Thermal barrier coating thickness measuring method based on shape function method

Abstract

The invention belongs to the technical field of conventional eddy current detection, and particularly relates to a thermal barrier coating thickness measuring method based on a shape function method.The method comprises the steps that firstly, an eddy current coil is used for obtaining a reactance variation signal and a phase signal of a calibration test piece; secondly, establishing a characteristic value coordinate grid of the ceramic layer thickness, the bonding layer thickness, the eddy current reactance variable quantity signal and the phase signal of the calibration test piece; then constructing a mapping relation between a characteristic value coordinate system and a normalized coordinate system based on a four-point shape function; and finally, applying an eddy current coil to a to-be-tested piece to obtain a reactance variation signal and a phase signal, substituting the reactance variation signal and the phase signal into the mapping relation, and calculating the thickness of the ceramic layer and the thickness of the bonding layer of the thermal barrier coating. According to the method, the problem that signals of the bonding layer and the ceramic layer are difficult to decouple in current thermal barrier coating thickness measurement is solved by applying a four-point shape function method, the thickness of the ceramic layer and the thickness of the bonding layer can be measured at the same time, and the thickness measurement precision and the detection efficiency of the thermal barrier coating are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of conventional eddy current detection, and in particular relates to a thermal barrier coating thickness measurement method based on a shape function method. Background Art

[0002] With the advancement of aviation technology, various functional coatings are widely used in aviation hot-end components. Because the operating temperature of aircraft engine turbine blades exceeds their melting point, thermal barrier coatings (TBCs) are crucial for improving their high-temperature resistance. TBCs consist of a ceramic layer and a bond coat. Due to limitations in their preparation technology, TBCs can degrade thermal insulation, impacting the service life of aircraft blades. Therefore, accurate thickness measurement of TBCs is crucial for quality control and evaluation.

[0003] Thermal barrier coatings (TBCs) are multi-layer coating systems with a top ceramic layer. This layer is resistant to oxidation and corrosion, and has extremely low thermal conductivity, significantly reducing the temperature of the substrate. A bonding layer is located in the middle, ensuring a good bond between the coating and the substrate. The bottom layer is a nickel-based high-temperature alloy substrate that requires protection. Atmospheric plasma spraying is often used in the preparation of TBCs. This involves using a plasma flame to heat the sprayed material to a molten or highly plastic state. Guided by a high-speed plasma flame, the sprayed material impacts the workpiece surface at high speed. This process can cause voids in the ceramic and bonding layers, resulting in uneven porosity and irregular distribution of the coating due to particle interlacing, coating impurities, and particle fluctuations. Currently, the preparation process for TBCs still has certain limitations, making thickness testing crucial for quality control during TBC preparation.

[0004] Currently, conventional testing methods primarily rely on destructive sampling and analysis, which can cause permanent damage to the material. Common methods for testing thermal barrier coating thickness include ultrasound, infrared, and eddy current. Ultrasonic measurement offers the advantage of ease of operation, but its requirement for a coupling agent can lead to contamination or corrosion of the specimen surface. Infrared testing has a wider range of applications, but ambient temperature fluctuations can significantly affect the detection signal-to-noise ratio and are limited by the power of the available heat source. 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. This electromagnetic induction triggers a chain reaction: a closed eddy current forms within the specimen, which in turn stimulates an opposing secondary magnetic field. Electromagnetic coupling causes characteristic changes in the equivalent impedance parameters of the detection coil. Due to the rapid nature of electromagnetic induction, eddy current nondestructive testing is fast. Eddy current testing is nondestructive, noncontact, efficient, convenient, and suitable for online testing, making it an ideal method for measuring thermal barrier coating thickness.

