0080] Steps for establishing a Coulomb force model for the magnetic charge in a subregion:

[0081] like Figure 1 As shown, plane S1 represents the first sidewall of the defect region, and plane S2 represents the second sidewall of the defect region. A mathematical model is established using plane S1. The magnetic charge experiences a repulsive force on plane S1 and an attractive force from the magnetic charge on plane S2. When the magnetic charge on the sidewall of the defect region is in a stable state, the sum of the magnetic forces acting on the magnetic charge is zero. Therefore, the Coulomb force model for the magnetic charge in the sub-region is:

[0082]

[0083]

[0084]

[0085] Among them, Q (i，j)+ Q represents the magnetic charge of any sub-region of the first sidewall of the defect region, in Wb. (i，j)- q represents the magnetic charge of any subregion of the second sidewall of the defect region, in Wb. (a,b) Let r be the unit point magnetic charge within the planar region, with units of Wb; a equals 1, 2, 3…n-1, b equals 1, 2, 3…m-1, and a is not equal to b; r3 represents the distance between magnetic charges in the same plane; r4 represents the distance between magnetic charges in different planes; K is the Coulomb constant.

[0086] Therefore, any q (a,b) Unit magnetic charge is subjected to Q in the subregion (i,j) The horizontal and vertical components of the Coulomb force are expressed as follows:

[0087]

[0088]

[0089]

[0090]

[0091] Among them, F m For the horizontal component; F n For the horizontal component; Q (i，j)+ Q represents the magnetic charge of m×n subregions in the S1 plane, in Wb. (i，j)- q represents the magnetic charge of m×n subregions in the S2 plane, in Wb.(a,b) Rb represents the unit point magnetic charge within the planar region; a and b are constants, with units of mm; r3 represents the distance between magnetic charges within the same plane, with units of mm; r4 represents the distance between magnetic charges in different planes, with units of mm; K is the Coulomb constant, K = 8.986 × 109, with units of Nm. 2 / c 2 .

[0092] Steps to establish the magnetic charge equations for the defect region:

[0093] Since there are m×n magnetic charge sub-regions within planes S1 and S2, and based on the Coulomb force model of the magnetic charge in each of the m×n sub-regions, the Coulomb force models of the magnetic charge in each of the sub-regions are combined to obtain the following set of equations for the magnetic charge in the defect region:

[0094]

[0095]

[0096]

[0097] Where i equals 1, 2, 3…n, j equals 1, 2, 3…m; Q (i，j)+ Q represents the magnetic charge of m×n sub-regions on the first sidewall of the defect region, in Wb. (i，j)- q represents the magnetic charge of m×n sub-regions on the second sidewall of the defect region, in Wb. (a,b) denoted as , where is the unit point magnetic charge within the sidewall of the defect region, in Wb; a and b are constants, in mm; r3 is the distance between magnetic charges within the same sidewall of the defect region, in mm; r4 is the distance between magnetic charges between the first and second sidewalls of the defect region, in mm; K is the Coulomb constant, in Nm. 2 / c 2 .

[0098] Steps to establish a magnetic charge density model:

[0099] The magnetic charge Q of each sub-region was calculated using the set of magnetic charge equations for the defect region. (n,m)+ And the magnetic charge Q of each sub-region (n,m)+ Substituting into the sub-region magnetic charge distribution density model, the magnetic charge density model of the first sidewall of the defect region is obtained as follows:

[0100]

[0101] Among them, D y D represents the width of the defect area, in mm. z D represents the depth of the defect area, in mm. xThe length of the defect area is in mm.

[0102] In this embodiment, the magnetic charge density model of the second sidewall of the defect region is also obtained as follows:

[0103]

[0104] Among them, D y D represents the width of the defect area. z D represents the depth of the defect area. x The length of the defective region.

[0105] The magnetic charge density of each sub-region within the defect area can be calculated using formulas (13) and (14). By analyzing the magnetic charge density of each sub-region, the distribution of the magnetic charge density in the defect area can be obtained, such as... Figure 2 As shown, the magnetic charge distribution on the sidewall of the defect region S1 is non-uniform.

[0106] Steps to establish an improved effective field model:

[0107] The defect region contains a stress concentration area, and the stress in this area affects the distribution of magnetic charge. Therefore, the magnetic field strength in the defect region is:

[0108]

[0109] Where H is the excitation magnetic field strength; H eff Effective magnetic field; It is an elastic effective field; It is a plastic effective field.

