Multi-objective optimization method for double-material injection molding process parameters

Abstract

The invention discloses a multi-objective optimization method for double-material injection molding process parameters. The multi-objective optimization method comprises the following steps: firstly, obtaining a simulation result data set based on Moldflow simulation analysis and a Taguchi test; then, on the basis of the simulation test data set, a GAM model is constructed and then trained, super-parameters of GAM are optimized through a GTO algorithm, and a GTO-GAM model between injection molding process parameters and a quality optimization target is established; then, performing multi-target optimization on the GTO-GAM model through an MODA algorithm to obtain a Pareto leading edge of a quality optimization target; and finally, determining an optimal combination of process parameters in the obtained Pareto leading edge of the quality optimization target through a CRITIC-TOPSIS evaluation method. According to the method, the buckling deformation and the volume shrinkage rate of the double-material injection molding plastic part can be effectively reduced, and a theoretical basis and data support can be provided for obtaining the optimal technological parameter combination of double-material injection molding.

Description

Technical Field

[0001] The present invention relates to a multi-objective optimization method for injection molding process parameters, in particular to a multi-objective optimization method for double-material injection molding process parameters based on GTO-GAM and MODA, and belongs to the technical field of injection molding. Background Art

[0002] Double-shot window (PC / TPU) injection molding involves sequentially injecting two different materials into the mold cavity. Although the molding process is divided into two steps, the product only needs one ejection. This process is typically completed using a single mold set. Compared to traditional single-shot injection molding machines, double-shot injection molding machines are equipped with two molding nozzles and a different molding mechanism. Double-shot injection molding excels in added value, energy efficiency, production efficiency, and environmental friendliness, making it a key process in modern manufacturing. Double-shot molding not only improves the aesthetics and assembly performance of injection-molded products, but also increases added value and labor productivity. Polycarbonate (PC) is a high-performance thermoplastic widely used in electronic housings for its excellent mechanical strength, transparency, heat resistance, and electrical insulation properties. Thermoplastic polyurethane (TPU) is a high-performance elastomer material that combines the high elasticity of rubber with the processability of plastic. Its high toughness and wear resistance make it an ideal material for protective products such as mobile phone and tablet cases. However, due to the interaction between the entire PC macromolecular chains and the difference in melting temperature between PC and TPU, defects such as weld marks, warping deformation, and volume shrinkage will appear during the molding process of double-injection molded products. These defects will reduce the molding quality of double-injection molded products. Therefore, the optimization of double-injection molding process parameters has become the focus of double-injection molding quality research.

[0003] Currently, combining simulation analysis with mathematical model prediction is a common method for optimizing process parameters. Generally, the injection molding process of thin-walled plastic parts is first simulated and analyzed using Moldflow software to analyze cooling effects and flow properties. A mathematical model is then constructed based on the simulation data to establish the relationship between quality objectives and process parameters. Finally, an optimal combination of process parameters is determined through a search-based optimization algorithm. For example, Cao Y et al. constructed an adaptive network fuzzy inference system (ANFIS) between warpage and process parameters and used a genetic algorithm (GA) to obtain an optimal process parameter solution. Sun Zheng et al. constructed a mathematical surrogate model between warpage, volumetric shrinkage, and process parameters based on a gradient-enhanced Kriging (GEK) model. They used a multi-objective differential evolution (MODE) algorithm to search for Pareto solutions and determined the optimal process parameter solution based on weighted coefficients. Liu X et al. constructed a mathematical surrogate model between warpage, volumetric shrinkage, and process parameters using a GA-optimized extreme learning machine (ELM) model. They then applied a multi-objective firefly algorithm combined with the GRA-TOPSIS multi-objective decision-making method to determine the optimal process parameter solution.

