A method for measuring thickness of thermal barrier coating based on shape function method

Abstract

The present application belongs to the technical field of conventional eddy current testing, and particularly relates to a thermal barrier coating thickness measurement method based on a shape function method. First, an eddy current coil is used to obtain the reactance variation signal and the phase signal of a calibration test piece. Second, a characteristic value coordinate grid of the ceramic layer thickness, the bond coat thickness, and the eddy current reactance variation signal and the phase signal of the calibration test piece is established. Third, a mapping relationship between the characteristic value coordinate system and the normalized coordinate system is constructed based on a four-point shape function. Finally, the eddy current coil is applied to the test piece to obtain the reactance variation signal and the phase signal of the test piece, which are substituted into the above mapping relationship to calculate the ceramic layer thickness and the bond coat thickness of the thermal barrier coating. The present application solves the problem of decoupling the signals of the bond coat and the ceramic layer in the current thermal barrier coating thickness measurement by using the four-point shape function method, and can simultaneously measure the ceramic layer thickness and the bond coat thickness, thereby effectively improving the precision and the detection efficiency of the thermal barrier coating thickness measurement.

Description

Technical Field

[0001] This invention belongs to the field of conventional eddy current testing technology, specifically relating to a method for measuring the thickness of thermal barrier coatings based on the shape function method. Background Technology

[0002] With the development of aviation technology, various functional coatings are widely used in aviation hot-end components. Since the operating temperature of aero-engine turbine blades is higher than their melting point, thermal barrier coatings are of great significance in improving the high-temperature resistance of turbine blades. Thermal barrier coatings consist of a ceramic layer and a binder layer. Due to limitations in manufacturing technology, the thermal insulation properties of the coating can deteriorate, affecting the service life of the aero-engine blades. Therefore, accurate thickness measurement of thermal barrier coatings is crucial for their quality control and evaluation.

[0003] Thermal barrier coatings (TBCs) are multilayer coating systems. The top layer is a ceramic layer, which is oxidation-resistant, corrosion-resistant, and has extremely low thermal conductivity, significantly reducing the temperature of the substrate material. The middle layer is a bonding layer, ensuring good adhesion between the coating and the substrate material. The bottom layer is a nickel-based superalloy substrate that needs protection. Atmospheric plasma spraying technology is often used in the preparation of TBCs, where a plasma flame heats the coating material to a molten or highly ductile state. Guided by the high-speed plasma flame, the material impacts the workpiece surface at high speed. This process, due to particle cross-linking, coating impurities, and particle undulations, can lead to voids, pores, uneven coating distribution, and other issues in the ceramic and bonding layers. Currently, the preparation process of TBCs still has certain limitations; therefore, thickness measurement is crucial for quality control during TBC preparation.

[0004] Currently, conventional testing methods mainly employ destructive sampling and analysis, causing permanent damage to the material. Common methods for measuring the thickness of thermal barrier coatings include ultrasonic, infrared, and eddy current methods. Ultrasonic measurement offers the advantage of ease of operation, but its requirement for a coupling agent may lead to surface contamination or corrosion of the specimen. Infrared detection has a wide range of applications, but ambient temperature fluctuations significantly affect the signal-to-noise ratio and are limited by the power of existing heat sources. Eddy current testing is based on Faraday's law of electromagnetic induction. Applying an alternating sinusoidal excitation signal to an eddy current coil generates a magnetic field in its vicinity. Based on electromagnetic induction, a chain of physical effects is triggered: closed eddy currents are formed within the specimen, which excite a reverse secondary magnetic field. Electromagnetic coupling causes a characteristic change in the equivalent impedance parameter of the detection coil. Due to the rapid electromagnetic induction, eddy current non-destructive testing is fast. Eddy current testing is non-destructive, non-contact, highly efficient, convenient, and suitable for online testing, making it an ideal method for measuring the thickness of thermal barrier coatings.

