Method for predicting permeability of 3D printing breathable steel based on data and physical coupling model

Abstract

The invention discloses a method for predicting the permeability of 3D printing breathable steel based on a data and physical coupling model, and belongs to the technical field of 3D printing. The method for predicting the permeability of the 3D printing breathable steel comprises the following steps: carrying out experimental design on 3D printing process parameters; obtaining experimental data under the corresponding process parameters; constructing and training a 3D printing permeability prediction model; and permeability prediction is conducted on different technological parameters of 3D printing, so that the 3D printing breathable steel component with the target permeability is obtained. According to the method, the permeability under the corresponding parameters can be accurately predicted according to the process parameter range on the premise that a large number of experiments are not needed, the repeated debugging process in a traditional experiment is avoided, the production efficiency is remarkably improved, and the manufacturing cost is effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of 3D printing, and in particular to the fabrication of breathable steel components with controllable permeability using 3D printing technology. Background Technology

[0002] 3D printing technology is applicable to the fabrication of various types of metal structures, and has received increasing attention, especially in the fabrication of porous structures. Porous structures are multifunctional materials with interconnected pores formed by rods or curved surfaces as supports. They have characteristics such as low density, high specific strength, good heat dissipation and wave absorption, and have extremely high application value in aerospace, filtration and medical implants. Although 3D printing technology can theoretically achieve fine porous structures through high-resolution modeling and printing, there are still many challenges in actual manufacturing: (1) the pore size is limited by the machine resolution, and it is difficult to print small pores or complex three-dimensional features; (2) it requires a three-dimensional feature model of the entire porous structure, and when the model is too large or the structure is fine, it will increase the amount of data processing on the computer. In contrast, by adjusting the process parameters so that complete melting does not occur during the layer-by-layer forming process, the formation, distribution and connectivity of pores can be controlled to a certain extent, and finally a regular and controllable porous structure can be obtained. This method does not require detailed three-dimensional modeling of porous parts, which greatly reduces the computational cost. Therefore, the fabrication of porous structures using process control is a problem worthy of attention.

[0003] However, current methods for preparing porous structures using process control are still limited to establishing empirical correlations and verifying process feasibility, and the design process remains highly dependent on experimental trial and error. Although some studies have adopted forward exploration, establishing empirical parameter-performance relationships through a limited number (6-12 groups) of experiments, while helpful in understanding the influence of process parameters on permeability and providing important scientific observations and foundations, they are mainly limited to regular forward mapping. In summary, traditional 3D printing methods for preparing permeable steel are insufficient to meet the demands of rapid product iteration and market-oriented production, hindering the practical application and widespread adoption of 3D-printed permeable steel technology. To address this challenge, this invention proposes a data and physics-coupled model framework that transforms process design from a "passive response" to an "active prediction," fundamentally reducing reliance on traditional trial-and-error experiments and fully demonstrating the method's innovation and engineering application potential. It transforms the iterative optimization model of traditional additive manufacturing, which relies on "guessing parameters → manufacturing → measuring performance → adjusting parameters," into a predictive design model of "setting process parameters → model predicting target performance → manufacturing." It significantly reduces the amount of experimentation and parameter adjustments required by traditional trial and error, thereby saving time and economic costs. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model. This method predicts the permeability under corresponding process parameters, and can be applied to the industrial fabrication of 3D-printed permeable steel. The method provided by this invention can construct the relationship between process parameters, porosity, and permeability, achieving accurate prediction of permeability under corresponding parameters based on a range of process parameters without requiring extensive experiments. This solves the current problem of production processes that heavily rely on experimental trial-and-error methods for manufacturing permeable steel. Using the method of this invention, process parameters that are compatible with mechanical properties and permeability were predicted. When the porosity is in the range of 17.71% to 22.33%, good compatibility between mechanical properties and permeability is observed. In particular, at a laser power of 350W and a scanning speed of 1800 / s, a yield strength of 196.77MPa can be achieved while ensuring low-to-high permeability (bubbling pressure of 2.16kPa).

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention provides a method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model, comprising the following steps:

[0007] S1. Design of process parameters for 3D printing breathable steel: Based on the air permeability index of 3D printed breathable steel, the scanning rate and laser power are adjusted, and the process parameters for 3D printed breathable steel are designed according to the DOE experimental design method.

