A method for zirconium cladding base thickness and conductivity measurement based on swept frequency eddy current

Abstract

The application provides a zirconium-based cladding base thickness and conductivity measurement method based on frequency sweeping eddy current, which comprises the following steps: establishing an eddy current analytical theory model based on the parameters of two detection coils and the zirconium-based cladding and the inductance change measurement data of the coils; obtaining the high-frequency inductance change of the coils under different lift-off distances, and calculating the lift-off value of each detection coil according to the lift-off distance fitting curve; setting the lift-off value, obtaining the low-frequency inductance change of the coils under different base thicknesses, and calculating the base thickness according to the base thickness fitting curve; and setting the base thickness, obtaining the low-frequency inductance change of the coils under different base conductivities, and calculating the base conductivity according to the base conductivity fitting curve. The method can simultaneously measure the thickness and conductivity of the zirconium-based cladding base, improves the accuracy and diversity of the measurement results of the zirconium-based cladding, and can effectively evaluate the corrosion state of the zirconium-based cladding.

Description

Technical Field

[0001] This application relates to the field of electromagnetic eddy current detection technology, and in particular to a method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy currents. Background Technology

[0002] Currently, zirconium-based fuel cladding serves as the first pressure boundary and safety barrier of nuclear reactors, effectively preventing the escape of nuclear fission products and avoiding fuel corrosion during cooling while removing heat. Although zirconium-based cladding exhibits excellent corrosion resistance, long-term operation under extreme environments such as high temperature, high pressure, strong neutron irradiation, and high-flow-rate cooling water can lead to the formation of heterogeneous film structures such as oxide films and hydrogen-absorbing layers on its surface. This can even result in fuel defects, severely impacting the structural strength and performance of fuel assemblies and potentially causing nuclear fuel assembly failure accidents. Therefore, regular monitoring of the condition of in-service zirconium-based fuel cladding is a crucial way to ensure its safe operation.

[0003] In related technologies, the detection of zirconium-based fuel cladding typically only measures the thickness of the oxide film layer. However, due to the highly complex heterogeneous film structure and electromagnetic properties of zirconium-based cladding, the detection methods in these technologies are significantly affected. Consequently, the detection results of zirconium-based cladding in these technologies may contain substantial errors, and the obtained data is relatively limited, making it difficult to meet practical requirements.

[0004] Therefore, how to perform accurate and comprehensive measurements on zirconium-based cladding to achieve an effective assessment of its condition has become an urgent problem to be solved. Summary of the Invention

[0005] This application aims to at least partially address one of the technical problems in the related art.

[0006] Therefore, the first objective of this application is to propose a method for measuring the thickness and conductivity of a zirconium-based cladding substrate based on swept-frequency eddy current. This method assesses the corrosion state of the zirconium-based cladding by measuring its thickness and conductivity, and improves the accuracy and diversity of the measurement results through non-contact and highly sensitive detection.

[0007] The second objective of this application is to provide a device for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current.

[0008] The third objective of this application is to provide a non-transitory computer-readable storage medium.

[0009] To achieve the above objectives, the first aspect of this application is to propose a method for measuring the thickness and conductivity of a zirconium-based cladding substrate based on swept-frequency eddy currents, the method comprising the following steps:

[0010] Two coaxial eddy current detection coils with identical geometric parameters were fabricated. The two detection coils were placed above a zirconium-based cladding shell and in the air, respectively. A sweep frequency excitation signal was applied to the two detection coils, and the change in inductive reactance was calculated based on the measurement results.

[0011] Based on the parameters of the two detection coils and the zirconium-based cladding, as well as the inductive reactance change measurement data, a multilayer structure eddy current analytical theoretical model is established.

[0012] The model is used to obtain the high-frequency inductive reactance change of the coil under different lift-off distances, and the real logarithm of the lift-off distance and the high-frequency inductive reactance change is linearly fitted. The lift-off value of each detection coil is calculated based on the obtained lift-off distance fitting curve.

[0013] In the model, the lift-off value is set to obtain the low-frequency inductive reactance change of the coil under different substrate thicknesses, and the ratio of the imaginary part of the substrate thickness and the low-frequency inductive reactance change is subjected to exponential fitting. The substrate thickness of the zirconium-based cladding is calculated based on the obtained substrate thickness fitting curve.

[0014] The substrate thickness is set in the model, the low-frequency inductive reactance change of the coil under different substrate conductivity is obtained, and the imaginary part of the substrate conductivity and the current low-frequency inductive reactance change is linearly fitted. The substrate conductivity of the zirconium-based cladding is calculated based on the obtained substrate conductivity fitting curve.

