I carried out a systematic numerical study of the gravity casting process for a bearing seat produced from ductile iron castings. The objective was to understand how pouring temperature, mold temperature, and pouring speed interact with the formation of volumetric defects, and then to use that knowledge to optimize the casting process. The bearing seat is a load-bearing transmission component. In service, it supports rotating shafts, reduces friction through the bearing interface, and protects the surrounding support structure from concentrated stress. Because the component must maintain dimensional stability and structural integrity, internal shrinkage porosity and gas-related defects are unacceptable. I therefore treated the defect volume fraction as the primary response variable and investigated the filling and solidification behavior of ductile iron castings under several process conditions.
The geometry I studied has a length of 0.321 m, a width of 0.127 m, and a height of 0.099 m. Its mass is 8.34 kg. The shape is symmetric but complex, with many rounded corners, curved surfaces, inclined faces, and a large internal cavity. The wall thickness is not uniform, and the thin sections, thick sections, and corner regions differ substantially in local modulus. The top and internal arc surfaces are especially important because they are functional surfaces. If the casting process is not controlled, these locations may develop shrinkage cavities, porosity, or even cracking. This makes the bearing seat a suitable case for detailed numerical analysis of ductile iron castings.
Physical and Material Definition
I selected a sand casting route for the ductile iron castings. The material was a nodular graphite iron equivalent to QT400-18. The chemical composition and the measured values are summarized in Table 1 and Table 2. The carbon and silicon contents are important because they control graphitization, eutectic solidification, and the expansion behavior of ductile iron castings. The magnesium and rare-earth additions are necessary for spheroidization, but excessive residuals can affect the freezing range and defect susceptibility.
| Attribute | Value |
|---|---|
| Component type | Bearing seat |
| Material family | Ductile iron castings |
| Length | 0.321 m |
| Width | 0.127 m |
| Height | 0.099 m |
| Mass | 8.34 kg |
| Average wall thickness | 6.5 mm |
| Casting method | Sand gravity casting |
| Element | Specified range, wt.% | Measured value, wt.% |
|---|---|---|
| C | 3.50-3.60 | 3.50 |
| Si | 2.50-3.00 | 3.12 |
| Mn | 0.45-0.57 | 0.14 |
| P | 0.05-0.06 | 0.04 |
| S | 0.01-0.03 | 0.01 |
| Mg | 0.03-0.06 | 0.04 |
| Re | 0.03-0.05 | Measured below detection limit |
Governing Equations and Defect Criterion
I modeled the filling and solidification of ductile iron castings as a transient incompressible flow and heat transfer problem. The liquid iron was treated as a Newtonian fluid. The density, viscosity, specific heat, and thermal conductivity were temperature-dependent in the numerical solver, but the governing balance statements can be written in the classical form. The continuity equation enforces mass conservation:
$$ D=\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0 $$
The momentum conservation equations in the three coordinate directions are expressed by the Navier-Stokes equations:
$$ \rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=-\frac{\partial P}{\partial x}+\mu\nabla^{2}u $$
$$ \rho\left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)=-\frac{\partial P}{\partial y}+\mu\nabla^{2}v $$
$$ \rho\left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=-\frac{\partial P}{\partial z}+\rho g+\mu\nabla^{2}w $$
The energy conservation equation governs heat transport during filling and solidification:
$$ \rho c\left(\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z}\right)=\frac{\partial}{\partial x}\left(\lambda\frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(\lambda\frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(\lambda\frac{\partial T}{\partial z}\right)+S $$
In these equations, \(u\), \(v\), and \(w\) are velocity components, \(\rho\) is density, \(P\) is pressure, \(\mu\) is dynamic viscosity, \(g\) is gravitational acceleration, \(c\) is specific heat, \(T\) is temperature, \(\lambda\) is thermal conductivity, and \(S\) is the latent heat source term. I used the SOLA-VOF method to track the free surface of the liquid metal. This approach is well suited to gravity casting of ductile iron castings because it can capture the advancing front, gas entrapment, and incomplete filling events.
