Curve path-based curved surface additive manufacturing and remanufacturing finite element modeling method

Abstract

According to the curved surface additive manufacturing and remanufacturing finite element modeling method based on the curve path, a parameterization analysis step creation program is written through the Python language, traditional manual operation is replaced, and the modeling efficiency is remarkably improved; the unit is dynamically activated or removed by using a'unit life and death 'technology, the welding bead accumulation process is simulated layer by layer, and the thermal-mechanical coupling effect is accurately reduced; a DFLUX user subprogram is secondarily developed on the basis of the Fortran language, a double-ellipsoid heat source model is defined, synchronous translation and rotation of a heat source along an arc-shaped path are achieved through coordinate transformation, and the requirement for complex curved surface additive manufacturing is met. In addition, a geometric model, material attributes and process parameters are integrated through a parameterized driving technology, and full-life-cycle automatic management and control from design, manufacturing to remanufacturing are supported. According to the method, the dynamic evolution laws of the temperature field and the stress field can be efficiently analyzed, a high-precision and intelligent simulation tool is provided for additive manufacturing and remanufacturing process optimization of large complex metal curved surface components, and the method has remarkable engineering application value.

Description

Technical Field

[0001] The present invention relates to the fields of additive manufacturing and remanufacturing, and particularly to a finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path. Background Art

[0002] With the continuous development of additive manufacturing technology, the application of surface additive manufacturing and remanufacturing in industrial production is becoming increasingly widespread. Large and complex metal surface structures, such as aeroengine blades, large hydroturbine blades, etc., are key mechanical equipment in our country and national treasures. Due to their structural characteristics such as complex curved surfaces and large sizes, additive manufacturing methods with high flexibility have natural advantages for manufacturing and remanufacturing. In the process of theoretical research and technology development of additive manufacturing of large and complex metal surface structures, experimental testing is the main research method, but there are problems such as high cost and long cycle. Therefore, the current optimal solution is to carry out relevant research in the way of mainly using numerical simulation and supplemented by experiments. The underlying technology of the numerical simulation technology for additive manufacturing and remanufacturing of large and complex metal surface structures is the finite element numerical simulation of curved additive manufacturing of metal materials. There has been no relevant research report so far.

[0003] Currently, the relevant reports in the industry mainly carry out finite modeling of straight-line additive manufacturing through the GUI method and use pre-placed weld beads for simulation. On the one hand, creating analysis steps through the GUI method has problems such as complex process, low efficiency, and poor reliability, and it is difficult to meet the requirements of the simulation of the additive manufacturing and remanufacturing processes of large and complex metal surface components. On the other hand, using the method of pre-placing weld beads ignores the process of gradual accumulation of weld beads, which causes the previously deposited weld beads / weld layers to be affected by preheating and structural stress, resulting in a significant decrease in the accuracy of the finite element model and deviation from the engineering reality. In addition, this finite element modeling method for the additive process without parameter drive is difficult to adapt to the technological development trend of the full life cycle automation and intelligent control of large and complex metal surface components from design, manufacturing, service to remanufacturing. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path in view of the above-mentioned deficiencies of the prior art. This method can establish an accurate and efficient finite element model for curved additive manufacturing and remanufacturing, deeply analyze the temperature field and stress field of additive manufacturing and the dynamic evolution law formed by the coupling of the two, which is beneficial to guiding actual production and facilitating the realization of the full life cycle automation and intelligent control of products.

[0005] In order to achieve the above technical features, the object of the present invention is realized as follows: A finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path, comprising the following steps: Step 1, geometric model construction: According to the actual situation of surface additive manufacturing and remanufacturing engineering, a required geometric model is established by using finite element software; Step 2, material property setting: In the finite element software, the material physical property parameters of the geometric model established in Step 1 are set; Step 3, assembling components: In the finite element software, the geometric model with parameters set in Step 2 is assembled into a solid model; Step 4, mesh generation: The corresponding module in the finite element software is used to generate a mesh for the solid model established in Step 3; Step 5, setting analysis steps: A certain number of analysis steps are established for the solid model with mesh generation completed; Step 6, applying loads and setting boundary conditions: According to the actual situation of surface additive manufacturing and remanufacturing engineering, loads are applied to the finite element model established in Step 5, and the corresponding boundary conditions are set; Step 7, writing and calling the heat source subroutine: According to the characteristics of the welding heat source and process parameters, a user subroutine is written, and the solution is carried out by calling the user subroutine; Step 8, result analysis and post-processing: The calculation results in Step 7 are visually analyzed, and the surface additive manufacturing and remanufacturing processes are optimized based on the relevant results.

[0006] Preferably, the specific method of Step 1 is as follows: According to the actual situation of surface additive manufacturing and remanufacturing engineering, a geometric model including a surface welding plate and a semi-circular cross-section weld is established by drawing in the finite element software ABAQUS or importing from other 3D modeling software. The length, width, height of the surface welding plate and the geometric dimensions of the weld are user-defined.

[0007] Preferably, the specific method of Step 2 is as follows: In the ABAQUS Property module, the material physical property parameters matching the surface additive manufacturing and remanufacturing processes are set, including general physical property parameters, mechanical parameters, and thermal property parameters; The specific method of Step 3 is as follows: The geometric model is assembled into a solid through the ABAQUS Assembly module.

[0008] Preferably, the specific method of Step 4 is as follows: According to the built model structure size and calculation accuracy, mesh division is carried out on it in the ABAQUS Mesh module, and appropriate mesh strategies and element types are selected according to the model structure characteristics and the established analysis types to precisely control the mesh size and density; The specific method of the fifth step is as follows: In the ABAQUS Step module, a certain number of analysis steps are created according to the weld size and the number of element layers, the solution parameters are set, and based on the number of analysis steps and the number of elements in the weld zone, the weld additive deposition process is simulated through element birth and death.