[0004] In the study of practical injection molding problems, multiple interrelated objectives and constraints often require comprehensive consideration and trade-offs. For example, when warpage and volumetric shrinkage are considered, reducing the cooling rate to minimize warpage also increases volumetric shrinkage due to extended cooling time. Multi-objective optimization, as a method for solving optimization problems involving multiple conflicting objectives, aims to find reasonable trade-offs between these objectives and generate a Pareto frontier of multi-objective optimal values. Current research on multi-objective optimization typically transforms multi-objective problems into single-objective ones through the concept of weighted combination. Commonly used methods include grey relational analysis (GRA), topology of successive ideal solutions (TOPSIS), entropy weighting, and fuzzy comprehensive evaluation (FCE). However, from a multi-objective perspective, all objectives are often mutually constrained, and improving one objective often comes at the expense of others. Consequently, a multi-objective optimization problem typically generates a large number of non-dominated solutions (Pareto frontiers). Current research on multi-objective optimization of injection molding process parameters often relies on engineering experience and trial and error to determine the optimal process parameter combination. However, determining the optimal trade-off solution to achieve the best overall goal remains a challenge within the industry. Summary of the Invention

[0005] In response to the above problems, the present invention provides a multi-objective optimization method for double-injection molding process parameters, which can effectively reduce the warping deformation and volume shrinkage of double-injection molded parts, thereby obtaining high-quality double-injection molded plastic parts. It can provide a theoretical basis and data support for obtaining the optimal process parameter combination for double-injection molding.

[0006] To achieve the above objectives, the present multi-objective optimization method for double-injection molding process parameters specifically includes the following steps:

[0007] Step 1: The warpage and volume shrinkage of the first injection, as well as the warpage and volume shrinkage of the second injection, are taken as quality optimization targets. The process parameters that affect these four targets are selected as optimization design variables. The value ranges of the process parameters are determined based on the recommended values. The value ranges of each process parameter are used as the experimental design space to design a Taguchi experiment. Then, an injection molding simulation is performed based on Moldflow to obtain a simulation test data set.

[0008] Step 2: Based on the simulation test data set, the simulation test data set is divided into a training set and a test set. After the GAM model is constructed, the training set is trained using the GAM model. The hyperparameters of the GAM model are optimized using the GTO algorithm to establish a nonlinear mathematical regression model between the injection molding process parameters and the quality optimization target.

[0009] Step 3: Use the MODA algorithm to perform multi-objective optimization on the established nonlinear mathematical regression model to obtain the Pareto frontier of the quality optimization objective;

[0010] Step 4: Determine the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method.

[0011] Furthermore, in Step 2, when constructing the GAM model, first select the nonlinear function g; secondly, use the least squares method to estimate the parameters to obtain the nonlinear function of each explanatory variable; finally, add each nonlinear function to obtain the GAM model.

[0012] Furthermore, in Step 2, the hyperparameters of the GAM model are optimized using the GTO algorithm, as follows:

[0013] ① Determine the range of hyperparameters in the GAM model that need to be optimized;

[0014] ② Initialize the population and parameters of the GTO algorithm, randomly generate a gorilla population, and each gorilla individual corresponds to a set of GAM hyperparameter settings;

[0015] ③Evaluate the fitness of each gorilla individual;

[0016] ④ Based on the fitness value of each iteration, record the current optimal hyperparameter combination and dynamically adjust the weight parameters of GTO, gradually reducing the proportion of random migration to find the optimal solution;

[0017] ⑤ If the number of iterations has reached the maximum number of iterations, or the fitness of the current optimal solution no longer improves significantly, the GTO algorithm has converged and outputs the optimal GAM hyperparameter combination; if the above conditions are not met, continue to iterate.

[0018] Furthermore, in Step 3, the MODA algorithm is used to perform multi-objective optimization on the established nonlinear mathematical regression model, as follows:

[0019] ① Initialize MODA parameters;

[0020] ② Update the dragonfly's position by attracting, repelling, aligning, approaching food, and avoiding enemies;

[0021] ③ Use the inertia weight to update the speed and position of the dragonfly individual. As the iteration proceeds, the inertia weight gradually decreases.

[0022] ④ If the dragonfly individual exceeds the defined search space, use the boundary processing strategy to pull it back into the valid area;

[0023] ⑤If the current number of iterations is less than the maximum number of iterations, the MODA algorithm continues to execute, otherwise it ends and outputs the Pareto frontier.

[0024] Furthermore, in Step 4, when determining the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method, firstly, the CRITIC method is used to assign weights to each evaluation indicator, and the weights of the warpage deformation and volume shrinkage rate of the first injection and the warpage deformation and volume shrinkage rate of the second injection are calculated based on the correlation coefficient and standard deviation between the targets; then, following the steps of the TOPSIS method, the degree of proximity of each evaluation object to the idealized target is calculated based on the obtained weights to obtain a comprehensive evaluation score.

