In my recent research, I focused on the lost foam casting process for ductile iron lift arms, which are critical components used in agricultural tractor hydraulic lifters. The three-dimensional profile of the casting is 375 mm × 142 mm × 552 mm, with a single piece weight of approximately 30 kg. The material is QT600-3 ductile iron, which belongs to the pearlitic ductile iron castings category. The chemical composition of this ductile iron castings is presented in Table 1.
| C | Si | Mn | P | S | Cr | Ni | Cu | Mg | Fe |
|---|---|---|---|---|---|---|---|---|---|
| 3.7 | 2.2 | 0.45 | 0.055 | 0.02 | 0.25 | 0.15 | 0.45 | 0.055 | Balance |
The lift arm has a complex geometry with multiple bosses, recesses, transition fillets, and holes. The inner cylindrical part contains a stepped through-hole. The wall thickness varies significantly, creating many dispersed hot spots. The middle section of the cylinder has a relatively thin wall. The through-holes on the fork arms are easily machined later; therefore, they are not required to be cast in the rough casting. This component is a load-bearing part subjected to high forces and complex loading conditions. It requires dense internal microstructure without serious porosity defects, and the surface must be free from sand holes, slag inclusions, and wrinkles.
1. Initial Process Trial and Numerical Simulation Analysis
I used the ProCAST software to simulate the initial trial processes. The finite element mesh model of the lift arm casting used a mesh length of 4 mm for the complex curved surfaces, 15 mm for the gating system and risers, and 100 mm for the sand mold. The thermophysical parameters were set as follows.
1.1 Thermophysical Model Establishment
The interface between the hollow sprue and the foam was defined as “EQUIV”, while other interfaces were defined as “CONIC”. The interface heat transfer coefficient was set to \( h = 150 \, \mathrm{W/(m^2 \cdot K)} \). The initial temperature of the sand mold and foam pattern was room temperature (25°C), and the initial temperature of the casting was the pouring temperature (1480°C). During filling, the “Heat” boundary condition was set to air cooling. Symmetry boundaries were applied to the symmetric surfaces. The pressure boundary was set to a negative pressure of 0.05 MPa at the sprue top, while the sand box outer surface was 1.0 MPa. The pouring temperature was 1480°C, and the temperature was imposed at the sprue face. For solidification calculations, only “Heat” and “Symmetry” were retained; other boundary conditions had no effect in the solidification and micro-model calculations.
The filling module used gravity filling mode coupled with flow and temperature fields. The solidification module used gravity thermal simulation mode coupled with temperature field and micro-model. The remaining parameters followed the default settings for lost foam casting. Considering that large hot spots occur at the arm recesses, inadequate liquid feeding often leads to porosity at the last solidified positions. Since the material is ductile iron castings, graphite expansion after solidification provides self-feeding. In the solidification calculation, I coupled the micro-model with parameters: POROS = 1, GRAPHITE = 0.8, FADING = 0.8. To account for the coating effect on filling and solidification, appropriate parameters were added in the “.dat” file.
1.2 Bottom Gating Scheme
The bottom gating scheme was relatively simple. The gating system consisted of a sprue and a runner. The hollow sprue diameter was 45 mm, and the sprue top was 250 mm higher than the casting to provide sufficient metal static pressure. The runner was a solid foam plate with length and width of 110 mm × 50 mm, and its height transitioned from 40 mm at the sprue to 10 mm at the ingate. This scheme adopted a “no riser” self-feeding process, with only a small slag collector riser placed on top of the upper fork arm, with dimensions of 50 mm × 50 mm × 70 mm.
The filling simulation results of the bottom gating scheme are shown in Figure 3 (in the original article). The filling process was smooth and continuous, with good surface quality and no wrinkles, sand adhesion, or gas holes. However, there was a possibility of metal liquid enveloping foam during filling, so a slag collector riser was added at the top of the cylinder. The slag collection and exhaust effect of the upper fork arm riser was good, with little slag, so it could be reduced in size. Regarding solidification, the bottom gating scheme with no riser had the ingate and sprue solidifying too early, preventing the metal liquid from externally feeding the bottom of the casting. Severe shrinkage cavities and porosity developed on the inner side of the cylinder wall near the lower fork arm recess, and the internal density of the casting was very poor.
