CN114111604A - Terahertz thickness measurement method for thermal barrier coating ceramic layer without reference sample - Google Patents

Terahertz thickness measurement method for thermal barrier coating ceramic layer without reference sample Download PDF

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CN114111604A
CN114111604A CN202111673397.7A CN202111673397A CN114111604A CN 114111604 A CN114111604 A CN 114111604A CN 202111673397 A CN202111673397 A CN 202111673397A CN 114111604 A CN114111604 A CN 114111604A
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ceramic layer
terahertz
refractive index
thermal barrier
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CN114111604B (en
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赵纪元
何普
姚振文
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Xian Jiaotong University
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    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
    • G01B11/0616—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
    • G01B11/0625—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating with measurement of absorption or reflection
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Abstract

The invention discloses a terahertz thickness measurement method of a thermal barrier coating ceramic layer without a reference sample, wherein terahertz waves emitted by a terahertz time-domain spectroscopy system vertically enter a thermal barrier coating, and the vertically incident terahertz waves are reflected for multiple times in the ceramic layer to obtain the amplitude of the previous three echo signals; obtaining the amplitude intensity according to the average amplitude of the first three echo signals, and calculating the refractive index of the ceramic layer according to the amplitude intensity; the thickness of the ceramic layer is calculated from the refractive index of the ceramic layer. The method provided by the invention uses the terahertz time-domain signal, and can realize non-contact, efficient and nondestructive detection of the thickness of the thermal barrier coating ceramic layer on the premise of not needing a reference sample.

Description

Terahertz thickness measurement method for thermal barrier coating ceramic layer without reference sample
Technical Field
The invention belongs to the field of nondestructive testing, and particularly relates to a terahertz thickness measuring method for a thermal barrier coating ceramic layer without a reference sample.
Background
With the increasing thermal efficiency and thrust-weight ratio of aircraft engines and gas turbines, the temperature of the combustion chamber is increasing, and turbine blades and other hot-end components are subjected to severe high temperature tests. In order to improve the heat resistance of hot end components, thermal barrier coating technology is widely applied to aeroengines and gas turbines to achieve the purposes of reducing the temperature of a substrate of a high-temperature component and improving the corrosion resistance and the abrasion resistance of the substrate. The thermal barrier coating is a typical multilayer structure and comprises a ceramic layer, a bonding layer and a superalloy substrate, wherein the ceramic layer is directly contacted with high-temperature fuel gas and has the main functions of playing a thermal barrier role and delaying the oxidation of a bottom layer material. The thickness of the ceramic layer directly influences the performance and quality of the thermal barrier coating, the ceramic layer cannot achieve the expected heat insulation effect due to being too thin, and the ceramic layer is easy to have increased internal stress due to being too thick so as to fall off. And the thickness of the thermal barrier coating can be continuously reduced under the action of the thermal cycle load of the working condition. Therefore, the thickness of the ceramic layer is a key factor influencing the service life and the working condition of the thermal barrier coating, and the accurate measurement of the thickness of the ceramic layer has important significance on the quality and service life management of the thermal barrier coating.
The terahertz nondestructive testing technology is a novel electromagnetic nondestructive testing technology, and the performance and the defects of the material are detected and evaluated by utilizing terahertz waves with the frequency between microwave and infrared. The terahertz technology has the advantages of convenience in optical constant extraction, non-ionization, non-destructive property, high detection precision and the like, can realize accurate measurement of the thickness of the thermal barrier coating ceramic layer, and has a wide application prospect. The method mainly solves the problem that the refractive index of a material in a terahertz wave band is accurately obtained by utilizing the terahertz technology to measure the thickness of a thermal barrier coating, and has two main methods. Firstly, preparing a standard test block with known thickness and the same material, calculating the refractive index of the material through experiments, and carrying out thickness measurement under the condition of the known refractive index; secondly, the refractive index of the material is obtained through the terahertz wave signal through the characteristic that the terahertz wave contains abundant spectral information, and the thickness is further calculated. The first method is time-consuming and labor-consuming, and has low detection efficiency and high detection cost. Most of calculation models for extracting the refractive index in the second detection method at present have the problems of complex calculation models, large calculation amount, need of comparison before and after multiple detections, low detection efficiency and the like, and cannot well adapt to industrial requirements.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a terahertz thickness measuring method of a thermal barrier coating ceramic layer without a reference sample, which can realize accurate measurement of the thickness of the thermal barrier coating ceramic layer on the premise of only single detection, no need of a complex calculation model and no need of special signal processing.