For shrinkage defect prediction, I used the temperature-gradient-to-cooling-rate ratio criterion. The local thermal condition is evaluated using
$$ \frac{G}{\sqrt{R}}<c,\qquad $$=""
Here, \(G\) is the temperature gradient, \(R\) is the cooling rate, \(T_u\) is the liquidus temperature, \(T_l\) is the solidus temperature, \(t_u\) is the time when the liquidus is reached, \(t_l\) is the time when the solidus is reached, and \(C\) is a critical value related to the casting size and alloy. When the local \(G/\sqrt{R}\) value falls below \(C\), the region is prone to shrinkage porosity. This criterion allowed me to compare different designs for ductile iron castings without relying only on visual inspection of hot spots.
Numerical Setup and Mesh Independence
I first established a numerical model of the bearing seat and the mold. The initial pouring temperature was 1420 °C, the initial mold temperature was 150 °C, and the heat transfer coefficient between the casting and the chill was set to 0.1 W/(m·K) in the initial trial. The mold wall thickness was 0.03 m, and the overall mold envelope was 0.381 m × 0.1871 m × 0.280 m. I placed five virtual sensors in thin-wall regions, arc sections, and important functional surfaces to record local thermal histories.
Mesh independence is essential because the predicted filling time and defect fraction can change with element size. I compared mesh sizes of 16, 8, 6, 4, 2, and 1 mm. When the mesh size was reduced below 6 mm, the filling time continued to increase, but the change became gradually smaller. The 4 mm mesh gave results close to the 2 mm and 1 mm meshes, while the computational cost increased sharply. Therefore, I selected a uniform 6 mm mesh for the subsequent simulations of ductile iron castings. This mesh produced 23,294 surface elements and 1,451,034 volume elements. The meshing time was 0.372 s.
| Mesh size, mm | Relative filling time | Relative computational cost | Decision |
|---|---|---|---|
| 16 | Lowest | Very low | Rejected |
| 8 | Low | Low | Rejected |
| 6 | Stable | Moderate | Selected |
| 4 | Slightly higher | High | Reference only |
| 2 | Close to 4 mm | Very high | Rejected |
| 1 | Close to 2 mm | Extreme | Rejected |
Pouring System Comparison
I compared top pouring and bottom pouring systems for the ductile iron castings. The pouring system is the path through which the liquid iron enters the mold cavity. For a sound casting, the system must deliver metal at a controlled rate, avoid turbulence, and provide feeding during solidification. I used a yield of approximately 70%, an initial riser and runner mass of 3.57 kg, and a total liquid metal mass of 11.91 kg. The average wall thickness was 6.5 mm, the intended pouring time was 7.6 s, and the filling time was approximately 4.4 s. The resulting rising velocity was 22.73 mm/s, which lies within the recommended range of 19-30 mm/s. For the closed pouring system, I used an inner runner, cross runner, and sprue cross-sectional ratio of 1:1.2:1.5.
| Scheme | Pouring temperature, °C | Pouring speed, m/s | Mold preheat temperature, °C | Riser |
|---|---|---|---|---|
| 1 | 1400 | 0.50 | 125 | No |
| 2 | 1400 | 0.50 | 125 | Yes |
| 3 | 1380 | 0.40 | 100 | Yes |
| 4 | 1420 | 0.60 | 150 | Yes |
For the top pouring system, the cavity filled more slowly. At 25.01% filling, the time was 2.60 s, and the lowest local temperature was about 1325 °C. There were small surface fluctuations and at least three locations where gas entrapment was possible. At 50.01% filling, the time was 5.19 s. At 75% filling, the time was 7.82 s. Complete filling occurred at 10.64 s, and much of the casting had cooled below 1250 °C. The top pouring system had a smaller temperature gradient, but the pouring system itself cooled faster than the casting and could not reliably feed the upper regions. This is why I added a riser to the top pouring design.
For the bottom pouring system, the cavity filled more smoothly. At 25.01% filling, the time was 1.32 s, and the lowest local temperature was about 1375 °C. There was no large fluctuation or splashing, no gas entrainment, and no premature solidification. At 50.01% filling, the time was 2.70 s. At 75% filling, the time was 4.08 s. Complete filling occurred at 5.44 s, with the casting temperature still above about 1300 °C. Although bottom pouring filled faster and more stably, it could not feed the top of the casting. Even with two pouring cups, the filling path was more complicated and almost twice as fast as top pouring. Therefore, I continued the process optimization using the top pouring system for the ductile iron castings.
