Thermodynamic information guided recurrent graph network for reconstructing temperature field of cutting tools

Abstract

The application belongs to the technical field of temperature field simulation and data-driven reconstruction, and relates to a thermodynamic information guided cutting tool temperature field reconstruction method based on a cycle graph network. Firstly, based on the heat transfer characteristics in the cutting process of the tool, the heat flux is determined. The Latin hypercube sampling method is used for parameter design on the heat flux, a finite element model of tool heat transfer is established, and temperature field data under different parameter conditions are obtained to provide sample data for model training. Subsequently, a graph structure model is constructed according to the node space topological relationship, a gating cycle unit is introduced to depict the time evolution characteristics of the temperature field, and a temperature field reconstruction model is established in combination with physical consistency information such as global maximum value maintenance and local extreme value constraint. The model parameters are trained by an optimizer, so that the model can learn the spatial correlation and time dependence of the temperature field. For unknown spatial nodes or unknown heat load states, the trained model is used for temperature prediction to realize three-dimensional temperature field information reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing and thermodynamic field simulation calculation, specifically involving a thermodynamic information-guided method for reconstructing the temperature field of a cutting tool using a cyclic graph network. Background Technology

[0002] High-precision components are widely used in aerospace, energy equipment, and precision manufacturing. During machining, tool temperature directly affects workpiece dimensional accuracy, geometric errors, and tool wear, significantly impacting machining quality and production costs. Therefore, accurate reconstruction and dynamic prediction of the cutting tool temperature field are of significant engineering importance. Existing tool temperature field analysis methods mainly include numerical simulation and experimental measurement. Numerical methods involve large computational loads, are highly dependent on material parameters and boundary conditions, are difficult to model under complex geometries, and are prone to introducing discrete errors. Experimental methods are limited by sensor placement and testing conditions, making it difficult to obtain a complete temperature field distribution and are subject to measurement errors. Therefore, these methods have shortcomings in terms of real-time performance, accuracy, and cost control. Machine learning-based surrogate models are increasingly being applied to physical field reconstruction. However, traditional neural networks typically rely on regular data structures, making it difficult to directly process unstructured mesh data on the tool surface and limiting their ability to characterize complex spatial relationships. Furthermore, the cutting temperature field exhibits strong nonlinearity, multi-scale characteristics, and significant spatiotemporal coupling, making it difficult for conventional models to effectively model its dynamic evolution. In addition, existing data-driven methods do not adequately integrate thermodynamic laws such as heat conduction and convection, potentially leading to a lack of physical consistency in prediction results.

[0003] In the prior art, various temperature field reconstruction schemes have been disclosed in relevant patents, but each has its limitations. For example, patent CN118981928A discloses a method for reconstructing the temperature field of a cutting tool in an ultra-precision cutting process based on the tip temperature. This method is based on a finite element simulation model of tool heat conduction and reconstructs the temperature field by inversely solving the heat flux density through a physical model. Although this scheme incorporates physical constraints, its core relies on a structured mesh finite element model. This method is difficult to effectively handle geometric changes in the tool caused by wear, chipping, etc. (unstructured structures), and the repeated solution of partial differential equations leads to low computational efficiency, failing to meet the real-time requirements of dynamic processes, thus presenting a contradiction between "computational efficiency" and "applicability".

[0004] Furthermore, patent CN119927711A discloses an intelligent temperature-measuring cutting tool and a temperature field reconstruction method. The core of this scheme lies in combining the heat source method with the particle swarm optimization algorithm to predict the temperature field by optimizing and inversely calculating the heat source intensity parameters. However, this method couples "inversion" and "prediction" into the same iterative optimization process: for each new temperature field prediction, the particle swarm optimization algorithm needs to be run again to inversely calculate a set of optimal heat source parameters. This results in high computational costs, essentially preventing truly fast, end-to-end prediction and sacrificing computational efficiency. More importantly, this analytical model is essentially a "white-box" physical equation; its structure cannot be deeply integrated with data-driven methods, lacking physical constraints such as thermodynamic laws, thus limiting its generalization and predictive reliability under complex boundary conditions.

