A method and system for SLM energy density prediction based on spatiotemporal decoupling tensors and GPU acceleration.

Abstract

This invention discloses a method and system for predicting energy density in additive manufacturing based on spatiotemporal decoupling and hardware acceleration. The invention transforms continuous geometric space into a mesh through voxel discretization; constructs a total heat source tensor representing the cumulative energy distribution along the laser scanning path; performs spatiotemporal decoupling on the heat conduction model, transforming the four-dimensional transient problem into a three-dimensional static spatial integration problem; equivalences this integration problem to convolution operations, solving for the energy density field through the convolution of the total heat source tensor and the heat diffusion kernel tensor; utilizes GPU parallel acceleration for the convolution calculation; and finally, performs defect prediction and process optimization based on the energy density field. This invention avoids the time-consuming iterations of traditional transient simulations, achieving efficient and high-fidelity thermal process simulation at the part scale, significantly shortening the process development cycle.

Description

Technical Field

[0001] This application relates to the field of additive manufacturing, specifically to a method and system for predicting energy density in SLM based on spatiotemporal decoupling tensors and GPU acceleration. Background Technology

[0002] In the development of high-quality, repeatable SLM processes, accurate and efficient simulation and prediction of thermal behavior during processing, thereby optimizing process parameters and suppressing defect generation, has become a key technology urgently needed by both academia and industry. Currently, numerical simulation methods in this field mainly rely on transient thermo-mechanical simulation techniques based on the finite element method (FEM). This type of method iteratively solves the classical transient heat conduction partial differential equations step-by-step in the discrete spatial and temporal domains, obtaining relatively accurate evolution histories of temperature and stress fields, thereby assessing the molten pool morphology and predicting defects.

[0003] However, traditional FEM-based simulation methods suffer from inherent computational efficiency bottlenecks when dealing with problems like SLM, which exhibit "moving heat source" characteristics, severely limiting their application in practical process development.

[0004] The computational cost is extremely high: Laser scanning speeds are extremely fast during SLM (Sequencing and Manufacturing), the molten pool size is tiny, while the part dimensions are relatively large. To accurately capture transient thermal behavior, simulations must be performed with extremely fine spatial meshes and extremely short time steps, resulting in a huge degree of computational freedom. Simulating a single layer or several scans of an actual part often takes several hours, while simulating the entire manufacturing process of a 3D part requires several days or even weeks of computation time, completely failing to meet the needs of rapid iterative process development and optimization.

[0005] The contradiction between simulation scale and computational accuracy: In order to achieve macroscopic simulation at the "part level", it is often necessary to use oversimplified heat source models or coarse meshes, but this sacrifices simulation accuracy and cannot accurately reflect the details and key thermal history accumulation effects at the "melt pool level". On the other hand, high-fidelity "melt pool level" simulations are limited by computational resources and can only simulate very limited scan trajectories and times, making them difficult to apply to the evaluation of the overall forming quality and stability of the part.

[0006] Process optimization heavily relies on physical trial and error: Traditional high-fidelity simulation is slow and costly, making it difficult to quickly screen and evaluate multiple sets of process parameters. Currently, SLM process development still largely depends on expensive and time-consuming physical "trial and error" experiments, repeatedly adjusting parameters, conducting printing tests, and then performing non-destructive / destructive testing to find the optimal process window. This leads to long R&D cycles and high material and equipment costs.

[0007] Therefore, there is an urgent need in this field to develop a new numerical simulation method that can fundamentally break through the bottleneck of computational efficiency, enabling rapid or even near real-time prediction of the thermal field of the SLM process at the part scale while ensuring physical accuracy. This would provide an efficient and reliable digital tool for process parameter optimization and defect control, thereby breaking through the current bottleneck in the development and application of SLM technology. Summary of the Invention

[0008] To address the aforementioned technical problems, the purpose of this application is to provide a method and system for predicting SLM energy density based on spatiotemporal decoupling tensors and GPU acceleration, wherein the method for predicting SLM energy density based on spatiotemporal decoupling tensors and GPU acceleration includes the following steps:

[0009] Voxelization preprocessing steps: Obtain the 3D model of the part to be processed, construct a 3D computational domain covering the molten pool and heat-affected zone, and perform voxelization preprocessing based on the preset mesh step size. The three-dimensional computational domain is discretized into a voxel mesh, and a global coordinate index is assigned to each voxel. , , ) and its node coordinates ;

[0010] Steps for constructing the space heat source tensor: Based on the energy density distribution function of the laser scanning path and the Gaussian heat source, calculate the instantaneous position of each laser spot on the laser scanning path. Corresponding spatial heat source tensor Furthermore, discrete sampling is performed on a voxel grid, and the instantaneous position of each laser spot is recorded. The spatial heat source tensors are superimposed to generate the total heat source tensor. ;

[0011] The spatiotemporal decoupling and static transformation steps are as follows: Quasi-steady-state assumptions are made for the transient heat conduction equation in the additive manufacturing process, thus reasonably neglecting the partial derivatives of the temperature field with respect to time; a dimensionless coordinate system that moves synchronously with the laser spot is introduced. The problem is then transformed into a four-dimensional transient heat conduction problem along the scanning direction in a global coordinate system. The three-dimensional spatial integration problem yields the integral expression of the temperature field in the global coordinate system. ;

