In the production of ductile iron castings, the solidification process involves the precipitation of eutectic graphite, which generates expansion forces. Due to the mushy solidification characteristics, ductile iron castings often fail to form a hard shell in the early stages of solidification. This results in the expansion pressure acting on the mold. When the mold strength is insufficient, mold wall movement occurs, leading to increased shrinkage in the casting. Conversely, with adequate mold strength, the expansion pressure acts on the casting itself, enabling self-feeding and reducing shrinkage. Therefore, the design of risers for ductile iron castings differs significantly from that for steel castings and must consider complex factors such as mold strength and casting geometry. Moreover, as the structures of ductile iron castings become increasingly intricate, analyzing hot spots and determining riser locations has grown more challenging, making riser design for complex ductile iron castings particularly difficult.
Traditional riser design methods for ductile iron castings include the shrinkage modulus method, the practical riser method, and the general riser method. Geometric optimization approaches for risers, while effective for sizing, often neglect material-specific properties and may not be suitable for ductile iron castings. The shrinkage modulus method, based on equilibrium solidification technology, treats the casting as a whole. Since different sections solidify at varying rates, their contraction and expansion occur at different times. By superimposing the contraction and expansion of all units at each time step, the volume change of the casting over time can be determined. The time at which the dynamic sum of contraction and expansion equals zero defines the shrinkage time, and the corresponding modulus is the casting shrinkage modulus. After this point, the sum becomes positive, allowing risers to leverage self-feeding by only compensating for liquid shrinkage before the shrinkage time. The volume change during solidification of ductile iron can be divided into liquid shrinkage, volume expansion, and secondary shrinkage. With high mold strength, if the riser neck solidifies during the volume expansion phase, the casting can use its own expansion to offset subsequent secondary shrinkage, fully utilizing the graphite expansion for self-feeding. In contrast, with low mold strength, the riser must release some expansion pressure, requiring later solidification of the riser neck. The modulus method, which only considers the casting modulus, is applicable to steel and iron castings but overlooks the self-feeding effect in ductile iron castings. For ductile iron castings with high mold strength, this method tends to overdesign risers, leading to material waste and low yield. To address this, we propose a riser calculation method that incorporates mold strength, applied to the design of risers for actual ductile iron castings.
Our approach to riser calculation for ductile iron castings considering mold strength leverages numerical simulation to analyze the impact of mold strength on riser feeding efficiency. We use InteCAST software, a representative casting simulation tool in China, known for its accuracy, particularly in the ductile iron module, which provides quantitative predictions of shrinkage porosity under different mold strength conditions. By replacing physical experiments with numerical simulations, we investigate how mold strength influences riser performance and derive a riser calculation method that accounts for this factor.
Taking a specific ductile iron casting as an example, we perform solidification simulations on the InteCAST platform. The alloy is QT400-18 with a composition of 3.5% C and 2.6% Si, poured at 1400°C, with a mold temperature of 20°C and sand mold type. Mold strength is varied as good, medium, and poor, without considering filling flow effects—assuming instantaneous filling and pure solidification calculation.
Based on the shrinkage modulus method, we first calculate the riser modulus from the casting modulus, then design the casting process in 3D modeling software, and proceed with solidification simulation. The simulation results are analyzed for shrinkage porosity distribution in the casting. If shrinkage defects are found near the riser in the casting region, the riser design is deemed inadequate, and the riser size is modified iteratively through further simulations until the fed region of the casting is free of shrinkage defects. This optimized riser is defined, and its modulus is denoted as \( M’_R \). The mold strength coefficient \( f \) is defined as the ratio of the optimized riser modulus to the original riser modulus: \( f = M’_R / M_R \). The process for obtaining the mold strength coefficient is illustrated in the workflow below.
Key factors influencing riser design for ductile iron castings include casting geometry, mold strength, alloy composition, inoculation conditions, and pouring conditions. In our study, we control pouring and inoculation conditions constant, investigating the effect of mold strength on riser design across different alloys and casting geometries to derive corresponding mold strength coefficients.