[0110] In the case of magnetic leakage It can be represented as:

[0111]

[0112] Where θ is the angle between the magnetization direction and the stress direction, in degrees; ν is Poisson's ratio; σ is stress, in MPa; λ s M is the magnetostriction coefficient, measured in ppm. s It is the saturation magnetization, measured in A / m. -1 μ0 is the permeability of free space, in units of H / m.

[0113] The effective field model for plasticity is expressed as:

[0114]

[0115] Where k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume in the defect region; ε pIt is the amount of plastic deformation, expressed as a percentage; λ s M is the magnetostriction coefficient, measured in ppm; μ0 is the free permeability, measured in H / m; E is Young's modulus, measured in GPa; M s It is the saturation magnetization, measured in A / m. -1 .

[0116] Substituting the elastic and plastic effective field models into the effective field model, we obtain the improved effective field model as follows:

[0117]

[0118] Where H is the excitation magnetic field; θ is the angle between the magnetization direction and the stress direction; ν is Poisson's ratio; σ is the stress, in MPa; λ s M is the magnetostriction coefficient, measured in ppm. s It is the saturation magnetization, measured in A / m. -1 μ0 is the free magnetic permeability, in H / m; k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume in the defect region; ε p E is the amount of plastic deformation, expressed as a percentage; E is Young's modulus, expressed as GPa.

[0119] Steps for establishing an improved model of the relationship between magnetization and stress:

[0120] In the case of leakage magnetic flux in ferromagnetic materials, the relationship between magnetization and stress is modeled as follows:

[0121]

[0122] Where M is the magnetization, with units of A / m. -1 M s It is the magnetic saturation magnetization, with units of A / m. -1 H is the leakage magnetic field strength, in units of H / m; α is the shape factor of the magnetization curve.

[0123] Substituting the improved effective field model into the relationship model between magnetization and stress, we obtain an improved relationship model between magnetization and stress:

[0124]

[0125] Where M is the magnetization, with units of A / m. -1 M s It is the magnetic saturation magnetization, with units of A / m. -1 H eff The effective field is expressed in H / m.

[0126] Improved magnetic charge density model steps:

[0127] By combining the improved model of the relationship between magnetization and stress with the magnetic charge density model of the first sidewall of the defect region, the improved magnetic charge density model is obtained as follows:

[0128]

[0129] Where, ρ (i,j) Magnetic charge density, in Wb / mm² 2 M represents magnetization, measured in A / m. -1 ; a is the shape factor of the magnetization curve.

[0130] Steps for establishing an analytical model of a composite magnetic charge:

[0131] In the step of establishing the analytical model of the composite magnetic charge, the improved magnetic charge density model is substituted into the magnetic charge model, which is a classical magnetic charge model, thus obtaining the analytical model of the composite magnetic charge:

[0132]

[0133] Where, ρ (i,j) Magnetic charge density, in Wb / mm² 2 μ0 is the vacuum permeability in H / m; r is the distance between the detection point and the sidewall of the defect region in mm; m is the horizontal sub-region of the sidewall of the defect region in mm; n is the vertical sub-region of the sidewall of the defect region in mm; i is a vertical sub-region of the sidewall of the defect region in mm; j is a horizontal sub-region of the sidewall of the defect region in mm.

[0134] This embodiment also includes an experimental verification step to verify the accuracy of the improved magnetic charge density model and the composite magnetic charge analytical model. The experimental verification step takes X70 steel in actual engineering applications as an example, and the specific steps are as follows:

[0135] The parameters in formula (22) are specifically set according to X70 steel:

[0136] k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume; E is Young's modulus, E = 207 GPa; υ is Poisson's ratio, υ = 0.3; M s M is the saturation magnetization. s = 1.585 × 10⁶ A / m -1 ;λ s λ is the magnetostriction coefficient. s =1.2ppm; σ is stress, in MPa; θ is the angle between stress and magnetic field, θ = 0°; ε p It is the amount of plastic deformation.