[0012] Energy density field calculation steps: Solve the integral expression of the temperature field on the voxel grid to construct the total heat source tensor. The influence of thermal diffusion on the nuclear tensor The energy density field is obtained by performing a three-dimensional discrete convolution operation. The thermal diffusion affects the nuclear tensor. Constructed based on voxel meshes, its element values The relative offset vector between the target voxel and the heat source voxel and the preset characteristic diffusion length. The decision was made to simulate the spatial decay of thermal diffusion effects;

[0013] Hardware-accelerated computation steps: The 3D discrete convolution computation is accelerated in parallel using a graphics processing unit (GPU); the computation task of the voxel mesh is mapped to the parallel thread architecture of the GPU; the thermal diffusion effect kernel tensor is... Preloaded into the GPU's shared memory; the GPU's TensorCore hardware unit is used to decompose the 3D convolution calculation into a 2D matrix multiplication operation for accelerated computation;

[0014] Process optimization steps: Based on the calculated energy density field, identify potential defect areas where the energy density value exceeds the overheating threshold and falls below the insufficient melting threshold, and adjust the laser power and scanning speed parameters accordingly. Iterate the above process until the energy density field distribution is in the ideal range.

[0015] Preferably, the energy density distribution function of the Gaussian heat source is:

[0016] ;

[0017] In the formula, Indicates laser power; Laser energy in global coordinate system Standard deviation of the distribution in three directions; The coordinates are in an instantaneous local coordinate system with the instantaneous position of the laser spot as the origin. The coordinate axes of this instantaneous local coordinate system are parallel to the global coordinate system.

[0018] The energy density distribution function of the Gaussian heat source describes the distribution of laser energy density relative to the center of the laser spot in the surrounding space centered on the current instantaneous position of the laser spot, using an instantaneous local coordinate system.

[0019] Preferably, in the spatial heat source tensor construction step, for each instantaneous position of the laser spot... Calculate its spatial heat source tensor The method is as follows: for the index of any voxel in the voxel grid ( , , ), by calculating the node coordinates of the voxel. With the instantaneous position coordinates of the laser spot The difference is used to obtain its coordinates in the instantaneous local coordinate system. ;

[0020] coordinates Substituting the energy density distribution function of the Gaussian heat source, the heat source intensity value of the voxel is obtained. ;

[0021] By traversing all voxels, the discrete spatial heat source tensor at the instantaneous position of the current laser spot can be obtained. .

[0022] Preferably, the spatiotemporal decoupling and static transformation steps specifically include:

[0023] By introducing a coordinate system that moves synchronously with the moving laser spot heat source and performing a dimensionless transformation, the observation perspective is shifted from a static global coordinate system containing time variables. Transform to the moving coordinate system ,in, For laser scanning speed, laser spot radius, It characterizes the instantaneous axial offset of a spatial point relative to the center of the moving heat source, thereby achieving a relatively stationary moving laser spot heat source in a moving coordinate system;

[0024] Introducing dimensionless temperature variables Furthermore, by performing dimensionless processing on the transient heat conduction equation and simplifying it by neglecting thermal diffusion effects under the high Pecklet number condition, a coordinate gradient equation based on the high Pecklet number approximation can be obtained. ;in, Dimensionless temperature exist Rate of change of direction Where is the thermal diffusivity, This is the heat source term after dimensionless transformation.

[0025] Preferably, the integral solution of the coordinate gradient equation based on the high Peklay number approximation is the dimensionless temperature of a point in the moving coordinate system, approximately equal to the temperature of the laser beam from... Scan to point During the process, the cumulative contribution of all heat sources along the path;

[0026] According to the transformation relationship between the moving coordinate system and the global coordinate system, when observed at a fixed time, the derivative of the integral variable in the moving coordinate system is linearly proportional to the derivative of the integral variable in the global coordinate system. When the integral variable in the moving coordinate system changes from its initial value to its current value, the integral variable in the global coordinate system changes from its corresponding initial position to the spatial coordinates of the target point.

[0027] The temperature field expression in the global coordinate system is as follows: ,in, , It is a global coordinate system Integral variables on the axis.

[0028] Preferably, the thermal diffusion effect kernel function is:

[0029] ;

[0030] In the formula, The relative offset vector between the target voxel and the heat source voxel; It is a normalization constant that makes the sum of all elements of the kernel tensor equal to 1; It is the characteristic diffusion length, a physical parameter determined through experimental or simulation calibration; These represent the grid step size in the three coordinate directions of the voxel.

[0031] Preferably, the three-dimensional convolution operation is accelerated using an algorithm based on the Fast Fourier Transform (FFT), specifically:

[0032] A three-dimensional fast Fourier transform is performed on the total heat source tensor and the heat diffusion effect kernel tensor. The two transform results are multiplied point by point in the frequency domain. A three-dimensional inverse fast Fourier transform is performed on the frequency domain result obtained by multiplication to obtain the energy density field in the spatial domain, thereby significantly reducing the computational complexity from the sixth power level to close to the cubic logarithmic level.

