Lost foam casting is a near-net-shape technology that significantly reduces production steps and costs while offering excellent dimensional accuracy and surface quality. However, the process itself is complex due to the pyrolysis and gasification of the foam pattern during mold filling. The research presented in this thesis focuses on the numerical simulation of the lost foam casting process for iron castings, the development of a quantitative gating and riser design methodology, and the preliminary investigation of grain growth prediction. By integrating ladle analysis with JMatPro software, accurate material parameters for gray cast iron were obtained, enabling the filling and solidification processes of iron lost foam castings to be completed within a single computational model. The simulation results for filling time, filling patterns, and air gap behavior showed good agreement with experimental observations. A novel design approach for combined gating and riser systems was proposed and validated through the production of a gray cast iron bearing pedestal. Furthermore, the feasibility of predicting grain growth in lost foam castings using the CAFE method coupled with KGT growth models was demonstrated. This thesis provides a comprehensive framework for the numerical simulation and process optimization of lost foam castings, offering practical value for industrial applications.
1 Introduction
In the fields of aerospace, defense, and heavy machinery, the rapid development of new products requires short-cycle and small-batch manufacturing capabilities. Simultaneously, there is an increasing demand for energy-saving, environmentally friendly, and high-quality casting processes. Lost foam casting technology has emerged as a promising solution to these challenges. This process, which was invented in the 1950s, eliminates the need for mold extraction, simplifies the production workflow, and enables the casting of complex geometries with high precision. It is widely regarded as “the casting technology of the 21st century”. Compared with traditional sand casting, the lost foam casting method offers several advantages, including reduced production procedures, lower labor intensity, improved working conditions, high dimensional accuracy, and enhanced casting integrity. However, despite these benefits, the industrialization of lost foam casting in China has faced significant hurdles. The process involves complex physical and chemical reactions during mold filling, and there is currently no universally accepted design methodology for the gating system. Consequently, the traditional “trial-and-error” approach often leads to high development costs and prolonged production cycles.
To address these challenges, numerical simulation technology has become an indispensable tool. By leveraging advanced simulation software, it is possible to visualize the entire casting process, predict potential defects, and optimize process parameters before physical trials. The work presented here employs the ProCAST software, which is widely adopted in both academic research and industrial practice. The primary objectives of this study are as follows: first, to develop a reliable simulation method for the filling and solidification stages of iron lost foam castings; second, to establish a quantitative design approach for gating and riser systems based on solidification analysis; and third, to explore the feasibility of simulating grain growth during the solidification of gray iron lost foam castings.
2 Theoretical Foundations of Numerical Simulation
2.1 Governing Equations for Mold Filling
The mold filling process in lost foam casting involves the flow of molten metal, which can be treated as an incompressible Newtonian fluid. The fundamental equations governing this process include the continuity equation, the momentum equation (Navier-Stokes), and the energy conservation equation.
The continuity equation, which expresses the conservation of mass, is given by:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{V}) = 0 \tag{2-1} $$
For an incompressible fluid, this simplifies to:
$$ \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 \tag{2-2} $$
The momentum equations for the x, y, and z directions are expressed as:
$$ \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z} = -\frac{1}{\rho}\frac{\partial P}{\partial x} + \nu \nabla^2 u + F_x \tag{2-3} $$
$$ \frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} + w\frac{\partial v}{\partial z} = -\frac{1}{\rho}\frac{\partial P}{\partial y} + \nu \nabla^2 v + F_y \tag{2-4} $$
