In the field of dredging engineering, the pump shell is one of the most critical wear-resistant components. Its casting quality directly determines the service life of the dredging pump and the operational efficiency of the dredger. Compared with imported products, domestic pump shells often suffer from poor wear resistance, severe cavitation, low dimensional accuracy, and frequent maintenance. To solve these problems, I applied numerical simulation technology to the sand casting foundry process for the dredging pump shell. By using the software ProCAST, I was able to predict filling behavior, solidification shrinkage, and thermal stress distribution, and then optimize the gating, feeding, and chilling systems. The entire study follows a logical sequence from initial design to iterative simulation-based improvement.
Sand casting foundry is still the most economical route for producing large steel castings such as dredging pump shells. However, traditional trial-and-error approaches cannot meet the high quality requirements. In this thesis, I focus on combining theoretical casting design rules with numerical simulation to eliminate shrinkage defects and improve the overall integrity of the sand casting foundry product. The work covers gating system design, filling process simulation, solidification analysis, stress-strain prediction, and final optimization. Through this research, I demonstrate how sand casting foundry simulations can significantly reduce defects and shorten the development cycle.
1Introduction
The dredging pump shell is the core overcurrent component of a dredging pump. During operation, it is continuously eroded by sand particles, causing severe wear and cavitation. Therefore, the casting quality of the pump shell has a direct impact on the reliability and lifetime of the whole dredging equipment. In recent years, the demand for more durable and precise pump shells has grown substantially in the dredging industry. To achieve higher quality, I employed computer-aided engineering (CAE) technology to perform numerical simulations of the sand casting foundry process. Although physical experiments remain necessary, simulation can provide detailed insight into transient fluid flow, heat transfer, and solidification that cannot be easily measured in practice.
With the continuous advancement of computational methods, casting simulation has evolved from a purely academic tool into an industrial standard. The software ProCAST offers a comprehensive finite-element environment for simulating mold filling, solidification, and stress evolution. In my research, I used ProCAST together with pre-processing tools such as GeoMESH and MeshCAST. The numerical results guided me in modifying the casting design and allowed me to verify the modified process before actual production.
This thesis is organized as follows. Chapter 2 presents the gating system design for the dredging pump shell. Chapter 3 describes the filling process simulation and the final selection of the filling system. Chapter 4 covers the feeding and chilling system design. Chapter 5 discusses the solidification and stress-strain simulation results. Chapter 6 presents the optimized process and its verification. Chapter 7 summarizes the main findings and gives an outlook for future work.
2Gating System Design for the Sand Casting Foundry Process
The gating system is responsible for delivering molten steel into the mold cavity in a controlled manner. A well-designed gating system must ensure smooth and continuous filling, avoid air entrapment, promote favorable temperature gradients, and facilitate sequential solidification. In the sand casting foundry of large steel castings, the gating system also affects the pouring time, liquid-metal velocity, and the final soundness of the casting.
2.1 Design Principles and Classification
The gating system can be divided into closed, semi-open, and open systems according to the cross-sectional area ratios. For steel castings, open gating systems with large cross-sectional areas are preferred because they reduce turbulence and oxidation. According to the pouring position, gating systems are classified as top gating, bottom gating, middle gating, and step gating. Each type has its own advantages and limitations. Top gating provides a favorable temperature gradient but tends to cause splashing and oxidation. Bottom gating gives smooth filling but results in an unfavorable temperature distribution. Step gating achieves a balance between smoothness and directional solidification if designed properly.
2.2 Casting Process Analysis of the Dredging Pump Shell
The dredging pump shell is made of ZG35 medium carbon cast steel. The chemical composition is summarized in Table 1.
| Element | C | Si | Mn | S | P |
|---|---|---|---|---|---|
| Content (wt.%) | 0.32–0.42 | 0.20–0.45 | 0.50–0.80 | ≤0.04 | ≤0.04 |
The main wall thickness of the pump shell is 85 mm, with a minimum thickness of 75 mm. The maximum overall dimensions are 3595 mm × 3376 mm × 1240 mm. The minimum wall thickness is greater than the limiting thickness recommended for small steel sand castings, so the design is castable. The outer surface is equipped with multiple stiffening ribs, which prevent sand expansion defects, reduce distortion, and improve rigidity.
I first analyzed the casting process characteristics. The flange holes with a diameter of 30 mm are not cast, because they are too small for economical sand casting. However, the holes on the lifting lugs with a diameter of 60 mm are cast because they exceed the minimum castable hole size.