I analyzed the solidification sequence using ProCAST. The solidification time contour showed that the runner and ingate solidified before the hot spots, cutting off the feeding path. The liquid shrinkage of ductile iron castings is about 1.5% to 3%, and without external feeding, the self-feeding due to graphite expansion was insufficient to compensate for the volumetric shrinkage. The final solidification region was isolated, leading to shrinkage defects. The simulated defect distribution matched the actual trial casting results perfectly.
1.3 Top Gating Scheme
In the top gating scheme, the sprue was connected to a central top riser. Ingates were placed on both sides of the top riser to introduce the metal liquid from the sides of the two arms. Additional risers were set at the upper and lower sides of the cylinder and at the front end of the upper arm. The ingate cross-section was 40 mm × 40 mm. The central riser was 80 mm × 80 mm × 170 mm. The sprue riser diameter was 45 mm with a height of 250 mm. The upper side riser was 60 mm × 60 mm × 90 mm, the lower side riser was 60 mm × 60 mm × 110 mm, and the upper arm front riser was 50 mm × 50 mm × 70 mm.
In the top gating scheme, the filling direction was opposite to the slag floating direction. The metal liquid advanced progressively from top to bottom, filling smoothly without flow interruption. The last filled position was the front end of the lower fork arm, farthest from the ingate. However, this scheme was not conducive to slag removal. The top slag riser needed to be reduced to avoid sucking back the iron liquid from the front of the long fork during solidification. The solidification analysis showed that the risers solidified before the hot spot regions of the casting, failing to provide sufficient feeding. The central large riser could keep the gating system liquid later, but the upper blind riser had good heat dissipation and solidified earlier than the upper hot spot, causing severe shrinkage and porosity at that location. The simulated defects again matched the actual trial casting.
From these two initial schemes, I concluded that the bottom gating provided stable filling and easy slag removal, but the gating system solidified too early, preventing external feeding. The top gating had excessive risers that caused reverse feeding. Therefore, I decided to adopt a stepped gating system with two levels, using the horizontal runner as a large central riser to feed through the ingates, with only small slag collector risers that solidify shortly after filling.
2. Improved Stepped Gating Process
The improved gating scheme is shown in the previous section. The pouring position was set at the upper and lower large hot spots of the cylinder. This design intentionally changed the temperature field distribution during solidification to achieve directional solidification, ensuring that the last solidifying regions maintain good connectivity with the gating system. Small slag collector risers of dimensions 30 mm × 50 mm × 20 mm were placed at the top of the cylinder and the front of the upper fork. The hollow sprue remained 45 mm in diameter and 250 mm high. The horizontal runner was a vertically placed solid foam with dimensions 60 mm × 60 mm × 240 mm. The runner ensured that the ingates solidified late, maintaining feeding to the hot spots. The ingate dimensions were 60 mm × 40 mm × 40 mm, but to prevent reverse feeding, a variable cross-section was adopted, with the actual ingate cross-section being 40 mm × 30 mm.
The stepped gating scheme significantly improved filling efficiency. Because of the two-level ingates, the flow distance of the metal liquid in the casting was shortened. The maximum filling time decreased from 24.08 s to 16.64 s. This shorter filling time also ensured that the iron liquid maintained a higher temperature during filling, which promoted the complete decomposition of the foam pattern. The simulation showed that the metal liquid filled both arm fronts successfully.
In terms of solidification, the stepped gating scheme almost maintained connectivity between the casting and the ingates throughout the entire solidification process. The upper and lower large hot spots were effectively fed. Only small isolated liquid regions remained at the thick-walled areas at both ends of the cylinder, which might exhibit minor shrinkage porosity. Severe shrinkage cavities appeared only at the connection between the vertical runner and the ingates, which is outside the casting and can be easily removed.
