Process control method for eliminating shrinkage cavity and shrinkage porosity defects of brake caliper casting

Abstract

This invention provides a process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings, belonging to the technical field of process control for eliminating shrinkage cavities and porosity defects in brake caliper castings. This invention collects the three-dimensional geometric data and composition parameters of the brake caliper casting, inputs them into a physical embedded time-series prediction model to output a shrinkage cavity probability heatmap, and extracts the hot spot location and hot spot modulus. The hot spot modulus is then input into a graphite expansion compensation adaptive riser modulus iterative convergence algorithm to calculate the optimal riser size. Based on the optimal parameters, high-pressure actual casting and bottom-pouring are performed, and the internal iteration number parameters of the artificial intelligence model are adjusted in real time. After pouring, the measured shrinkage cavity volume is compared with the predicted value, triggering incremental training. This solves the technical problem of inaccurate riser size design caused by hot spot identification deviation in brake caliper casting shrinkage cavities and porosity defects.

Description

Technical Field

[0001] This invention belongs to the field of process control technology for eliminating shrinkage cavities and porosity defects in brake caliper castings. Specifically, it relates to a process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings. Background Technology

[0002] Brake caliper castings are safety-critical components, and eliminating internal shrinkage cavities and porosity defects relies on accurately identifying hot spots and designing appropriate riser dimensions. In existing technologies, hot spot identification typically employs the Chvorinov modular method or purely data-driven models, while riser dimensions are manually set based on empirical formulas or solidification simulations. Both methods have been widely used in the production of complex geometric castings such as brake calipers, but both have significant limitations.

[0003] The Chvorinov modular method ignores the graphitization expansion effect during the solidification process of ductile iron, resulting in oversized risers and low process yield. Pure data-driven models are prone to physically inconsistent predictions when training data is insufficient, leading to unstable hot spot identification accuracy. When hot spot location identification is inaccurate, the prior input for subsequent riser size calculations becomes distorted, causing errors in the design of the feeding channel, ultimately resulting in shrinkage cavities and porosity defects that cannot be eliminated at the source.

[0004] In other words, existing technologies have technical problems such as shrinkage cavities and porosity defects in brake caliper castings leading to inaccurate riser size design due to thermal joint identification deviations. Summary of the Invention

[0005] In view of this, the present invention provides a process control method for eliminating shrinkage and porosity defects in brake caliper castings, which can solve the technical problem in the prior art where shrinkage and porosity defects in brake caliper castings are caused by thermal joint identification deviations leading to inaccurate riser size design.

[0006] This invention is implemented as follows: This invention provides a process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings, comprising the following steps:

[0007] Collect the three-dimensional geometric data, carbon equivalent, silicon content, copper content, tin content, local wall thickness and initial pouring temperature of the brake caliper casting. Input the three-dimensional geometric data and composition parameters into the physical embedding time-series prediction model and output a time-by-time shrinkage probability heat map. Extract the hot spot location and hot spot modulus from the shrinkage probability heat map.

[0008] The thermal modulus is input into the graphite expansion compensation adaptive riser modulus iterative convergence algorithm to calculate the staged volume balance of liquid shrinkage, solidification shrinkage and graphitization expansion, and output the optimal riser size through iterative loops.

[0009] Based on the optimal riser size, the compensation pressure gradient index is extracted from the solidification simulation results. When the compensation pressure gradient index is in the unobstructed range, proceed to the next step. When the compensation pressure gradient index is below the unobstructed lower limit, perform inoculation enhancement treatment, adjust the amount of spheroidizing agent and inoculant added, and return to the first step.

[0010] The process parameter vector is constructed by carbon equivalent, silicon content, copper content, tin content, initial casting temperature, spheroidizing agent addition amount, inoculant addition amount, pressure and casting rate. It is then input into a multi-physics gradient collaborative descent optimization algorithm to output the globally optimal combination of process parameters.

[0011] Based on the global optimal combination of process parameters and the optimal riser size, high-pressure solid casting mold preparation and bottom pouring are carried out. During the pouring process, the solidification stage comprehensive criterion value is calculated in real time by the solidification stage adaptive iteration number adjustment function, and the internal iteration number parameter of the physical embedding time sequence diagram prediction model is adjusted according to the solidification stage comprehensive criterion value.

[0012] After casting is completed, the actual shrinkage cavity volume of the casting is measured. The actual shrinkage cavity volume is compared with the sum of the volumes of nodes whose shrinkage cavity probability values ​​exceed the probability threshold in the shrinkage cavity probability heatmap. The relative deviation is calculated. When the relative deviation exceeds the deviation threshold, all the collected data and the actual shrinkage cavity volume are included in the training dataset of the physical embedding time series graph prediction model and incremental training is triggered.

[0013] Specifically, the structure of the physical embedded time-series graph prediction model is to discretize the three-dimensional finite element mesh of the brake caliper casting into a graph structure. The node feature vector includes local carbon equivalent, silicon content, copper content, tin content, local wall thickness and initial pouring temperature. The edge weight between nodes is encoded by the ratio of thermal conductivity to Euclidean distance between nodes.

[0014] The physical embedding temporal graph prediction model includes graph convolutional layers. Each graph convolutional layer embeds the residual term of the Fourier heat conduction equation as physical loss during message passing, forcing the temperature field predicted by the network to satisfy the local energy conservation constraint after each layer output. The physical loss weight coefficient is dynamically increased from the initial weight value to the target weight value by an adaptive balancing strategy during training.

[0015] The timing part of the physical embedded timing graph prediction model adopts an improved gated graph loop unit, which performs graph message passing iteration within each time step. The number of iterations is adaptively adjusted by the solidification stage determiner based on the relative position of the current node temperature with the liquidus temperature and solidus temperature.

[0016] The physical embedding time-series graph prediction model introduces skip connections, directly concatenating the three-dimensional geometric feature vector of the input layer to the input of the final fully connected prediction layer. The output layer consists of node-by-node pinhole probability values, which are then activated by Sigmoid to form a pinhole probability heatmap.

[0017] Specifically, the training dataset for the physical embedded time-series prediction model is established by collecting no less than a threshold of historical data sets of historical brake caliper casting experimental data. For each set of experimental data, a three-dimensional finite element solidification simulation is performed to obtain the time-by-time temperature field as a time-series label. The measured shrinkage cavity position is projected onto the finite element mesh node to generate a node-level shrinkage cavity probability label. After the composition parameters and the initial pouring temperature are subjected to maximum and minimum normalization, the training set and the validation set are divided.

[0018] Specifically, the training of the physical embedded time series graph prediction model uses the Adam optimizer. The loss function is composed of a weighted sum of node-level binary cross-entropy loss and physical residual mean square error loss. When the cross-union ratio index of the hole position prediction on the validation set does not increase the threshold number of consecutive early stops, an early stop is triggered, and the optimal weights are saved.

