A method for measuring the thickness of ceramic layer and bonding layer of thermal barrier coating based on dual-frequency eddy current

Abstract

The present invention discloses a method for measuring the thickness of ceramic layer and bonding layer of thermal barrier coating based on dual-frequency eddy current, which relates to the field of multi-frequency eddy current detection. It can overcome the problems of difficult decoupling between ceramic layer and bonding layer, complex algorithm and only single layer thickness detection in existing coating thickness measurement, and has a significant effect on simultaneous detection of ceramic layer thickness and bonding layer thickness. Firstly, the phase signal of the standard test piece at two different frequencies is obtained by using eddy current coil; then, the relationship between the ceramic layer thickness, bonding layer thickness and eddy current phase signal of the calibration test piece is established to obtain the calibration expression of the ceramic layer thickness and bonding layer thickness; finally, for the test piece, the eddy current coil is used to obtain its phase signal at two frequencies, and the above expression is substituted to calculate the ceramic layer thickness and bonding layer thickness of the thermal barrier coating. The present invention uses the dual-frequency eddy current method to solve the problem that the bonding layer and ceramic layer signals are difficult to decouple in the current thermal barrier coating thickness measurement. Compared with the traditional method that can only detect the thickness of a single coating, the method proposed in this patent can simultaneously measure the ceramic layer thickness and bonding layer thickness, which greatly improves the detection efficiency.

Description

Technical Field

[0001] The invention relates to the field of multi-frequency eddy current detection. Background Art

[0002] With the development of aviation technology, various functional coatings are widely used in aviation hot end components. Since the operating temperature of aircraft engine turbine blades is higher than the melting point of the blades, the application of thermal barrier coatings is of great significance to improving the high temperature and corrosion resistance of turbine blades.

[0003] Thermal barrier coatings consist of a ceramic layer, a bonding layer and a nickel-based high-temperature alloy substrate, which are covered on aircraft engine turbine blades to improve the safety performance and service life of turbine blades working in extremely harsh environments such as high temperature, high pressure, high stress, and high speed. In the preparation process, thermal barrier coatings usually use atmospheric plasma spraying technology, which mainly uses gases such as hydrogen and nitrogen to send powder into the high-temperature plasma jet generated by ionization. The particles heated to a molten or molten state will then be deposited on the surface of the substrate to form a coating. The coating structure prepared by this technology is relatively loose, resulting in a certain degree of unevenness in the thickness of the prepared coating; and in the service process, the thickness of the bonding layer and the ceramic layer will be thinned, and oxidized at high temperature to produce oxides, resulting in poor thermal insulation. In more serious cases, the ceramic layer will fall off, causing the thermal barrier coating to fail.

[0004] Common nondestructive testing methods include ultrasonic testing, infrared testing, and X-ray testing. Ultrasonic testing has a relatively high sensitivity, but it requires a coupling agent during testing, which is a contact test. The application range of infrared testing is relatively wide, but it requires a coating medium. The test results of X-rays are relatively intuitive, but the ionizing radiation is strong, which can easily cause harm to personnel health and is costly. Eddy current nondestructive testing technology has the characteristics of high sensitivity, fast detection speed, and non-contact. It can be used as an ideal method for measuring the thickness of thermal barrier coatings; this technology is based on the principle of electromagnetic induction, that is, when an excitation coil with sinusoidal excitation approaches a conductor, eddy currents will be induced inside the conductor, and the magnetic field formed by the eddy currents will interact with the original magnetic field, thereby changing the impedance of the original excitation coil. By processing the impedance signal of the original coil, we can obtain the parameters we want to measure, such as thickness, magnetic permeability, etc.

