Method and system for producing non-standard precision parts

Abstract

The invention discloses a non-standard precision part production method and system, and the method comprises the steps: collecting key data in a machining process, and the key data comprise temperature, pressure, speed and vibration data; establishing a digital twinborn model, and inputting the key data into the digital twinborn model so as to simulate an actual processing process in real time; in the process of simulating the actual machining process, the thermal mechanical behavior of the material in the machining process is analyzed, and the machining process and machining parameters of the material are optimized based on the analysis result; and on the basis of an optimization result, production of non-standard precision parts is realized.

Description

Technical Field

[0001] The present application relates to the technical field of precision parts production, and specifically to a method and system for producing non-standard precision parts. Background Art

[0002] With the rapid development of industrial manufacturing, the demand for the production of non-standard precision parts is increasing. The traditional production method of non-standard precision parts mainly relies on manual experience and trial and error, and has problems such as low production efficiency, unstable quality, and high cost. Although the introduction of digital technology has improved production efficiency to a certain extent, it is still difficult to accurately predict and control the thermomechanical behavior of materials in complex processing environments, making it difficult to ensure product quality. In addition, the existing technology lacks the ability to monitor and optimize the processing process in real time, and cannot respond to abnormal situations in the processing process in a timely manner, affecting the stability and reliability of production. Summary of the invention

[0003] The present application provides a method and system for producing non-standard precision parts, which solves the problems in the prior art of low production efficiency, unstable quality, and difficulty in accurately predicting and controlling the thermomechanical behavior of materials for non-standard precision parts.

[0004] The present application provides a method for producing non-standard precision parts, including:

[0005] Collect key data during the processing, including temperature, pressure, speed and vibration data;

[0006] Establishing a digital twin model, and inputting the key data into the digital twin model, so as to simulate the actual processing process in real time;

[0007] In the simulation of the actual processing process, the thermomechanical behavior of the material during processing is analyzed, and the material processing technology and processing parameters are optimized based on the analysis results;

[0008] Based on the optimization results, the production of non-standard precision parts is realized.

[0009] Establishing a digital twin model and inputting the key data into the digital twin model so as to simulate the actual machining process in real time, including:

[0010] Performing data preprocessing and data cleaning on the key data;

[0011] Collect component parameters of non-standard parts and processing parameters of processing equipment, establish a digital twin model, and perform mathematical description and simulation parameter setting in the physical processing process in the digital twin model;

[0012] The key parameters of the processing are added to the digital twin model to simulate the actual processing and obtain the changes of the parameters of the non-standard parts in the processing in real time.

[0013] Analyze the thermomechanical behavior of materials during processing and optimize material processing technology and processing parameters based on the analysis results, including:

[0014] According to the actual processing object and process requirements, a geometric model and a physical field model of the non-standard parts are established, and the processing process is a laser welding process;

[0015] In the geometric model, meshing the geometric structure;

[0016] Use thermodynamic models to describe the thermomechanical behavior of materials under high temperature and high stress environments;

[0017] Numerical simulation of thermomechanical behavior using finite element method, coupling the geometric model of the non-standard component with the thermodynamic model;

[0018] Based on the simulation results, analyze the problems existing in the actual processing of the non-standard parts, including thermal stress concentration and uncontrolled deformation;

[0019] Combined with the optimization algorithm, the process parameters are adjusted to optimize the design and production process of the non-standard parts.

[0020] Use thermodynamic models to describe the thermomechanical behavior of materials in high temperature and high stress environments, including:

[0021] Define the key thermal variables in the manufacturing process, and define the boundary conditions and initial states of the thermal system;

[0022] Develop a set of coupled nonlinear equations representing the thermal system using the KATO framework;

[0023] In the coupled nonlinear equations, a finite element method is used to discretize the spatial domain;

[0024] The chaotic map is iterated at discrete time steps and converged nonlinearly to simulate the thermomechanical behavior of materials under high temperature and high stress environments.

[0025] Combined with the optimization algorithm, the process parameters are adjusted to optimize the design and production process of the non-standard parts, including:

[0026] Obtain time series data during thermomechanical behavior, including temperature, stress, and deformation data;

[0027] Constructing an observation function, and using the observation function to map an original state space to a high-dimensional feature space, wherein the original state space is composed of the time series data;

[0028] Constructing an observation matrix based on the observation function, and performing singular value decomposition (SVD) on the observation matrix;

[0029] Use the results of SVD to construct a finite-dimensional approximation of the Koopman operator;

[0030] Use the Koopman operator to predict the short-term and long-term condition of non-standard parts;

[0031] Based on the prediction results, the process parameters are adjusted using a gradient descent algorithm.

[0032] Numerical simulation of thermomechanical behavior using finite element method, coupling the geometric model of the non-standard component with the thermodynamic model, including:

[0033] Defining thermal boundary conditions, wherein the thermal boundary conditions include a heat source, a convection heat transfer boundary, and a radiation boundary;

[0034] defining mechanical boundary conditions, the mechanical boundary conditions comprising fixed constraints, symmetry constraints, and external loads;

[0035] Define the coupling relationship and coupling type between thermal analysis and structural analysis;

[0036] A direct solver or an iterative solver is constructed, and the geometric model and the thermodynamic model of the non-standard component are coupled by using the direct solver or the iterative solver, and transient thermal analysis and material phase change are performed.

[0037] The method further comprises:

[0038] The discontinuous Galerkin time discretization method is used to perform prior and a posteriori error estimation through maximum regularization to optimize the digital twin model.

[0039] A priori and a posteriori error estimates for discontinuous Galerkin time-discrete methods are performed via maximum regularization, including:

[0040] Discretize the heat conduction equation using the discontinuous Galerkin method:

[0041]

[0042] Where u is the temperature and f is the heat source term;

[0043] Define maximum regularity:

[0044]

[0045] Here C is a constant, and L2 represents the space of square integrable functions;

[0046] Based on the maximal regularity, calculate the a priori error estimate:

[0047] ||u - uh||L2 ≤ Chk + 1 + Cτr

[0048] where h is the spatial mesh size, τ is the time step, k is the polynomial order of the spatial discretization, and r is the order of the time discretization; use the residual - type a posteriori error estimator: η2 = ΣK(hK2||RK||L22 + hK||JK||L22)

[0049] where RK is the in - element residual, JK is the inter - element jump term, and η is the numerical value of the error magnitude of the a posteriori error estimator;

[0050] Based on the a posteriori error estimate, calculate the adaptive time - step control:

[0051] If η > tolerance, then τ_new = τ_old / 2;

[0052] If η < tolerance / 2, then τ_new = 2*τ_old.

[0053] The digital twin model is an analytical model based on physical laws or a data - driven model based on machine learning and deep learning.

[0054] The embodiment of the present application further provides a non - standard precision component production system, and the system includes:

[0055] An acquisition module, configured to acquire key data during the processing, and the key data includes temperature, pressure, speed, and vibration data;

[0056] A simulation module, configured to establish a digital twin model and input the key data into the digital twin model to simulate the actual processing process in real time;

[0057] An analysis and optimization module, configured to analyze the thermo - mechanical behavior of the material during the processing and optimize the material processing technology and processing parameters based on the analysis results during the simulation of the actual processing process;

[0058] A production module, configured to realize the production of non - standard precision components based on the optimization results.

[0059] The embodiment of the present application further provides a computer device, and the computer device includes:

[0060] At least one processor; and,

[0061] A memory communicatively connected to the at least one processor; wherein,

[0062] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned method for producing non-standard precision parts.

[0063] An embodiment of the present application also provides a computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute the above-mentioned method for producing non-standard precision parts.

[0064] An embodiment of the present application also provides a computer program product, including computer instructions, characterized in that when the computer instructions are executed by a processor, the steps of the above-mentioned method for producing non-standard precision parts are implemented.

