The quality of castings produced by the lost foam casting process is profoundly influenced by the design of its gating system. Currently, the design of these systems often lacks a systematic theoretical foundation and reliable empirical formulas, which acts as a constraint on the advancement and broader application of lost foam casting technology. Numerical simulation of the lost foam casting process using computers presents a powerful tool to overcome this limitation. It allows for the visualization of metal filling and solidification, enabling the study of how the gating system impacts the entire process. Furthermore, it facilitates the prediction of potential defects such as shrinkage cavities, porosity, slag inclusions, and gas holes. This predictive capability is invaluable for designing rational pouring processes and providing critical guidance for production practice.
Valve castings, while often geometrically simple, present unique challenges. They typically feature significant variations in wall thickness and have stringent requirements for surface finish and internal soundness, as they must undergo hydrostatic and pneumatic pressure tests. This study focuses on a typical valve casting. By integrating computer simulation with the orthogonal experimental design method, we investigate the effects of gating system type, pouring method, and ingate cross-sectional shape on the quality of valve castings produced via lost foam casting. The analysis aims to determine the relative significance of each factor and identify the optimal gating system design configuration.
Numerical Model and Definition of Experimental Factors
Geometry and Material
The subject of this investigation is a representative valve casting with a mass of approximately 15 kg and a maximum envelope dimension of 550 mm. The required surface roughness ranges from Ra 12.5 to 25.0 μm, with dimensional and weight tolerances adhering to grades 8-10 and 7-8, respectively. The casting material is AISI 304 stainless steel.
Simulation Setup and Thermal Parameters
The simulation was performed using specialized foundry simulation software. The thermal-physical properties for both the 304 stainless steel and the expendable foam pattern, which are crucial for accurately modeling the lost foam casting process, are provided by the software’s internal database and are summarized in the table below. A key aspect of modeling lost foam casting is accounting for the heat consumed during the pyrolysis of the foam pattern. This endothermic reaction necessitates a higher pouring temperature compared to conventional sand casting, typically by 30–50°C.
For this simulation of the dry sand, vacuum-assisted lost foam casting process, the following parameters were set:
- Pouring Temperature: 1600°C
- Sand Properties: Density = 1520 kg/m³, Thermal Conductivity = 0.53 W/(m·K), Specific Heat = 1.22 kJ/(kg·K), Permeability = 1×10⁻⁷ cm⁻².
- Interface Heat Transfer Coefficient: 500 W/(m²·K) (between sand/metal and sand/foam).
- Vacuum Pressure: -0.60 MPa.
| Material | Density (kg/m³) | Latent Heat (kJ/kg) | Thermal Conductivity (W/(m·K)) | Specific Heat (kJ/(kg·K)) | Liquidus Temp. (°C) | Solidus Temp. (°C) |
|---|---|---|---|---|---|---|
| Foam Pattern | 25 | 100 | 0.15 | 3.700 | 350 | 330 |
| 304 Stainless Steel | 7,420 | 271.7 | 12.55 | 0.669 | 1,476 | 1,460 |
The heat transfer at the interface is governed by a boundary condition. The heat flux $q$ across the interface can be modeled as:
$$ q = h_{int} (T_{metal} – T_{sand}) $$
where $h_{int}$ is the interfacial heat transfer coefficient (set to 500 W/(m²·K)), and $T_{metal}$ and $T_{sand}$ are the temperatures of the metal and sand at the interface, respectively.
Orthogonal Experimental Design
The orthogonal experimental method was employed to efficiently and scientifically study the effects of multiple factors. This method utilizes standardized orthogonal arrays to select test conditions and arrange experiments. The general procedure involves defining the objective, selecting factors and levels, choosing an orthogonal table, designing the test plan, conducting experiments, and analyzing the results to determine factor significance and optimal level combinations.
For this study on optimizing the gating system in lost foam casting, three key factors were selected, each with three levels:
- Factor A: Gating System Type.
- Level 1 (A1): Closed System (Sprue > Runner > Ingate cross-sectional area).
- Level 2 (A2): Partially Closed System (Runner > Sprue > Ingate).
- Level 3 (A3): Open System (Sprue < Runner < Ingate).
- Factor B: Pouring Method.
- Level 1 (B1): Top Gating.
- Level 2 (B2): Side Gating.
- Level 3 (B3): Bottom Gating.
- Factor C: Ingate Cross-Sectional Shape.
- Level 1 (C1): Rectangular.
- Level 2 (C2): Circular.
- Level 3 (C3): Triangular.