[0025] Compared with the existing technology, the multi-objective optimization method of double-material injection molding process parameters first obtains a simulation result data set based on Moldflow simulation analysis and Taguchi test; then, based on the simulation test data set, the simulation test data set is divided into a training set and a test set. After constructing the GAM model, the training set is trained using GAM, and the hyperparameters of GAM are optimized using the GTO algorithm to establish a GTO-GAM model between the injection molding process parameters and the quality optimization target; then, the GTO-GAM model is optimized for multiple objectives using the MODA algorithm to obtain the Pareto frontier of the quality optimization target; finally, the optimal combination of process parameters is determined in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method. Simulation verification shows that the prediction error of the GTO-GAM model for the warpage deformation and volume shrinkage of the double-material PC and TPU after optimization is controlled within 5%, and the model prediction accuracy is good. In addition, the warpage deformation and volume shrinkage of the double-material PC and TPU after optimization are significantly lower than the simulation results before optimization, indicating that the optimization effect is good, which can provide a theoretical basis and data support for obtaining the optimal process parameter combination for double-material injection molding. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of the present invention;

[0027] Figure 2 Schematic diagrams of the structure of a sensor housing plastic part formed by double injection molding according to an embodiment of the present invention, wherein (a) shows a first injection-molded plastic part obtained by injecting PC material into a first injection mold, and (b) shows a second injection-molded plastic part obtained by injecting a second TPU material into a second injection mold;

[0028] Figure 3 Schematic diagrams of the cooling system and pouring system of PC / TPU plastic parts according to an embodiment of the present invention, wherein (a) is a schematic diagram of the cooling system and pouring system of PC plastic parts, and (b) is a schematic diagram of the cooling system and pouring system of TPU plastic parts;

[0029] Figure 4 1 is a diagram illustrating a mold flow simulation analysis of a PC plastic part according to an embodiment of the present invention, wherein (a) is a simulation diagram illustrating the warpage deformation, and (b) is a simulation diagram illustrating the volume shrinkage rate;

[0030] Figure 5 1 is a diagram illustrating a mold flow simulation analysis of a TPU plastic part according to an embodiment of the present invention, wherein (a) is a simulation diagram illustrating the warpage deformation amount, and (b) is a simulation diagram illustrating the volume shrinkage rate;

[0031] Figure 6 3. This is a diagram showing the accuracy comparison of the warpage deformation prediction model for PC plastic parts according to an embodiment of the present invention;

[0032] Figure 7 3. This is a diagram showing the accuracy comparison of the volume shrinkage prediction model for PC plastic parts according to an embodiment of the present invention;

[0033] Figure 8 2 is a graph showing a comparison of the accuracy of the warpage deformation prediction model of the TPU plastic part according to the embodiment of the present invention;

[0034] Figure 9 2. This is a diagram comparing the accuracy of the volume shrinkage prediction model of the TPU plastic parts according to the embodiment of the present invention;

[0035] Figure 10 1 is a Pareto front diagram of a PC plastic part according to an embodiment of the present invention;

[0036] Figure 11 1 is a Pareto frontier diagram of a TPU plastic part according to an embodiment of the present invention;

[0037] Figure 12 1 is a diagram showing simulation verification results of a PC plastic part according to an embodiment of the present invention;

[0038] Figure 13 2 is a diagram showing the simulation verification results of the TPU plastic part according to the embodiment of the present invention. DETAILED DESCRIPTION

[0039] like Figure 1 As shown in the figure, the multi-objective optimization method of double-injection molding process parameters takes the warpage deformation and volume shrinkage of the first injection and the warpage deformation and volume shrinkage of the second injection as quality optimization targets. First, the double-injection molding process parameters that can affect the quality targets are selected as optimization design variables, and a Taguchi test scheme is designed to perform Moldflow simulation. Then, the data set obtained by the simulation is preprocessed and divided into a training set and a test set. The training set is trained using the generalized additive model (GAM), and the hyperparameters of the generalized additive model (GAM) are optimized using the artificial gorilla troop optimization algorithm (GTO) to establish a nonlinear mathematical model between the injection molding process parameters and the quality targets. After the constraint range of the process parameters is set, the established nonlinear mathematical model is optimized using the multi-objective dragonfly algorithm (MODA) to obtain the Pareto frontier of the quality optimization target. Finally, the optimal combination of process parameters is determined by the CRITIC-TOPSIS evaluation method.