[0065] This application has the following technical effects:

[0066] 1. By collecting key data in the processing process and establishing a digital twin model, real-time simulation and monitoring of the production process of non-standard precision parts are realized, improving the visualization and controllability of the production process.

[0067] 2. Through the analysis and optimization of the thermomechanical behavior of materials during the processing, the problem of difficulty in accurately predicting and controlling material behavior in traditional production methods is effectively solved, and product quality and production efficiency are improved.

[0068] 3. The finite element method is used to perform numerical simulation of thermomechanical behavior, realizing the coupling of the geometric model and thermodynamic model of non-standard components, providing a reliable theoretical basis for optimizing processing technology and parameters.

[0069] 4. The Koopman operator is used for state prediction, combined with the gradient descent algorithm to adjust the process parameters, to achieve intelligent optimization and control of the production process of non-standard precision parts.

[0070] 5. The error estimation of the discontinuous Galerkin time discrete method is performed through maximum regularity, which further optimizes the accuracy and reliability of the digital twin model. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A flowchart of a method for producing non-standard precision parts provided in an embodiment of the present application.

[0072] Figure 2 A structural block diagram of a non-standard precision parts production system provided in an embodiment of the present application.

[0073] Figure 3 A composition diagram of another non-standard precision parts production system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0075] Figure 1 : is a schematic diagram of a method for producing non-standard precision parts in an embodiment of the present invention. Figure 1 As shown, the embodiment of the present invention includes the following steps:

[0076] S1: Collect key data during the processing, including temperature, pressure, speed and vibration data.

[0077] In S1, real-time data of the processing of non-standard precision parts is obtained to provide input for the subsequent digital twin model. The technical principle of collecting key data is to install various sensors on the processing equipment to monitor various parameters in the processing process in real time. It mainly includes:

[0078] Temperature data acquisition: Use thermocouples or infrared thermal imagers to measure the temperature distribution of the processing area. Thermocouples can measure the temperature at a specific point, while infrared thermal imagers can provide a temperature distribution map of the entire processing area.

[0079] Pressure data acquisition: Install pressure sensors at key locations of processing equipment, such as hydraulic systems, pneumatic systems, or mechanical fixtures. These sensors can monitor pressure changes during processing in real time.

[0080] Speed ​​data acquisition: Use encoders or photoelectric sensors to measure the speed of various moving parts of processing equipment. For example, in the laser welding process, the movement speed of the welding head or the rotation speed of the workpiece can be measured.

[0081] Vibration data collection: Accelerometers or vibration sensors are installed at key locations on processing equipment to monitor vibration during processing. This is very important for detecting abnormal conditions during processing.

[0082] Data acquisition system: Use high-speed data acquisition cards and industrial computers to build a data acquisition system. The system can simultaneously collect data from multiple sensors and perform preliminary data processing and storage.

[0083] Data transmission: Use industrial Ethernet or wireless communication technology (such as WiFi 6 or 5G) to transmit the collected data to the central control system in real time.

[0084] Through the above methods, the embodiments of the present invention can comprehensively and real-time collect key data in the processing process of non-standard precision parts, providing a reliable data foundation for subsequent digital twin models and optimization.

[0085] S2: Establish a digital twin model and input the key data into the digital twin model to simulate the actual processing process in real time.

[0086] Create a virtual digital twin model that can accurately reflect the physical characteristics and behavior of the actual processing process. The technical principle of the digital twin model is to map and simulate the entity or system in the physical world in the digital world, and through the input of real-time data, the virtual model can synchronously reflect the status and behavior of the actual system.

[0087] Specifically, the appropriate model framework can be selected according to the characteristics and processing requirements of non-standard precision parts. Physics-based analytical models (such as finite element models) or data-based machine learning models (such as deep neural networks) can be used.

[0088] First, geometric modeling is used, for example, using CAD software (such as SolidWorks or CATIA) to create an accurate 3D geometric model of non-standard precision parts. This model should include all key features and dimensions of the parts.

[0089] Secondly, physical modeling is performed. Based on the geometric model, a mathematical model is established to describe the physical phenomena in the machining process. This may include heat conduction models, stress-strain models, fluid dynamics models, etc., depending on the nature of the machining process. After that, the key parameters in the model are set as variable parameters so that they can be dynamically adjusted according to the real-time collected data. These parameters may include material properties, boundary conditions, machining parameters, etc.

[0090] Thirdly, choose the appropriate solver based on the complexity and real-time requirements of the model. For complex physical models, it may be necessary to use high-performance computing (HPC) technology to accelerate the calculation process.

[0091] Finally, develop a 3D visualization interface that allows operators to intuitively observe and understand the state and behavior of the digital twin model. This can be achieved using game engines such as Unity3D or Unreal Engine.

[0092] Specifically, step 2 includes S2.1-S2.3:

[0093] S2.1: Perform data preprocessing and data cleaning on the key data.

[0094] The purpose of this sub-step is to ensure the quality of data input into the digital twin model and improve the accuracy and reliability of the model. The technical principle of data preprocessing and cleaning is to remove or correct noise, outliers and missing values ​​in the original data through a series of data processing techniques, and convert the data into a format suitable for model use.

[0095] The specific implementation is as follows:

[0096] A1. Data denoising: Use filtering algorithms (such as Kalman filtering and wavelet transform) to remove high-frequency noise in sensor data.

[0097] A2. Outlier detection and processing: Use statistical methods (such as the Z-score method, IQR method) or machine learning methods (such as the isolation forest algorithm) to detect outliers, and decide whether to delete or correct these outliers based on the specific situation.

[0098] A3. Missing value processing: For short-term data missing, interpolation methods (such as linear interpolation and spline interpolation) can be used to fill in the missing data; for long-term data missing, more complex methods may need to be used, such as filling methods based on time series prediction.

[0099] A4. Data standardization / normalization: Convert data of different dimensions to the same scale for easier model processing. Common methods include MinMax scaling and Zscore normalization.

[0100] A5. Data alignment: Ensure that data from different sensors are aligned in time, which may involve data resampling and timestamp correction.

[0101] A6. Feature extraction: Extract meaningful features from raw data, for example, extract spectral features from vibration data and extract statistical features (mean, variance, etc.) from temperature data.

[0102] A7.Data format conversion: Convert the processed data into the format required by the digital twin model, which may involve the reorganization of the data structure and the conversion of the data type.

[0103] Through these data preprocessing and cleaning steps, embodiments of the present invention can significantly improve the quality of data input into the digital twin model, thereby improving the accuracy and reliability of the model.

[0104] S2.2: Collect component parameters of non-standard parts and processing parameters of processing equipment, establish a digital twin model, and perform mathematical description and simulation parameter setting in the physical processing process in the digital twin model.

[0105] The purpose of this sub-step is to build a comprehensive digital twin model that contains not only the geometric information of the parts, but also the material properties, processing equipment characteristics, and physical and mathematical descriptions of the processing process. Such a model can more accurately simulate the actual processing process and provide a reliable basis for subsequent optimization.

[0106] The specific implementation is as follows:

[0107] B1. Parts parameter collection:

[0108] Geometric parameters: Use 3D scanning technology (such as laser scanning, structured light scanning) to obtain accurate geometric data of non-standard parts.

[0109] Material parameters: Obtain the physical and mechanical properties of component materials, such as density, elastic modulus, thermal conductivity, specific heat capacity, etc., through material testing or consulting the material database.

[0110] Surface characteristics: Use a surface roughness tester to measure the microscopic morphology parameters of the component surface.

[0111] B2. Processing equipment parameter collection:

[0112] Equipment specifications: Collect basic parameters of processing equipment, such as power, accuracy, working range, etc.

[0113] Dynamic parameters: measure the dynamic response characteristics of the equipment, such as acceleration, velocity curve, vibration characteristics, etc.