[0033] Preferably, the hardware-accelerated computing step specifically includes:

[0034] The NVIDIA CUDA parallel computing framework is used to map the computational tasks of the voxel grid onto the massively parallel thread architecture of the GPU.

[0035] The shared memory of the GPU is used to cache local data of the thermal diffusion affecting the kernel tensor, thereby reducing memory access latency;

[0036] The 3D convolution calculation is accelerated by decomposing and reconstructing it into a series of 2D matrix multiplication operations using the GPU's TensorCore hardware unit.

[0037] Preferably, the process optimization step specifically includes:

[0038] Set an overheated energy density threshold and an undermelting energy density threshold for the energy density field;

[0039] Regions with energy density values ​​exceeding the overheating energy density threshold are identified as overheated zones.

[0040] Regions with energy density values ​​lower than the insufficient melting energy density threshold are identified as insufficient melting zones;

[0041] For the identified defective areas, adjust the laser power or scanning speed parameters and iterate the calculation until the energy density field distribution of the entire part is within the ideal range.

[0042] A system for performing an additive manufacturing energy density prediction method based on spatiotemporal decoupling and hardware acceleration, the system comprising:

[0043] A graphics processing unit (GPU) equipped with a CUDA parallel computing architecture and TensorCore hardware units;

[0044] System memory is used to store the 3D model, voxel mesh data, and total heat source tensor. Thermal diffusion affects the nuclear tensor ;

[0045] The GPU is configured to: perform the voxelization preprocessing step and the spatial heat source tensor construction step; and load the total heat source tensor from system memory. The influence of thermal diffusion on the nuclear tensor The energy density field is transferred to the video memory; the energy density field calculation step and the hardware-accelerated calculation step are executed, and the three-dimensional discrete convolution operation is completed by calling the kernel function and the TensorCore instruction; the calculated energy density field is transferred back to the system memory;

[0046] A processor is configured to perform the process optimization steps, including defect identification and parameter optimization based on an energy density field. Beneficial effects

[0047] This application has at least the following beneficial effects:

[0048] This invention transforms the moving heat source in SLM into a static spatial integration problem through spatiotemporal decoupling technology, completely avoiding time-consuming iterations. Furthermore, it innovatively equates the physical problem to three-dimensional tensor convolution and utilizes GPU parallel computing and FFT algorithms for extreme acceleration, further reducing the computational complexity of a single thermal field prediction to O(NlogN). This allows the prediction of the three-dimensional energy density field of the entire part to be completed within minutes or even seconds, transforming simulation-based process optimization from "offline analysis" to "online tool." It achieves efficient and high-fidelity thermal process simulation at the part scale, fundamentally overcoming the time-sensitive bottleneck of traditional simulation methods that cannot be used for actual process development.

[0049] The output of this invention is a physical quantity that directly maps to the SLM forming process—energy density. This field quantity comprehensively reflects the laser power, scanning speed, scanning strategy, and most importantly, the thermal accumulation effect. It is the core basis for predicting the stability of the molten pool and judging whether defects such as spheroidization, lack of fusion, or overheating have occurred. Based on this energy density field, overheated areas and under-melted areas in parts can be quickly and automatically identified, thereby guiding process engineers to adjust the laser power and scanning speed in a directional and quantitative manner, effectively suppressing the generation of defects. This provides a strong technical guarantee for achieving "success on the first print" of high-performance metal parts. The obtained energy density field is a key technical indicator for evaluating the SLM forming quality and provides a direct and reliable quantitative basis for defect prediction and process optimization.

[0050] This invention is a complete technical system that deeply integrates physical modeling, mathematical transformation, and hardware acceleration. By accurately mapping the optimized tensor convolution algorithm onto the massively parallel architecture of the GPU and its TensorCore dedicated computing units, it fully leverages the performance of modern computing hardware and successfully solves the computational bottleneck of high-resolution simulation at the component level. The system can handle the entire process from rapid voxelization of large-scale STL models to energy density field reconstruction, forming an efficient "design-simulation-optimization" closed loop, which has extremely high engineering application value and industrial promotion prospects. Attached Figure Description

[0051] To more clearly illustrate the technical solutions and advantages in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 The flowchart shows the steps of the SLM energy density prediction method based on spatiotemporal decoupling tensor and GPU acceleration.

[0053] Figure 2 This is a comparison diagram of the traditional FEM process and the process of this invention;

[0054] Figure 3 This is a flowchart of the process optimization method for SLM energy density prediction based on spatiotemporal decoupling tensor and GPU acceleration. Detailed Implementation

[0055] To further illustrate the technical means and effects adopted by this application to achieve the intended inventive objective, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of the SLM energy density prediction method and system based on spatiotemporal decoupling tensors and GPU acceleration proposed in this application. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0057] The following description, in conjunction with the accompanying drawings, details the specific scheme of the SLM energy density prediction method and system based on spatiotemporal decoupling tensor and GPU acceleration provided in this application.

