A machining deformation prediction method of blank stress and cutting stress coupling mapping

Abstract

The present application belongs to the technical field of cutting deformation prediction, and proposes a machining deformation prediction method of blank stress and cutting stress coupling mapping, including the following steps: 1. Establish a finite element model, and obtain the blank stress information, the integral point coordinates of the blank model and the part model, the element and node information, and the machining area information; 2. Establish the element mapping relationship between the blank model and the part model, solve the local coordinates of each point in the corresponding blank element, interpolate the blank residual stress according to the local coordinates, and obtain the blank stress physical field quantity mapped to the part model; 3. Train a lightweight data-driven prediction model to predict the machining stress field introduced by cutting; 4. Apply the mapped blank stress and the predicted machining stress to the part model, and automatically release the applied stress through numerical calculation to obtain the deformation prediction result of the part. The present application improves the overall calculation efficiency, shortens the prediction time, and improves the prediction accuracy.

Description

Technical Field

[0001] This invention relates to a method for predicting deformation during the machining of metal casting blanks, belonging to the field of cutting deformation prediction technology. Background Technology

[0002] In the aerospace and defense fields, lightweight, high-strength materials such as aluminum alloys are increasingly used to meet the demands for larger and more integrated structural components in next-generation rockets, aircraft, and other equipment. These materials are lightweight, have high specific strength, and good corrosion resistance, making them suitable for manufacturing critical components such as aircraft fuselages and missile casings. Casting processes can efficiently form complex, large, thin-walled structures, reducing weight while ensuring structural integrity under extreme conditions; therefore, casting technology is widely used in large, complex aluminum alloy structural components. However, the thermal and mechanical stresses generated during casting make parts prone to deformation during subsequent processing, leading to dimensional deviations or even part scrap, seriously affecting manufacturing quality and efficiency.

[0003] Machining deformation of large-sized cast aluminum alloys directly affects the quality, cost, and reliability of manufactured components. These parts often exhibit high material removal rates, and the low stiffness of the material makes them more susceptible to deformation. Accurate deformation prediction is a prerequisite for implementing control strategies, but it is constrained by the coupled effects of multiple factors: casting residual stress is released non-uniformly during machining; cutting forces and cutting heat lead to elasto-plastic deformation and localized thermal stress; and workpiece geometry and fixture constraints further influence stiffness distribution and stress state. The complex interactions among these factors pose a significant challenge to the accuracy of deformation prediction.

[0004] Current research on deformation during aluminum casting machining primarily focuses on pre-stretched plates, with insufficient systematic research on as-cast aluminum alloys and complex components. Existing prediction methods mainly fall into three categories: numerical simulation, analytical models, and data-driven approaches. The finite element method predicts deformation by integrating residual stress and cutting loads, but relies on a consistent finite element model; analytical models, due to oversimplification, struggle to capture the multi-field coupling effects in actual machining; machine learning methods, while capable of rapid approximate predictions, are limited by data quality and model generalization ability. Overall, existing methods still face significant limitations in terms of applicability, accuracy, and practical deployment. Summary of the Invention

[0005] In view of this, in order to solve the problems of existing cutting deformation prediction technology, this invention proposes a machining deformation prediction method based on the coupled mapping of blank stress and cutting stress, which can effectively and accurately predict machining deformation. It is particularly suitable for milling of large and complex aluminum alloys.

[0006] The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress of the present invention includes the following steps:

[0007] Step 1: Using the stress of the hot-worked metal blank as the initial stress, the metal blank as the blank model, and the final part after machining as the part model, establish a finite element model, and obtain the blank stress information, the integral point coordinates, element and node information, and machining area information of the blank model and the part model.