[0019] Specifically, the graphite expansion compensation adaptive riser modulus iterative convergence algorithm calculates the initial modulus of the casting hot spot using the Chvorinov modulus method, establishes a phased volume balance equation for liquid shrinkage, solidification shrinkage, and graphitization expansion, and estimates the graphitization expansion by combining the spheroidization rate, graphite spheroid density, and carbon equivalent. The algorithm iterates until the riser volume change between two adjacent iterations is less than the convergence threshold, at which point it converges.

[0020] Among them, the comprehensive criterion value of the solidification stage It is obtained by weighted summation of the current overall average dimensionless temperature of the casting and the current volume fraction of the mushy region. When the temperature is not lower than the lower limit threshold of the liquid stage, it is determined to be in the liquid stage. When the temperature falls between the upper and lower thresholds of the mushy region stage, it is determined to be in the liquid-solid two-phase mushy region stage. When the value is below the upper limit threshold of the solid contraction stage, it is determined to be in the solid contraction stage.

[0021] Specifically, the multi-physics gradient collaborative descent optimization algorithm defines the objective function for eliminating shrinkage as a weighted negative utility function of shrinkage volume and process yield. In each iteration, the partial gradient of the objective function with respect to the three physical field parameters of thermal field, flow field and stress field is calculated. The joint gradient direction is constructed using the Jacobian matrix of the three fields, and the process parameter vector is updated along the opposite direction of the joint gradient.

[0022] The multiphysics gradient cooperative descent optimization algorithm introduces a simulated annealing perturbation mechanism, accepts inferior solutions with Boltzmann probability, and the annealing temperature decays according to a logarithmic law. It converges when the change in the objective function after a threshold number of consecutive iterations is less than a threshold number of convergence changes.

[0023] Specifically, the inoculation enhancement treatment involves increasing the amount of inoculant added to the range of inoculant addition amounts, while simultaneously increasing the amount of spheroidizing agent added based on the original process parameter vector according to the spheroidizing agent enhancement ratio, in order to improve the graphite spheroid number density and spheroidization rate, and enhance the amount of graphitization expansion.

[0024] The compensation pressure gradient index refers to the average pressure gradient along the hot spot direction of the feeding channel extracted from the solidification simulation results. The unobstructed lower limit is determined by performing a binary statistical analysis on whether the feeding channel is unobstructed in the solidification simulation results of different optimal riser sizes.

[0025] Specifically, the high-pressure solid casting mold preparation involves applying high-pressure compaction to the molding sand using a vertical molding line, so that the hardness of the compacted sand mold reaches the sand mold hardness threshold. The bottom-pouring pouring involves injecting molten metal from the bottom of the mold and filling it smoothly from bottom to top.

[0026] The specified parameters are as follows: probability threshold is 0.5; deviation threshold is 5%; convergence threshold is 1%; convergence change threshold is 0.1%; continuous iteration convergence round threshold is 20 times; early stop round threshold is 10 rounds; historical data volume threshold is 500 sets; liquid stage lower limit threshold is 0.95; mushy zone stage upper limit threshold is 0.95 and lower limit threshold is 0.60; solid shrinkage stage upper limit threshold is 0.60; sand mold hardness threshold is 100; initial weight value is 0.1; target weight value is 0.5; inoculant addition range is 0.5% to 0.7% of molten iron weight; and spheroidizing agent enhancement ratio is 10% to 15%.

[0027] This invention employs a physical embedded time-series graph prediction model to make high-confidence predictions of the hot spot location and hot spot modulus of brake caliper castings. This model then drives an iterative convergence algorithm for graphite expansion compensation adaptive riser modulus to calculate the optimal riser size, thus solving the technical problem of inaccurate riser size design caused by hot spot identification deviation.

[0028] The physical embedding time-series graph prediction model constrains the embedding graph convolution message passing process with the Fourier heat conduction equation, enabling network prediction to be carried out under the hard constraint of physical conservation laws. This fundamentally avoids the problem of physically inconsistent hot spot prediction caused by insufficient training data in pure data-driven models. The time-series graph structure captures the topological evolution of hot spots as they migrate dynamically with solidification time, and the skip connections retain the direct influence of the local geometric features of the brake caliper on the formation of constriction holes, so that the hot spot location prediction has both physical consistency and geometric sensitivity.

[0029] In summary, the present invention solves the technical problem mentioned in the background art of misdesigning riser dimensions due to thermal joint identification deviation in brake caliper casting shrinkage and porosity defects. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention.

[0031] Figure 2 This is a line graph showing the change of the comprehensive criterion value during the solidification stage with the pouring time.

[0032] Figure 3 This is a schematic diagram of the node distribution in the heat map of the probability of shrinkage cavities in brake caliper castings. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0034] like Figure 1 The diagram shows a flowchart of a process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings provided by this invention. The method includes the following steps:

[0035] S01. Collect the three-dimensional geometric data, carbon equivalent, silicon content, copper content, tin content, local wall thickness and initial pouring temperature of the brake caliper casting. Input the three-dimensional geometric data and composition parameters into the physical embedding time-series prediction model and output a time-by-time shrinkage probability heat map. Extract the hot spot location and hot spot modulus from the shrinkage probability heat map.

[0036] S02. Input the thermal modulus output from S01 into the graphite expansion compensation adaptive riser modulus iterative convergence algorithm to calculate the staged volume balance of liquid shrinkage, solidification shrinkage and graphitization expansion, and iteratively output the optimal riser size. The convergence criterion is that the riser volume change between two adjacent iterations is less than 1%.

[0037] S03. Based on the optimal riser size output in S02, extract the compensation pressure gradient index from the solidification simulation results. When the compensation pressure gradient index is in the unobstructed range, proceed to S04. When the compensation pressure gradient index is below the unobstructed lower limit, perform inoculation strengthening treatment, adjust the amount of spheroidizing agent and inoculator added, and return to S01.

[0038] S04. The carbon equivalent, silicon content, copper content, tin content, and initial casting temperature collected in S01, as well as the amount of spheroidizing agent and inoculant added as confirmed in S03, together with the pressure and casting rate, form a process parameter vector. Input it into the multi-physics gradient collaborative descent optimization algorithm. When the objective function changes by less than 0.1% for 20 consecutive iterations, the globally optimal combination of process parameters is output.

[0039] S05. Based on the global optimal process parameter combination output by S04 and the optimal riser size output by S02, perform high-pressure solid casting mold preparation and bottom pouring. During the pouring process, the solidification stage adaptive iteration number adjustment function calculates the solidification stage comprehensive criterion value in real time, and adjusts the internal iteration number parameter of the physical embedded timing diagram prediction model according to the solidification stage comprehensive criterion value.

[0040] S06. After casting is completed, measure the actual shrinkage cavity volume of the casting. Compare the measured shrinkage cavity volume with the sum of the volumes of nodes with shrinkage cavity probability values ​​exceeding 0.5 in the shrinkage cavity probability heatmap output in S01. Calculate the relative deviation between the two. When the relative deviation exceeds 5%, include all the collected data and the measured shrinkage cavity volume into the training dataset of the physical embedding time series graph prediction model and trigger incremental training to complete the closed-loop iterative optimization.