[0058] Please see Figure 1 and Figure 2 The diagram illustrates a flowchart of an embodiment of the SLM energy density prediction method based on spatiotemporal decoupling tensors and GPU acceleration provided in this application. The method includes the following steps:

[0059] S1, Voxelization Preprocessing and Voxel Mesh

[0060] Obtain a three-dimensional computer-aided design model of the part to be processed, construct a three-dimensional computational domain covering the molten pool and heat-affected zone, and discretize the three-dimensional computational domain into a voxel mesh along the global coordinate system.

[0061] Specifically, the three-dimensional computational domain is moved along the global coordinate system. Discretization of directions, determining the grid step size as follows , and voxel node coordinates ,in To calculate the coordinates of the origin of the computational domain, ( , , () is a voxel index.

[0062] In this embodiment, the step size of the voxel mesh can be determined according to the required computational accuracy and computational resources, transforming the continuous geometric space into a voxel mesh, providing a data foundation for subsequent tensor operations.

[0063] S2. Construction of the spatial heat source tensor based on the energy density distribution function of the Gaussian heat source.

[0064] The energy distribution of the laser is described using the energy density distribution function of a Gaussian heat source:

[0065] ;

[0066] In the formula, Indicates laser power; Do not consider the laser energy in the global coordinate system The standard deviation of the distribution in three directions is used to characterize the anisotropic distribution characteristics of laser energy; The instantaneous position of the laser spot The instantaneous local coordinates of the origin are used to characterize the anisotropic distribution of laser energy.

[0067] Instantaneous local coordinate system The origin of the system coincides with the instantaneous position of the laser spot at a certain moment during the processing. The three axes of the instantaneous local coordinate system correspond one-to-one with the axes of the global coordinate system. With the help of the instantaneous local coordinate system, the energy density distribution function of the Gaussian heat source can describe the distribution state of the laser energy density in the surrounding space centered on the instantaneous position of the current laser spot, thus reflecting the anisotropic distribution characteristics of laser energy in different directions.

[0068] Spatial heat source tensor construction: for the instantaneous position of a laser spot on the scanning path The energy density distribution function of the Gaussian heat source is discretized on a voxel grid, and the heat source intensity value of each voxel is calculated to construct a three-dimensional spatial heat source tensor at the instantaneous position of the laser spot. .

[0069] The specific steps are as follows: For voxel index ( , , The voxels of ) and their node coordinates First, calculate the instantaneous local coordinates of the node with the current instantaneous position of the laser spot as the origin:

[0070] ;

[0071] Subsequently, this instantaneous local coordinates were substituted into the Gaussian heat source energy density distribution function. The heat source intensity value of the voxel was obtained. By traversing all voxels, the discrete spatial heat source tensor at the instantaneous position of the current laser spot can be obtained. .

[0072] Total energy distribution along the scanning path: The entire scanning path is discretized into a set consisting of a finite number of sequential laser spot instantaneous positions. This is achieved by representing the spatial heat source tensor corresponding to each instantaneous position of the laser spot along the path. The elements are superimposed to generate a total heat source tensor for the scan path. :

[0073] ;

[0074] in, The total number of discrete locations on the path; the total heat source tensor. It characterizes the cumulative energy density distribution deposited in three-dimensional space along the entire laser scanning path, transforming the continuous energy input process into the superposition operation of discrete tensors, and providing an accurate input data foundation for subsequent use of efficient temperature field calculation algorithms based on convolution.

[0075] S3. Spatiotemporal decoupling and static transformation of the heat conduction model

[0076] In this embodiment, the heat conduction behavior during laser powder bed melting (SLM) is controlled by the classical transient heat conduction equation:

[0077] ;

[0078] in, For material density, For specific heat capacity, Thermal conductivity, For temperature field, For time, This is a heat source term characterizing the spatial and temporal distribution of laser thermal input. This equation reflects the temporal and spatial coupling characteristics of heat transfer, and its high solution complexity and computational cost make it a long-standing challenge in numerical simulation.

[0079] To overcome the limitations of traditional transient simulation methods and achieve rapid calculation of part dimensions and efficient evaluation of scanning strategies, this embodiment introduces the integral transform method and, combined with the process characteristics of laser powder bed melting, simplifies and transforms the above-mentioned control equations in a series of ways.

[0080] S3.1 Quasi-steady-state assumption

[0081] Considering the high-speed laser scanning characteristic in SLM (Sequencing Laser Processing), when the scanning speed is sufficiently high, the heat source moves rapidly, and its time evolution characteristics are significantly suppressed. When observed in a coordinate system where the heat source moves synchronously with the moving laser spot, the temperature field distribution exhibits steady-state characteristics. Based on this, the partial derivatives of the temperature field with respect to time can be reasonably ignored, i.e.: This quasi-steady-state assumption is the physical premise for subsequently eliminating time variables and achieving spatiotemporal decoupling.