[0137] The experimental verification steps in this embodiment include the calculation of magnetic charge density under stress, the calculation of leakage magnetic signal in the elastic stage, and the calculation of leakage magnetic signal in the plastic stage. The specific calculations are as follows:

[0138] (1) Calculation of magnetic charge density under stress:

[0139] In this embodiment, the size of the defect area is length D. x =1mm, width D y =10mm, depth D z =10mm, apply tensile forces of 0-50MPa at 10MPa intervals, substitute the size and tensile force data into the improved magnetic charge density model for calculation, and then analyze the variation law of magnetic charge density in the stress concentration area of ​​different defect areas under stress based on the calculated magnetic charge density of the defect area.

[0140] Figure 3 As shown, as the stress in the stress concentration zone increases, the magnetic charge density on the defect sidewall gradually decreases, and the overall magnetic charge still exhibits a non-uniform distribution.

[0141] Figure 4 As shown, the magnetic charge density decreases approximately linearly with increasing stress in the stress concentration area. The rates of change of magnetic charge density are, in order: 6.25%, 6.67%, 4.28%, 3.73%, and 3.87%.

[0142] (2) Calculation of leakage magnetic field signal in the elastic stage:

[0143] The magnetic flux leakage signal of the defect region under different stresses; in this embodiment, the size of the defect region is D. x =10mm, width D y =1mm, depth D z =1mm, and a tensile force of 0-50kN was applied at intervals of 10kN. The dimensional and tensile force data were substituted into a composite magnetic charge analytical model for calculation, thereby obtaining the leakage magnetic signal of the defect area in the elastic stage.

[0144] like Figure 5 As shown, the leakage magnetic flux signal of the axial component under different stresses, from Figure 5 As can be seen, the axial component has two maxima. As the stress in the stress concentration area increases, the amplitude of the leakage magnetic signal gradually decreases, which indicates that the magnetic charge density decreases as the stress in the stress concentration area increases.

[0145] like Figure 6 As shown, the radial component of the leakage magnetic field signal under different stresses, from Figure 6As can be seen, the radial component exhibits peaks and valleys, and the amplitude of the leakage magnetic field signal gradually decreases as the stress in the stress concentration area increases. Similarly, it can be concluded that the magnetic charge density decreases as the stress in the stress concentration area increases.

[0146] like Figure 7 As shown, the eigenvalues ​​of the magnetic signal decrease nonlinearly with increasing stress. The eigenvalues ​​of the axial component change at rates of 20.36%, 6.5%, 16.7%, and 9.2%, while those of the radial component change at rates of 23.24%, 7.82%, 18.12%, and 5.51%. This indicates that the radial component eigenvalues ​​change at a larger rate and are more sensitive to stress changes in stress concentration areas.

[0147] (3) Calculation of leakage magnetic field signal during the plastic stage:

[0148] In this embodiment, the stress magnitude and plastic deformation in the stress concentration zone of the defect area were changed. The applied stress ranged from 0 to 50 kN with an interval of 10 kN, and the plastic deformation ranged from 0% to 50% with an interval of 5%. The size and tensile data were substituted into the composite magnetic charge analytical model for calculation. Then, for the leakage magnetic signal of the defect area in the plastic stage, the characteristic values ​​of the axial component peak value and the radial component peak-valley value were extracted, and the variation law of plastic deformation on the characteristic values ​​was analyzed.

[0149] like Figure 8 As shown, with the increase of plastic deformation, the leakage magnetic signal of the axial component first increases and then decreases.

[0150] like Figure 9 As shown, with the increase of plastic deformation, the leakage magnetic signal of the radial component first increases and then decreases.

[0151] The influence of plastic deformation under different stresses in the stress concentration zone on the magnetic signal and the influence of stress on the inflection point were analyzed. The influence of plastic deformation under stress of 10-50kN on the leakage magnetic signal was also analyzed.

[0152] like Figure 10 As shown, during the plastic stage, the leakage magnetic signal intensity of the axial component decreases with increasing stress, and then increases with increasing plastic deformation, with an inflection point appearing between 0.2 and 0.3 plastic deformation.

[0153] like Figure 11 As shown, during the plastic stage, the leakage magnetic signal intensity of the radial component decreases with increasing stress, and then increases with increasing plastic deformation, with an inflection point appearing between 0.2 and 0.3 plastic deformation.

[0154] The magnetostriction coefficient was analyzed under a tensile force of 10 kN, and the magnetostriction λ was adjusted accordingly.s It is 1ppm, 2ppm, 3ppm, 4ppm.

