In the modern manufacturing environment, sand casting foundry remains the backbone of producing large and complex metal components, particularly for machine tool structures. This paper focuses on the research of a sliding seat used in a machine tool, which is a critical component that directly affects machining accuracy, stability, and service life. The work presented here integrates advanced casting process simulation with additive and subtractive manufacturing technologies to optimize the sand casting foundry process, reduce defects, and achieve rapid mold production. The primary metal material used is HT250 gray cast iron, selected for its excellent castability, damping capacity, and strength-to-cost ratio. Three gating systems—top gating, parting gate (middle injection), and bottom gating—were designed and evaluated using ProCAST software. The parting gate system was found to offer the most stable filling and minimal shrinkage defects. Subsequent process optimization, including the addition of chills, insulating risers, and venting holes, reduced the predicted shrinkage porosity volume from 132.58 cm³ to 1.42 cm³. To further improve quality, orthogonal experiments were conducted to optimize pouring temperature, pouring time, and sand mold preheating temperature. The optimal parameters were determined as: pouring temperature 1440 °C, pouring time 26 s, and sand mold preheating temperature 510 °C. This combination reduced the predicted, residual stress, and deformation to minimum levels. In parallel, the mold was fabricated using a hybrid approach: the upper sand mold was produced by 3D printing (binder jetting), while the lower sand mold was machined by CNC milling. This hybrid additive-subtractive method significantly shortened the production cycle and lowered costs compared to traditional pattern-based mold making. The entire workflow—from simulation to mold manufacturing—demonstrates a digitalized, efficient, and sustainable route for sand casting foundry production of machine tool components.
1. Introduction and Research Background
Sand casting foundry processes are widely used to manufacture machine tool components such as beds, columns, and sliding seats. The sliding seat of a machine tool is a core functional part that supports the worktable, transmits cutting forces, and ensures precise motion. Its quality directly determines the machining precision, stability, and durability of the machine tool. However, the traditional sand casting foundry route faces several challenges, including long tooling lead times, high costs for small-batch production, and environmental concerns. Moreover, predicting casting defects such as shrinkage porosity, residual stress, and deformation is difficult without advanced simulation tools. The conventional trial-and-error approach is both time-consuming and expensive, especially for complex castings with variable wall thicknesses and internal ribs.
To overcome these limitations, this research adopts a comprehensive methodology that combines numerical simulation with additive and subtractive manufacturing. The investigation focuses on a sliding seat with overall dimensions of 1510 mm × 445 mm × 516 mm and a net weight of 305.68 kg. The cast structure has wall thicknesses ranging from 18 mm to 45 mm, which creates thermal gradients and potential hot spots. By using ProCAST, a finite element-based casting simulation package, the filling, solidification, and defect formation during the sand casting foundry process were analyzed. The results guided the design of an optimized gating system and feeding strategy. Furthermore, the mold was produced directly from CAD data using a hybrid approach, eliminating the need for traditional wooden or metal patterns. This paper presents a complete digital workflow for the sand casting foundry production of a high-quality machine tool sliding seat.
2. Casting Process Design and Theoretical Basis
2.1 Casting Process Analysis of the Sliding Seat
The sliding seat is a gray cast iron component. Due to its moderate size and relatively uniform wall thickness, it falls into the category of medium-small castings. The material HT250 was selected because of its good combination of strength, machinability, and damping properties. Table 1 lists the typical chemical composition of HT250.
| C | Si | Mn | S | P |
|---|---|---|---|---|
| 3.16–3.30 | 1.79–1.93 | 0.89–1.04 | 0.094–0.125 | 0.120–0.170 |
According to the casting shrinkage rules for gray iron in sand casting foundry, the casting shrinkage rate was set to 1% for free contraction and 0.9% for restrained contraction; a value of 1% was adopted. The machining allowance was determined to be 2 mm based on the casting tolerance standard GB/T6414-1999. Holes smaller than 50 mm in diameter were not cast but left for subsequent machining, while larger holes were directly formed during casting.
