Method and apparatus for determining thermal stress distribution in thermal barrier coatings on curved substrates

Abstract

This application discloses a method and apparatus for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate. The method includes: establishing a mathematical and geometric model corresponding to the thermal barrier coating system, determining the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating, then obtaining the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process, and determining the normal strain at any point in the thermal barrier coating system; then determining the first normal stress at any point on the curved substrate and the second normal stress at any point in the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating; finally, determining the stress distribution of the thermal barrier coating system based on the first and second normal stresses. The method and apparatus for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate according to the embodiments of this application can quickly, conveniently, and accurately calculate the thermal stress generated during the preparation of the thermal barrier coating system on the curved substrate.

Description

Technical Field

[0001] This application relates to the field of thermal barrier coating stress calculation technology, and in particular to a method and apparatus for determining the thermal stress distribution of thermal barrier coatings prepared on curved substrates. Background Technology

[0002] Gas turbines are one of the core power equipment in clean and efficient thermal power energy systems that use high-temperature gas as the working fluid. The inlet gas temperature is a key factor affecting the energy conversion efficiency of a gas turbine. Currently, the inlet gas temperature of internationally used G / H / J class heavy-duty gas turbines can reach 1500–1600℃, far exceeding the tolerance limit of high-temperature alloys used in blades. Thermal barrier coatings (TBCs) are widely used surface coatings, commonly applied to high-temperature components such as turbine engines, gas turbines, and combustion chambers. They reduce heat conduction and radiation in high-temperature environments, thus protecting the performance and lifespan of equipment and components. They also improve the corrosion resistance and wear resistance of materials, offering significant benefits at a relatively low cost. Therefore, thermal barrier coatings (TBCs) have become one of the key technologies for improving the temperature rating of gas turbines. Traditional thermal barrier coatings (TBCs) mainly consist of three parts: a superalloy substrate (such as Inconel 617, or Substrate), a binder coating (such as NiCrAlY, or BC coating), and a top yttrium oxide-stabilized zirconia ceramic coating (ZrO2-8% Y2O3, or YSZ coating). Dual ceramic layer TBC systems add a novel ceramic material (La2ZrO7, or LZ coating) to the traditional YSZ ceramic coating to provide excellent anti-sintering properties at high temperatures, while also offering advantages such as thermal insulation, corrosion resistance, and high thermal stability, thus improving the overall performance of the TBC. However, the preparation of dual ceramic layer TBCs generates quenching stress and thermal mismatch stress, resulting in residual stress in the final TBC system. This residual stress can lead to the initiation and propagation of microcracks, coating debonding, and even system failure, significantly impacting the service performance and lifespan of the TBC system.

[0003] Currently, existing technologies have proposed calculation methods for the residual stress caused during the quenching process. Patent CN103926025 discloses a test device and method for measuring the residual stress of a coating. By measuring the curvature change of the coating and substrate during spraying online, the internal stress of the coating during preparation is calculated within the elastic range, yielding the final residual stress. However, this method is only applicable to test device scenarios. In actual thermal barrier coating preparation, it is impossible to record the spraying path using displacement sensors, making it unsuitable for practical thermal barrier coating preparation. Furthermore, it suffers from measurement errors and is relatively complex. In addition, this patent does not consider the coefficient of thermal expansion when calculating thermal mismatch stress, leading to inaccurate calculation results. Patent CN110046402 discloses a method for calculating the quenching stress of a functionally graded thermal barrier coating with a gradient index. This method obtains the quenching stress of the thermal barrier coating by establishing a mathematical model during the calculation process; however, this method is not applicable to the calculation of thermal mismatch stress. Therefore, existing methods are complex and prone to errors when calculating the forces generated during quenching, and cannot be applied to the actual preparation process of thermal barrier coatings. Summary of the Invention

[0004] This application aims to at least partially address one of the aforementioned technical problems.

[0005] Therefore, the first objective of this application is to propose a method for determining the thermal stress distribution during the preparation of thermal barrier coatings on curved substrates, so as to quickly, conveniently and accurately calculate the thermal stress distribution generated during the preparation of thermal barrier coating systems on curved substrates.

[0006] The second objective of this application is to provide a device for determining the thermal stress distribution during the preparation of thermal barrier coatings on curved substrates.

[0007] To achieve the above objectives, the first aspect of this application proposes a method for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate, comprising:

[0008] Establish the mathematical and geometric model corresponding to the thermal barrier coating system;

[0009] The curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is determined based on the mathematical geometric model.

[0010] To obtain the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process;

[0011] Determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value.

[0012] The first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating are determined based on the normal strain and the physical properties of the thermal barrier coating.

[0013] The stress distribution of the thermal barrier coating system is determined based on the first normal stress and the second normal stress.

[0014] Optionally, the mathematical geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system.

[0015] Optionally, the equation of the curve corresponding to the interface between the curved substrate and the thermal barrier coating is y = ax 2 , where a represents parameters related to the curve shape.

[0016] Optionally, the physical properties of the thermal barrier coating include the coefficient of thermal expansion α and the temperature change value ΔT. Based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value, the normal strain at any point in the thermal barrier coating system is determined, including:

[0017] The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined based on the curve equation;

[0018] Based on the coefficient of thermal expansion α, the temperature change ΔT, and the radius of curvature R, the normal strain at any point in the thermal barrier coating system is determined using Formula 1: Formula 1: Where δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, ω0 represents the second parameter, and the first and second parameters are unknowns.

[0019] Optionally, the radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined according to the curve equation, including:

[0020] The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined using Formula 2: Where 'a' represents the curve shape-related parameters, and 'x' represents the horizontal coordinate at any point within the thermal barrier coating system.

