Method and system applied to combined measurement of outer diameter and wall thickness of non-magnetic metal pipeline

Abstract

The invention provides a method and system applied to combined measurement of the outer diameter and the wall thickness of a non-magnetic metal pipeline. The internal relation between the inner diameter and the outer diameter of the pipeline and inductive impedance is obtained through an eddy current detection analysis model, and the thickness of the pipeline is detected under the condition that no prior parameter exists. The method comprises the following steps: S1, establishing a mathematical model of a sensor and a pipeline, namely calculating an impedance variable quantity, solving a complex inductance variable quantity, and obtaining an imaginary part and a real part of the complex inductance variable quantity; s2, establishing a relation model of the wall thickness and the skin depth according to the peak frequency of the imaginary part of the complex inductance variable quantity; s3, solving a relation model of the real part of the complex inductance variable quantity and the pipe outer diameter; and finally, in combination with the relation model of the wall thickness and the skin depth in the step S2, the outer diameter and the wall thickness are solved at the same time.

Description

Technical Field

[0001] This invention proposes a method and system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes, relating to the field of thickness detection of non-magnetic metal pipes. Background Technology

[0002] In critical industrial sectors such as aviation, petrochemicals, and nuclear power, the thickness of non-magnetic metal pipes (such as aluminum alloys, titanium alloys, and stainless steel pipes) is a core parameter determining their pressure resistance, corrosion resistance life, and structural safety. Abnormal thickness (such as corrosion thinning or wear) can lead to major accidents such as media leakage and explosions. Therefore, efficient and accurate non-destructive thickness measurement technology is crucial. Eddy current testing technology has become the mainstream research direction for pipe thickness measurement due to its advantages of non-contact, fast response, and no radiation. However, existing eddy current testing methods still have many defects and shortcomings.

[0003] Existing eddy current detection methods are based on the classical Dodd-Deeds analytical model or the finite element numerical method. For example, one existing technique proposes an analytical solution for pipe eddy currents that requires impedance expressions containing multi-order Bessel functions, complex integral terms, and parameter coupling terms (such as modified Bessel functions and multiple integrals in the formula), resulting in cumbersome calculations and significant time consumption. Another existing technique proposes an inversion method using the characteristics between the cross frequency of stacked array eddy current sensors and the stack thickness and pipe thickness. Yet another existing technique proposes a wobble analysis model within the pipe, which establishes a relationship between coil impedance and pipe radius, but requires prior input of the pipe's inner diameter to calculate the impact of coil offset on thickness measurement. It also requires prior knowledge of parameters such as the pipe's outer and inner diameters to solve for thickness through iterative inversion, making it unable to independently measure the thickness of "unknown parameter pipes," thus limiting its applicability. Summary of the Invention

[0004] In view of this, in order to fill the gaps and deficiencies in the existing technology, the present invention proposes a method and system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes.

[0005] This invention proposes a method and system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes, comprising the following:

[0006] This invention proposes a method for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes. The method is characterized by obtaining the intrinsic relationship between the inner and outer diameters of the pipe and the induced impedance through an eddy current detection analytical model and detecting the pipe thickness without prior parameters.

[0007] The method for jointly measuring the outer diameter and wall thickness of non-magnetic metal pipes includes the following:

[0008] Step S1: Establish a mathematical model of the sensor and the pipeline, including calculating the impedance change ΔZ, obtaining the complex inductance change ΔL, and obtaining the imaginary part Im[ΔL] and the real part Re[ΔL] of the complex inductance change;

[0009] Step S2: Establish a relationship model between wall thickness and skin depth based on the peak frequency of the imaginary part Im[ΔL] of the change in complex inductance;

[0010] Step S3: Obtain the relationship model between the real part Re[ΔL] of the change in complex inductance and the outer diameter of the tube; finally, combine the relationship model between the wall thickness and skin depth obtained in step S2 to simultaneously solve for the outer diameter and wall thickness.