[0015] Optionally, in one embodiment of this application, the step of calculating the inductive reactance change based on the measurement results includes: measuring the impedance of each of the detection coils, calculating the inductive reactance of each of the detection coils based on the impedance and the frequency of the sweep excitation signal; and performing differential processing on the calculated inductive reactance data to obtain the inductive reactance change.

[0016] Optionally, in one embodiment of this application, the low-frequency inductive reactance change is calculated in the model using the following formula:

[0017]

[0018] Where ΔL0 is a variable related to the coil size, ω is the excitation frequency, μ0 is the vacuum permeability, σ is the substrate conductivity, α0 is the spatial resolution, and c is the substrate thickness.

[0019] Optionally, in one embodiment of this application, obtaining the high-frequency inductive reactance change of the coil at different lift-off distances includes: setting a high-frequency frequency and detecting multiple lift-off distance values ​​of the coil; calculating the coil inductive reactance change corresponding to each lift-off distance value at the high-frequency frequency; the lift-off distance fitting curve is represented by the following formula:

[0020] ln(ReΔL(ω1))=al+b

[0021] Where ω1 is the high-frequency frequency, ΔL(ω1) is the high-frequency reactance change of the coil, and a and b are real numbers, a<0, b<0.

[0022] Optionally, in one embodiment of this application, obtaining the low-frequency inductive reactance variation of the coil under different substrate thicknesses includes: setting a low-frequency frequency and multiple substrate thicknesses of the zirconium-based cladding; calculating the ratio of the imaginary part of the low-frequency inductive reactance variation corresponding to each substrate thickness at the low-frequency frequency; the substrate thickness fitting curve is represented by the following formula:

[0023] |ImΔL1(ω2) / ImΔL2(ω2)|=k1e αt +m1

[0024] Where ω2 is the low-frequency frequency, ΔL1(ω2) is the low-frequency inductive reactance change of the upper coil, ΔL2(ω2) is the low-frequency inductive reactance change of the lower coil, k1, α and m1 are real numbers, k1>0, α<0, m1>0.

[0025] Optionally, in one embodiment of this application, obtaining the low-frequency inductive reactance change of the coil under different substrate conductivity includes: setting multiple substrate conductivityes for the zirconium-based cladding, and calculating the imaginary part of the low-frequency inductive reactance change of the upper coil corresponding to each substrate conductivity at the low-frequency frequency; the substrate conductivity fitting curve is represented by the following formula:

[0026] ImΔL1(ω2)=k2σ+m2

[0027] Where k2 and m2 are real numbers, k2<0, m2<0.

[0028] Optionally, in one embodiment of this application, the high frequency is used to reduce the eddy current skin depth, the low frequency is used to increase the eddy current skin depth, the high frequency is greater than or equal to 1MHz, and the low frequency is less than or equal to 1kHz.

[0029] Optionally, in one embodiment of this application, the geometric parameters of the detection coil include the inner diameter, outer diameter, height, and number of turns of the coil.

[0030] Optionally, in one embodiment of this application, both the substrate and the coating of the zirconium-based cladding are non-ferromagnetic conductive materials, and the thickness of the substrate is much greater than the thickness of the coating.

[0031] To achieve the above objectives, a second aspect of this application also proposes a device for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy currents, comprising the following modules:

[0032] The module is used to fabricate two coaxial eddy current detection coils with identical geometric parameters. The two detection coils are placed above the zirconium-based cladding and in the air, respectively. A sweep frequency excitation signal is applied to the two detection coils, and the change in inductive reactance is calculated based on the measurement results.

[0033] A module is established to build a multi-layer structure eddy current analytical theoretical model based on the parameters of the two detection coils and the zirconium-based cladding, as well as the inductive reactance change measurement data.

[0034] The lift-off calculation module is used to obtain the high-frequency inductive reactance change of the coil under different lift-off distances through the model, and to perform linear fitting on the real logarithm of the lift-off distance and the high-frequency inductive reactance change, and to calculate the lift-off value of each detection coil based on the obtained lift-off distance fitting curve.

[0035] The thickness measurement module is used to set the lift-off value in the model, obtain the low-frequency inductive reactance change of the coil under different substrate thicknesses, and perform exponential fitting on the ratio of the imaginary part of the substrate thickness and the low-frequency inductive reactance change, and calculate the substrate thickness of the zirconium-based cladding based on the obtained substrate thickness fitting curve.

[0036] The conductivity measurement module is used to set the substrate thickness in the model, obtain the low-frequency inductive reactance change of the coil under different substrate conductivity, and perform linear fitting on the imaginary part of the substrate conductivity and the current low-frequency inductive reactance change, and calculate the substrate conductivity of the zirconium-based cladding based on the obtained substrate conductivity fitting curve.