| Pouring system | 25% fill time, s | 50% fill time, s | 75% fill time, s | 100% fill time, s | Lowest early temperature, °C | Gas entrapment tendency |
|---|---|---|---|---|---|---|
| Top pouring | 2.60 | 5.19 | 7.82 | 10.64 | 1325 | High |
| Bottom pouring | 1.32 | 2.70 | 4.08 | 5.44 | 1375 | Low |
| Solidification feature | Top pouring | Bottom pouring |
|---|---|---|
| Approximate 25% solidification time, s | 57.55 | 57.90 |
| Complete solidification time, s | 502 | 440 |
| Feeding of top region | Possible with riser | Poor |
| Temperature gradient | Smaller | Larger |
| Overall suitability for ductile iron castings | Better after optimization | Limited by top feeding |
Initial Defect Analysis and Process Improvements
After comparing the two pouring systems, I simulated schemes 2, 3, and 4 and evaluated the defect distribution in the ductile iron castings. The best initial result appeared at a pouring temperature of 1420 °C and a pouring speed of 0.60 m/s. The defects were fewer and were mainly located on the inner surfaces. However, an isolated liquid region remained in the thick-wall area. This region formed a thermal hot spot. During solidification, it did not receive sufficient feeding, and shrinkage porosity developed. The simulation also showed that the lower part near the inner runner remained overheated because liquid metal continued to flow through that area during filling.
To reduce the defect volume fraction, I redesigned the feeding and cooling strategy. For ductile iron castings with a relatively large modulus, the solidification time can be long. A long solidification time can reduce nodularity and increase the probability of coarse graphite and graphite distortion. Chills are therefore useful because they increase the local cooling rate and reduce the time spent in the mushy zone. I used external iron chills with a spacing of 20-30 mm. I placed additional chills below the inner runner and along the thick-wall side to expand the cooling area. I also added an open vent and an exhaust path on the thick-wall side to remove gases generated during filling. Finally, I optimized the cylindrical riser with a neck. The optimized pouring system reduced the isolated liquid region and shifted the shrinkage cavities into the riser.
| Improvement action | Purpose | Expected effect on ductile iron castings |
|---|---|---|
| Add external iron chills | Increase local cooling rate | Shorten mushy-zone time and reduce shrinkage porosity |
| Place chills below the inner runner | Remove local overheating | Reduce hot spots caused by continuous metal flow |
| Add chills on the thick-wall side | Accelerate thick-section cooling | Reduce isolated liquid regions |
| Add an exhaust system | Remove mold gases | Lower gas porosity and entrapment risk |
| Optimize the cylindrical riser | Improve feeding | Move shrinkage cavities into the riser |
When I applied these improvements in scheme 4, the shrinkage cavities appeared almost entirely in the riser. The casting itself was well formed, and the major internal defects were eliminated. This confirmed that the combination of chills, riser optimization, and venting is effective for the ductile iron castings considered here.
Orthogonal Simulation Experiment Design
To quantify the influence of the main process variables, I designed a Box-Behnken orthogonal experiment. The three factors were pouring temperature \(A\), mold temperature \(B\), and pouring speed \(C\). The response variable was the volume defect fraction \(Y_1\), expressed as a percentage. The factor levels are listed in Table 3. The design contained 17 simulation runs, including five center-point repetitions. This type of design is efficient because it provides information about main effects, interactions, and quadratic curvature without requiring a full factorial experiment.