[0009] Preferably, the specific method of the sixth step is as follows: According to the actual situation of surface additive manufacturing and remanufacturing engineering, loads are applied to the established finite element model in the ABAQUS Interaction and Load modules, and corresponding boundary conditions are set, where the boundary conditions include thermal boundary conditions and displacement boundary conditions; The specific method of the seventh step is as follows: According to the characteristics of the welding heat source and process parameters, a DFLUX user subroutine is written to define the heat source model and the heat source movement trajectory, and the user subroutine is set to be called for solution in the ABAQUS Job module.

[0010] Preferably, the specific method of the eighth step is as follows: After the calculation in the seventh step is completed, data results such as the temperature field, stress field, and strain field are extracted in the ABAQUS Visualization module for visualization analysis, the thermo-mechanical coupling process of surface additive manufacturing and remanufacturing is analyzed, the evolution laws of the temperature field and stress field are revealed, and the surface additive manufacturing and remanufacturing processes are optimized based on the relevant results.

[0011] Preferably, the realization of the weld additive deposition process by element birth and death in the fourth step is achieved by writing Python code using the "Model change" instruction; The establishment of the analysis steps in the fifth step is achieved by GUI operation or by writing Phython code. To define multiple analysis steps according to the weld size and the number of element layers, first enter the ABAQUS software interface, click the Model button, and successively open Model-Edit keywords-model-1 to enter the analysis step interface, and write the analysis steps through python code.

[0012] Preferably, the specific steps of writing Phython code using the "Model change" instruction in the fourth step include: Step 4.1, initialize variables; Step 4.2, set the model keyword block; Step 4.3, process the data in a loop; Step 4.4, generate the birth and death elements.

[0013] Preferably, in step seven of writing and calling the heat source subroutine, the heat source is selected as a surface heat source or a volume heat source according to the actual engineering situation. The movement of the heat source is realized through the coordinate transformation of the global coordinates ( x , y , z ) and the local coordinates ( , , ): ; ; ; Among them, Rot is the rotation transformation matrix of the local coordinate system relative to the global coordinate system; Trans is the corresponding translation transformation matrix.

[0014] Preferably, the coordinates of the double ellipsoidal heat source in the global coordinate system ( x , y , z ) are used to represent its coordinates in the local coordinate system ( x 1, y 1, z 1). Substitute the obtained expression of the local coordinates into the heat source mathematical model and write the corresponding program, then the program code for the synchronous translation and rotation of the double ellipsoidal heat source along the arc curve can be obtained; The heat source subroutine code is a FORTRAN subroutine used to calculate the heat flux during the welding process. The heat source subroutine specifically includes the following processes: Step 7.1, program header and variable definition; Step 7.2, welding parameter definition and assignment; Step 7.3, double ellipsoidal heat source related numerical values and calculations; Step 7.4, calculate the heat flux density according to the conditions; Step 7.5, end of the subroutine.

[0015] Advantages of the present invention: 1. Improve the efficiency and reliability of creating analysis steps: By using the parameter-driven method to replace the traditional GUI for creating analysis steps, the complexity and low efficiency of the GUI method are avoided. Using this method simplifies the modeling process, improves the efficiency and automation level of creating analysis steps, reduces human operation errors, enhances the reliability of modeling, and can better meet the simulation requirements of the additive manufacturing and remanufacturing processes of large components.

[0016] 2. Accurately simulate the step-by-step build-up process of the weld bead to improve the model accuracy: Different from the traditional pre-placed weld bead method, the parameter-driven modeling method can gradually build up the weld bead, taking into account the influence of the previously deposited weld bead on the subsequent weld bead (such as the accumulation of preheating and structural stress). By simulating the build-up process of the weld bead layer by layer, it can more realistically reproduce the thermo-mechanical coupling effect in additive manufacturing, improve the accuracy of the finite element model, ensure compliance with the actual engineering situation, and avoid the problem of excessive model error in the traditional method.

[0017] 3. Enhance the scalability and cross-platform compatibility of the model: This patent realizes the seamless integration of the finite element model with various engineering software (such as SolidWorks, CATIA) and simulation platforms through parametric scripts (such as Python) and standardized interface design. Users can quickly transplant the model to different environments according to their needs, or expand functional modules (such as adding new heat source types, material libraries) without reconstructing the underlying architecture. This feature not only improves the reusability of the model but also supports multi-disciplinary co-simulation (such as thermo-mechanical-fluid coupling), providing a unified technical framework for cross-domain research in complex manufacturing scenarios.

[0018] 4. Meet the simulation requirements for complex curved surface structures: Combining the double-ellipsoid heat source model and the arc trajectory coordinate transformation technology, it solves the limitations of traditional straight-line path modeling. By dynamically adjusting the position and direction of the heat source through the local coordinate system, it can accurately simulate the additive manufacturing process of complex curved surfaces (such as aero-engine blades, hydro-turbine blades), filling the technical gaps in related fields. Brief Description of the Drawings

[0019] The present invention will be further described below in conjunction with the drawings and embodiments.

[0020] Figure 1 It is the overall flowchart of the present invention.

[0021] Figure 2 It is the arc curve trajectory diagram of the present invention.

[0022] Figure 3 It is the analysis step case of the present invention.

[0023] Figure 4 It is the element birth and death case of the present invention.