[0008] S2. Obtain experimental data under the corresponding process parameters: 3D print permeable steel is manufactured according to the 3D printing experimental design table. The porosity data of the permeable steel under the corresponding process parameters is obtained by metallographic analysis and recorded as y; and the permeability data is determined by directly measuring the relationship between fluid flow rate and pressure drop and recorded as K.

[0009] S3. Constructing a data and physical coupling model: The model is trained based on the dataset (each set of process parameters corresponds to a set of porosity data and permeability data). The model construction process includes data-driven and physical simulation.

[0010] S4. Model Training: Train the penetration rate prediction model based on the experimental dataset in S2;

[0011] S5. Make predictions using the trained model: Based on the model trained in S4, input the 3D printing process parameters and output the predicted 3D printing penetration rate.

[0012] The above-described construction of the data and physical coupling model includes the following steps:

[0013] (1) The relationship between process parameters and porosity is determined by constructing a multilayer feedforward neural network.

[0014] The neural network demonstrated better fitting ability in data regression prediction. The input layer of the neural network had two nodes, representing scanning speed and laser power, while the output layer had one node, representing porosity. To improve the efficiency and stability of the training process, all data was standardized using the mean-standard deviation normalization method before being input into the network. Different numbers of hidden layer nodes were tested to determine the optimal ANN architecture providing the best performance. Furthermore, an early stopping strategy was used to further optimize the training process, allowing training to stop if the error did not improve after a maximum of six validation iterations. 80% of the data was used for training, and the remaining 20% ​​was used to validate the porosity prediction. Finally, a process parameter-porosity relationship was constructed; given process parameters, the porosity was predicted for those parameters.

[0015] (2) The relationship between porosity and permeability was determined through physical fluid simulation.

[0016] To investigate the internal flow characteristics of porous structures, 316L stainless steel was used as the material. First, a systematic mesh dependence study was conducted on the porous structure model to ensure the accuracy and reliability of the finite element analysis results. Considering that porous structures typically contain a large number of micron-sized pores in actual fabrication processes, and that the complexity of the microstructure in large-scale components greatly increases the computational complexity and workload, appropriate simplification is essential. Analysis of the pore morphology of a 0-degree phase angle porous structure revealed that it possesses truss-like structural characteristics, exhibiting periodicity and regularity. This structural feature allows for effective simulation using a simplified model in finite element analysis, thereby significantly reducing computational costs while maintaining the accuracy of the results. Therefore, to improve simulation efficiency and operability, this invention selected a simplified 3×3×3 element structure model.

[0017] In the FEA simulation, the representative unit cell geometry is used as the control basis. The key geometric dimensions of the melt channel (the diameter of the connecting rod in the model) are adjusted to simulate the changes in pore structure under different process parameters. For each target porosity, a geometric model matching that porosity is generated to ensure that the simplified model is consistent with the porosity of the experimental sample, and it is used for subsequent FEA calculations.

[0018] This adjustment strategy is based on an understanding of the porosity formation mechanism in the SLM process, thereby determining and adjusting the molten pool size. Metallographic observation and single-pass molten pool experiments confirmed that within the process parameter range where unfused (LOF) defects dominate, porosity formation and size are primarily controlled by the relative size (overlap ratio H / W) of the molten pool width W (determined by process parameters) and the scanning distance H. Single-pass experiments further verified this pattern: with a fixed scanning distance H, reducing the molten pool width W, i.e., decreasing the overlap ratio, increases the size of the unfused gap between adjacent molten pools (i.e., LOF-type porosity), and vice versa. Therefore, controlling the relative relationship between the molten pool width W and the scanning distance H is the core physical mechanism for controlling porosity size and overall porosity. Specifically, for each set of process parameters, the overall porosity is first obtained through experimental measurement. Then, in a 3×3×3 unit cell model, the model porosity is adjusted to achieve the target porosity by adjusting the molten pool geometry (diameter of the connecting rod), thus realizing the correspondence between the experiment and the simulation. By adjusting this geometric model, we indirectly reproduced the porosity changes caused by altering P and V (and thus the overlap of the weld width W relative to the fixed H) in the actual process during FEA simulation.