2.3 Two Gating System Designs
Based on the structural features and the material properties, I proposed two alternative gating systems:
- Plan 1: A multi-step gating system with an open configuration. The bottom layer has three ingates, and the upper layer has one ingate. All runners have circular cross sections.
- Plan 2: A bottom gating system with an open configuration. The bottom layer has three ingates, also with circular cross sections.
For both plans, the pouring was designed with a single ladle and a single nozzle. The nozzle diameter was chosen as 100 mm, giving an average flow rate of 195 kg/s according to standard tables. The pouring time could then be estimated using the following empirical equation used in sand casting foundry practice:
$$t = \frac{2}{3}\frac{G}{N n q}$$
where \( t \) is the pouring time (s), \( G \) is the casting weight (kg), \( N \) is the number of ladles, \( n \) is the number of nozzles per ladle, and \( q \) is the metal flow rate (kg/s). After computing \( t \), the metal rise speed can be checked using:
$$v = \frac{C}{t}$$
where \( C \) is the casting height. The rise speed should be above the minimum value given in standard tables but should not exceed 30 mm/s. The calculated rise speed for the proposed design fell within the acceptable range for a complex steel casting.
2.4 Runner Sizes
The open step gating system was designed according to the cross-sectional area ratios used in steel sand casting foundry:
$$\sum A_k : \sum A_z : \sum A_h : \sum A_n = 1 : 2 : 1.8\text{–}2.2 : 2\text{–}2.5$$
Here \( A_k \) is the controlling cross-sectional area, \( A_z \) is the area of the sprue, \( A_h \) is the area of the bottom runner, and \( A_n \) is the area of the bottom ingates. Taking the ladle nozzle area as the controlling area, I designed the initial dimensions as shown in Table 2.
| Plan | Sprue diameter (mm) | Runner diameter (mm) | Bottom ingate diameter (mm) | Upper ingate diameter (mm) |
|---|---|---|---|---|
| Plan 1 (step) | 140 | 160 | 100 | 140 |
| Plan 2 (bottom) | 140 | 160 | 120 | – |
3Filling Process Analysis of the Dredging Pump Shell
The filling process is highly transient and involves complex free-surface flow. In ProCAST, the finite element method is used to solve the continuity equation, the Navier–Stokes equation, and the energy equation.
3.1 Governing Equations
The continuity equation for an incompressible fluid can be written as:
$$\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} + \frac{\partial u_z}{\partial z} = 0$$
The momentum equation (N–S equation) in the \( x \)-direction has the form:
$$\frac{\partial (\rho u)}{\partial t} + \nabla \cdot (\rho u \mathbf{u}) = -\frac{\partial p}{\partial x} + \nabla \cdot (\mu \nabla u) + \rho g_x$$
Similarly, the energy equation is:
$$\frac{\partial (\rho c_p T)}{\partial t} + \nabla \cdot (\rho c_p \mathbf{u} T) = \nabla \cdot (\lambda \nabla T) + S$$
where \( S \) represents the latent heat source. For the filling simulation, I used the SOLA-VOF method to track the free surface. The volume-of-fluid function \( F \) satisfies:
$$\frac{\partial F}{\partial t} + \mathbf{u} \cdot \nabla F = 0$$
3.2 Three-Dimensional Modeling and Mesh Generation
I performed the three-dimensional modeling of the pump shell using the software Creo 3.0. The complex volute shape was generated with sweep mixing commands and boundary surface operations. After assembling the shell, gating system, and mold, I exported the model in STEP format. Since the ProCAST mesh module could not directly handle assembly positions, I used GeoMESH to check and repair the geometry and then exported each part in gmrst format. Finally, MeshCAST was used to generate the finite element mesh. An appropriate non-uniform mesh was generated, with finer mesh in the pump tail region and in the gating system, whereas a coarser mesh was used in the mold. This approach reduced the computational time while preserving the critical geometric details.
3.3 Material Properties and Boundary Conditions
Because ZG35 was not available in the built-in material database, I used the property calculation module in ProCAST. The liquidus temperature was 1503 °C, the solidus temperature was 1412 °C, and the latent heat was 250.8 J/g. The calculated temperature-dependent thermal conductivity, density, enthalpy, and solid fraction are shown in Figure 1 (not numbered here). The mold material was silica sand taken from the standard database.
The initial temperature of the molten steel was set to 1560 °C, while the sand mold was set to 20 °C. The pouring velocity was set to 1.0 m/s. The interface between the casting and the gating system was defined as an EQUIV interface, because they are the same material and the temperature and velocity fields remain continuous. The interface between the casting and the mold was defined as a COINC interface, with a heat transfer coefficient of \( 500\ \text{W/(m}^2\cdot\text{K)} \).