[0024] Figure 5 It is the boundary condition application case of the present invention.

[0025] Figure 6 It is the load application case of the present invention.

[0026] Figure 7It is the locus diagram of the arc curve in the specific embodiment 2 of the present invention.

[0027] Figure 8 It is the heat source subroutine case of the present invention.

[0028] Figure 9 It is the stress distribution diagram of the present invention. Specific embodiments

[0029] The following further explains the embodiments of the present invention with reference to the accompanying drawings.

[0030] The following describes the preferred embodiments of the present invention with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0031] Embodiment 1: As Figure 1 shown, a finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path is characterized by including the following steps: Step 1, geometric model construction: According to the actual situation of surface additive manufacturing and remanufacturing engineering, a geometric model including a surface welding plate and a semi-circular cross-section weld is established by drawing in a finite element software (preferably ABAQUS) or importing from other 3D modeling software. The length, width, height of the surface welding plate and the geometric dimensions of the weld are user-defined.

[0032] Step 2, material property setting: In the ABAQUS Property module, set the material physical property parameters matching the surface additive manufacturing and remanufacturing process, including general physical property parameters, mechanical parameters, thermal property parameters, etc.

[0033] Step 3, assembling components: Assemble the geometric model into a solid through the ABAQUS Assembly module.

[0034] Step 4, mesh generation; According to the structural dimensions and calculation accuracy of the established model, perform mesh generation on it in the ABAQUS Mesh module, and select appropriate mesh strategies and element types according to the model structural characteristics and the established analysis type to precisely control the mesh size and density.

[0035] Step 5, setting analysis steps: In the ABAQUS Step module, create a certain number of analysis steps according to the weld size and the number of element layers, set the solution parameters, and simulate the weld additive stacking process through element birth and death based on the number of analysis steps and the number of elements in the weld area.

[0036] Step 6, Load application and boundary conditions: According to the actual situation of surface additive manufacturing and remanufacturing engineering, load is applied to the established finite element model in the ABAQUS Interaction and Load modules, and corresponding boundary conditions are set, where the boundary conditions include thermal boundary conditions and displacement boundary conditions, etc.

[0037] Step 7, Write and call the heat source subroutine: According to the characteristics of the welding heat source and process parameters, write the DFLUX user subroutine to define the heat source model and heat source movement trajectory, and set the call of the user subroutine for solution in the ABAQUS Job module.

[0038] Step 8, Result analysis and post-processing: After the calculation is completed, extract data results such as the temperature field, stress field, and strain field in the ABAQUS Visualization module for visual analysis, analyze the thermo-mechanical coupling process of surface additive manufacturing and remanufacturing, reveal the evolution laws of the temperature field and stress field, and optimize the surface additive manufacturing and remanufacturing processes based on the relevant results.

[0039] Furthermore, the establishment of the analysis step in Step 5 can be achieved by using GUI operations or by writing Python code. According to the weld size and element layer, define multiple analysis steps. First, enter the ABAQUS software interface, click the Model button, and successively open Model-Edit keywords-model-1 to enter the analysis step interface. Write the analysis step through Python code. The following is the process of writing the analysis step by Python code.

[0040] (1) "from abaqus import *": Import all contents in the ABAQUS module.

[0041] (2) "from abaqusConstants import *": Import all contents in the ABAQUS constant module.

[0042] (3) "from caeModules import *": Import all contents in the caeModules module.

[0043] (4) "maxnum=, minnum=, cnum=": Define the maximum value, minimum value of the weld elements and the number of weld layers according to the defined weld size and number of element layers.

[0044] "zcnum=(maxnum-minnum+1) / cnum": The calculation formula for the number of analysis steps, which is calculated through the values given in (4).

[0045] (5)"alltime": Defines the total welding simulation time. "dt=alltime / zcnum": Calculation formula for time step size.

[0046] (6)"mdb.models['Model-1'].CoupledTempDisplacementStep": Creates a coupled temperature-displacement analysis step. "name='Step-1'": The step name is Step-1; "previous='Initial'": The previous step is the initial step; "timePeriod,maxNumInc,initialInc,minInc,maxInc,deltmx": Are the time period, maximum number of increments, initial increment, minimum increment size, maximum increment size, and time step size in sequence.

[0047] (7)"for j in range(zcnum):": Loops through all integers from 0 to zcnum - 1. The loop is as follows: "stepname1='Step-'+str(j + 1), stepnuma2='Step-'+str(j + 2)": Generates the current step name and the next step name, looping up to the maximum number of analysis steps at a time.

[0048] (8)"mdb.models['Model-1'].CoupledTempDisplacementStep": Creates a new coupled temperature-displacement analysis step; "name=stepnuma2": The step name is stepnuma2; "previous=stepname1": The previous step is stepname1; "timePeriod=dt,nlgeom,maxNumInc,initialInc,minInc,maxInc,deltmx": Are the time period, geometric nonlinearity option, maximum number of increments, initial increment, minimum increment, maximum increment, and time step size in sequence.

[0049] (9)After generating multiple analysis steps through a loop in the Python code, add the compiled Python code to the ABAQUS text box to complete the editing of the analysis steps.

[0050] Furthermore, the realization of the weld additive deposition process in the fourth step using element birth and death is achieved by writing Python code using the "Model change" instruction.

[0051] The operation steps for editing birth and death elements using Python code are as follows: (1)Initialize variables: ① "maxnum=, minnum=, cnum=": Define the maximum value, minimum value, and the number of elements per layer of the weld elements according to the defined weld size and the number of element layers.