[0021] Optionally, the physical properties of the thermal barrier coating also include Young's modulus E. The first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating are determined based on the normal strain and the physical properties of the thermal barrier coating, including:

[0022] Formula 3 is used to determine the first normal stress at any point on the curved surface base. Formula 3: Where, α s E represents the coefficient of thermal expansion of the curved substrate. s ΔT represents the Young's modulus of the curved surface base. sThe value represents the temperature change of the curved substrate, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0023] Formula 4 is used to determine the second normal stress at any point in the thermal barrier coating. Formula 4: Where, α c E represents the coefficient of thermal expansion of the thermal barrier coating. c ΔT represents the Young's modulus of the thermal barrier coating. c The value represents the temperature change of the thermal barrier coating, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0024] Optionally, the stress distribution of the thermal barrier coating system is determined based on the first normal stress and the second normal stress, including:

[0025] Solve for the first parameter ε0 and the second parameter ω0 in formulas 3 and 4 using formulas 5 and 6. Formula 5: Formula Six: Among them, t s t represents the temperature value of the curved substrate. c σ represents the temperature value of the thermal barrier coating. θs σ represents the first normal stress. θc The second normal stress is represented by δ, which represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating.

[0026] The stress distribution of the thermal barrier coating system is determined based on the first parameter ε0 and the second parameter ω0.

[0027] Optionally, the thermal barrier coating is a double ceramic layer structure, including an i-layer BC coating, a j-layer YSZ coating, and a k-layer LZ coating. The normal stress includes deposition stress and thermal mismatch stress. The second normal stress is the sum of the deposition stress of the i-layer BC coating, the j-layer YSZ coating, and the k-layer LZ coating, plus the sum of the thermal mismatch stress of the i-layer BC coating, the j-layer YSZ coating, and the k-layer LZ coating, where i≥1, j≥1, and k≥1.

[0028] The method for determining the thermal stress distribution in the preparation of a thermal barrier coating on a curved substrate according to embodiments of this application establishes a mathematical geometric model corresponding to the thermal barrier coating system. Based on the mathematical geometric model, the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is determined. Then, the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process are obtained. Based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change values, the normal strain at any point in the thermal barrier coating system is determined. Then, based on the normal strain and the physical properties of the thermal barrier coating, the first normal stress at any point on the curved substrate and the second normal stress at any point in the thermal barrier coating are determined. Finally, the stress distribution of the thermal barrier coating system is determined based on the first and second normal stresses. Therefore, by fully considering the physical properties and temperature changes of the thermal barrier coating system, and based on the precise morphological parameter values ​​in the mathematical geometric model and the general calculation method of the normal strain at any point in the thermal barrier coating system, the thermal stress and its distribution of the thermal barrier coating system can be obtained. Furthermore, the residual stress in the thermal barrier coating system can be reduced by optimizing the geometric parameters in the mathematical geometric model.

[0029] To achieve the above objectives, a second aspect of this application provides an apparatus for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate, comprising:

[0030] A module is established to create the mathematical and geometric model corresponding to the thermal barrier coating system;

[0031] The first determining module is used to determine the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model.

[0032] The acquisition module is used to acquire the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process;

[0033] The second determining module is used to determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value.

[0034] The third determining module is used to determine the first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating.

[0035] The fourth determining module is used to determine the stress distribution of the thermal barrier coating system based on the first normal stress and the second normal stress.

[0036] Optionally, the mathematical geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system.

[0037] Optionally, the equation of the curve corresponding to the interface between the curved substrate and the thermal barrier coating is y = ax 2 , where a represents parameters related to the curve shape.

[0038] Optionally, the physical properties of the thermal barrier coating include the coefficient of thermal expansion α and the temperature change value ΔT. A second determining module is used for:

[0039] The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined based on the curve equation;

[0040] Based on the coefficient of thermal expansion α, the temperature change ΔT, and the radius of curvature R, the normal strain at any point in the thermal barrier coating system is determined using Formula 1: Formula 1: Where δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, ω0 represents the second parameter, and the first and second parameters are unknowns.

[0041] Optionally, a second determining module is used for:

[0042] The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined using Formula 2: Where 'a' represents the curve shape-related parameters, and 'x' represents the horizontal coordinate at any point within the thermal barrier coating system.

[0043] Optionally, the physical properties of the thermal barrier coating also include Young's modulus E, a third determining module used for:

[0044] Formula 3 is used to determine the first normal stress at any point on the curved surface base. Formula 3: Where, α s E represents the coefficient of thermal expansion of the curved substrate. s ΔT represents the Young's modulus of the curved surface base. s The value represents the temperature change of the curved substrate, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0045] Formula 4 is used to determine the second normal stress at any point in the thermal barrier coating. Formula 4: Where, α c E represents the coefficient of thermal expansion of the thermal barrier coating. c ΔT represents the Young's modulus of the thermal barrier coating. c The value represents the temperature change of the thermal barrier coating, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0046] Optional, a fourth determining module, used for:

[0047] Solve for the first parameter ε0 and the second parameter ω0 in formulas 3 and 4 using formulas 5 and 6. Formula 5: Formula Six: Among them, t s t represents the temperature value of the curved substrate. c σ represents the temperature value of the thermal barrier coating. θs σ represents the first normal stress. θc The second normal stress is represented by δ, which represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating.

[0048] The stress distribution of the thermal barrier coating system is determined based on the first parameter ε0 and the second parameter ω0.

[0049] Optionally, the thermal barrier coating is a double ceramic layer structure, including an i-layer BC coating, a j-layer YSZ coating, and a k-layer LZ coating. The normal stress includes deposition stress and thermal mismatch stress. The second normal stress is the sum of the deposition stress of the i-layer BC coating, the j-layer YSZ coating, and the k-layer LZ coating, plus the sum of the thermal mismatch stress of the i-layer BC coating, the j-layer YSZ coating, and the k-layer LZ coating, where i≥1, j≥1, and k≥1.