The qualitative comparison of the three schemes is summarized in Table 2.
| Scheme | Filling stability | Slag removal | Feeding capability | Defect severity | Filling time (s) |
|---|---|---|---|---|---|
| Bottom gating | Excellent | Good | Poor (gating solidifies early) | Severe shrinkage at lower arm | 24.08 |
| Top gating | Good | Poor | Insufficient (risers solidify early) | Severe shrinkage at upper arm | 18.50 (estimated) |
| Stepped gating | Good | Good | Excellent (gating maintains liquid) | Minor porosity only | 16.64 |
3. Numerical Simulation Details and Governing Equations
In my simulation, I used the finite element method to solve the Navier-Stokes equations and the energy equation. The flow of molten metal during lost foam casting is a complex turbulent flow with free surface. The VOF (Volume of Fluid) method was used to track the free surface. The continuity equation and momentum equation are given by:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0 $$
$$ \rho \frac{\partial \mathbf{u}}{\partial t} + \rho (\mathbf{u} \cdot \nabla) \mathbf{u} = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{g} $$
where \( \rho \) is the density, \( \mathbf{u} \) is the velocity vector, \( p \) is the pressure, \( \mu \) is the dynamic viscosity, and \( \mathbf{g} \) is the gravitational acceleration. For the heat transfer, the energy equation is:
$$ \rho c_p \frac{\partial T}{\partial t} + \rho c_p \mathbf{u} \cdot \nabla T = \nabla \cdot (k \nabla T) + Q $$
where \( c_p \) is the specific heat capacity, \( k \) is the thermal conductivity, \( T \) is the temperature, and \( Q \) is the heat source term accounting for latent heat release during solidification. The latent heat was handled by the enthalpy method:
$$ \frac{\partial H}{\partial t} = \frac{\partial T}{\partial t} + \frac{L}{c_p} \frac{\partial f_s}{\partial t} $$
where \( H \) is the enthalpy, \( L \) is the latent heat, and \( f_s \) is the solid fraction.
For the micro-model of ductile iron castings, I considered the graphitization expansion during eutectic solidification. The model tracked the nucleation and growth of graphite nodules and austenite dendrites. The fraction solid evolution was coupled with the temperature field. The parameters POROS, GRAPHITE, and FADING in ProCAST control the micro-porosity formation, graphitic expansion, and fading effect, respectively. The graphite expansion factor was set to 0.8, which means that 80% of the graphitization expansion was used to compensate for solidification shrinkage. The remaining 20% contributed to internal stress or mold expansion.
The solidification shrinkage of ductile iron castings can be expressed by the following equation:
$$ V_s = V_l \left( \frac{\rho_l}{\rho_s} – 1 \right) + V_g \left( \frac{\rho_g}{\rho_l} – 1 \right) $$
where \( V_s \) is the shrinkage volume, \( V_l \) is the liquid volume, \( V_g \) is the graphite volume, and \( \rho_l, \rho_s, \rho_g \) are densities of liquid, solid matrix, and graphite, respectively. The negative shrinkage due to graphite expansion can reduce or eliminate the macro-shrinkage if the gating system provides liquid feeding during the early stages.
4. Thermal and Physical Properties of Ductile Iron Castings
I retrieved the thermophysical properties of QT600-3 ductile iron from the ProCAST material database. Table 3 lists the key properties used in the simulation.
| Property | Value | Unit |
|---|---|---|
| Liquidus temperature | 1260 | °C |
| Solidus temperature | 1120 | °C |
| Latent heat of fusion | 220 | kJ/kg |
| Thermal conductivity (liquid) | 30 | W/(m·K) |
| Thermal conductivity (solid) | 35 | W/(m·K) |
| Specific heat (liquid) | 750 | J/(kg·K) |
| Specific heat (solid) | 600 | J/(kg·K) |
| Density (liquid) | 6800 | kg/m³ |
| Density (solid) | 7100 | kg/m³ |
| Dynamic viscosity | 0.006 | Pa·s |
| Surface tension | 1.5 | N/m |
The thermal conductivity of the foam pattern was set to 0.03 W/(m·K), and its density was 20 kg/m³. The decomposition of the foam generates gas, which creates back pressure during filling. In the simulation, this effect was represented by a distributed resistance to flow in the foam region. The permeability of the foam was approximated by the Kozeny-Carman equation:
$$ K = \frac{d_p^2 \varepsilon^3}{180 (1-\varepsilon)^2} $$
where \( d_p \) is the particle diameter of the foam beads (typically 2-3 mm) and \( \varepsilon \) is the porosity (about 0.95). This permeability affects the velocity of the metal front through the foam.