[0155] like Figure 12 As shown, the magnetostriction coefficient affects the position of the inflection point. As the magnetostriction coefficient increases, the inflection point shifts to the right. Therefore, it can be concluded that the inflection point is related to the properties of the ferromagnetic material itself.

[0156] In the experimental verification steps of this embodiment, a rectangular plate-shaped sample made of X70 material is used. The sample size is 800mm*60mm*16mm, the cross-sectional area is 60mm*16mm, and the defect size is 16mm*1mm*2mm.

[0157] The experimental setup mainly consists of a tensile testing machine, an excitation device, a software control system, and a signal acquisition system.

[0158] First, the tensile testing machine is model SHT-4106, with clamps on both the top and bottom sides. The sample material is placed on the tensile testing machine, tightened, and tension is applied.

[0159] The probe in the signal acquisition system is a three-axis MLX90393 magnetic induction sensor with 16-bit magnetic field resolution. The signal detected by the sensor is received via serial port, filtered and amplified, converted from analog to digital, and then transmitted to the host computer. Finally, the signal is stored and displayed by LabVIEW software.

[0160] The specific steps for experimental verification in this embodiment are as follows:

[0161] Step 1): Place the X70 steel sample on the tensile testing machine and fix it in place, and use the clamps on both sides of the tensile testing machine to tighten the sample;

[0162] Step 2): Wrap the excitation coil around the sample and adjust the current to 10A / m to generate a magnetic field and achieve a strong magnetic field.

[0163] Step 3): Start the tensile testing machine and perform the first stretch. During the elastic stage, use the probe to test the X70 steel sample from top to bottom and record the magnetic leakage signal through the software control system. Continue to stretch the X70 steel sample until plastic deformation is achieved. Then, use the probe again to test the X70 steel sample and record the magnetic leakage signal until the set tensile force value is reached and the tensile force is restored to 0 MPa.

[0164] Step 4): Repeat Step 1, replace the X70 steel sample and perform a second tensile test. Stop when the set tensile force value is reached and the tensile force is restored to 0 MPa.

[0165] Step 5): Repeat step 1, replace the X70 steel sample and perform a third tensile test. Stop when the set tensile force value is reached and the tensile force is restored to 0 MPa.

[0166] Step 6): Repeat step 1, replace the X70 steel sample and perform the fourth tensile test. Stop when the set tensile force value is reached and the tensile force is restored to 0 MPa.

[0167] Step 7): After the test is completed, stop the tensile testing machine, read the data from the signal acquisition system, organize the leakage magnetic field test data, and observe and analyze the leakage magnetic field signal change curve under stress.

[0168] The tensile force values ​​in this embodiment are 10kN, 20kN, 30kN, and 40kN.

[0169] In addition, in this embodiment, five identical X70 type specimens were used for tensile testing during the experimental verification step.

[0170] Depend on Figure 13 and Figure 14 It can be seen that during the elastic tensile stage, the axial component of the specimen has peak characteristics, and the radial signal has peak-to-peak characteristics at zero crossing. As the pressure increases, the leakage magnetic signal intensity gradually decreases, and the peak values ​​of the axial and radial components also gradually decrease.

[0171] like Figure 15 As shown, in the elastic stage, the eigenvalues ​​of the axial component decrease nonlinearly with the increase of tension. The experimental data and the calculation model show the same trend. Compared with the uniform magnetic charge model, the eigenvalues ​​of the axial component of the improved magnetic charge model are all greater than those of the uniform magnetic charge model. The accuracy of the eigenvalues ​​of the axial component of the fitted curve of the improved magnetic charge model is 87%, while that of the uniform magnetic charge model is 70%, an improvement of 17%. This shows that the accuracy of the improved magnetic charge model in this embodiment is higher than that of the uniform magnetic charge model.

[0172] like Figure 16 As shown, during the elastic stage, the eigenvalues ​​of the radial component decrease nonlinearly with increasing tension. The experimental data and the computational model show the same trend. Compared with the uniform magnetic charge model, the eigenvalues ​​of the radial component of the improved magnetic charge model are all smaller than those of the uniform magnetic charge model. Furthermore, the accuracy of the radial component eigenvalues ​​of the fitted curve of the improved magnetic charge model is 88%, while the accuracy of the axial and radial components of the uniform magnetic charge model is 72%, representing an improvement of 16%. This further verifies that the accuracy of the improved magnetic charge model in this embodiment is higher than that of the uniform magnetic charge model.