[0005] How to construct a cutting tool temperature field reconstruction method that can be applied to unstructured structures, has spatiotemporal dynamic modeling capabilities, effectively integrates thermodynamic constraints, and balances prediction accuracy and computational efficiency has become an urgent technical problem to be solved. Summary of the Invention

[0006] This invention aims to provide a thermodynamic information-guided method for reconstructing the temperature field of a cutting tool using a cyclic graph network, in order to solve the problems of insufficient reconstruction accuracy, limited dynamic modeling capabilities, and difficulty in integrating thermodynamic constraints in existing technologies under complex geometries, thereby achieving high-precision, real-time, and physically consistent reconstruction of the temperature field of the cutting tool.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A thermodynamically information-guided method for reconstructing the temperature field of a cutting tool using a cyclic graph network, comprising the following steps:

[0009] Step 1: Determine the heat flux based on the heat transfer characteristics during tool cutting. The Latin hypercube sampling method is used to design parameters for the heat flux, establishing a finite element model of tool heat transfer. Temperature field data under different parameter conditions are obtained to provide sample data for subsequent model construction and training.

[0010] Step 2: Based on the tool heat transfer finite element model established in Step 1, the tool geometry is meshed. A graph structure is constructed using the spatial adjacency relationships between mesh nodes. The finite element nodes are treated as graph nodes, the connections between nodes are treated as edges, and the node features and dynamic temperature information are used as node features to form graph data for training.

[0011]

[0012] Among them, the node feature matrix Features of each node From node space coordinates With time step The node temperature splicing is composed of, , Indicates the total number of nodes. The feature dimension of a node; adjacency matrix It represents the connection relationships between nodes, ensures the integrity of information transmission between nodes, and is used to capture spatial dependencies between nodes. Indicates the starting point of the edge. Represents the endpoint of an edge; global physical feature vector Includes heat flux and the position of heat action It is used to guide node feature updates.

[0013] Step 3: Construct a gated cyclic graph neural network model guided by thermodynamic information.

[0014] Node spatial feature extraction: for each time step Node feature matrix Perform layer normalization to obtain the initial node input:

[0015] Extracting hidden features of nodes using a two-layer graph convolutional network:

[0016] in, This represents the initial node features after layer normalization. These are the hidden features extracted from the first layer of GCN. The hidden features extracted from the second layer GCN For layer normalization operation, It is a non-linear activation function. and These represent the first-level and second-level GCN operations, respectively.

[0017] Time series modeling: using hidden features Hidden state compared to the previous time step Input gated recurrent units (GRUs) to update node states, thereby achieving dynamic evolution modeling of the temperature field:

[0018]

[0019] in, For time steps The updated node state matrix.

[0020] Iterative prediction: The temperature prediction of each time step node is determined by the temperature of the previous time step and the adjacency matrix, and is used as the input for the next time step, forming an iterative prediction process to realize the continuous dynamic reconstruction of the tool temperature field.

[0021] Step 4: Construct a thermodynamically guided physical constraint loss function.

[0022] In the training process of the thermodynamically guided gated cyclic graph neural network model constructed in the third step, to improve the physical consistency of the temperature field prediction results, multi-dimensional thermodynamic constraints are introduced on the basis of data-driven loss, and a physics-guided hybrid loss function is constructed. Its expression is:

[0023] in, The first term is the data-driven loss term, used to constrain the difference between the model's predicted values ​​and the actual values; the other four terms are thermodynamic constraint terms, constraining the model predictions from four physical dimensions: temporal evolution, spatial distribution characteristics, local key regions, and global extreme value range. Details are as follows:

[0024] Data-driven loss terms The mean squared error function is used to account for the overall difference between the temperature predicted by the degree-constrained model and the actual temperature.

[0025]

[0026] in, It is the total length of the time series. Indicates the model at time step ,node The predicted temperature value at that location, Indicates the actual data at time step ,node The temperature value at that location.

[0027] Time gradient constraint Based on the time-discrete form of the heat transfer equation, a central difference approximation is constructed to constrain the smooth evolution of the temperature field over time, ensuring that it satisfies the physical laws of heat conduction.

[0028]

[0029] in, Indicates the model at time step ,node The predicted temperature value at that location, Indicates the model at time step ,node The predicted temperature value at that location.