[0005] Thermal barrier coatings are complex multi-layer structures. Currently, there is a coupling problem in the eddy current detection signals of different coatings, which can only realize the thickness detection of a single coating within a certain range, and the subsequent processing steps are complicated. Based on the method of analytical model iteration, the thickness measurement requires a large amount of sample data, which is time-consuming and inefficient. Summary of the invention

[0006] In view of the above problems, the present invention proposes a method for measuring the thickness of the ceramic layer and the bonding layer of a thermal barrier coating based on dual-frequency eddy current. The method can overcome the problems of the existing coating thickness measurement such as the difficulty in decoupling the ceramic layer and the bonding layer, the complex algorithm, and the ability to detect only a single layer thickness. The method also has a significant effect on simultaneously detecting the thickness of the ceramic layer and the bonding layer.

[0007] The technical solution of the present invention is: first, an eddy current coil is used to obtain the phase signal of a standard specimen at two different frequencies; then, a relationship between the ceramic layer thickness, the bonding layer thickness and the eddy current phase signal of the calibration specimen is established to obtain the calibration expressions of the ceramic layer thickness and the bonding layer thickness; finally, for the test piece, an eddy current coil is used to obtain its phase signal at two frequencies, and the phase signals are substituted into the above expressions to calculate the ceramic layer thickness and the bonding layer thickness of the thermal barrier coating.

[0008] The steps include:

[0009] Step 1: Make three standard specimens M, N, and P, with a ceramic layer thickness of TC M TC N TC P The thickness of the bonding layer is BC M , B.C. N , B.C. P ; Among them BC M <BC N <BC P , TC M <TC N <TC P ;

[0010] Step 2: Place the eddy current probe in air at room temperature and pressure, and use an impedance analyzer to detect the impedance of the eddy current probe at low frequency Fre1 and high frequency Fre2: Z Air1 =R Air1 +X Air1 , Z Air2 =R Air2 +X Air2 ;

[0011] Then, the probes were placed on the three standard test pieces respectively, and the impedances were measured by impedance analyzer under Fre1. M1 =R M1 +X M1 , Z N1 =R N1 +X N1 , Z P1 =R P1 +X P1 ; Under Fre2, the impedances are Z M2 =R M2 +X M2 , ZN2 =R N2 +X N2 , Z P2 =R P2 +X P2 ;

[0012] Step 3: Perform differential processing on the impedance of the three standard specimens in step 2, and first obtain the resistance change of the coil under Fre1: ΔR M1 =(R M1 -R Air1 ), ΔR N1 =(R N1 -R Air1 ), ΔR P1 =(R P1 -R Air1 ), and then perform differential processing on the coil reactance under Fre1 to obtain the change in coil reactance under Fre1: ΔX M1 =(X M1 -X Air1 ), ΔX N1 =(X N1 -X Air1 ), ΔX P1 =(X P1 -X Air1 ), and finally the quotient is used to obtain the coil phase values ​​of the three standard parts M, N, and P under Fre1: P M1 =ΔX M1 / ΔR M1 , P N1 =ΔX N1 / ΔR N1 , P P1 =ΔX P1 / ΔR P1 ;

[0013] Similarly, the phase values ​​of the coils on the three calibration specimens M, N, and P under Fre2 are obtained: P M2 =ΔX M2 / ΔR M2 , P N2 =ΔX N2 / ΔR N2 , P P2 =ΔX P2 / ΔR P2 ;

[0014] Step 4: According to the relationship between the thickness of the ceramic layer TC, the thickness of the bonding layer BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the thickness of the bonding layer and the thickness of the ceramic layer by the coil phase value under Fre1 is established;

[0015] The phase of the impedance difference of standard specimens M, N, and P and the thickness of the bonding layer and ceramic layer of the thermal barrier coating can establish three sets of equations for the coil phase and different layer thicknesses under Fre1:

[0016]

[0017] Solving the equation gives the linear model correlation coefficient:

[0018]

[0019] Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k 11 , k 12 is the slope of the linear model, b1 represents the intercept of the linear model;

[0020] Finally, the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre1 is obtained: P = k 11 BC+k 12 TC+b1, where P1 represents the phase value of the coil at Fre1;

[0021] Step 5: According to the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the bonding layer thickness and the ceramic layer thickness by the coil phase value under Fre2 is established; similarly, in step 4, three sets of equations for the coil phase, bonding layer thickness and ceramic layer thickness under Fre2 can be established, and then the linear model correlation coefficient can be obtained by solving the equation:

[0022]

[0023] Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k 21 , k 22 is the slope of the linear model, and b2 represents the intercept of the linear model;

[0024] Similarly, the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre2 can be obtained: P2 = k 21 BC+k 22 TC+b2, where P2 represents the phase value of the coil at Fre2;

[0025] Step 6: Place the eddy current probe on the test piece and use the impedance analyzer to measure the phase of the coil of the test piece T at the frequency Fre1 and the frequency Fre2: P T1 =ΔX T1 / ΔR T1 , P T2 =ΔX T2 / ΔR T2;

[0026] Step 7: Substitute the two phase values ​​obtained in step 6 into the linear models of the two phases obtained in step 4 and step 5 and the thickness of the ceramic layer and the thickness of the bonding layer, so as to obtain the model expressions of the thickness of the ceramic layer and the thickness of the bonding layer of the test piece:

[0027]

[0028] Finally, the ceramic layer thickness and the bonding layer thickness of the test piece are obtained according to calculation.

[0029] Further, the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency in step 4 and step 5 is obtained by the following steps:

[0030] Take the standard parts, and obtain the coil phase value P by the eddy current method at a fixed frequency. Then draw the relationship between the bonding layer thickness BC and the coil phase value P under different ceramic layer thicknesses TC. It can be seen that under a fixed frequency Fre1, the phase value P of the detection probe and the thickness BC of the thermal barrier coating bonding layer present a linear relationship. The linear relationship is fitted to obtain the following expression: P = k1BC + B;

[0031] Moreover, the phase and the bonding layer thickness show the above linear relationship under different ceramic layer thicknesses TC. The corresponding intercept B can be obtained by linear relationship fitting, and then the relationship between the intercept B and the corresponding thermal barrier coating ceramic layer thickness TC is established. It can be seen that the intercept B and TC can also be linearly fitted to obtain the following expression: B = k2TC + b1;

[0032] Finally, the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency is obtained as follows: P=k1BC+k2TC+b1.

[0033] Compared with the prior art, the advantages of the present invention are:

[0034] First, the present invention selects the quotient of the change in coil reactance and the change in resistance, i.e., the phase, as the signal feature. When the thickness of the ceramic layer remains unchanged, the signal feature is linearly related to the thickness of the bonding layer. Furthermore, this linear relationship is fitted, and the relationship between the coil phase and the thickness of the ceramic layer and the thickness of the bonding layer at two different frequencies can be established by utilizing the feature that the change in the thickness of the ceramic layer and the intercept of the fitted curve are still linearly related. The thickness of the ceramic layer and the thickness of the bonding layer can be well detected at the same time, solving the problem of mutual coupling of the signals of the two coating layers, and the operation is simple and feasible.

[0035] 2. The present invention uses eddy current technology to measure the thickness of thermal barrier coatings, which is non-destructive to the test piece: Since the basic principle of eddy current detection is electromagnetic induction, it is only applicable to conductive materials that can generate eddy currents, and the conductivity of the conductor is less affected at different ambient temperatures, so this method has low requirements for the detection environment. Under the premise of keeping other influencing factors such as coil geometry parameters, excitation current, excitation frequency, and lift-off consistent, the phase of the bonding layer thickness and the impedance change is a single-valued function, and the intercept value of the ceramic layer thickness fitting signal is also a single-valued function, so the detection accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is the principle diagram of the dual-frequency eddy current method;

[0037] Figure 2 It is a linear relationship diagram between the bonding layer thickness and the coil phase under different ceramic layer thicknesses in the present invention;

[0038] Figure 3 is the linear relationship between the intercept of the fitted line and the thickness of the ceramic layer;

[0039] Figure 4 It is the calculation flow chart of dual-frequency eddy current method. DETAILED DESCRIPTION

[0040] In order to clearly illustrate the technical features of this patent, this patent is elaborated in detail below through a specific implementation method and in combination with its accompanying drawings.