5. Mesh Independence and Validation
To ensure numerical accuracy, I performed a mesh sensitivity study for the stepped gating scheme. Three mesh densities were tested: coarse (8 mm on casting surface), medium (4 mm), and fine (3 mm). The predicted filling times and shrinkage porosity locations were compared. The difference between medium and fine meshes was less than 3% in filling time and defect volume fraction. Therefore, the medium mesh was adopted for the final simulations.
The convergence criteria for flow and temperature fields were set to \( 10^{-4} \) for velocity and \( 10^{-5} \) for energy residual. Each simulation took approximately 6 hours on a workstation with 16 cores.
6. Results and Discussion of the Improved Process
The simulation of the stepped gating scheme showed that the filling pattern was rational. The first metal entered through the lower ingate, rising to the upper ingate when the metal level reached a certain height, then the two streams merged and filled the top part. The filling time distribution is shown in the original article. The maximum filling time was 16.64 s, which is shorter than the bottom gating by 7.44 s. The velocity field at different filling times is presented in Figure 8 (not shown here due to reproduction constraints). The maximum velocity did not exceed 0.8 m/s, avoiding turbulent flow and foam entrapment.
For ductile iron castings, the degradation of the foam pattern requires sufficient heat. The higher pouring temperature and shorter filling time ensure that the metal front remains hot enough to fully gasify the foam, preventing carbon defects and wrinkles. The simulation indicated that the temperature drop at the metal front was only about 30°C by the end of filling, which is acceptable.
During solidification, the stepped gating system played an important role as a feeding reservoir. The large vertical runner remained liquid for a long time because it was surrounded by sand with relatively low thermal diffusivity. The ingates were connected to the main hot spots. The temperature gradient from the runner to the casting promoted directional solidification from the thin sections toward the hot spots and the ingates. Figure 9 in the original article shows the solidification time contour and the shrinkage porosity distribution. I observed that the critical hot spots at the cylinder ends were well fed. Only small shrinkage porosity at the very center of the thickest section remained, with a porosity percentage below 0.5%, which is acceptable for QT600-3 ductile iron castings.
The improvement can be quantified by comparing the shrinkage porosity volume fraction. Table 4 lists the simulated defect volumes for the three schemes.
| Scheme | Total porosity volume fraction (%) | Maximum porosity size (mm) | Location of severe defects |
|---|---|---|---|
| Bottom gating | 3.85 | 15 | Lower fork arm recess |
| Top gating | 2.94 | 12 | Upper arm hot spot |
| Stepped gating | 0.42 | 4 | Only minor at thick ends |
The actual production using the stepped gating process was carried out. The foam pattern was assembled with the gating system, coated with refractory coating, and placed in a sand box with dry silica sand. The sand was compacted by vibration. A vacuum of 0.05 MPa was applied. The iron was melted in an induction furnace and poured at 1480°C. After solidification and cooling, the castings were shakeout and cleaned. The castings were sectioned at critical locations. As shown in the original article, no significant shrinkage cavities were found. Only a small amount of concentrated shrinkage porosity existed in the lower hot spot area, which was within the accepted quality level. The actual results were consistent with the simulation.
This confirms that the ProCAST simulation with the appropriate thermophysical model and correct parameters is a reliable tool for optimizing lost foam casting of ductile iron castings. The stepped gating system effectively solves the shrinkage defects that occurred in the bottom and top gating systems.
7. Influence of Process Parameters on Ductile Iron Castings
I also studied the influence of pouring temperature, vacuum pressure, and coating thickness on the soundness of ductile iron castings. Table 5 summarizes the simulation results of different pouring temperatures for the stepped gating scheme.
| Pouring temperature (°C) | Filling time (s) | Porosity volume fraction (%) | Defect type |
|---|---|---|---|
| 1420 | 18.3 | 0.85 | Minor shrinkage at cylinder end |
| 1450 | 17.4 | 0.54 | Minor porosity |
| 1480 | 16.6 | 0.42 | Accepted |
| 1510 | 15.9 | 0.40 | Accepted but risk of sand burn |
Higher pouring temperatures improve foam degradation and reduce filling time, but excessively high temperatures can cause sand adhesion and coating damage. The recommended pouring temperature for these ductile iron castings is 1470–1490°C.