[0030] Spatial gradient constraint term Based on the graph structure adjacency relationship of the finite element mesh, in the edge set The structure above reflects the thermal conduction coupling relationship between nodes to ensure the spatial continuity of the temperature field.

[0031]

[0032] in, Indicates the model at time step ,node The predicted temperature value at that location.

[0033] The physical consistency constraint for critical response regions aims to enhance the prediction accuracy of high-temperature critical regions, including:

[0034] Global peak hold constraint Consistency between predicted global maximum temperature field and actual value:

[0035]

[0036] in, express The maximum value, express The maximum value.

[0037] Local extremum constraint term Error constraints are applied to the nodes with the highest temperatures to maintain the prediction accuracy of key high-temperature locations:

[0038]

[0039] in, The index representing the node with the highest temperature; Indicates at time step At that time, the highest temperature node in the corresponding predicted temperature field Temperature value; Indicates at time step At that time, the highest temperature node in the corresponding real temperature field Temperature value.

[0040] To avoid excessive physical constraints in the early stages of training affecting the model's data fitting ability, an adaptive weight adjustment strategy is introduced:

[0041]

[0042] in, and These are the initial weighting coefficients. To adjust the time constant, this mechanism adjusts the time gradient constraint weights. The value gradually increases from 0 to a certain value as the number of training epochs increases. Spatial gradient constraint weights Then from The coefficients asymptotically decay to 0, thus achieving a dynamic balance between focusing on spatial smoothness constraints in the early stages of training and focusing on temporal evolution constraints in the later stages. and These are preset fixed values, representing the fixed weight coefficients of local and extreme value constraints, respectively, used to control the stability strength of local and extreme value constraints.

[0043] Step 5: Construct a dataset containing multiple sets of simulation conditions. Each sample set contains a sequence of node states across multiple time steps, used to characterize the dynamic evolution of the tool's three-dimensional temperature field. The dataset is proportionally divided into training, validation, and test sets for model training and performance evaluation.

[0044] During training, a sequence-to-sequence prediction framework is used to model the temperature field over time. To avoid error accumulation during recursive prediction and improve model convergence speed, a teacher forcing (TF) training strategy is introduced. The actual temperature and model predictions are mixed with a certain probability and used as the input for the current time step, expressed as:

[0045] in, Indicates the model at time step Input temperature value. TF ratio. With training rounds Increased dynamic decay:

[0046] in, This represents the initial value of the TF ratio. The attenuation coefficient is used. This strategy enables the model to accelerate convergence by relying on real data in the early stages of training, and then gradually enhances the model's ability to perform multi-step recursion based on its own prediction results by dynamically reducing the proportion of real data input, thereby effectively improving the stability and generalization of long-term predictions.

[0047] After training, the thermodynamically guided gated cyclic graph neural network model can continuously predict the temperature field over multiple time steps and update the node input features in real time during the prediction process, thereby realizing the dynamic reconstruction of the tool temperature field.

[0048] Step 6: Input the heat flux parameters and initial temperature field under the operating condition to be predicted into the pre-trained thermodynamically guided gated cyclic graph neural network model to construct the corresponding graph data structure, using the initial time step temperature as the initial state. The model then performs multi-step predictions in a time-step recursive manner: in each time step, the current node state is updated based on the node temperature and neighborhood relationship of the previous time step, realizing the dynamic evolution calculation of the temperature field. During this process, the model updates the node feature matrix in real time, obtaining the temperature distribution prediction results for each subsequent time step in sequence. Finally, the node temperature sequence of each time step output by the model is mapped back to the corresponding finite element mesh node, completing the reconstruction of the spatiotemporal distribution of the tool's three-dimensional temperature field, thereby achieving rapid and accurate calculation of the temperature field evolution process under different operating conditions.