[0005] As complex multilayer structures, thermal barrier coatings currently suffer from coupling issues in eddy current detection signals from different coatings, limiting the detection of thickness to a single coating within a limited range. Therefore, model inversion methods require multiple iterations, resulting in low efficiency, poor transferability, and unsuitability for online testing, leading to relatively low detection efficiency. Furthermore, traditional eigenvalue methods often suffer from signal interference when detecting thermal barrier coatings, making it difficult to simultaneously and accurately measure the thickness of two coatings, and exhibiting low accuracy in detecting the thickness of the adhesive layer. Summary of the Invention

[0006] The purpose of this invention is to provide a thermal barrier coating thickness measurement method based on the shape function method, which can overcome the problems of existing coating thickness measurement methods, such as difficulty in decoupling between the ceramic layer and the adhesive layer, complex algorithms, the ability to detect only a single layer thickness, and low accuracy in adhesive layer thickness detection. Furthermore, it has a significant effect on simultaneously detecting the thickness of the ceramic layer and the adhesive layer.

[0007] The specific technical solution adopted by this invention is as follows:

[0008] A method for measuring the thickness of thermal barrier coatings based on the shape function method includes the following steps:

[0009] First, the reactance change signal and phase signal of the calibration specimen are obtained using an eddy current coil;

[0010] Secondly, establish a coordinate grid of eigenvalues ​​for the ceramic layer thickness, adhesive layer thickness, eddy current reactance change signal, and phase signal of the calibration specimen;

[0011] Then, based on the four-point shape function, a mapping relationship is constructed between the eigenvalue coordinate system and the normalized coordinate system;

[0012] Finally, an eddy current coil was used to obtain the reactance change signal and phase signal of the test piece, and these signals were substituted into the above mapping relationship to calculate the thickness of the ceramic layer and the adhesive layer of the thermal barrier coating.

[0013] Furthermore, it includes the following steps:

[0014] Step 1: Prepare four calibration specimens, numbered 1, 2, 3, and 4, with ceramic layer thicknesses of TC1, TC2, TC3, and TC4, and adhesive layer thicknesses of BC1, BC2, BC3, and BC4, respectively; where BC1 = BC2, BC3 = BC4, TC1 = TC4, and TC2 = TC3.

[0015] Step 2: Place the eddy current coil in air and measure its impedance at frequency f: Z Air =R Air +X AirThen, the eddy current coils were placed above the four calibration test pieces respectively, and the impedances of the eddy current coils above the four calibration test pieces at frequency f were measured as follows: Z1=R1+X1, Z2=R2+X2, Z3=R3+X3, Z4=R4+X4;

[0016] Step 3: Differentiate the impedances of the three calibration specimens from Step 2 to obtain the resistance change of the eddy current coil at frequency f: ΔR1=|R1-R Air |,ΔR2=|R2-R Air |,ΔR3=|R3-R Air |,ΔR4=|R4-R Air Then, differential processing is performed on the reactance of the eddy current coil at frequency f to obtain the change in reactance of the eddy current coil at frequency f: ΔX1=|X1-X Air |,ΔX2=|X2-X Air |,ΔX3=|X3-X Air |,ΔX4=|X4-X Air Finally, by quotienting, the characteristic phase quantities of the eddy current coil at frequency f are obtained: P1=ΔX1 / ΔR1, P2=ΔX2 / ΔR2, P3=ΔX3 / ΔR3, P4=ΔX4 / ΔR4;

[0017] Step 4: Construct eigenvalue coordinates (ΔX) based on the changes in reactance of the eddy current coil and the characteristic phase measured at frequency f for the four calibration specimens. i ,P i ), where i = 1, 2, 3, 4; thus construct the ΔX-P eigenvalue coordinate system, and map the ΔX-P eigenvalue coordinate system to the normalized α-β coordinate system according to the two-dimensional first-order four-node shape function. The calibration nodes of the normalized α-β coordinate system are (0,0), (1,0), (1,1), (0,1).

[0018] Step 5: Place the eddy current coil above the test piece m, and use an impedance analyzer to measure the impedance of the eddy current coil at frequency f: Z m =R m +X m Similarly, the resistance change ΔR of the eddy current coil at frequency f is obtained based on steps two and three. m =|R m -R Air | Reactance change ΔX m =|X m -X Air Then, by quotienting, the characteristic phase of the eddy current coil under the condition f is obtained: P m =ΔX m / ΔR m The eigenvalue coordinates (ΔX) corresponding to the test piece m can be obtained. m ,Pm ); its coordinates in the α-β coordinate system are obtained through the mapping relationship in step four (α m ,β m );

[0019] Step 6: Using the linear interpolation formula, based on the aforementioned α... m ~ and β m Calculate the adhesive layer thickness BC of the test specimen m. m and ceramic layer thickness TC m The formula is as follows:

[0020]

[0021] Among them, BC m TC represents the adhesive layer thickness of the test piece m. m Let m be the thickness of the ceramic layer on the test piece.