[0005] Thermal barrier coatings are complex multilayer structures, and current eddy current testing methods for different coatings suffer from coupling issues, limiting the ability to measure the thickness of only a single coating within a certain range. Consequently, model inversion methods require multiple iterations, resulting in low efficiency and poor transferability, making them unsuitable for online testing and resulting in relatively low detection efficiency. Furthermore, when testing thermal barrier coatings, traditional eigenvalue methods often experience signal interference, making it difficult to accurately measure the thickness of two coatings simultaneously, and also resulting in low accuracy for bondline thickness detection. Summary of the Invention

[0006] The purpose of the present invention is to provide a thermal barrier coating thickness measurement method based on the shape function method, which can overcome the problems of difficult decoupling between the ceramic layer and the bonding layer in existing coating thickness measurement, complex algorithm, only single layer thickness can be detected, and low bonding layer thickness detection accuracy, and has a significant effect on simultaneously detecting the thickness of the ceramic layer and the bonding layer.

[0007] The technical solutions adopted by the present invention are as follows:

[0008] A method for measuring the thickness of a thermal barrier coating based on a shape function method comprises the following steps:

[0009] Firstly, the eddy current coil is used to obtain the reactance variation signal and phase signal of the calibration specimen;

[0010] Secondly, the characteristic value coordinate grid of the ceramic layer thickness, bonding layer thickness and eddy current reactance variation signal and phase signal of the calibration specimen is established;

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

[0012] Finally, an eddy current coil is applied to the test piece to obtain its reactance variation signal and phase signal, and the signals are substituted into the above mapping relationship to calculate the thickness of the ceramic layer and the bonding layer of the thermal barrier coating.

[0013] Further, the following steps are included:

[0014] Step 1: Prepare four calibration specimens, numbered 1, 2, 3, and 4, with ceramic layer thicknesses of TC1, TC2, TC3, and TC4, and bonding 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 the air and detect the impedance of the eddy current coil at frequency f: Z Air =R Air +X Air, and then place the eddy current coils on the four calibration specimens respectively. The impedances of the eddy current coils on the four calibration specimens at frequency f are measured as follows: Z1 = R1 + X1, Z2 = R2 + X2, Z3 = R3 + X3, Z4 = R4 + X4;

[0016] Step 3: Perform differential processing on the impedance of the three calibration specimens in step 2, and first 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 perform differential processing on the eddy current coil reactance at frequency f to obtain the change in eddy current coil reactance at frequency f: ΔX1=|X1-X Air |, ΔX2=|X2-X Air |, ΔX3=|X3-X Air |, ΔX4=|X4-X Air |, and finally take the quotient to obtain the characteristic phase of the eddy current coil at frequency f: P1 = ΔX1 / ΔR1, P2 = ΔX2 / ΔR2, P3 = ΔX3 / ΔR3, P4 = ΔX4 / ΔR4;

[0017] Step 4: Construct the characteristic value coordinates (ΔX i ,P i ), where i = 1, 2, 3, 4; thereby constructing the ΔX-P eigenvalue coordinate system, and mapping the ΔX-P eigenvalue coordinate system to the normalized α-β coordinate system according to the 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);

[0018] Step 5: Place the eddy current coil on the test piece m and use the impedance analyzer to detect the impedance of the eddy current coil at frequency f: Z m =R m +X m , similarly, according to the second and third steps, obtain the resistance change ΔR of the eddy current coil at frequency f m =|R m -R Air |, reactance change ΔX m =|X m -X Air |, and then do the quotient to get the characteristic phase of the eddy current coil under f: P m =ΔX m / ΔR m , we can get the eigenvalue coordinates (ΔX m ,Pm ); through the mapping relationship in the fourth step, its coordinates in the α-β coordinate system (α m , β m );

[0019] Step 6: Using the linear interpolation formula, according to the α m ~ and β m Calculate the bonding layer thickness BC of the test piece m m and the ceramic layer thickness TC m , the formula is as follows:

[0020]

[0021] Among them, BC m is the bonding layer thickness of the test piece m, TC m is the thickness of the ceramic layer of the test piece m.