[0041] The specific structure of the physical embedding time-series graph prediction model is as follows: the three-dimensional finite element mesh of the brake caliper casting is discretized into a graph structure, with each mesh element being a node. The node feature vector contains six dimensions: local carbon equivalent, silicon content, copper content, tin content, local wall thickness, and initial pouring temperature. The edge weights between nodes are encoded by the ratio of thermal conductivity coefficient to the Euclidean distance between nodes. The graph convolutional layer consists of four layers. Each layer embeds the residual term of the Fourier heat conduction equation as the physical loss during message passing, forcing the network to satisfy the local energy conservation constraint after each layer's output. The physical loss weight coefficient is dynamically increased from an initial value of 0.1 to 0.5 during training using an adaptive balancing strategy. The time-series part employs an improved gated graph loop unit, performing graph message passing iterations within each time step. The number of iterations is adaptively adjusted by the solidification stage determiner based on the relative position of the current node temperature with the liquidus and solidus temperatures: 2 iterations for the liquid stage, 6 iterations for the liquid-solid two-phase mushy region stage, and 4 iterations for the solid shrinkage stage. Skip connections are introduced within the network to directly concatenate the 3D geometric feature vectors of the input layer to the input of the final fully connected prediction layer, preventing excessive smoothing of node features and loss of local geometric information caused by deep graph convolution. The output layer is a per-node aperture probability value, which, after sigmoid activation, forms an aperture probability heatmap, where the probability value of each node in the aperture probability heatmap ranges from 0 to 1. The entire network consists of 4 graph convolutional layers, 3 time steps of an improved gated graph recurrent unit, 1 skip connection, and 2 fully connected output layers, with a total of approximately [number missing] parameters. indivual.

[0042] The steps for establishing the training dataset for the physical embedding time-series prediction model specifically include: collecting no less than 500 sets of historical brake caliper casting experimental data, each set of data including carbon equivalent, silicon content, copper content, tin content, initial pouring temperature, pressure, optimal riser size, measured shrinkage cavity location, and measured shrinkage cavity volume; performing three-dimensional finite element solidification simulation on each set of experimental data to obtain the time-series temperature field as a time-series label; projecting the measured shrinkage cavity location onto the finite element mesh nodes to generate node-level shrinkage cavity probability labels, with a label value of 1 when shrinkage cavity occurs at the node and a label value of 0 when no shrinkage cavity occurs; after performing maximum-minimum normalization on the carbon equivalent, silicon content, copper content, tin content, and initial pouring temperature, dividing the dataset into a training set and a validation set in an 8:2 ratio.

[0043] The specific steps for training the physical embedding time-series graph prediction model include: using the Adam optimizer, with an initial learning rate set to... The loss function is composed of a weighted sum of node-level binary cross-entropy loss and physical residual mean square error loss, with the physical residual weight adaptively increasing from 0.1 to 0.5; the training rounds are 200, with a batch size of 16 per round; early stopping is triggered when the intersection-union ratio of the hole probabilities heatmap on the validation set with the predicted hole location of the measured hole distribution does not improve for 10 consecutive rounds, and the optimal weight is saved; after training, the accuracy of hot spot recognition and the prediction deviation rate of the hole reduction channel are used as the final performance indicators on the independent test set, and if insufficient, the training data is expanded and retraining is performed.

[0044] The physical embedding time-series graph prediction model constrains the embedding graph convolution message passing process by the Fourier heat conduction equation, so that the network is subject to the hard constraint of physical conservation laws while learning in a data-driven manner. This avoids the physical inconsistency prediction that occurs when the training data is insufficient in a purely data-driven model. The time-series graph structure captures the topological evolution of hot spots during the solidification process. The skip connections retain the direct influence of the local geometric features of the brake caliper on the formation of shrinkage cavities. This makes the final output shrinkage cavity probability heat map reflect both the coupling effect of composition and thermal properties and retain the spatial distribution information of the casting geometry. This provides a high-confidence spatial prior for subsequent iterative calculation of the optimal riser size and optimization of the global optimal process parameter combination, thereby reducing the inaccuracy of the optimal riser size design and the prediction error of the feeding channel caused by the hot spot identification deviation at the source.

[0045] In the adaptive iteration number adjustment function of the solidification stage, the comprehensive criterion value of the solidification stage... The current overall average dimensionless temperature of the casting With the current volume fraction of the pasty region The weighted summation yields the following formula: ;in The current overall average temperature, in Kelvin (K). Liquidus temperature, in Kelvin (K). The volume fraction of the pasty region is dimensionless; when When the state is determined to be in the liquid phase, the internal iteration count parameter is set to 2; when When the condition is determined to be in the liquid-solid two-phase mushy region stage, the internal iteration number parameter is set to 6; when The solid shrinkage stage was determined, and the internal iteration number parameter was set to 4. The boundary values ​​of 0.95 and 0.60 were determined by performing piecewise regression analysis on solidification simulation data of no less than 30 sets of brake caliper castings with different wall thicknesses, and the boundary values ​​that minimized the prediction error of the liquid-solid two-phase mushy zone stage were selected.

[0046] The principle of the graphite expansion compensation adaptive riser modulus iterative convergence algorithm and its specific implementation in the method are as follows: the initial modulus of the casting hot spot is calculated using the Chvorinov modulus method, and a phased volume balance equation is established for liquid shrinkage, solidification shrinkage, and graphitization expansion. The graphitization expansion is estimated by the spheroidization rate, graphite spheroid density, and carbon equivalent. The current optimal riser size is substituted into the solidification simulation and the compensation pressure gradient index is extracted to determine whether the feeding channel remains unobstructed before the final solidification of the hot spot. If the feeding channel closes too early, the riser modulus is reduced proportionally and the riser neck cross-sectional area is increased; otherwise, the riser volume is reduced proportionally. The iteration continues until the riser volume change between two adjacent iterations is less than 1%, at which point convergence is achieved, and the optimal riser size is output. The algorithm directly embeds the physical mechanism of graphitization expansion of spheroidal iron into the iterative calculation process of optimal riser size, transforming the design of optimal riser size from relying on empirical estimation to quantitative optimization driven by physical volume balance equations. This eliminates the problem of optimal riser size being too large due to the neglect of graphitization expansion in the Chvorinov modulus method. It improves the process yield while ensuring unobstructed feeding channels, and ensures the stability and repeatability of the iteration results through convergence criteria.

