A method and system for producing non-standard precision parts

Abstract

The present application discloses a method and system for producing non-standard precision parts, which includes: collecting key data in the processing process, wherein the key data includes temperature, pressure, speed and vibration data; establishing a digital twin model, and inputting the key data into the digital twin model to simulate the actual processing process in real time; in the simulation of the actual processing process, analyzing the thermomechanical behavior of the material in the processing process, and optimizing the material processing technology and processing parameters based on the analysis results; based on the optimization results, realizing the production of non-standard precision parts.

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 the industrial manufacturing industry, the demand for the production of non-standard precision parts is increasing. Traditional methods for producing non-standard precision parts rely mainly on manual experience and trial and error, resulting in low production efficiency, unstable quality, and high costs. 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, existing technologies lack the ability to monitor and optimize the processing process in real time, and are unable to 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 invention 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 to simulate the actual machining process in real time;

[0007] In the simulation of actual processing, 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 to simulate the actual machining process in real time, including:

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

[0011] Collecting component parameters of non-standard parts and processing parameters of processing equipment, establishing a digital twin model, and performing mathematical description and simulation parameter setting of 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 in the parameters of the non-standard parts in the processing in real time.

[0013] Analyze the thermomechanical behavior of materials during processing and optimize the 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 the 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 under 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 nonlinear convergence is performed to simulate the thermomechanical behavior of materials under high temperature and high stress environments.

[0025] Combined with optimization algorithms, 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 mapping an original state space to a high-dimensional feature space using the observation function, wherein the original state space is composed of the time series data;

[0028] Constructing a measurement matrix based on the observation function, and performing singular value decomposition (SVD) on the measurement 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 the 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, wherein the mechanical boundary conditions include 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 digital twin model is optimized by performing a priori and a posteriori error estimation on the discontinuous Galerkin time discretization method through maximum regularization.

[0039] A priori and a posteriori error estimates for discontinuous Galerkin time-discrete methods via maximum regularization are provided, 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] h is the spatial mesh size, τ is the time step size, 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 residual within the cell, JK is the inter-cell 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 process and processing parameters based on the analysis results during the simulation of the actual processing process;

[0058] A production module, configured to implement 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 to enable the at least one processor to 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 during the processing and establishing a digital twin model, real-time simulation and monitoring of the production process of non-standard precision parts are achieved, improving the visualization and controllability of the production process.

[0067] 2. By analyzing and optimizing the thermomechanical behavior of materials during processing, the problem of difficulty in accurately predicting and controlling material behavior in traditional production methods is effectively solved, thereby improving product quality and production efficiency.

[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 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, further optimizing 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 This is a structural block diagram of a non-standard precision parts production system provided in an embodiment of the present application.

[0073] Figure 3 This is a diagram showing the composition 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 this application more clear, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for explaining this application and are not intended to limit this application. In addition, the technical features involved in the various embodiments of this application described below may be combined with each other as long as they do not conflict with each other.

[0075] Figure 1 FIG. 1 is a flow chart of a method for producing non-standard precision parts according to 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 from 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 real time during the processing. 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 of a specific point, while infrared thermal imagers can provide a temperature distribution map of the entire processing area.

[0079] Pressure data acquisition: Pressure sensors are installed at key locations on 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 the process. This is crucial for detecting abnormalities during processing.

[0082] Data acquisition system: A data acquisition system is built using high-speed data acquisition cards and industrial computers. This 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 accurately reflects the physical characteristics and behavior of the actual machining process. The technical principle of the digital twin model is to map and simulate the physical entity or system in the digital world. 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 based on 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, CAD software (such as SolidWorks or CATIA) is used to create an accurate 3D geometric model of the non-standard precision component. This model should include all the key features and dimensions of the component.

[0089] Next, physical modeling is performed. Based on the geometric model, a mathematical model is developed to describe the physical phenomena during the machining process. This may include a heat conduction model, a stress-strain model, a fluid dynamics model, and so on, depending on the nature of the machining process. Key parameters in the model are then set as variable parameters so that they can be dynamically adjusted based on real-time data. These parameters may include material properties, boundary conditions, machining parameters, and so on.

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

[0091] Finally, a 3D visualization interface is developed to enable operators to intuitively observe and understand the status and behavior of the digital twin model. This can be achieved using a game engine 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 the data input into the digital twin model and improve the model's accuracy and reliability. The technical principle of data preprocessing and cleaning is to remove or correct noise, outliers, and missing values in the raw 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 from sensor data.