In order to achieve the purpose, the invention adopts the following technical scheme:
a terahertz thickness measuring method for a thermal barrier coating ceramic layer without a reference sample comprises the following steps:
step 1, vertically irradiating a terahertz wave emitted by a terahertz time-domain spectroscopy system into a thermal barrier coating, and reflecting the vertically irradiated terahertz wave in a ceramic layer for multiple times to obtain the amplitude of the previous three echo signals;
step 2, obtaining amplitude intensity according to the average amplitude of the echo signals of the previous three times, and calculating the refractive index of the ceramic layer according to the amplitude intensity;
and 3, calculating the thickness of the ceramic layer according to the refractive index of the ceramic layer.
Further, the thickness of the ceramic layer is calculated by the following formula:
Figure BDA0003450142350000021
where c is the speed of light, Δ t is the time difference between adjacent echoes, n1The refractive index of the ceramic layer.
Further, the refractive index of the ceramic layer is calculated by the following formula:
Figure BDA0003450142350000022
in the formula, E1Amplitude intensity of the first echo signal, E2Amplitude intensity of the second echo signal, E3The amplitude intensity of the third echo signal.
Further, the amplitude intensity E of the first echo signal among the amplitudes of the first three echo signals1Calculated by the following formula:
E1＝-E0r01
wherein E is0Is the intensity of the amplitude of the incident wave, r01The reflectivity of the air to the ceramic layer direction;
amplitude intensity E of second echo signal among amplitudes of first three echo signals2By passingThe following formula is calculated:
E2＝-E0t01r12t1t10
wherein E is0As intensity of amplitude of incident wave, t01Transmittance of air to the ceramic layer, r12Reflectivity of ceramic layer to metal layer, t1Transmission coefficient, t, for the ceramic layer taking into account terahertz signal losses10The transmittance of the ceramic layer to the air direction;
amplitude intensity E of third echo signal among amplitudes of first third echo signals3Calculated by the following formula:
Figure BDA0003450142350000031
wherein E is0As intensity of amplitude of incident wave, t01Transmittance of air to the ceramic layer, r12Reflectivity of ceramic layer to metal layer, t1Transmission coefficient r for considering terahertz signal loss in ceramic layer10、t10The reflectivity and transmissivity of the ceramic layer in the air direction are respectively.
Further, r01The reflectivity for the air to ceramic layer direction is calculated by:
Figure BDA0003450142350000032
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
Further, the reflectivity r of the ceramic layer to the air direction10Calculated by the following formula:
Figure BDA0003450142350000033
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
Further, the transmittance t of air to the ceramic layer01Calculated by the following formula:
Figure BDA0003450142350000034
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
Further, the transmittance t of the ceramic layer to the air direction10Calculated by the following formula:
Figure BDA0003450142350000035
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
Compared with the existing detection method, the invention has the beneficial effects that:
according to the invention, the refractive index of the ceramic layer is calculated by utilizing the multiple echo relationship of the terahertz waves in the ceramic layer of the thermal barrier coating. In a terahertz waveband, the imaginary part of the complex refractive index of the medium is far smaller than the real part, so that the complex refractive index is subjected to approximate real number processing in calculation; since the material of the ceramic layer of the thermal barrier coating is a non-ferromagnetic substance and has limited dispersive power, the influence of the dispersion of the ceramic layer on the refractive index is neglected. The approximate average refractive index of the terahertz waveband of the thermal barrier coating ceramic layer can be calculated by the method. The invention can obtain the measured parameters by one-time measurement and has high measurement efficiency. The refractive index of the ceramic layer is calculated based on Fresnel law and multiple echo propagation relation of terahertz signals in the ceramic layer, the model is simple and accurate, only terahertz time-domain signals are used in the whole process, and special signal processing means are not needed. The thickness of the thermal barrier coating ceramic layer can be measured without any reference, the processes of manufacturing a standard sample and measuring required parameters in a pre-experiment are omitted, a large amount of manpower, materials and process cost are saved, and the method has application value.
Drawings
FIG. 1 is a model of terahertz wave propagation in a thermal barrier coating.