[0022] Furthermore, the two-dimensional linear four-node shape function in the fourth step is defined as:

[0023]

[0024] Where α and β are the coordinate values ​​in the normalized coordinate system.

[0025] A thermal barrier coating thickness detection system, comprising:

[0026] Eddy current coils and impedance analyzers are used to measure the impedance signals of calibration specimens and test specimens.

[0027] The data processing module is used to perform differential processing, eigenvalue coordinate system construction, shape function mapping, and thickness calculation.

[0028] The calibration database stores the thickness data and fitting coefficients of the calibration specimens.

[0029] The technical effects achieved by this invention are as follows:

[0030] The present invention provides a thermal barrier coating thickness measurement method based on the shape function method. This method uses a four-point shape function to solve the problem of difficulty in decoupling the signals of the adhesive layer and the ceramic layer in the current thermal barrier coating thickness measurement. When detecting the thickness of the ceramic layer, the influence of temperature can be reduced and the detection accuracy can be improved. Compared with the traditional method that can only detect the thickness of a single coating and has low accuracy, the method proposed in this patent can simultaneously measure the thickness of the ceramic layer and the adhesive layer, effectively improving the accuracy and detection efficiency of thermal barrier coating thickness measurement. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the present invention;

[0032] Figure 2This is a diagram showing the construction of eigenvalue coordinates and eigenvalue coordinate systems under different ceramic layer thicknesses and adhesive layers in this invention.

[0033] Figure 3 It is the normalized coordinate system after mapping the eigenvalue coordinate system of this invention;

[0034] Figure 4 This is a flowchart of the calculation process for the shape function method of this invention;

[0035] Figure 5(a) shows the relationship between ΔX and the thickness of the adhesive layer in this invention;

[0036] Figure 5(b) shows the relationship between ΔX and ceramic layer thickness in this invention;

[0037] Figure 6(a) shows the relationship between P and the thickness of the adhesive layer in this invention;

[0038] Figure 6(b) shows the relationship between P and the thickness of the ceramic layer in this invention;

[0039] Figure 7 This invention relates to the ΔX-P grid error at different frequencies.

[0040] Figure 8 This is the ΔX-P eigenvalue grid of the present invention;

[0041] Figure 9 These are the α-β coordinates after the ΔX-P eigenvalue grid mapping of this invention. Detailed Implementation

[0042] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0043] Example 1:

[0044] like Figure 1 As shown, a method for measuring the thickness of a thermal barrier coating based on the shape function method includes the following steps:

[0045] Step 1: Prepare four calibration specimens, numbered 1, 2, 3, and 4, with ceramic layer thicknesses of TC1, TC2, TC3, and TC4, and adhesive layer thicknesses of BC1, BC2, BC3, and BC4, respectively; where BC1 = BC2, BC3 = BC4, TC1 = TC4, and TC2 = TC3.

[0046] Step 2: Place the eddy current coil in the air and use an impedance analyzer to measure the resistance R of the eddy current coil in the air at frequency f. Air and reactance X Air Impedance: Z Air =RAir +X Air Then, the eddy current coils were placed above the four calibration test pieces respectively, and the impedances of the eddy current coils above the four calibration test pieces at frequency f were measured as follows: Z1=R1+X1, Z2=R2+X2, Z3=R3+X3, Z4=R4+X4;

[0047] Here, in order to achieve the purpose of environmental compensation, this technical solution introduces baseline calibration (such as periodically measuring air impedance Z). Air This is to eliminate the effects of temperature drift.