[0037] To achieve the above objectives, a third aspect of this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for measuring the thickness and conductivity of a zirconium-based cladding substrate based on swept-frequency eddy current, as described in any one of the first aspects.

[0038] The technical solution provided by the embodiments of this application brings at least the following beneficial effects: This application first uses a high-frequency band measurement coil with sweep frequency excitation to measure the lift-off distance from the zirconium-based cladding surface, which is unaffected by properties such as the conductivity of the zirconium-based cladding; then, it further measures the thickness and conductivity of the zirconium-based cladding layer in the low-frequency band. The measurement method used is highly operable and accurate. Therefore, this application can simultaneously measure the thickness and conductivity of the zirconium-based cladding layer, directly reflecting the corrosion state of the cladding body, avoiding decoupling analysis of the complex characteristics of heterogeneous films, and is convenient to operate with reliable test results, possessing practical engineering value. Thus, this application improves the accuracy and diversity of zirconium-based cladding measurement results, enabling effective evaluation of the zirconium-based cladding state, which is beneficial to the normal operation of the zirconium-based cladding.

[0039] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0040] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0041] Figure 1 This is a flowchart illustrating a method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current, as proposed in an embodiment of this application.

[0042] Figure 2 This is a schematic diagram of the coil inductive reactance variation curve under frequency sweep excitation according to an embodiment of this application;

[0043] Figure 3 This is a schematic diagram of a lift-off distance relationship curve proposed in an embodiment of this application;

[0044] Figure 4 This is a schematic diagram of a substrate thickness relationship curve proposed in an embodiment of this application;

[0045] Figure 5 This is a schematic diagram of a substrate conductivity relationship curve proposed in an embodiment of this application;

[0046] Figure 6 A flowchart illustrating a specific method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current, as proposed in this application embodiment;

[0047] Figure 7 This is a schematic diagram of a zirconium-based clad substrate thickness and conductivity measurement device based on swept-frequency eddy current, as proposed in an embodiment of this application. Detailed Implementation

[0048] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0049] It should be noted that eddy current testing is a non-destructive testing method based on the principle of electromagnetic induction. It involves applying an alternating magnetic field to a metal conductor to induce eddy currents within it, and then analyzing the distribution and changes of these eddy currents to assess the material's properties and structural integrity. This technology offers advantages such as high testing speed and high sensitivity. Therefore, this application utilizes swept-frequency eddy current testing for zirconium-based cladding.

[0050] The following describes in detail, with reference to the accompanying drawings, a method and apparatus for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current, as proposed in the embodiments of this application.

[0051] Figure 1 This is a flowchart illustrating a method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy currents, as proposed in an embodiment of this application. Figure 1 As shown, the method includes the following steps:

[0052] Step S101: Fabricate two coaxial eddy current detection coils with identical geometric parameters, place the two detection coils above the zirconium-based cladding and in the air respectively, apply a sweep frequency excitation signal to the two detection coils, and calculate the change in inductive reactance based on the measurement results.

[0053] Specifically, two coaxial eddy current detection coils are fabricated. The two coils have identical geometric parameters, differing only in their distance from the zirconium-based cladding. When a sweep frequency excitation signal is applied to the coils simultaneously, eddy currents can be induced on the surface of the zirconium-based cladding.

[0054] In one embodiment of this application, the geometric parameters of the detection coil include the inner diameter r1, outer diameter r2, height h1, and number of turns N. Both the zirconium-based cladding substrate and the coating are non-ferromagnetic conductive materials, and the substrate thickness is much greater than the coating thickness.

[0055] For example, the outer and inner diameters of the coil designed in this embodiment are 2.6 mm and 1.4 mm, respectively, the coil height is 1 mm, the number of turns is 100, and the relative positions of the two coils are fixed; the bottom layer of the zirconium-based cladding is a zirconium alloy with a conductivity of 1.43 MS / m and a thickness of 570 μm, the metal coating has a conductivity of 7.57 MS / m and a thickness of 15 μm, and the frequency sweep excitation range is from 500 Hz to 5 MHz.

[0056] Furthermore, measurements were taken by placing the detection coils above the zirconium-based cladding and in air, respectively, and the inductive reactances of the two coils, L(ω) and L, were calculated based on the measurement results. A (ω), further differential processing yields the change in inductive impedance.

[0057] In one embodiment of this application, calculating the change in inductive reactance based on the measurement results includes: measuring the impedance of each detection coil, calculating the inductive reactance of each detection coil based on the impedance and the frequency of the sweep excitation signal, and performing differential processing on the calculated inductive reactance data to obtain the change in inductive reactance.

