Thin-wall casting shrinkage porosity control method based on machine learning and sequential solidification

Abstract

In order to improve the metallurgical quality of a thin-wall casting in the investment casting process, the invention provides a novel control method based on machine learning and a sequential solidification principle. The method comprises the steps that firstly, geometric structure parameters related to the solidification process are calculated on discretization representation of a casting model, and the geometric structure parameters comprise the distance from a local position to a casting head, the geometric modulus and the mold shell thickness; secondly, in combination with a numerical simulation result, a random forest algorithm is used for establishing a mapping model of geometric structure parameters and solidification time of the casting, and R2 on a verification set is 0.9974; based on the model, the gradient of a solidification curve on a geodesic path is quantitatively adjusted in combination with measures of local formwork thickness reduction and heat preservation cotton coating, and sequential solidification is achieved. And after optimization, the total shrinkage porosity volume of the casting is reduced to 24.78 mm < 3 > from 71.69 mm < 3 >, and is reduced by 65%. The effectiveness of the method is further verified through a pouring experiment, an efficient and quantitative solution is provided for shrinkage porosity control of the thin-wall complex casting, and a new thought is provided for intelligent control over investment casting defects.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of casting, in particular to a thin-walled casting shrinkage control method based on machine learning and sequential solidification, which is especially suitable for the casting process optimization of equiaxed crystal thin-walled castings of high-temperature alloys in the fields of aerospace and the like. BACKGROUND

[0002] Equiaxed crystal cast high-temperature alloys have the advantages of low manufacturing cost and excellent medium-low temperature mechanical properties, and are widely used in the fields of aerospace and the like. Lightweight structure of an aero-engine is a key approach to improve the thrust-to-weight ratio, reduce fuel consumption and resource utilization, which leads to an increasing demand for thin-walled castings in the industry. However, thin-walled castings obtained by conventional gravity pouring of the investment casting process are difficult to fill due to the thin end face wall thickness, which is affected by the Laplace force. In the pouring process, the shrinkage channel is narrow, and the solidification is insufficient, which is prone to cause cold shut, insufficient pouring and shrinkage porosity and other defects in the casting process, directly leading to the rejection of the castings and unable to use, which seriously damages the quality and the pass rate of the castings. Due to the structural characteristics of the thin-walled castings, the casting process has been a challenge for the industry for a long time.

[0003] Shrinkage is a common defect in equiaxed crystal investment casting, especially in thin-walled castings. As known, the shrinkage defect is generated in the solidification process of the metal liquid and is directly affected by the solidification sequence. Generally speaking, the directional solidification mode from bottom to top and from outside to inside is a guarantee for good casting quality. The casting process optimization based on the combination of numerical simulation and experimental design is a common method to eliminate shrinkage at present, however, this method has the disadvantages of long cycle and inability to quantitatively control. SUMMARY

[0004] In order to improve the metallurgical quality of thin-walled castings in the investment casting process, the present application proposes a new control method based on machine learning and the principle of sequential solidification. Firstly, the geometric structure parameters related to the solidification process are calculated on the discrete representation of the casting model, including the distance from the local position to the sprue, the geometric modulus and the shell thickness; secondly, combined with the numerical simulation results, a mapping model of the casting geometric structure parameters and the solidification time is established using the random forest algorithm, and the R 2 on the validation set is 0.9974. Based on the model, combined with the local shell thickness reduction and the insulation cotton covering measures, the slope of the solidification curve on the geodesic path is quantitatively adjusted to realize the sequential solidification. The total volume of shrinkage of the optimized castings is reduced from 71.69mm 3 to 24.78mm 3 , which is reduced by 65%. The pouring experiment further verifies the effectiveness of the proposed method, which not only provides an efficient and quantitative solution for the shrinkage control of thin-walled complex castings, but also provides a new idea for the intelligent control of investment casting defects.