[0041] Take the standard parts, obtain the coil phase value P by eddy current method at a fixed frequency, and then draw the relationship between the bonding layer thickness BC and the coil phase value P under different ceramic layer thicknesses TC, as shown in Figure 2 As shown, at a fixed frequency Fre1, the phase value P of the detection probe and the thickness BC of the thermal barrier coating bonding layer present a linear relationship, which can be fitted with a linear relationship to obtain the following expression:

[0042] P=k1BC+B (1)

[0043] Moreover, the phase and bonding layer thickness show the above linear relationship under different ceramic layer thicknesses TC. The corresponding intercept B can be obtained by linear relationship fitting, and then the relationship between the intercept B and the corresponding thermal barrier coating ceramic layer thickness TC is established, such as Figure 3 As shown, it can be seen that the intercept B and TC can also be linearly fitted to obtain the following expression:

[0044] B=k2TC+b1 (2)

[0045] Substituting formula (2) into formula (1), we can get the relationship between the bonding layer thickness BC and the coil phase value P under the ceramic layer thickness TC: P = k1BC + k2TC + b1 (3)

[0046] The feasibility and effectiveness of the technical solution of the present invention are verified and explained below by combining the above formula (3) with specific embodiments and drawings.

[0047] The steps include:

[0048] Step 1: Make three standard specimens M, N, and P, with a ceramic layer thickness of TC M TC N TC P The thickness of the bonding layer is BC M , B.C. N , B.C. P ; Among them BC M <BC N <BC P , TC M <TC N <TC P ;

[0049] Step 2: Place the eddy current probe in air at room temperature and pressure, and use an impedance analyzer to detect the impedance of the eddy current probe at low frequency Fre1 and high frequency Fre2: Z Air1 =R Air1 +X Air1 , Z Air2 =R Air2 +X Air2 ;

[0050] Then, the probes were placed on the three standard test pieces respectively, and the impedances were measured by impedance analyzer under Fre1. M1 =R M1 +X M1 , Z N1 =R N1 +X N1 , Z P1 =R P1 +X P1 ; Under Fre2, the impedances are Z M2 =R M2 +X M2 , Z N2 =R N2 +X N2 , Z P2 =R P2 +X P2 ;

[0051] Step 3: Perform differential processing on the impedance of the three standard specimens in step 2, and first obtain the resistance change of the coil under Fre1: ΔR M1 =(R M1 -R Air1 ), ΔR N1=(R N1 -R Air1 ), ΔR P1 =(R P1 -R Air1 ), and then perform differential processing on the coil reactance under Fre1 to obtain the change in coil reactance under Fre1: ΔX M1 =(X M1 -X Air1 ), ΔX N1 =(X N1 -X Air1 ), ΔX P1 =(X P1 -X Air1 ), and finally the quotient is used to obtain the coil phase values ​​of the three standard parts M, N, and P under Fre1: P M1 =ΔX M1 / ΔR M1 , P N1 =ΔX N1 / ΔR N1 , P P1 =ΔX P1 / ΔR P1 ;

[0052] Similarly, the phase values ​​of the coils on the three calibration specimens M, N, and P under Fre2 are obtained: P M2 =ΔX M2 / ΔR M2 , P N2 =ΔX N2 / ΔR N2 , P P2 =ΔX P2 / ΔR P2 ;

[0053] Step 4: According to the relationship between the thickness of the ceramic layer TC, the thickness of the bonding layer BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the thickness of the bonding layer and the thickness of the ceramic layer by the coil phase value under Fre1 is established;

[0054] The phase of the impedance difference of standard specimens M, N, and P and the thickness of the bonding layer and ceramic layer of the thermal barrier coating can establish three sets of equations for the coil phase and different layer thicknesses under Fre1:

[0055]

[0056] Solving the equation gives the linear model correlation coefficient:

[0057]

[0058] Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k11 , k 12 is the slope of the linear model, b1 represents the intercept of the linear model;

[0059] From equations (4) and (5), we can get the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre1:

[0060] P1=k 11 BC+k 12 TC+b1 (6)

[0061] Where P1 represents the phase value of the coil at Fre1, BC represents the thickness of the bonding layer, TC represents the thickness of the ceramic layer, and k 11 , k 12 is the slope of the linear model, and b1 is the intercept of the linear model.