[0019] In summary, we adjusted the rod diameter in the simplified unit cell model to ensure its porosity aligns with experimental measurements under different process parameters. This adjustment strategy, guided by the core mechanism of molten pool overlap (W vs. H relationship) controlling pore formation in the SLM process, effectively integrates the influence of process parameters on pore properties into structure-based FEA simulations. Ultimately, we constructed a porosity-permeability relationship, built a predicted pore structure, and predicted the permeability at the corresponding porosity. Attached Figure Description

[0020] To more clearly illustrate the technical solution and specific embodiments of the present invention, the accompanying drawings used will be briefly described below.

[0021] Figure 1 This is a flowchart of a method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model, as described in this invention.

[0022] Figure 2 This refers to the FEA simulation based on a geometric structure model in the embodiment of the method described in this invention for 3D printing of breathable steel.

[0023] Figure 3 These are the predicted and actual results of the 3D printing porosity in the embodiment of the method described in this invention for 3D printing of breathable steel.

[0024] Figure 4 These are the predicted and actual results of the 3D printing permeability in the embodiment of the method described in this invention for 3D printing of breathable steel.

[0025] Figure 5 In the embodiment of the present invention, the method described herein uses the established predictive model to design and manufacture irregularly shaped parts with breathable areas. Detailed Implementation

[0026] The present invention will now be described in detail with reference to specific embodiments. The description in this section is merely exemplary and explanatory, and not all of the embodiments, and should not be construed as limiting the scope of protection of the present invention.

[0027] Implementation Case 1

[0028] This invention provides a method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model. The specific implementation steps are as follows:

[0029] Step 1: Design 25 sets of orthogonal process parameters for 3D printing of 316L stainless steel material, determine the printing layer thickness as 0.04, the scanning spacing as 0.2, the scanning strategy as 90-degree rotation, and the laser power range as 150-350W and the scanning speed as 1000mm / s-1800mm / s.

[0030] The second step involves preparing 3D-printed breathable steel according to the design parameters, and grinding the metallographic sample to P3000 ISO with SiC sandpaper for OM observation. The porosity is calculated using the metallographic method, and the porosity value is obtained by Image Pro Plus.

[0031] Step 3: This model employs a multi-layer feedforward neural network architecture, containing two input nodes (scanning speed and laser power) and one output node (porosity). To improve training efficiency and stability, all data is standardized using mean-standard deviation normalization before being input into the network. The normalized input and output variables are represented as follows: y norm The calculation formula is as follows:

[0032]

[0033] To determine the optimal artificial neural network (ANN) architecture, the study tested different numbers of hidden nodes. The final configuration consisted of two hidden layers: the first layer had 15 neurons, and the second layer had 10 neurons. The model used the rectified linear unit (ReLU) as the activation function and was trained using the Levenberg-Marquardt (LM) algorithm. To prevent overfitting, an L2 regularization term with a coefficient of 0.1 was added during training. Furthermore, an early stopping mechanism was implemented to optimize the training process, allowing training to stop if the validation error did not improve after a maximum of six iterations. The dataset was divided into 80% for training and 20% for validating porosity predictions. After training, the model was evaluated using a standardized test set and measured by mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). 2 The performance was calculated using the mean squared error (MAE), root mean squared error (RMSE), and correlation coefficient squared (R²) to evaluate the model's fit. The results showed that as the number of training steps increased, the prediction performance gradually approached its optimal value, with an MAE of 0.1142, an RMSE of 0.1276, and an R² of 0.1276. 2 The MSE reached 0.9822. By the 8th iteration, the training error was below the optimal value, and the corresponding prediction error gradually approached the optimal value. The porosity values ​​under the corresponding process parameters were predicted and compared with the actual porosity (see...). Figure 3 )

[0034] Step 4: Based on the pore morphology and its truss-like structural characteristics, a 3×3×3 element structural model was constructed for finite element analysis. Considering that porous structures typically contain a large number of micron-sized pores in actual fabrication processes, and that the complexity of the microstructure in large-scale components greatly increases the computational complexity and workload, appropriate simplification is essential. Analysis of the pore morphology of the 0-degree phase angle porous structure revealed its truss-like structural characteristics, exhibiting periodicity and regularity. This structural feature allows for effective simulation using a simplified model in finite element analysis, significantly reducing computational costs while maintaining accuracy. Therefore, to improve simulation efficiency and operability, this study selected a simplified 3×3×3 element structural model for analysis.