Fig. 2 is a set of terahertz detection time-domain signals.
FIG. 3 is a comparison of the calculated results of the refractive index and the thickness of the ceramic layer according to the method with the reference true value.
Detailed Description
The invention will be described in further detail below with reference to the accompanying drawings:
the thermal barrier coating includes a bond coat and a ceramic layer disposed on the bond coat.
The invention discloses a method for measuring the thickness of a thermal barrier coating ceramic layer by one-time detection by utilizing a terahertz time-domain signal without a reference sample or a reference signal, which comprises the following steps:
step 1, determining a position of a thermal barrier coating to be measured, vertically irradiating terahertz waves emitted by a terahertz time-domain spectroscopy system into the thermal barrier coating, and reflecting the vertically incident terahertz waves in a ceramic layer for multiple times to obtain amplitudes of first echo signals, namely amplitude intensities of first echo signals, second echo signals and third echo signals, which is shown in fig. 1;
in the invention, four times or more times of taking can obtain results similar to three times of taking by reduction, and the calculation process is complex but consistent.
Step 2, calculating the average amplitude of each echo signal according to the amplitude of the previous third echo signal to serve as the amplitude intensity of the echo signal, and calculating the refractive index n of the thermal barrier coating ceramic layer according to the Fresnel law, the amplitude intensity and the propagation relation among the previous third echo signals1(ii) a The specific process is as follows:
step 2.1, assuming that the amplitude intensity of the terahertz incident wave signal emitted by the terahertz time-domain spectroscopy system is E0Then, the amplitude intensities of the first, second, and third echo signals can be respectively expressed as:
E1＝-E0r01
E2＝-E0t01r12t1t10
Figure BDA0003450142350000051
wherein r is01、t01Respectively the reflectivity and transmissivity of air to the ceramic layer10、t10Respectively the reflectivity and transmissivity from the ceramic layer to the air direction, t1Transmission coefficient r for considering terahertz signal loss in ceramic layer12The negative signs of the first and second echo equations represent the phase change of the terahertz wave signal at the interface due to half-wave loss, which is the reflectivity from the ceramic layer to the metal layer. E1Amplitude intensity of the first echo signal, E2Amplitude intensity of the second echo signal, E3The amplitude intensity of the third echo signal.
Step 2.2, based on the equation of the triple echo signal, eliminating parameters which are difficult to measure through experiments in the triple echo through mathematical operation, and obtaining the relationship between the amplitude of the triple echo signal and the transmittance and reflectivity, as follows:
Figure BDA0003450142350000052
the left side of the equation is a parameter which can be obtained by measuring the amplitude relation of the terahertz triple echo, and the assumption is that
Figure BDA0003450142350000053
The value is X.
Step 2.3, obtaining the reflectivity r of the air to the ceramic layer direction according to the Fresnel law01The reflectivity r of the ceramic layer in the direction from the air10Air to ceramic layer transmittance t01The transmittance t of the ceramic layer to the air direction10Respectively as follows:
Figure BDA0003450142350000061
Figure BDA0003450142350000062
Figure BDA0003450142350000063
Figure BDA0003450142350000064
in the formula, the refractive index n of air is taken0＝1，n1The refractive index n of the ceramic layer can be obtained by substituting the transmission coefficient and the reflection coefficient into the equation in step 2.21：
Figure BDA0003450142350000065
According to Maxwell electromagnetic field theory, the refractive index of the material is not less than 1, and the refractive index n of the ceramic layer can be obtained by eliminating unreasonable results1。
And 3, extracting the time difference delta t of adjacent echoes in the terahertz signal, namely the propagation time of the terahertz wave in the ceramic layer, wherein the propagation speed of the terahertz wave in the ceramic layer is the ratio of the light speed to the refractive index of the ceramic layer, and the propagation distance between the adjacent echoes is 2 times of the thickness of the ceramic layer. Calculating the thickness d of the ceramic layer according to the relation among the speed, the time and the distance;
Figure BDA0003450142350000066
where c is the speed of light.
Example 1
Using a terahertz time-domain spectroscopy system (such as TeraView TeraPulse Lx), terahertz waves are vertically incident on the thermal barrier coating and reflected signals in a window of a long enough time are collected, as shown in FIG. 2.