[0005] The technical solutions of the present application to achieve the above-mentioned purposes include the following steps:

[0006] Step 1:

[0007] The discrete geometry parameters of the casting, including the pouring distance, the geometric modulus and the mold shell thickness, are calculated. For the purpose of calculation, the tetrahedral mesh of the casting is voxelized using the PyVista library, and the entire casting area is uniformly divided into hexahedral units. The geodesic distance is defined as the shortest path length between two points in the feature space, and the distance from the local position of the casting to the pouring riser (pouring distance) can be approximately measured by the geodesic distance. The geodesic distance field inside the casting is calculated using the heat method to approximately represent the distance from each discrete position to the surface of the pouring riser. In order to compare the solidification time of different positions in a single casting, the geometric modulus of any discrete position in the casting can be calculated using the following formula

[0008]

[0009] where N is the number of cooling directions, and in this paper N is 6, i.e. the normal direction of each surface of the hexahedron, d i is the distance between the mold shell along direction i.

[0010] Step 2:

[0011] A continuous numerical simulation of the equiaxed casting process is carried out, including the transfer of the preheated mold shell, the alloy filling and the solidification process. A three-dimensional geometric model of the complete casting system is established in UG software, which consists of the casting, the pouring cup, the sprue, the inner gate and the riser, etc. Different grid sizes are set for different regions of the geometric model according to the simulation accuracy requirements of different regions. The key parameters of ProCAST casting simulation are set, including the material type, the mold shell thickness h, the mold shell transfer time t tr , the pouring temperature T pr , the mold shell preheating temperature T po and the location of the insulation cotton covering, etc. The cooling to below the solidus temperature of the alloy is the calculation termination condition, and the numerical simulation of the pouring to the solidification stage of the thin-walled casting is completed, and the simulated solidification time ST of the casting required for building the mapping model is derived.

[0012] Step 3:

[0013] Based on the data obtained from Step 1 and Step 2, a mapping model of the geometric structure parameters and the solidification time is established, so as to realize the rapid prediction of the solidification process parameters. Based on the discrete geometric representation of a single splash plate casting, each voxel point is a sample, and the total amount is 42617. Each sample is composed of a feature vector and a label, the feature vector contains the geometric modulus, the pouring distance and the mold shell thickness information, and the label The sample set is constructed using the solidification time information obtained by numerical simulation. The data set is randomly divided into a training set and a validation set according to an 8:2 ratio. The training set is input into a random forest regression model for fitting to obtain model parameters. The validation set is used to evaluate the performance of the model.

[0014] Step 4:

[0015] The local solidification time of the casting is optimized to achieve sequential solidification. First, several key remote nodes of the sprue and runner are selected, and the solidification time curve on the measured path from different remote nodes to the sprue and runner is calculated. The local solidification time of the casting is controlled by reducing the local shell thickness and wrapping insulation cotton. Combined with the mapping model established in step 3, the slope of the flat region of the solidification time curve is quantitatively increased to avoid the occurrence of local simultaneous solidification.

[0016] The method of the present application has the following advantages: the method adopts a shrinkage control method based on machine learning and sequential solidification principles. First, the geometric discretization is used to introduce the geodesic distance to approximate the distance from the sprue and runner, and a random forest regression model containing the distance from the sprue and runner, the geometric modulus and the shell thickness is established, realizing high-precision prediction of the local solidification time. Second, the slope of the solidification time curve on the geodesic path is optimized by quantitative adjustment of the shell thickness and insulation cotton, and finally the sequential solidification of the casting is realized, realizing efficient and precise shrinkage defect suppression. The method is suitable for high-temperature alloy thin-walled casting process optimization in the fields of aerospace, etc. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flowchart of the shrinkage control method of the present application based on machine learning and sequential solidification principles;

[0018] Figure 2 is a schematic diagram of the discrete volume Laplacian operator of an embodiment of the present application;

[0019] Figure 3 is a schematic diagram of the local solidification time of an example casting of an embodiment of the present application;

[0020] Figure 4 is a scatter point density distribution diagram of the solidification time prediction results of an embodiment of the present application;

[0021] Figure 5 is a schematic diagram of the optimization region division of an embodiment of the present application;

[0022] Figure 6 is a comparison diagram before and after shrinkage optimization of an embodiment of the present application. DETAILED DESCRIPTION

[0023] In order to more clearly illustrate the specific embodiments of the present application, the present application is described in detail in conjunction with the drawings and specific embodiments. However, the scope of protection of the present application is not limited to the following examples. Obviously, the drawings described below are only part of the embodiments of the present application, and other drawings can also be obtained according to the present application without creative labor for ordinary researchers in the art.