[0050] The thermal stress distribution determination device for thermal barrier coating preparation on a curved substrate according to this application embodiment establishes a mathematical geometric model corresponding to the thermal barrier coating system, determines the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model, then obtains the physical properties of the thermal barrier coating and the temperature change value during the spraying process, and determines the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value. Then, it determines the first normal stress at any point on the curved substrate and the second normal stress at any point in the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating, and finally determines the stress distribution of the thermal barrier coating system based on the first and second normal stresses. Therefore, by fully considering the physical properties and temperature changes of the thermal barrier coating system, and based on the precise morphological parameter values ​​in the mathematical geometric model and the general calculation method for the normal strain at any point in the thermal barrier coating system, the thermal stress and its distribution of the thermal barrier coating system can be obtained, and the residual stress in the thermal barrier coating system can be reduced by optimizing the geometric parameters in the mathematical geometric model.

[0051] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0052] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0053] Figure 1A flowchart of a method for determining the thermal stress distribution in the preparation of a thermal barrier coating on a curved substrate, according to one embodiment, is provided;

[0054] Figure 2 A schematic diagram of the mathematical and geometric model corresponding to a thermal barrier coating system of one embodiment is shown;

[0055] Figure 3 A schematic diagram of a thermal barrier coating system according to a specific embodiment is shown;

[0056] Figure 4 A flowchart of a method for determining the thermal stress distribution in the preparation of a thermal barrier coating on a curved substrate, according to a specific embodiment, is presented;

[0057] Figure 5(a) shows the deposition stress distribution in the axial thickness direction within the substrate in a specific embodiment;

[0058] Figure 5(b) shows the deposition stress distribution in the axial thickness direction within the BC coating in a specific embodiment;

[0059] Figure 5(c) shows the deposition stress distribution in the axial thickness direction of the YSZ coating in a specific embodiment;

[0060] Figure 5(d) shows the deposition stress distribution in the axial thickness direction of the LZ coating in a specific embodiment;

[0061] Figure 6 The total thermal stress distribution along the axial thickness direction after the thermal barrier coating is deposited in a specific embodiment is shown;

[0062] Figure 7 A schematic diagram of a device for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate is shown in one embodiment. Detailed Implementation

[0063] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0064] The present application will be further described in detail below with reference to specific embodiments, which should not be construed as limiting the scope of protection claimed in the present application.

[0065] The following describes, with reference to the accompanying drawings, a method and apparatus for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate according to embodiments of this application.

[0066] Figure 1 This is a flowchart of a method for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate, according to an embodiment of this application. The method specifically includes the following steps:

[0067] S1. Establish the mathematical and geometric model corresponding to the thermal barrier coating system.

[0068] In this embodiment, as Figure 2 As shown, the thermal barrier coating system includes a curved substrate t s and thermal barrier coating t c δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, and R represents the radius of curvature of the interface between the curved substrate and the thermal barrier coating.

[0069] Furthermore, such as Figure 2 As shown, the mathematical geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system.

[0070] The above-mentioned mathematical and geometric model establishment process enables a more intuitive display of the thermal barrier coating system, while achieving an accurate description of the morphological parameters of the thermal barrier coating system, thus providing a foundation for obtaining the data required for subsequent simulation calculation of thermal stress.

[0071] S2, determine the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model.

[0072] Specifically, such as Figure 2 As shown, the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is y = ax 2 , where a represents parameters related to the curve shape.

[0073] S3, obtain the physical properties of the thermal barrier coating and the temperature change value during the spraying process.

[0074] The physical properties of the thermal barrier coating may include the coefficient of thermal expansion α, Young's modulus E, etc.

[0075] Meanwhile, the substrate temperature remains constant during plasma spraying, while the temperature of the thermal barrier coating drops rapidly to the same level as the substrate the instant the coating comes into contact with the substrate. The temperature change value ΔT at any point in the thermal barrier coating system can be obtained by calculating the difference between the melting point of the thermal barrier coating material and the substrate temperature.

[0076] The above process, based on the mathematical model established in S1, obtains the physical properties of the thermal barrier coating and the temperature change at any point in the thermal barrier coating system caused by quenching, providing comprehensive data for subsequent calculations of the overall distribution of thermal stress. Furthermore, by incorporating physical properties such as the elastic modulus and coefficient of thermal expansion, along with actual temperature changes, into the simulation calculations, the calculation of thermal stress becomes more accurate.

[0077] S4. Determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value.

[0078] Specifically, firstly, the radius of curvature of the interface between the curved substrate and the thermal barrier coating can be determined using Formula 2 based on the curve equation. Where 'a' represents parameters related to the curve shape, and 'x' represents the horizontal coordinate at any point within the thermal barrier coating system. Then, based on the coefficient of thermal expansion α, the temperature change value ΔT, and the radius of curvature R, the normal strain at any point within the thermal barrier coating system can be determined using Formula 1. Where δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, ω0 represents the second parameter, and the first and second parameters are unknowns.

[0079] The different coefficients of thermal expansion of materials in a thermal barrier coating system lead to different degrees of thermal contraction between the substrate and the thermal barrier coating material, which in turn causes different normal strains at various points in the thermal barrier coating system. The above process can be applied to the calculation of normal strain at any point in the substrate and the thermal barrier coating, thus enabling flexible and convenient acquisition of normal strain at any point in the thermal barrier coating system.

[0080] S5, determine the first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating.

[0081] Specifically, the normal stress at any point in the thermal barrier coating system is determined by the normal strain at that point and the physical properties of the thermal barrier coating: σ θ =E(ε-αΔT), where E represents the elastic modulus at that location, α represents the coefficient of thermal expansion at that location, and ΔT represents the temperature change at that location.