[0047] The principle of the multi-physics gradient collaborative descent optimization algorithm and its specific implementation in the method are as follows: The objective function for eliminating shrinkage is defined as a weighted negative utility function of shrinkage volume and process yield, with independent variables being the process parameter vector composed of initial casting temperature, spheroidizing agent addition, copper and tin content ratio, pressure and casting rate; in each iteration, the partial gradients of the objective function with respect to the three physical field parameters (thermal field, flow field, and stress field) are calculated, and a joint gradient direction is constructed using the three-field Jacobian matrix, updating the process parameter vector along the opposite direction of the joint gradient; a simulated annealing perturbation mechanism is introduced to accept inferior solutions with Boltzmann probability, and the annealing temperature decays logarithmically; convergence occurs when the objective function changes by less than 0.1% after 20 consecutive iterations, outputting the globally optimal process parameter combination. The algorithm simultaneously utilizes the gradient information of the three physical fields (thermal field, flow field, and stress field) to avoid the destruction of constraints in other physical fields due to optimization of a single physical field. The simulated annealing perturbation mechanism gives the algorithm the ability to escape local minima, ensuring that the final output globally optimal process parameter combination has global optimality under multi-physics constraints.

[0048] The compensation pressure gradient index refers to the average pressure gradient along the hot spot direction of the feeding channel extracted from the solidification simulation results, which is used to quantitatively describe the unobstructedness of the feeding channel. The unobstructed lower limit of the unobstructed interval is determined by performing a binary classification statistical analysis on whether the feeding channel is unobstructed in no less than 20 sets of solidification simulation results with different optimal riser sizes, and taking the pressure gradient value that minimizes the classification error as the unobstructed lower limit.

[0049] The inoculation enhancement treatment refers to increasing the amount of inoculant added to 0.5% to 0.7% of the weight of molten iron, while increasing the amount of spheroidizing agent added by 10% to 15% based on the original process parameter vector, in order to improve the graphite spheroid number density and spheroidization rate, and enhance the amount of graphitization expansion; the two numerical ranges of 0.5% to 0.7% and 10% to 15% are determined by response surface analysis using no less than 15 sets of orthogonal experiments with graphite spheroid number density and elongation as response values.

[0050] The predicted intersection-union ratio of the hole location refers to the ratio obtained by dividing the intersection volume of the predicted hole area and the measured hole area by the union volume of the two. It is used to measure the degree of spatial agreement between the predicted hole location and the measured hole location in the hole probability heatmap. The value range is 0 to 1, and the larger the value, the better the agreement between the prediction and the measurement.

[0051] The Chvorinov modulus method refers to the method of obtaining a local modulus value by dividing the local volume of the casting by the local heat dissipation surface area, and using this to estimate the solidification rate of each part of the casting. The larger the local modulus, the slower the solidification of the part. The hot spot is the area with the largest local modulus.

[0052] The liquid-solid two-phase mushy zone stage refers to the stage in which the temperature of the casting is between the liquidus temperature and the solidus temperature during the solidification process. In this stage, the solid and liquid phases coexist, and whether the feeding channel is unobstructed directly determines whether shrinkage cavities and porosity defects will form.

[0053] Bottom-pouring casting refers to a casting method in which molten metal is injected from the bottom of the mold and fills the mold smoothly from bottom to top. Compared with top-pouring casting, it can reduce turbulence and air entrapment during the filling process of molten iron.

[0054] The high-pressure compaction mold preparation refers to applying high-pressure compaction to the molding sand using a vertical molding line of DISA, so that the hardness of the compacted sand mold reaches 100, in order to meet the requirements of graphitization expansion self-compensation for mold rigidity and compressive strength.

[0055] The three-dimensional finite element mesh refers to a discrete mesh composed of a finite number of polyhedral elements that divide the three-dimensional geometry of the brake caliper casting. It is used to establish the node and edge relationships of the graph structure in the physical embedded time-series graph prediction model.

[0056] The specific implementation of step S01 is as follows: Technicians first acquire the three-dimensional geometric data of the brake caliper casting using 3D scanning or computer-aided design software. A spectrometer is used to determine the carbon equivalent, silicon content, copper content, and tin content of the molten iron. A thermocouple is used to determine the initial pouring temperature, and an ultrasonic thickness gauge is used to acquire local wall thickness data. Subsequently, the three-dimensional geometric data is discretized into a finite element mesh, forming a graph structure with mesh elements as nodes and the ratio of thermal conductivity to Euclidean distance as edge weights. The aforementioned 6-dimensional node feature vectors are then input into a physical embedding time-series graph prediction model. The physical embedding temporal graph prediction model consists of four graph convolutional layers, three time-step improved gated graph recurrent units, and skip connections. During message passing, the graph convolutional layers embed the residual terms of the Fourier heat conduction equation as physical loss, forcing each layer's output to satisfy local energy conservation constraints. The physical loss weight coefficient is dynamically increased from 0.1 to 0.5 using an adaptive balancing strategy. The temporal part adaptively adjusts the number of iterations within each time step based on the relative position of the current node temperature with the liquidus and solidus temperatures: two iterations in the liquid phase, six iterations in the liquid-solid two-phase mushy region phase, and four iterations in the solid contraction phase. Skip connections directly concatenate the 3D geometric feature vectors of the input layer to the fully connected prediction layer, preventing excessive smoothing of local geometric information caused by deep graph convolution. The model's output layer, after Sigmoid activation, outputs node-by-node porosity probability values, forming a porosity probability heatmap. The set of nodes with the highest porosity probability is extracted as the hotspot location, and the corresponding hotspot modulus is calculated using the Chvorinov modulus method.

[0057] The specific implementation of step S02 is as follows: using the hot spot modulus extracted in S01 as the initial input, a phased volume balance equation is established for liquid shrinkage, solidification shrinkage, and graphitization expansion. Liquid shrinkage is calculated based on the thermal expansion coefficient of molten iron and the temperature difference between the pouring temperature and the liquidus temperature. Solidification shrinkage is calculated based on the phase transformation shrinkage rate and the local volume of the casting. Graphitization expansion is estimated jointly by the spheroidization rate, graphite spheroid density, and carbon equivalent. After substituting the current riser size into the solidification simulation, the compensation pressure gradient index is extracted to determine whether the feeding channel remains unobstructed before the final solidification of the hot spot. If the feeding channel closes prematurely, the riser modulus is reduced proportionally and the riser neck cross-sectional area is increased; otherwise, the riser volume is reduced proportionally. The process is iterated until the riser volume change between two adjacent iterations is less than 1%, at which point convergence occurs, and the optimal riser size is output. The above algorithm explicitly embeds the physical mechanism of graphitization expansion in spheroidal iron into the iterative process, eliminating the systematic error caused by the Chvorinov modulus method neglecting graphitization expansion, which leads to an overly large riser size.