[0049] The effective effects of this invention are as follows:

[0050] This invention employs a gated cyclic graph neural network guided by thermodynamic information to dynamically reconstruct the temperature field of cutting tools. Compared to traditional finite element repetitive simulation methods, it obtains high-precision temperature field distribution results without repeatedly solving heat transfer control equations, significantly reducing computational costs, improving computational efficiency, and enabling rapid prediction of temperature fields under different operating conditions. By constructing a graph structure corresponding to the finite element mesh and combining it with temporal recursive modeling, it can accurately characterize the heat conduction coupling relationship and temperature evolution characteristics in complex spatial structures, improving the accuracy of temperature field reconstruction and the stability of multi-step prediction. Simultaneously, by introducing temporal and spatial gradient physical constraints based on the discrete form of heat transfer into the loss function and combining it with consistency control of key high-temperature regions, the physical rationality and engineering reliability of the prediction results are enhanced. Therefore, this invention achieves efficient, accurate, and physically consistent reconstruction of the tool temperature field under complex cutting conditions, meeting the needs of rapid prediction of temperature fields in the cutting process and engineering applications. The method of this invention can achieve high-precision temperature field prediction even under small sample conditions, and has good generalization ability and engineering application value. Attached Figure Description

[0051] Figure 1 This is a framework diagram of the thermodynamic information-guided cyclic graph network cutting tool temperature field reconstruction method of the present invention.

[0052] Figure 2 This is a schematic diagram of the tool thermal boundary conditions in an embodiment of the present invention. S1 represents the heat transfer contact surface, i.e. the position where heat flux is applied, and the other surfaces are heat dissipation surfaces.

[0053] Figure 3 This is a diagram showing the mesh division result of the tool structure according to an embodiment of the present invention.

[0054] Figure 4 This is a diagram showing the finite element temperature field distribution results of an embodiment of the present invention.

[0055] Figure 5 R, as an embodiment of the present invention 2 Evaluation results. Detailed Implementation

[0056] The present invention will be further described below with reference to specific embodiments.

[0057] like Figure 1 As shown, this invention provides a thermodynamically information-guided method for reconstructing the temperature field of a cutting tool using a cyclic graph network. First, for the three-dimensional tool structure, its thermal boundary conditions and thermal load conditions are determined. Finite element analysis software is used to perform three-dimensional mesh generation on the tool, generating a finite element model containing node and element information. Then, within a heat flux range of 6×10⁻⁶... 4 ~3×10 6 Within a W / m² area, multiple thermal load input samples are generated using the Latin hypercube sampling method. The temperature response data of each thermal load sample at different time steps is calculated through finite element simulation, forming a time-series dataset of the temperature field. A graph structure model is constructed based on the node connectivity of the finite element mesh, where mesh nodes serve as graph nodes, spatial adjacency relationships between nodes are represented as graph edges, node features include spatial coordinates and temperature values, and global features are heat flux parameters. A gated recurrent graph neural network (TIGR-GNN) model is constructed based on the above training data and trained using a Teacher Forcing exponential decay strategy to learn the spatiotemporal evolution of the temperature field. For temperature fields under unknown thermal load conditions or unknown time steps, predictions are made using the trained model, and tool temperature field distribution cloud maps are plotted based on the prediction results, achieving rapid reconstruction of the three-dimensional temperature field.

[0058] Figure 2 This is a schematic diagram of the thermal boundary conditions of a cutting tool, where the bottom of the tool is a fixed temperature boundary, the other surfaces are convective heat transfer boundaries, and a uniform heat flux load is applied to the cutting area. Figure 3 The result of the tool structure mesh generation. Figure 4 This is the finite element temperature field distribution result under a certain thermal load condition. The mesh in this embodiment contains 8,085 nodes and 24,255 edges.

[0059] The temperature field reconstruction process of this invention is as follows:

[0060] Data Preparation: Twenty sets of thermal load state input samples were generated within the heat flux range, including 15 training samples and 5 test samples. Transient heat conduction finite element analysis was performed on each set of thermal loads, with a total simulation time of 3 seconds and a time step of ΔT = 0.15 seconds, obtaining temperature field data for 20 time steps. The dataset was divided into a 70% training set, a 20% validation set, and a 10% test set.

[0061] Model training: The TIGR-GNN model is constructed based on the collected training data. A sequence-to-sequence framework is used to achieve multi-time step prediction, and the model training is completed through the Teacher Forcing exponential decay strategy.