$$ \frac{\partial w}{\partial t} + u\frac{\partial w}{\partial x} + v\frac{\partial w}{\partial y} + w\frac{\partial w}{\partial z} = -\frac{1}{\rho}\frac{\partial P}{\partial z} + \nu \nabla^2 w + F_z \tag{2-5} $$
The energy conservation equation, accounting for the heat transfer between the molten metal and the decomposing foam, is expressed as:
$$ \rho_L C_L \frac{\partial T}{\partial t} + \rho_L C_L \mathbf{V} \cdot \nabla T = \lambda_L \nabla^2 T + \rho_P L_s \frac{\partial f_s}{\partial t} \tag{2-6} $$
The boundary condition at the free surface of the molten metal is crucial for modeling the foam decomposition. This can be written as:
$$ k \frac{\partial T}{\partial n} = \rho_P L_s u_1 \tag{2-7} $$
The air gap pressure, a critical factor influencing the filling behavior in lost foam castings, is calculated using the following model:
$$ P_{i+1} = -\frac{\alpha_P V_p (T_i – T_m) \Delta t}{L_P x} + \frac{F \Delta t K (P_i + P_0) \delta_i}{V_i T_i S \delta_{i+1}} – \frac{(P_i + P_0) \delta_i}{T_i \delta_{i+1}} + \frac{P_i \delta_i T_{i+1}}{\delta_{i+1} T_i} \tag{2-8} $$
2.2 Solidification and Heat Transfer
The solidification process is governed by the transient heat conduction equation with a heat source term representing the latent heat of crystallization:
$$ \rho C_p \frac{\partial T}{\partial t} = \lambda \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + Q \tag{2-9} $$
where Q is the latent heat release rate, expressed as:
$$ Q = \rho L \frac{\partial f_s}{\partial t} = \rho L \frac{\partial f_s}{\partial T} \frac{\partial T}{\partial t} \tag{2-10} $$
The enthalpy method is often preferred for handling the latent heat release during solidification. The enthalpy H is defined as:
$$ H = H_0 + \int_{T_0}^{T} C_p dT + L(1 – f_s) \tag{2-11} $$
2.3 Prediction of Shrinkage Defects
Shrinkage porosity and macro-porosity are common defects in lost foam castings. The prediction of these defects relies on the analysis of the temperature field. The concept of the critical solid fraction is central to this analysis, which is typically set at 0.7 in this research. The solid fraction as a function of temperature can be described by the Scheil equation:
$$ f_s = 1 – \left( \frac{T – T_L}{T_0 – T_L} \right)^{\frac{1}{K_0 – 1}} \tag{2-12} $$
For each isolated hot spot, the total volumetric shrinkage can be calculated by summing the solidification contraction and liquid contraction of each element:
$$ \Delta V_m = \sum_{i=1}^{n} (\Delta V_{si}^m + \Delta V_{li}^m) \tag{2-13} $$
where the solid and liquid shrinkage components are calculated as:
$$ \Delta V_{si}^m = \beta_s \Delta f_{si}^m V_i \tag{2-14} $$
$$ \Delta V_{li}^m = \alpha_l (1 – f_{si}^{m-1}) (T_i^m – T_i^{m-1}) V_i \tag{2-15} $$
2.4 Simulation Software and Preprocessing
The ProCAST software, developed by ESI Group, was chosen for this study. The workflow involves geometry creation in CAD software (UG), mesh generation in Visual-Mesh, material property assignment, boundary condition definition, and finally the solving and post-processing in Visual-Viewer. The key simulation parameters for the lost foam casting process are summarized in Table 1.
| Parameter | Value |
|---|---|
| FOAMHTC (heat transfer coefficient between metal and foam) | 0.02 (CGS units) |
| FOAMHTCMAX (maximum heat transfer coefficient) | 0.25 (CGS units) |
| BURNZONE (burning zone distance) | 1.0 cm |
| GASFRAC (gas generation efficiency) | 0.1 |
3 Numerical Simulation of Iron Lost Foam Castings
3.1 Material Property Determination
Accurate material properties are essential for reliable simulation results. In this study, the chemical composition of the gray cast iron was determined by ladle analysis. For the HT250 alloy, the composition is listed in Table 2. The material properties were simulated using the JMatPro software, which calculates the phase evolution and physical properties based on the chemical composition.
| Element | Fe | Mn | Si | C | P | S |
|---|---|---|---|---|---|---|
| Content | 93.936 | 0.81 | 2.0 | 3.24 | 0.014 | 0.009 |
The solidification simulation of HT250 showed that the phase transformation occurs in the range of 1152°C to 1218°C, with the sequential formation of austenite, graphite, and MnS. The density variation of the alloy during solidification is particularly important for accurate shrinkage prediction. The density curve obtained from JMatPro is shown in Figure 3.6, which accounts for the graphitic expansion. This density curve replaces the default data in ProCAST, allowing for the accurate simulation of iron lost foam castings.