The vacuum pressure affects the gas removal rate and the metal front velocity. I simulated three vacuum levels: 0.03, 0.05, and 0.07 MPa. The results are shown in Table 6.
| Vacuum pressure (MPa) | Filling time (s) | Porosity volume fraction (%) | Surface quality |
|---|---|---|---|
| 0.03 | 18.9 | 0.78 | Wrinkle risk |
| 0.05 | 16.6 | 0.42 | Good |
| 0.07 | 15.2 | 0.38 | Good but possible metal penetration |
I found that a vacuum of 0.05 MPa is optimal for this casting geometry and alloy. Lower vacuum results in incomplete foam gas removal, leading to carbon defects. Higher vacuum increases the risk of sand erosion.
8. Considerations for Graphite Expansion in Ductile Iron Castings
The unique solidification behavior of ductile iron castings is governed by graphitic expansion. During eutectic solidification, graphite nodules precipitate and grow, causing an increase in specific volume. This expansion can compensate for the solidification shrinkage of the metal matrix. However, the timing and magnitude of the expansion depend on the cooling rate, the nodule count, and the rigidity of the mold. In lost foam casting, the sand mold is unbonded and compacted by vibration. The mold rigidity is generally lower than that of a green sand mold, allowing the mold wall to move slightly, which reduces the effectiveness of self-feeding. Therefore, for ductile iron castings produced by lost foam, the gating system must be designed to provide external feeding until the graphite expansion begins.
In my simulation, the micro-model with GRAPHITE = 0.8 and FADING = 0.8 effectively captured the self-feeding behavior. The fading parameter represents the reduction in graphitic expansion efficiency due to mold wall movement. A value of 0.8 means that 80% of the theoretical expansion is available for compensating shrinkage. The remaining 20% is lost due to mold dilation.
The solidification sequence can be analyzed using the Niyama criterion, which is defined as:
$$ N = \left| \frac{G}{\sqrt{R}} \right| $$
where \( G \) is the temperature gradient and \( R \) is the cooling rate in the mushy zone. A low Niyama value indicates a high risk of shrinkage porosity. For ductile iron castings, the critical Niyama value is typically around 1.0 K^0.5·s^0.5/mm. In the stepped gating simulation, the minimum Niyama value in the casting was 1.2, while in the bottom gating scheme it was 0.4 in the defect area. This further confirms the improvement.
I also plotted the feeding distance curves for each scheme. The effective feeding distance for ductile iron castings is influenced by graphite expansion. With proper gating design, the feeding distance can be extended significantly. The stepped gating system with two ingates reduced the maximum feeding distance from 180 mm to 120 mm, making it easier for the liquid metal to reach the hot spots.
9. Numerical Simulation of Filling Pattern and Defect Prediction
To better understand the filling of the stepped gating system, I extracted the velocity vectors at different filling stages. During the first 3.3 seconds, the metal filled the sprue and the vertical runner. Then it entered through the lower ingate and started to fill the bottom part of the cylinder. After 5.6 seconds, the metal level reached the upper ingate, and the upper ingate began to deliver metal to the upper cylinder. This simultaneous filling from two levels reduced the overall filling time. At 7.5 seconds, the metal front had passed through the complex inner geometry. At 11 seconds, the arms were nearly full. The final filling completed at 16.64 seconds. The flow pattern was free of severe turbulence, with Froude number below 0.8 at most locations.
The temperature field during filling showed that the metal in the thin sections cooled faster, but the large runner maintained a high temperature. At the end of filling, the average temperature in the casting was about 1390°C, which is above the liquidus of 1260°C, ensuring good feeding before solidification started. The cooling rate in the thick sections was about 0.05 K/s, while in the thin sections it was 0.2 K/s. This gradient is beneficial for directional solidification.
For ductile iron castings, the formation of shrinkage porosity is also related to the carbon equivalent. The carbon equivalent of QT600-3 is:
$$ CE = w_C + \frac{1}{3}(w_{Si} + w_P) = 3.7 + \frac{2.2 + 0.055}{3} \approx 4.45\% $$
This near-eutectic composition promotes graphitization and self-feeding. However, the Mg treatment and inoculant addition affect the nodule count and the expansion behavior. In the production of ductile iron castings, inoculation is critical to achieve a high nodule count, which increases the effective expansion and reduces porosity. I recommend an in-mold inoculation with a late addition of 0.1% inoculant to improve the soundness of the lift arm.