[0052] ② "zcnum=(maxnum - minnum + 1) / cnum": Calculate the number of weld element layers according to the above formula.

[0053] ③ "positionnum=": Set the insertion position.

[0054] (2) Set the model keyword block: ① "mdb.models['Model-1'].keywordBlock.setValues(edited=0)": Set the keyword block of the model'model-1' to the unedited state.

[0055] ② "import job": Import the job model block.

[0056] "mdb.models['Model1'].keywordBlock.synchVersions(storeNodesAndElements=False)": Synchronize the keyword block versions of the model'model-1' without storing nodes and elements.

[0057] "mdb.models['Model1'].keywordBlock.insert(positionnum, "*MODELCHANGE,TYPE=ELEMENT,REMOVE Set-NAME")": Insert an instruction at position positionnum to remove the element set named Set-NAME. The element set name can be customized.

[0058] (3) Process data in a loop: ① "lab1=minnum": Initialize the label lab1 to minnum.

[0059] ② "for j in range(zcnum):": Loop through each group. The loop is as follows. "data=range(cnum) ": Initialize the data range to cnum.

[0060] "for i in range(cnum):": Loop through each element in each group.

[0061] " data[i]=lab1+I": Assign a number to each element.

[0062] "initialstr = """*MODEL CHANGE,TYPE=ELEMENT,ADD""": The initialization string indicates adding an element.

[0063] "if i % 4 == 3:": If it is the last one among every four elements, then loop as follows. "initialstr = initialstr +'model-1.'+ str(data[i]) + ',\n'": Add the element number and start a new line.

[0064] "else": Otherwise.

[0065] "initialstr = initialstr +'model-1.'+ str(data[i]) + ','": Add the element number.

[0066] "import job": Import the job module.

[0067] "mdb.models['Model1'].keywordBlock.synchVersions(storeNodesAndElements=False)": Synchronize the keyword block version of model'model-1' without storing nodes and elements.

[0068] "mdb.models['Model-1'].keywordBlock.insert(positionnum + 9 + j * 9, initialstr)": Insert the instruction to add an element at the specified position.

[0069] "lab1 = lab1 + cnum": Update the label lab1.

[0070] (4) Generation of birth and death elements: Through these codes, batch addition and removal operations of elements in model'model-1' are realized. Adding the compiled python code to the ABAQUS text box can generate birth and death elements.

[0071] Further, in the seventh step of writing and calling the heat source subroutine, the heat source can be selected as a surface heat source (preferably a Gaussian surface heat source) or a volume heat source (preferably a double ellipsoid heat source) according to the actual engineering situation. The movement of the heat source can be realized through coordinate transformation of the global coordinates (x, y, z) and local coordinates ( , , ).

[0072] There are the following transformation relationships: ; = * Rot ; ; Among them, Rot is the rotation transformation matrix of the local coordinate system relative to the global coordinate system; Trans is the corresponding translation transformation matrix.

[0073] If an arc-shaped surface is used to represent the finite element modeling process of general surface additive manufacturing and remanufacturing, then the local coordinate system where the heat source is located ( , , ) will perform translation and rotation along the arc curve trajectory. Let the center point coordinates of the arc curve be ( m , n ), the radius of the circle be R , and the arc curve trajectory is as shown in Figure 2 . The trajectory equation of the arc curve is: y= ; Assume that at a certain moment, the heat source moves along the arc curve to point P, that is, the origin of the local coordinate system where the heat source is located moves to point P, and the total length of movement along the arc curve is d , then the coordinates of point P in the global coordinate system can be expressed as: ; Assume that the initial position of the arc curve trajectory is not at the origin of the global coordinate system, but at an arbitrary position ( x 0, y 0, z 0). Then, when the heat source moves along the arc curve trajectory, the translation transformation matrix of the local coordinate system relative to the global coordinate system is: Trans = ; From the equation y= , the tangent slope corresponding to any point on the arc curve trajectory can be obtained as: = ; The rotation angle of the local coordinate system ( , , ) with an arbitrary point on the arc curve as the origin relative to the global coordinate system ( x , y , z ) can be expressed as: ; Therefore, when the heat source moves along the arc curve to point P, the rotation transformation matrix of the local coordinate system ( , , ) of the heat source relative to the global coordinate system ( x , y , z ) can be expressed as: Rot = ; Substitute the above formula into = * Rot In the formula, the transformation matrix can be obtained: TR = ; Further, use the coordinates of the double-ellipsoid heat source in the global coordinate system ( x , y , z ) to represent its coordinates in the local coordinate system ( x 1, y 1, z 1). Substitute the obtained expression of the local coordinates into the heat source mathematical model and write the corresponding program, and the program code for the synchronous translation and rotation of the double-ellipsoid heat source along the arc curve can be obtained.

[0074] The heat source subroutine code is a FORTRAN subroutine used to calculate the heat flux during welding. The description of the heat source subroutine is as follows: (1) Program header and variable definition: ① "SUBROUTINE DFLUX": A subroutine of DFLUX that can accept multiple parameters; "FLUX,SOL,JSTEP,JINC,TIME,NOEL,NPT,COORDS,JLTYP" includes multiple parameters such as heat flux density (FLUX), solution (SOL), time step (JSTEP), etc.

[0075] ② "INCLUDE “ABA_PARAM.INC”": Include an external file named ABA_PARAM.INC. The file defines relevant global variables or constants, and these variables or constants participate in subsequent calculations.

[0076] ③ "DIMENSION COORDS(3),FLUX(2),TIME(2)": Define three arrays. COORDS is a three-dimensional array, and FLUX and TIME are both two-dimensional arrays.