3.2 Simulation of the Filling Process
To validate the filling simulation approach, a plate-shaped casting was modeled and compared with the experimental results published in the literature. The casting material was HT150 with a wall thickness of 10 mm. The geometric model consisted of three parts: the casting (empty), the foam pattern, and the sand mold. The simulation settings are listed in Table 3.
| Parameter | Condition |
|---|---|
| Number of mesh elements | 120,000 |
| Material | HT150 |
| Heat transfer coefficient | 150 W/(m²·K) |
| Vacuum pressure | 15 mbar |
| Initial temperature | 1450°C |
| Solver mode | LOST FOAM |
The simulated filling process is depicted in Figure 3.8. The entire filling time was predicted to be 3.5 seconds, which closely matches the experimental value of 3.38 seconds. The simulation successfully reproduced the key features of the lost foam casting process, including the radiation pattern of the air gap progression and the variation in air gap volume, which initially increases and then decreases. The flow patterns, including the formation of a vortex near the bottom of the casting, were also accurately captured. These results confirm that the simulation methodology is capable of reproducing the complex filling behavior of lost foam castings.
3.3 Simulation of the Solidification Process
For the solidification study, a fork-shaped ductile iron casting (QT600-3) was selected. Ductile iron exhibits a significant graphitic expansion effect, making it an ideal candidate for validating the simulation methodology. Two gating system designs were considered: a stepped (bottom) gating system and a top gating system. The key simulation parameters are provided in Table 4.
| Parameter | Condition |
|---|---|
| Number of mesh elements | 1,470,000 |
| Material | QT600-3 |
| Heat transfer coefficient | 150 W/(m²·K) |
| Vacuum pressure | 0.05 MPa |
| Initial temperature | 1480°C |
The simulation results were analyzed by monitoring the molten metal level in the sprue during solidification. This level changes reflect the balance between liquid shrinkage and graphitic expansion. For the stepped gating system, the liquid metal level decreased rapidly for solid fractions between 0% and 3%, indicating predominantly liquid shrinkage. The level then stabilized, and at approximately 40% solid fraction, a slight rise in the metal level was observed, signaling the onset of graphitic self-feeding. For the top gating system, the liquid shrinkage was observed up to a solid fraction of 9.6%, followed by a period of combined shrinkage and expansion, with self-feeding becoming active after 20% solid fraction.
The most critical validation of the simulation is the prediction of shrinkage defects. The predicted shrinkage distribution for both gating systems showed excellent agreement with the actual trial castings. For the stepped gating system, no significant internal shrinkage defects were predicted or observed. For the top gating system, shrinkage defects were predicted and found in the upper regions of the casting. These results confirm that the simulation method, using the density curve obtained from JMatPro, can accurately predict the occurrence and location of shrinkage defects in iron lost foam castings.
4 Design of Gating and Riser System for Gray Iron Castings
4.1 Chvorinov Thermal Modulus Analysis
In the design of gating and riser systems, the Chvorinov modulus (M) is a critical parameter. The modulus was calculated by extracting results from the ProCAST solidification simulation, using the following relationship:
$$ M = \frac{V}{A} = \rho_{al,sol} \left( \frac{k_{mold,ini} \rho_{mold,ini} c_{p,mold,ini} t_{sol} (T_{al,sol} – T_{mold,ini})^{1/2}}{\pi \rho_{al,sol} \Delta H_{al}} \right)^{1/2} \tag{4-1} $$
For the bearing pedestal casting analyzed in this chapter, the material was HT150, with a body wall thickness ranging from 25 to 50 mm. A solidification simulation was performed to obtain the thermal modulus distribution across the casting. The analysis revealed that the highest modulus region (approximately 2.0 cm) was located at the central part of the bearing ring. This information was crucial for positioning the gating and riser systems.
4.2 Quantitative Design of the Gating System
Based on the modulus analysis and using the principles of proportional solidification and the section ratio design method, the gating system was designed quantitatively. The casting was oriented with its axis horizontal, and a bottom gating system was adopted to ensure smooth filling. A single mold contained two castings.