[0040] The present invention will be specifically described below by taking a double-injection-molded sensor housing plastic part as an example.

[0041] like Figure 2 As shown, firstly, the first PC material is injected into the first injection mold to obtain the outer surface of the product, and then the filling, pressure holding, cooling and other steps are performed. The mold is opened without ejection, as shown in FIG. Figure 2As shown in (a), the first injection molded part is obtained; then the movable mold is rotated 180° to the second injection mold position, and then the second TPU material is injected into the second injection mold cavity, and the filling, pressure holding and cooling steps are performed, as shown in FIG. Figure 2 As shown in (b), the first injection molded part and the second injection molded part form a two-material product. The PC molded part has a size of 101mm×43mm×14mm and a volume of 8171mm 3 , with an average wall thickness of 1.5mm. The TPU molded part size is 100mm×42mm×2mm, and the volume is 1345mm 3 The average wall thickness is 0.42 mm. Simulation software is used to mesh the 3D solid. Before meshing, CAD Doctor is used to repair the 3D model.

[0042] Moldflow software can analyze the best gate position of plastic parts, and the cooling system and gating system can be manually created and meshed according to the actual mold production and mold design. Figure 3 As shown, the gating system and cooling system are established and the connectivity is tested. The red main runner and the green secondary runner constitute the gating system. The main runner is a circular cross-section with a grid size of 5mm, while the secondary runner is a semicircular cross-section with a grid size of 3mm. The cross-section of the secondary secondary runner is circular and the grid size is 3mm. There are two point gates that are in direct contact with the molded part. The blue cylinders on both sides are the cooling system with a diameter of 8mm and a grid size of 20mm.

[0043] Finite element analysis was performed using Moldflow. When performing warpage analysis on plastic parts, the analysis sequence was "cooling + filling + holding pressure + warpage". Generally, the smaller the warpage deformation and volume shrinkage of the light-transmitting window, the higher the molding quality of the plastic part. The PC material used was grade 02-10R, and the recommended process parameters were: melt temperature 290°C, mold temperature 90°C, filling volume 99%, and molding cycle time 30s. Figure 4 As shown in the figure, the initial warpage deformation obtained after the first injection is 0.5044mm, and the initial volume shrinkage is 6.123%, which does not meet the requirements of the plastic product (the required warpage deformation and volume shrinkage are 0.475mm and 5% respectively). The TPU material used is brand Desmopan 150, and the recommended process parameters are: melt temperature 240℃, mold temperature 45℃, fill volume 99%, and molding cycle time 30s. Figure 5 As shown, the initial warpage deformation obtained after the second injection is 0.6013 mm, and the initial volume shrinkage is 12.10%, which still does not meet the requirements (the required warpage deformation and volume shrinkage are 0.54 mm and 11.513% respectively).

[0044] Step 1. Determine the quality optimization goal, select the injection molding process parameters and their value ranges, use the value ranges of each process parameter as the experimental design space, design the Taguchi test according to the value ranges of each process parameter, and perform injection molding simulation based on Moldflow to obtain the simulation test results.

[0045] Warpage (Q1 / mm) and volume shrinkage (T1 / %) were selected as quality optimization targets for the light-transmitting window for the first shot, while warpage (Q2 / mm) and volume shrinkage (T2 / %) were selected for the second shot. Six process parameters, including melt temperature (A / °C), mold temperature (B / °C), injection pressure (C / MPa), holding pressure (D / MPa), holding time (E / s), and cooling time (F / s), were selected as factors influencing product quality.

[0046] According to the experimental factors and levels, select L 50 (5 11 ) orthogonal table to conduct experiments and record the experimental results in the Taguchi experimental design shown in Tables 1 and 2.

[0047] Table 1 PC test design arrangement and simulation results

[0048]

[0049]

[0050] Table 2 TPU test design arrangement and simulation results

[0051]

[0052] Step 2. Based on the simulation test results, the generalized additive model (GAM) parameters are optimized through the artificial gorilla troop optimization algorithm (GTO) to establish a nonlinear mathematical regression model between the injection molding process parameters and the quality targets.