[0097] A2. Outlier detection and processing: Use statistical methods (such as the Z-score method and the 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 forecasting.

[0099] A4. Data standardization / normalization: Convert data of different dimensions to the same scale to facilitate 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 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 data types.

[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 goal of this sub-step is to build a comprehensive digital twin model that encompasses not only the component's geometry but also its material properties, machining equipment characteristics, and a physical and mathematical description of the machining process. This model can more accurately simulate the actual machining process and provide a reliable foundation 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 and 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 material databases.

[0110] Surface characteristics: Use a surface roughness meter to measure the microscopic topography 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. Digital Twin Model Construction:

[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 corresponding physical models, such as heat conduction model, stress-strain model, etc.

[0118] Equipment model building: Create a virtual model of the processing equipment, including its geometric structure 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] Mechanical process description: Use stress-strain relationship equations to describe the deformation behavior of materials, such as:

[0124] σ=Cε

[0125] Where 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 based on the complexity of the model and the required accuracy.

[0129] Boundary condition setting: Set the boundary conditions of the model according to the actual processing conditions, 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 in the parameters of the non-standard parts during the processing in real time.

[0134] S2.3 combines real-time processing data with the digital twin model to enable dynamic model updates and real-time simulation. This ensures that the digital twin model always stays synchronized with the actual processing process, 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 transmission 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 system change speed.

[0150] C5. Parameter change monitoring:

[0151] Develop key parameter change monitoring algorithms to track the changes in 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 processing.

[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 present invention effectively integrates real-time collected machining process data into the digital twin model, enabling real-time and accurate simulation of the machining process 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 machining 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 machining, especially the thermomechanical coupling effect, and optimize the machining process and parameters accordingly. This is crucial for improving product quality, reducing defects, and increasing production efficiency.

[0159] Specifically include:

[0160] S3.1: Establish a geometric model and a physical field model of the non-standard component based on the actual processing object and process requirements, 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 accurate 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 exponent.

[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 transformations.

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

[0180] For regions with regular shapes, hexahedral meshes are used to improve computational efficiency, while for regions with complex shapes, tetrahedral meshes are used to better accommodate geometric features.

[0181] Use a fine mesh near welds and in areas of stress concentration to improve calculation accuracy. Use a coarser mesh in areas away from welds to reduce calculation complexity. Achieve smooth transitions in 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 an adaptive mesh refinement algorithm to dynamically adjust mesh density based on calculation results. Automatically refine the mesh in areas with large temperature gradients and concentrated stresses.

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

[0185] Through these steps, the present invention establishes a detailed geometric and physical model and performs reasonable meshing. This lays the foundation for subsequent thermomechanical behavior analysis and enables the present invention to more accurately simulate and analyze the 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] Definition of key thermal variables:

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

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

[0192] Thermal stress σth(x,y,z,t);

[0193] Phase transition 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 present invention uses it to establish the coupled equations for the laser welding process:

[0205] Heat conduction equation:

[0206]

[0207] Thermoelastoplastic mechanics equations:

[0208]

[0209] σ=C:(ε-εth-εp)

[0210] εth=α(TT_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 capacity, and 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, use the finite element method 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 a linear combination 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 heat conduction 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 implicit time integration methods (such as Newmark 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] Iterative 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 the laser welding process, including phenomena such as heat conduction, thermal stress, and phase change, providing a solid theoretical basis for subsequent analysis and optimization.

[0250] S3.4: Numerical simulation of thermomechanical behavior is performed using the finite element method, coupling the geometric model and thermodynamic model of the non-standard component.

[0251] The purpose of this step is to combine the previously established geometric and thermodynamic models to predict the actual behavior of non-standard parts during the laser welding process through numerical simulation. This coupled simulation can help embodiments of the present invention better understand the complex physical phenomena during the machining 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 convective 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, including 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] To account for thermal expansion of the fixture, it may be necessary to use elastic supports rather than rigid fixation.

[0272] 2. Symmetry constraints:

[0273] If your model utilizes 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. Heat stress:

[0279] Define the thermal expansion coefficient 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 analyses.

[0282] 1. One-way coupling:

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

[0284] Use the temperature field as input to perform structural analysis and 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 in 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 the Newmark 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. Coupled 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 structural equations and calculate displacements, strains and stresses.