[0062] Temperature field reconstruction and experimental verification: Temperature field prediction was performed using the trained model. Four sets of experiments were set up. Experiment 1 used the method proposed in this invention, which adopted graph structure modeling and physical consistency constraints. Experiment 2 used a pure data-driven model without physical information guidance. Experiment 3 retained the physical consistency constraints of global maximum and local extrema, and removed time and space constraints. Experiment 4 used a graph attention network model.

[0063] Experimental results show that the method of the present invention can obtain the highest R² value (all greater than 0.6) under different unknown nodes and unknown thermal load conditions, such as... Figure 5 As shown, under small sample conditions, the model exhibits significantly better prediction accuracy and stability than Experiments 2, 3, and 4. Experiments 2 and 3 are unstable under unknown node and unknown thermal load conditions, especially with large errors in extrapolation predictions, indicating that purely data-driven or only partially physical constraints are insufficient to fully capture spatial-temporal correlations; Experiment 4's model shows unstable convergence and low prediction accuracy under limited data conditions.

[0064] Further results verify that the method of this invention, through graph structure modeling combined with physical consistency constraints, effectively captures the temperature correlation and global characteristics of thermal loads between spatially adjacent nodes, achieving high-fidelity reconstruction of the temperature field. Simultaneously, the sequence-to-sequence framework and the Teacher Forcing decreasing strategy improve training convergence speed and stability. In summary, the method of this invention can quickly and accurately reconstruct the temperature field of a three-dimensional cutting tool, possessing good generalization ability and engineering application value, and can be widely applied in fields such as tool thermal analysis, machining process optimization, and high-temperature structure prediction.

Claims

1. A method for reconstructing the temperature field of a cutting tool using a gated cyclic graph neural network guided by thermodynamic information, characterized in that, The steps are as follows: Step 1: Determine the heat flux based on the heat transfer characteristics during the cutting process; use the Latin hypercube sampling method to design parameters for the heat flux, establish a finite element model of tool heat transfer, and obtain temperature field data under different parameter conditions to provide sample data for subsequent model construction and training. Step 2: Based on the tool heat transfer finite element model established in Step 1, mesh the tool geometry; A graph structure is constructed using the spatial adjacency relationships between mesh nodes. Finite element nodes are treated as graph nodes, and the connections between nodes are treated as edges. Node features and dynamic temperature information are used as node features to form graph data for training. Among them, the node feature matrix Features of each node From node space coordinates With time step The node temperature splicing is composed of, , Indicates the total number of nodes. The feature dimension of a node; adjacency matrix It represents the connection relationships between nodes, ensures the integrity of information transmission between nodes, and is used to capture spatial dependencies between nodes. Indicates the starting point of the edge. Represents the endpoint of an edge; global physical feature vector Includes heat flux and the position of heat action , used to guide node feature updates; Step 3: Construct a thermodynamically guided gated cyclic graph neural network model; Node spatial feature extraction: for each time step Node feature matrix Perform layer normalization to obtain the initial node input: Extracting hidden features of nodes using a two-layer graph convolutional network: in, This represents the initial node features after layer normalization. These are the hidden features extracted from the first layer of GCN. The hidden features extracted from the second layer GCN For layer normalization operation, It is a non-linear activation function. and These represent the first-level and second-level GCN operations, respectively. Time series modeling: using hidden features Hidden state compared to the previous time step Input gated recurrent units (GRUs) to update node states, thereby achieving dynamic evolution modeling of the temperature field: in, For time steps Updated node state matrix; Iterative prediction: The temperature prediction of each time step node is determined by the temperature of the previous time step and the adjacency matrix, and is used as the input for the next time step, forming an iterative prediction process to realize the continuous dynamic reconstruction of the tool temperature field. Step 4: Construct a thermodynamically guided physical constraint loss function; In the training process of the thermodynamically guided gated cyclic graph neural network model constructed in the third step, to improve the physical consistency of the temperature field prediction results, multi-dimensional thermodynamic constraints are introduced on the basis of data-driven loss, and a physics-guided hybrid loss function is constructed. Its expression is: in, This is a data-driven loss term used to constrain the difference between the model's predicted values ​​and the actual values. This is a time gradient constraint term; For spatial gradient constraints; Constraints are maintained to preserve global peak values; This is a local extremum constraint term; For time gradient constraint weights, These are the spatial gradient constraint weights; These are the weighting coefficients for local constraints. These are the weighting coefficients for the extreme value constraints; Step 5: Construct a dataset containing multiple sets of simulation conditions. Each set of samples contains a sequence of node states at multiple time steps, used to characterize the dynamic evolution of the three-dimensional temperature field of the tool; the dataset is divided into training set, validation set and test set according to the proportions for model training and performance evaluation. Step 6: Input the heat flux parameters and initial temperature field under the working condition to be predicted into the pre-trained thermodynamic information-guided gated cyclic graph neural network model to construct the corresponding graph data structure, using the initial time step temperature as the initial state; the model then performs multi-step predictions in a time-step recursive manner: in each time step, the current node state is updated based on the node temperature and neighborhood relationship of the previous time step, realizing the dynamic evolution calculation of the temperature field; during this process, the model updates the node feature matrix in real time, and obtains the temperature distribution prediction results of each subsequent time step in sequence; finally, the node temperature sequence of each time step output by the model is mapped back to the corresponding finite element mesh node, completing the reconstruction of the spatiotemporal distribution of the tool's three-dimensional temperature field, thereby realizing the rapid and accurate calculation of the temperature field evolution process under different working conditions.