[0114] Control system parameters: Get the parameters of the device control system, such as PID controller parameters, servo system response time, etc.

[0115] B3. Construction of digital twin model:

[0116] Geometric model construction: Based on the collected geometric parameters, use CAD software to build an accurate three-dimensional model.

[0117] Physical model construction: According to the physical characteristics of the processing process, establish the corresponding physical model, such as heat conduction model, stress-strain model, etc.

[0118] Equipment model building: Create a virtual model of the processing equipment, including its geometry and dynamic characteristics.

[0119] B4. Mathematical description of physical processing:

[0120] Thermal process description: Use heat conduction equations to describe heat transfer during processing, such as:

[0121]

[0122] Where ρ is the density, cp is the specific heat, k is the thermal conductivity, T is the temperature, and q is the heat source term.

[0123] Description of mechanical processes: Use stress-strain relationship equations to describe the deformation behavior of materials, such as:

[0124] σ=Cε

[0125] Among them, σ is the stress tensor, C is the elastic constant tensor, and ε is the strain tensor.

[0126] Material phase change description: Use the phase field method or the Johnson Mehl Avrami Kolmogorov (JMAK) equation to describe the phase change process of the material.

[0127] B5. Simulation parameter settings:

[0128] Meshing: Set appropriate meshing parameters according to the complexity of the model and the required accuracy.

[0129] Boundary condition setting: According to the actual processing conditions, set the boundary conditions of the model, such as thermal boundary conditions, mechanical boundary conditions, etc.

[0130] Solver parameter setting: Select a suitable solution algorithm (such as finite element method, finite difference method), and set the corresponding solution parameters, such as time step, convergence criterion, etc.

[0131] Output parameter setting: define the physical quantities and observation points that need to be output for subsequent analysis and optimization.

[0132] Through these steps, the embodiment of the present invention can establish a comprehensive and accurate digital twin model, which can accurately reflect the processing process of non-standard parts and provide a reliable basis for subsequent analysis and optimization.

[0133] S2.3: Add key parameters of the processing to the digital twin model to simulate the actual processing and obtain the changes of the parameters of the non-standard parts in the processing in real time.

[0134] S2.3 combines the real-time collected processing data with the digital twin model to achieve dynamic model update and real-time simulation. This ensures that the digital twin model is always synchronized with the actual processing process, thus providing more accurate simulation results and predictions.

[0135] It includes:

[0136] C1. Data interface design:

[0137] Develop standardized data interfaces for receiving real-time data from sensor networks.

[0138] Use industrial communication protocols (such as OPC UA, MQTT) to ensure real-time and reliable data transmission.

[0139] Implement a data buffering mechanism to handle possible data transfer delays or interruptions.

[0140] C2. Parameter mapping:

[0141] Establish a mapping relationship between real-time data and digital twin model parameters.

[0142] For example, the data from the temperature sensor is mapped to the temperature field in the model, and the data from the pressure sensor is mapped to the stress field.

[0143] C3. Model update mechanism:

[0144] Implement real-time update algorithms for model parameters, such as Kalman filtering or particle filtering, to fuse model predictions and measured data.

[0145] For complex nonlinear systems, one can consider using ensemble Kalman filtering (EnKF) or variational data assimilation methods.

[0146] C4. Real-time solution strategy:

[0147] An incremental solution method is used to update only the model parts affected by real-time data, reducing the computational burden.

[0148] Use parallel computing technology (such as GPU acceleration) to increase the speed of model solution.

[0149] Implement adaptive time step control and dynamically adjust the solution frequency according to the speed of system changes.

[0150] C5. Parameter change monitoring:

[0151] Develop key parameter change monitoring algorithms to track the changes of important parameters of non-standard parts during the processing process in real time.

[0152] Set parameter change thresholds and trigger alarms or adjust control strategies when the thresholds are exceeded.

[0153] C6. Data Visualization:

[0154] Develop a real-time data visualization interface to intuitively display parameter changes during the machining process.

[0155] Use visualization techniques such as color mapping and contour plots to display the distribution of physical quantities such as temperature field and stress field.

[0156] Through the above implementation, the embodiment of the present invention can effectively integrate the real-time collected processing data into the digital twin model, and realize the real-time and accurate simulation of the processing of non-standard parts. This not only improves the accuracy of the model, but also provides a powerful tool for real-time monitoring, prediction and optimization of the processing process.

[0157] S3: In the simulation of the actual processing process, the thermomechanical behavior of the material during the processing is analyzed, and the material processing technology and processing parameters are optimized based on the analysis results.

[0158] In S3, it is necessary to deeply understand the material behavior of non-standard precision parts during processing, especially the thermomechanical coupling effect, and optimize the processing technology and parameters accordingly. This is crucial to improving product quality, reducing defects and improving production efficiency.

[0159] Specifically include:

[0160] S3.1: According to the actual processing object and process requirements, a geometric model and a physical field model of the non-standard parts are established, especially when the processing process is a laser welding process.

[0161] 1. Geometric model establishment:

[0162] Use high-precision 3D scanning technology (such as structured light scanning) to obtain precise geometric data of non-standard parts.

[0163] Process the scan data with reverse engineering software, such as Geomagic Design X, to generate an editable CAD model.

[0164] Define key geometric features such as weld location and welding path in the CAD model.

[0165] 2. Establishment of physical field model:

[0166] Thermal field model: A three-dimensional transient thermal field model is established based on the heat conduction equation.

[0167] Heat conduction equation:

[0168] Where ρ is the density, cp is the specific heat, k is the thermal conductivity, T is the temperature, and Q is the heat source term.

[0169] Mechanical field model: Establish an elastic-plastic mechanical model taking thermal stress into account.

[0170] Stress-strain relationship: σ ij =C ij k l (εk l *εk l th *εk lp )

[0171] Among them, σ ij is the stress tensor, C ij k l is the elastic constant tensor, εk l is the total strain, εεk l th is the thermal strain, εk l p is the plastic strain.

[0172] Phase change model: The Johnson Mehl Avrami Kolmogorov (JMAK) equation is used to describe the phase change process of the material.

[0173] JMAK equation: f = 1-exp(kt n )

[0174] Where f is the phase transition fraction, k is the rate constant, t is the time, and n is the Avrami index.

[0175] 3. Laser welding characteristics simulation:

[0176] Establish a laser heat source model, such as a conical cylindrical heat source model or a double ellipsoid heat source model.

[0177] Simulate melt pool dynamics including surface tension, Marangoni convection, and evaporation effects.

[0178] Consider phase changes during welding, such as melting, solidification, and solid-state phase changes.

[0179] S3.2: In the geometric model, the geometric structure is meshed.

[0180] For regular shape areas, hexahedral meshes are used to improve computational efficiency. For complex shape areas, tetrahedral meshes are used to better fit geometric features.

[0181] Use fine mesh near welds and stress concentration areas to improve calculation accuracy. Use coarser mesh in areas away from welds to reduce calculation workload. Achieve smooth transition of mesh size to avoid sudden changes in mesh quality.

[0182] Check and optimize the mesh's aspect ratio, distortion, orthogonality, etc. Use mesh smoothing algorithms (such as Laplacian smoothing) to improve mesh quality.

[0183] Implements mesh adaptive refinement algorithm to dynamically adjust mesh density based on calculation results. Automatically refine mesh in areas with large temperature gradients and concentrated stresses.

[0184] Transition elements are used at weld joints to ensure mesh continuity. Consistent meshes are used at material interfaces to avoid discontinuities in numerical calculations.

[0185] Through these steps, the embodiment of the present invention establishes a detailed geometric and physical model and performs reasonable meshing, which lays the foundation for subsequent thermomechanical behavior analysis and enables the embodiment of the present invention to more accurately simulate and analyze complex physical phenomena in the laser welding process.

