1. Introduction
In the industrial landscape, ball mills play a crucial role in various sectors such as mineral processing, construction materials, and power generation. The liner, as a core component of the ball mill, is responsible for protecting the mill’s body from the impact and wear of grinding media and materials. High manganese steel is a popular choice for manufacturing ball mill liners due to its excellent mechanical properties after water toughening treatment. However, the high shrinkage rate and low thermal conductivity of high manganese steel make it prone to shrinkage porosity and cavity defects during the casting process.
Lost foam casting, a modern casting technology, offers advantages like high design flexibility, high casting accuracy, low production cost, and reduced environmental pollution. Nevertheless, due to its unique negative pressure casting mechanism, traditional gravity casting theories and experiences are often inapplicable. This necessitates a large number of experimental studies or extensive experience to optimize the production process, which is time – consuming and labor – intensive.
Finite element simulation software, such as ProCAST, provides a powerful tool to simulate the filling and solidification processes of lost foam casting. By analyzing the flow, temperature field, and solidification fraction changes, and using relevant criteria to predict casting defects, it is possible to optimize the casting process, reduce defect occurrence, shorten the product development cycle, and save costs. This paper focuses on the optimization of the lost foam casting process for high manganese steel liners through finite element simulation, aiming to provide valuable insights for industrial production.
2. High Manganese Steel Liners and Lost Foam Casting Technology
2.1 Characteristics of High Manganese Steel Liners
High manganese steel, especially ZGMn13 steel used in this study, has a unique chemical composition (Table 1). After water toughening treatment, it exhibits a single austenite structure. The presence of manganese enhances the stability of austenite, reducing the formation of carbides at grain boundaries. This gives the liner excellent plasticity and toughness. Under strong impact or extrusion loads, the surface of the high – manganese – steel liner undergoes rapid strain hardening, while the core maintains good plasticity and toughness. This property makes it highly suitable for the harsh working environment of ball mill liners. However, compared with conventional steel types, high manganese steel has a high shrinkage rate and low thermal conductivity, leading to a high tendency to form shrinkage porosity and cavity defects during casting.
| Element | C | S | Mn | P | Si | Cr | Ni | V | Al | Fe |
|---|---|---|---|---|---|---|---|---|---|---|
| Content (%) | 1.40 | 0.005 | 13.35 | 0.038 | 0.70 | 2.10 | 0.03 | 0.025 | 0.005 | Balance |
| Table 1 Chemical Composition of High Manganese Steel Liners |
2.2 Lost Foam Casting Process
Lost foam casting is a near – net – shape casting method. It uses a polystyrene foam pattern (white mold) to replace the traditional sand mold. During the casting process, the high – temperature molten metal melts and vaporizes the foam pattern, filling the cavity left behind. The process typically relies on negative pressure to assist in the filling and ensure the compactness of the casting. Compared with traditional casting methods, lost foam casting has the following advantages:
- High Design Flexibility: Complex – shaped castings can be easily produced without the need for complex core – making and mold – assembly processes.
- High Casting Accuracy: It can achieve high – precision casting with less dimensional deviation.
- Low Production Cost: Reduces the cost of mold – making and labor, especially for small – batch and medium – batch production.
- Reduced Environmental Pollution: Generates less waste sand and harmful emissions compared to traditional sand casting.
However, the heat transfer and fluid flow during lost foam casting are complex. The interaction between the molten metal and the foam pattern, as well as the gas generated by the decomposition of the foam, need to be carefully considered to ensure a high – quality casting.
3. Finite Element Simulation Methodology
3.1 Three – Dimensional Model and Simulation Parameter Settings
3.1.1 Casting Dimensions and Casting Process Comparison
The liner casting in this study is approximately rectangular, with a large – plane size of about 590 mm×340 mm. Its working surface has a single – peak large – wave shape, being thick in the middle and thin on both sides, with the thickest part at 120 mm and the thinnest at 80 mm. There are two through – holes at the thickest position, an elliptical through – hole on the working surface, and a ϕ150 mm through – hole on the outer surface.
Three lost foam casting processes were designed (Figure 1). Process A is a top – pouring method, casting 8 liners at a time without a riser; Process B is a stepped side – pouring method, casting 10 liners at a time without a riser; Process C is a side – pouring method, casting 4 liners at a time with a riser.
3.1.2 Thermal Physical Parameters
The thermal physical properties of ZGMn13 steel were calculated using the Database module in ProCAST software. The Back – diffusion solidification module was selected, and the cooling rate was set at 5 °C/s. The density, enthalpy, thermal conductivity, and solid – phase fraction as functions of temperature are shown in Figure 2. The white mold was made of an EPS model with a density of \(25~kg/m^{3}\), a specific heat capacity of \(3.7~kJ/(kg·K)\), a latent heat of \(100~kJ/kg\), a thermal conductivity of \(0.15~W/(m·K)\), and an initial gasification temperature range of 330 – 350 °C. Resin sand was chosen as the molding sand, with a density of \(1520~kg/m^{3}\), a specific heat capacity of \(1.22~kJ/(kg·K)\), a thermal conductivity of \(0.53~W/(m·K)\), and an air permeability of \(1e – 7\).