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

[0023]

[0024] Among them, α and β are the coordinate values of the normalized coordinate system.

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

[0026] Eddy current coil and impedance analyzer, used to measure the impedance signals of calibration specimens and test pieces;

[0027] Data processing module, 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 the present invention are:

[0030] The present invention discloses a thermal barrier coating thickness measurement method based on the shape function method. The four-point shape function method is used to solve the problem that the bonding layer and the ceramic layer signals are difficult to decouple 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 bonding layer, effectively improving the accuracy and detection efficiency of the thermal barrier coating thickness measurement. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0032] Figure 2It is a diagram of the construction of eigenvalue coordinates and eigenvalue coordinate systems under different ceramic layer thicknesses and bonding layers in the present invention;

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

[0034] Figure 4 It is a calculation flow chart of the shape function method of the present invention;

[0035] FIG5( a ) shows the relationship between ΔX and the thickness of the bonding layer of the present invention;

[0036] FIG5( b ) shows the relationship between ΔX and the thickness of the ceramic layer of the present invention;

[0037] FIG6( a ) shows the relationship between P and the thickness of the bonding layer of the present invention;

[0038] FIG6( b ) shows the relationship between P and the thickness of the ceramic layer of the present invention;

[0039] Figure 7 is the ΔX-P grid error at different frequencies of the present invention;

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

[0041] Figure 9 It is the coordinate of the α-β coordinate system after the ΔX-P eigenvalue grid mapping of the present invention. DETAILED DESCRIPTION

[0042] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is described in detail below with reference to the following examples. It should be understood that the following text is only used to describe one or more specific embodiments of the present invention and does not strictly limit the scope of protection of the present invention.

[0043] Example 1:

[0044] like Figure 1 As shown, a thermal barrier coating thickness measurement method 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 bonding 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 detect 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 , and then place the eddy current coils on the four calibration specimens respectively. The impedances of the eddy current coils on the four calibration specimens at frequency f are 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 regularly measuring the air impedance Z Air ) to eliminate the influence of temperature drift.

[0048] Step 3: Perform differential processing on the impedance of the four calibration specimens in step 2, and first 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 perform differential processing on the eddy current coil reactance at frequency f to obtain the change in eddy current coil reactance at frequency f: ΔX1=|X1-X Air |, ΔX2=|X2-X Air |, ΔX3=|X3-X Air |, ΔX4=|X4-X Air |, and finally take the quotient to obtain the characteristic phase of the eddy current coil at frequency f: P1 = ΔX1 / ΔR1, P2 = ΔX2 / ΔR2, P3 = ΔX3 / ΔR3, P4 = ΔX4 / ΔR4;

[0049] Here, the 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: 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. The characteristic value coordinates (ΔX i ,P i ), where i = 1, 2, 3, 4. The ΔX-P eigenvalue coordinate system is thus constructed, and the ΔX-P eigenvalue coordinate system can be transformed into the α-β coordinate system through shape function transformation. The calibration nodes of the α-β coordinate system after mapping are (0,0), (1,0), (1,1), (0,1). According to the characteristics of the two-dimensional 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 on the test piece m and use the impedance analyzer to detect the impedance of the eddy current coil at frequency f: Z m =R m +X m , similarly, according to the second and third steps, obtain the resistance change ΔR of the eddy current coil at frequency f m =|R m -R Air |, reactance change ΔX m =|X m -X Air |, and then do the quotient to get the characteristic phase of the eddy current coil under f: P m =ΔX m / ΔR m , we can get the eigenvalue coordinates (ΔX m ,P m ). Similarly, at a fixed frequency f, as Figure 3 As shown, the eigenvalue coordinates corresponding to the test piece can be mapped to the α-β coordinate system by establishing a coordinate mapping relationship based on the shape function of formula (1) in the fourth step. The coordinate mapping function is as follows:

[0053]