[0186] S3.3: Use thermodynamic models to describe the thermomechanical behavior of materials under high temperature and high stress environments.

[0187] By establishing a comprehensive thermodynamic model, embodiments of the present invention can better understand and predict the behavior of materials during processing.

[0188] S3.3.1: Define the key thermal variables in the manufacturing process and define the boundary conditions and initial states of the thermal system.

[0189] Key thermal variables definitions:

[0190] Temperature field T(x,y,z,t);

[0191] Heat flux q(x,y,z,t);

[0192] Thermal stress σth(x,y,z,t);

[0193] Phase change fraction f(x,y,z,t);

[0194] Boundary condition definition:

[0195] Laser heat source boundary: q = q_laser(x, y, z, t), where q_laser is the laser heat source function;

[0196] Convective Boundary: Where h is the convective heat transfer coefficient, T∞ is the ambient temperature;

[0197] Radiation Boundary: Where ε is the emissivity and σ is the Stefan Boltzmann constant;

[0198] Adiabatic Boundary:

[0199] Initial state definition:

[0200] Initial temperature distribution: T(x,y,z,0) = T_initial(x,y,z)

[0201] Initial stress state: σ(x,y,z,0) = σ_initial(x,y,z)

[0202] Initial phase distribution: f(x,y,z,0) = f_initial(x,y,z)

[0203] S3.3.2: Use the KATO framework to develop a set of coupled nonlinear equations that represent the thermal system.

[0204] The KATO framework is a mathematical framework for describing complex thermodynamic systems. Here, the embodiment of the present invention will use it to establish the coupled equations of the laser welding process:

[0205] Heat conduction equation:

[0206]

[0207] Thermoelastic-plastic mechanics equations:

[0208]

[0209] σ=C:(ε-εth-εp)

[0210] εth=α(T T_ref)I

[0211] Phase transition kinetic equation:

[0212]

[0213] Coupling terms:

[0214]

[0215] k=k(T,f) / / Thermal conductivity depends on temperature and phase

[0216] C=C(T,f) / / elastic constant depends on temperature and phase

[0217] in:

[0218] ρ is density, cp is specific heat, k is thermal conductivity;

[0219] Q_laser is the laser heat source term, Q_phase is the phase change latent heat;

[0220] σ is the stress tensor, ε is the strain tensor, εth is the thermal strain, and εp is the plastic strain;

[0221] C is the elastic constant tensor, α is the thermal expansion coefficient;

[0222] f is the phase change fraction, L is the latent heat of phase change;

[0223] b is the volume force;

[0224] S3.3.3: In the coupled nonlinear equations, a finite element method is used to discretize the spatial domain.

[0225] 1. Weak form derivation:

[0226] Convert the above partial differential equation into integral form (weak form).

[0227] 2. Spatial discretization:

[0228] Using the Galerkin method, the temperature field, displacement field and phase change fraction field are expressed as linear combinations of shape functions.

[0229] For the temperature field: T(x,t)≈ΣNi(x)Ti(t)

[0230] For the displacement field: u(x,t)≈ΣNi(x)ui(t)

[0231] For phase transition fraction: f(x,t)≈ΣNi(x)fi(t)

[0232] 3. Matrix equation assembly:

[0233] Assemble the discretized equations into a global matrix equation:

[0234]

[0235] [M]{ü}+[K_u]{u}={F_u}

[0236]

[0237] Where [C] is the heat capacity matrix, [K_T] is the thermal conductivity matrix, [M] is the mass matrix, and [K_u] is the stiffness matrix.

[0238] S3.3.4: Iterate the chaotic map at discrete time steps and perform nonlinear convergence to simulate the thermomechanical behavior of materials in high temperature and high stress environments.

[0239] 1. Time discretization:

[0240] Discretize the time domain using an implicit time integration method such as Newmark's β method.

[0241] 2. Nonlinear solution:

[0242] For each time step, the nonlinear system of equations is solved using the Newton-Raphson iteration method.

[0243] Iteration process: {X_k+1}={X_k}-[J]{R(X_k)}

[0244] where [J] is the Jacobian matrix and {R} is the residual vector.

[0245] 3. Chaotic Map Iteration:

[0246] At each time step, chaos mapping is used to simulate the uncertainty and sensitivity of material behavior.

[0247] 4. Convergence criteria:

[0248] Define appropriate convergence criteria, such as the residual norm or the change in the solution being less than a specified threshold.

[0249] Through this comprehensive thermodynamic model, the embodiments of the present invention can accurately describe the complex thermomechanical behavior of materials during laser welding, including phenomena such as heat conduction, thermal stress, and phase change, providing a solid theoretical basis for subsequent analysis and optimization.

[0250] S3.4: Use the finite element method to perform numerical simulation of thermomechanical behavior and couple the geometric model and thermodynamic model of the non-standard component.

[0251] The purpose of this step is to combine the previously established geometric model and thermodynamic model to predict the actual behavior of non-standard parts during laser welding through numerical simulation methods. This coupled simulation can help the embodiments of the present invention better understand the complex physical phenomena in the processing process and provide an important basis for subsequent process optimization.

[0252] S3.4.1: Define thermal boundary conditions, which include heat sources, convection heat transfer boundaries, and radiation boundaries.

[0253] 1. Laser heat source modeling:

[0254] Use the moving Gaussian heat source model: q(x,y,z,t)=q0*exp(r 2 / r0 2 )

[0255] Where q0 is the intensity at the center of the heat source, r is the distance to the center of the heat source, and r0 is the characteristic radius.

[0256] Consider the movement of heat source: r 2 =(xvt) 2 +y 2 , where v is the welding speed.

[0257] 2. Convective heat transfer boundary:

[0258] Define the convection heat transfer coefficient h, which may vary with temperature: h = h(T)

[0259] Convective heat transfer boundary conditions:

[0260] Different surfaces (such as top surface, side surface) may have different convective heat transfer coefficients.

[0261] 3. Radiation boundary:

[0262] Define the emissivity ε, which may vary with temperature: ε = ε(T)

[0263] Radiation boundary conditions:

[0264] Considering the view factor F, the radiation heat exchange is corrected:

[0265] 4. Latent heat of phase change:

[0266] Add an equivalent heat source term within the phase change temperature range: Q_phase = ρL(df / dT)(dT / dt)

[0267] Where L is the latent heat of phase change and f is the phase change fraction.

[0268] S3.4.2: Define mechanical boundary conditions, which include fixed constraints, symmetry constraints, and external loads.

[0269] 1. Fixed constraints:

[0270] Set displacement constraints at the workpiece fixed point: u=0,v=0,w=0

[0271] Taking thermal expansion of the fixture into account, it may be necessary to use elastic supports rather than rigid fixation.

[0272] 2. Symmetry constraints:

[0273] If your model exploits symmetry, set appropriate symmetry constraints on the symmetry planes.

[0274] For example, when the xz plane is symmetrical: v = 0,

[0275] 3. External load:

[0276] Consider the clamp pressure during welding: a distributed pressure is applied across the contact surfaces.

[0277] Consider the effect of gravity: add body force F_g=ρg

[0278] 4. Thermal stress:

[0279] Define the coefficient of thermal expansion α, which may vary with temperature: α = α(T)

[0280] Thermal strain calculation: εth=α(T-T_ref)

[0281] S3.4.3: Define the coupling relationship and coupling type between thermal and structural analysis.

[0282] 1. One-way coupling:

[0283] First, thermal analysis is performed to obtain the temperature field distribution.

[0284] Take the temperature field as input and perform structural analysis to calculate thermal stresses and deformations.

[0285] 2. Bidirectional coupling:

[0286] Consider the effect of deformation on heat conduction, such as changes in contact thermal resistance.

[0287] A thermal-structural iterative solution is performed at each time step.