[0173] like Figure 17 As shown, this is a diagram of the axial component of the leakage magnetic field signal under different plastic deformations in this embodiment. The magnitude of the axial component does not follow a single trend, and this feature can be used to determine the signal at this stage.

[0174] like Figure 18 As shown, this is a radial component diagram of the leakage magnetic field signal under different plastic deformations in this embodiment. The magnitude of the radial component does not follow a single trend, and this feature can be used to judge the signal at this stage.

[0175] like Figure 19 As shown, the eigenvalues ​​exhibit similar variation patterns under different tensile forces; the magnetic signal eigenvalues ​​decrease with increasing tensile force. With increasing plastic deformation, the eigenvalues ​​first gradually decrease and then gradually increase. This leads to the improved magnetic charge model achieving an average accuracy of 84.55% for the axial component eigenvalues ​​and 86.1% for the radial component eigenvalues. The uniform magnetic charge model achieves an average accuracy of 75.4% for the axial component eigenvalues ​​and 77.1% for the radial component eigenvalues, representing improvements of 9.15% and 9%, respectively. Therefore, this model can be used to predict the variation patterns of this signal characteristic during the plastic deformation stage under stress.

[0176] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for quantizing leakage magnetic signal characteristics, characterized in that: Based on the step of establishing the sub-region magnetic charge distribution density model, m×n sub-regions of the defect region and the sub-region magnetic charge distribution density model are obtained. Then, in the step of establishing the Coulomb force model of the sub-region magnetic charge, the Coulomb force model of the m×n sub-region magnetic charge is obtained. In the step of establishing the magnetic charge equation system of the defect region, the Coulomb force models of the m×n sub-region magnetic charge are combined to obtain the magnetic charge equation system of the defect region. In the step of establishing the magnetic charge density model, the magnetic charge of each sub-region is calculated according to the magnetic charge equation system of the defect region. The magnetic charge of each sub-region is substituted into the sub-region magnetic charge distribution density model to obtain the magnetic charge density model of the first sidewall of the defect region. Based on the step of establishing an improved effective field model, the elastic effective field model and the plastic effective field model are substituted into the effective field model to obtain an improved effective field model. In the step of establishing an improved relationship model between magnetization intensity and stress, the improved effective field model is substituted into the relationship model between magnetization intensity and stress to obtain an improved relationship model between magnetization intensity and stress. The improved relationship model between magnetization intensity and stress is combined with the magnetic charge density model of the first sidewall of the defect region to obtain an improved magnetic charge density model. Based on the step of establishing a composite magnetic charge analytical model, the improved magnetic charge density model is substituted into the magnetic charge model to obtain a composite magnetic charge analytical model. The improved magnetic charge density model and the composite magnetic charge analytical model were then verified through experimental steps. In the step of establishing the magnetic charge distribution density model of the sub-region, the magnetic charge in the steady state under the action of Coulomb force exhibits a non-uniform distribution. The sidewall length at the defect location of the ferromagnetic material is given as D. y ×D z The defective region is divided into m×n sub-regions, each with a side length of m. Therefore, the magnetic charge distribution density model of the sub-region is obtained as follows: （1） Where i equals 1, 2, 3…n; j equals 1, 2, 3…m; ρ ij Q represents the magnetic charge density of the subregion. ij is the magnetic charge of the sub-region; s is the area of ​​the sidewall of the defect region; In the step of establishing the Coulomb force model of the magnetic charge in the sub-region, based on m×n sub-regions, when the magnetic charge on the sidewall of the defect region is in a stable state, the sum of the magnetic force vectors on the magnetic charge on the sidewall of the defect region is 0, thus obtaining the Coulomb force model of the magnetic charge in the sub-region: （2） （3） （4） Among them, Q （i，j）+ Q represents the magnetic charge of each sub-region of the first sidewall of the defect region. （i，j）- q represents the magnetic charge of each sub-region of the second sidewall of the defect region. （a,b） Let r3 be the unit point magnetic charge within the sidewall of the defect region; a equals 1, 2, 3…n-1, b equals 1, 2, 3…m-1, and a is not equal to b; r3 is the distance between magnetic charges within the same sidewall of the defect region; r4 is the distance between magnetic charges between the first and second sidewalls of the defect region; K is the Coulomb constant. In the step of establishing the improved effective field model, based on the effective field model and combined with the influence of stress in the stress concentration area of ​​the defect region on the magnetic charge density distribution, the effective field model for the elastic stage is obtained as follows: （9） in, The effective elastic field is represented by θ, the angle between the magnetization direction and the stress direction, ν, Poisson's ratio, σ, and λ. s M is the magnetostriction coefficient; s μ is the saturation magnetization; μ0 is the free permeability; The effective field model for the plastic stage is obtained as follows: （10） in, For the plastic effective field; k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume; ε p λ represents the amount of plastic deformation. s ρ is the magnetostriction coefficient; μ0 is the free permeability; E is Young's modulus; M s The saturation magnetization; Substituting the elastic and plastic effective field models into the effective field model, we obtain the improved effective field model as follows: (11) Where H is the excitation magnetic field; θ is the angle between the magnetization direction and the stress direction; ν is Poisson's ratio; σ is the stress; λ s M is the magnetostriction coefficient; s ε is the saturation magnetization; μ0 is the free permeability; k is the ratio of elastic energy to magnetic energy; k' is the average density of pinning points per unit volume in the defect region; ε p E is the amount of plastic deformation; E is Young's modulus. In establishing the improved model of the relationship between magnetization and stress, under the condition of leakage magnetic field in ferromagnetic materials, the improved effective field model is substituted into the model of the relationship between magnetization and stress to obtain the improved model of the relationship between magnetization and stress: （12） Where M is the magnetization; M s H represents the magnetic saturation magnetization. eff The effective field is α; the shape factor of the magnetization curve is α. In the improved magnetic charge density model step, the improved relationship model between magnetization and stress is combined with the magnetic charge density model of the first sidewall of the defect region to obtain the improved magnetic charge density model as follows: （13） Where, ρ (i,j) denoted as magnetic charge density; μ0 as free permeability; M as magnetization; α as shape factor of magnetization curve; In the step of establishing the analytical model of the composite magnetic charge, the improved magnetic charge density model is substituted into the magnetic charge model to obtain the analytical model of the composite magnetic charge: （14） Where, ρ (i,j) denoted as , where μ is the magnetic charge density; μ0 is the vacuum permeability; r is the distance between the detection point and the sidewall of the defect region; m is a sub-region in the horizontal direction of the sidewall of the defect region; n is a sub-region in the vertical direction of the sidewall of the defect region; i is a sub-region in the vertical direction of the sidewall of the defect region; and j is a sub-region in the horizontal direction of the sidewall of the defect region.