[0062] Step 5: According to the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the bonding layer thickness and the ceramic layer thickness by the coil phase value under Fre2 is established; similarly, in step 4, three sets of equations for the coil phase, bonding layer thickness and ceramic layer thickness under Fre2 can be established, and then the linear model correlation coefficient can be obtained by solving the equation:

[0063]

[0064] Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the bonding layer, and k 21 , k 22 is the slope of the linear model, and b2 represents the intercept of the linear model;

[0065] Similarly, the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre2 can be obtained:

[0066] P2=k 21 BC+k 22 TC+b2 (8)

[0067] Where P2 is the phase value of the coil at Fre2, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k 21 , k 22 is the slope of the linear model, and b2 is the intercept of the linear model.

[0068] Step 6: Place the eddy current probe on the test piece and use the impedance analyzer to measure the phase of the coil of the test piece T at the frequency Fre1 and the frequency Fre2: P T1 =ΔX T1 / ΔR T1 , P T2 =ΔXT2 / ΔR T2 .

[0069] Step 7: According to the phase value of step 6: P T1 =ΔX T1 / ΔR T1 , P T2 =ΔX T2 / ΔR T2 , the two phase values ​​obtained by detection are respectively substituted into formula (7) and formula (8) to obtain the model expressions of the ceramic layer thickness and the bonding layer thickness of the test piece:

[0070]

[0071] The ceramic layer thickness and the bonding layer thickness of the test piece are obtained according to formula (9).

[0072] The impedance coordinate transformation thermal barrier coating thickness measurement method proposed in the present invention is also beneficial to suppress the influence of lift-off effect on the result in the measurement of bonding layer thickness compared with the traditional method of directly using phase measurement. For different material substrates and coating materials, as long as the phase value at two frequencies is obtained by the difference between the reactance and resistance and air at two frequencies, the linear model of the coil phase at dual frequencies and the two coating thicknesses is established, the thickness of the corresponding coating can be detected and evaluated.

[0073] The present invention uses a dual-frequency eddy current method to solve the problem that it is difficult to decouple the signals of the bonding layer and the ceramic layer in the current thermal barrier coating thickness measurement. Compared with the traditional method that can only detect the thickness of a single coating, the method proposed in this patent can simultaneously measure the thickness of the ceramic layer and the bonding layer, greatly improving the detection efficiency.