[0288] 3. Material property coupling:

[0289] Define temperature-dependent material properties: E(T), ν(T), σy(T), k(T), cp(T)

[0290] Consider the effect of phase change on material properties: Property = f1*property phase 1 + f2*property phase 2

[0291] 4. Contact thermal resistance coupling:

[0292] Define the contact thermal conductivity hc, which is related to the contact pressure p: hc = hc(p)

[0293] Update the heat flow of the contact surface: q = hc (T1-T2)

[0294] S3.4.4: Construct a direct solver or an iterative solver, use the direct solver or the iterative solver to couple the geometric model and the thermodynamic model of the non-standard component, and perform transient thermal analysis and material phase change.

[0295] 1. Solver selection:

[0296] For small to medium-sized problems, use a direct solver such as PARDISO.

[0297] For large-scale problems, an iterative solver (such as the conjugate gradient method CG) is used.

[0298] 2. Time integration method:

[0299] Use an implicit time integration method such as Newmark's beta method.

[0300] Time step adaptive control: dynamically adjust the step size according to the temperature change rate and stress change rate.

[0301] 3. Nonlinear solution strategy:

[0302] The Newton-Raphson method is used to handle nonlinear problems.

[0303] Line search techniques are used to improve convergence.

[0304] 4. Coupling solution process:

[0305] (1) Initialize the temperature field and stress field.

[0306] (2) For each time step:

[0307] a. Solve the heat conduction equation and update the temperature field.

[0308] b. Update material properties and boundary conditions based on the new temperature field.

[0309] c. Solve the structural equations and calculate displacements, strains and stresses.

[0310] d. Check convergence. If not, return to step a for iteration.

[0311] (3) Update the mesh (if adaptive mesh technology is used).

[0312] (4) Enter the next time step.

[0313] 5. Phase change treatment:

[0314] The phase change progress is tracked at each integration point.

[0315] Update the phase change fraction using the JMAK equation.

[0316] Consider the effect of latent heat of phase change on the temperature field.

[0317] 6. Post-processing:

[0318] Calculate key output quantities such as maximum temperature, residual stress, deformation, etc.

[0319] Generate cloud maps of temperature field, stress field, phase change distribution, etc.

[0320] Through this detailed thermomechanical coupling analysis, the embodiments of the present invention can accurately simulate the complex behavior of non-standard parts during laser welding, including temperature distribution, thermal stress evolution, material phase change, etc. This provides an important theoretical basis and data support for subsequent process optimization and quality control.

[0321] S3.5: Based on the simulation results, analyze the problems existing in the actual processing of the non-standard parts, including thermal stress concentration and uncontrolled deformation.

[0322] The purpose of this step is to use the simulation results obtained above to deeply analyze the problems that non-standard parts may encounter during laser welding, with a particular focus on the two common key problems of thermal stress concentration and uncontrolled deformation. Through this analysis, the embodiment of the present invention can identify potential quality risks and provide a clear direction for subsequent process optimization.

[0323] The specific implementation is as follows:

[0324] Thermal stress concentration analysis:

[0325] a. Stress distribution visualization:

[0326] Generate Von Mises stress contours to identify high stress areas.

[0327] Draw a vector diagram of the principal stress directions and analyze the stress state.

[0328] b. Stress time evolution:

[0329] Trace stress-time curves at key points.

[0330] Analyze the time and location of stress peaks.

[0331] c. Calculation of stress concentration factor:

[0332] Calculate the stress concentration factor Kt=σmax / σnom.

[0333] Identify areas where stress concentration factors exceed critical values.

[0334] d. Fatigue life assessment:

[0335] Estimate fatigue safety factors based on the Goodman criterion or the Soderberg criterion.

[0336] For cyclic loading, cumulative damage analysis (such as Miner's criterion) is performed.

[0337] Deformation out of control analysis:

[0338] a. Visualization of deformation:

[0339] Generate a cloud map of the total deformation and identify the area of ​​maximum deformation.

[0340] Plot the deformation components in the X, Y, and Z directions respectively.

[0341] b. Deformation time evolution:

[0342] Track the deformation time curve of a key point.

[0343] Analyze deformation rates and identify critical moments when deformation accelerates.

[0344] c. Residual deformation assessment:

[0345] Calculate the residual deformation after cooling.

[0346] Compare with product tolerance requirements and identify out-of-tolerance areas.

[0347] d. Buckling analysis:

[0348] Perform a linear buckling analysis and calculate the critical buckling load.

[0349] For thin-walled structures, thermoelastic buckling effects are considered.

[0350] Problem identification and classification:

[0351] a. Establish a problem severity evaluation system:

[0352] Define stress safety factor: SF_stress = σyield / σmax

[0353] Define deformation safety factor: SF_deform = δallowable / δmax

[0354] b. Problem classification:

[0355] High risk: SF < 1.0

[0356] Medium risk: 1.0≤SF<1.5

[0357] Low risk: SF ≥ 1.5

[0358] c. Heat Affected Zone (HAZ) Analysis:

[0359] Identify the extent of the heat affected zone.

[0360] Analyze the grain growth and phase transformation in the HAZ.

[0361] Root Cause Analysis:

[0362] a. Parameter sensitivity analysis:

[0363] Perform parameter scanning to analyze the effects of welding speed, power and other parameters on stress and deformation.

[0364] Generate response surfaces to find out the key parameters and their optimal ranges.

[0365] b. Geometric factor analysis:

[0366] Analyze the relationship between part geometric features (such as sharp corners and sudden cross-sections) and stress concentration.

[0367] Evaluate how the structural stiffness distribution relates to the deformation patterns.

[0368] c. Material factor analysis:

[0369] Analyze the impact of the material's thermophysical properties (such as thermal expansion coefficient, thermal conductivity) on the problem.

[0370] Evaluate the contribution of phase transformation properties of materials (such as martensitic transformation) to residual stress.

[0371] 5. Problem visualization and report generation:

[0372] a. Generate a comprehensive problem map:

[0373] High-risk areas are marked on the 3D model.

[0374] Use color coding to indicate problem type and severity.

[0375] b. Generate a problem summary report:

[0376] List all issues identified, including location, type, and severity.

[0377] Provide a brief causal analysis for each problem.

[0378] c. Interactive visualization tools:

[0379] Develop interactive 3D visualization tools that allow users to freely explore stress and deformation distribution on the model.

[0380] Realize the time axis sliding function to observe the dynamic evolution of stress and deformation.

[0381] Through this systematic analysis, the embodiments of the present invention can fully understand the thermal stress concentration and deformation uncontrollable problems that non-standard parts may face during laser welding. This information provides clear goals and directions for the next step of process parameter optimization and structural design improvement, which helps to improve product quality and reliability.

[0382] S3.6: Combine the optimization algorithm, adjust the process parameters, and optimize the design and production process of the non-standard parts.

[0383] In S3.6, based on the previous analysis results, advanced optimization algorithms are used to adjust process parameters and optimize the design and production process of parts. In this way, the embodiment of the present invention can minimize the problems of thermal stress concentration and uncontrolled deformation, and improve product quality and production efficiency.

[0384] S3.6.1: Obtain time series data during thermomechanical behavior, including temperature, stress, and deformation data.

[0385] Extract the time-varying data of temperature, stress and deformation at key points from the finite element simulation results.

[0386] Ensure that the temporal resolution of the data is high enough to capture rapidly changing thermomechanical behavior.

[0387] Calculate statistical characteristics such as maximum, minimum, mean, standard deviation, etc.

[0388] Extract time domain features such as rise time, peak time, cooling rate, etc.

[0389] For periodic behavior, frequency domain analysis is performed to extract the main frequency components.

[0390] S3.6.2: Construct an observation function and use the observation function to map the original state space to a high-dimensional feature space, wherein the original state space is composed of the time series data.