[0077] (2)Welding parameter definition and assignment: ① Parameter definition and assignment: "wu, welding voltage; wi, welding current; effi, welding efficiency coefficient; q, effective arc thermal power W; v, welding speed m / s; q = wu * wi * effi; d = v * TIME(2)": This subroutine code comment defines the meanings of multiple variables, including welding voltage (wu), welding current (wi), welding efficiency coefficient (effi), effective arc thermal power (q), and welding speed (v), and assigns specific values to multiple variables. Some variables can be obtained through formula calculation.

[0078] ② Coordinate variable assignment: "x = COORDS(1), y = COORDS(2), z = COORDS(3)": Assign the three elements of the COORDS array to the x, y, and z variables respectively, representing spatial coordinates. These three variables represent the spatial coordinates of any point during the welding process.

[0079] (3)Numerical values and calculations related to the double-ellipsoid heat source: ① Double-ellipsoid parameter definition and initialization: "Starting from the coordinates x0, y0, z0, moving along the z direction, x0 = ; y0 = ; z0 = ": Define the starting coordinates of the double-ellipsoid heat source movement 、 、 and the moving direction, and the coordinate values are obtained from the defined model.

[0080] "a1, a2, b, c are the shape parameters of the double-ellipsoid, a1 = ; a2 = ; b = ; c =, f1 is the heat source distribution coefficient, f1 = 1.0, PI = 3.1415926": Define the shape parameters of the double-ellipsoid heat source 、 、 b, c and the heat source distribution coefficient 。

[0081] "heat1 = 6.0 * sqrt(3.0) * q / (a1 * b * c * PI * sqrt(PI)) * f1 heat2 = 6.0 * sqrt(3.0) * q / (a2 * b * c * PI * sqrt(PI)) * (2.0 - f1) ": Calculate two heat-related parameters, heat1 and heat2, based on the above-defined parameters.

[0082] (4)Calculate the heat flux density according to conditions: ① Calculate FLUX(1) based on coordinate conditions "JLTYP = 1, indicating a volume heat source, JLTYP = 1 IF (x.LE.(x0 + 0.05 - (SQRT(2.0)*COS(PI / 4.0 + 10.0*SQRT(2.0)*d)) / 20.0)) THEN FLUX(1)=heat1*shape1 ": Define JLTYP = 1 (volume heat source), and select different formulas to calculate FLUX(1) according to the transformation of the heat source coordinate values.

[0083] ② Time-based heat flux density adjustment "IF (x.LE.(x0 + 0.05 - (SQRT(2.0)*COS(PI / 4.0 + 10.0*SQRT(2.0)*d)) / 20.0)) THEN FLUX(1)=heat1*shape1 ELSE FLUX(1)=heat2*shape2 ENDIF IF (TIME(2).GE.18.5) THEN FLUX(1)=0": Determine FLUX(1) finally by achieving a certain conditional relationship between the two parameters of TIME(2) and FLUX(1).

[0084] (5)"ENDIF RETURN END": The subroutine ends.

[0085] Example 2: See Figure 1 , this embodiment of the present invention provides a finite element modeling method for curved surface additive manufacturing and remanufacturing based on a curved path, and this method includes the following steps: Initial model setting: Parameter-driven curve additive model and additive layer geometry creation: Use 3D modeling software (such as SolidWorks, CATIA, Creo, etc.) to import or draw a cuboid surface welding plate with a curve length of 0.095m, a width of 0.035m, and a height of 0.01m and a semi-circular cross-section weld with a radius of 0.021m in ABAQUS / CAE. The number of layers in the additive layer area is set to 111 layers, and each layer has 36 weld elements.

[0086] Material property setting: In the ABAQUS Property module, set the material physical property parameters that match the surface additive manufacturing and remanufacturing processes. The material properties include conductivity, density, elasticity, thermal expansion, latent heat, specific heat, etc. Specific material parameters are defined through a material library or can be calculated using JMatPro.

[0087] The heat source model adopts a double-ellipsoid heat source model, where: (1) wu (welding voltage) is 23; (2) wi (welding current) is 220; (3) effi (welding efficiency coefficient) is 0.5; (4) Q (input power) is wu * wi * effi; (5) Starting point coordinates ( 、 、 ) are = 0, = 0, = 0; (6) Shape parameters of the double-ellipsoid heat source 、b、c are = 0.004、 = 0.008、b = 0.004、c = 0.0055 (7) Heat source distribution coefficient is 1.0; Assembly of components: Assemble the geometric model into a solid through the ABAQUS Assembly module.

[0088] Mesh generation: According to the process characteristics and requirements, it can be mainly divided into the following regions (hexahedral meshes are used for all mesh types) (1) Additive region: The additive region is the area where materials are gradually added during the surface additive manufacturing and remanufacturing processes. In this region, the mesh needs to be finer to accurately capture the changes in physical quantities such as temperature gradients and stress-strain during the material deposition process.

[0089] (2) Manufactured region: The manufactured region represents the area where additive manufacturing or remanufacturing has been completed. Compared with the additive region, since the changes in physical quantities in this region are relatively gentle, the mesh should be relatively sparse.

[0090] (3) Transition region: The transition region represents the connection between the additive region and the manufactured region. The density of the mesh in this region needs to gradually transition to avoid computational instability or inaccurate results caused by sudden changes in mesh size.

[0091] (4) Heat - affected zone: The heat - affected zone represents the area where heat sources are used during the additive manufacturing process. The mesh in this area needs to be fine enough to accurately simulate the effects of the heat source on the material and the resulting thermal stress, thermal deformation, etc.