[0054] where i = 1, 2, 3, 4; ΔX i is the reactance change of the calibration specimen; P i is the phase of the calibration specimen; ΔX m P is the reactance change of the test piece m; m is the characteristic phase of the test piece m; α m is the horizontal coordinate after the eigenvalue coordinates of the test piece m are mapped to the α-β coordinate system; β m is the ordinate after the eigenvalue coordinates of the test piece m are mapped to the α-β coordinate system;

[0055] Step 6: Through step 5, the corresponding characteristic value coordinates (ΔX m ,P m ) coordinates are mapped to the coordinates of the α-β coordinate system (α m ,β m ) are all inside or near a square with a side length of 1. By combining the side length analogy with the linear relationship of the finite element shape function, the thickness of the bonding layer and the thickness of the ceramic layer of the test piece can be calculated simultaneously, as shown in the following formula:

[0056]

[0057] Among them, BC m is the bonding layer thickness of the test piece m, TC mis the thickness of the ceramic layer of the test piece m.

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

[0059] To suppress noise, this technical solution uses digital filtering, a sliding mean filter, which sets a fixed-length window that slides across the signal over time. At each time point, the filter calculates the arithmetic mean of all sample values within the window and outputs this mean. The output values form a filtered sequence, improving the signal-to-noise ratio.

[0060] Example 2:

[0061] This embodiment, based on the first embodiment, discloses a thermal barrier coating thickness detection system using the thermal barrier coating thickness measurement method based on the shape function method in the first embodiment, including:

[0062] Eddy current coil and impedance analyzer, used to measure the impedance signals of calibration specimens and test pieces;

[0063] Data processing module, 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] In order to more clearly illustrate the technical effect of the thermal barrier coating thickness measurement method based on the shape function method, this embodiment is based on Comsol simulation to compare the detection accuracy of the broken line method and the shape function method, setting the excitation frequency to 0.8MHz, 1.0Mhz, 1.2MHz, and 1.4MHz, the ceramic layer thickness is also 200μm to 500μm, stepping 30μm, and the bonding layer thickness is 50μm to 200μm, stepping 15μm.

[0067] As shown in Table 1, the shape function method requires one more calibration piece than the dual-frequency broken line method, but the detection accuracy of the ceramic layer thickness and the bonding layer thickness are improved. Due to the nonlinear distribution between the bonding layer and the eigenvalue, the dual-frequency broken line method has a large error in the detection of the bonding layer thickness. The shape function method is suitable for the problem of nonlinear decoupling, so it has higher detection accuracy for the bonding layer thickness.

[0068] Table 1 Comparison of detection between broken line method and shape function method

[0069]

[0070] From the above content, we can draw the following conclusions:

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

[0072] like Figure 8 As shown in , the characteristic of shape function is that it can map nonlinear relationships, thereby achieving decoupling. The grid distribution based on the combination of reactance change ΔX and phase P eigenvalue is as follows Figure 8 As shown, the curve of the constructed eigenvalue grid presents a nonlinear distribution, and the use of straight line fitting for a feature distribution with poor linearity will result in low detection accuracy.

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

[0074] like Figure 8-Figure 9 As shown in formula (2), the relationship between the characteristic coordinates and the mapping coordinates can be established through formula (2) above, and the coordinate mapping of the eigenvalue grid of ΔX-P can be realized.

[0075] In summary, the shape function method can achieve nonlinear feature fitting, that is, decoupling nonlinear relationships, achieving thickness measurement with higher detection accuracy. As shown in Table 1, based on Comsol simulation, the shape function method demonstrates higher detection accuracy for both ceramic and bonding layer thicknesses, particularly bonding layer thickness.

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

[0077] Depend on Figure 1 The transformer model and the expressions of resistance change and reactance change can be obtained as shown in formula (4):

[0078]

[0079] Where 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 includes lift-off information.