[0024] Taking the optimization of the shrinkage defect of a certain type of splash plate as an example, the specific implementation process of the present application is as shown in Figure 1

[0025] Step 1:

[0026] The discrete geometric structure parameters of the casting, including the pouring distance, the geometric modulus and the mold shell thickness, are calculated. The tetrahedral mesh of the casting is voxelized using the PyVista library, and the entire casting area is uniformly divided into hexahedral units. The geodesic distance field inside the casting is calculated using the Crane heat method to approximate the distance from each discrete position to the pouring and riser surface.

[0027] First, time discretization, the heat conduction equation is discretized under a fixed time step, in order to ensure the numerical stability of the solution, the backward Euler method is used for iterative solution.

[0028] (I-tΔ)u t =u0 (2)

[0029] Where I is the unit matrix, L is the matrix form of the Laplacian operator, u t is the temperature field column vector at time t, and u0 is the initial temperature field column vector (the temperature of the pouring and riser surface vertex is set to 1, and the temperature of other vertices is set to 0).

[0030] Next, spatial discretization, the number of vertices of the computational domain tetrahedral mesh is |V|, and is an n-dimensional piecewise linear function on the tetrahedral mesh, and the discretization format of the Laplacian operator at vertex i is

[0031]

[0032] Where V i is one quarter of all tetrahedral volumes associated with vertex i, N(i) is the set of vertices adjacent to vertex i, for the kth tetrahedron T k (i,j,p,q) adjacent to edge (i,j), l k is the length of edge (p,q) opposite to edge (i,j), and θ k is the dihedral angle of edge (p,q), as shown in Figure 2 Therefore, formula (2) can be further represented as​

[0033] (I-tV -1 L c )u t =u0 (4)

[0034] where is a diagonal matrix containing the volume of the vertices, is the Laplacian matrix. From the temperature scalar field obtained by solving, the normalized temperature gradient vector g k in any tetrahedron is calculated. Finally, the geodesic distance field φ

[0035] L c φ=b (5)

[0036] where is the integrated divergence vector of the normalized gradient field. Finally, the geodesic distance field on the hexahedral element is obtained by interpolating the geodesic distance field of the tetrahedral vertices.

[0037] Step 2:

[0038] A three-dimensional geometric model containing the complete gating system is established in UG software, which consists of splash plate castings, sprue cups, straight runners, ingates, and risers, etc. According to the simulation accuracy requirements of different areas, when the surface mesh is divided, the gating system selects a grid size of 5mm, while the casting uses a more detailed 2mm. The Mesh module of the commercial finite element software ProCAST is used to complete the generation of the insulation cotton grid, with a thickness of 12mm, and the final calculation domain automatically generates a body grid. Set the simulation parameters: mold shell thickness h = 5mm, material type is sand_silica, mold shell transfer time t tr = 90s, pouring temperature T pr = 1580℃, mold shell preheating temperature T po = 1120℃. In the running parameter part, set the termination step to 200000 and the end termination temperature to 1200℃ in general. After completing the solidification simulation of the casting, export the solidification time ST of all nodes on the casting, and the result cloud map is shown in Figure 3 .

[0039] Step 3:

[0040] Figure 4 is the scatter plot density distribution of the validation set in the random forest model obtained by training the solidification time prediction. The determination coefficient R 2 is one of the model evaluation indicators, its value range is [0,1], the value is closer to 1, indicating that the model prediction effect is better, and its calculation formula is as follows

[0041]

[0042] Among them, y i is the true value, is the predicted value, is the mean of the true value, and N is the sample size.

[0043] Step 4:

[0044] When the number of sampled geodesic paths increases, nonlinear curve fitting is performed on each curve, and the intersection of the solidification curve and the fitting curve on each path forms a dividing line, such as Figure 5 As shown, the area above the dividing line requires delayed solidification, while the area below the dividing line requires accelerated solidification. Using the mapping model established in Step 3, we can quantitatively determine the required formwork thinning and insulation coating thickness at each location to achieve the target solidification time. The specific implementation method is as follows: The concave formwork at the large end corner is thinned from a maximum thickness of 7mm to 1.5mm, and the formwork at the large end face is coated with two layers of 6mm thick insulation.