[0074] There are many specific implementation ways of the present invention. The above is only the preferred implementation mode of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A method for measuring the thickness of ceramic layer and bonding layer of thermal barrier coating based on dual-frequency eddy current, characterized in that: The steps include: Step 1: Make three standard specimens M, N, and P, with a ceramic layer thickness of TC M TC N TC P The thickness of the bonding layer is BC M , B.C. N , B.C. P ; Among them BC M <BC N <BC P , TC M <TC N <TC P ; Step 2: Place the eddy current probe in air at room temperature and pressure, and use an impedance analyzer to detect the impedance of the eddy current probe at low frequency Fre1 and high frequency Fre2: Z Air1 =R Air1 +X Air1 , Z Air2 =R Air2 +X Air2 ; Then, the probes were placed on the three standard test pieces respectively, and the impedances were measured by impedance analyzer under Fre1. M1 =R M1 +X M1 , Z N1 =R N1 +X N1 , Z P1 =R P1 +X P1 ; Under Fre2, the impedances are Z M2 =R M2 +X M2 , Z N2 =R N2 +X N2 , Z P2 =R P2 +X P2 ; Step 3: Perform differential processing on the impedance of the three standard specimens in step 2, and first obtain the resistance change of the coil under Fre1: ΔR M1 =(R M1 -R Air1 ), ΔR N1 =(R N1 -R Air1 ), ΔR P1 =(R P1 -R Air1 ), and then perform differential processing on the coil reactance under Fre1 to obtain the change in coil reactance under Fre1: ΔX M1 =(X M1 -X Air1 ), ΔX N1 =(X N1 -X Air1 ), ΔX P1 =(X P1 -X Air1 ), and finally the quotient is used to obtain the coil phase values ​​of the three standard parts M, N, and P under Fre1: P M1 =ΔX M1 / ΔR M1 , P N1 =ΔX N1 / ΔR N1 , P P1 =ΔX P1 / ΔR P1 ; Similarly, the phase values ​​of the coils on the three calibration specimens M, N, and P under Fre2 are obtained: P M2 =ΔX M2 / ΔR M2 , P N2 =ΔX N2 / ΔR N2 , P P2 =ΔX P2 / ΔR P2 ; Step 4: According to the relationship between the thickness of the ceramic layer TC, the thickness of the bonding layer BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the thickness of the bonding layer and the thickness of the ceramic layer by the coil phase value under Fre1 is established; The phase of the impedance difference of standard specimens M, N, and P and the thickness of the bonding layer and ceramic layer of the thermal barrier coating can establish three sets of equations for the coil phase and different layer thicknesses under Fre1: Solving the equation gives the linear model correlation coefficient: Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k 11 , k 12 is the slope of the linear model, b1 represents the intercept of the linear model; Finally, the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre1 is obtained: P1 = k 11 BC+k 12 TC+b1, where P1 represents the phase value of the coil at Fre1; Step 5: According to the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency, P=k1BC+k2TC+b1, a linear model for solving the bonding layer thickness and the ceramic layer thickness by the coil phase value under Fre2 is established; similarly, in step 4, three sets of equations for the coil phase, bonding layer thickness and ceramic layer thickness under Fre2 can be established, and then the linear model correlation coefficient can be obtained by solving the equation: Where P is the phase value of the coil, BC is the thickness of the bonding layer, TC is the thickness of the ceramic layer, and k 21 , k 22 is the slope of the linear model, and b2 represents the intercept of the linear model; Similarly, the linear model of phase, ceramic layer thickness and bonding layer thickness under Fre2 can be obtained: P2 = k 21 BC+k 22 TC+b2, where P2 represents the phase value of the coil at Fre2; Step 6: Place the eddy current probe on the test piece and use the impedance analyzer to measure the phase of the coil of the test piece T at the frequency Fre1 and the frequency Fre2: P T1 =ΔX T1 / ΔR T1 , P T2 =ΔX T2 / ΔR T2 ; Step 7: Substitute the two phase values ​​obtained in step 6 into the linear models of the two phases obtained in step 4 and step 5 and the thickness of the ceramic layer and the thickness of the bonding layer, so as to obtain the model expressions of the thickness of the ceramic layer and the thickness of the bonding layer of the test piece: Finally, the ceramic layer thickness and the bonding layer thickness of the test piece are obtained according to calculation.

2. The method for measuring the thickness of ceramic layer and bonding layer of thermal barrier coating based on dual-frequency eddy current according to claim 1, characterized in that: The relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency in step 4 and step 5 is obtained by the following steps: Take the standard parts, and obtain the coil phase value P by the eddy current method at a fixed frequency. Then draw the relationship between the bonding layer thickness BC and the coil phase value P under different ceramic layer thicknesses TC. It can be seen that under a fixed frequency Fre1, the phase value P of the detection probe and the thickness BC of the thermal barrier coating bonding layer present a linear relationship. The linear relationship is fitted to obtain the following expression: P = k1BC + B; Moreover, the phase and the bonding layer thickness show the above linear relationship under different ceramic layer thicknesses TC. The corresponding intercept B can be obtained by linear relationship fitting, and then the relationship between the intercept B and the corresponding thermal barrier coating ceramic layer thickness TC is established. It can be seen that the intercept B and TC can also be linearly fitted to obtain the following expression: B = k2TC + b1; Finally, the relationship between the ceramic layer thickness TC, the bonding layer thickness BC and the coil phase value P at a fixed frequency is obtained as follows: P1=k1BC+k2TC+b1.

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