| Level | Pouring temperature \(A\), °C | Mold temperature \(B\), °C | Pouring speed \(C\), m/s |
|---|---|---|---|
| Level 1 | 1380 | 100 | 0.05 |
| Level 2 | 1400 | 125 | 0.06 |
| Level 3 | 1420 | 150 | 0.07 |
| Run | \(A\), °C | \(B\), °C | \(C\), m/s | \(Y_1\), % |
|---|---|---|---|---|
| 1 | 1400 | 150 | 0.05 | 0.574 |
| 2 | 1380 | 125 | 0.05 | 0.426 |
| 3 | 1400 | 125 | 0.06 | 0.550 |
| 4 | 1400 | 150 | 0.07 | 0.457 |
| 5 | 1380 | 125 | 0.07 | 0.372 |
| 6 | 1420 | 125 | 0.07 | 0.663 |
| 7 | 1400 | 100 | 0.07 | 0.424 |
| 8 | 1400 | 125 | 0.06 | 0.543 |
| 9 | 1400 | 150 | 0.06 | 0.517 |
| 10 | 1420 | 100 | 0.06 | 0.596 |
| 11 | 1400 | 125 | 0.05 | 0.577 |
| 12 | 1420 | 125 | 0.05 | 0.678 |
| 13 | 1380 | 150 | 0.06 | 0.461 |
| 14 | 1420 | 150 | 0.06 | 0.727 |
| 15 | 1380 | 100 | 0.06 | 0.411 |
| 16 | 1400 | 100 | 0.05 | 0.424 |
| 17 | 1420 | 125 | 0.06 | 0.565 |
I fitted a second-order polynomial to the response. The regression equation for the volume defect fraction of the ductile iron castings is
$$ Y_1=0.5504+0.1243A+0.0455B-0.0232C+0.0202AB+0.0098AC-0.0292BC+0.0317A^{2}-0.0333B^{2}-0.0473C^{2} $$
The analysis of variance is given in Table 4. The model is highly significant, with \(P<0.0001\). The lack-of-fit term is not significant, which means that the model can represent the response surface without systematic lack of fit. The main effect of pouring temperature is the most significant factor, followed by mold temperature and then pouring speed. The interaction between mold temperature and pouring speed is also significant at the 5% level. The quadratic terms are significant, indicating curvature in the response surface.
| Source | Sum of squares | Degrees of freedom | Mean square | \(F\) value | \(P\) value | Significance |
|---|---|---|---|---|---|---|
| Model | 0.1678 | 9 | 0.0186 | 37.970 | <0.0001 | Significant |
| \(A\) | 0.1235 | 1 | 0.1235 | 251.490 | <0.0001 | Highly significant |
| \(B\) | 0.0166 | 1 | 0.0166 | 33.720 | 0.0007 | Significant |
| \(C\) | 0.0043 | 1 | 0.0043 | 8.810 | 0.0209 | Significant |
| \(AB\) | 0.0016 | 1 | 0.0016 | 3.340 | 0.1103 | Not significant |
| \(AC\) | 0.0004 | 1 | 0.0004 | 0.774 | 0.4081 | Not significant |
| \(BC\) | 0.0034 | 1 | 0.0034 | 6.970 | 0.0334 | Significant |
| \(A^2\) | 0.0042 | 1 | 0.0042 | 8.600 | 0.0219 | Significant |
| \(B^2\) | 0.0047 | 1 | 0.0047 | 9.520 | 0.0177 | Significant |
| \(C^2\) | 0.0094 | 1 | 0.0094 | 19.200 | 0.0032 | Significant |
| Residual | 0.0034 | 7 | 0.0005 | |||
| Lack of fit | 0.0013 | 3 | 0.0004 | 0.8585 | 0.5312 | Not significant |
| Pure error | 0.0021 | 4 | 0.0005 | |||
| Total | 0.1712 | 16 |
The fit statistics are summarized in Table 5. The coefficient of determination \(R^2\) is 0.9799, and the adjusted \(R^2\) is 0.9541. Both are greater than 0.9, which indicates that the model has high reliability. The coefficient of variation is 4.20%, below the commonly accepted limit of 10%. The signal-to-noise ratio is 21.2543, which indicates adequate model discrimination. The predicted \(R^2\) is 0.8551, so the model can be used to navigate the design space. The residuals follow a normal distribution, and the predicted values agree well with the actual values.
| Statistic | Value |
|---|---|
| Standard deviation | 0.0222 |
| Mean | 0.5274 |
| Coefficient of variation | 4.20% |
| \(R^2\) | 0.9799 |
| Adjusted \(R^2\) | 0.9541 |
| Predicted \(R^2\) | 0.8551 |
| Adequate precision | 21.2543 |
Response Surface Interpretation
I examined the response surface for the volume defect fraction of the ductile iron castings. When the pouring speed was held at its middle level, the volume defect fraction increased with pouring temperature over most of the investigated range. The effect of mold temperature was also positive, but smaller than the effect of pouring temperature. When the mold temperature was between 100 °C and 125 °C, the defect fraction first increased and then decreased slightly as pouring temperature increased. When the mold temperature was between 125 °C and 150 °C, the defect fraction increased monotonically with pouring temperature. In all cases, the dominant trend was a positive correlation between pouring temperature and defect fraction.