[0058] Specifically, in this embodiment, the coil inductive reactance can be calculated using the following formula: L(ω)=Z(ω) / jω, where Z(ω) is the coil impedance, which can be directly measured. Then, the change in inductive reactance is obtained by differential processing using the following formula: ΔL(ω)=L(ω)-L A (ω).

[0059] In step S102, based on the parameters of the two detection coils and the zirconium-based cladding, as well as the measurement data of inductive reactance change, a multi-layer structure eddy current analytical theoretical model is established.

[0060] Specifically, a multi-layer eddy current analytical theoretical model is established, the geometric parameters of the coil and the zirconium-based cladding parameters are set, and after a sweep frequency excitation signal is given, the inductive reactance change ΔL(ω)=L(ω)-L is calculated. A (ω).

[0061] It should be noted that this application establishes a multilayer structure eddy current analytical theoretical model based on the parameters of the zirconium-based cladding to be measured, the geometric parameters of the two detection coils, and the inductive reactance change data obtained through actual measurement and calculation in the previous step. That is, a theoretical model is built based on the determined actual data, thereby ensuring that the established analytical theoretical model is consistent with the corresponding real situation, so that the actual measurement results can be obtained through subsequent calculations within the theoretical model.

[0062] In one embodiment of this application, the low-frequency inductive reactance change can be calculated in the established model using the following formula:

[0063]

[0064] Where ΔL0 is a variable related to the coil size, ω is the excitation frequency, μ0 is the vacuum permeability, σ is the substrate conductivity, α0 is the spatial resolution, and c is the substrate thickness.

[0065] That is, when the coil inductive reactance change ΔL(ω) is in the low frequency range (ω≤1kHz), it can be calculated using the above formula, ensuring that the result calculated by the formula under the same parameters is consistent with the actual result obtained in the previous step.

[0066] As an example, this application is able to obtain such Figure 2 The curves showing the change in coil reactance under frequency sweep excitation are shown.

[0067] Step S103: Obtain the high-frequency inductive reactance change of the coil under different lift-off distances through the model, and perform linear fitting on the real logarithm of the lift-off distance and the high-frequency inductive reactance change. Calculate the lift-off value of each detection coil based on the obtained lift-off distance fitting curve.

[0068] Specifically, by changing only the lift-off distance l of the coil and repeatedly executing the above step S102, the high-frequency inductive reactance change ΔL(ω1) under different lift-off distances is obtained. A linear fit is performed on l and ln(ReΔL(ω1)) to obtain ln(ReΔL(ω1))=F1(l). Based on the lift-off distance fitting curve, the lift-off values ​​l1 and l2 of each coil are calculated.

[0069] In one embodiment of this application, obtaining the high-frequency inductive reactance change of the coil at different lift-off distances includes: setting a high-frequency frequency and detecting multiple lift-off distance values ​​for the coil; calculating the coil inductive reactance change corresponding to each lift-off distance value at the high-frequency frequency; and the lift-off distance fitting curve obtained thereby is represented by the following formula:

[0070] ln(ReΔL(ω1))=al+b

[0071] Where ω1 is the high-frequency frequency, ΔL(ω1) is the high-frequency reactance change of the coil, and a and b are real numbers, a<0, b<0.

[0072] For example, in this embodiment, a single coil is used in the established analytical theoretical model. 29 lift-off values ​​are uniformly selected within the range of 0.085mm to 1.5mm. The corresponding inductive reactance change at frequency ω1 = 1MHz is extracted, and the fitted lift-off distance curve is shown below. Figure 3 As shown, through data processing and analysis, the curve can be expressed by the following formula: ln(ReΔL(ω1))=-1720.4l-11.0509. Then, through experiments, the change in inductive reactance of the lower coil was obtained as ln(ReΔL1(ω1))=-12.0573, and the change in inductive reactance of the upper coil was ln(ReΔL1(ω1))=-15.498. Based on the lift-off distance curve, the lift-off value of the lower coil is 0.585mm, and the lift-off value of the upper coil is 2.585mm.

[0073] In one embodiment of this application, a high frequency is used to reduce the skin depth of the eddy current, and the high frequency is greater than or equal to 1MHz.

[0074] Specifically, in the calculation of high-frequency inductive reactance changes in this application, high frequency refers to frequency ω1≥1MHz, which can make the eddy current skin depth smaller, thereby ignoring the influence of zirconium-based cladding conductivity and thickness on lift-off distance measurement and improving the accuracy of the calculation results.

[0075] Step S104: Set the lift-off value in the model, obtain the low-frequency inductive reactance change of the coil under different substrate thicknesses, and perform exponential fitting on the ratio of the imaginary part of the substrate thickness and the low-frequency inductive reactance change. Calculate the substrate thickness of the zirconium-based cladding based on the obtained substrate thickness fitting curve.