[0011] Further, step S1 includes the following:

[0012] Step S11: Establish a mathematical model of the sensor and the pipeline, wherein the mathematical model includes the calculation of the impedance change ΔZ, and the mathematical model includes the following:

[0013]

[0014] Δ=K m (α k r i )I m '(α k r i )-I m (α k r i )K m '(α k r i (5)

[0015] k2=jωσμ0μ r (6)

[0016]

[0017] Where r o r i Let be the outer diameter and inner diameter of the pipe, and α be the axial wavenumber of the electromagnetic field along the pipe. Let I be the complex wave number, where I is the excitation coil current, ω is the angular frequency, σ is the conductivity of the metal tube, and μ0 and μ r These are the vacuum permeability and the relative permeability of the material, respectively, C s R is the coil coefficient, B is the reflection coefficient, and B is the reflection coefficient. s I represents the eddy current field coefficients, and i and j represent the field component indices; m (αr), K m (αr) represent the first and second type modified Bessel functions, respectively, and I' m (αr) and K' m(αr) is its derivative.

[0018] Furthermore, step S1 also includes the following:

[0019] Step S12: According to the Wronskian identity of the Bessel function, we obtain the content shown in formula (12):

[0020]

[0021] Substituting formula (12) into formulas (4) and (5) yields:

[0022]

[0023] Where α< <jωσμ0μ r Therefore α k ≈jωσμ0μ r ;

[0024] Furthermore, the following is obtained:

[0025]

[0026] Substituting formulas (13) and (14) into formulas (10) and (11) yields the following:

[0027]

[0028] Formula (15) is the unmodified expression for intermediate variables.

[0029] Furthermore, step S1 also includes the following:

[0030] Step S13: Modify formula (15) using the modified Bessel function infinite approximation, wherein the modified Bessel function infinite approximation includes the following:

[0031]

[0032] Substituting formula (16) into formula (15), we obtain the modified formula (17).

[0033]

[0034] Substituting formula (17) into formula (3), we get the simplified R as:

[0035]

[0036] Finally, substitute formula (18) into formula (1) to obtain the simplified impedance change, and complete the fitting curve verification between the simplified formula and the original formula.

[0037] Further, step S2 includes the following:

[0038] Step S21: By finding the minimum point of Im[ΔL], the peak frequency of Im[ΔL] is obtained;

[0039] The minimum point of Im[ΔL] is:

[0040]

[0041] Skin depth Will By performing an equivalent transformation, we obtain the following:

[0042]

[0043] Where to obtain Equivalent to obtaining

[0044] Step S22: Obtain Includes the following:

[0045]

[0046] in A and B are constants independent of δ and r;

[0047] Step S23: Taking the logarithm of formula (19) yields By simplification, we can obtain the correlation model between wall thickness and peak frequency:

[0048]

[0049] Where C is an expression containing a small parameter δ, which can be fitted as a simple function of δ to increase the accuracy of the inversion.

[0050] Further, step S3 includes the following:

[0051] Step S31: When f > 1MHz, I m (a k r o )·V2< <K m (a k r o )·V1, further simplifying R, we get:

[0052]

[0053] Furthermore, we obtain:

[0054]

[0055] By combining formulas (20) and (22), the peak frequency of the change in the imaginary part of the complex inductance and the change in the real part of the complex inductance at high frequencies are obtained through experiments, thus completing the simultaneous calculation of the tube outer diameter and wall thickness.

[0056] This invention also proposes a system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes, used to perform a method for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes as described in this invention. The system employs a dual-coil eddy current sensor to perform eddy current detection on the outer diameter and wall thickness of the metal pipe.

[0057] Eddy current detection uses a steady-state, continuously excited sinusoidal signal, with the sinusoidal signal operating at both single and multiple frequencies.

[0058] Eddy current testing includes detecting impedance changes and phase differences in the outer diameter and wall thickness of metal pipes.