[0048] Step 3: Differentiate the impedances of the four calibration specimens from Step 2 to obtain the resistance change of the eddy current coil at frequency f: ΔR1=|R1-R Air |,ΔR2=|R2-R Air |,ΔR3=|R3-R Air |,ΔR4=|R4-R Air Then, differential processing is performed on the reactance of the eddy current coil at frequency f to obtain the change in reactance of the eddy current coil at frequency f: ΔX1=|X1-X Air |,ΔX2=|X2-X Air |,ΔX3=|X3-X Air |,ΔX4=|X4-X Air Finally, by quotienting, the characteristic phase quantities of the eddy current coil at frequency f are obtained: P1=ΔX1 / ΔR1, P2=ΔX2 / ΔR2, P3=ΔX3 / ΔR3, P4=ΔX4 / ΔR4;

[0049] Here, this technical solution uses an additional sensor to monitor the distance between the eddy current coil and the test piece (calibration test piece or test piece) in real time, and corrects the measured values ​​of ΔX and P.

[0050] Step 4: From Figure 2 It can be seen that at a fixed frequency f, the reactance change ΔX and phase value P of the eddy current coil can be obtained. Based on the reactance change and characteristic phase of the eddy current coil detected by four calibration specimens at frequency f, the characteristic value coordinates (ΔX) can be constructed. i ,P i ), where i = 1, 2, 3, 4. Thus, a ΔX-P eigenvalue coordinate system is constructed. This ΔX-P eigenvalue coordinate system can be transformed into an α-β coordinate system through shape function transformation. The calibration nodes of the mapped α-β coordinate system are (0,0), (1,0), (1,1), (0,1). Based on the characteristics of a two-dimensional linear four-node shape function and the mapped calibration nodes, the shape function N can be obtained. i (i = 1, 2, 3, 4) are as follows:

[0051]

[0052] Step 5: Place the eddy current coil above the test piece m, and use an impedance analyzer to measure the impedance of the eddy current coil at frequency f: Z m =R m +X m Similarly, the resistance change ΔR of the eddy current coil at frequency f is obtained based on steps two and three. m =|R m -R Air | Reactance change ΔX m =|X m -X Air Then, by quotienting, the characteristic phase of the eddy current coil under the condition f is obtained: P m =ΔX m / ΔR m The eigenvalue coordinates (ΔX) corresponding to the test piece m can be obtained. m ,P m Similarly, at a fixed frequency f, such as Figure 3 As shown, the coordinates of the eigenvalues ​​corresponding to the test piece can all be mapped to the α-β coordinate system based on the shape function of equation (1) in step 4. The coordinate mapping function is as follows:

[0053]

[0054] Where i = 1, 2, 3, 4; ΔX i To calibrate the change in reactance of the test specimen; P i To calibrate the phase of the specimen; ΔX m P represents the change in reactance of the test piece m; m Let α be the phase of the characteristic quantity of the test piece m; m Let β be the abscissa of the eigenvalue coordinates of the test piece m mapped to the α-β coordinate system; m The ordinate is the eigenvalue coordinate of the test piece m mapped to the α-β coordinate system.

[0055] Step 6: Based on step 5, the eigenvalue coordinates (ΔX) corresponding to the test piece m are obtained. m ,P m The coordinates are mapped to the coordinates in the α-β coordinate system (α...). m ,β m The thicknesses of the adhesive layer and ceramic layer of the test specimen can be calculated simultaneously by using the analogy of the side lengths and the linear relationship of the finite element shape function, as shown in the following formula:

[0056]

[0057] Among them, BC m TC represents the adhesive layer thickness of the test piece m. mLet m be the thickness of the ceramic layer on the test piece.

[0058] Here, the preferred value of frequency f is 7.0MHz, ranging from 5 to 10MHz. Figure 7 As shown, under the ΔX-P grid, the average relative error of the ceramic layer thickness fluctuates relatively little, ranging from 3.0% to 3.4%. Similarly, the average relative error decreases with increasing frequency. The average relative error of the adhesive layer thickness ranges from 1.81% to 13.01%, also showing a pattern of first decreasing and then increasing. Therefore, considering the detection accuracy of BC thickness, a frequency of 7.0MHz is selected.

[0059] To suppress noise, this technical solution employs digital filtering, specifically moving average filtering. A fixed-length window is defined, which slides across the signal over time. At each time point, the filter calculates the arithmetic mean of all sample values ​​within the window and uses this average as the output. The output values ​​form the filtered sequence to improve the signal-to-noise ratio.