[0053] The generalized additive model (GAM) is a nonparametric statistical model used to predict the relationship between a dependent variable and an independent variable. It extends the generalized linear model (GLM) to allow for the modeling of nonlinear relationships and nonparametric effects. The basic idea of ​​a GAM is to represent the relationship between the dependent variable and multiple predictor variables as a sum of nonlinear functions, which can be smooth curves (such as spline functions) or non-smooth functions (such as step functions). By combining these nonlinear functions with linear combinations, a GAM is able to capture complex nonlinear relationships. A GAM is represented as follows:

[0054] y i =g(x i1 )+g(x i2 )+…+g(x ik)+ζ i

[0055] Where: y i is the response variable; x ij (j=1,2,3…k) are j explanatory variables; g is a separate nonlinear function; ζ i is the error term. In order to avoid the impact of collinearity between independent variables, all explanatory variables are usually standardized.

[0056] The method of constructing a GAM model is: first, select a nonlinear function g. The most commonly used nonlinear function is the spline function; second, use the least squares method to estimate the parameters to obtain the nonlinear function of each explanatory variable; finally, add each nonlinear function to obtain the GAM model.

[0057] The Artificial Gorilla Troop Optimization (GTO) algorithm, proposed by Abdollahzadeh et al., is a new metaheuristic algorithm based on the social intelligence of gorilla troop systems in nature. In this algorithm, gorilla behavior is mathematically modeled through a novel mechanism of exploration and exploitation phases. It mimics gorilla social behavior in population migration and courtship, and is used to solve global optimization problems. The GTO algorithm consists of an exploration phase (three migration strategies) and an exploitation phase. The GTO algorithm's computational approach generally includes the following steps: ① initialization; ② fitness evaluation; ③ position update; ④ convergence determination; and ⑤ output of the optimal solution.

[0058] GAMs fit data by representing the response variable as the sum of multiple smooth functions. This approach offers advantages such as high flexibility, strong interpretability, and good predictive performance. However, it also suffers from drawbacks such as high computational complexity, the risk of overfitting, and difficulty in selecting smoothing parameters. Therefore, optimizing the smoothing functions of GAM models using the GTO algorithm can improve their accuracy. In practical applications, it is necessary to select an appropriate model and parameter settings based on the specific problem and data characteristics to fully leverage the advantages of GAMs.

[0059] The hyperparameters of the GAM model are optimized using the GTO algorithm, as follows:

[0060] ① Determine the range of hyperparameters in the GAM model that need to be optimized. Common hyperparameters include: smoothing parameters, spline functions, and step functions.

[0061] ② Initialize the population and parameters of the GTO algorithm: Randomly generate a gorilla population, and each gorilla individual corresponds to a set of GAM hyperparameter settings.

[0062] ③Fitness evaluation: Fitness evaluation is performed on each gorilla individual (i.e., each set of GAM hyperparameter settings). The smaller the fitness value, the better the performance of the hyperparameter combination.

[0063] ④ Find the optimal solution: Based on the fitness value of each iteration, record the current optimal hyperparameter combination, and dynamically adjust the weight parameters of GTO to gradually reduce the proportion of random migration.

[0064] ⑤ Determine whether the convergence conditions are met: If the maximum number of iterations is reached, or the fitness of the current optimal solution no longer increases significantly, the algorithm is considered to have converged. If the above conditions are not met, continue iterating.

[0065] ⑥ Output the optimal hyperparameter combination: When the GTO algorithm converges, the optimal GAM hyperparameter combination is output.

[0066] Based on the GTO-GAM algorithm, nonlinear mathematical regression models are established between the injection molding process parameters and the warpage deformation and volume shrinkage targets. The random migration weight is 0.5, the escape follow-up individual weight is 0.3, the regression weight is 0.6, and the maximum number of iterations is 100. 80% of the sample data is used to train the model, and the remaining 20% ​​of the sample data is used to test the accuracy of the model. Through running, the evolutionary convergence of GTO occurs in 50 iterations. Finally, the accuracy of the GAM model optimized by the GTO algorithm is compared with the accuracy of the standard GAM model, as shown in Figure 2. Figure 6 、 Figure 7 、 Figure 8 and Figure 9 As shown in the figure, it can be seen that the GAM prediction value after dual PC and TPU optimization is closer to the real data.

[0067] Step 3: Globally optimize the established mathematical model based on the multi-objective dragonfly algorithm (MODA) to obtain the Pareto frontier of the quality optimization objective.