[0008] Integration points are specific locations chosen within an element to numerically approximate the integrals within that element. In finite element analysis, it is often necessary to numerically solve for the integrals within the element, such as calculating the element's stiffness matrix and load vector. To perform integral approximation, a set of specific locations within the element is typically selected as integration points, and numerical integration is performed at these points. By performing weighted summations at these integration points, the integral results within the element can be approximately calculated, thus obtaining the element's stiffness matrix and load vector, and subsequently, the stress and deformation information can be determined.

[0009] The core idea of ​​finite element analysis is to decompose a complex, physically inhomogeneous model into several simple, regular, and interconnected "discrete bodies," namely finite element elements, also known as units. In a three-dimensional model, units are often tetrahedral or hexahedral, and the vertices of an element are called nodes, such as the five corners of a tetrahedron (triangular pyramid) and the eight corners of a hexahedron (cube). In this patent, the blank model corresponds to blank elements, and the blank elements correspond to blank nodes; the part model corresponds to part elements, and the part elements correspond to part nodes. The information for blank nodes and part nodes refers to the node's coordinate number.

[0010] Step 2: Based on the element and node information of the part model obtained in Step 1, establish the element mapping relationship between the blank model and the part model, solve the local coordinates of each node in the corresponding blank element, interpolate the blank stress according to the local coordinates, and obtain the blank stress physical field quantity mapped to the part model.

[0011] Step 3: Construct a dataset using data obtained from finite element simulation and experiments, train a lightweight data-driven prediction model to predict the machining stress field introduced by cutting, and obtain the machining stress field of each machining area;

[0012] To address the correlation between machining parameters and additional stress, a lightweight process parameter-machining stress prediction model is constructed. The exponentially decaying cosine function (EDC) is preferred to characterize the cutting parameters and deformation behavior, combined with Levenberg-Warshall equations. Marquardt (LM) nonlinear least squares fitting and Gaussian process regression (GPR) are used to jointly model the additional stress in each processing area.

[0013] Step 4: Based on the stress selection method, apply the mapped blank stress physical field obtained in Step 2 and the machining stress field predicted in Step 3 to the part model, and call the finite element solver to calculate the stress physical field release process to obtain the machining deformation prediction result at the end of machining.

[0014] Each step is further defined as follows.

[0015] The specific process of establishing the finite element model in step 1 is to import the part model into the finite element software, set the material properties and constraints, and create a new static general analysis step in which no force or displacement is applied; after completing the property settings, the model is divided into elements and an inp file is generated, which is the finite element part model carrier.

[0016] The process of obtaining blank stress information in step 1 is to export the blank stress field, i.e. blank stress information, from the post-processing file containing blank stress field after thermal processing simulation by calling the Abaqus secondary development interface.

[0017] In step 1, the integral point coordinates, element and node information of the part model are obtained by setting the attributes of the original .inp file using a Python script, submitting the .inp file to the Abaqus solver for calculation using the command line, generating a post-processing file, and then calling the Abaqus secondary development interface to export the integral point coordinates, element and node information from the post-processing file and store it in a file in a specified format. The machining area information is obtained by automatically traversing and reading it using a Python script to generate a file containing the machining area name and the elements contained in the machining area, i.e., the machining area information file.

[0018] In step 2, the unit mapping relationship between the blank model and the part model is established by using the volume method in the matrix operator method. If a point is contained in a unit, then the sum of the volumes of the tetrahedron formed by the point and the various surfaces of the unit is equal to the volume of the unit; otherwise, the point is outside the unit.

[0019] The specific process in step 2 of interpolating the residual stress of the blank based on local coordinates to obtain the physical field quantity of the blank stress mapped to the part model is as follows:

[0020] Based on the mapping relationship, the local coordinates of the nodes in the element are solved using the Newton-Raphson method, and the physical field quantities of the part element are obtained by combining local coordinate interpolation. For a hexahedral part element, the process of determining the local coordinates of the nodes in the element is as follows: First, the local coordinates of the part nodes are determined using the following formula:

[0021] ,

[0022] in: For the coordinates of the part nodes, The coordinates of the 8 nodes of the blank element hexahedron. Let be the shape function of the blank element. Since this system of equations is nonlinear, it must be linearized. After linearization, the following formula is obtained:

[0023] ,

[0024] Then, the Newton-Raphson method is used for iterative solution to obtain the local coordinates of the component nodes, and the stress field of the component nodes is obtained using the following formula:

[0025]

[0026] Based on the stress field at the nodal points of the component, the physical field quantities of the component elements are obtained using the following formula:

[0027]

[0028] in This represents the stress field quantity at the node of the component. For the stress field quantity of the component unit, m This represents the number of component nodes. Let i represent the equivalent force field of the i-th element.

[0029] The process of training the lightweight data-driven prediction model in step 3 involves using cutting parameters as input, EDC coefficients as intermediate representations, and leveraging Levenberg-Warshall technology. The Marquardt (LM) algorithm is used to perform nonlinear least squares fitting to obtain the EDC coefficients, and Gaussian process regression (GPR) is used to regress the relationship between the EDC coefficients and machining deformation under small sample conditions, outputting the predicted machining stress and machining deformation.

[0030] In step 3, the machining stress field introduced by the cutting process is predicted using simulation. The experimental coupling correction process is used for calibration, including building training and validation datasets with finite element simulation data and experimental data, and determining the accuracy and improving the stability of the prediction model through bias correction and cross-validation.

[0031] The stress selection method in step 4 is based on the processing area information exported in step 1. Specifically, when reading the processing area unit information, a special mark is added to the unit group corresponding to the processing area. Then, during the stress application process, the script traverses all units one by one: if the currently traversed unit has the special mark, the processing stress predicted in step 3 is automatically selected and applied; otherwise, if no special mark is detected, the blank stress mapped in step 2 is automatically selected and applied.

[0032] The above method uses the stress of the hot-worked metal blank as the initial stress. First, it parameterizes the geometry and topology of the blank and part elements, and then uses the matrix operator method to establish the element mapping relationship between the blank and the part. Next, it applies Newton's law to the finite element shape function equations. Lafferson linearization is used to solve for local coordinates, enabling high-fidelity numerical mapping and interpolation of the stress field between blank and part elements. Then, considering the correlation between machining parameters and additional stress, a lightweight process parameter-machining stress prediction model is constructed. The exponentially decaying cosine function (EDC) is preferred to characterize the cutting parameters and deformation behavior, combined with Levenberg's algorithm. Marquardt (LM) nonlinear least squares fitting and Gaussian process regression (GPR) are used to jointly model and obtain the additional stress in each machining area. Finally, the mapped blank stress and additional stress are applied to the part model as initial conditions, and the finite element global equilibrium solver is called to calculate and obtain the stress release deformation prediction results at the end of machining.

[0033] The shape function is a continuous function defined within the element and related to the coordinates in the finite element method. The shape function is used to construct interpolated approximate solutions for unknown quantities such as displacement in finite element analysis, by ensuring continuity between adjacent elements and including linear terms to satisfy the constant strain condition.

[0034] This invention achieves high-fidelity inheritance of blank stress through matrix operator mapping and local coordinate interpolation. A lightweight joint model combining EDC+LM / GPR balances fast convergence, generalization performance, and uncertainty estimation, enabling the application and release of both blank and predicted stresses. The stress selection mechanism allows for precise stress partitioning. Compared to existing machining deformation prediction methods, this invention improves overall computational efficiency, effectively shortens prediction time, increases model building efficiency, and provides rapid responses. It also significantly improves prediction accuracy, expands method applicability, and reduces deployment difficulty. With advantages of high efficiency, reusability, and controllable accuracy, it is suitable for predicting machining deformation and optimizing processes in complex castings. Attached Figure Description

[0035] Figure 1 This is a flowchart of the machining deformation prediction method based on the coupling mapping of blank stress and cutting stress according to the present invention. Detailed Implementation

[0036] For the detailed process of the machining deformation prediction method based on the coupled mapping of blank stress and cutting stress in this invention, please refer to [link / reference]. Figure 1 The following is a detailed explanation.