[0310] d. Check convergence. If not, return to step a and iterate.

[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 transformation progress is tracked at each integration point.

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

[0316] Consider the influence 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, embodiments of the present invention can accurately simulate the complex behavior of non-standard components during laser welding, including temperature distribution, thermal stress evolution, and material phase transitions. This provides 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 leverage the previously generated simulation results to conduct an in-depth analysis of potential issues encountered during laser welding of non-standard components, focusing specifically on two common key issues: thermal stress concentration and uncontrolled deformation. This analysis allows the present invention to identify potential quality risks and provide clear guidance 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] Track 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 or 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] Tracks the deformation time curve of a key.

[0343] Analyze deformation rates and identify critical moments of deformation acceleration.

[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 linear buckling analysis and calculate the critical buckling load.

[0349] For thin-walled structures, the thermoelastic buckling effect is 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 identify 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 deformation patterns.

[0368] c. Material factor analysis:

[0369] Analyze the impact of the material's thermophysical properties (such as thermal expansion coefficient and 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] Mark high-risk areas 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 issue.

[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 present invention provides a comprehensive understanding of the thermal stress concentration and uncontrolled deformation that non-standard components may face during laser welding. This information provides clear goals and directions for further process parameter optimization and structural design improvements, helping 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 component design and production processes. This approach minimizes thermal stress concentration and uncontrolled deformation, improving product quality and production efficiency.

[0384] S3.6.1: Obtain time series data on the thermomechanical behavior of the process, including temperature, stress, and deformation data.

[0385] Extract the time-varying data of temperature, stress and deformation of 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 to 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 to the Koopman operator.

[0414] 1. Construct 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 mode.

[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 for 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 a 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, adjust the process parameters using the gradient descent algorithm. 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, and 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 algorithms 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, optimized algorithm-based approach, embodiments of the present invention can automatically adjust process parameters and optimize the design and production process of non-standard parts. This not only reduces thermal stress concentration and uncontrolled deformation, but also improves production efficiency and product quality consistency. The advantage of this approach is that it can handle complex nonlinear systems and continuously improves 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 verifying the optimization results, setting production parameters, and establishing a quality control system.

[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 testing:

[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 the algorithm 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] Prepare detailed process guidance documents, including specific parameters for each production step. Develop operating procedures to ensure consistent operation.

[0470] c. Device programming:

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

[0472] Set upper and lower limits for 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, and vibration 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 the normal range.

[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 three-dimensional 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.Automated upgrade:

[0496] Introduce robotic systems to automate welding, handling and other processes.

[0497] Develop intelligent scheduling systems to optimize production schedules.

[0498] c. Human-machine collaboration:

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

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

[0501] Through these steps, the embodiments of the present invention can effectively transform optimization results into actual production capacity, achieving high-quality, high-efficiency production of non-standard precision parts. This approach not only solves current production problems but also establishes a system of continuous improvement, enabling the production process to continuously adapt to new demands and challenges. Furthermore, through digital and intelligent means, the embodiments of the present invention can achieve precise control and real-time optimization of the production process, minimizing scrap rates and improving production efficiency.

[0502] S5: Perform a priori and a posteriori error estimation on the discontinuous Galerkin time discrete method through maximum regularization 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, embodiments of the present invention can better understand the performance of the model and optimize it accordingly.

[0504] S5.1: Discretize the heat conduction 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. The concept of maximum regularity:

[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. Application of maximum regularity:

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

[0539] S5.4: Use the residual posterior 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 error size of the posterior error estimator.

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

[0541] (In each unit K)

[0542] 2. Jump item 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] $C_1\eta\leq\lVert u - u_h\rVert\leq C_2\eta$

[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] $\tau_{new}=\tau_{old} / 2$ # Decrease 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 decreased, 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 $\tau_{n + 1}$ of the next step according to the error estimate

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

[0572] Through this rigorous mathematical analysis and adaptive control method, embodiments of the present invention can significantly improve the accuracy and reliability of digital twin models. This not only enables more accurate simulation of the machining process of non-standard precision parts, but also provides reliable error bounds, providing a solid theoretical foundation for process optimization and quality control. At the same time, adaptive time step control can improve computational efficiency while ensuring accuracy, enabling the model to 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 in the embodiments of the present invention:

[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 quality of data input into the digital twin model through data preprocessing and cleaning.