[0082] Therefore, firstly, the first normal stress at any point on the curved surface base can be determined using Formula 3: Formula 3: Where, α s E represents the coefficient of thermal expansion of the curved substrate. s ΔT represents the Young's modulus of the curved surface base. s ε0 represents the temperature change value of the curved substrate, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0083] Then, the second normal stress at any point in the thermal barrier coating can be determined using Formula 4: Where, α c E represents the coefficient of thermal expansion of the thermal barrier coating. c ΔT represents the Young's modulus of the thermal barrier coating. c The value represents the temperature change of the thermal barrier coating, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0084] The above process, based on the normal strain obtained by S4, can be used to conveniently and accurately calculate the first normal stress generated on the substrate and the second normal stress generated during the deposition of the thermal barrier coating and after the thermal barrier coating system cools down.

[0085] S6, determine the stress distribution of the thermal barrier coating system based on the first normal stress and the second normal stress.

[0086] Specifically, considering that the resultant force of all external forces acting on an object and the torques generated by those forces is zero, a balance between force and torque is achieved. Since the thermal barrier coating system is unaffected by external forces, the first parameter ε0 and the second parameter ω0 in formulas three and four can be solved using formulas five and six. Formula five: Formula Six: Among them, t s t represents the temperature value of the curved substrate. c σ represents the temperature value of the thermal barrier coating. θs σ represents the first normal stress. θc The second normal stress is represented by δ, which represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating.

[0087] Then, the stress distribution of the thermal barrier coating system can be determined based on the first parameter ε0 and the second parameter ω0. Specifically, by substituting the solved first parameter ε0 and the second parameter ω0 into Formulas 3 and 4, the values ​​of the first normal stress and the second normal stress at any point in the thermal barrier coating system can be obtained.

[0088] The above process can be used to obtain the deposition stress generated by the substrate and thermal barrier coating during the deposition process and to obtain the deposition stress distribution of the substrate and thermal barrier coating. At the same time, it can be used to obtain the thermal mismatch stress generated after the thermal barrier coating system is cooled as a whole. Thus, the final thermal stress of the thermal barrier coating system can be directly calculated by superimposing the deposition stress of the substrate and thermal barrier coating on the thermal mismatch stress of the thermal barrier coating system, and the distribution of the final thermal stress can be displayed.

[0089] The method for determining the thermal stress distribution in the preparation of a thermal barrier coating on a curved substrate according to embodiments of this application establishes a mathematical geometric model corresponding to the thermal barrier coating system. Based on the mathematical geometric model, the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is determined. Then, the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process are obtained. Based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change values, the normal strain at any point in the thermal barrier coating system is determined. Then, based on the normal strain and the physical properties of the thermal barrier coating, the first normal stress at any point on the curved substrate and the second normal stress at any point in the thermal barrier coating are determined. Finally, the stress distribution of the thermal barrier coating system is determined based on the first and second normal stresses. Therefore, by fully considering the physical properties and temperature changes of the thermal barrier coating system, and based on the precise morphological parameter values ​​in the mathematical geometric model and the general calculation method of the normal strain at any point in the thermal barrier coating system, the thermal stress and its distribution of the thermal barrier coating system can be obtained. Furthermore, the residual stress in the thermal barrier coating system can be reduced by optimizing the geometric parameters in the mathematical geometric model.

[0090] The following is a detailed description of a specific embodiment.

[0091] In this embodiment, the thermal barrier coating is a double ceramic layer structure, such as... Figure 3 As shown, the dual-ceramic thermal barrier coating system consists of, from the inside out, a superalloy substrate (such as Inconel 617, i.e., Substrate), a bonding coating (such as NiCrAlY, i.e., BC coating), a top yttrium oxide-stabilized zirconia ceramic coating (ZrO2-8%Y2O3, i.e., YSZ coating), and a novel ceramic material with good anti-sintering properties (La2ZrO7, i.e., LZ coating). In this embodiment, the substrate material is selected as a nickel-based alloy, and the BC coating material is NiCoCrALY.

[0092] Furthermore, to achieve the required thickness, the same thermal barrier coating often requires multiple coats. In this embodiment, the dual-ceramic thermal barrier coating system includes an i-layer BC coating, a j-layer YSZ coating, and a k-layer LZ coating, where i≥1, j≥1, and k≥1.

[0093] Specifically, the substrate thickness is 2000 μm, and the thicknesses of the BC, YSZ, and LZ coatings are 100 μm, 150 μm, and 150 μm, respectively. Simultaneously, the thermal barrier coatings are prepared using plasma spraying, deposited layer by layer at a thickness of 50 μm. Assuming that the thickness of the thermal barrier coating is consistent each time the same type of coating is sprayed, then the BC, YSZ, and LZ coatings are deposited 2, 3, and 3 times, respectively, i.e., i = 2, j = 3, and k = 3. From this, t can be obtained. BC =t YSZ =t LZ =50μm, n BC=2, n YSZ =3, n LZ =3, where t represents the coating thickness formed by each spraying, and n represents the number of sprayings during coating preparation.

[0094] Figure 4 This is a flowchart of a method for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate, according to a specific embodiment. The method includes the following steps:

[0095] S401, Establish the mathematical and geometric model corresponding to the thermal barrier coating system.

[0096] Specifically, the cross-section of the double-ceramic thermal barrier coating system is used as the calculation plane, the vertex of the curved interface between the metal substrate and the thermal barrier coating is used as the origin, the central axis is used as the Y-axis, and the curved interface between the metal substrate and the thermal barrier coating is used as the reference plane. Therefore, the position of any point within the thermal barrier coating system can be determined by the horizontal coordinate x of any point on the interface and the distance δ from that point to the reference plane.

[0097] The above-mentioned mathematical and geometric model establishment process enables a more intuitive display of the thermal barrier coating system, while achieving an accurate description of the morphological parameters of the thermal barrier coating system, thus providing a foundation for obtaining the data required for subsequent simulation calculation of thermal stress.

[0098] S402, determine the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model.

