Design method for heat insulation performance of silicon carbide ceramic gradient TPMS structure

Abstract

The invention discloses a silicon carbide ceramic gradient TPMS structure heat insulation performance design method. The method comprises the steps that the volume fraction of a surface area of a TPMS structure is changed by adjusting a regulation and control parameter t; fitting the relationship between the volume fraction P and the change of the regulation and control parameter t; the structure is divided into m continuous layers in the heat transfer direction, porosity gradient distribution of each layer i is achieved by distributing different parameters ti, the porosity layer heat conductivity coefficients from the first layer to the mth layer are calculated, and the total heat conductivity coefficients of all layers on each plane perpendicular to the heat flow direction are overlapped; changing the volume fraction of any layer or changing multiple layers at the same time until the total heat conductivity coefficient meets the requirement. And through a structure correlation coefficient library and a universal volume fraction model, rapid parameterization design of various TPMS types is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of additive manufacturing and optimization design, and the present invention relates to a method for designing thermal insulation performance of a silicon carbide ceramic gradient TPMS structure. Background Art

[0002] SiC ceramics also have high strength, high hardness, low thermal expansion coefficient, excellent thermal shock resistance, oxidation resistance and corrosion resistance, making them an ideal material for manufacturing high-performance heat exchangers. At present, SiC-based ceramic plates are often used in complex operating environments, and their operating temperatures are usually between 600 and 1300°C. However, the SiC solid structure is heavy and large in volume, which reduces the overall heat dissipation efficiency. The thermal conductivity of SiC ceramics is higher but still does not reach the thermal conductivity of metals. In addition, the agglomeration problem or lattice defects of silicon carbide prevents the composite from achieving the required degree of sealing, resulting in its thermal conductivity far below its respective theoretical value.

[0003] In order to solve the above problems, some lattice structures such as the triply periodic minimum surface (TPMS) have structures with high symmetry and optimal physical properties. The TPMS structure can shorten the melting time of phase change materials, and the system has better heat transfer performance, and is widely used in the forming of ceramics such as silicon carbide. The uniform structure has a good effect on stable and uniform heat sources, but the heat dissipation characteristics are different under different heat source conditions. Hot spot heat dissipation in power integrated circuits has been widely studied for directional heat dissipation of hot spots. Therefore, a non-uniform structure TPMS is required. The heat dissipation design method for different heat source conditions is still unclear. The existing methods currently have problems such as single structure, low efficiency, and limited optimization dimension. Summary of the invention

[0004] The object of the present invention is to provide a method for designing the thermal insulation performance of a silicon carbide ceramic gradient TPMS structure, and to achieve rapid parameterized design of various TPMS types through a structure correlation coefficient library and a universal volume fraction model.

[0005] The technical solution to achieve the purpose of the present invention is: A method for designing thermal insulation performance of a silicon carbide ceramic gradient TPMS structure comprises the following steps: S01: By adjusting the control parameters Changing the volume fraction of the surface area of ​​the TPMS structure; S02: Fitting volume fraction and control parameters the relationship between changes in S03: Divide the structure into continuous Layer, each layer By assigning different parameters , realize the porosity gradient distribution, calculate the first layer to the The porosity of the layer is the thermal conductivity of the layer, which is the total thermal conductivity of all layers in each plane perpendicular to the direction of heat flow; S04: Change the volume fraction of any layer or multiple layers simultaneously until the total thermal conductivity meets the requirements.

[0006] In the preferred technical solution, step S01 further includes defining an implicit function of any TPMS structure, which is expressed as: ; In the formula, , , is the three-dimensional coordinate, is a periodic function of a specific TPMS type, is the unit cell size, To control the parameters; Defining Volume Fraction is the ratio of the solid area to the total volume of the unit cell: ; in, To control the parameters The corresponding volume of the entity.

[0007] In the preferred technical solution, in step S01, in a specific parameter range Internal volume fraction Expressed as a linear or piecewise linear relationship: In the formula, the coefficient and Determined by TPMS type, coefficient and Determination methods include: Select typical parameter values , ; The corresponding volume fraction is measured by finite element method or X-ray tomography , ; Fitting a linear equation , .