[0068] MODA is an optimization algorithm that simulates the flight and feeding behavior of dragonflies in nature and is designed to solve multi-objective optimization problems. It leverages swarm intelligence and individual behavior to find optimal solutions to multiple objective functions. The positions and velocities of the dragonfly swarm are randomly initialized in the search space, and the fitness of each dragonfly is calculated. Each solution is evaluated against the objective function. The positions and velocities of the dragonflies are then updated according to the principles of attraction, repulsion, alignment, food orientation, and predator avoidance. At each iteration, a set of non-inferior solutions is selected and stored. This process is repeated until the maximum number of iterations is reached or convergence conditions are met.

[0069] In MODA, the dragonfly's position and velocity update formulas are as follows:

[0070]

[0071] Where: ΔX i is the step length; S i is the current position; t is the number of iterations; Xi is the attraction component; B i is the repulsive component; J i is the alignment component; K i Is the tendency towards food quantity; L i is the component of escaping from the enemy; s, b, j, k, l and ω are the weight coefficients of these behaviors respectively.

[0072] Based on the established nonlinear mathematical model of warpage deformation and volume shrinkage, MODA is used to perform multi-objective optimization, as follows:

[0073] ① Initialize MODA parameters: First, the algorithm needs to initialize all necessary parameters, including the size of the population, number of iterations, mutation rate, etc.

[0074] ②A dragonfly updates its position through the following five behaviors: attraction component, repulsion component, alignment component, food approach component, and enemy avoidance component.

[0075] ③ Speed ​​and position update: Use inertia weight to update the speed and position of the dragonfly individual. As the iteration proceeds, the inertia weight gradually decreases to enhance the local search capability.

[0076] ④ Boundary processing: If the dragonfly individual exceeds the defined search space, a boundary processing strategy (such as reflection boundary or reinitialization) is used to pull it back into the valid area.

[0077] ⑤ Whether the maximum number of iterations has been reached: If the current number of iterations is less than the maximum number of iterations, the algorithm continues to execute, otherwise it ends and outputs the Pareto frontier.

[0078] In the optimization search, the population size is set to 30, the maximum number of iterations is 100, the mutation rate is 0.1, and the other parameters are selected at their default values. Figure 10 、 Figure 11 As shown in Figure 2, a set of Pareto frontiers are output for double-injection molding PC and TPU respectively, indicating relatively balanced solutions on multiple objective functions.

[0079] Step 4: Determine the optimal combination of process parameters through the CRITIC-TOPSIS evaluation method.

[0080] CRITIC-TOPSIS is a multi-attribute decision-making method. CRITIC uses the variance and correlation of the criteria to determine the weights of each criterion. The weights for warpage and volumetric shrinkage of PC are calculated as [0.5599, 0.4401], and for TPU as [0.4887, 0.5113]. The TOPSIS model utilizes these weights to rank and select options by calculating their distance from the ideal solution and the negative ideal solution, resulting in a comprehensive evaluation. The scores for the 11 datasets shown in Table 3 and the 53 datasets shown in Table 4 were calculated, with lower scores being preferred. It was found that the sixth group of PC had the lowest score, with warpage deformation and volume shrinkage of 0.4551mm and 4.7987% respectively; the corresponding process group was: melt temperature (A) of 317.8384℃, mold temperature (B) of 100.8405℃, injection pressure (C) of 183.1899MPa, holding pressure (D) of 56.3463MPa, holding time (E) of 42.8073s, and cooling time (F) of 37.3918s. The 25th group of TPU has the lowest score, with warpage deformation and volume shrinkage of 0.5214mm and 11.5584% respectively; the corresponding process group is: melt temperature (A) is 220.1186℃, mold temperature (B) is 30℃, injection pressure (C) is 155.7668MPa, holding pressure (D) is 48.8273MPa, holding time (E) is 22.4720s, and cooling time (F) is 22s.