3.4 Results and Discussion for Plan 1
Figure 2 shows the filling sequence and velocity fields for the step gating system (Plan 1). At 10% filling, the molten metal entered the cavity from the bottom ingates. At 20% filling, the metal level rose steadily, but the upper ingate was about to be reached. By 30% filling, the upper ingate had already opened, and a high-speed jet entered the cavity, causing splashing and severe erosion of the mold wall. This early opening occurred because the metal level in the sprue had not yet reached the upper ingate height, meaning that the upper runner became active too soon. At 40% filling, fountains from both layers entered the cavity, but by 60% filling the metal level had reached the upper ingate, and the remaining filling became calm.
The temperature field for Plan 1 (Figure 3) indicated that after 40% filling, the bottom of the pump shell was cooler than the upper part, which is favorable for sequential solidification. When the filling was nearly complete, the shell temperature remained around 1510 °C. Thus, the overall temperature drop was small, reducing the risk of oxidation and shrinkage defects.
3.5 Results and Discussion for Plan 2
For the bottom gating system (Plan 2), the filling was smooth and calm from beginning to end. The velocity field (Figure 4) showed almost no splashing or air entrapment. However, the temperature field (Figure 5) revealed a much larger temperature drop. After filling the bottom of the cavity, the metal temperature had already fallen below 1500 °C, and in some local regions it dropped to 1420 °C. By the end of filling, the main body temperature was around 1480 °C, and some regions near the bottom had already begun to solidify. The long filling time caused severe oxidation of the molten steel surface, created oxide films, and prevented a good temperature gradient. These conditions would lead to shrinkage porosity and poor feeding during solidification.
3.6 Selection of the Gating System
Comparing the two plans, I concluded that Plan 2, despite its smooth filling, did not provide a proper temperature distribution and caused excessive cooling. Plan 1, although not perfect because of the early opening of the upper ingate, established a favorable bottom-to-top temperature gradient and kept the metal hot. Therefore, I selected the step gating system and decided to optimize its proportions. The final gating system would be redesigned with enlarged runner sections and multiple upper ingates to avoid early flow from the upper layer.
4Feeding System and Chilling System Design
During solidification, the liquid steel undergoes liquid shrinkage and solidification shrinkage. Without a proper feeding system, shrinkage cavities and porosity will form in the last-solidifying regions. The feeding system consists of risers and padding. Chilling blocks are used to accelerate local cooling and extend the effective feeding distance of the risers. This is a classic technique in sand casting foundry.
4.1 Modulus Calculation and Hot Spot Determination
The pump shell was decomposed into several simple geometric units to calculate the modulus \( M = V/A \). The modulus results are summarized in Table 3.
| Region | Description | Modulus (cm) |
|---|---|---|
| ① | Flange | 2.6 |
| ② | Rib | 5.7 |
| ③ | Side junction | 8.4 |
| ④ | Main shell wall | 4.3 |
| ⑤ | Thick plate section | 4.5 |
From these modulus values, I identified the hot spots and feeding channels. The rib (region ②) and side junction (region ③) had larger moduli and would solidify later. The shrinking sections between the hot spots required additional chilling or risers to ensure directional solidification.
4.2 Riser Design
I used the modulus method to design the risers. The riser modulus must be larger than the fed region modulus by a safety factor \( f \):
$$M_r = f \cdot M_c$$
For a plain open riser, \( f = 1.2 \). If an exothermic topping or insulating sleeve is used, a smaller riser can be adopted. The feeding capacity of a riser must also satisfy the volume condition. The maximum castable volume without defects can be estimated by:
$$V_c \leq V_r \left( \eta \frac{1}{\varepsilon} – 1 \right)$$
where \( \eta \) is the riser efficiency, and \( \varepsilon \) is the solidification shrinkage rate. For ZG35, \( \varepsilon \approx 4.5\% \).