[0008] In the preferred technical solution, in step S03, the general formula Calculate the porosity of each layer and the equivalent thermal conductivity of each layer Calculated by the following formula: ;

[0009] represents the thermal conductivity of silicon carbide; The total equivalent thermal conductivity is: .

[0010] In the preferred technical solution, step S04 includes calling the coefficient according to the selected TPMS type , , the optimization goal is to minimize , maximize thermal shock resistance and obtain the gradient control parameters Distribute and export STL models.

[0011] The present invention also discloses an STL model obtained by using the above-mentioned silicon carbide ceramic gradient TPMS structure insulation performance design method, comprising the following steps: (a) Using a 3D printing device to shape silicon carbide ceramic slurry, the emitted ultraviolet light intensity is set to 20-30 mW / cm², the wavelength is 405 nm, and the exposure parameters are adjusted to a radiation intensity of 72 mW / cm², a sheet thickness of 50 μm, and an exposure time of 4-6 seconds; (b) After printing, the sample was immersed in an ultrasonic cleaner containing anhydrous ethanol for 2 min. (c) The sintering process heats the sample at a rate of 2 °C per minute until it reaches 300 °C and is kept at this temperature for 1 hour. Subsequently, it is further heated to 800 °C at a rate of 5 °C per minute and kept for another hour. The heating process continues at a rate of 2 °C per minute until it reaches 1700 °C. The sample is kept for 16 hours. Finally, the sample is cooled naturally to room temperature.

[0012] Compared with the prior art, the present invention has the following significant advantages: 1. Generalized volume fraction model: through structure correlation coefficient library and linear formula , realizing rapid parametric design of various TPMS types. Through technology integration and dimensional expansion, the present invention solves the core problems of single structure, low efficiency and limited optimization dimension in existing methods, and has significant application value in the fields of aerospace high-temperature insulation, nuclear reactor shielding structure, etc.

[0013] 2. Normalized parameter mapping: Normalize the parameters of different TPMS Map to a uniform interval (such as [-1,1]) to simplify cross-type comparison and optimization.

[0014] 3. Automated design process: Integrates numerical calibration, parameter allocation, and manufacturing constraint verification functions to support collaborative optimization of multiple types of TPMS. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1is a flow chart of the method for designing thermal insulation performance of the silicon carbide ceramic gradient TPMS structure of the present embodiment; Figure 2 Schematic diagram of the gradient structure of this embodiment; Figure 3 This is the thermal insulation performance of this embodiment at 800 degrees Celsius. DETAILED DESCRIPTION

[0016] The principle of the present invention is to realize rapid parametric design of various TPMS types through a structure correlation coefficient library and a universal volume fraction model. By precisely controlling the geometric parameters and porosity distribution of the TPMS structure, combined with multi-scale equivalent thermal conductivity calculation and optimization algorithms, directional optimization of thermal insulation performance is achieved.

[0017] Embodiment 1:

[0018] like Figure 1 As shown, a method for designing thermal insulation performance of a silicon carbide ceramic gradient TPMS structure comprises the following steps: S01: By adjusting the control parameters Changing the volume fraction of the surface area of ​​the TPMS structure; S02: Fitting volume fraction and control parameters the relationship between changes in S03: Divide the structure into continuous Layer, each layer By assigning different parameters , realize the porosity gradient distribution, calculate the first layer to the The porosity of the layer is the thermal conductivity of the layer, which is the total thermal conductivity of all layers in each plane perpendicular to the direction of heat flow; S04: Change the volume fraction of any layer or multiple layers simultaneously until the total thermal conductivity meets the requirements.

[0019] The specific instructions are as follows: 1. TPMS implicit function formula and volume fraction definition Any TPMS structure can be represented by the following implicit function: ; In the formula, is a periodic function of a specific TPMS type (such as Gyroid, Diamond, Primitive), is the unit cell size, is the control parameter.