[0058] The specific implementation of step S03 is as follows: Solidification simulation is performed based on the optimal riser size output from S02. The compensation pressure gradient index, i.e., the average pressure gradient along the hot spot direction of the feeding channel, is extracted from the simulation results. The unobstructed lower limit is determined by performing binary classification statistical analysis on solidification simulation results of no less than 20 groups of different optimal riser sizes, and the pressure gradient value that minimizes the classification error is taken as the unobstructed lower limit. When the compensation pressure gradient index is within the unobstructed range, it is determined that the feeding channel remains unobstructed before the final solidification of the hot spot, and the process proceeds directly to S04. When the compensation pressure gradient index is below the unobstructed lower limit, inoculation strengthening treatment is performed, increasing the amount of inoculant added to 0.5% to 0.7% of the molten iron weight, while simultaneously increasing the amount of spheroidizing agent added by 10% to 15% based on the original process parameter vector to improve the graphite spheroid density and spheroidization rate, and enhance the graphitization expansion. The process then returns to S01 to re-execute the prediction and iteration.

[0059] The specific implementation of step S04 is as follows: A process parameter vector is constructed using nine parameters: carbon equivalent, silicon content, copper content, tin content, initial casting temperature, spheroidizing agent dosage, inoculant dosage, pressure, and casting rate. This vector is then input into a multi-physics gradient collaborative descent optimization algorithm. The algorithm defines the objective function for eliminating voids as a weighted negative utility function of void volume and process yield. In each iteration, the partial gradients of the objective function with respect to the three physical field parameters (thermal field, flow field, and stress field) are calculated. A joint gradient direction is constructed using the Jacobian matrix of the three fields, and the process parameter vector is updated along the opposite direction of the joint gradient. A simulated annealing perturbation mechanism is introduced, accepting inferior solutions with Boltzmann probability. The annealing temperature decays logarithmically, enabling the algorithm to escape local minima. The algorithm converges when the objective function changes by less than 0.1% after 20 consecutive iterations, and outputs the globally optimal combination of process parameters.

[0060] The specific implementation of step S05 is as follows: Based on the globally optimal process parameter combination output in S04, a high-pressure compaction is applied to the molding sand using a vertical molding line, ensuring that the hardness of the compacted sand mold reaches 100, thus meeting the requirements of graphitization expansion and self-compensation for mold rigidity. Bottom-pouring is used for pouring, with molten metal injected from the bottom of the mold and filling smoothly from bottom to top, reducing turbulence and air entrapment during the filling process. During pouring, the adaptive iteration number adjustment function for the solidification stage calculates the comprehensive criterion value for the solidification stage in real time. The formula is ,in The current overall average temperature, Liquidus temperature This represents the volume fraction of the pasty region. When the state is determined to be in the liquid phase, the internal iteration count parameter is set to 2; when When the condition is determined to be in the liquid-solid two-phase mushy region stage, the internal iteration number parameter is set to 6; when The time frame was determined to be in the solid-state shrinkage stage, and the internal iteration number parameter was set to 4. The boundary values ​​of 0.95 and 0.60 were determined by piecewise regression analysis on solidification simulation data of no less than 30 sets of brake caliper castings with different wall thicknesses.

[0061] The specific implementation of step S06 is as follows: After the casting cools, the measured shrinkage cavity volume is measured using a computed tomography (CT) scanner. The measured shrinkage cavity volume is compared with the sum of the volumes of nodes with a shrinkage cavity probability value exceeding 0.5 in the shrinkage cavity probability heatmap, and the relative deviation between the two is calculated. When the relative deviation exceeds 5%, it indicates that the physical embedding time series graph prediction model has a deviation in its prediction of the casting. All collected data and the measured shrinkage cavity volume are then included in the training dataset, and incremental training is triggered, using the Adam optimizer. The initial learning rate is used to update the model, completing closed-loop iterative optimization, so that the model's prediction accuracy continues to improve with production accumulation.

[0062] It should be noted that the key technologies of this invention include: the physical embedding time-series graph prediction model constrains the Fourier heat conduction equation to embed the graph convolution message passing, making hot spot identification subject to both physical conservation laws and geometric topological constraints, overcoming the inherent defect of physical inconsistency in pure data-driven models under small sample conditions; the graphite expansion compensation adaptive riser modulus iterative convergence algorithm explicitly introduces the graphitization expansion of spheroidal iron into the volume balance equation, transforming riser size from empirical estimation to physical-driven quantitative convergence, eliminating the systematic overestimation error of the Chvorinov modulus method; the multi-physics gradient collaborative descent optimization algorithm simultaneously utilizes the gradient information of three physical fields—thermal field, flow field, and stress field—to construct a joint gradient direction, avoiding the problem of single-physics field optimization violating the constraints of other physical fields, and the simulated annealing perturbation mechanism endows the algorithm with global search capabilities. The three key technologies work synergistically to eliminate shrinkage porosity defects from three dimensions: hot spot identification accuracy, quantitative riser size design, and global optimization of process parameters, forming a complete closed loop from source prediction to end verification, ensuring that errors in any link can be identified and corrected by subsequent links.

[0063] It should be noted that this invention also solves the following technical problem: In current brake caliper casting process optimization, the adjustment of process parameters usually relies on the simulation results of a single physics field. For example, the pouring temperature is adjusted only based on the thermal field simulation, or the pouring rate is adjusted only based on the flow field simulation. This ignores the coupling relationship between the thermal field, flow field, and stress field, resulting in the destruction of constraints in other physics fields after the optimization of parameters in one physics field, leading to new defects. The multi-physics gradient cooperative descent optimization algorithm of this invention calculates the partial gradients of the objective function with respect to the three physics field parameters in each iteration and constructs a joint gradient direction using the Jacobian matrix of the three fields. This ensures that each update of the process parameter vector is performed in the intersection direction of the constraint surfaces of the three physics fields, guaranteeing the simultaneous satisfaction of multi-physics field constraints from the algorithm level. The introduced simulated annealing perturbation mechanism further enables the algorithm to escape the local minima that only satisfy the constraints of a single physics field, and finally outputs a combination of process parameters with global optimality under the coupling constraints of multiple physics fields, solving the technical problem of multi-physics field constraint conflict caused by single-physics field optimization.

[0064] Specifically, the principle of this invention is as follows: The technical solution of this invention can solve the above-mentioned technical problems because: the physical embedded temporal graph prediction model uses a three-dimensional finite element mesh as the graph structure, embeds the residual terms of the heat conduction equation as physical loss into the message passing of each layer of graph convolution, and forces the network to satisfy the local energy conservation constraint after each layer output. This ensures that even under the condition of limited training data, the network's prediction of the temperature field is strongly constrained by physical laws and will not result in misjudgment of hot spots due to energy non-conservation. The temporal gated graph loop unit adaptively adjusts the number of internal iterations according to the solidification stage, with the highest number of iterations in the liquid-solid two-phase mushy region stage, ensuring that the key stage of the formation of the compensation channel has the highest temporal resolution. Skip connections directly stitch three-dimensional geometric features to the output layer, preventing excessive smoothing of local geometric information caused by deep graph convolution, thereby ensuring that the extraction of the hot spot modulus strictly corresponds to the actual geometric structure of the brake caliper. Using the high-confidence hot spot location and hot spot modulus as the input prior for riser modulus iterative calculation, the graphite expansion compensation adaptive riser modulus iterative convergence algorithm explicitly introduces graphitization expansion into the volume balance equation, so that the convergence result of riser size directly reflects the real solidification physics of ductile iron material, thereby eliminating the transmission error of hot spot identification deviation to riser size design at the source.