[0092] Establishment of analysis steps: A certain number of analysis steps are created according to the weld size and the number of element layers. The solution parameters are set, and based on the number of analysis steps and the number of elements in the weld zone, the process of weld additive build - up is simulated by element birth and death. The analysis steps are compiled using Python code as Figure 3 shown, and the parameters are set as follows.

[0093] "maxnum = 3996, minnum = 1, cnum = 36": Define the maximum value 3996, minimum value 1 of the weld elements and the number of elements per layer of the weld 36 according to the defined weld size and the number of element layers.

[0094] "alltime = 37.074": Define the total welding simulation time as 37.074; "nlgeom = 1, maxNumInc = 10000, initialInc = 0.1; minInc = dt * 1e - 15, maxInc = dt, deltmx = 1500.0": Set the nonlinear geometry (nlgeom) to 1, the maximum number of time increment steps to 10000 time cycles, the initial increment step size to 0.1, the minimum increment step size to dt * 1e - 15, and the maximum increment step size to 1500.0.

[0095] Substitute the above parameters into the Python code for compilation and input into the ABAQUS text box to generate the analysis steps.

[0096] Creation of element birth and death: The realization of the weld additive build - up process by element birth and death is achieved by writing Python code using the "Model change" instruction. The birth and death elements are compiled using Python code as Figure 4 shown, and the parameters are set as follows.

[0097] "maxnum = 3996, minnum = 1, cnum = 36": Define the maximum value of 3996, minimum value of 1 of the weld elements and the number of elements per layer of the weld as 36 according to the defined weld size and the number of element layers.

[0098] "zcnum=(maxnum - minnum + 1) / cnum": Calculate the number of weld element layers according to the above formula.

[0099] "mdb.models['Model1'].keywordBlock.insert(positionnum, "*MODELCHANGE,TYPE=ELEMENT,REMOVE Set-WZ")": Insert an instruction at position positionnum to indicate removing the element set named Set-WZ. The name of the element set can be customized.

[0100] Substitute the above parameters into the Python code for compilation and input into the ABAQUS text box to generate element birth and death.

[0101] Load application and boundary conditions: According to the actual situation of curve additive manufacturing and remanufacturing engineering, apply loads to the established finite element model in the ABAQUS Interaction and Load modules and set the corresponding boundary conditions, such as Figure 5 , Figure 6 as shown.

[0102] (1) Open the Interaction Manager editing section in the Interaction interface and edit the surface film conditions on the top surface, bottom surface, and both side surfaces of the geometric models of the surface welding plate and the semi-circular cross-section weld.

[0103] Set the "film condition" and "sink temperature" of the upper surface to 100 and 20 respectively; Set the "film condition" and "sink temperature" of both side surfaces and the bottom surface to 1000 and 20 respectively; Due to the required stronger heat conduction ability, set the "film condition" value of both sides and the bottom to 1000.

[0104] (2) Open the Load Manager section in the Load interface and edit the "Body heat flux" body heat flux interface.

[0105] Set "Distribution" to "User-defined"; set the "User-defined" part to the subsequent heat source subroutine.

[0106] Set "Magnitude" to 1.

[0107] (3) Open the editing section of the Boundary Condition Manager in the Load interface, and apply the boundary condition type of "Displacement / Rotation" to constrain the model in the selected region (Region). The selected region is the entire surface weld plate and the geometric model of the semi-circular cross-section weld. The coordinate system type (CSYS) adopted is "Global", indicating that all displacements and rotations are defined based on the global coordinate system.

[0108] Select "U1, U2, U3, UR1, UR2, UR3".

[0109] "U1, U2, U3": respectively represent the linear displacements along the x, y, and z axes of the global coordinate system; "UR1, UR2, UR3" respectively represent the rotations around the x, y, and z axes of the global coordinate system.

[0110] The above operations fix the linear displacements and rotations along the x, y, and z axes.

[0111] Write and call the heat source subroutine: According to the characteristics of the welding heat source and the process parameters, write the DFLUX user subroutine to define the heat source model and the heat source movement trajectory, and set the call of the user subroutine in the ABAQUS Job module for solution. The heat source movement can be achieved through the coordinate transformation between the global coordinates (x, y, z) and the local coordinates ( ) coordinates.

[0112] There are the following transformation relationships: ; = * Rot ; ; Among them, Rot is the rotation transformation matrix of the local coordinate system relative to the global coordinate system; Trans is the corresponding translation transformation matrix.

[0113] Use an arc-shaped surface to represent the finite element modeling process of general surface additive manufacturing and remanufacturing. Then, the local coordinate system ( , , ) where the heat source is located will translate and rotate along the arc-shaped curve trajectory. Select an arc-shaped surface in the first quadrant with the center at (0.05, 0.05) and as the radius, as shown in Figure 7 . The trajectory equation of the arc-shaped curve is: y = 0.05; Assume that at a certain moment, the heat source moves along an arc curve to point P, that is, the origin of the local coordinate system where the heat source is located moves to point P, and the total length of the movement along the arc curve is d , then the coordinates of point P in the global coordinate system can be expressed as: ; Assume that the initial position of the arc curve trajectory is not at the origin of the global coordinate system, but at an arbitrary position ( x 0, y 0, z 0). Then, when the heat source moves along the arc curve trajectory, the translation transformation matrix of the local coordinate system relative to the global coordinate system is: Trans = ; From y = 0.05, the tangent slope corresponding to any point on the arc curve trajectory can be obtained as: = ; The rotation angle of the local coordinate system ( , , ) with an arbitrary point on the arc curve as the origin relative to the global coordinate system ( x , y , z ) can be expressed as: ; When the heat source moves along the arc curve to point P, the rotation transformation matrix of the local coordinate system ( , , ) where the heat source is located relative to the global coordinate system ( x , y , z ) can be expressed as: Rot = ; Substitute the above formulas into = * Rot in the formula, and the transformation matrix TR can be obtained as: TR = ; Write FORTRAN code according to the following parameters to obtain a heat source subroutine, and the heat source subroutine is as Figure 8 shown.