[0060] Example 2:

[0061] This embodiment discloses a thermal barrier coating thickness detection system based on the shape function method of embodiment one, which is used to measure the thickness of thermal barrier coatings in embodiment one. The system includes:

[0062] Eddy current coils and impedance analyzers are used to measure the impedance signals of calibration specimens and test specimens.

[0063] The data processing module is used to perform differential processing, eigenvalue coordinate system construction, shape function mapping, and thickness calculation.

[0064] The calibration database stores the thickness data and fitting coefficients of the calibration specimens.

[0065] Example 3:

[0066] To more clearly illustrate the technical effectiveness of the thermal barrier coating thickness measurement method based on the shape function method, this embodiment compares the detection accuracy of the piecewise linear method and the shape function method based on Comsol simulation. The excitation frequencies are set to 0.8MHz, 1.0MHz, 1.2MHz, and 1.4MHz, the ceramic layer thickness is 200μm to 500μm in 30μm increments, and the adhesive layer thickness is 50μm to 200μm in 15μm increments.

[0067] As shown in Table 1, compared with the dual-frequency piecewise linear method, the shape function method requires an additional calibration component, but it improves the detection accuracy for both ceramic layer thickness and adhesive layer thickness. Due to the nonlinear distribution between the adhesive layer and the eigenvalues, the dual-frequency piecewise linear method has a larger error in detecting the adhesive layer thickness, while the shape function method is suitable for nonlinear decoupling problems, thus achieving higher accuracy in detecting the adhesive layer thickness.

[0068] Table 1 Comparison of detection methods using the broken line method and the shape function method

[0069]

[0070] The following conclusions can be drawn from the above:

[0071] Conclusion 1: The shape function method is more suitable for nonlinear decoupling problems;

[0072] like Figure 8 As shown, the shape function has the characteristic of mapping nonlinear relationships, thereby achieving decoupling. The grid distribution based on the combination of reactance change ΔX and phase P eigenvalues ​​is as follows... Figure 8 As shown, the curves of the feature value grid exhibit a non-linear distribution, and using linear fitting for feature distributions with poor linearity will lead to low detection accuracy.

[0073] like Figure 8 As shown, the coordinates of the calibration nodes are (0,0), (1,0), (1,1) and (0,1), and the shape function is Equation (1).

[0074] like Figures 8-9 As shown in equation (2), the relationship between the feature index coordinates and the mapped coordinates can be established through equation (2) above, so as to realize the coordinate mapping of the feature value grid of ΔX-P.

[0075] In summary, the shape function method can achieve nonlinear feature fitting, that is, decouple the nonlinear relationship to realize thickness measurement, resulting in higher detection accuracy. As shown in Table 1, based on Comsol simulation, the shape function method exhibits higher detection accuracy in ceramic layer thickness and adhesive layer thickness, especially adhesive layer thickness.

[0076] Conclusion 2: The shape function method can reduce the influence of temperature when detecting the thickness of ceramic layers;

[0077] Depend on Figure 1 The transformer model and the expressions for the changes in resistance and reactance are given in equation (4):

[0078]

[0079] In the formula, ω is the angular frequency of the excitation signal, ΔR and ΔX are the changes in resistance and reactance of the eddy current coil, respectively, ω=2πf represents the angular frequency of the sine wave, f represents the excitation frequency of the eddy current coil, and M represents the mutual inductance between the detection coil and the equivalent eddy current. The mutual inductance M contains the lift-off information.

[0080] The equivalent resistance and equivalent inductance can be expressed by the equivalent integral model, as shown in equation (5):

[0081]

[0082] In the formula R x L represents the equivalent coil resistance. x The equivalent coil inductance is represented by σ, the thickness of the equivalent coil is represented by h, the conductivity of the specimen is represented by σ, and the permeability of free space is represented by μ0, with a value of 4π × 10⁻⁶. -7 H / m. A(r1,r2) is an extremely complex function, the specific content of which has been given. The value of this function depends only on the geometric parameters r1 and r2.