Terahertz wave amplitude intensity E emitted by terahertz time-domain spectroscopy system0Then, the amplitude intensities of the first, second, and third echoes can be expressed as:
E1＝-E0r01
E2＝-E0t01r12t1t10
Figure BDA0003450142350000067
wherein n is0Is the refractive index of air, n1Refractive index of the ceramic layer, r01、t01Respectively the reflectivity and transmissivity of air to the ceramic layer10、t10Reflectivity and transmissivity of ceramic layer to air direction, t1Transmission coefficient r for considering terahertz signal loss in ceramic layer12The negative signs of the first and second echo equations represent the phase change of the terahertz wave signal at the interface due to half-wave loss, which is the reflectivity from the ceramic layer to the metal layer.
Based on the cubic echo signal equation, parameters which are difficult to measure in cubic echoes are eliminated through mathematical operation, and a relation equation of the amplitude of the cubic echoes and the reflectivity and the transmissivity can be obtained:
Figure BDA0003450142350000071
the left side of the equation is a parameter which can be obtained by measuring the amplitude relation of the terahertz triple echo, and the value of the parameter is assumed to be X.
The reflectivity r of the air to the ceramic layer direction can be obtained according to Fresnel law01The reflectivity r of the ceramic layer in the direction from the air10Air to ceramic layer transmittance t01The transmittance t of the ceramic layer to the air direction10Respectively as follows:
Figure BDA0003450142350000072
Figure BDA0003450142350000073
Figure BDA0003450142350000074
Figure BDA0003450142350000075
taking refractive index n of air0The refractive index n of the ceramic layer can be obtained by substituting the transmission coefficient and the reflection coefficient into a relation equation of the amplitude of the third echo and the reflectivity and the transmissivity as 11The calculation formula is as follows:
Figure BDA0003450142350000076
extracting three echoes from the collected terahertz detection signals, respectively calculating the average value of the absolute values of the amplitudes of the three echoes to obtain the average amplitude intensity E of the three echoes1、E2、E3And calculates X. The calculation method of X is shown by the following formula:
Figure BDA0003450142350000077
the refractive index n of the thermal barrier coating is calculated by substituting X into a calculation formula of the refractive index of the ceramic layer1。
According to Maxwell electromagnetic field theory, the refractive index of vacuum is 1, the refractive index of general substances is a value not less than 1, and a value more than 1 is taken as the refractive index n of the final thermal barrier coating1。
According to the collected terahertz detection signal, extracting the time interval delta t between two adjacent echoes, wherein the thickness d calculation model of the thermal barrier coating is as follows:
Figure BDA0003450142350000081
where c is the speed of light.
The thickness of the thermal barrier coating ceramic layer at the detection position can be calculated according to the process. And then, the terahertz time-domain spectroscopy system can be controlled by a motion system (such as a gantry type motion platform) to change the terahertz incidence position, the whole area to be detected of the thermal barrier coating is scanned, and terahertz detection signals of all target positions are obtained. And repeating the steps to obtain the thickness information of the thermal barrier coating at each position. One set of test results is shown in FIG. 3. In fig. 3, the straight line and the dotted line represent reference true values of the refractive index and the thickness of the thermal barrier coating ceramic layer, which are 5.97 μm and 300 μm respectively, data at ten positions are randomly collected on a target thermal barrier coating sample, and the refractive index and the thickness of the thermal barrier coating ceramic layer calculated by the method are shown as rectangular dots and triangular dots respectively. The calculated results of the refractive indexes of the ceramic layers are 5.89, 6.01, 5.39, 6.66, 6.39, 6.11, 5.62, 6.24, 6.07 and 5.45 respectively, and the average value is 5.98; the calculated thickness of the ceramic layers was 308.24 μm, 302.29 μm, 336.84 μm, 272.60 μm, 284.12 μm, 297.14 μm, 323.05 μm, 290.95 μm, 299.10 μm and 333.13 μm, respectively, and the average value was 303.45 μm.