[0114] wu (welding voltage); wi (welding current); effi (welding efficiency coefficient); Q (input power); Starting point coordinates ( , , ); Shape parameters of the double ellipsoidal heat source , , b, c; Heat source distribution coefficient ; Implementation code for the double ellipsoidal heat source to move along an arc curve: "shape1=exp(-3.0*(x / sqrt(2 / (-400*x**2+40*x+1)) $ -(20*x+20*y0-400*x*y0+sqrt(2.0)*sin(pi / 4+10*sqrt(2.0)*d) $ +400*x0*sqrt(-x**2+x / 10+0.0025)+20*sqrt(-x**2+x / 10+0.0025) $ -20*sqrt(2.0)*cos(pi / 4+10*sqrt(2.0)*d)*sqrt(-x**2+x / 10+0.0025) $ -20*sqrt(2.0)*x*sin(pi / 4+10*sqrt(2.0)*d)-1) $ / (400*sqrt(2 / (-400*x**2+40*x+1))*sqrt(-x**2+x / 10+0.0025)) $ -(y*(20*x-1)) / (20*sqrt(2 / (-400*x**2+40*x+1)) $*sqrt(-x**2+x / 10+0.0025)))**2.0 / (a1)**2.0-3.0*(y / sqrt(2 / (-400*x**2+40*x+1)) $ -(20*x-20*x0+400*x*x0+sqrt(2.0)*cos(pi / 4+10*sqrt(2.0)*d) $ +400*y0*sqrt(-x**2+x / 10+0.0025) $ -20*sqrt(-x**2+x / 10+0.0025) $ +20*sqrt(2.0)*sin(pi / 4+10*sqrt(2.0)*d)*sqrt(-x**2+x / 10+0.0025) $ -20\sqrt{2.0}x\cos(\frac{\pi}{4} + 10\sqrt{2.0}d) - 1 $ / (400\sqrt{\frac{2}{-400x^{2}+40x + 1}}\sqrt{-x^{2}+\frac{x}{10}+0.0025}) $ +\frac{x(20x - 1)}{20\sqrt{\frac{2}{-400x^{2}+40x + 1}} $ \sqrt{-x^{2}+\frac{x}{10}+0.0025})^{2.0} / b^{2.0} $ - 3.0(z - z_0)^{2.0} / c^{2.0}) shape2=\exp(-3.0(\frac{x}{\sqrt{\frac{2}{-400x^{2}+40x + 1}}} $ -(20x + 20y_0 - 400xy_0+\sqrt{2.0}\sin(\frac{\pi}{4}+10\sqrt{2.0}d) $ +400x_0\sqrt{-x^{2}+\frac{x}{10}+0.0025}+20\sqrt{-x^{2}+\frac{x}{10}+0.0025} $ -20\sqrt{2.0}\cos(\frac{\pi}{4}+10\sqrt{2.0}d)\sqrt{-x^{2}+\frac{x}{10}+0.0025} $ -20\sqrt{2.0}x\sin(\frac{\pi}{4}+10\sqrt{2.0}d)-1) $ / (400\sqrt{\frac{2}{-400x^{2}+40x + 1}}\sqrt{-x^{2}+\frac{x}{10}+0.0025}) $ -\frac{y(20x - 1)}{20\sqrt{\frac{2}{-400x^{2}+40x + 1}} $ \sqrt{-x^{2}+\frac{x}{10}+0.0025})^{2.0} / (a2)^{2.0}-3.0(\frac{y}{\sqrt{\frac{2}{-400x^{2}+40x + 1}}} $ -(20x - 20x_0+400xx_0+\sqrt{2.0}\cos(\frac{\pi}{4}+10\sqrt{2.0}d) $ +400y_0\sqrt{-x^{2}+\frac{x}{10}+0.0025} $ -20\sqrt{-x^{2}+\frac{x}{10}+0.0025} $ +20*sqrt(2.0)*sin(pi / 4+10*sqrt(2.0)*d)*sqrt(-x**2+x / 10+0.0025) $ -20*sqrt(2.0)*x*cos(pi / 4+10*sqrt(2.0)*d)-1) $ / (400*sqrt(2 / (-400*x**2+40*x+1))*sqrt(-x**2+x / 10+0.0025)) $ +(x*(20*x-1)) / (20*sqrt(2 / (-400*x**2+40*x+1)) $ *sqrt(-x**2+x / 10+0.0025)))**2.0 / b**2.0 $ -3.0*(z-z0)**2.0 / c**2.0) ": Calculate the shapes shape1 and shape2 of the double-ellipsoid heat source according to a specific mathematical formula and substituting data.

[0115] Result analysis and post-processing: After the calculation is completed, in the ABAQUS Visualization module, extract data results such as the temperature field, stress field, and strain field according to the user's customized requirements for visual analysis, analyze the thermo-mechanical coupling process of parametric curve additive manufacturing and remanufacturing, reveal the evolution laws of the temperature field and stress field, and optimize the surface additive manufacturing and remanufacturing processes based on the relevant results. As Figure 9 shown is the stress distribution of the model during the welding simulation.