[0020] Volume fraction Defined as the ratio of the solid area to the total volume of the unit cell: ;

[0021] in, For parameters The corresponding entity volume needs to be calibrated through numerical integration or experiments.

[0022] 2. Volume fraction and parameters The general relationship model For any TPMS structure, within a specific parameter range Inside, , To control the parameters The lower and upper limits of volume fraction It can be approximately expressed as a linear or piecewise linear relationship: ;

[0023] In the formula, the coefficient and Determined by the TPMS type, determined by the following steps: (1) Numerical calibration: Select typical parameter values , (like ); The corresponding volume fraction is measured by finite element method or X-ray tomography , ; Fitting a linear equation , .

[0024] The structural correlation coefficient library is as follows Table 1:

[0025] 3. Gradient porosity design and equivalent thermal conductivity calculation (1) Gradient parameter allocation: Divided along the heat transfer direction Layer, each layer is assigned parameters , through the general formula Calculate the porosity of each layer.

[0026] Example (Primitive structure, target gradient porosity 30% → 20%): Layer 1: t 1=0.8→ P 1 = −25 × 0.8 + 50 = 30%; Layer 2: t 2=1.0→ P 2=25%; Layer 3:t 3=1.2→ P 3=20%.

[0027] (2) Calculation of equivalent thermal conductivity: Equivalent thermal conductivity of each layer Calculated by the following formula: ;

[0028] The total equivalent thermal conductivity is superimposed by harmonic mean: ;

[0029] 4. Optimization algorithm and design verification (1) Multi-objective optimization framework: Design variables: Number of layers ,parameter Distribution, TPMS type selection; Constraints: manufacturing process limitations (e.g. minimum wall thickness ≥ 0.3 mm); Optimization goal: Minimize , maximizing thermal shock resistance.

[0030] The calculation of seismic resistance is based on the simplified formula ,in is the average porosity, is the thermal conductivity of silicon carbide matrix. The optimization goal is to minimize and maximize , through the weighted objective function Make multi-objective trade-offs (default weights , ). The optimization algorithm traverses the parameters of each layer Combined with the TPMS type, the Pareto optimal solution set is output for users to choose, ensuring a balance between thermal insulation performance and mechanical reliability.

[0031] (2) Automatic parameter calibration: Automatic parameter calibration is implemented in the Rhino Grasshopper plug-in: after the user selects the TPMS type from the drop-down menu, the plug-in automatically calls the coefficients from the pre-stored database , and parameter range; input the target porosity gradient (such as 30%→20%), and the system will calculate the Generate parameters for each layer and automatically check them Is it beyond the limit (as required by Gyroid) ); If the parameter exceeds the limit, it will prompt to adjust the target or switch the TPMS type. The final output is an STL model that meets the requirements of 3D printing, which can be directly imported into the printing equipment to achieve an integrated process from design to manufacturing.

[0032] In the Grasshopper plug-in of the universal design software Rhino, the coefficients are automatically called according to the selected TPMS type , , generate gradient key parameters Distribute and export STL models.

[0033] The TPMS structure correlation coefficient library contains three types of core data: 1.TPMS mathematical expression library: pre-store implicit functions of Gyroid, Primitive, Diamond and other structures; 2. Linear coefficient library: record a, b and valid parameter range in the volume fraction formula P=a⋅t+b corresponding to each type; 3. Manufacturing constraint library: define process restriction parameters such as minimum wall thickness and maximum number of layers.

[0034] After the user selects the TPMS type, the system automatically calls the corresponding data to avoid repeated modeling and calibration.

[0035] Through the structural correlation coefficient library and linear formula , to achieve rapid parameterized design of various TPMS types. Taking the Gyroid structure as an example, its implicit function is , calibrate the volume fraction through finite element simulation or experiment and control parameters The linear relationship (such as ). After the user selects the TPMS type, the system automatically calls the corresponding linear coefficient , , directly through The porosity of each layer is calculated, avoiding the tedious process of repeated calibration in traditional methods. This method shortens the parametric design time by more than 80% and is suitable for rapid switching and iterative optimization of various TPMS structures.