[0076] Specifically, the coil lift-off values ​​in the model are set to l1 and l2, respectively. Only the substrate thickness t of the zirconium cladding is changed. The above step S102 is repeated to obtain the low-frequency inductive reactance changes ΔL1(ω2) and ΔL2(ω2) under different substrate thicknesses. The exponential fitting of t and |ImΔL1(ω2) / ImΔL2(ω2)| is used to obtain |ImΔL1(ω2) / ImΔL2(ω2)|=F2(t). The substrate thickness t of the zirconium cladding is calculated based on the substrate thickness fitting curve.

[0077] In one embodiment of this application, obtaining the low-frequency inductive reactance variation of a coil under different substrate thicknesses includes: setting a low-frequency frequency and multiple substrate thicknesses for the zirconium-based cladding; calculating the ratio of the imaginary part of the low-frequency inductive reactance variation corresponding to each substrate thickness at the low-frequency frequency; and the resulting substrate thickness fitting curve is expressed by the following formula:

[0078] |ImΔL1(ω2) / ImΔL2(ω2)|=k1e αt +m1

[0079] Where ω2 is the low-frequency frequency, ΔL1(ω2) is the low-frequency inductive reactance change of the upper coil, ΔL2(ω2) is the low-frequency inductive reactance change of the lower coil, k1, α and m1 are real numbers, k1>0, α<0, m1>0.

[0080] For example, in this embodiment, the lift-off values ​​of the two coils are set to 0.585 mm and 2.585 mm respectively in the analytical theoretical model. 57 thickness values ​​are uniformly selected from 0.002 mm to 3 mm for the substrate thickness parameter. The 57 corresponding |ImΔL1(ω2) / ImΔL2(ω2)| values ​​at ω2 = 1 kHz are extracted, and the fitted substrate thickness curve is shown below. Figure 4 As shown, the specific expression for this curve is |ImΔL1(ω2) / ImΔL2(ω2)|=1.4254e -925.5917t +3.1716. Through experiments and subsequent calculations, |ImΔL1(ω2) / ImΔL2(ω2)|=4.0118. Based on the substrate thickness curve, the substrate thickness can be obtained as 571μm, with a relative error of 0.18%.

[0081] In one embodiment of this application, a low frequency is used to increase the skin depth of the eddy current, and the low frequency is less than or equal to 1 kHz.

[0082] Specifically, in the calculation of low-frequency inductive reactance changes in this application, low frequency refers to a frequency ω2≤1kHz, which enables a larger skin depth of the eddy current, thereby achieving the measurement of substrate thickness and conductivity.

[0083] Step S105: Set the substrate thickness in the model, obtain the low-frequency inductive reactance change of the coil under different substrate conductivity, and perform linear fitting on the imaginary part of the substrate conductivity and the current low-frequency inductive reactance change. Calculate the substrate conductivity of the zirconium-based cladding based on the obtained substrate conductivity fitting curve.

[0084] Specifically, after setting the lift-off value and substrate thickness in the model to the actual values ​​calculated in the above steps, the substrate conductivity σ of the zirconium-based cladding is changed, and the above step S102 is repeatedly executed to obtain the low-frequency inductive reactance change ΔL1(ω2) under different substrate conductivity. Linear fitting is performed on σ and ΔL1(ω2) to obtain ImΔL1(ω2)=F3(σ). The substrate conductivity σ of the zirconium-based cladding is calculated based on the fitted substrate conductivity curve.

[0085] In one embodiment of this application, obtaining the low-frequency inductive reactance change of the coil under different substrate conductivity includes: setting multiple substrate conductivityes for the zirconium-based cladding, and calculating the imaginary part of the low-frequency inductive reactance change of the upper coil corresponding to each substrate conductivity at a low frequency; the fitted substrate conductivity curve obtained thereby is represented by the following formula:

[0086] ImΔL1(ω2)=k2σ+m2

[0087] Where k2 and m2 are real numbers, k2<0, m2<0.

[0088] For example, in this embodiment, after setting the lift-off value and substrate thickness to the calculated measured values ​​in the analytical theoretical model, 19 conductivity values ​​from 1 MS / m to 10 MS / m are uniformly selected for the substrate conductivity parameter, and 19 corresponding ImΔL1(ω2) at ω2 = 1 kHz are obtained. The fitted conductivity curve is shown below. Figure 5 As shown, the specific expression for this curve is ImΔL1(ω2)=-2.2923×10 -14 σ-6.7427×10 -9 H. Through experiments and subsequent calculations, ImΔL1(ω2) = -4.825 × 10 -8 H, based on the conductivity curve, the substrate conductivity was found to be 1.42 MS / m, with a relative error of 0.7%.