When the pouring speed was varied with pouring temperature, the response was more complex. For pouring speeds at or above 0.06 m/s, the change in defect fraction with pouring temperature was steeper than for lower pouring speeds. The best result appeared when the pouring temperature was moderate and the pouring speed was above 0.06 m/s. In the interaction between mold temperature and pouring speed, both factors had a strong influence. However, when the mold temperature was above 125 °C and the pouring speed was above 0.06 m/s, the response became less sensitive. The curvature of the response surface indicated that pouring speed had a greater effect than mold temperature in that region.
From a physical standpoint, these trends are consistent with the behavior of ductile iron castings. A higher pouring temperature increases the superheat of the liquid metal. This delays solidification locally and enlarges the mushy zone. It also increases the total liquid shrinkage that must be compensated by riser feeding and graphite expansion. If the mold temperature is also high, the mold removes heat more slowly, and the hot spot remains liquid for a longer time. The combination of high pouring temperature and high mold temperature therefore increases the volume defect fraction. A lower pouring temperature reduces superheat and shortens the solidification time, but if it is too low, the metal may become too viscous or solidify before the cavity is completely filled. The orthogonal analysis showed that the most effective way to reduce the defect volume fraction is to reduce the pouring temperature while keeping the mold temperature moderate and the pouring speed at an appropriate level.
Optimized Process and Verification
Using the fitted model, I optimized the process for the ductile iron castings. The optimization suggested a pouring temperature of 1400 °C, a mold temperature of 145 °C, and a pouring speed of 0.061 m/s. Under these conditions, the predicted volume defect fraction was 0.556%. The simulation showed that surface defects on the arc surface and other important surfaces were essentially eliminated. In the interior, the thick-wall region that had previously formed an isolated liquid pool was substantially improved by the chilling and feeding action. The remaining shrinkage was concentrated in the riser. The optimized parameters therefore produced a stable filling and solidification process and improved the casting performance.
| Parameter | Initial scheme 4 | Optimized scheme |
|---|---|---|
| Pouring temperature, °C | 1420 | 1400 |
| Mold temperature, °C | 150 | 145 |
| Pouring speed, m/s | 0.60 | 0.061 |
| Volume defect fraction, % | 0.727 | 0.556 |
| Main defect location | Inner surface and isolated thick-wall region | Riser and negligible residual interior |
| Filling stability | Acceptable | Stable |
| Feeding behavior | Partial | Effective |
Mechanistic Discussion
The numerical results show that the thermal history of ductile iron castings is governed by a coupling between filling dynamics and solidification. During filling, the liquid metal loses heat to the mold and to the surrounding air. The local temperature at the end of filling determines the initial condition for solidification. If the pouring temperature is high, the casting enters solidification with more superheat. The temperature gradient may be smoother, but the total solidification time is longer. A longer solidification time increases the opportunity for shrinkage porosity to form in regions that are not fed effectively. In the bearing seat, the thick-wall section and the region near the inner runner are especially vulnerable.
Mold temperature plays a secondary but still important role. A higher mold temperature reduces the heat extraction rate. This keeps the casting hotter, prolongs the mushy state, and increases the defect volume fraction. In ductile iron castings, mold temperature also affects graphitization and the expansion that accompanies graphite growth. If the mold is too cold, the casting may cool too rapidly, which can cause chill formation, carbides, or incomplete feeding. If the mold is too hot, the cooling rate is too low, and shrinkage defects become more likely. The optimized mold temperature of 145 °C is a compromise between these two extremes.
Pouring speed controls the filling pattern and the local velocity field. A very low pouring speed may cause the metal to cool before the cavity is filled, especially in thin sections. A very high pouring speed may cause turbulence, gas entrapment, and mold erosion. In the orthogonal experiment, pouring speed had a smaller main effect than pouring temperature and mold temperature, but its interaction with mold temperature was significant. When the pouring temperature was at its optimum and the mold temperature was moderate, the pouring speed could be reduced to the lowest level within the selected range. At that point, the filling and solidification processes were stable, and the casting performance was best. This is an important practical conclusion for ductile iron castings because it shows that speed does not need to be maximized once the thermal conditions are properly set.
