The lost foam casting (LFC) process has achieved significant maturity for industrial production, particularly for ferrous alloys. However, a comprehensive understanding of its mold filling dynamics remains elusive, especially when compared to traditional empty-mold casting. The filling process in LFC is governed by a more complex interplay of numerous parameters. These typically include vacuum level, foam pattern density, coating permeability, pouring temperature, metallostatic pressure head, ingate dimensions, pouring orientation (top, bottom, or stepped), pattern geometry, and sand permeability. While substantial experimental research exists for aluminum alloys in LFC, focusing on parameters like pouring temperature and coating properties, systematic investigations for cast iron parts are relatively scarce, with only limited literature reporting on the influence of certain factors. Prior studies have suggested that the most influential parameters on the filling speed of cast iron parts in LFC are vacuum degree, pattern density, pouring temperature, and metallostatic head. This work employs an integrated experimental setup to investigate the filling speed of cast iron parts using the electrode contact method. The influence laws of the aforementioned four key process factors are studied. Based on extensive浇注 trials within their common operational ranges, a multiple linear regression analysis is performed to establish an empirical formula for predicting the average filling speed. This formula is subsequently validated with experimental data.
1. Experimental Methodology for Measuring Filling Process
1.1 Apparatus and Materials
The experimental foam patterns were manufactured by cutting and assembling expandable polystyrene (EPS) boards. To study the effect of pattern density, boards of different densities were utilized. After applying a refractory coating, the pattern was placed in a flask with a base layer of sand. The flask was then filled with unbonded sand and compacted on a three-dimensional vibration table. The top of the flask was sealed with a plastic film, and the bottom was connected via a quick-seal coupling to a vacuum reservoir. The molten iron, with a grade equivalent to HT250, was melted in a 50 kg medium-frequency induction furnace.
1.2 Principle of Filling Speed Measurement
A specifically designed computer data acquisition system was used to measure the velocity of the liquid metal/foam degradation interface during filling. The core principle of this method is illustrated in the following diagram. A set of fine copper wires is pre-embedded at specific locations within the foam pattern to detect the arrival time of the liquid metal. A common contact (anode) is established at the initial point of metal entry. As the metal advances into the cavity, it sequentially makes contact with the cathodic wires positioned at different locations. The exact moment each circuit closes is recorded by the computer. From the known distances between successive wires and their recorded arrival times, the progression of the metal front can be mapped and the filling speed calculated.
The test casting geometry used is shown in the accompanying schematic, which also indicates the positions of the electrode contacts. The height of the sprue (h) was varied according to the experimental design. The average filling speed discussed in the results and analysis is determined using the two most distant measurement points along the filling path, representing the mean velocity over the longest section of the casting.
2. Influence Laws of Key Process Parameters on Filling Speed
The influence of individual parameters was studied by varying one factor while keeping the other three at their baseline values. The established baseline conditions were: pattern density of 13.2 g/l, pouring temperature of 1400°C, sprue height of 20 cm, and vacuum degree of 0.053 MPa. The observed effects on the average filling speed are summarized below:
| Process Parameter | Baseline Value |
|---|---|
| Pattern Density | 13.2 g/l |
| Pouring Temperature | 1400 °C |
| Sprue Height (Metallostatic Head) | 20 cm |
| Vacuum Degree | 0.053 MPa |
2.1 Effect of Vacuum Degree
The application of vacuum to the sand mold is a critical distinguishing feature of LFC for cast iron parts. It serves multiple purposes: stabilizing the mold, extracting gaseous pyrolysis products, and enhancing the pressure differential driving filling. Experimental results demonstrate that the average filling speed increases essentially linearly with increasing vacuum level. Higher vacuum more effectively removes the gases generated from the decomposing foam, reducing back-pressure at the metal front and thus facilitating faster advancement. The relationship can be initially expressed as:
$$ v \propto V_d $$
where $v$ is the average filling speed and $V_d$ is the applied vacuum degree.