[0089] In summary, the zirconium-based cladding substrate thickness and conductivity measurement method based on swept-frequency eddy current in this application first uses a high-frequency sweep-excited method to measure the lift-off distance of the coil from the zirconium-based cladding surface, which is unaffected by properties such as the conductivity of the zirconium-based cladding. Then, the thickness and conductivity of the zirconium-based cladding layer are further measured in the low-frequency band. This measurement method is highly operable and accurate. Therefore, this method can simultaneously measure the thickness and conductivity of the zirconium-based cladding layer, directly reflecting the corrosion state of the cladding body, avoiding decoupling analysis of the complex characteristics of heterogeneous films, and is convenient to operate with reliable test results, possessing practical engineering value. Thus, this method improves the accuracy and diversity of zirconium-based cladding measurement results, enabling effective evaluation of the zirconium-based cladding state and facilitating the normal operation of the zirconium-based cladding.

[0090] Based on the above embodiments, in order to more clearly describe the specific implementation process of measuring substrate thickness and conductivity in this application, the measurement method in a specific embodiment is described below as an example. Figure 6 A flowchart illustrating a specific method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy currents, as proposed in this application, is shown below. Figure 6 As shown, the method includes the following steps:

[0091] Step S1: Fabricate two coaxial eddy current detection coils with identical geometric parameters, differing only in their distance from the zirconium-based cladding. Simultaneously apply a sweep frequency excitation signal to the coils to induce eddy currents on the surface of the zirconium-based cladding.

[0092] Step S2: The detection coil is placed above the zirconium-based cladding and in the air to measure the coil inductive reactance, and then the inductive reactance change is obtained through differential processing.

[0093] Step S3: Establish a simplified analytical theoretical model of eddy current in a multi-layer structure, set the geometric parameters of the coil and the zirconium-based cladding parameters, and calculate the change in inductive reactance after giving a sweep frequency excitation signal.

[0094] Step S4: Change only the lift-off distance of the coil to obtain the high-frequency inductive reactance change under different lift-off distances. Perform linear fitting on the logarithmic data of the real part of the lift-off distance and the high-frequency inductive reactance change, and calculate the lift-off value based on the lift-off distance fitting curve.

[0095] Step S5: Set the corresponding lift-off value, change the substrate thickness of the zirconium-based cladding, obtain the ratio of the change in the imaginary part of the low-frequency inductive reactance under different substrate thicknesses, perform exponential fitting on the substrate thickness and the ratio of the change in the imaginary part of the low-frequency inductive reactance, and calculate the substrate thickness of the zirconium-based cladding based on the substrate thickness fitting curve.

[0096] Step S6: After setting the lift-off value and substrate thickness to actual values, change the substrate conductivity of the zirconium-based cladding to obtain the change in the imaginary part of the low-frequency inductive reactance of the lower coil under different substrate conductivity. Perform linear fitting on the substrate conductivity and the change in the imaginary part of the low-frequency inductive reactance. Calculate the substrate conductivity of the zirconium-based cladding based on the substrate conductivity fitting curve.

[0097] To achieve the above embodiments, this application also proposes a device for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy currents. Figure 7 This is a schematic diagram of a zirconium-based clad substrate thickness and conductivity measurement device based on swept-frequency eddy current, as proposed in an embodiment of this application. Figure 7 As shown, the device includes: a setting module 100, a setup module 200, a lift-off calculation module 300, a thickness measurement module 400, and a conductivity measurement module.

[0098] The setting module 100 is used to fabricate two coaxial eddy current detection coils with identical geometric parameters. The two detection coils are placed above the zirconium-based cladding and in the air, respectively. A sweep frequency excitation signal is applied to the two detection coils, and the change in inductive reactance is calculated based on the measurement results.

[0099] Module 200 is established to build an analytical theoretical model of multilayer eddy current based on the parameters of two detection coils and zirconium-based cladding, as well as the measurement data of inductive reactance change.

[0100] The lift-off calculation module 300 is used to obtain the high-frequency inductive reactance change of the coil under different lift-off distances through the model, and to perform linear fitting on the real logarithm of the lift-off distance and the high-frequency inductive reactance change, and to calculate the lift-off value of each detection coil based on the obtained lift-off distance fitting curve.

[0101] The thickness measurement module 400 is used to set the lift-off value in the model, obtain the low-frequency inductance change of the coil under different substrate thicknesses, and perform exponential fitting on the ratio of the imaginary part of the substrate thickness and the low-frequency inductance change, and calculate the substrate thickness of the zirconium cladding based on the obtained substrate thickness fitting curve.