[0082] S3.2 Dimensionlessness and Coordinate Transformation

[0083] To completely eliminate the time variable in the equations and reveal the dimensionless number of the dominant physical process, this embodiment performs a strict dimensionless transformation:

[0084] Introducing dimensionless temperature variables ,in This is the preheating temperature. For ambient temperature, For laser power, thermal conductivity and The laser spot radius is used to construct a scale with temperature dimensions, which is then used to make the temperature dimensionless.

[0085] Subsequently, a coordinate system is introduced that moves synchronously with the moving laser spot heat source, and dimensionless moving coordinates are defined:

[0086] ;

[0087] in, This refers to the laser scanning speed; This characterizes the instantaneous axial offset of a spatial point relative to the moving laser beam heat source. This transformation shifts the viewpoint from a static global coordinate system. Transform to a coordinate system that moves with the heat source of the moving laser spot. In the moving coordinate system, the moving laser spot heat source is relatively stationary. The transient problem that originally depended on time is transformed into a steady-state problem that mainly depends on spatial coordinates. This achieves dimensionality reduction and decoupling from four dimensions to three dimensions, fundamentally reducing the solution complexity.

[0088] Based on the above transformation, and through dimensional analysis, the simplified dimensionless governing equations are obtained:

[0089] ;

[0090] in, Where is the thermal diffusivity, For the dimensionless heat source term, Represents the thermal diffusion effect. Represents the thermal convection effect caused by the movement of the heat source, the sum of thermal diffusion and thermal convection, and the input of the heat source. balance.

[0091] S3.3 Further simplification under high Pecklet number conditions

[0092] Pecklet number This characterizes the relative intensity of thermal convection and thermal diffusion. Under the high-speed scanning conditions of SLM, it typically satisfies... This means that thermal convection is dominant, and thermal diffusion is negligible. Therefore, the governing equations can be further simplified to coordinate gradient equations based on the high Peklay number approximation: The high Pecklet number approximation of the coordinate gradient equation shows that, along the scanning direction in the moving coordinate system... The temperature gradient is mainly determined by the distribution of the heat source of the moving laser spot.

[0093] S3.4 Solving the integral

[0094] It is about First-order ordinary differential equation, coordinates along the scanning path By integrating, the instantaneous solution for the dimensionless temperature can be directly obtained:

[0095] ;

[0096] in, The variable is the integral variable, representing the translation coordinate system. A point on the axis. The physical meaning of this integral solution is: moving a point in the coordinate system. The dimensionless temperature is approximately equal to the laser's temperature from which it travels. Scan to this point During the process, the cumulative contribution of all heat sources along the path.

[0097] S3.5 Convert to global space integral form

[0098] This step aims to transform the solution of S3.4 back to the global coordinate system. In this process, the time variable is completely eliminated, resulting in a pure spatial integral form.

[0099] Transformation Relationship Therefore, when observed at a fixed time... ,satisfy When the integral variable in the moving coordinate system Change to At that time, the corresponding integration variable in the global coordinate system Change to Therefore, we can obtain:

[0100] ;

[0101] in, It is a global coordinate system The integral variable on, and These are the fixed coordinates of the target point. Let... Finally, the temperature field expression in the global coordinate system is obtained: .

[0102] Thus, through the quasi-steady-state assumption, dimensionless transformation, coordinate transformation, and integral solution method proposed in this embodiment, a four-dimensional transient heat conduction problem with implicit time variables has been successfully transformed into a pure three-dimensional spatial integration problem in the global coordinate system. This fundamentally avoids the time-consuming time step iteration process in traditional methods, and improves computational efficiency by orders of magnitude, laying the core theoretical foundation for realizing rapid thermal process simulation at the part scale.

[0103] S4. Efficient calculation of energy density field based on tensor convolution

[0104] As described in S3.5, after spatiotemporal decoupling and coordinate transformation, the thermal accumulation effect in the laser processing process can be transformed into a three-dimensional spatial integration problem in a global coordinate system, i.e., a point... The temperature field at that location can be expressed as: This integral represents the historical cumulative sum of contributions from all heat sources along the scanning path. To achieve efficient calculation of this integral, this embodiment proposes an innovative tensor convolution algorithm: the physical process of "integration along the path" is mathematically equivalent to the operation of "first superimposing all heat sources along the path, and then performing three-dimensional convolution with a kernel function that represents the heat diffusion effect".

[0105] Construction of S4.1 Total Heat Source Tensor and Thermal Diffusion Kernel Tensor

[0106] As described in S2, all instantaneous spatial heat source tensors generated after the entire scan path is discretized have been pre-stacked to obtain the total heat source tensor. This tensor is numerically equivalent to the original energy distribution in three-dimensional space of all heat sources along the path, without considering diffusion.

[0107] Subsequently, a thermal diffusion effect on the nuclear tensor is constructed. Although S3 ignores the thermal diffusion term in the derivation process to obtain a simplified integral form based on the high Pecklet number assumption, in order to ensure that the final simulation results are close to physical reality, this embodiment introduces a kernel function to compensate for the ignored lateral and longitudinal thermal diffusion effects.