2.2 Design of Three Gating Systems
The gating system is a critical part of the sand casting foundry process; about 30% of casting defects are caused by improper gating design. In this work, three types of gating systems were designed based on the location of the ingate: top gating, parting gate (middle injection), and bottom gating. Each system consists of a pouring cup, sprue, well, runner, and ingates. The designs are illustrated conceptually in the following, but the actual CAD models were used for simulation.
For the top gating system, the molten metal enters from the top of the casting; it can easily fill thin sections and promote directional solidification, but it may cause splashing and oxidation. The bottom gating system introduces metal from the bottom, providing smooth filling, but it tends to create an unfavorable temperature gradient. The parting gate system, located at the middle height of the casting, combines the advantages of both top and bottom gating and is suitable for medium-wall-thickness castings.
2.3 Thermal-Physical and Thermodynamic Parameters
The Scheil model in ProCAST was used to calculate temperature-dependent properties of HT250. The solidus temperature was found to be 1146 °C and the liquidus temperature 1220 °C. The thermal conductivity, viscosity, solid fraction, enthalpy, and density as functions of temperature were extracted from the simulation database. For the stress analysis, key thermodynamic parameters such as thermal expansion coefficient, Young’s modulus, Poisson’s ratio, and yield stress were also obtained. Figures showing these curves were analyzed but are not reproduced here; the critical values were used as input data.
2.4 Pouring Process Parameters
Based on the main wall thickness of 18 mm, the recommended pouring temperature for HT250 gray cast iron is 1370–1440 °C. In this study, 1380 °C was initially selected for the comparative simulation. The pouring time was calculated using the empirical formula for gray cast iron:
$$t = S_1 \sqrt{G\delta} \tag{1}$$
where \(G\) is the total pouring weight (including gating and risers) equal to 452.7 kg, \(\delta\) is the main wall thickness (18 mm), and \(S_1\) is a coefficient taken as 1.2 for thick-walled castings with high quality requirements. Substituting these values gives:
$$t = 1.2 \sqrt{452.7 \times 18} \approx 24 \, \text{s} \tag{2}$$
The pouring time of 24 s was checked by calculating the liquid level rise rate:
$$v = \frac{h}{t} = \frac{288}{24} = 12 \, \text{mm/s} \tag{3}$$
Since the minimum recommended rise rate for a wall thickness of 18 mm is 10 mm/s, the computed value is acceptable. The sand mold preheating temperature was determined by:
$$T_{\text{mold}} = \frac{1}{3} T_{\text{pour}} \mp T_{\text{correction}} \tag{4}$$
With a correction factor of 30 °C, the preheating range was 430–510 °C; an initial value of 450 °C was used in the base simulation.
2.5 Numerical Simulation Theoretical Models
The filling process of molten metal follows the conservation laws of mass, momentum, and energy. The continuity equation for an incompressible fluid is:
$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 \tag{5}$$
The Navier-Stokes equations in the three coordinate directions are:
$$\rho \left( \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z} \right) = -\frac{\partial p}{\partial x} + \mu \nabla^2 u + \rho g_x \tag{6}$$
$$\rho \left( \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} \right) = -\frac{\partial p}{\partial y} + \mu \nabla^2 v + \rho g_y \tag{7}$$
$$\rho \left( \frac{\partial w}{\partial t} + u \frac{\partial w}{\partial x} + v \frac{\partial w}{\partial y} + w \frac{\partial w}{\partial z} \right) = -\frac{\partial p}{\partial z} + \mu \nabla^2 w + \rho g_z \tag{8}$$
The energy conservation equation is:
$$\rho c \left( \frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z} \right) = k \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + S \tag{9}$$
where \(T\) is temperature, \(c\) is specific heat, \(k\) is thermal conductivity, and \(S\) is the internal heat source. The volume of fluid function \(F\) tracks the free surface:
$$\frac{\partial F}{\partial t} + u \frac{\partial F}{\partial x} + v \frac{\partial F}{\partial y} + w \frac{\partial F}{\partial z} = 0 \tag{10}$$
During solidification, heat transfer occurs by conduction, convection, and radiation. The governing heat conduction equation is:
$$\rho c \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( \lambda \frac{\partial T}{\partial y} \right) + \frac{\partial}{\partial z} \left( \lambda \frac{\partial T}{\partial z} \right) + Q \tag{11}$$
For the prediction of shrinkage porosity, the POROS criterion in ProCAST was used because it is more suitable for gray cast iron than the Niyama criterion, which is primarily calibrated for steel. The Niyama parameter is defined as:
$$Niyama = \frac{G}{\sqrt{R}} \tag{12}$$
where \(G\) is the local temperature gradient and \(R\) is the cooling rate. However, for gray iron, the POROS model (POROS=1) was selected, which accounts for micro-porosity and macro-porosity coupling and pipe shrinkage. A porosity value above 0.01 is considered macro-porosity, while below 0.01 is micro-porosity.