[0102] The conductivity measurement module 500 is used to set the substrate thickness in the model, obtain the low-frequency inductive reactance change of the coil under different substrate conductivity, and perform linear fitting on the imaginary part of the substrate conductivity and the current low-frequency inductive reactance change. The substrate conductivity of the zirconium-based cladding is calculated based on the obtained substrate conductivity fitting curve.

[0103] It should be noted that the explanation of the above-described embodiment of the method for measuring the thickness and conductivity of zirconium-based cladding substrate based on swept frequency eddy current also applies to the device of this embodiment. The specific implementation of each mode to achieve its function can be referred to the relevant description in the above embodiment, and will not be repeated here.

[0104] In summary, the zirconium-based cladding substrate thickness and conductivity measurement device based on swept-frequency eddy current in this application embodiment can simultaneously measure the thickness and conductivity of the zirconium-based cladding layer, directly reflecting the corrosion state of the cladding body. It avoids the need for decoupled analysis of the complex characteristics of heterogeneous films, is easy to operate, and provides reliable test results, thus possessing practical engineering value. Therefore, this device improves the accuracy and diversity of zirconium-based cladding measurement results, enabling effective evaluation of the zirconium-based cladding condition and facilitating its normal operation.

[0105] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for measuring the thickness and conductivity of a zirconium-based cladding substrate based on swept-frequency eddy current as described in any of the first aspect embodiments above.

[0106] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0107] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0108] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0109] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0110] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0111] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0112] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0113] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current, characterized in that, Includes the following steps: Two coaxial eddy current detection coils with identical geometric parameters are fabricated. The two detection coils are placed above a zirconium-based cladding shell and in the air, respectively. A sweep frequency excitation signal is applied to the two detection coils, and the impedance of each detection coil is measured. Based on the impedance and the frequency of the sweep frequency excitation signal, the inductive reactance of each detection coil is calculated. The calculated inductive reactance data is differentially processed to obtain the change in inductive reactance; Based on the parameters of the two detection coils and the zirconium-based cladding, as well as the inductive reactance change measurement data, a multilayer structure eddy current analytical theoretical model is established. The high-frequency inductive reactance change of the coil under different lift-off distances is obtained by the multi-layer structure eddy current analytical theoretical model, and the real logarithm of the lift-off distance and the high-frequency inductive reactance change is linearly fitted. The lift-off value of each detection coil is calculated based on the obtained lift-off distance fitting curve. In the multilayer structure eddy current analytical theoretical model, the lift-off value is set, and the low-frequency frequency and multiple substrate thicknesses of the zirconium-based shell are set. The imaginary ratio of the low-frequency inductive reactance changes of the two detection coils corresponding to each substrate thickness at the low-frequency frequency is calculated respectively. The imaginary ratio of the substrate thickness and the low-frequency inductive reactance changes is subjected to exponential fitting. The substrate thickness of the zirconium-based shell is calculated based on the obtained substrate thickness fitting curve. In the multilayer structure eddy current analytical theoretical model, the lift-off value and the substrate thickness are set to obtain the low-frequency inductive reactance change of the coil under different substrate conductivity. The imaginary part of the substrate conductivity and the current low-frequency inductive reactance change is linearly fitted, and the substrate conductivity of the zirconium-based cladding is calculated based on the obtained substrate conductivity fitting curve. The low-frequency inductive reactance change is calculated using the following formula in the analytical theoretical model of the multilayer structure eddy current: Where, Δ L 0 is a variable related to the coil size. ω For the excitation frequency, μ 0 is the permeability of free space. σ The substrate conductivity, α 0 represents spatial resolution. c It is the thickness of the substrate; High frequencies are used to reduce the eddy current skin depth, which can make the eddy current skin depth smaller, thus ignoring the influence of the conductivity and thickness of the zirconium cladding on the lift-off distance measurement; low frequencies are used to increase the eddy current skin depth, which can make the eddy current skin depth larger, thus enabling the measurement of substrate thickness and conductivity.

2. The method according to claim 1, characterized in that, The method of obtaining the high-frequency inductive reactance change of the coil at different lift-off distances includes: Set multiple lift-off distance values ​​for the high-frequency frequency and the detection coil; Calculate the coil reactance change corresponding to each of the take-off distance values ​​at the high frequency; The lift-off distance fitting curve is expressed by the following formula: ln(ReΔ L ( ω 1))= al + b in, ω 1 represents a high frequency, Δ L ( ω 1) This refers to the high-frequency inductive reactance change of the coil. a and b For real numbers, a <0, b <0, where l is the lift-off distance value.