The standard L9(3⁴) orthogonal array was chosen, requiring only 9 simulation runs to evaluate the effects of these three 3-level factors. The experimental plan is shown in the table below.
| Experiment No. | Factor A: Gating Type | Factor B: Pouring Method | Factor C: Ingate Shape | Specific Combination |
|---|---|---|---|---|
| 1 | A1 (Closed) | B1 (Top) | C1 (Rectangular) | Closed / Top / Rectangular |
| 2 | A1 (Closed) | B2 (Side) | C2 (Circular) | Closed / Side / Circular |
| 3 | A1 (Closed) | B3 (Bottom) | C3 (Triangular) | Closed / Bottom / Triangular |
| 4 | A2 (Partially Closed) | B1 (Top) | C2 (Circular) | Partially Closed / Top / Circular |
| 5 | A2 (Partially Closed) | B2 (Side) | C3 (Triangular) | Partially Closed / Side / Triangular |
| 6 | A2 (Partially Closed) | B3 (Bottom) | C1 (Rectangular) | Partially Closed / Bottom / Rectangular |
| 7 | A3 (Open) | B1 (Top) | C3 (Triangular) | Open / Top / Triangular |
| 8 | A3 (Open) | B2 (Side) | C1 (Rectangular) | Open / Side / Rectangular |
| 9 | A3 (Open) | B3 (Bottom) | C2 (Circular) | Open / Bottom / Circular |
Analysis of Orthogonal Experiment Results
The nine distinct gating system designs, as per the orthogonal array, were modeled using the casting simulation software. The filling process for each configuration was simulated and analyzed. A critical output for assessing filling-related defects in lost foam casting is the metal velocity within the mold cavity. According to gating design principles for lost foam casting, the velocity of liquid metal entering the cavity should be controlled, typically between 0.5 and 0.7 m/s, to avoid excessive turbulence and splashing which can entrap gas and foam degradation products.
For the quantitative analysis, a velocity threshold of 0.5 m/s was selected. For each simulation, the total duration during which the metal velocity in the cavity equaled or exceeded this critical value was summed. A larger cumulative duration indicates a higher probability of gas and pyrolysis residue entrapment, leading to filling defects like slag inclusions and porosity. Therefore, minimizing this “high-velocity duration” is a key objective for optimizing the lost foam casting gating system for valve castings. The results for all nine experiments are listed below.
| Exp. No. | Factor A | Factor B | Factor C | Result (Y): Total Duration ≥0.5 m/s (s) |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 6.445 |
| 2 | 1 | 2 | 2 | 8.620 |
| 3 | 1 | 3 | 3 | 8.891 |
| 4 | 2 | 1 | 2 | 7.806 |
| 5 | 2 | 2 | 3 | 13.514 |
| 6 | 2 | 3 | 1 | 8.023 |
| 7 | 3 | 1 | 3 | 8.704 |
| 8 | 3 | 2 | 1 | 8.876 |
| 9 | 3 | 3 | 2 | 10.810 |
The results were analyzed using the range analysis method common to orthogonal experiments. For each factor (column), the average result ($K_{ij}$) for each level (i=1,2,3) is calculated. The range ($R_j$) for each factor is the difference between the maximum and minimum $K_{ij}$ values. A larger range indicates that the factor has a more significant influence on the result (total high-velocity duration). The calculations are as follows:
For Factor A (Gating Type):
$$ K_{A1} = (Y1 + Y2 + Y3) / 3 = (6.445+8.620+8.891)/3 = 7.985 $$
$$ K_{A2} = (Y4 + Y5 + Y6) / 3 = (7.806+13.514+8.023)/3 = 9.781 $$
$$ K_{A3} = (Y7 + Y8 + Y9) / 3 = (8.704+8.876+10.810)/3 = 9.463 $$
$$ R_A = max(7.985, 9.781, 9.463) – min(7.985, 9.781, 9.463) = 9.781 – 7.985 = 1.796 $$
For Factor B (Pouring Method):
$$ K_{B1} = (Y1 + Y4 + Y7) / 3 = (6.445+7.806+8.704)/3 = 7.652 $$
$$ K_{B2} = (Y2 + Y5 + Y8) / 3 = (8.620+13.514+8.876)/3 = 10.337 $$
$$ K_{B3} = (Y3 + Y6 + Y9) / 3 = (8.891+8.023+10.810)/3 = 9.241 $$
$$ R_B = 10.337 – 7.652 = 2.685 $$
For Factor C (Ingate Shape):
$$ K_{C1} = (Y1 + Y6 + Y8) / 3 = (6.445+8.023+8.876)/3 = 7.781 $$
$$ K_{C2} = (Y2 + Y4 + Y9) / 3 = (8.620+7.806+10.810)/3 = 9.079 $$
$$ K_{C3} = (Y3 + Y5 + Y7) / 3 = (8.891+13.514+8.704)/3 = 10.370 $$
$$ R_C = 10.370 – 7.781 = 2.589 $$
| Factor | Average Result for Level 1 ($K_1$) | Average Result for Level 2 ($K_2$) | Average Result for Level 3 ($K_3$) | Range ($R_j$) |
|---|---|---|---|---|
| A: Gating Type | 7.985 | 9.781 | 9.463 | 1.796 |
| B: Pouring Method | 7.652 | 10.337 | 9.241 | 2.685 |
| C: Ingate Shape | 7.781 | 9.079 | 10.370 | 2.589 |
Optimal Level per Factor: A1 (7.985), B1 (7.652), C1 (7.781).
Order of Factor Significance (based on Range R): B > C > A.
Predicted Optimal Combination: A1B1C1 (Closed Gating, Top Pouring, Rectangular Ingate).