For stress analysis, the elastoplastic model was used. The von Mises equivalent stress is:
$$\bar{\sigma} = \frac{1}{\sqrt{2}} \sqrt{(\sigma_1 – \sigma_2)^2 + (\sigma_2 – \sigma_3)^2 + (\sigma_3 – \sigma_1)^2} \tag{13}$$
The total strain was decomposed into elastic, plastic, and thermal components:
$$\{\varepsilon\} = \{\varepsilon_e\} + \{\varepsilon_p\} + \{\varepsilon_t\} \tag{14}$$
The thermal strain increment is given by:
$$\{\Delta \varepsilon_t\} = \alpha \Delta T + \left( \frac{\partial \alpha}{\partial T} (T – T_0) – \frac{1}{E} \frac{\partial E}{\partial T} \{\sigma\} \right) \Delta T \tag{15}$$
These models were implemented in the ProCAST solver to simulate the casting process.
3. Simulation of Three Gating Systems and Comparison
3.1 Model Setup and Boundary Conditions
The 3D models of the sliding seat with each gating system were imported into ProCAST. The sand mold dimensions were set to 1780 mm × 765 mm × 390 mm. Mesh sizes were 5 mm for the casting and gating system, and 20 mm for the sand mold. The boundary conditions are listed in Table 2.
| Parameter | Value |
|---|---|
| Pouring direction | Gravity, 9.8 m/s² |
| Metal material | HT250 |
| Mold material | Resin-bonded sand |
| Chill material | Steel |
| Pouring temperature | 1380 °C |
| Pouring time | 24 s |
| Sand mold preheating | 450 °C |
| Interface heat transfer (casting/mold) | 500 W/(m²·K) |
| Interface heat transfer (casting/chill) | 2000 W/(m²·K) |
| Interface heat transfer (mold/chill) | 500 W/(m²·K) |
| External boundary condition | Air cooling, h=10 W/(m²·K), T=20 °C |
3.2 Filling Process Simulation Results
The filling behavior at different percentages of the mold volume was monitored. For the top gating system, the molten metal entered from the top and initially produced slight splashing and turbulence. At 50% filling, the flow became more stable, and at 100% the mold was completely filled. However, the initial instability could cause sand erosion and gas entrapment.
The parting gate system showed smooth and stable filling throughout the entire process. The liquid level rose uniformly without splashing or vortex formation. At 25% filling, the metal flowed from the middle to the bottom; at 50%, the bottom was filled and the metal began filling the upper section; at 100%, the mold was completely filled without any misruns or cold shuts. This behavior was considered the most favorable.
The bottom gating system exhibited the smoothest filling, as expected, with no turbulence. However, the temperature distribution was less favorable for directional solidification because the bottom remained hotter than the top, which can reduce riser efficiency.
3.3 Solidification Process Simulation Results
The solidification sequence was visualized by tracking the solid fraction at 25%, 50%, 75%, and 100% solidification. For all three systems, thin sections solidified first, while the thicker bottom sections remained liquid longer. At 75% solidification, hot spots were evident at the thick walls and the important machined surface at the top. At 100% solidification, shrinkage porosity was clearly predicted at those regions. The bottom gating system had the longest total solidification time because of the higher temperature maintained at the bottom. The parting gate system exhibited a solidification pattern intermediate between top and bottom gating.