[0059] The present invention has the following advantages:

[0060] This invention proposes a method and system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes. Existing pipe thickness measurements rely on complex analytical calculations, resulting in low computational efficiency and requiring prior knowledge of the pipe's outer or inner diameter. A method for in-situ detection and rapid measurement of metal pipe wall thickness is lacking. This invention reduces computational load by simplifying formulas and replacing redundant terms. Simultaneously, it establishes a correlation model between the pipe's outer diameter and the real part of the complex inductance change, and between wall thickness and peak frequency, enabling the solution of outer diameter and wall thickness without prior parameters. Based on the eddy current detection principle, this method significantly improves computational and detection efficiency while ensuring measurement accuracy. It is suitable for in-service inspection of non-magnetic metal pipes with external insulation layers in fields such as aviation and petrochemicals. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the eddy current detection model of the coaxial double coil outside the metal pipe of the present invention.

[0062] Figure 2 This is a schematic diagram of the pipe thickness calculation process of the present invention.

[0063] Figure 3 This is a schematic diagram showing the changes in the real and imaginary parts of the complex inductance as a function of frequency, compared to the simplified formula of this invention and the original formula.

[0064] Figure 4 This is a schematic diagram showing the variation of the imaginary part of the complex inductance with frequency under different materials and inner diameters according to the present invention.

[0065] Figure 5 This is a schematic diagram showing the real part of the change in complex inductance versus frequency for different materials and outer diameters according to the present invention.

[0066] Figure 6 For the full model R and only the external component 1 / r of this invention o A comparative diagram showing the effects of the procedure.

[0067] Figure 7 This is a schematic diagram comparing the fitting degree images between the fitting function of the present invention and the simulation. Detailed Implementation

[0068] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0069] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0070] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0071] like Figures 1 to 7 As shown, a method and system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes includes the following:

[0072] In one embodiment of the present invention, such as Figure 1 As shown, this invention utilizes a dual-coil eddy current sensor to detect the outer diameter and wall thickness of a metal pipe. The coil parameters are shown in Table 1.

[0073] Table 1 Parameters of Dual-Coil Eddy Current Sensor

[0074] parameter numerical values Number of coil turns N 30 <![CDATA[Inner radius R of the excitation coil e,i (mm)]]> 7 <![CDATA[Inner radius R of the receiving coil r,i (mm)]]> 4 <![CDATA[Outer radius R of the excitation coil e,o (mm)]]> 6 <![CDATA[Outer radius R of the receiving coil r,o (mm)]]> 5 Coil height h (mm) 3

[0075] like Figure 2 As shown, this invention proposes a method for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes. The method is characterized by obtaining the intrinsic relationship between the inner and outer diameters of the pipe and the induced impedance through an eddy current detection analytical model and detecting the pipe thickness without prior parameters.

[0076] The method for jointly measuring the outer diameter and wall thickness of non-magnetic metal pipes includes the following:

[0077] Step S1: Establish a mathematical model of the sensor and the pipeline, including calculating the impedance change ΔZ, obtaining the complex inductance change ΔL, and obtaining the imaginary part Im[ΔL] and the real part Re[ΔL] of the complex inductance change;

[0078] Step S2: Establish a relationship model between wall thickness and skin depth based on the peak frequency of the imaginary part Im[ΔL] of the change in complex inductance;

[0079] Step S3: Obtain the relationship model between the real part Re[ΔL] of the change in complex inductance and the outer diameter of the tube; finally, combine the relationship model between the wall thickness and skin depth obtained in step S2 to simultaneously solve for the outer diameter and wall thickness.