[0080] The expressions of equivalent resistance and equivalent inductance can be obtained from the equivalent integral model, as shown in formula (5):

[0081]

[0082] Where R x Represents the equivalent coil resistance, L x represents the equivalent coil inductance, h represents the thickness of the equivalent coil, σ represents the conductivity of the specimen, and μ0 represents the vacuum permeability, which is 4π×10 -7 H / m. A(r1, r2) is an extremely complex function. The specific content of its expression has been given. The value of this function is only related to the geometric parameters r1 and r2.

[0083] Therefore, the expressions of resistance change, reactance change and phase are as follows:

[0084]

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

[0086] As shown in Figures 5-6 and formula (6), Figures 5 and 6 are simulation results. In formula (6), the resistance change ΔR is affected by thickness, conductivity and lift-off, and 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 formula (8), which shows that it is mainly affected by thickness, conductivity and lift-off.

[0087] As shown in Figure 5(a), when the thickness of the ceramic layer is fixed, the sensitivity of using the reactance change ΔX to characterize the thickness of the bonding layer is low, about 0.003Ω / μm, and different ceramic layer thicknesses have a significant impact on the reactance change ΔX. As shown in Figure 5(b), when the thickness of the bonding layer is fixed, the sensitivity of using the reactance change ΔX to characterize the thickness of the ceramic layer is high, about 0.027Ω / μm, and different bonding layer thicknesses have little impact on the reactance change ΔX. This shows that ΔX is suitable for characterizing the thickness of the ceramic layer, but it is only immune to the influence of the bonding layer thickness to a certain extent.

[0088] The phase P in Equation (6) is less affected by the mutual inductance M. As shown in Figure 6(a), when the thickness of the ceramic layer is fixed, the sensitivity of using phase P to characterize the thickness of the bonding layer is high, about 0.016Ω / μm, and different ceramic layer thicknesses have little effect on phase P. As shown in Figure 6(b), when the thickness of the bonding layer is fixed, the sensitivity of using phase P to characterize the thickness of the ceramic layer is low, about 0.002Ω / μm, and different bonding layer thicknesses have a greater impact on phase P. This shows that phase ΔP is suitable for characterizing the thickness of the bonding layer, but is only immune to the influence of the ceramic layer thickness to a certain extent.

[0089]

[0090] In general, the relationship between conductivity and temperature is complex, but within a small range, it can be expressed as:

[0091]

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

[0093] Since the mutual inductance M is mainly related to the lift-off, that is, 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 when detecting the thickness of ceramic layers compared with the dual-frequency broken line method.

[0095] In summary, the specific mathematical expressions of the ceramic layer, bonding layer, and characteristic signal are unclear and very complex, and there is mutual coupling. The main manifestations are: using a single eigenvalue to represent the coating thickness, the expression is very complex and nonlinear, and the detection error is large; when detecting the thickness of the thermal barrier coating, both the TC and BC thicknesses have an impact on the eddy current signal, that is, there is mutual coupling between them. Therefore, there is mutual influence when selecting a suitable eigenvalue to solve the thickness. Therefore, it is difficult to use a single eigenvalue to solve the ceramic layer thickness and the bonding layer thickness separately.

[0096] Therefore, for thermal barrier coating thickness detection, the shape function method has the following advantages:

[0097] (1) The shape function method can be used to decouple the eddy current signal from the thickness of the thermal barrier coating ceramic layer and the thickness of the bonding layer;

[0098] (2) Due to the nonlinear characteristics of the shape function method, the fitting of nonlinear eigenvalue distribution can be achieved;

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

[0100] The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.

Claims

1. A thermal barrier coating thickness measurement method based on a shape function method, characterized by: The following steps are involved: Firstly, the eddy current coil is used to obtain the reactance variation signal and phase signal of the calibration specimen; Secondly, the characteristic value coordinate grid of the ceramic layer thickness, bonding layer thickness and eddy current reactance variation signal and phase signal of the calibration specimen is established; Then, the mapping relationship between the eigenvalue coordinate system and the normalized coordinate system is constructed based on the four-point shape function; Finally, an eddy current coil is applied to the test piece to obtain its reactance variation signal and phase signal, and the signals are substituted into the above mapping relationship to calculate the thickness of the ceramic layer and the bonding layer of the thermal barrier coating.

