his paper focuses on the optimization of the investment casting process for engine stainless steel parts. With the aim of addressing casting defects such as shrinkage porosity and improving the quality of castings, a model combining Particle Swarm Optimization Neural Network (PSO – BP) and Genetic Algorithm (GA) is employed. Through orthogonal experimental analysis and numerical simulation using PROCAST software, the nonlinear mapping relationships between casting parameters (pouring temperature, mold shell baking temperature, pouring speed) and casting defects (shrinkage porosity volume and equivalent stress) are established. Subsequently, the PSO algorithm is utilized to optimize the BP neural network, and combined with the global optimization ability of the GA, the optimal combination of casting process parameters is obtained. Experimental results demonstrate that the proposed method effectively reduces the shrinkage porosity volume and equivalent stress of the castings, thereby enhancing the overall quality of the engine stainless steel parts.
1. Introduction
1.1 Background
Investment casting is widely used in the production of high – value alloy castings due to its ability to fabricate complex shapes with high surface finish and dimensional accuracy. However, in the production of engine stainless steel parts, issues such as shrinkage porosity and stress often occur, which severely affect the quality and performance of the parts. Traditional optimization methods relying on empirical trial and error are inefficient when dealing with a large number of process variables and a wide range of optimization requirements.
1.2 Significance
The optimization of the casting process for engine stainless steel parts is of great significance. It can not only improve the quality of the castings, reduce the defect rate, but also enhance the production efficiency and reduce the production cost. By accurately controlling the casting parameters, the mechanical properties of the parts can be improved, ensuring the reliable operation of the engine.
1.3 Research Objectives
The main objective of this study is to develop an effective optimization method for the investment casting process of engine stainless steel parts. Specifically, it aims to:
- Establish accurate nonlinear mapping models between casting parameters and casting defects.
- Utilize advanced optimization algorithms to find the optimal combination of casting parameters.
- Verify the effectiveness of the optimized parameters through numerical simulation and actual production.
2. Casting Process and Numerical Simulation
2.1 Casting Process Overview
The object of this study is a conical frustum – shaped casting made of 316 stainless steel, weighing approximately 3.46 kg. Its maximum contour dimension is 118 mm, height is 130 mm, and the main wall thickness is 8 mm. There are also side holes on the outside of the cone, with the thinnest wall thickness being only 3 mm, indicating a relatively complex structure. The casting and gating system 3D models required for numerical simulation are created using SOLIDWORKS software and then imported into PROCAST software for mesh generation, setting of casting process parameters and boundary conditions. In total, 182,214 surface mesh elements and 1,663,165 volume mesh elements are generated.
| Process Parameter | Value |
|---|---|
| Mold Shell Thickness | 6 mm |
| Mold Shell Material | Mullite Refractory Material |
| Interface Heat Transfer Coefficient | 500 W/(m²·K) |
| Cooling Method | Air Cooling |
2.2 Numerical Simulation Setup
Based on the actual production conditions of the factory, the numerical simulation settings are as follows. The original casting conditions are a pouring temperature of 1600 °C, a mold shell baking temperature of 1150 °C, and a pouring speed of 2 kg/s. Through numerical simulation, it is found that the shrinkage porosity volume of the original process casting is 0.37 cc, and the equivalent stress is 295.92 MPa.
2.3 Orthogonal Experimental Design
To study the influence of key process parameters on the casting quality of 316 stainless steel engine parts, an orthogonal experimental design method is adopted. Three factors, namely pouring temperature, mold shell baking temperature, and pouring speed, are considered, with each factor having five levels. The orthogonal table is used to arrange the experimental combinations of each factor level, as shown in Table 2.