According to the invention, based on the characteristic that terahertz waves are reflected in a thermal barrier coating ceramic layer for multiple times, a terahertz time-domain spectroscopy system is used for enabling the terahertz waves to vertically enter the thermal barrier coating, a window which is long enough is set, and terahertz wave front triple reflection echoes are collected; respectively calculating the average amplitude intensity of the first three echoes; calculating the refractive index of the ceramic layer according to the propagation relation between the amplitudes of the first three echoes and the Fresnel law; and extracting the time difference of flight between two adjacent echoes, and calculating the thickness of the thermal barrier coating ceramic layer according to the wave speed and the time of flight of the terahertz waves. The method provided by the invention uses the terahertz time-domain signal, and can realize non-contact, efficient and nondestructive detection of the thickness of the thermal barrier coating ceramic layer on the premise of not needing a reference sample. According to the invention, no reference sample is required to be made, no complex theoretical model is required to be established, the terahertz time-domain signal is completely used in the whole process, and an efficient, rapid and accurate detection method can be provided for thermal barrier coating thickness measurement.

Claims (8)

1. A terahertz thickness measuring method of a thermal barrier coating ceramic layer without a reference sample is characterized by comprising the following steps:
step 1, vertically irradiating a terahertz wave emitted by a terahertz time-domain spectroscopy system into a thermal barrier coating, and reflecting the vertically irradiated terahertz wave in a ceramic layer for multiple times to obtain the amplitude of the previous three echo signals;
step 2, obtaining amplitude intensity according to the average amplitude of the echo signals of the previous three times, and calculating the refractive index of the ceramic layer according to the amplitude intensity;
and 3, calculating the thickness of the ceramic layer according to the refractive index of the ceramic layer.
2. The terahertz thickness measuring method of the ceramic layer of the thermal barrier coating without the reference sample as claimed in claim 1, wherein the thickness of the ceramic layer is calculated by the following formula:
Figure FDA0003450142340000011
where c is the speed of light, Δ t is the time difference between adjacent echoes, n1The refractive index of the ceramic layer.
3. The terahertz thickness measuring method for the ceramic layer of the thermal barrier coating without the reference sample as claimed in claim 2, wherein the refractive index of the ceramic layer is calculated by the following formula:
Figure FDA0003450142340000012
in the formula, E1Amplitude intensity of the first echo signal, E2Amplitude intensity of the second echo signal, E3The amplitude intensity of the third echo signal.
4. The terahertz thickness measuring method for the thermal barrier coating ceramic layer without the reference sample as claimed in claim 3, wherein the amplitude intensity E of the first echo signal in the amplitudes of the first three echo signals1Calculated by the following formula:
E1＝-E0r01
wherein E is0Is the intensity of the amplitude of the incident wave, r01The reflectivity of the air to the ceramic layer direction;
amplitude intensity E of second echo signal among amplitudes of first three echo signals2Calculated by the following formula:
E2＝-E0t01r12t1t10
wherein E is0As intensity of amplitude of incident wave, t01Transmittance of air to the ceramic layer, r12Reflectivity of ceramic layer to metal layer, t1Transmission coefficient, t, for the ceramic layer taking into account terahertz signal losses10The transmittance of the ceramic layer to the air direction;
amplitude intensity E of third echo signal among amplitudes of first third echo signals3Calculated by the following formula:
Figure FDA0003450142340000021
wherein E is0As intensity of amplitude of incident wave, t01Transmittance of air to the ceramic layer, r12Reflectivity of ceramic layer to metal layer, t1Transmission coefficient r for considering terahertz signal loss in ceramic layer10、t10The reflectivity and transmissivity of the ceramic layer in the air direction are respectively.
5. The terahertz thickness measuring method for the thermal barrier coating ceramic layer without the reference sample as claimed in claim 4, wherein r is01The reflectivity for the air to ceramic layer direction is calculated by:
Figure FDA0003450142340000022
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
6. The terahertz thickness measuring method for the ceramic layer of the thermal barrier coating without the reference sample as claimed in claim 4, wherein the reflectivity r of the ceramic layer to the air direction10Calculated by the following formula:
Figure FDA0003450142340000023
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
7. The terahertz thickness measuring method for the thermal barrier coating ceramic layer without the reference sample as claimed in claim 4, wherein the transmittance t from air to the ceramic layer is01Calculated by the following formula:
Figure FDA0003450142340000024
in the formula, n0Is the refractive index of air, n1The refractive index of the ceramic layer.
8. The terahertz thickness measuring method for the ceramic layer of the thermal barrier coating without the reference sample as claimed in claim 4, wherein the transmittance t from the ceramic layer to the air direction10Calculated by the following formula:
Figure FDA0003450142340000025
in the formula, n0Is airRefractive index, n1The refractive index of the ceramic layer.
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