[0036] The parameters of different TPMS Map to a unified interval (such as [-1,1]) to simplify cross-type comparison and optimization. In order to achieve unified comparison and optimization of parameters of different TPMS types, the present invention proposes a normalized parameter mapping technology. Taking the Primitive structure as an example, its original parameter range is , through the linear formula Map it to the interval [-1,1]. After the optimization is completed, the inverse operation Restore to original parameter range. Definition is the original control parameter (i.e. the parameter in the TPMS implicit function ), is the normalized parameter (mapped to the interval [-1,1]). The two are converted to each other through linear transformation to ensure that the cross-type parameters are comparable. This method solves the problem of cross-type parameter scale differences. For example, After normalization, it can be directly optimized collaboratively with the Gyroid structure parameters.

[0037] Automated design process: Integrates numerical calibration, parameter allocation, and manufacturing constraint verification functions to support collaborative optimization of multiple types of TPMS. The automated design process integrates numerical calibration, parameter allocation, and manufacturing constraint verification to support collaborative optimization of multiple types of TPMS.

[0038] The specific process of collaborative optimization is as follows: Each layer divided along the heat transfer direction independently selects the TPMS type and assigns normalized parameters , For the The control parameters of the layer mapping to the unified interval; the total equivalent thermal conductivity and thermal shock resistance To optimize the target, the NSGA-II genetic algorithm is used for multi-objective optimization (NSGA-II (non-dominated sorting genetic algorithm II) is a multi-objective optimization algorithm that selects the Pareto optimal solution set through non-dominated sorting and crowding calculation, and is suitable for solving trade-off problems in complex design spaces.). During the optimization process, the system automatically verifies the minimum wall thickness (≥0.3 mm) and the porosity change rate of adjacent layers ( ) and other constraints, and adjust parameters in real time through voxel analysis to ensure the manufacturability of the structure. For example, in a five-layer gradient structure, Gyroid and Diamond types are mixed. After optimization, Reduced to 23.7 W / (m·K).

[0039] The specific implementation process is as follows: First, the geometric form of the TPMS structure is defined based on the implicit level set function. Taking the Schoen Gyroid structure as an example, its mathematical expression is: ; In the formula , , is the three-dimensional coordinate, is the unit cell size, By adjusting the parameters , the surface morphology of the TPMS structure can be changed, thereby controlling the volume fraction (i.e. relative density) of the solid area. Defined as the volume of the solid area Total volume of unit cell Ratio of: ;

[0040] Experiments show that for the Schoen Gyroid TPMS structure, when When the volume fraction With parameters Linear relationship: ;

[0041] For example, when hour, , corresponding to a semi-dense structure; when hour, , forming a high porosity skeleton. This linear relationship provides a direct parameterization basis for gradient porosity design.

[0042] Divide the structure into continuous Layers, each layer is assigned different parameters , to achieve a porosity gradient distribution. For example, when designing a five-layer gradient structure, the porosity of the middle layer is set to 30% (corresponding to ), the porosity of adjacent layers is 25% ( ) and 35% (=0.448), forming a decreasing sequence. The equivalent thermal conductivity of each layer By porosity Thermal conductivity of silicon carbide matrix (Take 120 W / (m·K)) and jointly determine the calculation formula: ;

[0043] For example, when the thermal conductivity of the three-layer structure is 72, 60, and 48 W / (m·K), the total equivalent thermal conductivity is , which is significantly lower than the homogeneous structure (60 W / (m·K)).

[0044] To verify the effectiveness of the design, the Diamond TPMS structure is taken as an example to set the target thermal conductivity The volume fraction formula is calibrated by experiment as follows: ( ), divided into 7 layers along the thickness direction, the porosity increases gradually from 18% to 66%. The total equivalent thermal conductivity is calculated , meeting the design requirements. The equivalent thermal conductivity of the homogeneous Diamond structure with the same porosity (18%~66%) is The gradient design of the present invention reduces the thermal conductivity by 37.9%, verifying that the gradient distribution significantly improves the thermal insulation performance.