[0081] Table 3 PC CRITIC-TOPSIS comprehensive score

[0082]

[0083] Table 4 TPU CRITIC-TOPSIS comprehensive score

[0084]

[0085]

[0086] In order to verify the accuracy and reliability of the optimization method combining the generalized additive model with the gorilla algorithm, the process parameters obtained by optimizing the lowest-scoring PC group 6 and TPU group 25 obtained by CRITIC-TOPSIS evaluation were imported into Moldflow software for simulation. The simulation results are shown in the figure below. Figure 12 、 Figure 13As shown. The warpage deformation and volume shrinkage of PC plastic parts are 0.4657mm and 4.666% respectively, and the errors of warpage deformation and volume shrinkage of PC obtained by algorithm optimization are 2.28% and 2.84% respectively. The warpage deformation and volume shrinkage of TPU plastic parts are 0.5334mm and 11.46% respectively, and the errors of warpage deformation and volume shrinkage of TPU obtained by algorithm optimization are 2.25% and 0.86% respectively. The errors of the four are all less than 5%, indicating that the model prediction accuracy is good. Compared with the initial data, the warpage deformation and volume shrinkage of PC are reduced by 9.77% and 21.63%, while the warpage deformation and volume shrinkage of TPU are reduced by 13.29% and 4.48%, indicating that the optimization effect is good.

Claims

1. A multi-objective optimization method for double-material injection molding process parameters, characterized in that: The specific steps include: Step 1: Take the warpage and volume shrinkage of the first injection and the warpage and volume shrinkage of the second injection as the quality optimization targets, select the process parameters that affect these four targets as the optimization design variables, determine the value range of the process parameters according to the recommended values ​​of the process parameters, and use the value range of each process parameter as the experimental design space to design the Taguchi test, then perform injection molding simulation based on Moldflow to obtain the simulation test data set; Step 2, based on the simulation test data set, the simulation test data set is divided into a training set and a test set. After the GAM model is constructed, the training set is trained using the GAM model, and the hyperparameters of the GAM model are optimized using the GTO algorithm to establish a nonlinear mathematical regression model between the injection molding process parameters and the quality optimization target; Step 3, use the MODA algorithm to perform multi-objective optimization on the established nonlinear mathematical regression model to obtain the Pareto frontier of the quality optimization target; Step 4: Determine the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method.

2. The multi-objective optimization method for double-material injection molding process parameters according to claim 1, characterized in that: In Step 2, when constructing the GAM model, first select the nonlinear function g; then use the least squares method to estimate the parameters to obtain the nonlinear function of each explanatory variable; finally, add each nonlinear function to obtain the GAM model.

3. The multi-objective optimization method for process parameters of double-material injection molding according to claim 1, characterized in that: In Step 2, the hyperparameters of the GAM model are optimized using the GTO algorithm, as follows: ① Determine the range of hyperparameters in the GAM model that need to be optimized; ② Initialize the population and parameters of the GTO algorithm, randomly generate a gorilla population, and each gorilla individual corresponds to a set of GAM hyperparameter settings; ③Evaluate the fitness of each gorilla individual; ④ According to the fitness value of each iteration, record the current optimal hyperparameter combination, and dynamically adjust the weight parameters of GTO, gradually reduce the proportion of random migration, and find the optimal solution; ⑤ If the number of iterations has reached the maximum number of iterations, or the fitness of the current optimal solution is no longer significantly improved, the GTO algorithm has converged and outputs the optimal GAM hyperparameter combination; if the above conditions are not met, continue to iterate.

4. The multi-objective optimization method for process parameters of double-material injection molding according to claim 1, characterized in that: In Step 3, the MODA algorithm is used to perform multi-objective optimization on the established nonlinear mathematical regression model, as follows: ① Initialize MODA parameters; ② Update the dragonfly position through attraction component, repulsion component, alignment component, food approach component, and enemy escape component; ③ Use the inertia weight to update the speed and position of the dragonfly individual. As the iteration proceeds, the inertia weight gradually decreases; ④ If the dragonfly individual exceeds the defined search space, use the boundary processing strategy to pull it back to the valid area; ⑤If the current number of iterations is less than the maximum number of iterations, the MODA algorithm continues to execute, otherwise it ends and outputs the Pareto frontier.

5. The multi-objective optimization method for process parameters of double-material injection molding according to claim 1, characterized in that: In Step 4, when determining the optimal combination of process parameters in the Pareto frontier of the obtained quality optimization target through the CRITIC-TOPSIS evaluation method, firstly, the weights of each evaluation index are assigned through the CRITIC method, and the weights of the warpage deformation and volume shrinkage rate of the first injection and the warpage deformation and volume shrinkage rate of the second injection are calculated according to the correlation coefficient and standard deviation between each target; Then, following the steps of the TOPSIS method, the degree of proximity between each evaluation object and the idealized goal is calculated based on the obtained weights to obtain a comprehensive evaluation score.

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