[0099] Specifically, if the cross-sectional shape of the curved substrate is defined as a parabola, the interface shape between the substrate and the coating can be described as the curve y = ax. 2 Wherein, parameter 'a' represents a parameter related to the shape of the parabola. In this embodiment, a = -0.2 is selected as the operating condition.

[0100] S403, obtain the physical properties of the thermal barrier coating and the temperature change value during the spraying process.

[0101] Specifically, the physical properties of the double ceramic thermal barrier coating include the elastic modulus E of each thermal barrier coating. C and the coefficient of expansion α C .

[0102] in, Where n represents the number of sprays during coating preparation, t represents the coating thickness formed by each spray, subscript C represents thermal barrier coating, and subscripts BC, YSZ, and LZ represent BC coating, YSZ coating, and LZ coating, respectively.

[0103] In this embodiment, based on the temperature change during the actual preparation process of the dual-ceramic thermal barrier coating, the physical property parameters of the material at 475°C are selected to calculate the deposition stress of the coating, and the physical property parameters of the material at 250°C are selected to calculate the thermal mismatch stress of the coating. The specific values ​​are obtained from the material property table.

[0104] Furthermore, in this embodiment, the melting points of the BC coating, YSZ coating, and LZ coating are 1680℃, 2680℃, and 2300℃, respectively. Since the temperature of the metal substrate remains constant at 475℃ during plasma spraying, the temperature of the coating material drops sharply to the same level as the substrate the instant the sprayed material contacts the metal. Therefore, ΔT1 = -1205K, ΔT2 = -2205K, and ΔT3 = -1825K. Simultaneously, after plasma spraying, the thermal barrier coating system cools to room temperature (25℃), so ΔT... CTE = -450K, where ΔT1 represents the temperature change of the BC coating, ΔT2 represents the temperature change of the YSZ coating, ΔT3 represents the temperature change of the LZ coating, and ΔT CTE This indicates the temperature change value after the thermal barrier coating system cools down.

[0105] The above process is based on the mathematical model established by S1. It comprehensively considers the number of sprayings and the thickness of the thermal barrier coating to obtain the physical property values ​​of each thermal barrier coating, and obtains the temperature change value at any point in the thermal barrier coating system caused by quenching, providing sufficient data for subsequent calculation of the overall distribution of thermal stress. At the same time, by taking into account physical properties such as elastic modulus and coefficient of thermal expansion, as well as actual temperature changes, the calculation of thermal stress can be made more accurate.

[0106] S404, determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value.

[0107] Specifically, the radius of curvature at a point on the interface is: Where a represents a parameter related to the shape of the parabola, a = -0.2 is the working condition in this embodiment, and x represents the horizontal coordinate of any point in the thermal barrier coating system.

[0108] Therefore, the normal strain at any point in the system can be expressed by the formula:

[0109] Where δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, ω0 represents the second parameter, and the first and second parameters are unknowns.

[0110] The different coefficients of thermal expansion of materials in a thermal barrier coating system lead to varying degrees of thermal contraction among the different coating materials, resulting in different normal strains at different locations within the system. The above process can be applied to the calculation of normal strain at any point in the substrate and any thermal barrier coating, thus enabling flexible and convenient acquisition of normal strain at any location within the thermal barrier coating system.

[0111] S405, calculate the deposition stress in the substrate and in each coating layer caused by quenching during the deposition process of each layer of BC coating, YSZ coating, and LZ coating.

[0112] Specifically, the deposition stress at any point in the thermal barrier coating system is determined by the normal strain at that point and the physical properties of the thermal barrier coating: σ θ =E(ε-αΔT), where E represents the elastic modulus at that location, α represents the coefficient of thermal expansion at that location, and ΔT represents the temperature change at that location.

[0113] In this embodiment, during the preparation of the thermal barrier coating, the spraying material is heated to a molten state using a plasma arc, and then the molten particles are sprayed onto the surface of the substrate using a spray gun. Upon contact with the substrate, the particles deform and spread out on the pre-treated substrate surface. During this process, the high-temperature particles flatten and cool to the substrate temperature within a very short time (typically a few milliseconds). This rapid temperature change of the molten particles leads to thermal shrinkage. Because the fixed substrate at the bottom restricts this thermal shrinkage, tensile stress is formed within the coating, i.e., deposition stress caused by quenching. The deposition stress of each thermal barrier coating during the quenching process of the thermal barrier coating system can be calculated using the following formula:

[0114] After depositing the i-th layer of the BC coating, the deposition stress on the curved substrate is:

[0115]

[0116] At this point, the deposition stress of the first to i-1 layers of the BC coating has been completed.

[0117]

[0118] At this point, the deposition stress of the BC coating itself is:

[0119]

[0120] Similarly, after depositing the j-th layer of the YSZ coating, the deposition stress on the curved substrate is:

[0121]

[0122] At this point, the overall deposition stress of the BC coating is:

[0123]

[0124] At this point, the deposition stress of the first to j-1 layers of YSZ coating has been completed, and its deposition stress is:

[0125]

[0126] At this point, the deposition stress of the YSZ coating itself is:

[0127]

[0128] Similarly, after depositing the k-th layer of the LZ coating, the deposition stress on the curved substrate is:

[0129]

[0130] At this point, the overall deposition stress of the BC coating is:

[0131]

[0132] At this point, the overall deposition stress of the YSZ coating is:

[0133]

[0134] At this point, the deposition stress of the first to k-1 LZ coating layers has been completed.

[0135]

[0136] At this point, the deposition stress of the LZ coating itself is:

[0137]

[0138] The above process, based on the normal strain obtained by S4, can be used to calculate the deposition stress of the substrate and each thermal barrier coating during the quenching process and to obtain the gradient change process of the deposition stress in each thermal barrier coating.

[0139] S406, calculate the thermal mismatch stress of each layer of the metal substrate, BC coating, YSZ coating and LZ coating after overall cooling.