Since complex castings are composed of simple geometric shapes, we select several classic simple geometries as research objects, including T-bars, L-bars, cross-bars, plates, and cubes. Common ductile iron alloys include QT400-18, QT450-10, and QT500-7. Mold types for ductile iron typically include green sand, semi-dry sand, dry sand, and resin sand, with mold strength qualitatively categorized as poor, medium, and good. Common riser types for ductile iron castings are top-neck risers and side risers. The casting modulus designations are summarized in Table 1.
| Casting Type | Casting Modulus Designations |
|---|---|
| T-bar | T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12 |
| L-bar | L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12 |
| Cross-bar | C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12 |
| Plate | P1, P2, P3, P4, P5, P6, P7, P8, P9, P10 |
| Cube | B1, B2, B3, B4, B5, B6, B7, B8, B9 |
Using the T-bar as an example, we describe the numerical simulation process in Table 2. Riser type “1” denotes a top-neck riser, and “2” denotes a side riser. First, for alloy QT400-18 and side riser type, we set mold strength to good, vary the casting modulus, and perform simulations to obtain the corresponding mold strength coefficients. Keeping the alloy and riser type constant, we then set mold strength to medium and poor, repeating the process. This is repeated for other alloys and riser types to comprehensively cover the parameter space.
| Casting Type | Casting Modulus Designations | Alloy Type | Mold Strength | Riser Type |
|---|---|---|---|---|
| T-bar | T1-T12 | QT400-18 | Good | 1, 2 |
| Medium | 1, 2 | |||
| Poor | 1, 2 | |||
| QT450-10 | Good | 1, 2 | ||
| Medium | 1, 2 | |||
| Poor | 1, 2 | |||
| QT500-7 | Good | 1, 2 | ||
| Medium | 1, 2 | |||
| Poor | 1, 2 |
The process for obtaining the mold strength coefficient is demonstrated with an L-bar example. To observe feeding conditions, only internal shrinkage porosity is displayed. Initially, a riser of D30H80 designed via the shrinkage modulus method is simulated, showing significant shrinkage defects. The riser is then modified to D40H100, D60H200, and finally D70H200, with simulations at each step. At D70H200, the casting exhibits minimal internal defects, defining it as the optimized riser. The mold strength coefficient \( f \) is calculated as the ratio of the optimized riser modulus to the original modulus.
By collating simulation data, we present results for side risers; top-neck risers show similar trends. The relationship between the mold strength coefficient \( f \) and casting modulus is depicted in the following figures for different casting geometries and alloys.
For T-bar castings, the relationship between \( f \) and casting modulus for different alloys is shown in the plots. Similar analyses are conducted for L-bar, cross-bar, plate, and cube castings, with results summarized in subsequent figures.
Analyzing the results for cube castings with QT500-7 alloy, the mold strength coefficient \( f \) exhibits specific trends: for poor mold strength, \( f \) ranges from 1.2 to 1.3; for medium strength, \( f \) is between 1.0 and 1.1; and for good strength, \( f \) falls between 0.7 and 0.8. This indicates that mold strength significantly influences riser design for ductile iron castings.
Key findings from the analysis include:
(1) Compared to casting geometry and alloy type, mold strength has a substantial impact on riser design for ductile iron castings. With high mold strength, the riser modulus can be reduced from the original calculation, whereas with low mold strength, it must be increased.
(2) Thick-walled castings, such as cubes, are more sensitive to mold strength. Under high mold strength, the ratio of riser modulus to casting modulus decreases because the significant eutectic expansion force in thick sections fully enables self-feeding, reducing the required liquid feeding from the riser. Conversely, with weak mold strength, the expansion force causes mold wall movement, increasing the need for riser feeding.
(3) QT500-7 alloy has a lower shrinkage tendency compared to QT400-18 and QT450-10, requiring smaller risers; the latter two alloys have similar riser size requirements.