[0080] Further, step S1 includes the following:

[0081] Step S11: Establish a mathematical model of the sensor and the pipeline, wherein the mathematical model includes the calculation of the impedance change ΔZ, and the mathematical model includes the following:

[0082]

[0083] Δ=K m (α k r i )I m '(α k r i )-I m (α k r i )K m '(α k r i (5)

[0084] k2=jωσμ0μ r (6)

[0085]

[0086]

[0087] Where r o r i Let be the outer diameter and inner diameter of the pipe, and α be the axial wavenumber of the electromagnetic field along the pipe. Where I is the complex wave number, ω is the excitation coil current, σ is the angular frequency, σ is the conductivity of the metal tube, and μ0 and μ r These are the vacuum permeability and the relative permeability of the material, respectively, C s R is the coil coefficient, B is the reflection coefficient, and B is the reflection coefficient. s I represents the eddy current field coefficients, and i and j represent the field component indices; m (αr), K m(αr) represent the first and second type modified Bessel functions, respectively, and I' m (αr) and K' m (αr) is its derivative.

[0088] Where ΔZ is the impedance change of the receiving coil.

[0089] The reflection coefficient R(α,m) is the ratio of the intensity of the "incident mode" generated by the coil in free space to the intensity of the scattered mode generated in a region with a certain lift-off distance between the coil and the metal tube when the metal tube is present. It is determined by the electromagnetic field boundary conditions and the geometric / material parameters of the metal tube, and is independent of the coil. If the metal tube is absent, there are no eddy currents, and therefore no scattered field, so R(α,m)→0. When the metal tube is present, if the conductivity of the metal tube is very high and its geometric dimensions are suitable, the eddy currents are very strong, the scattered field is large, and |R(α,m)| approaches 1.

[0090] Furthermore, step S1 also includes the following:

[0091] Step S12: According to the Wronskian identity of the Bessel function, we obtain the content shown in formula (12):

[0092]

[0093] Among them, I v (x)K v (x) is the general expression for the modified Bessel function, I v (x) represents the modified Bessel function of the first kind, K v (x) represents the modified Bessel function of the second kind. In this invention, x is (α, r), and v is the order of the Bessel function.

[0094] Substituting formula (12) into formulas (4) and (5) yields:

[0095]

[0096] Where α< <jωσμ0μ r Therefore α k ≈jωσμ0μ r ;

[0097] Furthermore, the following is obtained:

[0098]

[0099] Substituting formulas (13) and (14) into formulas (10) and (11) yields the following:

[0100]

[0101] Formula (15) is the unmodified expression for intermediate variables.

[0102] Furthermore, step S1 also includes the following:

[0103] Step S13: Modify formula (15) using the modified Bessel function infinite approximation, wherein the modified Bessel function infinite approximation includes the following:

[0104]

[0105] Substituting formula (16) into formula (15), we obtain the modified formula (17).

[0106]

[0107] Substituting formula (17) into formula (3), we get the simplified R as:

[0108]

[0109] Finally, substituting formula (18) into formula (1) yields the simplified impedance change, and the fitting curve between the simplified formula and the original formula is verified. Figure 3 As shown, the simplified formula reduces the coupling between complex integral operations and parameters. Due to the error introduced by the Bessel function approximation, the calculation results may have a small range of deviations; however, the calculations show good agreement at higher excitation frequencies.

[0110] In one embodiment of the present invention, simulation studies revealed that Im[ΔL] at high frequencies is related to r i Unrelated, but peak frequency is related to r i Relevant, such as Figure 4 As shown.

[0111] Further, step S2 includes the following:

[0112] Step S21: By finding the minimum point of Im[ΔL], the peak frequency of Im[ΔL] is obtained;

[0113] In this invention, the simplified expression for Im[ΔL] is:

[0114]

[0115] The peak frequency is the minimum point of Im[ΔL], i.e. In Im[ΔL], the mode is dominant when m is 0 and 1, so these two modes are used when performing integral summation.