2.2 Effect of Pattern Density
The density of the EPS foam pattern directly influences the mass of material that must be pyrolyzed per unit volume. For cast iron parts, higher pattern density means a greater volume of gaseous and liquid decomposition products are generated at the metal-foam interface. These products must be evacuated through the coating and sand mold. The data shows a significant, non-linear decrease in average filling speed with increasing pattern density. A denser foam presents a greater thermal barrier and generates more gas, both of which impede metal flow. The influence is pronounced and critical for process design.
$$ v \propto \frac{1}{d} $$
where $d$ is the pattern density.
2.3 Effect of Metallostatic Pressure Head
The height of the sprue, which determines the metallostatic pressure head, provides the driving force for filling. As expected, an increase in sprue height leads to an increase in the average filling speed for the cast iron parts. The relationship appears roughly linear within the tested range. A higher head increases the pressure forcing the metal into the cavity, overcoming frictional losses and the resistance from foam decomposition.
$$ v \propto h $$
where $h$ is the metallostatic head height.
2.4 Effect of Pouring Temperature
The effect of pouring temperature on the filling speed of cast iron parts in LFC is complex and non-monotonic. Initially, as the pouring temperature increases from a lower value, the average filling speed shows an increasing trend. This is attributed to the faster thermal degradation rate of the foam pattern at higher metal temperatures, which reduces the viscous liquid residue and allows quicker metal advance. However, beyond a certain temperature (observed around the baseline in this study), further increases in pouring temperature result in a decrease in filling speed. This phenomenon is likely due to a shift in the pyrolysis mechanism of the EPS foam. At very high temperatures, the decomposition produces a greater proportion of smaller hydrocarbon molecules, increasing the volumetric gas generation rate. If this larger gas volume cannot be evacuated rapidly enough through the coating, it leads to increased pressure in the gap ahead of the metal, thereby opposing the metallostatic pressure and slowing down the filling. This results in a parabolic relationship between pouring temperature ($T$) and filling speed.
3. Multiple Linear Regression Analysis
To quantitatively determine the relationship between the key process parameters and the filling speed for cast iron parts, a multiple linear regression analysis was performed. Twenty浇注 experiments were conducted following a comprehensive matrix designed around the common operational ranges of the parameters, as detailed in Table 2.
Based on the observed influence laws, vacuum degree ($V_d$), pattern density ($d$), and metallostatic head ($h$) were treated as having linear relationships with filling speed ($v$). The parabolic influence of pouring temperature ($T$) was linearized for the regression by including both a linear ($T$) and a quadratic term ($T^2$) in the model. The general form of the regression model was:
$$ v = \beta_0 + \beta_1 V_d + \beta_2 d + \beta_3 h + \beta_4 T + \beta_5 T^2 $$
where $\beta_0, \beta_1, …, \beta_5$ are regression coefficients.
| Exp. No. | Vacuum (MPa) | Pattern Density (g/l) | Pouring Temp. (°C) | Sprue Height (cm) | Avg. Speed (cm/s) |
|---|---|---|---|---|---|
| 1 | 0.027 | 9.4 | 1400 | 20 | 19.58 |
| 2 | 0.053 | 9.4 | 1400 | 25 | 28.28 |
| 3 | 0.027 | 9.4 | 1450 | 20 | 22.22 |
| 4 | 0.053 | 9.4 | 1450 | 25 | 32.18 |
| 5 | 0.053 | 13.2 | 1450 | 20 | 23.14 |
| 6 | 0.027 | 13.2 | 1450 | 25 | 21.21 |
| 7 | 0.027 | 13.2 | 1400 | 25 | 15.38 |
| 8 | 0.027 | 13.2 | 1400 | 20 | 17.00 |
| 9 | 0.040 | 13.2 | 1400 | 20 | 19.05 |
| 10 | 0.053 | 13.2 | 1400 | 20 | 21.35 |
| 11 | 0.067 | 13.2 | 1400 | 20 | 22.99 |
| 12 | 0.053 | 13.2 | 1400 | 25 | 25.49 |
| 13 | 0.053 | 9.4 | 1340 | 20 | 19.67 |
| 14 | 0.053 | 13.2 | 1370 | 20 | 30.15 |
| 15 | 0.053 | 13.2 | 1430 | 20 | 21.51 |
| 16 | 0.053 | 13.2 | 1400 | 15 | 13.48 |
| 17 | 0.053 | 13.2 | 1400 | 10 | 12.66 |
| 18 | 0.000 | 13.2 | 1400 | 20 | 17.54 |
| 19 | 0.053 | 20.0 | 1400 | 20 | 16.84 |
| 20 | 0.053 | 25.0 | 1400 | 20 | 13.18 |