3. The method according to claim 2, characterized in that, The method of obtaining the low-frequency inductive reactance change of the coil under different substrate thicknesses includes: Set low-frequency frequencies and multiple substrate thicknesses for zirconium-based cladding; Calculate the ratio of the imaginary parts of the low-frequency reactance changes of the two detection coils corresponding to each substrate thickness at the low-frequency frequency. The substrate thickness fitting curve is expressed by the following formula: |ImD L 1( ω 2) / ImΔ L 2( ω 2)|= k 1e αt + m 1 in, ω 2 represents the low-frequency range, Δ L 1( ω 2) This represents the low-frequency inductance change of the upper coil, Δ L 2( ω 2) This refers to the low-frequency inductance change of the lower coil. k 1. α and m 1 is a real number. k 1>0, α <0, m 1>0.

4. The method according to claim 3, characterized in that, The method of obtaining the low-frequency inductive reactance change of the coil under different substrate conductivity includes: Multiple substrate conductivity values ​​are set for the zirconium-based cladding, and the imaginary part of the low-frequency inductive reactance change of the upper coil corresponding to each substrate conductivity value is calculated at the low-frequency frequency. The substrate conductivity fitting curve is expressed by the following formula: ImD L 1( ω 2)= k 2 σ+m 2 in, k 2 and m 2 is a real number. k 2<0, m 2 < 0.

5. The method according to claim 3, characterized in that, The high frequency is used to reduce the eddy current skin depth, and the low frequency is used to increase the eddy current skin depth. The high frequency is greater than or equal to 1 MHz, and the low frequency is less than or equal to 1 kHz.

6. The method according to claim 1, characterized in that, The geometric parameters of the detection coil include the inner diameter, outer diameter, height, and number of turns.

7. The method according to claim 1, characterized in that, The zirconium-based cladding has a substrate and a coating that are both non-ferromagnetic conductive materials, and the thickness of the substrate is much greater than the thickness of the coating.

8. A device for measuring the thickness and conductivity of a zirconium-based clad substrate based on swept-frequency eddy current, characterized in that, Includes the following modules: The setup module is used to fabricate two coaxial eddy current detection coils with identical geometric parameters. The two detection coils are placed above a zirconium-based cladding shell and in the air, respectively. A sweep frequency excitation signal is applied to the two detection coils, and the impedance of each detection coil is measured. Based on the impedance and the frequency of the sweep frequency excitation signal, the inductive reactance of each detection coil is calculated. The calculated inductive reactance data is differentially processed to obtain the change in inductive reactance; A module is established to build an analytical theoretical model of the multilayer structure eddy current based on the parameters of the two detection coils and the zirconium-based cladding, as well as the inductive reactance change measurement data. The lift-off calculation module is used to obtain the high-frequency inductive reactance change of the coil under different lift-off distances through the multi-layer structure eddy current analytical theoretical model, and to perform linear fitting on the real logarithm of the lift-off distance and the high-frequency inductive reactance change, and to calculate the lift-off value of each detection coil based on the obtained lift-off distance fitting curve. The thickness measurement module is used to set the lift-off value in the multilayer structure eddy current analytical theoretical model, set the low frequency and multiple substrate thicknesses of the zirconium-based cladding; calculate the imaginary ratio of the low-frequency inductive reactance changes of the two detection coils corresponding to each substrate thickness at the low frequency, and perform exponential fitting on the substrate thickness and the imaginary ratio of the low-frequency inductive reactance changes, and calculate the substrate thickness of the zirconium-based cladding based on the obtained substrate thickness fitting curve; The conductivity measurement module is used to set the lift-off value and the substrate thickness in the multilayer structure eddy current analytical theoretical model, obtain the low-frequency inductive reactance change of the coil under different substrate conductivity, and perform linear fitting on the imaginary part of the substrate conductivity and the current low-frequency inductive reactance change, and calculate the substrate conductivity of the zirconium-based cladding based on the obtained substrate conductivity fitting curve. The low-frequency inductive reactance change is calculated using the following formula in the analytical theoretical model of the multilayer structure eddy current: Where ΔL0 is a variable related to the coil size, ω is the excitation frequency, μ0 is the vacuum permeability, σ is the substrate conductivity, α0 is the spatial resolution, and c is the substrate thickness. High frequencies are used to reduce the eddy current skin depth, which can make the eddy current skin depth smaller, thus ignoring the influence of the conductivity and thickness of the zirconium cladding on the lift-off distance measurement; low frequencies are used to increase the eddy current skin depth, which can make the eddy current skin depth larger, thus enabling the measurement of substrate thickness and conductivity.

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