[0037] Step 1: Using the stress of the hot-worked metal blank as the initial stress, the metal blank as the blank model, and the final part after machining as the part model, establish a finite element model, and obtain the stress information of the blank, the coordinates of the integration points, element and node information, and the machining area information of the blank model and the part model.

[0038] The core idea of ​​finite element analysis is to decompose a complex, physically inhomogeneous model into several simple, regular, and interconnected "discrete bodies," namely finite element elements, also known as units. In a three-dimensional model, units are often tetrahedral or hexahedral, and the vertices of an element are called nodes, such as the five corners of a tetrahedron (triangular pyramid) and the eight corners of a hexahedron (cube). In this patent, the blank model corresponds to blank elements, and the blank elements correspond to blank nodes; the part model corresponds to part elements, and the part elements correspond to part nodes. The information for blank nodes and part nodes refers to the node's coordinate number.

[0039] (1) Modify the part preprocessing file to realize the output of unit integration point coordinates.

[0040] Import the part model into the finite element software, set material properties and constraints, and create a new static general analysis step without applying any force or displacement. After setting the properties, divide the model into elements and generate an .inp file, which serves as the finite element model carrier. Subsequent information is obtained by manipulating the .inp file.

[0041] Read the preprocessing file (inp file), then query the file content to find the field *Element Output,directions=YES. Add ",coord" after the last output letter of the output line below. After adding, save and submit the calculation.

[0042] (2) Use the Abaqus software interface to export model information:

[0043] The system reads the post-processed file containing blank stress and exports the element, node, integration point, and stress information. When reading node and element information, it accesses all nodes and elements in the assembly set by calling the odb Assembly object to obtain node and element information; when exporting integration points and stress, it accesses the output database by calling the odb Set object to obtain stress and integration point information.

[0044] The stress information is derived using an extrapolation method based on element attribute weighting. The formula for the extrapolation method is as follows:

[0045] (1)

[0046] in: The stress vector at the Gaussian point. Let be the nodal stress vector, and E be the inverse matrix based on the shape function. For internal nodes, it receives extrapolated values ​​from all contributing elements.

[0047] For tensor outputs (such as stress and strain), two or more extrapolation results can be converted into an average scalar, and then the tensor values ​​are mapped to a single scalar value using a scalar transformation method. For example, the stress components S11, S22, S33, S12, S23, and S31 are used by Abaqus to determine Mises stress.

[0048] Step 2: Based on the element and node information of the part model obtained in Step 1, establish the element mapping relationship between the blank model and the part model, solve the local coordinates of each node in the corresponding blank element, interpolate the blank stress according to the local coordinates, and obtain the blank stress physical field quantity mapped to the part model.

[0049] (1) The matrix operator method is used to establish the unit mapping relationship:

[0050] Establish the element mapping relationship between the blank model and the part model. The volume method in the matrix operator method is adopted, that is, if a point is contained in a certain element, then the sum of the volumes of the tetrahedron formed by the point and the various surfaces of the element is equal to the volume of the element; otherwise, the point is outside the element.

[0051] Meanwhile, the volume of any hexahedron in space can be obtained by dividing it into multiple tetrahedrons and summing the results, and the formula for the volume of any tetrahedron in space is Equation (2).

[0052] (2)

[0053] Where x, y, and z are the coordinates of any vertex of a tetrahedron in space, resulting in four rows of coordinates, corresponding to the four vertices of the tetrahedron in space.

[0054] Therefore, if node P is within a certain unit, then it satisfies the following equation (3).

[0055] (3)

[0056] Where Vi is the tetrahedral volume formed by node P and the surfaces of the element, and V0 is the volume of the element. If the ratio is greater than 1, then node P is outside the hexahedral element.