3.4 Shrinkage Porosity Prediction
The shrinkage porosity volumes predicted by ProCAST for the three gating systems are summarized in Table 3.
| Gating System | Shrinkage Porosity Volume (cm³) |
|---|---|
| Top gating | 147.20 |
| Parting gate | 132.58 |
| Bottom gating | 136.43 |
The parting gate system produced the smallest shrinkage porosity volume and also provided stable filling. Therefore, it was selected as the optimal gating system for further optimization. The defects mainly concentrated at the thick-walled areas and on the important machined surfaces, where the solidification was slow and no liquid metal supply was available.
4. Casting Process Optimization
4.1 Optimization Measures
To eliminate shrinkage defects, several measures were implemented while maintaining the parting gate system:
- Chills: Steel chills of 10–15 mm thickness were placed on the thick-walled sections to accelerate cooling and reduce hot spots.
- Insulating risers: Four insulating risers were placed on the important machined surfaces to provide molten metal feed during solidification and to collect slag and gases.
- Venting holes: Vent holes were added at the highest points of the casting to allow mold gases to escape, preventing gas porosity and misruns.
The optimized 3D model was then re-simulated using the same boundary conditions.
4.2 Simulation Results of the Optimized Process
The filling process of the optimized model showed smooth and stable advance of the molten metal, with no turbulence, splashing, or entrapment. The temperature remained above the liquidus temperature until the mold was completely filled, ensuring no cold shuts or misruns.
The solidification process was significantly improved. The chills accelerated cooling at the thick sections, while the risers provided feeding to the hot spots. The casting solidified from the bottom upward, and the risers solidified last, satisfying the principle of directional solidification.
The predicted shrinkage porosity volume after optimization is presented in Table 4, along with the residual stress and deformation.
| Condition | Shrinkage Porosity Volume (cm³) | Residual Stress (MPa) | Deformation (mm) |
|---|---|---|---|
| Before optimization | 132.58 | 1351.1 | 2.32 |
| After optimization | 1.42 | 1351.1 | 2.32 |
It is important to note that the residual stress and deformation values were not initially separately optimized in the first stage; these were addressed later through the orthogonal experiment. The shrinkage porosity reduced drastically from 132.58 cm³ to 1.42 cm³, confirming the effectiveness of chills, risers, and venting. The small remaining porosity is below the macro-porosity threshold and does not impair the mechanical performance of the casting.
5. Rapid Mold Manufacturing Using Additive and Subtractive Technologies
After the casting process was optimized, the mold needed to be manufactured. Traditional sand casting foundry relies on patterns, which are expensive and time-consuming for single-piece or small-batch production. To overcome this, we adopted a hybrid digital manufacturing approach. The upper sand mold was fabricated by 3D printing (binder jetting), while the lower sand mold was made by CNC milling. This combination is often referred to as additive/subtractive composite manufacturing.
5.1 Selection of Sand Materials and Testing
The sand used for 3D printing was a 70/140 mesh silica sand, selected based on particle size distribution analysis. Figure below shows a typical example of resin-bonded sand molds produced for casting applications. We inserted a representative image from our manufacturing partners, illustrating the sand mold production.
Three types of silica sand were analyzed using scanning electron microscopy. The particle size distributions are shown in Table 5.
| Particle Size (μm) | Standard Sample (%) | Sample 1 (%) | Sample 2 (%) |
|---|---|---|---|
| 75 | 0.25 | 0.11 | 0 |
| 100 | 1.26 | 0.64 | 0.05 |
| 200 | 39.98 | 29.89 | 4.50 |
| 300 | 86.22 | 73.52 | 31.43 |
| 400 | 98.79 | 93.36 | 68.13 |
| 500 | 99.96 | 98.85 | 89.63 |
| 600 | 100 | 99.91 | 97.89 |
The standard sample with a finer and more uniform distribution was selected. Furan resin was used as the binder, with a proprietary sulfonic acid curing agent. Table 6 lists the specifications of the resin.