The regression analysis on the data from Table 2 yielded the following empirical formula:
$$ v = 661.967 + 153.96 \cdot V_d – 0.7632 \cdot d + 0.8074 \cdot h – 0.940321 \cdot T + 0.0003397 \cdot T^2 $$
where:
- $v$ is the average filling speed (cm/s)
- $V_d$ is the vacuum degree (MPa)
- $d$ is the pattern density (g/l)
- $h$ is the metallostatic head height (cm)
- $T$ is the pouring temperature (°C)
The significance of the regression model was evaluated using the F-test. The calculated F-value was 9.11. For a significance level $\alpha = 0.1$ with degrees of freedom (4, 15), the critical value $F_{0.1}(4,15) = 2.36$. Since $9.11 > 2.36$, the null hypothesis is rejected, confirming that the regression equation is statistically significant.
It is important to note that the coating permeability, while acknowledged as a factor, is not explicitly included in this formula. This omission stems from the current lack of a standardized, scientific method for quantifying coating permeability, especially under the high-temperature conditions pertinent to the filling of cast iron parts. Its influence, though secondary to the four main parameters studied, is not negligible. To account for it in practical calculations, the result from the empirical formula can be multiplied by a correction factor $\beta$. Based on additional浇注 experiments, $\beta$ typically ranges from 0.8 (for low-permeability coatings) to 1.1 (for high-permeability coatings). For the conditions of this study, $\beta$ was taken as 1.0.
4. Experimental Validation of the Regression Formula
To validate the predictive capability of the empirical formula, a test was conducted using a composite-density pattern. This pattern was constructed by bonding two EPS foam sections of different densities together. The objective was to compare the calculated filling speeds for each density section against the experimentally measured values within the same casting pour, thereby isolating the effect of density change. The configuration of the composite pattern and the recorded metal arrival times at various points are illustrated in the schematic.
From the experimental data for the composite pattern, the measured average filling speeds were determined to be 27.27 cm/s for the low-density section and 23.38 cm/s for the high-density section. Using the regression formula with the corresponding process parameters (vacuum, temperature, head) held constant, the calculated speeds were 28.47 cm/s and 25.56 cm/s for the low and high-density sections, respectively. The close agreement between the measured and calculated values, as summarized in Table 3, confirms the practical utility and reasonable accuracy of the derived empirical formula for estimating the filling speed of cast iron parts in lost foam casting.
| Pattern Section | Measured Speed (cm/s) | Calculated Speed (cm/s) | Deviation |
|---|---|---|---|
| Low Density | 27.27 | 28.47 | +4.4% |
| High Density | 23.38 | 25.56 | +9.3% |
5. Conclusions
1. The electrode contact method, coupled with computer data acquisition, proves to be an effective technique for monitoring the filling process in lost foam casting of cast iron parts, enabling accurate calculation of the interfacial filling speed.
2. The influence laws of the four main process parameters on the average filling speed for cast iron parts are established:
- Filling speed increases approximately linearly with increasing vacuum degree.
- Filling speed decreases significantly with increasing foam pattern density.
- Filling speed shows an increasing trend with greater metallostatic pressure head.
- The relationship with pouring temperature is parabolic, with speed initially increasing then decreasing after an optimum temperature, due to changes in foam pyrolysis products and gas generation.
3. Through multiple linear regression analysis of systematic experimental data, an empirical formula has been developed. This formula quantitatively relates the average filling speed of cast iron parts to the key parameters of vacuum degree, pattern density, pouring temperature, and metallostatic head. The formula’s significance is confirmed by statistical F-test, and its predictive accuracy is validated through independent experiments with composite-density patterns. This model provides a valuable tool for process design and optimization in the lost foam casting of cast iron parts.