[0108] The concept behind this influence kernel is derived from the decay characteristics of the fundamental solution (Green's function) of the steady-state heat conduction equation. In an infinite medium, the steady-state temperature field generated by a point heat source is inversely proportional to the distance. Drawing on this physical law, and considering computational efficiency and the characteristics of discrete meshes, the influence kernel is designed as a function that decays with distance.

[0109] Based on the voxel mesh constructed using S1, the target voxel is denoted by its global coordinate index as ( , , Global coordinate index of the heat source voxel (the voxel corresponding to the instantaneous position of the laser spot). Then the relative offset vector between the target voxel and the heat source voxel is The value of the three-dimensional thermal diffusion-affected kernel tensor at the relative offset is defined as follows:

[0110] ;

[0111] In the formula, It is a normalized constant that ensures the volume sum of the kernel tensor is 1, thus satisfying energy conservation; The characteristic diffusion length controls the decay rate of the thermal diffusion effect and can be determined by calibration with finite element simulation or experimental results; this influence kernel function It characterizes the degree of thermal influence of a unit heat source located at the heat source voxel on the target voxel, and its influence decreases with increasing distance.

[0112] S4.2 Energy Density Field Calculation Based on Convolution

[0113] Energy density field Through the total heat source tensor The influence of thermal diffusion on the nuclear tensor The three-dimensional discrete convolution calculation yields: The physical meaning of this convolution operation is extremely clear: for any voxel in the three-dimensional computational domain, the energy density field It equals the sum of the intensities of the spatial heat source distribution corresponding to the instantaneous positions of all laser spots along the laser scanning path. The sum of energy contributions transferred to the target voxel after the thermal diffusion effect of the nuclear simulation has decayed due to thermal diffusion influence.

[0114] S4.3 Algorithm Acceleration Based on Fast Fourier Transform (FFT)

[0115] Directly calculating 3D discrete convolutions is extremely complex. To overcome this computational bottleneck, this embodiment uses a convolution theorem based on the Fast Fourier Transform (FFT) for acceleration.

[0116] First, perform three-dimensional fast Fourier transforms on the total heat source tensor and the heat diffusion kernel tensor respectively to obtain their complex representations in the frequency domain. Then, multiply the two transform results point by point in the frequency domain. Finally, perform a three-dimensional inverse fast Fourier transform on the frequency domain result obtained by multiplication to finally restore the energy density field in the spatial domain.

[0117] The FFT-based acceleration algorithm significantly reduces the computational complexity from the sixth power level to near the cubic logarithmic level. This fundamental improvement makes it possible for the first time to perform rapid calculations of high-resolution three-dimensional thermal processes at the part scale, fully utilizing the massively parallel computing architecture of modern graphics processors to achieve the ultimate computational acceleration effect.

[0118] S5, Parallel computing implementation based on GPU hardware acceleration

[0119] To efficiently perform the large-scale three-dimensional tensor convolution calculations described in S4, this embodiment uses a graphics processing unit (GPU) for hardware acceleration and has made specific optimizations to its parallel computing architecture to achieve engineering applications that enable rapid simulation at the part scale.

[0120] S5.1 Parallel Computing Design Based on CUDA Framework

[0121] The NVIDIA CUDA parallel computing framework is used to map the computational task of 3D voxel mesh onto the massively parallel thread architecture of the GPU. The specific implementation is as follows:

[0122] Task mapping: indexing each voxel ( , , It is uniquely mapped to a two-dimensional grid index of GPU block and thread, enabling fine-grained parallel computing.

[0123] Voxelization preprocessing: During the voxel mesh initialization stage, the geometric coordinates and heat source intensity values ​​of each voxel are calculated in parallel to make full use of the parallel processing capabilities of the GPU.

[0124] Convolution computation optimization: In the tensor convolution stage, each GPU thread is responsible for calculating the convolution result of a target voxel in the energy density field. By cleverly utilizing the GPU's shared memory to cache the local data of the thermal diffusion effect kernel, the high-latency access to global memory is significantly reduced, thereby greatly improving computational efficiency.

[0125] S5.2 Matrix Multiplication Acceleration Based on TensorCore

[0126] To further explore the hardware potential of modern GPUs, this embodiment utilizes its built-in Tensor Core hardware unit to accelerate convolution calculations. Tensor Core is a hardware component designed specifically for efficiently performing matrix multiplication and accumulation operations.

[0127] Algorithm mapping: The computation of 3D tensor convolution is mathematically decomposed and reconstructed into a series of 2D matrix multiplication operations. This decomposition makes the computation pattern perfectly match the dedicated computation instructions of Tensor Core.

[0128] Accuracy and performance: By utilizing the mixed-precision computing mode supported by Tensor Core, extremely high theoretical computational throughput is achieved while ensuring the accuracy of the final calculation results, significantly improving the efficiency of convolution operations.

[0129] S5.3 acceleration effect

[0130] After the aforementioned GPU hardware-specific optimizations, the overall computational efficiency of the energy density field prediction is improved by orders of magnitude. The originally computationally complex 3D convolution operation has its effective computational complexity significantly reduced with the joint acceleration of FFT and GPU hardware, making it possible to perform high-fidelity and high-efficiency rapid evaluation of thermal processes for part-level models.