[0140] Specifically, the thermal barrier coating system at any point is determined by the normal strain at that point and the physical properties of the thermal barrier coating: σ θ =E(ε-αΔT), where E represents the elastic modulus at that location, α represents the coefficient of thermal expansion at that location, and ΔT represents the temperature change at that location.

[0141] After the thermal barrier coating (TBC) deposition is completed, the TBC system temperature remains above room temperature. The entire system is then cooled to room temperature. During this process, due to the different coefficients of thermal expansion of the TBC materials and the curved substrate, the degree of thermal contraction between the layers will vary. Furthermore, due to the fixed constraints between the TBC materials and the curved substrate, the stress generated within each TBC and the curved substrate is known as thermal mismatch stress. The thermal mismatch stress of the TBC system after cooling can be calculated using the following formula:

[0142] After the thermal barrier coating system has cooled completely, the thermal mismatch stress within the curved substrate is:

[0143]

[0144] After the thermal barrier coating system has cooled down, the thermal mismatch stress within the BC coating is:

[0145]

[0146] After the thermal barrier coating system is cooled as a whole, the thermal mismatch stress within the YSZ coating is:

[0147]

[0148] After the thermal barrier coating system has cooled down, the thermal mismatch stress within the LZ coating is:

[0149]

[0150] The above process, based on the normal strain obtained by S4, can be used to calculate the thermal mismatch stress of the substrate and each thermal barrier coating after cooling.

[0151] S407. Based on the calculated deposition stress and thermal mismatch stress of each layer, the stress of each layer is superimposed to obtain the final distribution of total thermal stress.

[0152] The unknowns in S5 and S6 are solved based on the balance of forces and moments, and the deposition stress and thermal mismatch stress of each thermal barrier coating are obtained:

[0153] Based on the balance of force and torque, ε i ω i Solve the following:

[0154]

[0155] Substitute the unknowns obtained from the solution into the expression of S5 to obtain the deposition stress after the i-th layer of the BC coating is deposited.

[0156] Based on the balance of force and torque Solve the following:

[0157]

[0158] Substitute the unknowns obtained from the solution into the expression of S5 to obtain the deposition stress of the j-th layer of the YSZ coating after deposition.

[0159] Based on the balance of force and torque Solve the following:

[0160]

[0161]

[0162] Substitute the unknowns obtained from the solution into the expression of S5 to obtain the deposition stress after the kth layer of the LZ coating is deposited.

[0163] Based on the balance of force and torque, ε CTE ω CTE Solve the following:

[0164]

[0165]

[0166] Substitute the unknowns obtained from the solution into the S6 expression to obtain the thermal mismatch stress of the curved substrate and each thermal barrier coating after the overall thermal barrier coating system has cooled.

[0167] Therefore, as Figures 5(a)-5(d) As shown, based on the deposition stress variations of the substrate and each thermal barrier coating in the thermal barrier coating system, the deposition stress distribution along the axial thickness direction after layer-by-layer deposition can be obtained. Here, a positive stress indicates tensile stress, and a negative stress indicates compressive stress.

[0168] Specifically, in Figure 5(a), the horizontal axis from left to right is LZ-3rd, LZ-2nd, BC-2nd, LZ-1st, BC-1st, YSZ-3rd, YSZ-2nd, YSZ-1st. In Figure 5(b), the horizontal axis from left to right, and the vertical axis from top to bottom, the first layer, is LZ-3rd, LZ-2nd, LZ-1st, YSZ-3rd, YSZ-2nd, YSZ-1st, BC-2nd; the vertical axis from top to bottom, the second layer, is LZ-3rd, LZ-2nd, LZ-1st, YSZ-3rd, YSZ-2nd, YSZ-1st, BC-2nd, BC-1st. In Figure 5(c), the horizontal axis is taken from left to right, and the vertical axis is taken from top to bottom. The first layer is LZ-3rd, LZ-2nd, LZ-1st, YSZ-3rd. The second layer is taken from top to bottom. The third layer is taken from top to bottom.

[0169] Here, the total thermal stress of the thermal barrier coating is obtained by summing the deposition stresses of the i-th BC layer, j-th YSZ layer, and k-th LZ layer, and then adding the sum of the thermal mismatch stresses of the i-th BC layer, j-th YSZ layer, and k-th LZ layer. This is the second normal stress in the previous embodiment. Adding this to the deposition stress of the substrate due to quenching and the thermal mismatch stress due to cooling, the total stress distribution in the thermal barrier coating system is obtained, as shown below. Figure 6 The figure shows the total thermal stress distribution along the axial thickness direction after deposition.

[0170] The above process can be used to solve the deposition stress distribution of any thermal barrier coating and the curved substrate during the deposition process, while showing the evolution of the deposition stress distribution. After deposition is completed, the thermal mismatch stress formed after overall cooling is solved. By superimposing the deposition stress of the substrate and each thermal barrier coating on the thermal mismatch stress of the curved substrate and each thermal barrier coating, the final thermal stress of the thermal barrier coating system can be directly calculated to show the final thermal stress distribution.

[0171] This specific embodiment fully considers the physical properties and temperature changes of the thermal barrier coating system. Based on the precise morphological parameter values ​​in the mathematical geometric model and the general calculation method of normal strain at any point in the thermal barrier coating system, it is possible to obtain the deposition stress and its distribution of each thermal barrier coating in the thermal barrier coating system, as well as the final thermal stress and its distribution of the thermal barrier coating system. This helps to study the influence of geometric parameters on the thermal stress during the preparation of thermal barrier coatings, such as the curvature of the parabolic surface, the thickness of the substrate, and the thickness ratio of the YSZ coating to the LZ coating. Furthermore, by optimizing these geometric parameters, the residual stress in the thermal barrier coating system can be reduced.