[0083] Therefore, the expressions for the change in resistance, the change in reactance, and the phase are as shown in equation (6):

[0084]

[0085] As can be seen from equation (6), it is theoretically possible to solve the ceramic layer thickness and the adhesive layer thickness by using a single eigenvalue. However, the specific mathematical expressions of the ceramic layer, the adhesive layer and the characteristic signal are unclear and very complex, and there is mutual coupling.

[0086] As shown in Figures 5 and 6 and Equation (6), Figures 5 and 6 are simulation results. In Equation (6), the resistance change ΔR is affected by thickness, conductivity and lift-off. The reactance change ΔX is mainly related to the mutual inductance M, that is, it is mainly affected by lift-off. The impedance change is shown in Equation (8), which shows that it is mainly affected by thickness, conductivity and lift-off.

[0087] As shown in Figure 5(a), when the ceramic layer thickness is fixed, the sensitivity of characterizing the binder layer thickness using the reactance change ΔX is low, approximately 0.003 Ω / μm, and different ceramic layer thicknesses have a significant impact on the reactance change ΔX. As shown in Figure 5(b), when the binder layer thickness is fixed, the sensitivity of characterizing the ceramic layer thickness using the reactance change ΔX is high, approximately 0.027 Ω / μm, and different binder layer thicknesses have a smaller impact on the reactance change ΔX. Therefore, ΔX is suitable for characterizing the ceramic layer thickness, but it is only partially immune to the influence of the binder layer thickness.

[0088] The phase P in equation (6) is less affected by the mutual inductance M. As shown in Figure 6(a), when the ceramic layer thickness is fixed, the sensitivity of phase P in characterizing the adhesive layer thickness is high, approximately 0.016 Ω / μm, and different ceramic layer thicknesses have little effect on phase P. As shown in Figure 6(b), when the adhesive layer thickness is fixed, the sensitivity of phase P in characterizing the ceramic layer thickness is low, approximately 0.002 Ω / μm, and different adhesive layer thicknesses have a significant effect on phase P. Therefore, phase ΔP is suitable for characterizing the adhesive layer thickness, but it is only immune to the influence of ceramic layer thickness to a certain extent.

[0089]

[0090] Generally speaking, although the relationship between conductivity and temperature is complex, it can be expressed as follows within a very small range:

[0091]

[0092] Where σ represents the conductivity at temperature T, σ0 represents the conductivity at temperature T0, c represents the temperature resistance coefficient, and c represents the rate at which the resistance changes with temperature.

[0093] Since the mutual inductance M is mainly related to the lift-off, i.e. the thickness of the ceramic layer, the conductivity has little effect on the mutual inductance M. Therefore, ΔX can be immune to the influence of temperature to a certain extent.

[0094] Therefore, the shape function method can be immune to the influence of temperature to a certain extent compared with the dual-frequency piecewise linear method in detecting the thickness of ceramic layers.

[0095] In summary, the specific mathematical expressions for the ceramic layer, adhesive layer, and characteristic signals are unclear and highly complex, exhibiting mutual coupling. This is mainly manifested in the following ways: using a single characteristic value to characterize the coating thickness results in a very complex and nonlinear expression, leading to significant detection errors; when detecting the thickness of the thermal barrier coating, both TC and BC thicknesses affect the eddy current signal, indicating mutual coupling between them. Therefore, selecting a suitable characteristic value for thickness calculation results in mutual influence, making it difficult to separately calculate the thickness of the ceramic layer and the adhesive layer using a single characteristic value.

[0096] Therefore, the shape function method has the following advantages for measuring the thickness of thermal barrier coatings:

[0097] (1) The thickness of the thermal barrier coating ceramic layer and the thickness of the adhesive layer can be decoupled from the eddy current signal by the shape function method;

[0098] (2) Due to the nonlinear characteristics of the shape function method, it is possible to fit the distribution of nonlinear eigenvalues;

[0099] (3) By introducing the shape function method, the thickness of the ceramic layer and the thickness of the adhesive layer can be detected simultaneously.