3.1.3 Mesh Generation and Process Parameter Setting
The three – dimensional CAD model was imported into ProCAST software, and the mesh was generated in the Visual – Mesh module. The minimum mesh size was 5 mm near the liner grooves, and the maximum was 100 mm at the sand box. After hiding the sand box, the volume meshes for Process A, Process B, and Process C contained 1,352,871, 1,575,216, and 1,181,657 tetrahedral meshes, respectively (Figure 3).
In the Visual – Cast module, material parameters, initial conditions, boundary conditions, and process parameters were set. The pouring temperature was 1420 °C, the pouring rate was 20 kg/s, the ambient temperature was 20 °C, and the initial temperatures of the molding sand and the white mold were also 20 °C. The heat transfer coefficient at the interface between the white mold and the molding sand was \(20~W/(m^{2}·K)\), and that between the molten metal and the molding sand was \(50~W/(m^{2}·K)\). The outer surface of the molding sand was air – cooled, and the negative pressure was controlled at 0.045 MPa.
3.1.4 Simplification of Heat Transfer at the Interface during the Filling Process of Lost Foam Casting
During the filling process of lost foam casting, the high – temperature molten metal burns and vaporizes the white mold, and there is a complex heat exchange between the molten – metal front and the white mold. In ProCAST software, the heat transfer between the molten metal and the white mold depends on the distance between them. The heat – transfer coefficient is adjusted in real – time according to the distance. When the molten metal is 10 mm away from the white mold, the heat – transfer coefficient is approximately \(20~W/(m^{2}·K)\), and when they are in contact, it reaches about \(250~W/(m^{2}·K)\).
3.1.5 Prediction Criteria for Shrinkage Porosity and Cavity
- POROS Criterion: This is a solidification defect criterion built into ProCAST software. During the solidification of a casting, the edges solidify first, forming a solid shell that prevents the feeding liquid from entering the shell. As a result, isolated liquid – phase regions are formed. For most alloys, the density increases with decreasing temperature. When the molten metal in an isolated region cools, shrinkage cavity defects occur. In practical calculations, the shrinkage rate in the POROS criterion is used to predict the location of shrinkage porosity and cavity defects in the casting. When the POROS value is higher than 1%, shrinkage cavity defects are considered to exist.
- Niyama Criterion: This is a prediction criterion based on micro – shrinkage between dendrites. It uses the ratio of the temperature gradient G at the end of solidification to the square root of the cooling rate R (\(G/\sqrt{R}\)) to reflect the tendency and location of shrinkage porosity and cavity defects in the casting. When \(G/\sqrt{R}\) is less than a certain critical value, shrinkage porosity and cavity defects occur in that region. The smaller the \(G/\sqrt{R}\) value in the solidification region, the greater the tendency to form shrinkage porosity and cavity defects. In the studied range, this critical value is independent of the shape and size of the casting.
3.2 Simulation Results Analysis
3.2.1 Filling Process
The filling processes of the three casting processes are shown in Figures 4 – 6.
- Process A: The molten metal starts to enter the liner casting at 11.95 s (30% filling), but the filling amounts of the 8 liners are inconsistent, with the 2 liners closer to the sprue having a larger filling amount. At 29.62 s, 70% of the filling is completed. Due to the complex heat exchange between the molten – metal front and the foam pattern, the foam pattern gasifies rapidly, and the generated gas cannot be discharged in time, creating a gas gap between the molten metal and the pattern. The gas pressure in the gas gap hinders the filling of the molten metal, causing the molten – metal flow to become disordered in 3 liners at 44.90 s (90% filling).
- Process B: The molten metal enters the liner casting from the side in a stepped manner at 14.95 s (30% filling). At 35.81 s (90% filling), due to the formation of the gas gap, the filling ability of the molten metal is significantly reduced, and the filling processes of two liners become severely disordered.
- Process C: The molten metal enters the liner casting from the side at 6.94 s (30% filling). At 21.53 s (70% filling), the molten – metal flow in the model is stable. At 27.72 s (90% filling), the filling is completed, and the last – filled part is the bottom of the liner away from the gate. Since the number of simultaneously cast liners is small, the generated gas can be quickly discharged from the foam pattern, resulting in a stable filling process without turbulence.