I placed six top risers above the pump shell: one riser above region ③ and five risers above regions ④ and ⑤. The initial riser dimensions are listed in Table 4.
| Riser | Position | Type | Dimensions (diameter × height, mm) |
|---|---|---|---|
| #1 | Above side junction | Plain open riser | Φ340 × 500 |
| #2-1 to #2-5 | Above shell wall | Plain open riser | Φ260 × 400 |
4.3 Chilling System Design
Because the ribs were not directly fed by risers, external chills were placed on the ribs to avoid shrinkage defects. The weight of each chill was calculated from the heat balance equation:
$$W = \frac{(V_c – V_a) \cdot \rho (L + c \Delta T)}{c_c (T_m – T_0)}$$
where \( W \) is the chill weight, \( V_c \) is the volume of the chilled region, \( V_a \) is the adjacent region volume, \( \rho \) is the steel density, \( L \) is the latent heat, \( \Delta T \) is the superheat, \( c_c \) is the chill specific heat, \( T_m \) is the solidus temperature, and \( T_0 \) is the initial chill temperature.
For the rib region, I calculated that the required chill area was 672 cm². The ribs were divided into five chill blocks, each measuring roughly 20 cm × 10 cm × 6 cm. The weight of each block was approximately 9.36 kg. The thickness satisfied the condition for a chill with an air gap:
$$\delta_c = 0.75 \cdot t_c$$
where \( \delta_c \) is the chill thickness and \( t_c \) is the local casting thickness. The final chilling system is illustrated in the previous figure (not referenced by number).
5Solidification Process and Stress-Strain Analysis
The solidification process of the pump shell was simulated with the same finite element mesh. I employed the Niyama criterion to predict shrinkage porosity:
$$Niyama = \frac{G}{\sqrt{R}} < C_{Niyama}$$
where \( G \) is the temperature gradient and \( R \) is the cooling rate. For cast steel, a typical critical value is \( 1\ \text{K}^{1/2}\text{mm}^{-1/2}\text{s}^{-1/2} \). The governing heat conduction equation is given by:
$$\rho c_p \frac{\partial T}{\partial t} = \lambda \nabla^2 T + \dot{Q}$$
The latent heat was treated using the enthalpy method. For the stress analysis, I applied a thermal elastic-plastic constitutive model. The total strain increment is the sum of elastic, plastic, and thermal increments:
$$d\varepsilon_{\text{total}} = d\varepsilon_e + d\varepsilon_p + d\varepsilon_T$$
The elastic stress-strain relation is:
$$d\sigma = \mathbf{D}_e (d\varepsilon_{\text{total}} – d\varepsilon_p – d\varepsilon_T)$$
The temperature-dependent mechanical properties of ZG35, including Young’s modulus, yield stress, Poisson’s ratio, and plastic modulus, were calculated using the ProCAST property database.
5.1 Temperature Field Results
Figure 6 shows the temperature distribution during solidification. At 20% solidification, the rib regions had already dropped below the solidus due to the chills. At 50% solidification, the bottom and the flange were solidifying, while the upper parts remained hot. However, the temperature distribution was not truly directional. The internal regions of the pump shell cooled more slowly than the external parts because the inner sand mold retained heat. At 70% solidification, multiple isolated liquid regions were observed, especially between risers #2-1 and #2-2, where the feeding distance was too large. The riser necks of #1 and #2-1 solidified earlier than the riser centers, indicating premature closure of the feeding path.
Figure 7 shows the solid fraction evolution. The chills efficiently accelerated the solidification of the ribs. However, the bottom region contained more liquid at later stages than the upper part, because the bottom gating had already filled with cooler metal. Thus, the initial process did not achieve a smooth bottom-to-top solidification sequence.
5.2 Shrinkage Porosity Prediction
The simulated shrinkage defects are shown in Figure 8. The defects were primarily located in the risers and in the gating system, as expected. However, shrinkage porosity also appeared in the main body, particularly near the bottom and under the flange. The reason is that the risers #1 and #2-1 lost their feed path early. The bottom isolated liquid regions could not be compensated, leading to micro-porosity.
The ribs themselves were free of defects because the chills were effective. This verified the rationality of the chilling design. Nevertheless, the overall feeding system required improvement.
5.3 Stress and Strain Results
Figure 9 shows the equivalent stress distribution after solidification. The highest stresses appeared at the transition between the flange and the cylindrical pipe wall. Because these two sections have different thicknesses, they cool at different rates. The thin sand core at the junction creates a sharp temperature gradient and stress concentration. The equivalent stress exceeded the yield stress of ZG35 in that region, indicating a high risk of hot tearing. The deformation map (Figure 10) also showed a large displacement at the flange, confirming that the differential cooling caused distortion.
From these results, I concluded that the original gating, feeding, and chilling systems needed optimization. The riser neck should be redesigned to delay its solidification, and additional chills should be placed beneath the flange and between widely spaced risers to extend the feeding distance.
