Titanium plate thickness and conductivity synchronous measurement method based on eddy current amplitude-phase model iteration and application

Abstract

This invention discloses a method for synchronously measuring the thickness and conductivity of titanium plates based on an iterative eddy current amplitude-phase model. The steps are as follows: S1, initialize the measuring device and set an excitation current of a suitable frequency to pass through the eddy current coil; S2, place the eddy current coil in the air, sample the impedance of the eddy current coil, and obtain the reference impedance Z. air S3. Place the eddy current coil vertically on the titanium plate being measured, sample the resistance of the eddy current coil, and obtain the measured impedance. Z S4. Calculate the impedance change signal ΔZ= Z air - Z Extract the amplitude |ΔZ| and phase angle ∠ΔZ of the impedance change signal; S5, set the thickness of the titanium plate. c Electrical conductivity σ The initial value, along with the amplitude |ΔZ| and phase angle ∠ΔZ obtained in step S4, are substituted into the amplitude-phase model, and the conductivity of the titanium plate is obtained by iterative solution. σ ,thickness c This method eliminates the strong coupling caused by the difference in conductivity of titanium alloys, simplifies the inverse eddy current problem into solving a system of equations, and realizes simultaneous measurement of multiple parameters of titanium alloy plates at a single frequency, avoiding tedious calibration and adjustment.

Description

Technical Field

[0001] This invention belongs to the field of eddy current nondestructive testing technology, specifically relating to a method and application for simultaneous measurement of titanium plate thickness and conductivity based on eddy current amplitude-phase model iteration. Background Technology

[0002] In the production and processing of titanium alloy sheets, standard thickness is a critical quality indicator because it directly affects the sheet's strength and assembly precision. Furthermore, the electrical conductivity of titanium alloy sheets is related to their metallic composition, which in turn affects the sheet's chemical and physical properties. With the increasing demands for material performance in high-end manufacturing fields such as aerospace and nuclear power, the need for simultaneous non-destructive testing of the thickness and conductivity of titanium alloy sheets is becoming increasingly urgent. Accurate measurement of thickness and conductivity is crucial for improving the quality of titanium alloy sheets.

[0003] Eddy current testing is a non-destructive testing technique based on the principle of electromagnetic induction, commonly used to measure the thickness or conductivity of metal sheets. However, titanium alloy sheets come in numerous grades with varying properties, and both thickness and conductivity affect the eddy current response. Thin sheets with high conductivity and thick sheets with low conductivity may exhibit the same eddy current signal. Therefore, traditional methods measure only a single parameter and assume that conductivity or thickness is known. In actual measurements, however, all parameters may be unknown. Furthermore, existing methods mainly rely on multi-frequency or swept-frequency excitation to solve the parameter inversion problem, and efficiently achieving simultaneous measurement of multiple parameters at a single frequency remains a pressing issue. Therefore, a method for simultaneous measurement of titanium sheet thickness and conductivity based on an iterative eddy current amplitude-phase model has significant application value for overcoming existing technological bottlenecks and improving the quality assessment capabilities of titanium alloy sheets under complex working conditions. Summary of the Invention

[0004] This invention addresses the background technology by proposing a method for simultaneous measurement of titanium plate thickness and conductivity based on an iterative eddy current amplitude-phase model and its application. The invention uses a novel analytical model to characterize the complex coupling relationship between the impedance change (amplitude and phase) of the eddy current coil and the measured parameters (thickness and conductivity) of the titanium alloy plate. By substituting the measured coil impedance change into this model, a set of equations is formed. Iteratively solving these equations allows the measurement of the titanium alloy plate's thickness and conductivity at a single excitation frequency.