[0391] 1. Define the state vector:

[0392] X(t)=[T(t),σ(t),δ(t)]

[0393] Where T is temperature, σ is stress, and δ is deformation.

[0394] 2. Build delayed coordinate embedding:

[0395] Φ(X(t))=[X(t),X(t-τ),X(t2-τ),...,X(t(m1)-τ)]

[0396] where τ is the time delay and m is the embedding dimension.

[0397] 3. Kernel function mapping:

[0398] Choose an appropriate kernel function K(x,y), such as the radial basis function (RBF) kernel:

[0399] K(x,y)=exp(γ||xy|| 2 )

[0400] 4. Observation function construction:

[0401] g(X)=Σi-αi K(X,Xi)

[0402] Where αi is the unknown coefficient and Xi is the training data point.

[0403] S3.6.3: Construct an observation matrix based on the observation function, and perform singular value decomposition (SVD) on the observation matrix.

[0404] 1. Construct the observation matrix:

[0405] Y=[g(X(t1)),g(X(t2)),...,g(X(tN))]

[0406] Where N is the length of the time series.

[0407] 2. Perform SVD decomposition:

[0408] Y=UΣV T

[0409] where U and V are orthogonal matrices and Σ is a diagonal matrix of singular values.

[0410] 3. Analyze singular values:

[0411] Plot the singular value spectrum and determine the number of dominant modes.

[0412] Calculate the cumulative energy contribution and choose an appropriate cutoff threshold.

[0413] S3.6.4: Use the results of SVD to construct a finite-dimensional approximation of the Koopman operator.

[0414] 1. Construct the DMD matrix:

[0415] A=U T Y'VΣ1

[0416] where Y' is the matrix of Y shifted forward one time step.

[0417] 2. Calculate DMD mode:

[0418] Solve the eigenvalue problem: AΦ=λΦ

[0419] The eigenvalue λ gives the growth rate and frequency of the dynamics.

[0420] The eigenvector Φ gives the spatial structure of the dynamic modes.

[0421] 3. Construct an approximation of the Koopman operator:

[0422] K≈UDU T

[0423] where D is a diagonal matrix consisting of the eigenvalues ​​λ.

[0424] S3.6.5: Use the Koopman operator to predict the short-term and long-term status of non-standard parts. 1. Short-term prediction:

[0425] X(t+Δt)≈KX(t)

[0426] Iteratively apply K to predict the state several time steps into the future.

[0427] 2. Long-term forecast:

[0428] Use DMD to decompose long-term behavior:

[0429] X(t)≈Σi bi exp(ωit)Φi

[0430] Where ωi=log(λi) / Δt, bi is the coefficient determined by the initial conditions.

[0431] 3. Quantification of forecast uncertainty:

[0432] Use Monte Carlo methods, taking into account the uncertainties in initial conditions and parameters.

[0433] Generate confidence intervals for the predictions.

[0434] S3.6.6: Based on the prediction results, use the gradient descent algorithm to adjust the process parameters. 1. Define the objective function:

[0435] J(θ)=w1*J_stress(θ)+w2*J_deform(θ)+w3*J_efficiency(θ)

[0436] where θ is the process parameter vector, J_stress, J_deform and J_efficiency are the loss functions of stress, deformation and efficiency respectively.

[0437] 2. Calculate the gradient:

[0438]

[0439] Compute the gradient using finite difference methods or automatic differentiation techniques.

[0440] 3. Parameter update:

[0441]

[0442] Where α is the learning rate.

[0443] 4. Learning rate adaptation:

[0444] Adaptively adjust the learning rate using an algorithm such as the Adam optimizer or RMSprop.

[0445] 5. Constraint processing:

[0446] Parameter constraints are handled using the projected gradient method or the Lagrange multiplier method.

[0447] 6. Termination conditions:

[0448] The method terminates when the gradient norm is less than a threshold or the maximum number of iterations is reached.

[0449] Through this data-driven and optimization algorithm-based method, the embodiments of the present invention can automatically adjust process parameters and optimize the design and production process of non-standard parts. This can not only reduce the problems of thermal stress concentration and uncontrolled deformation, but also improve production efficiency and product quality consistency. The advantage of this method is that it can handle complex nonlinear systems and can continuously improve the optimization results as new data accumulates.

[0450] S4: Based on the optimization results, realize the production of non-standard precision parts.

[0451] The purpose of this step is to apply the previous optimization results to actual production to ensure high-quality and efficient production of non-standard precision parts. This process involves the verification of optimization results, the setting of production parameters, the establishment of a quality control system, and many other aspects.

[0452] The specific implementation is as follows:

[0453] 1. Optimization result verification:

[0454] a. Sample trial production:

[0455] Use the optimized process parameters to produce small batches of samples.

[0456] Conduct comprehensive quality inspections, including dimensional accuracy, surface quality, internal defects, etc.

[0457] b. Performance test:

[0458] Conduct mechanical property tests such as tension, compression, bending, etc.

[0459] Conduct thermal performance tests such as thermal expansion, thermal conductivity, etc.

[0460] For parts with special purpose, special functional tests are carried out.

[0461] c. Comparative analysis:

[0462] Compare the test results with the simulation predictions.

[0463] Analyze the differences and adjust model parameters or optimize algorithms if necessary.

[0464] 2. Production parameter settings:

[0465] a. Process parameter conversion:

[0466] Convert the optimized parameters to specific machine settings.

[0467] Consider the differences between different devices and make necessary parameter adjustments.

[0468] b. Preparation of process documents:

[0469] Write detailed process guidance documents, including specific parameters for each production step. Develop operating procedures to ensure consistency of operations.

[0470] c. Device programming:

[0471] For CNC equipment, write the corresponding processing programs.

[0472] Set upper and lower limits of parameters to prevent quality problems caused by misoperation.

[0473] 3. Production process monitoring system:

[0474] a. Real-time data collection:

[0475] Deploy a sensor network to collect key parameters such as temperature, pressure, vibration, etc. in real time. Use high-speed cameras to monitor the welding process and capture transient phenomena.

[0476] b. Data Analysis and Visualization:

[0477] Develop a real-time data analysis platform to process and analyze the collected data. Design an intuitive visual interface to facilitate operator monitoring.

[0478] c. Anomaly detection and early warning:

[0479] Based on statistical process control (SPC) methods, parameter fluctuations are monitored in real time.

[0480] Set warning thresholds and issue timely alarms when parameters deviate from normal ranges.

[0481] 4.Quality Control System:

[0482] a. Online detection:

[0483] Integrated laser scanner to detect part size and shape in real time.

[0484] Use infrared thermal imaging cameras to monitor temperature distribution and prevent overheating.

[0485] b. Offline detection:

[0486] Use a coordinate measuring machine for precise dimensional inspection.

[0487] Internal defect inspection using X-ray or ultrasonic testing.

[0488] c. Statistical quality control:

[0489] Implement Six Sigma management to continuously improve the production process.

[0490] Establish a quality database and conduct long-term trend analysis.

[0491] 5.Production efficiency optimization:

[0492] a. Process optimization:

[0493] Based on the optimization results, the production line layout is redesigned.

[0494] Implement lean manufacturing methods to reduce waste and improve efficiency.

[0495] b.Automation upgrade:

[0496] Introduce robot systems to automate processes such as welding and handling.

[0497] Develop intelligent scheduling system to optimize production schedule.

[0498] c. Human-machine collaboration:

[0499] Design human-robot collaborative workstations that combine human dexterity with machine precision.

[0500] Develop augmented reality (AR) assistance systems to provide real-time guidance to operators.

[0501] Through these steps, the embodiments of the present invention can effectively transform the optimization results into actual production capacity, and realize the high-quality and high-efficiency production of non-standard precision parts. This method can not only solve the current production problems, but also establish a system of continuous improvement so that the production process can continuously adapt to new needs and challenges. At the same time, through digital and intelligent means, the embodiments of the present invention can realize the precise control and real-time optimization of the production process, minimize the scrap rate, and improve production efficiency.