[0116] Skin depth Will By performing an equivalent transformation, we obtain the following:

[0117]

[0118] Where to obtain Equivalent to obtaining

[0119] Step S22: Obtain Includes the following:

[0120]

[0121] in A and B are constants independent of δ and r;

[0122] Step S23: Taking the logarithm of formula (19) yields By simplification, we can obtain the correlation model between wall thickness and peak frequency:

[0123]

[0124] Where C is an expression containing a small parameter δ, which can be fitted as a simple function of δ to increase the accuracy of the inversion.

[0125] In one embodiment of the present invention, it was found that at high frequencies, given the coil parameters and lift-off distance are known, Re[ΔL] is related to the material and r i Irrelevant, related to r o Relevant, such as Figure 5 As shown.

[0126] Further, step S3 includes the following:

[0127] Step S31: When f > 1MHz, I m (a k r o )·V2<<K m (a k r o )·V1, further simplifying R, we get:

[0128]

[0129] Furthermore, we obtain:

[0130]

[0131] Furthermore, in one embodiment of the present invention, simulation revealed that the integral sign r o The effect on Re[ΔL] is much smaller than that outside the integral sign. The impact on it, when r o When the control integral term remains unchanged, such as Figure 6 As shown, the calculated Re[ΔL] is essentially the same as the original value. Therefore, Re[ΔL] can be expressed as... Right now:

[0132]

[0133] The linear fitting results are as follows Figure 7 As shown.

[0134] Formulas (22) to (23) are derived from simulation and numerical analysis. Through numerical analysis, it is confirmed that the change of the integral term with the outer diameter is much smaller than the factor 1 / r. o The change in outer diameter can be considered a constant. 1 / r o The change in Re[ΔL] is dominant, combined with Figure 7 The fit can approximate their relationship as a linear first-order function.

[0135] By combining formulas (20) and (23), the peak frequency of the change in the imaginary part of the complex inductance and the change in the real part of the complex inductance at high frequencies are obtained through experiments, thus completing the simultaneous calculation of the tube outer diameter and wall thickness.

[0136] This invention also proposes a system for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes, used to perform a method for the joint measurement of the outer diameter and wall thickness of non-magnetic metal pipes as described in this invention. The system employs a dual-coil eddy current sensor to perform eddy current detection on the outer diameter and wall thickness of the metal pipe.

[0137] Eddy current detection uses a steady-state, continuously excited sinusoidal signal, with the sinusoidal signal operating at both single and multiple frequencies.

[0138] Eddy current testing includes detecting impedance changes and phase differences in the outer diameter and wall thickness of metal pipes.

[0139] In one embodiment of the present invention, the relative error of pipe thickness calculation is shown in Table 2.

[0140] Table 2. Relative Errors Between Calculated and Actual Values

[0141]

[0142]

[0143] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for combined measurement of the outer diameter and wall thickness of a non-magnetic metal pipe, characterized in that, The internal relationship between the inner and outer diameters of the pipe and the induced impedance is obtained by using the eddy current detection analysis model, and the pipe thickness is detected without prior parameters; The method for measuring the outer diameter and wall thickness of a non-magnetic metal pipe comprises the following steps: Step S1: establishing a mathematical model of the sensor and the pipe, including calculating the impedance change ΔZ, obtaining the complex inductance change ΔL, and obtaining the imaginary part Im[ΔL] and the real part Re[ΔL] of the complex inductance change; Step S2: establishing a relationship model of the wall thickness and the skin depth according to the peak frequency of the imaginary part Im[ΔL] of the complex inductance change; Step S3: obtaining a relationship model of the real part Re[ΔL] of the complex inductance change and the outer diameter of the pipe; and finally combining the relationship model of the wall thickness and the skin depth in step S2 to simultaneously solve the outer diameter and the wall thickness.