[0035] The FEA model developed in this study is primarily a simulation based on a geometric structure model. Using NTopology software, a geometric model with corresponding porosity is constructed. The changes in pore structure under different process conditions are simulated by adjusting the diameter of the connecting struts. This adjustment strategy is based on a fundamental understanding of the pore formation mechanism during selective laser melting (SLM). Specifically, for each set of process parameters (P, V), we first experimentally measure the total porosity y, and then adjust the diameter of the struts in a 3×3×3 unit cell model to match its porosity with the target porosity y, thus establishing an effective correspondence between experimental and simulated data. Through this geometric model adjustment method, we indirectly reproduce in FEA simulation the porosity changes caused by the relative changes in the melt pool width W and scanning spacing H due to process parameters (see...). Figure 2 ).

[0036] To investigate the internal flow characteristics of porous structures, 316L stainless steel was used as the material. First, a systematic mesh dependency study was conducted on the porous structure model to ensure the accuracy and reliability of the finite element analysis results. Specifically, two representative geometric models with porosities of approximately 12.5% ​​and 28% were selected, and a series of meshes with varying numbers of elements were generated, ranging from approximately 14,000 to 208,000. As the mesh density increased, the calculated permeability values ​​tended to converge. Specifically, for the model with a porosity of 12.5%, the permeability change was less than 1% when the number of elements exceeded approximately 63,000. Similarly, for the model with a porosity of 28%, convergence was also achieved when the mesh contained more than 76,000 elements, and the permeability change also decreased to below 1%. Considering both convergence behavior and computational efficiency, a mesh containing approximately 78,000 elements was ultimately selected and uniformly applied to all finite element analysis simulations in this study. In the numerical simulation, the computational domain was discretized using a three-dimensional hybrid mesh, containing approximately 76,800 volume elements. These volume elements are primarily composed of tetrahedral elements, with prism elements strategically deployed in the boundary layer region to improve resolution. Additionally, approximately 19,900 face elements, including triangular and quadrilateral elements, were generated.

[0037] Predict the Reynolds number using the formula: Where ρ represents the fluid density (kg / m³), μ represents the fluid viscosity (Pa·s), u represents the fluid velocity (m / s), and L represents the side length of the cross-section (m). Here, water is chosen as the fluid, with a density ρ = 1000 kg / m³ and a viscosity μ = 10. -3Pa·s yields Re = 0.01, therefore the peristaltic flow physics field is chosen for simulation calculations. In the "Peristaltic Flow" (SPF) physics field interface, both the velocity and pressure fields are linearly interpolated (P1+P1). This choice aims to strike a balance between computational efficiency and accuracy under the constraints of fine meshes and complex geometries. Mesh quality is quantitatively evaluated using key indicators. The average skewness of triangular face elements is approximately 0.797, and the average element growth rate of surface triangles is 0.944. These values, along with the overall element shape quality, are within acceptable ranges, ensuring the reliability of subsequent finite element analysis results. In finite element simulations, porosity is defined as the pore space volume V. fluid Total volume V tot The proportion is calculated using the following formula: Used in fluid simulations to calculate the porosity of geometric models.

[0038] Velocity vector u and permeability κ (m) 2 The relationship is in The pressure gradient is approximated here by dividing the pressure difference Δp between the inlet and outlet by the side length L, and the outlet velocity u is used as the approximation. out The flow direction replaces the velocity vector u, therefore the permeability calculation formula is: Used in fluid simulation to determine the permeability of the geometric model. The relationship between porosity and permeability is determined based on the porosity and permeability calculation formulas above. Step 5: Directly measure the fluid flow rate and pressure drop on the permeable steel, obtain the actual permeability data from the relationship between fluid flow rate and pressure drop, and compare it with the predicted permeability (see...). Figure 4 ).

[0039] Step 6: Using the established predictive model, the design was carried out in sections based on the design parameters of different areas, ultimately producing irregularly shaped parts with breathable designated areas (see...). Figure 5 ).