[0502] S5: Perform a priori and a posteriori error estimation on the discontinuous Galerkin time discrete method through maximum regularity to optimize the digital twin model.

[0503] The purpose of this step is to evaluate and improve the accuracy of the digital twin model through rigorous mathematical methods. By performing error analysis on the discontinuous Galerkin time discretization method, the embodiments of the present invention can better understand the performance of the model and optimize it accordingly.

[0504] S5.1: Discretize the heat equation using the discontinuous Galerkin method:

[0505] Where u is the temperature and f is the heat source term.

[0506] 1. Time discretization:

[0507] Divide the time interval [0, T] into N subintervals: 0 = t0 <t1<...<tN=T。

[0508] In each time interval [tn,tn+1], the approximate solution u is expressed by a polynomial.

[0509] 2. Weak form derivation:

[0510] For any test function v, solve:

[0511]

[0512] 3. Jump item processing:

[0513] Add a jump item at time node tn:

[0514] [[u]]n=u(tn+)-u(tn)

[0515] 4. Completely discrete format:

[0516] Find uh∈Vh such that for all vh∈Vh,

[0517]

[0518] S5.2: Define maximum regularity: Here C is a constant and L2 represents the space of square integrable functions.

[0519] 1. Maximum regularity concept:

[0520] The maximum regularity indicates the degree of dependence of the solution u on the right-hand term f.

[0521] It ensures that the higher-order derivatives of the solution have the same regularity as the right-hand side term.

[0522] 2. Space settings:

[0523] Define function space: V = H1(Ω), H = L2(Ω)

[0524] Operator A = Δ, domain D(A) = H2(Ω) ∩ H1_0(Ω)

[0525] 3. Maximum Regularity Estimation:

[0526] For the parabola problem There exists a constant C such that:

[0527]

[0528] S5.3: Based on maximum regularity, calculate the prior error estimate: ||uu h ||L2≤C hk +1+Cτr, h is the spatial grid size, τ is the time step, k is the polynomial order of spatial discretization, and r is the order of temporal discretization.

[0529] 1. Spatial error analysis:

[0530] Using interpolation theory, estimate the spatial discretization error: ||u-Πhu||L2≤C hk +1||u||Hk+1

[0531] where Πh is the L2 projection operator.

[0532] 2. Time error analysis:

[0533] Using Taylor expansion, estimate the time discretization error:

[0534] 3. Overall error estimate:

[0535] Combining the spatial and temporal errors, we get the upper bound of the overall error:

[0536] ||u-uh||L2≤||u-Πhu||L2+||Πhu-uh||L2≤Chk+1+Cτr

[0537] 4. Maximum regularity application:

[0538] Use maximum regularization to control higher-order derivative terms:

[0539] S5.4: Use the residual type a posteriori error estimator: η2 = ΣK(hK2||RK||L22+hK||JK||L22), where RK is the intra-unit residual, JK is the inter-unit jump term, and η is the numerical value of the error size of the a posteriori error estimator.

[0540] 1. Calculation of residual within the unit:

[0541] (In each unit K)

[0542] 2. Jump term calculation:

[0543] (On cell boundaries)

[0544] 3. Local error indicator:

[0545]

[0546] 4. Global error estimation:

[0547] η2=ΣK-ηK2

[0548] 5. Reliability and efficiency:

[0549] Prove that there exist constants C1,C2 such that:

[0550] $C_1\eta\leq \|u - u_h\| \leq C_2\eta$

[0551] S5.5: Calculate the adaptive time step control based on the posterior error estimate: If $\eta >$ tolerance, then $\tau_{new}=\tau_{old} / 2$; if $\eta <$ tolerance / 2, then $\tau_{new}=2*\tau_{old}$.

[0552] 1. Error control strategy:

[0553] Set the target error threshold TOL

[0554] After each time step, calculate the posterior error estimate $\eta$

[0555] 2. Time step adjustment:

[0556] if $\eta >$ TOL:

[0557] $\tau_{new}=\tau_{old} / 2$ # Reduce the time step

[0558] elif $\eta <$ TOL / 2:

[0559] $\tau_{new}=\min(2*\tau_{old},\tau_{max})$ # Increase the time step, but not exceed the maximum allowed step

[0560] else:

[0561] $\tau_{new}=\tau_{old}$ # Keep the current time step

[0562] 3. Recalculation of the solution:

[0563] If the time step is reduced, use interpolation to obtain the solution at the intermediate time

[0564] If the time step is increased, it may be necessary to re - solve the previous step

[0565] 4. Implementation of the adaptive algorithm:

[0566] Initialize the time step $\tau_0$

[0567] For each time step:

[0568] a. Solve using the current time step $\tau_n$

[0569] b. Calculate the posterior error estimate $\eta_n$

[0570] c. Adjust the time step $\tau_{n + 1}$ for the next step according to the error estimate

[0571] d. If the time step is reduced, return to step a for recalculation

[0572] Through this rigorous mathematical analysis and adaptive control method, the embodiment of the present invention can significantly improve the accuracy and reliability of the digital twin model. This can not only simulate the processing process of non-standard precision parts more accurately, but also provide a reliable error bound, providing a solid theoretical basis for process optimization and quality control. At the same time, adaptive time step control can improve the computational efficiency while ensuring accuracy, so that the model can be better applied to real-time monitoring and optimization.

[0573] Among them, the digital twin model is an analytical model based on physical laws or a data-driven model based on machine learning and deep learning.

[0574] The main features and advantages of the method and system for producing non-standard precision parts can now be summarized as follows:

[0575] 1. Comprehensive data collection and analysis:

[0576] Collect key data during the processing in real time, including temperature, pressure, speed and vibration data.

[0577] Ensure the data quality of the digital twin model input through data preprocessing and cleaning.

[0578] 2. Advanced Digital Twin Model:

[0579] Combine physical laws and data-driven methods to build high-precision digital twin models.

[0580] Real-time simulation and prediction are achieved to provide guidance for the production process.

[0581] 3. Accurate thermomechanical behavior analysis:

[0582] Thermomechanical coupling analysis was performed using the finite element method.

[0583] Accurately simulate the behavior of materials in high temperature and high stress environments.

[0584] 4. Intelligent optimization algorithm:

[0585] State prediction using the Koopman operator.

[0586] Combined with the gradient descent algorithm, the process parameters are automatically adjusted.

[0587] 5. Strict error control:

[0588] Apply maximum regularization theory to perform a priori and a posteriori error estimation.

[0589] Implement adaptive time step control to balance computational accuracy and efficiency.

[0590] 6. Closed-loop optimization and production:

[0591] Based on the optimization results, production parameters are adjusted in real time.

[0592] Establish a comprehensive quality control system to ensure product consistency.

[0593] The main advantages of this approach include:

[0594] 1. High precision: Through precise simulation and analysis, the processing accuracy of non-standard precision parts is greatly improved.

[0595] 2. High efficiency: Intelligent optimization algorithm can quickly find the best process parameters and reduce trial and error time.

[0596] 3.Flexibility: Suitable for a variety of non-standard precision parts and can quickly adapt to new production needs.

[0597] 4. Reliability: Strict error control and comprehensive quality monitoring ensure the stability of the production process.

[0598] 5. Continuous optimization: Achieve continuous improvement of the production process through data feedback and model updates.

[0599] 6. Cost saving: reduce material waste and production errors, and reduce overall production costs.

[0600] 7. Knowledge accumulation: Digital twin models are not only used for current production, but can also provide valuable data and insights for future product design and process improvements.