[0005] To achieve the objectives of this invention, the following technical solution is adopted:

[0006] In a first aspect, the present invention provides a method for simultaneously measuring the thickness and conductivity of titanium plates based on an iterative eddy current amplitude-phase model, the specific steps of which are as follows:

[0007] S1. Initialize the measuring device and set an excitation current of a suitable frequency to pass through the eddy current coil;

[0008] S2. Place the eddy current coil in the air and sample the impedance of the eddy current coil to obtain the reference impedance Z. air ;

[0009] S3. Place the eddy current coil vertically on the titanium plate to be measured, sample the resistance of the eddy current coil, and obtain the measured impedance Z.

[0010] S4. Calculate the impedance change signal ΔZ=Z air -Z, extract the amplitude |ΔZ| and phase angle ∠ΔZ of the impedance change signal;

[0011] S5. Set initial values ​​for the thickness c and conductivity σ of the titanium plate. Substitute these initial values, along with the amplitude |ΔZ| and phase angle ∠ΔZ obtained in step S4, into the following amplitude-phase model and iteratively solve to obtain the conductivity σ and thickness c of the titanium plate:

[0012]

[0013] Where r1 and r2 are the inner and outer radii of the eddy current coil, h is the height of the eddy current coil, n is the number of turns of the eddy current coil, ω is the angular frequency of the excitation current, μ0 is the permeability of free space, and α0 is the reciprocal of the average radius of the eddy current coil.

[0014] Preferably, the amplitude factor Int in step S5 is:

[0015]

[0016] Where J1(x) is a first-order Bessel function of the first kind;

[0017] Preferably, the iterative solution step in step S5 is as follows:

[0018] S51. Set the initial values ​​of the titanium plate thickness c and conductivity σ to c. i σ i The allowable error is ε c ε σ ;

[0019] S52. Calculate the Jacobian matrix expression:

[0020] ;

[0021] S53, Calculate the residual And the values ​​of the Jacobian matrix

[0022] S54. Solve the system of linear equations

[0023] We obtain Δc and Δσ;

[0024] S55, Update parameter c i+1=c i +Δc、σ i+1 =σ i +Δσ. If the error meets the requirement, i.e., Δc < ε c Δσ<ε σ Then c i+1 σ i+1 To output the final thickness c and conductivity σ, otherwise repeat steps S53-S55 until the error meets the requirements.

[0025] Secondly, the present invention also provides a storage medium burned with the method described in the first aspect for use in the quality inspection of titanium alloy plates.

[0026] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0027] 1. High efficiency: It transforms the complex inverse eddy current problem into a problem of solving a set of equations, realizing multi-parameter measurement of titanium alloy plates under a single excitation frequency.

[0028] 2. It has wide applicability, eliminating the strong coupling problem caused by the difference in electrical conductivity of different titanium alloys, and is suitable for various grades of titanium alloys such as TA1, TA2, and TC4.

[0029] 3. The method is simple and practical, and can simultaneously measure the thickness and conductivity of titanium alloys, avoiding the problems of extensive calibration and adjustment. Attached Figure Description

[0030] Figure 1 This is a schematic diagram illustrating the measurement principle of the present invention;

[0031] Figure 2 The flowchart shows the method for simultaneous measurement of titanium plate thickness and conductivity based on the electric eddy current amplitude-phase model iteration of this invention.

[0032] In the figure: 1. Eddy current coil; 2. Titanium alloy plate under test; 3. Impedance analyzer. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] The measurement principle of this embodiment is as follows: Figure 1 As shown. Connect the two ends of the eddy current coil 1 to the L of the impedance analyzer 3 respectively. POT L CUR and H POT H CURThe eddy current coil 1 is placed on the titanium alloy plate 2 under test. The impedance analyzer 3 provides an excitation current through the eddy current coil 1 according to a set frequency ω, which can be selected in the low-frequency range of 1kHz to 10kHz. The alternating magnetic field generated by the alternating current eddy current coil 1 acts on the titanium alloy plate 2 under test, and eddy currents will be generated in the titanium alloy plate 2 due to electromagnetic induction. The intensity and distribution of the eddy currents are closely related to the electromagnetic parameters and thickness of the material, and the reverse magnetic field generated by the eddy currents will affect the impedance of the eddy current coil 1. Therefore, by measuring the impedance of the eddy current coil 1 by the impedance analyzer 3, information such as the electromagnetic parameters and thickness of the sample under test can be inferred. The impedance difference of the eddy current coil 1 relative to the titanium alloy plate 2 without test is substituted into the amplitude-phase model, and the accurate thickness and conductivity of the titanium alloy plate 2 under test can be calculated by iterative solution.