[0065] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0066] The specific implementation method of step S01 is as follows.

[0067] Collect three-dimensional geometric data and carbon equivalent of brake caliper castings. (Unit: %) Silicon content (Unit: %) Copper content (Unit: %) Tin content (Unit: %), Local wall thickness (Unit: mm) and initial pouring temperature (Unit: K), the three-dimensional geometry is discretized into a finite element mesh structure, where each mesh element is a node, and the first... Feature vectors of each node The structure is as follows:

[0068] ;

[0069] In the formula, For nodes Carbon equivalent at that location, , , They are nodes The silicon content, copper content, and tin content at that location. For nodes Local wall thickness at the location, For nodes The initial pouring temperature at the location, , , , , , These represent the maximum values ​​of the corresponding parameters in the dataset. Each component has been converted to a dimensionless quantity through max-min normalization. (The superscript is not provided in the original text.) Indicates transpose. Edge weights between nodes Based on thermal conductivity (unit: The ratio encoding of the distance to the node's Euclidean distance is given by the following formula:

[0070] ;

[0071] In the formula, , They are nodes , Spatial coordinate vector (unit: m). Reference thermal conductivity (unit: ), Reference length (unit: m). To prevent small positive numbers from being divided by zero, the default value is 0. , Dimensionless edge weights. The residual terms of the Fourier heat conduction equation embedded in the message passing process of the graph convolutional layer of the physical embedding temporal graph prediction model are used as the physical loss. Layer The hidden features of each node are updated as follows:

[0072] ;

[0073] In the formula, For the first Layer nodes The hidden layer feature vectors For the first Layer trainable weight matrix, For bias vectors, For activation function, For nodes The set of neighboring nodes, For the first The physical loss weighting coefficient of the layer (dynamically increased from 0.1 to 0.5). For the Fourier heat conduction equation at the nodes , No. The residual terms of the layer reflect the local energy conservation constraint deviation, and are related to Same dimension, unified units. The timing section uses an improved gated graph loop unit, and the solidification stage determiner is based on the current node temperature. (Unit: K) Liquidus temperature (Unit: K) and solidus temperature (Unit: K) Determine the relevant stage and adaptively adjust the number of internal graph message passing iterations. :when hour ,when hour ,when hour Skip connections connect the input layer's geometric feature vectors. The data is directly concatenated to the input of the final fully connected layer to prevent over-smoothing of features. The output layer, after Sigmoid activation, outputs the pinhole probability value for each node. :

[0074] ;

[0075] In the formula, For fully connected output layer nodes Linear output (dimensionless). , by all nodes A heatmap of cavity probability is constructed. Extraction is performed from the heatmap. The set of nodes is used to calculate the thermal modulus using the Chvorinov modulus method. The formula is:

[0076] ;

[0077] In the formula, (unit: () represents the local volume of the thermal nodal. (unit: ( ) represents the local heat dissipation surface area of ​​the heat dissipation point. The unit is meters. The larger the value, the slower the solidification at that location.

[0078] The specific implementation method of step S02 is as follows.

[0079] Output of S01 Input the graphite expansion compensation adaptive riser modulus iterative convergence algorithm and establish the staged volume balance equation:

[0080] ;

[0081] In the formula, For the first Riser volume of the next iteration (unit: ), Liquid shrinkage (unit: ), Solidification shrinkage (unit: ), For the first The graphitization expansion estimated in the next iteration (unit: ), The dimensionless compensation efficiency coefficient has an empirical value of 0.85 to 0.95, with dimensions on both sides of the equation being zero. Graphitization expansion By sphericity Graphite spheroid density (unit: ) and carbon equivalent Joint estimation:

[0082] ;

[0083] In the formula, The graphitization expansion coefficient (unit: ), experience value to , is the dimensionless sphericity (range 0 to 1). The unit is %. Volume of casting (unit: The dimensions on the right are ,and Dimensionality is consistent. The convergence criterion is:

[0084] ;

[0085] The optimal riser size is output when the above convergence criteria are met.

[0086] The specific implementation method of step S03 is as follows.

[0087] Extract the compensating pressure gradient exponent from the solidification simulation results. (unit: ), This represents the average pressure gradient along the thermal junction direction of the feeding channel. When entering S04, (unit: The lower limit for smooth flow is determined by binary statistical analysis of no fewer than 20 solidification simulations. When... When performing inoculation enhancement treatment, the amount of inoculant added is increased to 0.5% to 0.7% of the weight of molten iron, and the amount of spheroidizing agent added is increased by 10% to 15% on the original basis. After adjustment, return to S01 for re-iteration.

[0088] The specific implementation method of step S04 is as follows.

[0089] Construction process parameter vector ,in Initial pouring temperature (unit: K). The amount of probiotic added (unit: %) Pressure strength (unit: MPa). Pouring rate (unit: ), , , , These represent the maximum values ​​of the corresponding parameters, and each component has been normalized to be dimensionless. The objective function is defined as:

[0090] ;

[0091] In the formula, Predicted shrinkage volume under current process parameters (unit: ), Initial cavity volume (unit: ), This represents the current process yield (dimensionless). The yield of the baseline process is dimensionless. , Weighting coefficients ( ,default , All values ​​are dimensionless ratios. Let be a dimensionless objective function. In the multiphysics gradient cooperative descent optimization algorithm, the joint gradient direction is constructed from the three-field Jacobian matrices, as shown in the formula:

[0092] ;

[0093] In the formula, thermal field parameter vector (Units consistent with thermal field parameters) For dimensionless process parameter vectors Jacobian matrix, For the flow field parameter vector right Jacobian matrix, Stress field parameter vector right Jacobian matrix, , , These are dimensionless objective functions. right , , The partial gradient vector, For the first The dimensionless joint gradient vector of the next iteration. If thermal field parameter vector ,but Flow field parameter vector but Stress field parameter vector but ,in , , These represent the number of parameters for the three physical fields. The formula for updating the process parameter vector is:

[0094] ;

[0095] In the formula, For the first The dimensionless step size of the next iteration is empirically valued as follows: to , , All are dimensionless vectors, with uniform dimensions on both sides of the equation. A simulated annealing perturbation is introduced, using Boltzmann probability... Accept inferior solutions, among which The difference (dimensionless) between two consecutive iterations of the objective function, and the annealing temperature. (Dimensionless) Decays according to a logarithmic law:

[0096] ;

[0097] In the formula, The initial annealing temperature (dimensionless) has an empirical value of 1.0 to 10.0. This represents the current iteration number (a dimensionless positive integer). The convergence criterion is that the condition is met for 20 consecutive iterations. Output the optimal process parameter vector at the time. .