[0100] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A method for measuring the thickness of thermal barrier coatings based on the shape function method, characterized in that: Includes the following steps: Step 1: Prepare four calibration specimens, numbered 1, 2, 3, and 4, with ceramic layer thicknesses of TC1, TC2, TC3, and TC4, and adhesive layer thicknesses of BC1, BC2, BC3, and BC4, respectively; where BC1 = BC2, BC3 = BC4, TC1 = TC4, and TC2 = TC3. Step 2: Place the eddy current coil in the air and measure the resistance R of the eddy current coil at frequency f. Air and reactance X Air , where through Z Air =R Air +X Air Obtaining impedance Z Air Then, the eddy current coils were placed above the four calibration test pieces respectively, and the impedances of the eddy current coils above the four calibration test pieces at frequency f were measured as follows: Z1=R1+X1, Z2=R2+X2, Z3=R3+X3, Z4=R4+X4; Step 3: Differentiate the impedances of the four calibration specimens from Step 2 to obtain the resistance change of the eddy current coil at frequency f: ΔR1=|R1-R Air |,ΔR2=|R2-R Air |,ΔR3=|R3-R Air |,ΔR4=|R4-R Air Then, differential processing is performed on the reactance of the eddy current coil at frequency f to obtain the change in reactance of the eddy current coil at frequency f: ΔX1=|X1-X Air |,ΔX2=|X2-X Air |,ΔX3=|X3-X Air |,ΔX4=|X4-X Air Finally, by quotienting, the characteristic phase quantities of the eddy current coil at frequency f are obtained: P1 = ΔX1 / ΔR1, P2 = ΔX2 / ΔR2, P3 = ΔX3 / ΔR3, P4 = ΔX4 / ΔR4; Step 4: Based on the reactance change ΔX of the eddy current coils detected at frequency f for the four calibration specimens. i and the characteristic phase P i Construct eigenvalue coordinates (ΔX) i ,P i ), where i = 1, 2, 3, 4, thus constructing the ΔX-P eigenvalue coordinate system. The ΔX-P eigenvalue coordinate system is then mapped to the normalized α-β coordinate system using a two-dimensional linear four-node shape function. The calibration nodes of the normalized α-β coordinate system are (0,0), (1,0), (1,1), (0,1); where the two-dimensional linear four-node shape function is defined as: ； in, α , β These are coordinate values ​​in a normalized coordinate system. Step 5: Place the eddy current coil above the test piece m, and use an impedance analyzer to measure the impedance of the eddy current coil at frequency f: Z m =R m +X m Similarly, the resistance change ΔR of the eddy current coil at frequency f is obtained based on steps two and three. m =|R m -R Air | Reactance change ΔX m =|X m -X Air Then, by quotienting, the characteristic phase of the eddy current coil under condition f is obtained: P m =ΔX m / ΔR m The eigenvalue coordinates (ΔX) corresponding to the test piece m can be obtained. m ,P m ); Based on the shape function of formula (1) in step four, establish a coordinate mapping function to map the test piece m Corresponding eigenvalue coordinates (Δ) X m , P m Mapping it to the α-β coordinate system yields its coordinates in the α-β coordinate system (α...). m ,β m The coordinate mapping function is as follows: ； Where ΔX i To calibrate the change in reactance of the test specimen; P i To calibrate the phase of the specimen; ΔX m P represents the change in reactance of the test piece m; m Let α be the phase of the characteristic quantity of the test piece m; m Let β be the abscissa of the eigenvalue coordinates of the test piece m mapped to the α-β coordinate system; m The ordinate is the eigenvalue coordinate of the test piece m mapped to the α-β coordinate system. Step 6: Using the linear interpolation formula, based on α m and β m Calculate the adhesive layer thickness BC of the test specimen m. m and ceramic layer thickness TC m The formula is as follows: ； in, BC m For the test piece m The thickness of the adhesive layer, TC m For the test piece m The thickness of the ceramic layer.

2. The method for measuring the thickness of a thermal barrier coating based on the shape function method according to claim 1, characterized in that: The frequency f is 7.0MHz.

3. A thermal barrier coating thickness detection system, employing the thermal barrier coating thickness measurement method according to any one of claims 1-2, characterized in that: include: Eddy current coils and impedance analyzers are used to measure the impedance signals of calibration specimens and test specimens. The data processing module is used to perform differential processing, eigenvalue coordinate system construction, shape function mapping, and thickness calculation. The calibration database stores the thickness data and fitting coefficients of the calibration specimens.

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