[0578] 2. Advanced digital twin models:

[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 is performed using the Koopman operator.

[0586] Combined with the gradient descent algorithm, 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: Applicable to various 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 Shown, including:

[0602] An acquisition module 21 is used to acquire key data during the processing, including 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 while simulating 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 method system for producing non-standard precision parts, 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. The internal structure diagram thereof can be as follows: Figure 3 As shown. The computer device includes a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O 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 processing unit, 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, which may include GPUs, FPGAs, etc. for accelerating processing. The processor is used to call the program code and data in the memory and execute the steps in the above-mentioned 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 this 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 functional 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] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0616] In the above embodiments, all or part of the embodiments may be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments may be implemented 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, all or part of the processes or functions according to the embodiments of the present application are generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions may be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium may 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 integrated therein. The available medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic medium such as a floppy disk, a hard disk, a tape, a magnetic disk, or an optical medium such as a digital versatile disc (DVD), or a semiconductor medium such as a solid state disk (SSD).

[0617] The above are only specific embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or replacements within the technical scope disclosed in this application, and such modifications or replacements should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection 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 to simulate the actual processing process in real time; also including performing a priori and a posteriori error estimation on the discontinuous Galerkin time discretization method through maximum regularity to optimize the digital twin model; wherein the discontinuous Galerkin method is used to discretize the heat conduction equation: ∂u / ∂t - Δu = f(x,t) Where u is the temperature and f is the heat source term; Define maximum regularity: ||∂u / ∂t|| L2 + ||Δu|| L2 ≤ C||f|| L2 Here C is a constant, and L2 represents the space of square integrable functions; Based on maximum regularization, calculate the a priori error estimate: ||u - u 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 temporal discretization; Use a residual-type 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 a posteriori error estimate, the adaptive time step control is calculated: If η > tolerance, then τ_new = τ_old / 2; If η < tolerance / 2, then τ_new = 2 * τ_old; In the simulation of actual processing, 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 to simulate the actual machining process in real time, including: Performing data preprocessing and data cleaning on the key data; Collecting component parameters of non-standard parts and processing parameters of processing equipment, establishing a digital twin model, and performing mathematical description and simulation parameter setting of 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 in the parameters of the non-standard parts during 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 the 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 the 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 and define the boundary conditions and initial states of the thermal system; Develop a set of coupled nonlinear equations representing the thermal system using the KATO framework; 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 nonlinear convergence is performed 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 optimization algorithms, 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 mapping an original state space to a high-dimensional feature space using the observation function, wherein the original state space is composed of the time series data; Constructing a measurement matrix based on the observation function, and performing singular value decomposition (SVD) on the measurement 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 Numerical simulation of thermomechanical behavior using the finite element method, coupling the geometric model of the non-standard component with the thermodynamic model, including: defining thermal boundary conditions, wherein the thermal boundary conditions include a heat source, a convection heat transfer boundary, and a radiation boundary; defining mechanical boundary conditions, wherein the mechanical boundary conditions include fixed constraints, symmetry constraints, and external loads; Define the coupling relationship and coupling type between thermal analysis and structural analysis; 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.

7. 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 deep learning.

8. A non-standard precision parts production system, characterized in that: include: An acquisition module is used to collect key data during the processing, including temperature, pressure, speed and vibration data; A simulation module is used 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; it also includes a priori and a posteriori error estimation of the discontinuous Galerkin time discretization method through maximum regularity to optimize the digital twin model; wherein the discontinuous Galerkin method is used to discretize the heat conduction equation: ∂u / ∂t - Δu = f(x,t) Where u is the temperature and f is the heat source term; Define maximum regularity: ||∂u / ∂t|| L2 + ||Δu|| L2 ≤ C||f|| L2 Here C is a constant, and L2 represents the space of square integrable functions; Based on maximum regularization, calculate the a priori error estimate: ||u - u 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 temporal discretization; Use a residual-type 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 a posteriori error estimate, the adaptive time step control is calculated: If η > tolerance, then τ_new = τ_old / 2; If η < tolerance / 2, then τ_new = 2 * τ_old; The analysis and optimization module is used to analyze the thermomechanical behavior of materials during processing while simulating the actual processing process, and optimize the material processing technology and processing parameters based on the analysis results; The production module is used to realize the production of non-standard precision parts based on the optimization results.

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