[0057] (2) The stress interpolation algorithm is used to realize the inheritance of physical field quantities:

[0058] Based on the mapping relationship, the local coordinates of the nodes in the element are solved using the Newton-Raphson method, and the physical field quantities of the part element are obtained by combining local coordinate interpolation. Taking a hexahedral part element as an example, the process of determining the local coordinates of the nodes in the element is as follows: First, the local coordinates of the part nodes are determined using formula (4):

[0059] (4)

[0060] in: For the coordinates of the part nodes, The coordinates of the 8 nodes of the hexahedral blank element are given. Let be the shape function of the blank element. Since this system of equations is a nonlinear system of equations, it must be linearized. After processing, we get formula (5):

[0061] (5)

[0062] Then, the Newton-Raphson method is used to iteratively solve the problem, thereby obtaining the local coordinates of the part node, and then the stress field of the part node can be obtained by using formula (6).

[0063] (6)

[0064] Based on the stress field at the nodal points of the component, the physical field quantities of the component elements can be obtained using formula (7):

[0065] (7)

[0066] in This represents the stress field quantity at the node of the component. For the stress field quantity of the component unit, m This represents the number of component nodes. Let i represent the equivalent force field of the i-th element.

[0067] Step 3. Construct a dataset using data obtained from finite element simulation and experiments, train a lightweight data-driven prediction model to predict the machining stress field introduced by cutting, and obtain the machining stress field of each machining area;

[0068] The LM algorithm is an efficient and stable nonlinear least squares optimization method that combines the fast convergence of the Gauss-Newton method with the global convergence of the gradient descent method. It is suitable for fitting problems with few parameters and nonlinear models.

[0069] Gaussian process regression (GPR) is a nonparametric regression method based on Bayesian theory that can model complex nonlinear relationships under small sample conditions and provide estimation of prediction uncertainty.

[0070] A joint modeling process based on the exponentially decaying cosine function (EDC) is adopted: Cutting parameters (cutting speed v (m / min), feed rate fz (mm / z), depth of cut ap (mm), and width of cut ae (mm), etc.) are used as inputs, and EDC coefficients are used as intermediate representations, utilizing Levenberg-Warshall curves. The Marquardt (LM) algorithm is used to perform nonlinear least squares fitting to obtain the EDC coefficients, and Gaussian process regression (GPR) is used to regress the relationship between the EDC coefficients and machining deformation under small sample conditions, outputting the predicted machining stress and machining deformation.

[0071] Step 4. Based on the stress selection method, apply the mapped blank stress physical field obtained in Step 2 and the machining stress field predicted in Step 3 to the part model, and call the finite element solver to calculate the stress physical field release process to obtain the machining deformation prediction results at the end of machining.

[0072] The stress selection method is based on the processing area information exported in step 1. Specifically, when automatically reading the processing area unit information, a special marker is added to the unit group corresponding to the processing area. Subsequently, during stress application, the script traverses all units one by one: if the currently traversed unit has the special marker, the processing stress predicted in step 3 is automatically selected and applied; otherwise, if no special marker is detected, the blank stress mapped in step 2 is automatically selected and applied. This selection mechanism enables precise partitioning of stress and improves overall computational efficiency.

Claims

1. A method for predicting machining deformation by coupling the stress of a blank with the stress of cutting, characterized in that, Includes the following steps: Step 1: Using the stress of the hot-worked metal blank as the initial stress, the metal blank as the blank model, and the final part after machining as the part model, establish a finite element model, and obtain the blank stress information, the integral point coordinates, element and node information, and machining area information of the blank model and the part model. Step 2: Based on the element and node information of the part model obtained in Step 1, establish the element mapping relationship between the blank model and the part model, solve the local coordinates of each node in the corresponding blank element, interpolate the blank stress according to the local coordinates, and obtain the blank stress physical field quantity mapped to the part model. Step 3: Construct a dataset using data obtained from finite element simulation and experiments, train a lightweight data-driven prediction model to predict the machining stress field introduced by cutting, and obtain the machining stress field of each machining area; Step 4: According to the stress selection method, apply the mapped blank stress physical field obtained in Step 2 and the machining stress field predicted in Step 3 to the part model, and call the finite element solver to calculate the stress physical field release process to obtain the machining deformation prediction result at the end of machining. The process of training the lightweight data-driven prediction model in step 3 involves taking the cutting parameters as input, using the exponentially decaying cosine function (EDC) coefficients as intermediate representations, performing nonlinear least squares fitting using the LM algorithm to obtain the EDC coefficients, and then using Gaussian process regression to regress the relationship between the EDC coefficients and machining deformation under small sample conditions to output the machining stress.

2. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, The specific process of establishing the finite element model in step 1 is to import the part model into the finite element software, set the material properties and constraints, and create a new static general analysis step in which no force or displacement is applied; after completing the property settings, the model is divided into elements and an inp file is generated, which is the finite element part model carrier.

3. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, The process of obtaining blank stress information in step 1 is to export the blank stress field, i.e. blank stress information, from the post-processing file containing blank stress field after thermal processing simulation by calling the Abaqus secondary development interface.

4. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, In step 1, the integration point coordinates, element and node information of the part model are obtained by setting the attributes of the original .inp file using a Python script, submitting the .inp file to the Abaqus solver for calculation using the command line, generating a post-processing file, and then calling the Abaqus secondary development interface to export the integration point coordinates, element and node information from the post-processing file and store it in a file in a specified format. The machining area information is obtained by automatically traversing and reading it using a Python script to generate a file containing the machining area name and the elements contained in the machining area, i.e., the machining area information file.

5. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, In step 2, the unit mapping relationship between the blank model and the part model is established by using the volume method in the matrix operator method. That is, if a point is contained in a unit, then the sum of the volumes of the tetrahedron formed by the point and the various surfaces of the unit is equal to the volume of the unit; otherwise, the point is outside the unit.

6. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, The specific process in step 2 of interpolating the residual stress of the blank based on local coordinates to obtain the physical field quantity of the blank stress mapped to the part model is as follows: Based on the mapping relationship, the local coordinates of the nodes in the element are solved using the Newton-Raphson method. Combined with local coordinate interpolation, the physical field quantities of the part element are obtained. For a hexahedral part element, the process of determining the local coordinates of the nodes in the element is as follows: First, use the following formula to determine the local coordinates of the part nodes: , in: For the coordinates of the part nodes, The coordinates of the 8 nodes of the hexahedral blank element are given. Let be the shape function of the blank element. Since this system of equations is nonlinear, it must be linearized. After linearization, the following formula is obtained: ， Then, the Newton-Raphson method is used for iterative solution to obtain the local coordinates of the component nodes, and the stress field of the component nodes is obtained using the following formula: Based on the stress field at the nodal points of the component, the physical field quantities of the component elements are obtained using the following formula: in This represents the stress field quantity at the node of the component. Let m represent the stress field quantity of a component element, and m be the number of nodes in the component. Let i represent the equivalent force field of the i-th element.

7. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, In step 3, the machining stress field introduced by the cutting process is predicted and calibrated using a simulation-experiment coupled correction process. This includes constructing training and validation datasets using finite element simulation data and experimental data, and determining the accuracy and improving the stability of the prediction model through bias correction and cross-validation.

8. The machining deformation prediction method based on the coupled mapping of blank stress and cutting stress according to claim 1, characterized in that, The stress selection method in step 4 is based on the processing area information exported in step 1. Specifically, when reading the processing area unit information, a special mark is added to the unit group corresponding to the processing area. Then, during the stress application process, the script traverses all units one by one: if the currently traversed unit has the special mark, the processing stress predicted in step 3 is automatically selected and applied. Conversely, if no special marker is detected, the blank stress mapped in step 2 is automatically selected and applied.

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