[0172] To achieve the above embodiments, this application also proposes a device for determining the thermal stress distribution during the preparation of thermal barrier coatings on curved substrates.

[0173] Figure 7 This is a schematic diagram of the structure of a device for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate according to an embodiment of this application.

[0174] like Figure 7 As shown, the device for determining the thermal stress distribution of a thermal barrier coating on a curved substrate includes a setup module 71, a first determination module 72, an acquisition module 73, a second determination module 74, a third determination module 75, and a fourth determination module 76.

[0175] Module 71 is used to establish the mathematical and geometric model corresponding to the thermal barrier coating system. The mathematical and geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system. Furthermore, the thermal barrier coating can be a double ceramic layer structure, which may include an i-layer BC coating, a j-layer YSZ coating, and a k-layer LZ coating.

[0176] The first determining module 72 is used to determine the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on a mathematical geometric model. The curve equation corresponding to the interface between the curved substrate and the thermal barrier coating can be y = ax. 2 , where a represents parameters related to the curve shape.

[0177] The acquisition module 73 is used to acquire the physical properties of the thermal barrier coating and the temperature change value during the spraying process. The physical properties of the thermal barrier coating may include the coefficient of thermal expansion α, Young's modulus E, etc., and the temperature change value is ΔT.

[0178] The second determining module 74 is used to determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value.

[0179] The second determining module 74 is specifically used to: determine the radius of curvature R of the interface between the curved substrate and the thermal barrier coating using Formula 2, Formula 2: Where 'a' represents the curve shape-related parameters, and 'x' represents the horizontal coordinate at any point within the thermal barrier coating system.

[0180] The second determining module 74 is specifically used for: firstly, determining the radius of curvature R of the interface between the curved substrate and the thermal barrier coating based on the curve equation; then, based on the coefficient of thermal expansion α, the temperature change value ΔT, and the radius of curvature R, determining the normal strain at any point in the thermal barrier coating system using Formula 1. Formula 1: Where δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, ω0 represents the second parameter, and the first and second parameters are unknowns.

[0181] The third determining module 75 is used to determine the first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating. The normal stress may include deposition stress and thermal mismatch stress, and the second normal stress is the sum of the deposition stresses of the i-th BC layer, j-th YSZ layer, and k-th LZ layer, plus the sum of the thermal mismatch stresses of the i-th BC layer, j-th YSZ layer, and k-th LZ layer, where i≥1, j≥1, and k≥1.

[0182] The third determining module 75 is specifically used for: First, determining the first normal stress at any point on the curved surface base using Formula 3, Formula 3: Where αs represents the coefficient of thermal expansion of the curved substrate, Es represents the Young's modulus of the curved substrate, and ΔT s Let R represent the temperature change of the curved substrate, δ represent the radius of curvature, ε represent the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represent the first parameter, and ω0 represent the second parameter. Then, the second normal stress at any point on the thermal barrier coating is determined using Formula 4: Where, α c E represents the coefficient of thermal expansion of the thermal barrier coating. c ΔT represents the Young's modulus of the thermal barrier coating. c The value represents the temperature change of the thermal barrier coating, R represents the radius of curvature, δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating, ε0 represents the first parameter, and ω0 represents the second parameter.

[0183] The fourth determining module 76 is used to determine the stress distribution of the thermal barrier coating system based on the first normal stress and the second normal stress.

[0184] The fourth module, 76, is specifically used for: First, solving for the first parameter ε0 and the second parameter ω0 in Formulas 3 and 4 based on Formulas 5 and 6. Formula 5: Formula Six: Among them, t st represents the temperature value of the curved substrate. c σ represents the temperature value of the thermal barrier coating. θs σ represents the first normal stress. θc The second normal stress is represented by ε, and δ represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Then, the stress distribution of the thermal barrier coating system is determined based on the first parameter ε0 and the second parameter ω0.

[0185] It should be understood that the device for determining the thermal stress distribution of thermal barrier coatings on curved substrates is consistent with the description of the corresponding method for determining the thermal stress distribution of thermal barrier coatings on curved substrates, so it will not be repeated in this embodiment.

[0186] The thermal stress distribution determination device for thermal barrier coating preparation on a curved substrate according to this application embodiment establishes a mathematical geometric model corresponding to the thermal barrier coating system, determines the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model, then obtains the physical properties of the thermal barrier coating and the temperature change value during the spraying process, and determines the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value. Then, it determines the first normal stress at any point on the curved substrate and the second normal stress at any point in the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating, and finally determines the stress distribution of the thermal barrier coating system based on the first and second normal stresses. Therefore, by fully considering the physical properties and temperature changes of the thermal barrier coating system, and based on the precise morphological parameter values ​​in the mathematical geometric model and the general calculation method for the normal strain at any point in the thermal barrier coating system, the thermal stress and its distribution of the thermal barrier coating system can be obtained, and the residual stress in the thermal barrier coating system can be reduced by optimizing the geometric parameters in the mathematical geometric model.

[0187] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0188] It should be noted that, in the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