| Property | Value |
|---|---|
| Appearance | Brown-red transparent liquid |
| Density (20 °C) | 1.10–1.20 g/cm³ |
| Viscosity (20 °C) | 13.5–17.0 mPa·s |
| Free formaldehyde | ≤0.2% |
| PH | 6.0–7.5 |
Standard test specimens were 3D printed and tested for strength, permeability, and gas evolution. Table 7 summarizes the test results compared with the required indicators.
| Property | Required | Test Result |
|---|---|---|
| Tensile strength (MPa) | >1.5 | 2.465 |
| Compressive strength (MPa) | >3.5 | 4.093 |
| Shear strength (MPa) | >1.5 | 1.820 |
| Permeability | 160 | 160.8 |
| Gas evolution (ml/g) | <12 | 10.0 |
The test results all meet the requirements, confirming the suitability of the selected materials for the sand casting foundry process.
5.2 Mold Design and Parting
The mold was designed in a vertical parting manner. The upper sand mold contained the risers and upper cavity, while the lower sand mold contained the lower cavity and the bottom part of the gating system. The mold outer dimensions were 1780 mm × 765 mm × 389 mm. The casting was oriented such that the important machined surface was at the top for better feeding.
5.3 3D Printing of the Upper Sand Mold
The upper sand mold had undercuts and complex features that made CNC milling difficult. Therefore, it was produced using a large-format sand 3D printer (model LSMP2000) with a working volume of 2000 mm × 1000 mm × 800 mm. The process workflow is as follows:
- The STL file of the upper mold was imported into Materialise Magics for orientation and support-free layout.
- The sliced data were transferred to the printer control software. The printing layer thickness was 0.3 mm, resolution 360 dpi, and the print head width was 1000 mm.
- The total number of layers was 951, with an estimated printing time of 6.56 hours.
- After printing, the mold was left to cure for several hours to allow complete polymerization of the resin.
The printed upper sand mold was visually inspected and found to be complete without any printing defects. Coating was applied to the cavity surface to improve the surface finish and refractoriness.
5.4 CNC Milling of the Lower Sand Mold
The lower sand mold had a simpler geometry without undercuts, so it was machined from a preformed sand block using a digital die-less casting precision forming machine. The machine has a working travel of 3000 mm × 1500 mm × 900 mm. Three tools were selected: a D50 face mill for planar machining, a D20 end mill for roughing, and a B8 ball-end mill for finishing. The tool path and G-code were generated in UG NX. The machining process was carried out in sequence, with tool changes and re-zeroing between operations. The resulting lower mold had the required dimensional accuracy and surface finish. The total machining time was about one day.
5.5 Mold Assembly
After cleaning and coating, the upper and lower sand molds were assembled. The core was placed, and the two halves were closed. This hybrid fabrication approach reduced the manufacturing cycle from about two weeks (traditional pattern making) to less than one week, with significantly lower costs and reduced environmental impact.
6. Optimization of Pouring Process Parameters via Orthogonal Experiments
6.1 Influence of Process Parameters on Defects
Before conducting the orthogonal experiments, the individual effects of pouring temperature, pouring time, and sand mold preheating temperature on shrinkage porosity, residual stress, and deformation were investigated by single-factor simulations.
For shrinkage porosity, increasing pouring temperature generally decreased the porosity volume. The effect of pouring time showed a nonlinear trend, with a local minimum at 26 s. Increasing preheating temperature first decreased porosity, then increased it, and then decreased again. The most influential factor was pouring temperature.
For residual stress, pouring temperature showed a small effect, while preheating temperature had a strong decreasing effect. Residual stress decreased as preheating temperature increased, likely due to reduced thermal gradients.
For deformation, preheating temperature was the dominant factor; deformation increased with increasing preheating temperature. Pouring time also had a moderate effect, while pouring temperature was less significant.