[0116] Through the above description, those skilled in the art can, without departing from the technical idea of this invention, make various changes and modifications within the protection scope of this invention. The matters not covered by this invention belong to the common general knowledge of those skilled in the art.

Claims

1. A finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path, characterized in that It includes the following steps: Step 1, geometric model construction: According to the actual situation of surface additive manufacturing and remanufacturing engineering, establish the required geometric model by using finite element software; Step 2, material property setting: Set the material physical property parameters of the geometric model established in Step 1 in the finite element software; Step 3, assembling components: Assemble the geometric model with set parameters in Step 2 into a solid model in the finite element software; Step 4, mesh generation: Use the corresponding module in the finite element software to generate a mesh for the solid model established in Step 3; Step 5, setting analysis steps: Establish a certain number of analysis steps for the solid model with mesh generation completed; Step 6, applying loads and setting boundary conditions: According to the actual situation of surface additive manufacturing and remanufacturing engineering, apply loads to the finite element model established in Step 5 and set the corresponding boundary conditions; Step 7, writing and calling the heat source subroutine: According to the characteristics of the welding heat source and process parameters, write a user subroutine and solve it by calling the user subroutine; Step 8, result analysis and post-processing: Conduct a visual analysis of the calculation results in Step 7 and optimize the surface additive manufacturing and remanufacturing process based on the relevant results.

2. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 1, characterized in that The specific method of Step 1 is as follows: According to the actual situation of surface additive manufacturing and remanufacturing engineering, establish a geometric model containing a surface welding plate and a semi-circular cross-section weld by drawing in the finite element software ABAQUS or importing from other 3D modeling software. The length, width, height of the surface welding plate and the geometric dimensions of the weld are user-defined.

3. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 1, characterized in that The specific method of Step 2 is as follows: Set the material physical property parameters matching the surface additive manufacturing and remanufacturing process in the ABAQUS Property module, including general physical property parameters, mechanical parameters and thermal property parameters; The specific method of Step 3 is as follows: Assemble the geometric model into a solid through the ABAQUS Assembly module.

4. A finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 1, characterized in that The specific method of Step 4 is as follows: According to the structural dimensions and calculation accuracy of the established model, generate a mesh for it in the ABAQUS Mesh module, and select appropriate mesh strategies and element types according to the model structural characteristics and the established analysis type to precisely control the mesh size and density; The specific method of Step 5 is as follows: In the ABAQUS Step module, create a certain number of analysis steps according to the weld size and the number of element layers, set the solution parameters, and simulate the weld additive deposition process through element birth and death based on the number of analysis steps and the number of elements in the weld area.

5. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 1, wherein The specific method of Step 6 is as follows: According to the actual situation of surface additive manufacturing and remanufacturing engineering, apply loads to the established finite element model in the ABAQUS Interaction and Load modules and set the corresponding boundary conditions, where the boundary conditions include thermal boundary conditions and displacement boundary conditions; The specific method of Step 7 is as follows: According to the characteristics of the welding heat source and process parameters, write a DFLUX user subroutine to define the heat source model and the heat source movement trajectory, and set to call the user subroutine for solution in the ABAQUS Job module.

6. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 1, characterized in that The specific method of Step 8 is as follows: After the calculation in Step 7 is completed, data results such as the temperature field, stress field, and strain field are extracted in the ABAQUS Visualization module for visualization analysis, to analyze the thermo-mechanical coupling process of surface additive manufacturing and remanufacturing, reveal the evolution laws of the temperature field and stress field, and optimize the surface additive manufacturing and remanufacturing processes based on the relevant results.

7. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 4, characterized in that, The realization of the weld additive deposition process by element birth and death in Step 4 is achieved by writing Python code using the "Model change" instruction. The establishment of the analysis steps in Step 5 is implemented by GUI operation or by writing Python code. For the steps of defining multiple analysis steps according to the weld size and element layer, first, enter the ABAQUS software interface, click the Model button, and successively open Model-Edit keywords-model-1 to enter the analysis step interface, and write the analysis steps through Python code.

8. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 7, characterized in that, The specific steps for implementing the writing of Python code using the "Model change" instruction in Step 4 include: Step 4.1, initialize variables; Step 4.2, set the model keyword block; Step 4.3, loop to process data; Step 4.4, generate birth and death elements.

9. A finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 7, characterized in that In step seven of writing and calling the heat source subroutine, the heat source is selected as a surface heat source or a volume heat source according to the actual engineering situation. The movement of the heat source is realized through the coordinate transformation of the global coordinates ( x , y , z ) and the local coordinates ( , , ): ； ； ； Among them, Rot is the rotation transformation matrix of the local coordinate system relative to the global coordinate system; Trans is the corresponding translation transformation matrix.

10. The finite element modeling method for surface additive manufacturing and remanufacturing based on a curved path according to claim 9, wherein: Use the coordinates of the double ellipsoidal heat source in the global coordinate system ( x , y , z ) to represent its coordinates in the local coordinate system ( x 1, y 1, z 1). Substitute the obtained expression of the local coordinates into the heat source mathematical model and write the corresponding program, then the program code for the synchronous translation and rotation of the double ellipsoidal heat source along the arc curve can be obtained; The heat source subroutine code is a FORTRAN subroutine used to calculate the heat flux during welding. The specific process of the heat source subroutine is as follows: Step 7.1, program header and variable definition; Step 7.2, welding parameter definition and assignment; Step 7.3, relevant values and calculations of the double ellipsoid heat source; Step 7.4, calculate the heat flux density according to the conditions; Step 7.5, end of the subroutine.

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