Claims

1. A method for determining the thermal stress distribution during the preparation of a thermal barrier coating on a curved substrate, characterized in that, include: Establish the mathematical and geometric model corresponding to the thermal barrier coating system; The curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is determined based on the mathematical and geometric model. To obtain the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process; The normal strain at any point in the thermal barrier coating system is determined based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value. The first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating are determined based on the normal strain and the physical properties of the thermal barrier coating. The stress distribution of the thermal barrier coating system is determined based on the first normal stress and the second normal stress. The physical properties of the thermal barrier coating include the coefficient of thermal expansion α, and the temperature change value is... Determining the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value includes: The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined according to the curve equation. Based on the thermal expansion coefficient α and the temperature change value The radius of curvature R is used to determine the normal strain at any point in the thermal barrier coating system using Formula 1. Formula 1: ,in, This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. This represents the second parameter, where the first and second parameters are unknowns. The physical properties of the thermal barrier coating also include Young's modulus. Determining the first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating includes: The first normal stress at any point on the curved surface base is determined using Formula 3: ,in, This represents the coefficient of thermal expansion of the curved substrate. This represents the Young's modulus of the curved surface substrate. This represents the temperature change value of the curved substrate, where R represents the radius of curvature. This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. Indicates the second parameter; The second normal stress at any point of the thermal barrier coating is determined using Formula 4: ,in, This represents the coefficient of thermal expansion of the thermal barrier coating. This represents the Young's modulus of the thermal barrier coating. This represents the temperature change value of the thermal barrier coating, where R represents the radius of curvature. This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. Indicates the second parameter; Determining the stress distribution of the thermal barrier coating system based on the first normal stress and the second normal stress includes: Solve equations three and four using equations five and six. Second parameter Formula 5: Formula Six: ,in, This indicates the temperature value of the curved substrate. This indicates the temperature value of the thermal barrier coating. Indicates the first normal stress. Indicates the second normal stress. This indicates the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating; According to the above and the second parameter Determine the stress distribution of the thermal barrier coating system.

2. The method according to claim 1, characterized in that, The mathematical geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system.

3. The method according to claim 2, characterized in that, The curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is: y=ax 2 ,in, a This indicates parameters related to the curve shape.

4. The method according to claim 1, characterized in that, The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined according to the curve equation, including: The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined using Formula 2: ,in, a Indicates parameters related to the curve shape. This represents the horizontal coordinate of any point within the thermal barrier coating system.

5. The method according to claim 1, characterized in that, The thermal barrier coating has a double ceramic layer structure, including i BC coating layer j YSZ coating and k The LZ coating layer, wherein the normal stress includes deposition stress and thermal mismatch stress, and the second normal stress is the... i Layer BC coating, the j YSZ coating layer, the k The sum of the deposition stresses of the LZ coating layers is superimposed on the above. i Layer BC coating, the j YSZ coating layer, the k The sum of thermal mismatch stresses of the LZ coating layers, i ≥1, j ≥1, k ≥1.

6. A device for determining the thermal stress distribution of a thermal barrier coating prepared on a curved substrate, characterized in that, include: A module is established to create the mathematical and geometric model corresponding to the thermal barrier coating system; The first determining module is used to determine the curve equation corresponding to the interface between the curved substrate and the thermal barrier coating based on the mathematical geometric model. The acquisition module is used to acquire the physical properties of the thermal barrier coating and the temperature change values ​​during the spraying process; The second determining module is used to determine the normal strain at any point in the thermal barrier coating system based on the curve equation, the physical properties of the thermal barrier coating, and the temperature change value. The third determining module is used to determine the first normal stress at any point on the curved substrate and the second normal stress at any point on the thermal barrier coating based on the normal strain and the physical properties of the thermal barrier coating. The fourth determining module is used to determine the stress distribution of the thermal barrier coating system based on the first normal stress and the second normal stress. The physical properties of the thermal barrier coating include the coefficient of thermal expansion α, and the temperature change value is... The second determining module is used for: The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined according to the curve equation. Based on the thermal expansion coefficient α and the temperature change value The radius of curvature R is used to determine the normal strain at any point in the thermal barrier coating system using Formula 1. Formula 1: ,in, This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. This represents the second parameter, where the first and second parameters are unknowns. The physical properties of the thermal barrier coating include Young's modulus. The third determining module is used for: The first normal stress at any point on the curved surface base is determined using Formula 3: ,in, This represents the coefficient of thermal expansion of the curved substrate. This represents the Young's modulus of the curved surface substrate. This represents the temperature change value of the curved substrate, where R represents the radius of curvature. This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. Indicates the second parameter; The second normal stress at any point of the thermal barrier coating is determined using Formula 4: ,in, This represents the coefficient of thermal expansion of the thermal barrier coating. This represents the Young's modulus of the thermal barrier coating. This represents the temperature change value of the thermal barrier coating, where R represents the radius of curvature. This represents the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating. Indicates the first parameter. Indicates the second parameter; The fourth determining module is used for: Solve equations three and four using equations five and six. Second parameter Formula 5: Formula Six: ,in, This indicates the temperature value of the curved substrate. This indicates the temperature value of the thermal barrier coating. Indicates the first normal stress. Indicates the second normal stress. This indicates the distance from the thermal barrier coating to the interface between the curved substrate and the thermal barrier coating; According to the above and the second parameter Determine the stress distribution of the thermal barrier coating system.

7. The apparatus according to claim 6, characterized in that, The mathematical geometric model uses the cross-section of the thermal barrier coating system as the calculation plane, the vertex of the interface between the curved substrate and the thermal barrier coating as the origin of the coordinate system, and the central axis of the thermal barrier coating system as the Y-axis of the coordinate system.

8. The apparatus according to claim 7, characterized in that, The curve equation corresponding to the interface between the curved substrate and the thermal barrier coating is: y=ax 2 ,in, a This indicates parameters related to the curve shape.

9. The apparatus according to claim 6, characterized in that, The second determining module is used for: The radius of curvature R of the interface between the curved substrate and the thermal barrier coating is determined using Formula 2: ,in, a Indicates parameters related to the curve shape. This represents the horizontal coordinate of any point within the thermal barrier coating system.

10. The apparatus according to claim 6, characterized in that, The thermal barrier coating has a double ceramic layer structure, including i BC coating layer j YSZ coating and k The LZ coating layer, wherein the normal stress includes deposition stress and thermal mismatch stress, and the second normal stress is the... i Layer BC coating, the j YSZ coating layer, the k The sum of the deposition stresses of the LZ coating layers is superimposed on the above. i Layer BC coating, the j YSZ coating layer, the k The sum of thermal mismatch stresses of the LZ coating layers, i ≥1, j ≥1, k ≥1.

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