[0098] The specific implementation method of step S05 is as follows.

[0099] in accordance with High-pressure casting and bottom-pouring were performed using the optimal riser size. The comprehensive criterion value for the solidification stage during casting was determined. The calculation formula is:

[0100] ;

[0101] In the formula, The current average temperature of the casting (unit: K). Liquidus temperature (unit: K). This represents the volume fraction of the pasty region (dimensionless, range 0 to 1). It is a dimensionless ratio. This is a dimensionless comprehensive criterion value. Based on... Determine the solidification stage and adjust the internal iteration number parameter. :when hour ,when hour ,when hour The boundary values ​​of 0.95 and 0.60 were determined by performing piecewise regression analysis on no fewer than 30 sets of solidification simulation data.

[0102] The specific implementation method of step S06 is as follows.

[0103] After casting, the actual volume of shrinkage cavity was measured. (unit: Extracting the heatmap of shrinkage probability The sum of the node volumes (unit: ),in For nodes Volume of corresponding finite element (unit: ), calculate the relative deviation:

[0104] ;

[0105] In the formula, This is a dimensionless relative deviation, with dimensions on both sides of the equals sign. The ratio. When At that time, all the data collected this time will be compared with... The dataset is included in the training dataset, triggering incremental training and completing closed-loop iterative optimization. The loss function during training is the node-level binary cross-entropy loss. Loss of mean square error of physical residual Weighted summation:

[0106] ;

[0107] In the formula, The physical residual weight (dimensionless) dynamically increases from 0.1 to 0.5. and All are dimensionless loss values, of which:

[0108] ;

[0109] In the formula, This represents the total number of nodes in the finite element mesh. For nodes The pinhole label (value is 0 or 1). For nodes The predicted value of the shrinkage cavity probability, The mean square error (dimensionless) of the Fourier heat conduction equation residuals. The cross-sectional area ratio index for predicting the location of constriction holes. Defined as:

[0110] ;

[0111] In the formula, To predict the intersection volume between the shrinkage cavity region and the measured shrinkage cavity region (unit: ), The volume of the union of the two (unit: ), It is a dimensionless ratio with a value range of 0 to 1. The larger the value, the higher the degree of agreement between the prediction and the actual space.

[0112] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: In order to verify the effect of the invention, the technicians set up a test environment and conducted a full-process test on the actual casting process of a certain type of brake caliper casting to verify the effectiveness of the method of the invention in eliminating shrinkage cavities and porosity defects.

[0113] The brake caliper casting is made of material grade QT500-7, with an average wall thickness of 12 mm and a maximum local wall thickness of 28 mm. The three-dimensional geometric data was exported from computer-aided design software, and the finite element mesh was discretized into 42,680 nodes. The molten iron composition parameters are shown in Table 1.

[0114] Table 1. Iron molten metal composition parameters

[0115]

[0116] The above parameters are input into the physical embedding time-series graph prediction model. The model performs 6 iterations of internal graph message passing during the liquid-solid two-phase mushy region stage, 2 iterations during the liquid stage, and 4 iterations during the solid shrinkage stage, outputting a time-by-time shrinkage probability heatmap. For example... Figure 3 As shown in the heat map of shrinkage probability, the hot spots of the brake caliper casting are concentrated in the area where the cylinder bore ends and the connecting ribs intersect. The shrinkage probability value of the nodes in this area reaches the highest value of 0.87. The hot spot modulus is confirmed as the local maximum modulus value of this node set after calculation by the Chvorinov modulus method.

[0117] The thermal expansion modulus is input into the graphite expansion compensation adaptive riser modulus iterative convergence algorithm to establish the volume balance equation: the liquid shrinkage is 1.8% of the total casting volume, the solidification shrinkage is 2.3% of the total casting volume, and the graphitization expansion is determined by a spheroidization rate of 92% and a graphite spheroid density. indivual / Combined with a carbon equivalent of 4.32%, the riser volume change was estimated to be 1.6% of the total casting volume. After four iterations, the riser volume change decreased to 0.7%, satisfying the 1% convergence criterion, and the optimal riser dimensions were output: riser diameter 48mm, riser height 72mm, and riser neck diameter 22mm. Compared with the empirical design without graphitization expansion compensation, the convergence result of the optimal riser size reflects the true solidification physics of ductile iron, avoiding the loss of process yield caused by an excessively large riser size.

[0118] The compensating pressure gradient exponent is extracted from the solidification simulation results. Pa / m, higher than the lower limit for unobstructed flow determined by binary statistical analysis. Pa / m indicates that the feeding channel remains unobstructed before the final solidification of the hot spot, eliminating the need for incubation strengthening treatment and allowing direct entry into the multi-physics gradient collaborative descent optimization algorithm stage.

[0119] The process parameter vector consisting of 9 process parameters is input into the multiphysics gradient collaborative descent optimization algorithm. After 23 iterations, the objective function changes by less than 0.1% for 20 consecutive times. The globally optimal combination of process parameters output after convergence is shown in Table 2.

[0120] Table 2 Global Optimal Process Parameter Combination Table

[0121]

[0122] Based on the globally optimal process parameter combination and optimal riser size shown in Table 2, high-pressure compaction is applied using a vertical molding line with sand, achieving a sand mold hardness of 100, and bottom-pouring is performed. During the pouring process, the adaptive iteration number adjustment function for the solidification stage calculates the comprehensive criterion value for the solidification stage in real time. 180 seconds after pouring =0.98, indicating the liquid stage; the internal iteration count parameter is set to 2; 420 s after pouring. =0.74, indicating the liquid-solid two-phase mushy stage, with the internal iteration number parameter set to 6; 780 s after casting. =0.51, which indicates the solid contraction stage. The internal iteration number parameter is set to 4. The trend of change with pouring time is as follows Figure 2 As shown, it can be seen The value decreases monotonically as the solidification process progresses, and the segmentation effect of the boundary values ​​of 0.95 and 0.60 matches well with the actual solidification stage transition time.

[0123] After the casting cooled, the actual shrinkage cavity volume was measured using a computed tomography (CT) scanner. cm The sum of the volumes of nodes with a shrinkage probability value exceeding 0.5 in the shrinkage probability heatmap is... cm The relative deviation between the two was 4.2%, which is below the 5% deviation threshold, and this data did not trigger incremental training. The cross-union ratio (CUI) between the model-predicted hole location and the measured hole location was 0.89, indicating that the physical embedding time series graph prediction model has a high degree of consistency in spatial prediction of hot spot locations.