2. The method for measuring thickness of thermal barrier coatings based on shape function method according to claim 1, characterized in that: The following steps are involved: Step 1: Prepare four calibration specimens, numbered 1, 2, 3, and 4, with ceramic layer thicknesses of TC1, TC2, TC3, and TC4, and bonding 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 probe in the air and detect the impedance of the eddy current coil at frequency f: Z Air =R Air +X Air , and then place the eddy current coils on the four calibration specimens respectively. The impedances of the eddy current coils on the four calibration specimens at frequency f are measured as follows: Z1 = R1 + X1, Z2 = R2 + X2, Z3 = R3 + X3, Z4 = R4 + X4; Step 3: Perform differential processing on the impedance of the three calibration specimens in step 2, and first 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 perform differential processing on the eddy current coil reactance at frequency f to obtain the change in eddy current coil reactance at frequency f: ΔX1=|X1-X Air |, ΔX2=|X2-X Air |, ΔX3=|X3-X Air |, ΔX4=|X4-X Air |, and finally take the quotient to obtain the characteristic phase of the eddy current coil at frequency f: P1 = ΔX1 / ΔR1, P2 = ΔX2 / ΔR2, P3 = ΔX3 / ΔR3, P4 = ΔX4 / ΔR4; Step 4: Construct the characteristic value coordinates (ΔX i ,P i ), where i = 1, 2, 3, 4; Thus, the ΔX-P eigenvalue coordinate system is constructed, and the ΔX-P eigenvalue coordinate system is mapped to the normalized α-β coordinate system according to the 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); Step 5: Place the eddy current coil on the test piece m and use the impedance analyzer to detect the impedance of the eddy current coil at frequency f: Z m =R m +X m , similarly, according to the second and third steps, obtain the resistance change ΔR of the eddy current coil at frequency f m =|R m -R Air |, reactance change ΔX m =|X m -X Air |, and then do the quotient to get the characteristic phase of the eddy current coil under f: P m =ΔX m / ΔR m , we can get the eigenvalue coordinates (ΔX m ,P m ); through the mapping relationship in the fourth step, its coordinates in the α-β coordinate system (α m , β m ); Step 6: Using the linear interpolation formula, according to the α m ~ and β m Calculate the bonding layer thickness BC of the test piece m m and the ceramic layer thickness TC m , the formula is as follows: Among them, BC m is the bonding layer thickness of the test piece m, TC m is the thickness of the ceramic layer of the test piece m.

3. The thermal barrier coating thickness measurement method based on the shape function method according to claim 2, characterized in that: The two-dimensional linear four-node shape function in the fourth step is defined as: Among them, α and β are the coordinate values of the normalized coordinate system.

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

5. The method for measuring thickness of thermal barrier coatings based on shape function method according to claim 2, characterized in that: In the fifth step, the eigenvalue coordinate points in the ΔX-P eigenvalue coordinate system are mapped to the α-β coordinate system using formula (2): where i = 1, 2, 3, 4; ΔX i is the reactance change of the calibration specimen; P i is the phase of the calibration specimen; ΔX m P is the reactance change of the test piece m; m is the characteristic phase of the test piece m; α m is the horizontal coordinate after the eigenvalue coordinates of the test piece m are mapped to the α-β coordinate system; β m is the ordinate after the eigenvalue coordinates of the test piece m are mapped to the α-β coordinate system.

6. A thermal barrier coating thickness detection system, using the thermal barrier coating thickness measurement method according to any one of claims 1 to 5, characterized in that: include: Eddy current coil and impedance analyzer, used to measure the impedance signals of calibration specimens and test pieces; Data processing module, 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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