| Process Parameter | Test Level 1 | Test Level 2 | Test Level 3 | Test Level 4 | Test Level 5 |
|---|---|---|---|---|---|
| Pouring Temperature (°C) | 1580 | 1590 | 1600 | 1610 | 1620 |
| Mold Shell Baking Temperature (°C) | 1140 | 1145 | 1150 | 1155 | 1160 |
| Pouring Speed (kg·s⁻¹) | 1 | 1.5 | 2 | 2.5 | 3 |
2.4 Simulation Results and Analysis
Taking the volume of shrinkage porosity and the equivalent stress of the casting as the main quality indicators, the simulation calculations are carried out according to the experimental arrangements in Table 2, and the corresponding experimental results are obtained. By calculating and comparing the range R of each factor, the influence degree of each factor on the two evaluation indicators is analyzed. The results show that for the shrinkage porosity size, the order of influence of each factor is pouring speed > pouring temperature > mold shell preheating temperature; for the equivalent stress size, the order is pouring temperature > pouring speed > mold shell preheating temperature. Variance analysis also verifies the consistency of the influence of each factor on shrinkage porosity and equivalent stress with the range analysis results.
| Factor | Pouring Temperature (°C) | Mold Shell Baking Temperature (°C) | Pouring Speed (kg·s⁻¹) |
|---|---|---|---|
| K1 | 2.63 | 2.33 | 1.00 |
| K2 | 2.68 | 2.53 | 2.14 |
| K3 | 2.10 | 2.30 | 2.42 |
| K4 | 2.00 | 2.29 | 2.44 |
| K5 | 1.88 | 1.82 | 3.28 |
| R1 | 0.80 | 0.71 | 2.28 |
| k1 | 1429.62 | 1467.98 | 1433.12 |
| k2 | 1450.66 | 1467.57 | 1455.94 |
| k3 | 1474.11 | 1471.37 | 1474.64 |
| k4 | 1486.41 | 1467.99 | 1488.89 |
| k5 | 1505.41 | 1471.31 | 1493.64 |
| R2 | 75.79 | 3.80 | 60.52 |
3. BP Neural Network Prediction Model
3.1 BP Neural Network Basics
BP neural network is a multi – layer feedforward neural network with error backpropagation. It has a simple structure and good operability, making it widely used in various fields. In this study, it is applied to study the complex relationship between investment casting process parameters and casting defects. However, the BP neural network is sensitive to initial weights and thresholds. Random selection of these parameters during training may cause the network to fall into local optima, resulting in large prediction errors.
3.2 Model Construction and Optimization
The process parameters of investment casting, namely pouring temperature, mold shell baking temperature, and pouring speed, are used as the inputs of the network, and the quality indicators of shrinkage porosity defects and equivalent stress of the casting are used as the outputs. Therefore, the BP neural network has 3 input nodes and 2 output nodes, and the number of hidden layer nodes is set to 7. The Levenberg – Marquardt algorithm is selected for training, which has the fastest convergence speed and relatively small mean square error. The training times of the BP neural network are set to 1000, the learning rate is 0.1, and the training accuracy is 0.0001. 20 groups of orthogonal experimental results are randomly selected as training samples, and 5 groups are used as test samples for network training.
To improve the performance of the BP neural network, the PSO algorithm is used to optimize its parameters. The parameters of the PSO – optimized BP neural network are set as follows: the maximum number of iterations is 100 generations, the number of population particles is 50, the particle length is 44, the learning factor is 1.5, the inertia weight is 0.8, the position range is [-0.7, 0.7], and the speed range is [-10, 10]. The prediction error of the BP neural network is used as the fitness value of the PSO algorithm. The iterative evolution curve shows that the prediction error of the PSO algorithm tends to be stable after 50 generations.
4. Casting Process Parameter Optimization
4.1 Optimization Model and Process
The GA is used to optimize the investment casting process parameters. Considering that defects such as shrinkage porosity are the main factors leading to high scrap rates and subsequent correction costs, and the smaller the values of shrinkage porosity and equivalent stress, the better the quality of the casting. The mathematical model of the optimization problem is simplified as follows:
where is the BP neural network optimized by the PSO algorithm, represents the shrinkage porosity, represents the equivalent stress value, is the pouring temperature, is the mold shell baking temperature, and is the pouring speed. The ranges of the process parameters are , , and .