[0045] Figure 6 The following is a comparison of the simulation results before and after shrinkage optimization. The solidification rate at the far end of the pouring riser is accelerated by thinning the mold shell, and the solidification rate near the pouring riser is slowed down by covering with thermal insulation cotton, thereby improving the local solidification order. The casting solidifies from the periphery to the center. The optimization scheme effectively eliminates the generation of isolated liquid phase areas at the corners of the large end, increases the solidification gradient of the large end face, and avoids the phenomenon of simultaneous solidification. The shrinkage defect volume is quantitatively analyzed using the built-in module of ProCAST. After optimization, the total volume of shrinkage defects in the final casting is reduced from 71.69mm 3 Reduced to 24.78mm 3 , a reduction of about 65% based on the original plan.

[0046] In summary, the present invention proposes a shrinkage control method based on machine learning and sequential solidification principles. Using machine learning methods, a mapping model between casting geometric parameters and local solidification time is established, successfully predicting the local solidification sequence of the casting. By optimizing the slope of the solidification time curve on the geodesic path, the solidification process is made closer to sequential solidification, effectively suppressing the occurrence of shrinkage defects. In addition, the method concept of the present invention can also be transferred to other parameter optimization areas, not limited to casting precision casting simulation and orthogonal experiments, and has high versatility and portability.

[0047] Of course, the above examples are merely examples of specific embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will appreciate that the present invention is susceptible to numerous modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for controlling shrinkage of thin-walled castings based on machine learning and sequential solidification, the method comprising the following steps: Step 1: Calculate the discrete geometric parameters of the casting, including the riser distance, geometric modulus and mold shell thickness. For calculation purposes, the PyVista library is used to voxelize the tetrahedral mesh of the casting, and the entire casting area is evenly divided into regular hexahedral units. The geodesic distance is defined as the shortest path length between two points in the feature space. The distance from the local position of the casting to the riser (riser distance) can be approximated by the geodesic distance. The geodesic distance field inside the casting is calculated using a thermal method to approximate the distance from each discrete position to the riser surface. In order to compare the solidification time of different positions of a single casting, the geometric modulus of any discrete position in the casting can be calculated using the following formula: Where N is the number of cooling directions. In order to balance the calculation efficiency and accuracy, N is taken as 6 in this paper, that is, the normal direction of each surface of the regular hexahedron, d i is the distance from the formwork along direction i; Step 2: Continuous numerical simulation of the equiaxed crystal casting process, including preheating mold transfer, alloy filling and solidification process. A three-dimensional geometric model of the complete casting system is established in UG software. The system consists of castings, pouring cups, sprues, ingates and risers. Different mesh sizes are set for different areas of the geometric model according to the simulation accuracy requirements of different areas. The key parameter settings of ProCAST casting simulation include material type, mold thickness h, mold transfer time t tr , pouring temperature T pr , mold shell preheating temperature T po The calculation termination condition is to cool the thin-walled casting to below the solidus temperature, complete the numerical simulation from pouring to solidification stage, and derive the casting simulation solidification time ST required for building the mapping model. Step 3: Based on the data obtained in Steps 1 and 2, a mapping model between geometric structure parameters and solidification time is established to achieve rapid prediction of solidification process parameters. Based on the discrete geometric representation of a single splash plate casting, each voxel point is a sample, with a total of 42617. Each sample consists of a feature vector and a label. Composition, feature vector Contains geometric modulus, pouring head distance and mold shell thickness information, label The dataset used in this paper is a collection of samples obtained from numerical simulations to determine the solidification time. The dataset was randomly divided into a training set and a validation set with an 8:2 ratio. The training set was input into a random forest regression model to fit the model parameters, and the validation set was used to evaluate the model's performance. Step 4: Optimize the local solidification time of the casting to achieve sequential solidification. First, select several key remote nodes of the riser and calculate the solidification time curves along the measurement path from different remote nodes to the riser. Local mold shell thickness reduction and insulation coating are used to control the local solidification time of the casting. Combined with the mapping model established in Step 3, the slope of the flat region of the solidification time curve is quantitatively increased to avoid local simultaneous solidification.

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