2. The method for reconstructing the temperature field of a cutting tool using a thermodynamically information-guided gated cyclic graph neural network according to claim 1, characterized in that, In the fourth step, the specific loss items are as follows: Data-driven loss terms The mean squared error function is used to constrain the overall difference between the model's predicted temperature and the actual temperature: in, It is the total length of the time series. Indicates the model at time step ,node The predicted temperature value at that location, Indicates the actual data at time step ,node Temperature value at; Time gradient constraint Based on the time-discrete form of the heat transfer equation, a central difference approximation is constructed to constrain the smooth evolution of the temperature field over time, ensuring that it satisfies the physical laws of heat conduction. in, Indicates the model at time step ,node The predicted temperature value at that location, Indicates the model at time step ,node The predicted temperature value at that location; Spatial gradient constraint term Based on the graph structure adjacency relationship of the finite element mesh, in the edge set The structure above reflects the thermal conduction coupling relationship between nodes to ensure the spatial continuity of the temperature field. in, Indicates the model at time step ,node The predicted temperature value at that location; The physical consistency constraint for critical response regions aims to enhance the prediction accuracy of high-temperature critical regions, including: Global peak hold constraint Consistency between predicted global maximum temperature field and actual value: in, express The maximum value, express The maximum value; Local extremum constraint term Error constraints are applied to the nodes with the highest temperatures to maintain the prediction accuracy of key high-temperature locations: in, The index representing the node with the highest temperature; Indicates at time step At that time, the highest temperature node in the corresponding predicted temperature field Temperature value; Indicates at time step At that time, the highest temperature node in the corresponding real temperature field Temperature value.

3. The method for reconstructing the temperature field of a cutting tool using a thermodynamically information-guided gated cyclic graph neural network according to claim 1, characterized in that, In the fourth step, to avoid excessive physical constraints in the early stages of training affecting the model's data fitting ability, an adaptive weight adjustment strategy is introduced: in, and These are the initial weighting coefficients. To adjust the time constant; this mechanism adjusts the time gradient constraint weights. The value gradually increases from 0 to 1 as the number of training epochs increases. Spatial gradient constraint weights Then from It gradually decays to 0.

4. The method for reconstructing the temperature field of a cutting tool using a thermodynamically information-guided gated cyclic graph neural network according to claim 1, characterized in that, In the fifth step, during the training process, a sequence-to-sequence prediction framework is used to model the temperature field over time. A teacher-mandated training strategy is introduced, where the actual temperature and the model's predicted value are mixed with a certain probability as input to the current time step. The expression for this is: in, Indicates the model at time step Input temperature value; TF ratio With training rounds Increased dynamic decay: in, This represents the initial value of the TF ratio. The attenuation coefficient; After training, the thermodynamically guided gated cyclic graph neural network model can continuously predict the temperature field over multiple time steps and update the node input features in real time during the prediction process, thereby realizing the dynamic reconstruction of the tool temperature field.

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