Practical Implications for Ductile Iron Castings
For production of ductile iron castings with complex geometry and non-uniform wall thickness, I recommend the following sequence of process decisions. First, select a pouring system that provides stable filling and adequate feeding. The top pouring system is preferable when a riser can be positioned to feed the upper hot spot. Second, place chills near thick sections and near regions that remain overheated because of runner placement. Third, add a venting system to remove gases from the cavity. Fourth, optimize the riser so that the final shrinkage cavity is located in the riser and not in the functional surfaces. Fifth, use a statistically designed experiment to quantify the effect of pouring temperature, mold temperature, and pouring speed. Sixth, select the lowest pouring temperature and mold temperature that still ensure complete filling and acceptable microstructure. Seventh, adjust pouring speed only after the thermal variables have been optimized.
| Process decision | Recommended action | Reason for ductile iron castings |
|---|---|---|
| Pouring system | Use top pouring with a properly sized riser | Provides a feeding path to upper hot spots |
| Chilling | Place external chills near thick sections and overheated runner zones | Reduces local solidification time and shrinkage porosity |
| Venting | Add open or blind vents on thick-wall side | Prevents gas entrapment and gas porosity |
| Riser | Optimize cylindrical necked riser | Moves shrinkage cavities into the riser |
| Pouring temperature | Use the lowest temperature that allows complete filling | Reduces superheat, liquid shrinkage, and defect volume fraction |
| Mold temperature | Use a moderate preheat temperature | Balances cooling rate and feeding behavior |
| Pouring speed | Reduce to the lowest stable level after thermal optimization | Minimizes turbulence and gas entrapment |
Model Reliability and Limitations
The regression model has a high \(R^2\), a high adjusted \(R^2\), and a non-significant lack-of-fit, so it is reliable within the investigated range. The Box-Behnken design provided enough information to estimate the curvature and interactions among the three factors. However, the model is empirical. It should not be extrapolated far beyond the tested ranges of 1380-1420 °C for pouring temperature, 100-150 °C for mold temperature, and 0.05-0.07 m/s for pouring speed. The numerical simulation also relies on material properties, interfacial heat transfer coefficients, and boundary conditions. Small changes in these inputs can shift the predicted defect fraction. In addition, the \(G/\sqrt{R}\) criterion predicts shrinkage porosity but does not directly predict gas porosity, slag inclusion, or microstructure. For a complete assessment of ductile iron castings, the numerical model should be combined with experimental validation, metallographic examination, and mechanical testing.
Another limitation is that the mold filling and solidification processes were modeled as a single continuous event, while in reality the pouring system, riser, and chill behavior may change during the casting cycle. The heat transfer coefficient between the casting and the chill can vary with contact pressure, surface roughness, and coating. The thermal conductivity and specific heat of ductile iron castings also change with temperature and phase. Even with these limitations, the relative trends are robust: pouring temperature is the dominant factor, mold temperature is secondary, and pouring speed has a smaller but non-negligible effect. The optimized process reduced the volume defect fraction and moved the remaining shrinkage to the riser.
Additional Numerical Observations
During filling, the top pouring system showed a slower rise of the metal front. At the quarter-fill stage, the metal surface fluctuated slightly. These fluctuations can entrap gas if the venting system is inadequate. The bottom pouring system produced a smoother front and lower gas entrapment risk, but it could not feed the top section. This trade-off is common in ductile iron castings. A pouring system that fills smoothly may not feed effectively, while a pouring system that feeds effectively may introduce turbulence. The best solution is to combine a feeding-friendly top pouring design with venting and localized chilling.
During solidification, the casting cooled from the outside inward. The thick-wall regions remained hot longer than the thin sections. The temperature peak was located in the thick-wall area. At about 57.5 s, approximately one quarter of the casting had solidified. The final solidification times were about 502 s for the top pouring system and 440 s for the bottom pouring system. Although the bottom pouring system solidified faster, it did not provide enough feeding to the top. The top pouring system required a riser but produced better feeding after optimization. This shows that a shorter solidification time alone is not sufficient; the thermal path and feeding path must be considered together.