[0045] According to the heat transfer characteristics of the gradient structure, the unit cell size is dynamically adjusted along the temperature change direction (such as the Z axis). Based on The layer cell size is change, is the reference temperature, is the total temperature difference (temperature difference from hot end to cold end), where is the coefficient of thermal expansion, is the local temperature. To ensure the continuity of the structure, the number of adjacent layer units Need to meet , ensuring seamless geometry when the unit cell size changes from 2 mm to 0.8 mm (compression ratio 60%). For example, in the 800°C insulation test, the equivalent thermal conductivity of the five-layer gradient structure was 23.7 W / (m·K), which was 52% lower than that of the homogeneous structure, verifying the effectiveness of the design method.

[0046] In another embodiment, a method for forming a silicon carbide ceramic gradient TPMS structure includes the following steps: (a) Silicon carbide ceramic slurry is formed using a 3D printing device (such as ADT-3D-ZP-Printer-Pro-192-50; Shenzhen Qiyu Technology Co., Ltd.). The 3D printing parameters are optimized based on the photocuring characteristics of the silicon carbide ceramic slurry: Through orthogonal experimental tests, it was found that when the UV light intensity is 20-30 mW / cm² and the exposure time is 4-6 seconds, the slurry curing depth and interlayer bonding strength reach the best balance (interlayer shear strength ≥ 15 MPa), avoiding defects caused by under-curing or over-curing. The optimal UV light intensity emitted by the device is 28 mW / cm² and the wavelength is 405 nm. The exposure parameters are adjusted to a radiation intensity of 72 mW / cm², a sheet thickness of 50 μm, and an exposure time of 5 seconds.

[0047] (b) After printing, the sample was immersed in an ultrasonic cleaner containing anhydrous ethanol for 2 min. The dimensional accuracy of the TPMS sample was 40 mm³.

[0048] (c) The sintering process heats the sample at a rate of 2 °C per minute until it reaches 300 °C and is kept at this temperature for 1 hour. Subsequently, it is further heated to 800 °C at a rate of 5 °C per minute and kept for another hour. The heating process continues at a rate of 2 °C per minute until it reaches 1700 °C, and the sample is kept for 16 hours. Finally, the sample is cooled naturally to room temperature.

[0049] The molding process of the present invention can be formed by conventional digital light processing, and has excellent and efficient heat dissipation after printing and sintering.

[0050] The variable density TPMS structure can increase the overall thermal resistance and improve the thermal insulation performance of the structure without changing the space occupied by the structure. This process achieves precise forming and design presentation.

[0051] Figure 2 , Figure 3 As shown in the figure, different heating sizes at the bottom (1.5 cm, 2 cm, 2.5 cm) will also lead to different heat dissipation effects. Figure 3 From the heating conditions shown in ac, it can be seen that the larger the hotspot size, the more consistent the heating curves of different structures, mainly because the larger hotspot is less affected by the pores. Regarding the upper surface temperature, when the heating size is 1.5 cm, the Schoen gyroid shows the best thermal insulation performance, which is stable at about 250°C, while the other two structures are stable at around 290°C ( Figure 3 d). When the heating size is 2 cm, Schoen gyroid has the worst thermal insulation performance, which is stable at around 350°C, followed by Neovius surface at 310°C and Schwarz diamond at 280°C ( Figure 3 e). In contrast, at a heating size of 2.5 cm, the thermal insulation properties of the three structures are comparable, with all structures being stable at approximately 335 °C ( Figure 3 f). Among them, the Schoenygroid changes most significantly with the hotspot size. In general, the overall temperature reduction of the insulation effect of the three structures exceeds 50%.

[0052] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure, characterized in that: The following steps are involved: S01: By adjusting the control parameters Changing the volume fraction of the surface area of ​​the TPMS structure; S02: Fitting volume fraction and control parameters the relationship between changes in S03: Divide the structure into continuous Layer, each layer By assigning different parameters , realize the porosity gradient distribution, calculate the first layer to the The porosity of the layer is the thermal conductivity of the layer, which is the total thermal conductivity of all layers in each plane perpendicular to the direction of heat flow; S04: Change the volume fraction of any layer or multiple layers simultaneously until the total thermal conductivity meets the requirements.

2. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 1, characterized in that: Step S01 also includes defining an implicit function of any TPMS structure, expressed as: ， In the formula, , , is the three-dimensional coordinate, is a periodic function of a specific TPMS type, is the unit cell size, To control the parameters; Defining Volume Fraction is the ratio of the solid area to the total volume of the unit cell: ， in, To control the parameters The corresponding volume of the entity.

3. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 1, characterized in that: In step S01, in a specific parameter range Inside, , To control the parameters The lower and upper limits of volume fraction Expressed as a linear or piecewise linear relationship: ， In the formula, the coefficient and Determined by TPMS type, coefficient and Methods for determination include: Select typical parameter values , ; The corresponding volume fraction is measured by finite element method or X-ray tomography , ; Fitting a linear equation , .

4. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 1, characterized in that: In step S03, the general formula Calculate the porosity of each layer and the equivalent thermal conductivity of each layer Calculated by the following formula: , represents the thermal conductivity of silicon carbide; The total equivalent thermal conductivity is: 。 5. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 4, characterized in that: Step S04 includes calling the coefficients according to the selected TPMS type , , the optimization goal is to minimize , maximize thermal shock resistance and obtain the gradient control parameters Distribute and export STL models.

6. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 5, characterized in that: Thermal shock resistance calculation formula ,in, is the average porosity, is the thermal conductivity of silicon carbide matrix; the optimization goal is to minimize and maximize , through the weighted objective function Make multi-objective trade-offs. , is the weight, and the optimization algorithm traverses the parameters of each layer Combined with the TPMS type, the optimal solution set is output.

7. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 5, characterized in that: Step S04 also includes setting the parameters of different TPMS Mapped to a uniform interval, the calculation of the normalized parameter is: , By inverse operation Restore to the original parameter range; in, is the original control parameter, is the normalized parameter.

8. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 7, characterized in that: Step S04 also includes multi-type TPMS collaborative optimization, and the specific method includes: independently selecting the TPMS type for each layer divided along the heat transfer direction and assigning normalized parameters; using the total equivalent thermal conductivity and thermal shock resistance To optimize the target, the NSGA-II genetic algorithm is used for multi-objective optimization. During the optimization process, the constraints of minimum wall thickness and porosity change rate of adjacent layers are verified, and the parameters are adjusted in real time through voxelized analysis to ensure the manufacturability of the structure.

9. The method for designing thermal insulation performance of silicon carbide ceramic gradient TPMS structure according to claim 5, characterized in that: Step S04 also includes dynamically adjusting the unit cell size along the temperature change direction according to the heat transfer characteristics of the gradient structure, using the reference size Based on The layer cell size is Changes, including is the reference temperature, is the total temperature difference, is the coefficient of thermal expansion, is the local temperature, the number of adjacent layer units Need to meet .

10. A method for forming a silicon carbide ceramic gradient TPMS structure, characterized in that: The STL model obtained by the method for designing the thermal insulation performance of the silicon carbide ceramic gradient TPMS structure according to any one of claims 1 to 5 comprises the following steps: (a) Using a 3D printing device to shape silicon carbide ceramic slurry, the emitted ultraviolet light intensity is set to 20-30 mW / cm², the wavelength is 405 nm, and the exposure parameters are adjusted to a radiation intensity of 72 mW / cm², a sheet thickness of 50 μm, and an exposure time of 4-6 seconds; (b) After printing, the sample was immersed in an ultrasonic cleaner containing anhydrous ethanol for 2 min. (c) The sintering process heats the sample at a rate of 2 °C per minute until it reaches 300 °C and is kept at this temperature for 1 hour. Subsequently, it is further heated to 800 °C at a rate of 5 °C per minute and kept for another hour. The heating process continues at a rate of 2 °C per minute until it reaches 1700 °C. The sample is kept for 16 hours. Finally, the sample is cooled naturally to room temperature.

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