The temperature field distributions of the liners at the end of filling for different processes are shown in Figure 7. Process A has a relatively uniform temperature field distribution, with the last – filled 4 liners having relatively higher temperatures, but the difference is not significant. Process B has an uneven temperature field distribution, with a temperature difference of 50 °C between the first – filled and the last – filled liners. Process C has a more uniform temperature field distribution among the 4 liners.
The temperature distributions of the liner castings during the solidification process for each process are shown in Figures 11 – 13. In all three casting processes, the temperature of the liners is highest in the core and lowest at the periphery, so the solidification starts from the periphery. Process A has a relatively small temperature difference in the liner, with the core temperature being the highest, and there is a temperature difference among the 4 liners. Process B has a significant temperature – distribution difference, and there is a large difference in the core temperatures of each liner, which may be due to the obvious instability during the filling process. Process C has no significant temperature – field difference, with only a small isolated liquid – phase region in the core of the liner. After solidification, only a small amount of shrinkage porosity and cavity defects are generated in the core, and the core temperature fields of each liner are basically the same.
3.2.3 Solidification Defect Prediction
The prediction results based on the POROS criterion are shown in Figure 14. All liners in the three processes show a tendency for shrinkage porosity. In Process A, the last – filled 4 liners have a larger shrinkage – pore area and tendency, and the defects are concentrated in the center of the liner. In Process B, all liners have severe shrinkage porosity and cavity defects, and the middle 6 liners have a higher probability of shrinkage porosity and cavity defects on the surface. In Process C, the defects in all liners are concentrated in the center of the liner.
The prediction results based on the Niyama criterion are shown in Figure 15. All liners in the three processes have shrinkage porosity and cavity defects. In Process A, the defects are concentrated in the core, and the defects in the middle 4 liners are closer to the surface. In Process B, the middle 6 liners’ surfaces and the inner surfaces of the outer 4 liners have a smaller \(G/\sqrt{R}\) ratio, with a higher probability of shrinkage porosity and cavity defects. In Process C, a small number of defects are concentrated in the center of the liner, and no defects are generated on the surface.
| Process | POROS Criterion Prediction | Niyama Criterion Prediction |
|---|---|---|
| Process A | Defects concentrated in the center of the last – filled 4 liners, with a large shrinkage – pore area and tendency | Defects concentrated in the core, and the defects in the middle 4 liners are closer to the surface |
| Process B | Severe shrinkage porosity and cavity defects in all liners, with a high probability of surface defects in the middle 6 liners | The middle 6 liners’ surfaces and the inner surfaces of the outer 4 liners have a high probability of shrinkage porosity and cavity defects |
| Process C | Defects concentrated in the center of all liners | A small number of defects concentrated in the center of the liner, no surface defects |
| Table 2 Comparison of Defect Prediction Results for Different Processes |
4. Production Verification
Based on the simulation results, Process C was selected for on – site casting. The obtained casting is shown in Figure 16. According to the simulation – predicted defect results, the core of the casting has a higher probability of defects. The casting was cut from the core with a bandsaw, and the cross – section of the core is shown in Figure 16b. It can be seen that the casting produced by Process C has fewer internal defects, and they are all concentrated in the core. The large defects in the casting may be caused by unstable molten – metal flow during actual filling or non – uniform air permeability of the molding sand. Overall, the internal defect distribution of the actual production casting is basically consistent with the simulation results.
5. Influence of Process Parameters on Casting Quality
5.1 Pouring Temperature
The pouring temperature of the molten metal has a profound impact on the filling and solidification processes. A higher pouring temperature can increase the fluidity of the molten metal, facilitating a more complete filling of the mold cavity. However, an excessively high pouring temperature may lead to several issues. For example, it can cause more intense gasification of the foam pattern, resulting in a larger gas gap between the molten metal and the pattern. This may disrupt the filling process and increase the risk of porosity formation. On the other hand, a lower pouring temperature may lead to incomplete filling, especially in complex – shaped parts of the liner. Table 3 shows the potential effects of different pouring temperatures on casting quality.
| Pouring Temperature | Impact on Filling Process | Impact on Solidification Process | Potential Defects |
|---|---|---|---|
| High | Good fluidity, easier filling | Delayed solidification, larger temperature gradient | Porosity due to gas evolution, shrinkage defects |
| Low | Poor fluidity, possible incomplete filling | Faster solidification, smaller temperature gradient | Incomplete filling, cold shuts |
| Table 3 Influence of Pouring Temperature on Casting Quality |
5.2 Pouring Rate
The pouring rate also plays a vital role in determining the casting quality. A high pouring rate can shorten the filling time, reducing the time available for gas to escape from the mold cavity. This may lead to gas entrapment and porosity in the casting. Moreover, a high – speed flow of molten metal can cause turbulent flow, which is detrimental to the filling process, as seen in Process A and Process B. In contrast, a low pouring rate may cause the molten metal to cool down too much during filling, resulting in incomplete filling and cold shuts. Table 4 summarizes the effects of different pouring rates on casting quality.