2. The quantization method for leakage magnetic signal characteristics according to claim 1, characterized in that: In establishing the magnetic charge equations for the defect region, since there are m×n magnetic charge sub-regions within both the first and second sidewalls of the defect region, the Coulomb force models of the sub-regions within the m×n sub-regions are combined to obtain the magnetic charge equations for the defect region: （5） （6） （7） Where i equals 1, 2, 3…n, j equals 1, 2, 3…m; Q （i，j）+ Q represents the magnetic charge of the m×n sub-regions of the first sidewall of the defect region; （i，j）- q represents the magnetic charge of m×n sub-regions on the second sidewall of the defect region; （a,b） R is the unit point magnetic charge within the sidewall of the defect region; a and b are both constants; r3 is the distance between magnetic charges within the same sidewall of the defect region; r4 is the distance between magnetic charges between the first and second sidewalls of the defect region; K is the Coulomb constant.

3. The quantization method for leakage magnetic signal characteristics according to claim 1, characterized in that: In the step of establishing the magnetic charge density model, the magnetic charge of each sub-region is calculated through the set of magnetic charge equations for the defect region. The magnetic charge of each sub-region is then substituted into the sub-region magnetic charge distribution density model to obtain the magnetic charge density model of the first sidewall of the defect region: （8） Among them, D y D represents the width of the defect area. z D represents the depth of the defect area. x The length of the defective region.

4. The quantization method for leakage magnetic signal characteristics according to claim 1, characterized in that: In the experimental verification step, the magnetic charge density under stress was calculated based on the improved magnetic charge density model to verify the improved magnetic charge density model. Based on the analytical model of composite magnetic charge, leakage magnetic signals in the elastic stage and the plastic stage were calculated to verify the analytical model of composite magnetic charge.

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