[0601] The embodiment of the present invention also provides a non-standard precision parts production system, such as Figure 2 As shown, including:

[0602] The acquisition module 21 is used to acquire key data during the processing, and the key data includes temperature, pressure, speed and vibration data;

[0603] A simulation module 22 is used to establish a digital twin model and input the key data into the digital twin model so as to simulate the actual processing process in real time;

[0604] An analysis and optimization module 23 is used to analyze the thermomechanical behavior of the material during the processing in the simulation of the actual processing process, and optimize the material processing technology and processing parameters based on the analysis results;

[0605] The production module 24 is used to realize the production of non-standard precision parts based on the optimization results.

[0606] An embodiment of the present invention also provides a non-standard precision parts production method system, including a memory and a processor, wherein the memory stores computer executable instructions, and the processor implements the above method when running the computer executable instructions on the memory.

[0607] An embodiment of the present application also provides a computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute the above-mentioned method for producing non-standard precision parts.

[0608] In one embodiment, a computer device is further provided. The computer device is the network security device mentioned in the above method embodiment. Its internal structure diagram can be as follows: Figure 3 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface.

[0609] Among them, the processor of the computer device is used to provide computing and control capabilities, and can be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto. The processor may include one or more processors, for example, one or more central processing units (CPUs). When the processor is a CPU, the CPU may be a single-core CPU or a multi-core CPU. The processor may also include one or more special-purpose processors, and the special-purpose processor may include a GPU, an FPGA, etc., for accelerated processing. The processor is used to call the program code and data in the memory and execute the steps in the above method embodiment. For details, please refer to the description in the method embodiment, which will not be repeated here.

[0610] The memory of the computer device includes, but is not limited to, non-volatile storage media and internal memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium.

[0611] The input / output interface of the computer device is used to exchange information between the processor and external devices.

[0612] The communication interface of the computer device is used to communicate with an external terminal via a network connection.

[0613] When the computer program is executed by a processor, a method for producing non-standard precision parts is implemented.

[0614] In the several embodiments provided in the present application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the division of each unit / module is only a logical function division, and there may be other division methods in actual implementation, for example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. The mutual coupling, direct coupling, or communication connection shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the system or unit can be electrical, mechanical or other forms.

[0615] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0616] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function according to the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrations. The available medium may be a read-only memory (ROM), or a random access memory (RAM), or a magnetic medium, such as a floppy disk, a hard disk, a tape, a disk, or an optical medium, such as a digital versatile disc (DVD), or a semiconductor medium, such as a solid state disk (SSD), etc.

[0617] The above are only specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present application, and these modifications or replacements should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for producing non-standard precision parts, characterized in that: include: Collect key data during the processing, including temperature, pressure, speed and vibration data; Establishing a digital twin model, and inputting the key data into the digital twin model, so as to simulate the actual processing process in real time; In the simulation of the actual processing process, the thermomechanical behavior of the material during processing is analyzed, and the material processing technology and processing parameters are optimized based on the analysis results; Based on the optimization results, the production of non-standard precision parts is realized.

2. The method according to claim 1, characterized in that Establishing a digital twin model and inputting the key data into the digital twin model so as to simulate the actual machining process in real time, including: Performing data preprocessing and data cleaning on the key data; Collect component parameters of non-standard parts and processing parameters of processing equipment, establish a digital twin model, and perform mathematical description and simulation parameter setting in the physical processing process in the digital twin model; The key parameters of the processing are added to the digital twin model to simulate the actual processing and obtain the changes of the parameters of the non-standard parts in the processing in real time.

3. The method according to claim 1, characterized in that Analyze the thermomechanical behavior of materials during processing and optimize material processing technology and processing parameters based on the analysis results, including: According to the actual processing object and process requirements, a geometric model and a physical field model of the non-standard parts are established, and the processing process is a laser welding process; In the geometric model, meshing the geometric structure; Use thermodynamic models to describe the thermomechanical behavior of materials under high temperature and high stress environments; Numerical simulation of thermomechanical behavior using finite element method, coupling the geometric model of the non-standard component with the thermodynamic model; Based on the simulation results, analyze the problems existing in the actual processing of the non-standard parts, including thermal stress concentration and uncontrolled deformation; Combined with the optimization algorithm, the process parameters are adjusted to optimize the design and production process of the non-standard parts.

4. The method according to claim 3, characterized in that Use thermodynamic models to describe the thermomechanical behavior of materials in high temperature and high stress environments, including: Define the key thermal variables in the manufacturing process, define the boundary conditions and initial states of the thermal system; use the KATO framework to develop a set of coupled nonlinear equations representing the thermal system; In the coupled nonlinear equations, a finite element method is used to discretize the spatial domain; The chaotic map is iterated at discrete time steps and converged nonlinearly to simulate the thermomechanical behavior of materials under high temperature and high stress environments.

5. The method according to claim 3, characterized in that: Combined with the optimization algorithm, the process parameters are adjusted to optimize the design and production process of the non-standard parts, including: Obtain time series data during thermomechanical behavior, including temperature, stress, and deformation data; Constructing an observation function, and using the observation function to map an original state space to a high-dimensional feature space, wherein the original state space is composed of the time series data; Constructing an observation matrix based on the observation function, and performing singular value decomposition (SVD) on the observation matrix; Use the results of SVD to construct a finite-dimensional approximation of the Koopman operator; Use the Koopman operator to predict the short-term and long-term condition of non-standard parts; Based on the prediction results, the process parameters are adjusted using a gradient descent algorithm.

6. The method according to claim 3, characterized in that Numerically simulate the thermo-mechanical behavior using the finite element method, and couple the geometric model and thermodynamic model of the non-standard component, including: Define the thermal boundary conditions, which include heat sources, convective heat transfer boundaries, and radiative boundaries; Define the mechanical boundary conditions, which include fixed constraints, symmetric constraints, and external loads; Define the coupling relationship and coupling type between thermal analysis and structural analysis; Construct a direct solver or an iterative solver, and use the direct solver or iterative solver to couple the geometric model and thermodynamic model of the non-standard component, and perform transient thermal analysis and material phase transformation.

7. The method according to claim 1, characterized in that The method further includes: Perform priori and posteriori error estimation on the discontinuous Galerkin time discretization method through maximal regularity to optimize the digital twin model.

8. The method according to claim 7, characterized in that Performing priori and posteriori error estimation on the discontinuous Galerkin time discretization method through maximal regularity includes: Use the discontinuous Galerkin method to discretize the heat conduction equation: where u is the temperature and f is the heat source term; Define maximal regularity: Here C is a constant and L2 represents the space of square-integrable functions; Based on maximal regularity, calculate the priori error estimate: ||uu h || L2 ≤C h k +1+Cτ r h is the spatial grid size, τ is the time step, k is the polynomial order of spatial discretization, and r is the order of time discretization; Use a residual a posteriori error estimator: η 2 =Σ K (h K 2 ||R K || L2 2 +h K ||J K || L2 2 ) Where R K is the intra-unit residual, J K is the inter-unit jump term, η is the numerical value of the error size of the posterior error estimator; Based on the posteriori error estimate, calculate the adaptive time step control: If η > tolerance, then τ_new = τ_old / 2; If η < tolerance / 2, then τ_new = 2 * τ_old.

9. The method according to claim 1, characterized in that: The digital twin model is an analytical model based on physical laws or a data-driven model based on machine learning and deep learning.

10. A non-standard precision parts production system, characterized in that: Including: An acquisition module for acquiring key data during the processing, where the key data includes temperature, pressure, speed, and vibration data; A simulation module for establishing a digital twin model and inputting the key data into the digital twin model to simulate the actual processing process in real time; An analysis and optimization module for analyzing the thermo-mechanical behavior of the material during the simulation of the actual processing process and optimizing the material processing technology and processing parameters based on the analysis results; A production module for realizing the production of non-standard precision components based on the optimization results.

Images