Claims

1. A method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model, characterized in that... Includes the following steps: S1. Based on the permeability index of 3D printed breathable steel, design the process parameters for 3D printed breathable steel, and adjust the scanning rate and laser power as x1 and x2 respectively. S2. Obtain experimental data under the corresponding process parameters: 3D print permeable steel according to the 3D printing experimental design table, obtain porosity data of the permeable steel under the corresponding process parameters by metallographic analysis, and record it as y; and determine the permeability data by directly measuring the relationship between fluid flow rate and pressure drop, and record it as κ. S3. Constructing a data and physical coupling model: Based on the dataset, i.e., each set of process parameters corresponds to a set of porosity data and permeability data, the model is trained. The model construction process includes data-driven and physical simulation. The relationship between S301, process parameters, and porosity is determined by constructing a multilayer feedforward neural network; A multi-layer feedforward neural network architecture is adopted, containing two input nodes (scanning speed and laser power) and one output node (porosity). All data are standardized using the mean-standard deviation normalization method before being input into the network. The normalized input and output variables are represented as follows: y norm The calculation formula is as follows: The artificial neural network architecture is configured with two hidden layers: the first layer has 15 neurons and the second layer has 10 neurons; the model uses the rectified linear unit (ReLU) as the activation function and is trained using the Levenberg-Marquardt (LM) algorithm; An L2 regularization term with a coefficient of 0.1 was added during training; the dataset was divided into two parts: one for training and the other for validating porosity predictions. The relationship between S302, porosity, and permeability was determined through physical fluid simulation. We used NTopology software to construct a geometric model of the corresponding porosity, and simulated the changes in pore structure under different process conditions by adjusting the diameter of the connecting pillars. Specifically, for each set of process parameters (P, V), we first measured the total porosity y experimentally, and then adjusted the diameter of the pillars in a 3×3×3 unit cell model to match its porosity with the target porosity y. For the porous structure model, a mesh containing 78,000 elements was selected. In the numerical simulation, the computational domain was discretized using a three-dimensional hybrid mesh. The simulation calculation uses a peristaltic flow physics field; in the "peristaltic flow" (SPF) physics field interface, both the velocity and pressure fields are linearly interpolated; in the finite element simulation, porosity is defined as the pore space volume V. fluid Total volume V tot The proportion is calculated using the following formula: Used in fluid simulations to calculate the porosity of geometric models; Velocity vector u and permeability κ (m) 2 The relationship is in The pressure gradient is approximated here by dividing the pressure difference Δp between the inlet and outlet by the side length L, and the outlet velocity u is used as the approximation. out The flow direction replaces the velocity vector u, therefore the permeability calculation formula is: Used in fluid simulation to determine the permeability of geometric models; the relationship between porosity and permeability is determined based on the above porosity and permeability calculation formulas; S4. Model Training: Train the penetration rate prediction model based on the experimental dataset; S5. Prediction using the trained model: Based on the model trained in S4, input the 3D printing process parameters and output the predicted 3D printing penetration rate under the corresponding process parameters.

2. The method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model according to claim 1, characterized in that, The method was applied to the preparation of permeable steel by selective laser melting; process parameters including scanning speed and laser power were set; the data range and number of levels for each process parameter were set; and an orthogonal design method was used to set up the experimental design table for 3D printing based on the number of process parameters and the number of levels corresponding to each process parameter.

3. The method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model according to claim 1, characterized in that, The complex end-to-end relationship between "process parameters and permeability" is decomposed into two sub-problems. The first sub-problem is the influence of process parameters on key microstructural features, which is mainly reflected in porosity in this study. The second sub-problem is the influence of microstructural features, i.e., porosity, on macroscopic performance, i.e., permeability.

4. The method for predicting the permeability of 3D-printed permeable steel based on a data and physical coupling model according to claim 1, characterized in that, There is a significant inverse relationship between energy density and permeation performance; the optimized process parameters are suitable when the energy density is between 22.32 and 26.79 J / cm³. 2 Within this range, when the porosity is between 17.71% and 22.33%, the foaming pressure and mechanical properties show good compatibility.

Images