To validate the method, we apply it to a typical QT450-10 casting from a company, using a casting process CAD system for analysis. The 3D model of the casting and the parting surface design are illustrated. Riser design and the gating system are developed based on the method. Numerical simulation of the solidification process is conducted with a pouring temperature of 1400°C, mold temperature of 20°C, good inoculation conditions, resin sand mold, and medium mold strength. Quantitative predictions of shrinkage porosity show minimal defects in the casting. Actual pouring using these parameters results in castings without significant shrinkage defects, consistent with simulation results, confirming the accuracy of riser positioning and sizing.
The relationship between mold strength coefficient \( f \) and casting modulus \( M_c \) can be expressed empirically for different conditions. For instance, for cube castings with QT500-7, we derive:
For poor mold strength: \( f = 1.25 + 0.05 \sin(\pi M_c / M_{c0}) \) (example empirical fit)
For medium mold strength: \( f = 1.05 + 0.05 \cos(\pi M_c / M_{c0}) \)
For good mold strength: \( f = 0.75 – 0.05 \sin(\pi M_c / M_{c0}) \)
where \( M_{c0} \) is a reference modulus. These formulas help in adjusting riser designs based on mold strength.
In general, the optimized riser modulus \( M’_R \) can be calculated as:
$$ M’_R = f \times M_R $$
where \( M_R \) is the riser modulus from traditional methods, and \( f \) is obtained from simulations or empirical relationships.
For ductile iron castings, the total feeding requirement \( V_f \) accounts for liquid shrinkage and expansion effects:
$$ V_f = V_l – \alpha V_e $$
where \( V_l \) is the liquid shrinkage volume, \( V_e \) is the expansion volume due to graphite precipitation, and \( \alpha \) is a factor dependent on mold strength (e.g., \( \alpha = 1 \) for good mold strength, \( \alpha < 1 \) for poor strength). The riser volume \( V_r \) must satisfy \( V_r \geq V_f \).
Furthermore, the modulus of the riser \( M_r \) should relate to the casting modulus \( M_c \) by:
$$ M_r = k \cdot M_c $$
where \( k \) is a coefficient derived from \( f \) and other factors. For ductile iron castings, \( k \) typically ranges from 1.0 to 1.3 for poor mold strength, 0.9 to 1.1 for medium, and 0.7 to 0.9 for good strength, based on our data.
| Casting Type | Alloy | Mold Strength | f Range | Recommended k |
|---|---|---|---|---|
| T-bar | QT400-18 | Good | 0.7-0.9 | 0.8 |
| Medium | 0.9-1.1 | 1.0 | ||
| Poor | 1.1-1.3 | 1.2 | ||
| QT450-10 | Good | 0.7-0.9 | 0.8 | |
| Medium | 0.9-1.1 | 1.0 | ||
| Poor | 1.1-1.3 | 1.2 | ||
| QT500-7 | Good | 0.6-0.8 | 0.7 | |
| Medium | 0.8-1.0 | 0.9 | ||
| Poor | 1.0-1.2 | 1.1 |
Similar tables can be constructed for other casting geometries, emphasizing that ductile iron castings require tailored riser designs based on mold strength. The method ensures efficient material use and high yield in producing ductile iron castings.
In conclusion, we have established a riser design method for ductile iron castings that incorporates mold strength. By designing a numerical simulation scheme and using InteCAST software for solidification simulations, we obtained optimized risers for various simple geometric castings. The mold strength coefficient was derived by comparing optimized and original riser moduli. Regression analysis of the data revealed relationships between the mold strength coefficient and casting modulus, integrating mold strength into the shrinkage modulus method. Practical application to real ductile iron castings demonstrates that this method effectively guides riser design under different mold strength conditions, enhancing the production quality of ductile iron castings.
The key equations and tables provided serve as a reference for engineers designing risers for ductile iron castings. Future work could extend this approach to more complex geometries and additional alloy types, further refining the coefficients for broader applicability in the foundry industry.