2. The method for combined measurement of the outer diameter and wall thickness of a non-magnetic metal pipe according to claim 1, characterized in that, Step S1 comprises the following steps: Step S11: establishing a mathematical model of the sensor and the pipe, wherein the mathematical model comprises calculating the impedance change ΔZ, and the mathematical model comprises the following steps: Delta = K m (Alpha k r i ) I m '(Alpha k r i ) - I m (Alpha k r i ) K m '(Alpha k r i ) (5) k2 = jco smo m r (6) where r o , r i are the outer and inner radii of the pipe, a is the axial wavenumber of the electromagnetic field along the pipe, is the complex wavenumber, I is the excitation coil current, w is the angular frequency, s is the electrical conductivity of the metal pipe, p0 and p r are the vacuum permeability and the relative permeability of the material, respectively, C s is the coil factor, R is the reflection coefficient, B s is the eddy current field factor, i, j are the field component indices; I m (αr), K m (αr) are first and second kind modified Bessel functions, respectively, m (αr) and K m (αr) are their derivatives.

3. The method for measuring the outer diameter and wall thickness of a non-magnetic metal pipe according to claim 2, wherein Step S1 further comprises the following steps: Step S12: obtaining the content shown in formula (12) according to the Wronskian identity of the Bessel function: Substitute formula (12) into formulas (4) and (5) to obtain the following content: where a « jco^sm0^ at high frequencies r Thus a k ≈ jco^sm0^ r ; Further, the following content is obtained: Substitute formulas (13) and (14) into formulas (10) and (11) to obtain the following content: Wherein, formula (15) is an uncorrected intermediate variable expression.

4. The method for measuring the outer diameter and wall thickness of a non-magnetic metal pipe according to claim 3, wherein Step S1 further comprises the following steps: Step S13: correcting formula (15) by using the modified Bessel function infinite approximation, wherein the modified Bessel function infinite approximation comprises the following steps: Substitute formula (16) into formula (15) to obtain the corrected formula (17) Substitute formula (17) into formula (3) to obtain the simplified R: Finally, substitute formula (18) into formula (1) to obtain the simplified impedance change, and complete the fitting curve verification of the simplified formula and the original formula.

5. The method for measuring the outer diameter and wall thickness of a non-magnetic metal pipe according to claim 4, wherein Step S2 comprises the following steps: Step S21: obtaining the peak frequency of Im[ΔL] by finding the minimum point of Im[ΔL]; Wherein, the minimum point of Im[ΔL] is: with a skin depth will be By equivalent transformations, we obtain the following: wherein the solution is equivalent to solving Step S22: Obtaining includes the following: wherein A, B are constants independent of δ and r Step S23: Taking logarithm of formula (19) can get By simplifying, the model of the wall thickness and the peak frequency can be obtained: Wherein, C is a formula containing a small parameter δ, which can be fitted as a simple function of δ to increase the accuracy of inversion.

6. The method for measuring the outer diameter and wall thickness of a non-magnetic metal pipe according to claim 5, wherein Step S3 comprises the following steps: Step S31: when f > 1 MHz, I m (a k r o )·V2<<K m (a k r o )·V1, further simplifying R to obtain: Further, the following content is obtained: Wherein, formulas (20) and (22) are solved simultaneously, the peak frequency of the imaginary part change of the complex inductance and the real part change of the complex inductance at high frequency are measured by experiments, and the outer diameter and the wall thickness of the pipe are calculated simultaneously.

7. A system for combined measurement of the outer diameter and wall thickness of a non-magnetic metal pipe for performing a method for combined measurement of the outer diameter and wall thickness of a non-magnetic metal pipe according to any one of claims 1 to 6, characterized in that The system for measuring the outer diameter and wall thickness of a non-magnetic metal pipe adopts a double-coil eddy current sensor to detect the outer diameter and wall thickness of the metal pipe by eddy current, wherein the eddy current detection adopts a steady-state continuous excitation sinusoidal wave signal, the working frequency of the sinusoidal wave signal includes single frequency working and multi-frequency working, and the eddy current detection includes detecting the impedance change and the phase difference of the outer diameter and wall thickness of the metal pipe.

Images