The chills changed the local thermal history significantly. In the thick-wall region, the chill increased the cooling rate, decreased the local \(G/\sqrt{R}\) value, and reduced the isolated liquid region. The venting system reduced the gas pressure in the mold cavity. The optimized riser maintained a liquid channel to the hot spot until the end of solidification. As a result, the shrinkage cavity moved into the riser. The defect volume fraction decreased from 0.727% in the initial scheme to 0.556% in the optimized scheme. The remaining defects were small and located in non-critical regions. The arc surface and other functional surfaces were essentially free of defects.
Orthogonal Analysis Summary
The range analysis and variance analysis both showed that pouring temperature is the most significant factor affecting the volume defect fraction of ductile iron castings. Mold temperature is the second most significant factor. Both are positively correlated with the defect volume fraction. Pouring speed has a smaller main effect, but its interaction with mold temperature is significant. The quadratic terms for all three factors are significant, which means the response is not a simple linear function. The optimum is a combination of moderate pouring temperature, moderate mold temperature, and a relatively low pouring speed. At the optimum, the filling and solidification processes are stable, and the casting performance is best.
| Factor | Main effect rank | Correlation with defect fraction | Practical recommendation |
|---|---|---|---|
| Pouring temperature \(A\) | 1 | Positive | Reduce to the lowest level that ensures complete filling |
| Mold temperature \(B\) | 2 | Positive | Use a moderate preheat temperature |
| Pouring speed \(C\) | 3 | Complex, with interactions | Reduce to the lowest stable level after thermal optimization |
Conclusions
I developed a numerical model for the gravity casting of a bearing seat from ductile iron castings. The model was based on the continuity equation, the Navier-Stokes equations, the energy conservation equation, and a temperature-gradient-to-cooling-rate defect criterion. I compared top pouring and bottom pouring, optimized the riser, added chills and venting, and designed a Box-Behnken orthogonal experiment with 17 simulation runs. The main conclusions are as follows.
First, the top pouring system required a longer filling time than the bottom pouring system, but it provided a feeding path to the upper hot spot. The bottom pouring system filled more smoothly but could not feed the top of the casting. For the ductile iron castings studied here, the top pouring system with a properly optimized riser was the better choice.
Second, adding chills, a venting system, and an optimized riser reduced the defect volume fraction. The chills increased the cooling rate in the thick-wall region, the venting system reduced gas entrapment, and the riser moved the final shrinkage cavity out of the casting. The optimized design produced a sound bearing seat with defects concentrated in the riser.
Third, the orthogonal experiment showed that pouring temperature is the most significant factor affecting the volume defect fraction of ductile iron castings, followed by mold temperature. Both factors are positively correlated with the defect volume fraction. Pouring speed has a smaller main effect, but its interaction with mold temperature is significant. The response surface has curvature, so the optimum is not at an extreme of the design space.
Fourth, the optimized process parameters were a pouring temperature of 1400 °C, a mold temperature of 145 °C, and a pouring speed of 0.061 m/s. Under these conditions, the predicted volume defect fraction was 0.556%. The filling and solidification processes were stable, and the casting performance was improved. These results provide theoretical and practical guidance for optimizing the casting process of ductile iron castings with complex geometry and non-uniform wall thickness.
| Conclusion | Key result | Implication for ductile iron castings |
|---|---|---|
| Pouring system | Top pouring with riser performed better than bottom pouring for feeding | Feeding path is as important as filling stability |
| Thermal control | Chills and venting reduced hot spots and gas entrapment | Local cooling and gas removal improve soundness |
| Main factor | Pouring temperature had the strongest effect | Superheat control is critical for defect reduction |
| Secondary factor | Mold temperature had a positive effect | Moderate mold preheat is preferable |
| Speed effect | Pouring speed had a smaller but interactive effect | Reduce speed after thermal optimization |
| Optimized result | Defect fraction decreased to 0.556% | Stable filling and solidification improve performance |
The overall finding is that numerical simulation combined with orthogonal experimentation is an effective method for optimizing ductile iron castings. It allows the designer to separate the dominant thermal factors from the secondary flow factors, identify interactions, and select a robust process window. For the bearing seat, the best process window was a moderate pouring temperature, a moderate mold temperature, and a low stable pouring speed. Under those conditions, the casting filled completely, solidified with adequate feeding, and retained only minor defects in non-critical locations. This approach can be transferred to other ductile iron castings with similar wall-thickness variations and functional surface requirements.