[0131] S6. Defect prediction and process parameter optimization method based on energy density field

[0132] Energy density field generated based on S4 This embodiment further provides a method for rapid prediction of defects and optimization of process parameters in laser powder bed melting (SLM) forming. This method combines physical simulation results with process knowledge to provide direct guidance for achieving high-quality forming.

[0133] S6.1 Defect Criteria and Automatic Identification of Regions

[0134] like Figure 3 As shown, energy density field It comprehensively reflects the combined effects of scanning path, laser power, scanning speed, thermal accumulation effect, and thermal diffusion effect, and is a key indicator for evaluating molten pool behavior and solidification quality.

[0135] This embodiment automatically identifies potential defect areas by setting an energy density threshold: setting an overheating energy density threshold. If the energy density at a certain voxel satisfies > If the temperature is too high, the region is identified as an overheated zone; a threshold for insufficient melting energy density is set. If the energy density at a certain voxel satisfies < If the threshold is not met, the region is identified as an under-melted area; the threshold can be determined by calibration based on experimental data or high-fidelity simulation results of a specific material system.

[0136] S6.2 Defect Cause Analysis and Process Optimization Recommendations

[0137] After identifying the defective areas, their causes can be further analyzed, and optimization directions for process parameters can be proposed accordingly.

[0138] For overheated areas, laser power can be reduced and scanning speed increased to lower the linear energy input in that region, bringing the energy density back to a reasonable range. For under-melted areas, laser power can be increased and scanning speed decreased to increase the energy input in that region. Furthermore, scanning strategies can be adjusted, such as increasing the scan line overlap rate, to improve heat accumulation and ensure complete powder melting.

[0139] S6.3 Process Optimization Flow

[0140] The rapid optimization process provided in this embodiment is as follows:

[0141] (1) Based on the initial laser power, scanning speed, and scanning path, the energy density field of the part is obtained using the rapid calculation method described in S1 to S5. ;

[0142] (2) Based on the energy density threshold, automatically identify the overheated area and the under-melting area in the part;

[0143] (3) Quantitatively adjust the laser power and scanning speed of the corresponding area according to the distribution and severity of the defect type;

[0144] (4) Re-enter the adjusted process parameters into the model for calculation, verify the optimization effect, and iterate the above steps until the energy density field distribution of the entire part is within the ideal range.

[0145] The core advantage of this method is that, by using the efficient computing model, a process evaluation can be completed in minutes or even seconds, replacing traditional trial-and-error experiments or simulation calculations that take hours or even days, which greatly shortens the process development cycle and reduces R&D costs.

[0146] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments of this specification have been described above. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0147] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0148] The above description is only a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the principles of this application should be included within the protection scope of this application.

Claims

1. A method for SLM energy density prediction based on spatiotemporal decoupled tensors and GPU acceleration, characterized in that, The method comprises the following steps: The voxel preprocessing step: obtaining a three-dimensional model of a part to be processed, constructing a three-dimensional calculation domain, and discretizing the three-dimensional calculation domain along a global coordinate system into a voxel grid; The spatial heat source tensor construction step: based on the energy density distribution function of the Gaussian heat source, calculating the spatial heat source of each instantaneous position of the laser spot on the laser scanning path, discretely sampling each spatial heat source based on the voxel grid to obtain a spatial heat source tensor, superimposing all spatial heat source tensors to generate a total heat source tensor; The space-time decoupling and static transformation step: based on the high Peclet number characteristic caused by the high scanning speed of the laser, the moving heat source quasi-steady state assumption is established; in the dimensionless coordinate system moving synchronously with the laser spot, the partial derivative term of time in the transient heat conduction equation is omitted, thereby realizing the transformation of the physical model from four-dimensional space-time coupling to three-dimensional spatial integral problem; The energy density field construction step: based on the voxel grid, the temperature field function is constructed as a three-dimensional discrete convolution operation between the total heat source tensor and a heat diffusion influence kernel tensor to obtain an energy density field; wherein each element value of the heat diffusion influence kernel tensor represents the heat influence degree of a unit heat source voxel on any target voxel in its periphery, which is determined by the relative spatial position of the two voxels and the attenuation speed of the heat diffusion influence, thereby simulating the physical attenuation of heat energy with spatial distance; The hardware acceleration calculation step: mapping the calculation task of the voxel grid to the parallel thread architecture of the GPU; preloading the heat diffusion influence kernel tensor into the shared memory of the GPU; and utilizing the parallel computing capability of the GPU to decompose the three-dimensional convolution calculation into two-dimensional matrix calculation; The process optimization step: identifying the defect area based on the energy density field, adjusting the laser power and scanning speed, and iterating the foregoing steps to make the energy density field distribution in the ideal interval.

2. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration according to claim 1, wherein, The energy density distribution function of the Gaussian heat source: ； In the formula, represents the laser power; respectively are the standard deviations of the distribution of the laser energy in the global coordinate system in the three directions; is a local instantaneous coordinate system with the instantaneous position of the laser spot as the origin, and the coordinate axis direction of the local instantaneous coordinate system is parallel to the global coordinate system. The energy density distribution function of the Gaussian heat source represents the distribution state of laser energy density in the surrounding space with the instantaneous position of the current laser spot as the center, thereby reflecting the anisotropic distribution state of laser energy in different directions by means of the instantaneous local coordinate system.

3. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 2, wherein, In the spatial heat source tensor construction step, the instantaneous local coordinate is obtained based on the node coordinates of the voxel and the coordinates of the instantaneous position of the laser spot as the origin at the same time; Based on the instantaneous local coordinate and the energy density distribution function of the Gaussian heat source, the heat source intensity value of the voxel is obtained; By traversing all voxels at this time, the discrete spatial heat source tensor of the instantaneous position of the current laser spot is obtained.

4. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 1, wherein, The space-time decoupling and static transformation step specifically comprises: A coordinate system moving synchronously with the heat source of the moving laser spot is introduced and a dimensionless transformation is made. The observation view angle is transformed from the static global coordinate system with time variable to the moving coordinate system Transforming to the moving coordinate system wherein, is the laser scanning speed, is the laser spot radius, characterizes the instantaneous axial offset of the spatial point relative to the center of the laser spot; Introducing a dimensionless temperature variable and nondimensionalizing the transient heat conduction equation, the coordinate gradient equation based on high Peclet number approximation can be obtained ; wherein, dimensionless temperature At the rate of change of the direction, is the thermal diffusivity, is the dimensionless heat source term.

5. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 4, wherein, The integral solution of the coordinate gradient equation is the dimensionless temperature at a point in a moving coordinate system, which is approximately equal to the cumulative contribution of all heat sources on the path during the process of scanning the laser spot to the point . ​ According to the transformation relationship between the moving coordinate system and the global coordinate system, when observed at a fixed time, the differential of the integral variable in the moving coordinate system is in a linear proportional relationship with the differential of the integral variable in the global coordinate system, and when the integral variable in the moving coordinate system changes from its initial value to the current value, the integral variable in the global coordinate system changes from the corresponding initial position to the target point in space. temperature field expression in the global coordinate system: ; wherein , is an integral variable on the global coordinate system axis.

6. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 1, wherein, The energy density field construction step specifically comprises: constructing a three-dimensional heat diffusion influence kernel tensor at the relative offset based on the relative offset vector of the target voxel and the heat source voxel of the target voxel: ； wherein, is the relative shift vector of the target voxel and the heat source voxel; is a normalization constant such that the sum of all elements of the kernel tensor is 1 ; is the characteristic diffusion length, which is a physical parameter determined by calibration through experiments or simulations; are the grid steps in the three coordinate directions of the voxel, respectively.

7. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 6, wherein, the energy density , where the index of the target voxel , , , the index of the heat source voxel , for any voxel in the three-dimensional computational domain, the energy density field is the intensity superposition of the total heat source tensor of the spatial heat source distribution corresponding to all the instantaneous positions of the laser spots on the laser scanning path , the sum of the energy contributions to the target voxel after the thermal diffusion effect attenuation of the heat diffusion effect influenced by the kernel simulation Performing a three-dimensional fast Fourier transform on the total heat source tensor and the heat diffusion influence kernel tensor to obtain an energy density field in the spatial domain, thereby significantly reducing the computational complexity from the order of six to the order of three times the logarithmic level.

8. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 1, wherein, The hardware acceleration calculation step specifically comprises: Using the NVIDIA CUDA parallel computing framework to map the calculation task of the voxel grid to the large-scale parallel thread architecture of the GPU; Using the shared memory of the GPU to cache the local data of the heat diffusion influence kernel tensor to reduce memory access delay; Using the TensorCore hardware unit of the GPU to decompose and reconstruct the three-dimensional convolution calculation into a series of two-dimensional matrix multiplication operations for acceleration.

9. The SLM energy density prediction method based on spatiotemporal decoupled tensors and GPU acceleration of claim 6, wherein, The process optimization step specifically comprises: Setting an overheating energy density threshold and an insufficient melting energy density threshold for the energy density field; Identifying the region with an energy density value exceeding the overheating energy density threshold as an overheating region; Identifying the region with an energy density value lower than the insufficient melting energy density threshold as an insufficient melting region; Adjusting the laser power and scanning speed parameters for the identified defect region and iteratively calculating until the energy density field distribution of the entire part is in the ideal interval.

10. System for performing the method according to any one of claims 1 to 9, characterized in that The system comprises: A graphics processing unit (GPU) equipped with a CUDA parallel computing architecture and a TensorCore hardware unit; System memory for storing the three-dimensional model, voxel grid data, total heat source tensor, and heat diffusion influence kernel tensor; The GPU is configured to perform the voxelization preprocessing step and the spatial heat source tensor construction step; load the total heat source tensor and the heat diffusion influence kernel tensor from the system memory to the video memory; perform the energy density field construction step and the hardware acceleration calculation step to complete the three-dimensional discrete convolution operation by calling the kernel function and the TensorCore instruction; and return the calculated energy density field to the system memory; A processor configured to perform the process optimization step to identify defects and optimize parameters based on the energy density field.

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