[0035] Based on the aforementioned detection principle, this application provides a method for simultaneously measuring the thickness and conductivity of titanium plates based on an iterative eddy current amplitude-phase model. Figure 2 As shown, the steps are as follows:

[0036] S1. Initialize the measuring device and set an excitation current of a suitable frequency to pass through the eddy current coil;

[0037] S2. Place the eddy current coil in the air and sample the impedance of the eddy current coil to obtain the reference impedance Z. air ;

[0038] S3. Place the eddy current coil vertically on the titanium plate to be measured, sample the resistance of the eddy current coil, and obtain the measured impedance Z.

[0039] S4. Calculate the impedance change signal ΔZ=Z air -Z, extract the amplitude |ΔZ| and phase angle ∠ΔZ of the impedance change signal;

[0040] S5. Set initial values ​​for the thickness c and conductivity σ of the titanium plate. Substitute these initial values, along with the amplitude |ΔZ| and phase angle ∠ΔZ obtained in step S4, into the following amplitude-phase model and iteratively solve to obtain the conductivity σ and thickness c of the titanium plate:

[0041]

[0042] Where r1 and r2 are the inner and outer radii of the eddy current coil, h is the height of the eddy current coil, n is the number of turns of the eddy current coil, ω is the angular frequency of the excitation current, μ0 is the permeability of free space, and α0 is the reciprocal of the average radius of the eddy current coil.

[0043] Preferably, the amplitude factor Int in step S5 is:

[0044]

[0045] Where J1(x) is a first-order Bessel function of the first kind;

[0046] Preferably, the iterative solution step in step S5 is as follows:

[0047] S51. Set the initial values ​​of the titanium plate thickness c and conductivity σ to c. i σ i The allowable error is ε c ε σ ;

[0048] S52. Calculate the Jacobian matrix expression:

[0049] ;

[0050] S53, Calculate the residual And the values ​​of the Jacobian matrix

[0051] S54. Solve the system of linear equations We obtain Δc and Δσ;

[0052] S55, Update parameter c i+1 =c i +Δc、σ i+1 =σ i +Δσ. If the error meets the requirement, i.e., Δc < ε c Δσ<ε σ Then c i+1 σ i+1 To output the final thickness c and conductivity σ, otherwise repeat steps S53-S55 until the error meets the requirements.

[0053] Furthermore, in one specific embodiment, a measurement system based on a precision impedance analyzer (TH2848-10) was used for testing. The eddy current coil was wound with enameled copper wire of 0.2 mm diameter, with inner and outer radii r1 and r2 of 5 mm and 5.4 mm, respectively. The coil height h was 5 mm, and the number of turns n was 50 turns. During the test, the impedance analyzer excitation frequency was set to 3.5 kHz, and 10 titanium alloy plates were used as samples. Each sample was measured 20 times, and the average value was taken. The comparison of the measured and calculated results is shown in Figure 1:

[0054] Table 1

[0055] 1 0.515 / 0.5 0.580 / 0.59 3.00 / -1.69 2 0.820 / 0.8 0.585 / 0.59 2.50 / -1.19 3 1.232 / 1.2 0.584 / 0.59 2.67 / -1.02 4 1.490 / 1.5 0.624 / 0.63 -0.67 / -1.11 5 1.968 / 2.0 0.632 / 0.63 -1.60 / 0.32 6 2.524 / 2.5 0.613 / 0.62 0.96 / -1.13 7 3.045 / 3.0 0.613 / 0.62 1.50 / -1.13 8 3.348 / 3.5 0.634 / 0.62 -1.14 / 2.26 9 4.239 / 4.0 0.590 / 0.61 5.98 / -3.28 10 5.264 / 5.0 0.612 / 0.63 5.28 / -2.86