The pouring time was calculated using the empirical formula:
$$ t = S_L \sqrt{G_L} \tag{4-2} $$
where G_L is the total weight of the metal in the mold cavity (124 kg) and S_L is a coefficient dependent on the wall thickness (2.2). The calculated pouring time was 24.7 seconds.
The cross-section ratio of the gating system components was determined as:
$$ \sum A_{直} : \sum A_{横} : \sum A_{内} = 1 : 1.1 : 1.1 \tag{4-3} $$
The dimensions of the gates (riser necks) were calculated using the method based on the balanced solidification theory. The key parameters were: the casting modulus M_c = 2 cm, the volume of the hot spot region V = 1368 cm³, and the mass of the hot spot G = 9.3 kg. The modulus of the riser neck (M_N) and the riser body (M_R) were calculated as follows:
$$ M_N = f_2 \cdot f_4 \cdot f_p \cdot M_c = 0.528 \, \text{cm} \tag{4-4} $$
$$ M_R = f_1^* \cdot f_2 \cdot f_3 \cdot M_c = 1.584 \, \text{cm} \tag{4-5} $$
Additionally, the fluid dynamics-based design method was applied. The cross-sectional area of the inner gate was calculated as:
$$ A_{内} = \frac{G_L}{\rho_L t \mu \sqrt{2 g h_p}} = 21 \, \text{cm}^2 \tag{4-6} $$
The final design adopted a combined gating and riser system. The riser dimensions were 5 cm × 4 cm × 5 cm, and the sprue had a cross-sectional area of 19 cm² with a radius of approximately 2.5 cm. An additional slag collection riser was placed at the final filling location.
4.3 Simulation Results and Analysis
The complete casting process was simulated using the designed gating system. The filling simulation results, as shown in Figure 4.7, revealed the following key features:
1. At t = 0.64 s, the molten metal exhibited unstable flow at the initial stage, suggesting a potential for metal spattering due to insufficient ferrostatic pressure.
2. The filling pattern exhibited a typical “wall attachment” phenomenon, as shown in Figure 4.7 (second frame), where the metal front preferentially wetted the mold walls due to the presence of the foam pattern.
3. The overall filling time was approximately 20 seconds.
By extracting the filling rate data and analyzing it with MATLAB, the filling velocity profile was found to follow a “slow-fast-slow” pattern, which was confirmed by the derivative of the filling rate curve. This result indicated that the pouring practice should be executed in three stages: a slow start to avoid spattering, a fast middle stage to take advantage of the stable filling, and a slow final stage to prevent overflow.
The solidification simulation results are presented in Figure 4.9. The temperature field evolution showed that the last-filled regions (the slag riser) had the lowest temperature at the beginning of solidification. The analysis of the metal level in the pouring cup provided information about the feeding behavior. The liquid metal level dropped significantly during the solid fraction range of 3% to 31%, indicating active liquid feeding from the gating system. During the solid fraction range of 57% to 68%, the shrinkage porosity predicted in the hot spot region gradually disappeared, demonstrating the positive effect of graphitic self-feeding. The fact that the metal level in the pouring cup did not rise during this period indicated that the graphitic expansion pressure was successfully retained within the casting, validating the effectiveness of the designed gating system. The final production trial produced high-quality castings without any internal shrinkage defects, confirming the design methodology.
5 Microstructural Simulation of Gray Iron Lost Foam Castings
5.1 Nucleation and Growth Models
To improve the mechanical properties of lost foam castings, it is essential to understand and control the microstructure. This chapter investigates the feasibility of simulating grain growth during solidification. The continuous nucleation model, proposed by Rappaz, assumes a Gaussian distribution of nucleation sites as a function of undercooling:
$$ \frac{dn}{d(\Delta T)} = \frac{n_{max}}{\sqrt{2\pi} \Delta T_\sigma} \exp\left[ -\frac{1}{2}\left(\frac{\Delta T – \Delta T_{max}}{\Delta T_\sigma}\right)^2 \right] \tag{5-1} $$
The grain growth kinetics were described using the KGT (Kurz-Giovanola-Trivedi) model. The relationship between the dendritic tip velocity (v) and the undercooling (ΔT) is simplified to:
$$ v = \alpha \Delta T^2 + \beta \Delta T^3 \tag{5-2} $$
where α and β are constants dependent on the alloy composition. These constants were calculated for both HT250 and a typical aluminum alloy. The values were:
| Alloy | α (m/(s·K²)) | β (m/(s·K³)) |
|---|---|---|
| HT250 | 3.82458 × 10⁻⁸ | 4.13428 × 10⁻⁹ |
| Aluminum alloy | 4.94606 × 10⁻⁷ | 1.51145 × 10⁻⁷ |
The analysis revealed that, for the same undercooling, the growth rate of cast iron is significantly slower than that of aluminum alloys.