To obtain the optimal solution of the investment casting process parameter optimization problem, the weight coefficient transformation method is adopted to convert each sub – objective function into a single – objective optimization by assigning weight coefficients. Considering that shrinkage porosity is the main cause of high scrap rates and the complexity of subsequent correction steps, the weight coefficient of is set to be greater than or equal to that of . The weight is set before the denormalization of the BP neural network prediction results to eliminate the influence of different dimensions of shrinkage porosity and equivalent stress.
The optimization process is as follows: first, the initial weights and thresholds of the BP neural network are optimized by the PSO algorithm; then, the optimized BP neural network is used to find the optimal combination of process parameters. The GA uses real number coding, the initial population is randomly generated within the parameter range corresponding to the variables, the number of population individuals is 50, the monarch scheme is used for selection and crossover operations, the gene crossover probability is 0.8, the mutation probability is 0.2, and the maximum number of genetic generations is 100.
4.2 Optimization Results and Analysis
When different weight coefficients are set, the optimization results of the casting process parameters are different. As the weight coefficient changes, the pouring temperature fluctuates within a relatively low temperature range compared to the test samples, the mold shell baking temperature is within a relatively high temperature range, and the pouring speed is basically around 1 kg·s⁻¹.
| Weight | Weight | Pouring Temperature (°C) | Mold Shell Baking Temperature (°C) | Pouring Speed (kg·s⁻¹) |
|---|---|---|---|---|
| 0.5 | 0.5 | 1582.41 | 1150.66 | 1.02 |
| 0.6 | 0.4 | 1582.29 | 1153.07 | 1.07 |
| 0.7 | 0.3 | 1581.03 | 1159.35 | 1.01 |
| 0.8 | 0.2 | 1617.01 | 1159.81 | 1.18 |
The optimization effect of the GA on casting defects also varies with different weight coefficients. For shrinkage porosity defects, the optimization effect increases with the increase of the weight coefficient. By comparing the optimization results and considering the actual production situation, a weight coefficient combination with an optimization effect of 70.27% for shrinkage porosity defects is selected.
| Weight | Weight | Shrinkage Porosity (cc) | Optimization Effect | Equivalent Stress (MPa) | Optimization Effect |
|---|---|---|---|---|---|
| 0.5 | 0.5 | 0.34 | 8.11% | 280.61 | 5.17% |
| 0.6 | 0.4 | 0.32 | 13.51% | 280.50 | 5.21% |
| 0.7 | 0.3 | 0.11 | 70.27% | 293.10 | 0.92% |
| 0.8 | 0.2 | 0.18 | 51.35% | 294.34 | 0.52% |
4.3 Process Simulation and Verification
Using the optimized process parameters for simulation, the filling process of the casting shows that the molten metal fills the mold smoothly and sequentially without splashing and turbulence, indicating that the design of the gating system and the selection of the pouring process parameters are reasonable. During the solidification process of the casting, the solid phase appears first at the edge of the casting, and the casting solidifies sequentially, with the gating system finally showing the solid phase, which is beneficial to the feeding of the casting, further verifying the rationality of the parameter selection.
Based on the ideal combination of optimized process parameters, the simulation verification results show that the shrinkage porosity volume is significantly reduced, and the position of shrinkage porosity defects at the edge of the product disappears. The calculated shrinkage porosity volume after optimization is 0.11 cc, which is reduced by 70.27% compared to the original process parameter combination. The equivalent stress value of the casting after optimization is 293.10 MPa, which is reduced by 0.92% compared to the original process.
5. Conclusion
In this study, a model combining PSO – BP and GA is successfully applied to the optimization of the investment casting process for engine stainless steel parts. Through orthogonal experiments and numerical simulations, accurate nonlinear mapping models between casting parameters and casting defects are established. The PSO algorithm optimizes the BP neural network to improve its prediction accuracy, and the GA is used for global optimization to find the optimal combination of process parameters. The experimental results show that when the pouring temperature is 1581 °C, the mold shell baking temperature is 1159 °C, and the pouring speed is 1 kg·s⁻¹, the shrinkage porosity volume of the casting is significantly reduced, and the equivalent stress is also improved to a certain extent. This method provides an effective solution for improving the quality of engine stainless steel parts and has important guiding significance for actual production.