[0124] Compared to traditional methods, this invention brings the following technological advancements: Traditional Chvorinov modular methods rely solely on geometric modulus when identifying hot spots, neglecting the temporal coupling between casting composition and solidification process, leading to systematic deviations in hot spot location prediction in complex geometric regions. The physical embedding time-series graph prediction model of this invention embeds the heat conduction equation constraint into each layer of message passing in the graph convolution, ensuring that network prediction is performed under strong constraints of physical conservation laws. Even with limited training samples, it maintains physical consistency, thus providing a reliable spatial prior for subsequent riser size iterative calculations. Traditional empirical formulas for riser design do not consider the self-compensating effect of graphitization expansion in ductile iron, resulting in oversized risers. This invention explicitly introduces graphitization expansion into the volume balance equation and ensures iterative stability through convergence criteria, transforming riser size design from empirical estimation to a quantitative convergence result driven by physical equations. Traditional single-physics optimization methods cannot guarantee the simultaneous satisfaction of multi-physics constraints. The multi-physics gradient collaborative descent optimization algorithm of this invention uses a three-field Jacobian matrix to construct a joint gradient direction, which at the algorithm level ensures that each update of the process parameter vector is performed in the intersection direction of the multi-physics constraint surfaces, fundamentally avoiding the problem of other physical constraints being violated due to single-physics optimization.

[0125] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0126] Table 3. Variable Explanation Table (Part 1)

[0127]

[0128] Table 4. Variable Explanation Table (Part Two)

[0129]

[0130] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings, characterized in that, Includes the following steps: Collect the three-dimensional geometric data, carbon equivalent, silicon content, copper content, tin content, local wall thickness and initial pouring temperature of the brake caliper casting. Input the three-dimensional geometric data and composition parameters into the physical embedding time-series prediction model and output a time-by-time shrinkage probability heat map. Extract the hot spot location and hot spot modulus from the shrinkage probability heat map. The thermal modulus is input into the graphite expansion compensation adaptive riser modulus iterative convergence algorithm to calculate the staged volume balance of liquid shrinkage, solidification shrinkage and graphitization expansion, and output the optimal riser size through iterative loops. Based on the optimal riser size, the compensation pressure gradient index is extracted from the solidification simulation results. When the compensation pressure gradient index is in the unobstructed range, proceed to the next step. When the compensation pressure gradient index is below the unobstructed lower limit, perform inoculation enhancement treatment, adjust the amount of spheroidizing agent and inoculant added, and return to the first step. The process parameter vector is constructed by carbon equivalent, silicon content, copper content, tin content, initial casting temperature, spheroidizing agent addition amount, inoculant addition amount, pressure and casting rate. It is then input into a multi-physics gradient collaborative descent optimization algorithm to output the globally optimal combination of process parameters. Based on the global optimal combination of process parameters and the optimal riser size, high-pressure solid casting mold preparation and bottom pouring are carried out. During the pouring process, the solidification stage comprehensive criterion value is calculated in real time by the solidification stage adaptive iteration number adjustment function, and the internal iteration number parameter of the physical embedding time sequence diagram prediction model is adjusted according to the solidification stage comprehensive criterion value. After casting is completed, the actual shrinkage cavity volume of the casting is measured. The actual shrinkage cavity volume is compared with the sum of the volumes of nodes whose shrinkage cavity probability values ​​exceed the probability threshold in the shrinkage cavity probability heatmap. The relative deviation is calculated. When the relative deviation exceeds the deviation threshold, all the collected data and the actual shrinkage cavity volume are included in the training dataset of the physical embedding time series graph prediction model and incremental training is triggered.

2. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 1, characterized in that, The structure of the physical embedded time-series graph prediction model is specifically to discretize the three-dimensional finite element mesh of the brake caliper casting into a graph structure. The node feature vector includes local carbon equivalent, silicon content, copper content, tin content, local wall thickness and initial pouring temperature. The edge weight between nodes is encoded by the ratio of thermal conductivity to Euclidean distance between nodes.

3. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 2, characterized in that, The physical embedding temporal graph prediction model includes graph convolutional layers. Each graph convolutional layer embeds the residual term of the Fourier heat conduction equation as physical loss during message passing, forcing the temperature field predicted by the network to satisfy the local energy conservation constraint after each layer output. The physical loss weight coefficient is dynamically increased from the initial weight value to the target weight value during training by an adaptive balancing strategy.

4. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 3, characterized in that, The timing part of the physical embedded timing graph prediction model adopts an improved gated graph loop unit, which performs graph message passing iteration within each time step. The number of iterations is adaptively adjusted by the solidification stage determiner based on the relative position of the current node temperature with the liquidus temperature and solidus temperature.

5. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 4, characterized in that, The physical embedding time series graph prediction model introduces skip connections, directly concatenating the three-dimensional geometric feature vector of the input layer to the input of the final fully connected prediction layer. The output layer is the hole probability value per node, which is converted into a hole probability heatmap after Sigmoid activation.

6. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 5, characterized in that, The training dataset for the physical embedding time-series prediction model is established by collecting no less than a threshold of historical data sets of historical brake caliper casting experimental data. For each set of experimental data, a three-dimensional finite element solidification simulation is performed to obtain the time-by-time temperature field as a time-series label. The measured shrinkage cavity location is projected onto the finite element mesh node to generate a node-level shrinkage cavity probability label. After the composition parameters and initial pouring temperature are subjected to maximum and minimum normalization, the training set and the validation set are divided.

7. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 6, characterized in that, The training of the physical embedded time series graph prediction model specifically uses the Adam optimizer. The loss function is composed of a weighted sum of node-level binary cross-entropy loss and physical residual mean square error loss. When the cross-union ratio index of the hole position prediction on the validation set does not increase the threshold number of consecutive early stops, an early stop is triggered, and the optimal weights are saved.

8. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 7, characterized in that, The graphite expansion compensation adaptive riser modulus iterative convergence algorithm specifically calculates the initial modulus of the casting hot spot using the Chvorinov modulus method, establishes a phased volume balance equation for liquid shrinkage, solidification shrinkage, and graphitization expansion, and estimates the graphitization expansion by combining the spheroidization rate, graphite spheroid density, and carbon equivalent. The algorithm iterates until the riser volume change between two adjacent iterations is less than the convergence threshold, at which point it converges.

9. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 8, characterized in that, The comprehensive criterion value of the solidification stage It is obtained by weighted summation of the current overall average dimensionless temperature of the casting and the current volume fraction of the mushy region. When the temperature is not lower than the lower limit threshold of the liquid stage, it is determined to be in the liquid stage. When the temperature falls between the upper and lower thresholds of the mushy region stage, it is determined to be in the liquid-solid two-phase mushy region stage. When the value is below the upper limit threshold of the solid contraction stage, it is determined to be in the solid contraction stage.

10. The process control method for eliminating shrinkage cavities and porosity defects in brake caliper castings according to claim 9, characterized in that, The multi-physics gradient collaborative descent optimization algorithm specifically defines the objective function for eliminating shrinkage as a weighted negative utility function of shrinkage volume and process yield. In each iteration, the partial gradients of the objective function with respect to the three physical field parameters of thermal field, flow field and stress field are calculated respectively. The joint gradient direction is constructed using the Jacobian matrix of the three fields, and the process parameter vector is updated along the opposite direction of the joint gradient.

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