| Pouring Rate | Impact on Filling Process | Impact on Solidification Process | Potential Defects |
|---|---|---|---|
| High | Short filling time, possible turbulent flow | Rapid filling may affect temperature distribution | Gas porosity, turbulent flow – induced defects |
| Low | Long filling time, risk of metal cooling | Uneven solidification due to slow filling | Incomplete filling, cold shuts |
| Table 4 Influence of Pouring Rate on Casting Quality |
5.3 Mold Material and Its Properties
The choice of mold material and its properties, such as thermal conductivity and permeability, can significantly influence the casting quality. Resin sand, used in this study, has specific thermal and physical properties. A higher thermal conductivity of the mold material can enhance heat transfer from the molten metal, promoting faster solidification. However, if the thermal conductivity is too high, it may cause uneven solidification, leading to thermal stress and potential cracking in the casting. The permeability of the mold material is also crucial. If the permeability is too low, the gas generated from the decomposition of the foam pattern cannot escape easily, increasing the risk of gas – related defects. Table 5 shows the relationship between mold material properties and casting quality.
| Mold Material Property | Impact on Filling Process | Impact on Solidification Process | Potential Defects |
|---|---|---|---|
| High Thermal Conductivity | – | Faster solidification, may cause uneven solidification | Thermal stress, cracking |
| Low Thermal Conductivity | – | Slower solidification, may lead to shrinkage defects | Shrinkage porosity, cavity |
| High Permeability | Facilitates gas escape during filling | – | Reduces gas – related defects |
| Low Permeability | Hinders gas escape, may disrupt filling | – | Gas porosity, incomplete filling |
| Table 5 Influence of Mold Material Properties on Casting Quality |
6. Optimization Strategies for Lost Foam Casting Process
6.1 Adjusting Process Parameters
Based on the analysis of the influence of process parameters on casting quality, appropriate adjustments can be made to optimize the lost foam casting process. For Process C, which has shown good performance in the simulation and production verification, fine – tuning of the pouring temperature and rate can further improve the casting quality. For example, slightly reducing the pouring temperature while ensuring complete filling can reduce the gas evolution from the foam pattern and the temperature gradient during solidification, minimizing the risk of shrinkage porosity and cavity defects. Adjusting the pouring rate to a moderate level can ensure smooth filling without causing turbulent flow or gas entrapment.
6.2 Modifying the Casting Design
The design of the casting, including the shape and size of the liner and the layout of the riser and gating system, can also be optimized. For the high – manganese – steel liner, adding additional feeding channels or modifying the shape of the riser can enhance the feeding effect during solidification, reducing the occurrence of shrinkage defects. In addition, optimizing the shape of the liner to make the thickness distribution more uniform can also help to achieve more even solidification and reduce thermal stress.
6.3 Using Advanced Simulation Techniques
With the continuous development of computer technology, more advanced simulation techniques can be employed. Multiphysics simulation, which combines fluid flow, heat transfer, and solidification models, can provide a more comprehensive understanding of the casting process. This can help in predicting complex phenomena such as the interaction between the molten metal, the gas generated from the foam pattern, and the mold material more accurately. Moreover, using artificial intelligence – based optimization algorithms in combination with simulation software can automatically search for the optimal process parameters, saving time and effort in the optimization process.
7. Conclusion
In conclusion, this study comprehensively investigated the lost foam casting process of high – manganese – steel liners using ProCAST software. By simulating the filling and solidification processes of three different casting processes, namely Process A (top – pouring without riser), Process B (stepped side – pouring without riser), and Process C (side – pouring with riser), and analyzing the flow, temperature field, and solidification fraction changes, as well as predicting casting defects using POROS and Niyama criteria, the following key findings were obtained:
- Process A and Process B experienced turbulent flow during the filling process, which was mainly caused by the complex heat exchange between the molten metal and the foam pattern and the gas generated during the decomposition of the foam pattern. In contrast, Process C had a smooth filling process.
- In terms of solidification, all processes showed sequential solidification. However, Process A and Process B, without risers, had a higher tendency to form shrinkage porosity and cavity defects in the core of the liners. Process C, with a riser, was able to reduce these defects to a certain extent, but still had some hot spots in the core.
- The defect prediction results based on the POROS and Niyama criteria showed that Process A and Process B had more severe and dispersed shrinkage porosity and cavity defects, especially on the surfaces of some liners in Process B. Process C had fewer defects, and they were concentrated in the core of the liners.
- The production verification using Process C demonstrated that the actual internal defect distribution of the casting was basically consistent with the simulation results, validating the effectiveness of the simulation – based process optimization method.