Discussion on the Influence of Gating System Factors in Lost Foam Casting
The analysis clearly indicates that for valve castings in lost foam casting, the pouring method (Factor B) has the most substantial influence on the filling turbulence metric, followed by the ingate shape (Factor C). The gating system type (Factor A) has a comparatively smaller, though still notable, effect.
1. Influence of Gating System Type (Factor A)
The closed system (A1) yielded the lowest average high-velocity duration ($K_{A1}=7.985$). A fundamental principle in lost foam casting gating design is to avoid prolonged non-filling of the sprue. A slow-filling sprue can cause the coating layer to be excessively baked, leading to cracking, collapse, and the formation of sand inclusions or a “bulging neck” defect. The closed system, where $A_{sprue} > A_{runner} > A_{ingate}$, ensures the sprue fills rapidly upon pouring. This creates a pressurized flow within the gating system, which helps prevent air aspiration from the coating walls and promotes slag trapping in the sprue well or runner. This pressurized flow is also beneficial for filling thin sections. In contrast, partially closed (A2) and open (A3) systems are more prone to slower sprue filling, increasing the risk of entrapping gas and slag, leading to defects in the final lost foam casting.
2. Influence of Pouring Method (Factor B)
Top pouring (B1) demonstrated a significantly lower propensity for turbulent filling ($K_{B1}=7.652$) compared to side (B2, $K_{B2}=10.337$) and bottom (B3, $K_{B3}=9.241$) pouring. While top gating in lost foam casting is sometimes associated with a risk of mold collapse (due to rapid foam gasification before the metal front provides structural support), it offers the shortest filling time and a thermally favorable gradient. For valve castings, which are generally medium to small in size, the volume of gas generated is manageable. If the filling is completed within a few seconds—before the vacuum in the flask degrades below a critical level—the mold can be fully replaced by metal without collapse. The longer fill times associated with side and bottom gating lead to extended periods where metal velocity exceeds the critical threshold, increasing the opportunity for gas and residue entrapment and thus the probability of filling defects.
The fill time $t_f$ can be approximated using Bernoulli’s equation and accounting for the back-pressure from foam decomposition:
$$ t_f \propto \frac{V_{cavity}}{A_{ingate} \cdot \sqrt{2gH_{eff}}} $$
where $V_{cavity}$ is the cavity volume, $A_{ingate}$ is the total ingate area, $g$ is gravity, and $H_{eff}$ is the effective metallostatic head, which is largest for top gating and smallest for bottom gating. A shorter $t_f$ generally reduces the time window for defect formation.
3. Influence of Ingate Cross-Sectional Shape (Factor C)
The rectangular ingate (C1) provided the most stable filling condition ($K_{C1}=7.781$). The relationship here is quite linear, with the triangular ingate (C3) performing worst ($K_{C3}=10.370$). A triangular cross-section tends to have a higher perimeter-to-area ratio for a given area, leading to faster cooling of the metal stream. This can prematurely lower the metal temperature, increasing the risk of mistruns and cold shuts. Furthermore, the geometry may promote a less stable flow profile entering the cavity, causing splashing and turbulence. The circular ingate (C2) offers a lower perimeter-to-area ratio but may still introduce a focused, jet-like flow. The rectangular shape, particularly if wider than it is tall, promotes a broader, sheet-like flow that enters the cavity more smoothly, minimizing splashing and the entrapment of pyrolysis products in the lost foam casting process.
The cooling effect can be conceptually related to the surface area through which heat is lost:
$$ \dot{Q}_{loss} \approx h \cdot P \cdot L \cdot (T_{metal} – T_{sand}) $$
where $\dot{Q}_{loss}$ is the heat loss rate, $h$ is an effective heat transfer coefficient, $P$ is the wetted perimeter of the ingate, $L$ is its length, and $(T_{metal} – T_{sand})$ is the temperature difference. For a fixed cross-sectional area $A$, the perimeter $P$ is minimized by a circle. A rectangle with a high aspect ratio or a triangle will have a larger $P$, leading to greater heat loss $\dot{Q}_{loss}$.
Conclusions
This integrated study utilizing numerical simulation and orthogonal experiment design leads to the following conclusions for optimizing the lost foam casting process for valve castings:
- Numerical simulation of the filling and solidification stages in lost foam casting is a highly effective tool for pre-production optimization of gating systems. It minimizes the need for costly and time-consuming physical trial-and-error, thereby enhancing final casting quality and improving production efficiency.
- For valve castings produced via the lost foam casting process under vacuum, the pouring method exerts the greatest influence on filling-related quality metrics (as measured by high-velocity duration). The shape of the ingate cross-section is the next most significant factor, while the type of gating system (closed, partially closed, open) has a relatively smaller, though still important, effect. The order of significance is: Pouring Method > Ingate Shape > Gating System Type.
- The optimal gating system design for the described lost foam casting of valve castings is a closed-type gating system (sprue area > runner area > ingate area), employing a top-pouring method, and utilizing rectangular ingates. This configuration (A1B1C1) promotes rapid sprue filling, minimizes filling time and turbulence, provides a favorable thermal gradient, and ensures a smooth metal entry into the cavity, collectively reducing the propensity for defects associated with the lost foam casting process.