6Casting Process Optimization
Based on the simulation results, I optimized the sand casting foundry process in several ways. First, I increased the number of upper ingates from one to two and redesigned them as inclined upward channels. I also enlarged the total cross-sectional area of the runners to reduce the filling time and the temperature drop. The modified gating system dimensions are given in Table 5.
| Component | Diameter (mm) |
|---|---|
| Sprue | 150 |
| Bottom runner | 160 |
| Bottom ingates | 110 |
| Upper runner | 160 |
| Upper ingates | 130 |
Second, I replaced the plain risers with insulating risers using low thermal conductivity sleeves, and added heat-generating (exothermic) topping powder on the free surface. This reduced the heat loss and increased the feeding efficiency. I also added padding under risers #1 and #2-1 to enlarge the feeding distance and prevent premature closure of the riser neck.
Third, I added more chills to the bottom of the pump shell and under the flange. I placed chills between risers #2-2 and #2-3 to create artificial end zones, thereby shortening the effective feeding distance and avoiding mid-span shrinkage. The optimized chilling system is shown in Figure 11.
6.1 Filling Simulation of the Optimized Process
Figure 12 shows the velocity field for the optimized gating system. At 20% filling, the molten steel entered from the bottom ingates only, and the liquid surface rose smoothly. At 55% filling, the metal level reached the upper ingates, which then started to deliver metal into the cavity. The bottom ingates essentially closed because the dynamic pressure pushed the metal upward. At 75% and 90% filling, only the upper ingates were active, giving a true step-wise filling behavior. No splashing or severe turbulence was observed.
The temperature field for the optimized process (Figure 13) showed a clear bottom-to-top increase in temperature. At the end of filling, the shell temperature remained above 1520 °C, and the temperature drop was very small. This is exactly what is desired in a sand casting foundry for sound solidification.
6.2 Solidification Simulation of the Optimized Process
The temperature field during solidification is shown in Figure 14. The chills on the ribs and at the bottom caused those regions to solidify first. The flange bottom also solidified quickly due to the additional chills. At 50% solidification, a clear temperature gradient from the bottom to the top was established. The riser neck and the padding remained hot, allowing the risers to feed properly. At 70% solidification, the isolated liquid regions were mostly connected to their respective risers. At 85% solidification, the casting body was almost fully solid, while the riser centers were still liquid, but the riser necks had already closed. This indicates that feeding was completed successfully.
The solid fraction distribution in Figure 15 confirms that the ribs solidified early, and the intermediate region between risers #2-2 and #2-3 solidified in a controlled manner. No isolated liquid pools remained at the end of solidification.
6.3 Defect Prediction after Optimization
Figure 16 shows the shrinkage porosity predicted by the Niyama criterion after optimization. The porosity is confined to the risers and the ingates. The main body of the pump shell is free of shrinkage defects. The flange, rib, and bottom regions are all sound. This demonstrates that the optimized sand casting foundry process effectively eliminated the defects found in the original design.
7Conclusions and Outlook
In this thesis, I carried out a systematic numerical simulation and optimization study of the sand casting foundry process for a dredging pump shell. The main conclusions can be summarized as follows:
- Through casting process analysis, I proposed two gating systems: a step gating system and a bottom gating system. I calculated the pouring time, metal rise speed, and runner dimensions using standard formulas for steel sand casting. The step gating system was selected after comparing the filling simulation results, because it provided a favorable temperature gradient and smaller temperature loss.
- I designed a feeding system with six risers and a chilling system with multiple external chills. The initial simulation revealed that the riser feeding distance was insufficient and that the riser necks solidified too early. Several isolated liquid regions formed, leading to shrinkage porosity in the lower part and under the flange.
- Stress-strain simulation showed that large equivalent stress and deformation occurred at the flange-pipe transition due to unequal wall thickness and differential cooling. This risk was mitigated by adding chills and optimizing the riser neck design.
- After optimizing the gating system, using insulating risers, adding padding and extra chills, and applying exothermic topping, the second simulation confirmed that all major shrinkage defects were eliminated. The filling process became well ordered, sequential solidification was achieved, and the casting quality was significantly improved.
For future work, I intend to perform microstructural simulation to predict grain size and mechanical properties. I also plan to validate the simulation results with actual pouring trials. The heat transfer coefficients and material property data need to be further refined by experimental measurements. Moreover, the influence of pouring temperature and casting speed should be studied more systematically. With the continuous advancement of computational resources, sand casting foundry simulation will become even more accurate and will help engineers design high-quality castings with shorter lead times and lower cost.