[0056] Based on the results in Table 1, the measurement results of the embodiments of this application are described in detail. The relative errors of the measured thickness and conductivity are -1.60% to 5.98% and 3.28% to 2.26%, respectively. All measurement errors are within a reasonable range, demonstrating the effectiveness of the embodiments of this application in the actual simultaneous measurement of the thickness and conductivity of titanium alloy plates.

[0057] In practice, the initial value c i and σ i The selection can be preset according to the common specifications of titanium alloy plates, such as c. i Initially set to 1.0 mm, σ i The initial value is set to 0.5 MS / m, allowing for rapid convergence without requiring precise matching to the actual value. Simultaneously, to ensure measurement accuracy, the calculated Jacobian matrix is ​​numerically stable during each iteration to prevent divergence due to matrix singularities. The allowable error ε... c It is usually set to 0.01 mm, ε σ Setting the value to 0.01 MS / m, the number of iterations is generally controlled within 5-10 times to meet the convergence condition, balancing measurement efficiency and accuracy. In the test of this embodiment, the above iterative steps were used to measure 10 titanium alloy samples. The results showed that the maximum relative error of thickness was 5.98%, and the maximum relative error of conductivity was 2.26%, both meeting the accuracy requirements for quality inspection of titanium alloy plates in high-end manufacturing fields such as aerospace and nuclear power, verifying the reliability and practicality of the iterative method.

[0058] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for simultaneous measurement of titanium plate thickness and conductivity based on an iterative eddy current amplitude-phase model, characterized in that, Includes the following steps: S1. Initialize the measuring device and set an excitation current of a suitable frequency to pass through the eddy current coil; S2. Place the eddy current coil in the air and sample the impedance of the eddy current coil to obtain the reference impedance Z. air ; S3. Place the eddy current coil vertically on the titanium plate to be measured, sample the resistance of the eddy current coil, and obtain the measured impedance Z. S4. Calculate the impedance change signal ΔZ=Z air -Z, extract the amplitude |ΔZ| and phase angle ∠ΔZ of the impedance change signal; S5. Set initial values ​​for the thickness c and conductivity σ of the titanium plate. Substitute these initial values, along with the amplitude |ΔZ| and phase angle ∠ΔZ obtained in step S4, into the following amplitude-phase model and iteratively solve to obtain the conductivity σ and thickness c of the titanium plate: ； Where r1 and r2 are the inner and outer radii of the eddy current coil, h is the height of the eddy current coil, n is the number of turns of the eddy current coil, ω is the angular frequency of the excitation current, μ0 is the permeability of free space, and α0 is the reciprocal of the average radius of the eddy current coil. Wherein, the amplitude factor Int is: in It is a first-order Bessel function of the first kind.

2. The method for simultaneous measurement of titanium plate thickness and conductivity based on an iterative eddy current amplitude-phase model according to claim 1, characterized in that, The iterative solution steps in step S5 are as follows: S51. Set the initial values ​​of the titanium plate thickness c and conductivity σ to c. i σ i The allowable error is ε c ε σ ; S52. Calculate the Jacobian matrix expression: ； S53, Calculate the residual And the values ​​of the Jacobian matrix S54. Solve the system of linear equations We obtain Δc and Δσ; S55, Update parameter c i+1 =c i +Δc、σ i+1 =σ i +Δσ; If the error meets the requirement, i.e., Δc < ε c Δσ<ε σ Then c i+1 σ i+1 To output the final thickness c and conductivity σ, otherwise repeat steps S53-S55 until the error meets the requirements.

3. A storage medium, characterized in that, The storage medium stores a computer program that executes the method as described in claim 1 for quality inspection of titanium alloy plates.

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