5.2 CAFE Coupling and Simulation Setup
The CAFE method couples a Cellular Automaton (CA) model with the Finite Element (FE) thermal field calculation. The FE model provides the temperature field, from which the undercooling at each node is extracted. The CA model then calculates the nucleation and growth of grains within the cells. The coupling scheme uses interpolation factors to transfer the temperature from the finite element nodes to the CA cells.
The simulation was performed on an elevator chassis component made of HT150. The part had a dimension of 770 mm × 640 mm × 60 mm and weighed approximately 114 kg. Due to the high computational cost of CAFE simulations, only a specific thin rod region of the casting was analyzed. The simulation parameters for the CAFE analysis are listed in Table 6.
| Parameter | ΔT_max (K) | ΔT_σ (K) | n_max (1/m²) |
|---|---|---|---|
| Surface nucleation | 2 | 1 | 1 × 10⁸ |
| Volume nucleation | 2 | 0.1 | 1 × 10⁷ |
5.3 Simulation Results and Discussion
The simulation results are shown in Figure 5.12. The grain structure was predicted to be predominantly equiaxed. In the early stages of solidification, nucleation occurred preferentially at the four corners of the rod section. This phenomenon can be explained by two factors. First, the corners experience two-dimensional heat dissipation, leading to a higher cooling rate and, consequently, a larger undercooling. Second, from a thermodynamic perspective, the energy barrier for nucleation at a corner is lower than that at a planar surface, since a smaller volume of the critical nucleus is in contact with the liquid. This is illustrated in Figure 5.13.
The final predicted grain structure, characterized by a fine-grained chilled zone at the surface and equiaxed grains in the interior, was compared with the experimental results. The experimental microstructure showed good agreement with the simulation, confirming that the CAFE method, when coupled with accurate thermal field data, is a viable tool for predicting grain growth in gray iron lost foam castings. This lays the groundwork for future research on microstructure control and property optimization.
6 Conclusions and Outlook
In this thesis, the numerical simulation and process design of iron lost foam castings were systematically investigated. The key findings and contributions are summarized as follows:
1. A reliable method for obtaining material parameters for iron lost foam castings was established by combining ladle analysis with JMatPro software. The density changes of HT250 during solidification were accurately predicted, providing a solid foundation for shrinkage defect prediction.
2. The filling and solidification processes of iron lost foam castings were successfully simulated within a single computational model. The simulation results, including filling time (3.5 s vs. 3.38 s experimentally), filling patterns, and air gap behavior, showed excellent agreement with experimental observations.
3. The shrinkage defect locations in a ductile iron fork-shaped casting were accurately predicted for both stepped and top gating system designs. The simulated solidification process captured the distinct stages of liquid feeding and graphitic self-feeding.
4. A novel quantitative design methodology for gating and riser systems was proposed. By extracting the Chvorinov thermal modulus and metal volume from solidification simulation results, the dimensions of the risers were calculated using a combination of the section ratio method and the balanced solidification theory.
5. The designed gating system for a gray iron bearing pedestal was validated through simulation and production. The filling process was characterized by a “slow-fast-slow” pouring sequence, and the solidification process exhibited effective liquid feeding and graphitic self-feeding, resulting in defect-free castings.
6. The feasibility of simulating grain growth in gray iron lost foam castings was demonstrated using the CAFE method. The simulation successfully predicted the formation of a fine-grained chilled zone and internal equiaxed grains, which was confirmed by experimental results.
Future work will focus on the coupling of the temperature field with grain growth calculations for improved accuracy. Furthermore, the application of grain growth simulation to control the microstructure of specific casting regions, tailored to service conditions, represents a promising avenue for the development of advanced lost foam casting technologies.