10. Industrial Validation and Quality Inspection
After implementing the improved stepped gating process, I manufactured a batch of 50 castings in the foundry. The process parameters were controlled as follows:
- Pouring temperature: 1480 ± 10°C
- Vacuum pressure: 0.05 MPa
- Coating thickness: 0.4–0.6 mm
- Vibration frequency: 50 Hz
- Vibration amplitude: 0.5 mm
- Pouring time: 15–17 s
The castings were inspected by ultrasonic testing and sectioning. The results showed that 94% of the castings had no visible defects. The remaining 6% had minor shrinkage porosity at the cylinder ends, within the acceptance criteria of ASTM E446 Level 2. The mechanical properties of the castings were tested. Table 7 shows the average tensile properties of the ductile iron castings.
| Property | Measured | QT600-3 requirement |
|---|---|---|
| Tensile strength (MPa) | 628 | ≥600 |
| Yield strength (MPa) | 412 | ≥370 |
| Elongation (%) | 4.5 | ≥3 |
| Brinell hardness (HB) | 220 | 190–270 |
| Nodularity (%) | 88 | ≥80 |
| Nodule count (mm⁻²) | 140 | – |
The results fully meet the QT600-3 standard, confirming the reliability of the optimized process.
11. Conclusions
Through this research, I have drawn the following conclusions:
- The initial bottom gating and top gating schemes for ductile iron lift arms both produced severe shrinkage and porosity defects, as predicted by ProCAST simulation and confirmed by actual trials. The bottom gating suffered from early solidification of the gating system, while the top gating suffered from premature riser solidification and reverse feeding.
- I proposed an improved stepped gating system with two ingates connected to a large vertical runner. This design significantly shortened the filling time from 24.08 s to 16.64 s, improved the temperature distribution, and maintained liquid feeding to the hot spots during almost the entire solidification process.
- The simulation of the stepped gating scheme showed a porosity volume fraction of only 0.42%, compared with 3.85% and 2.94% for the bottom and top gating schemes. The Niyama criterion confirmed a much lower shrinkage risk.
- Actual production trials with the stepped gating process produced sound ductile iron castings with no significant shrinkage cavities, and the mechanical properties met the QT600-3 requirements. The excellent agreement between simulation and practice proves that ProCAST, with appropriate thermophysical parameters and micro-models, is a powerful tool for optimizing lost foam casting of ductile iron castings.
- For ductile iron castings, the graphitic expansion self-feeding effect must be carefully considered. The lost foam mold rigidity is relatively low, so the gating system must provide external feeding until the graphite expansion is fully developed. The stepped gating system achieves this by keeping the runner liquid and properly positioning the ingates at the hot spots.
In future work, I plan to further optimize the coating permeability and vibration parameters to eliminate the minor residual porosity in the thickest sections. Additionally, I will extend this methodology to other ductile iron castings with complex geometries to establish a robust design guideline for lost foam gating systems.
This study demonstrates that numerical simulation is indispensable for designing casting processes, especially for high-integrity ductile iron castings produced by lost foam. The combination of filling, solidification, and micro-modeling allows foundry engineers to virtually test multiple gating designs in a short time, significantly reducing trial-and-error costs and improving the first-time-right rate.
Given the increasing demand for lightweight and near-net-shape components, lost foam casting of ductile iron castings will continue to expand in the automotive and agricultural machinery sectors. The methodology presented here can be readily applied to other thick-sectioned ductile iron castings to ensure soundness and reliability.
In summary, the stepped gating system has proven to be a simple yet effective solution for the problematic ductile iron lift arm. The lessons learned from this investigation are valuable for any foundry producing large ductile iron castings with isolated hot spots. The combination of ProCAST simulation and practical verification has established a reliable process window for the lost foam casting of this component.
I hope this detailed case study can serve as a reference for fellow engineers and researchers working on the numerical simulation of lost foam casting of ductile iron castings. Future improvements in simulation software will enable even more accurate prediction of foam decomposition gas flow, coating behavior, and microstructure evolution, further advancing the state of the art in ductile iron casting technology.