6.2 Orthogonal Experiment Design
To find the optimal combination of process parameters, an orthogonal experiment L25(5³) was designed. The three factors and five levels are listed in Table 8.
| Level | A: Pouring Temp (°C) | B: Pouring Time (s) | C: Preheating Temp (°C) |
|---|---|---|---|
| 1 | 1360 | 20 | 430 |
| 2 | 1380 | 22 | 450 |
| 3 | 1400 | 24 | 470 |
| 4 | 1420 | 26 | 490 |
| 5 | 1440 | 28 | 510 |
The 25 simulations were carried out, and three responses were recorded: shrinkage porosity volume, maximum residual stress, and maximum deformation. The results are presented in Table 9.
| No. | A (°C) | B (s) | C (°C) | Shrinkage (cm³) | Stress (MPa) | Deform. (mm) |
|---|---|---|---|---|---|---|
| 1 | 1360 | 20 | 430 | 1.89 | 1446.0 | 2.13 |
| 2 | 1360 | 22 | 450 | 1.81 | 1320.6 | 2.15 |
| 3 | 1360 | 24 | 470 | 1.71 | 1379.8 | 2.22 |
| 4 | 1360 | 26 | 490 | 1.77 | 1318.7 | 2.31 |
| 5 | 1360 | 28 | 510 | 1.74 | 1272.4 | 2.30 |
| 6 | 1380 | 20 | 450 | 1.58 | 1396.8 | 2.13 |
| 7 | 1380 | 22 | 470 | 1.51 | 1369.4 | 2.18 |
| 8 | 1380 | 24 | 490 | 1.70 | 1340.4 | 2.23 |
| 9 | 1380 | 26 | 510 | 1.35 | 1264.1 | 2.33 |
| 10 | 1380 | 28 | 430 | 1.69 | 1374.5 | 2.05 |
| 11 | 1400 | 20 | 470 | 1.17 | 1336.1 | 2.24 |
| 12 | 1400 | 22 | 490 | 1.31 | 1327.8 | 2.26 |
| 13 | 1400 | 24 | 510 | 1.28 | 1236.5 | 2.33 |
| 14 | 1400 | 26 | 430 | 1.22 | 1330.4 | 2.16 |
| 15 | 1400 | 28 | 450 | 1.36 | 1398.5 | 2.17 |
| 16 | 1420 | 20 | 490 | 1.35 | 1278.2 | 2.27 |
| 17 | 1420 | 22 | 510 | 1.16 | 1206.8 | 2.33 |
| 18 | 1420 | 24 | 430 | 1.20 | 1295.2 | 2.08 |
| 19 | 1420 | 26 | 450 | 1.13 | 1369.3 | 2.19 |
| 20 | 1420 | 28 | 470 | 1.19 | 1316.2 | 2.24 |
| 21 | 1440 | 20 | 510 | 1.01 | 1173.7 | 2.32 |
| 22 | 1440 | 22 | 430 | 1.02 | 1426.4 | 2.09 |
| 23 | 1440 | 24 | 450 | 1.02 | 1373.9 | 2.16 |
| 24 | 1440 | 26 | 470 | 0.99 | 1293.4 | 2.26 |
| 25 | 1440 | 28 | 490 | 1.02 | 1289.9 | 2.25 |
6.3 Range Analysis
The range analysis (R method) was performed to determine the significance and optimal level for each response. Table 10 shows the average responses \(K_{ij}\) and ranges \(R\) for each factor.
| Response | Level | A | B | C |
|---|---|---|---|---|
| Shrinkage (cm³) | 1 | 1.784 | 1.400 | 1.404 |
| 2 | 1.566 | 1.362 | 1.380 | |
| 3 | 1.206 | 1.382 | 1.314 | |
| 4 | 1.206 | 1.292 | 1.430 | |
| 5 | 1.012 | 1.400 | 1.308 | |
| R | 0.772 | 0.108 | 0.122 | |
| Stress (MPa) | 1 | 1347.5 | 1326.2 | 1374.5 |
| 2 | 1349.0 | 1330.2 | 1371.8 | |
| 3 | 1325.9 | 1325.2 | 1339.0 | |
| 4 | 1293.1 | 1315.2 | 1311.0 | |
| 5 | 1311.5 | 1330.3 | 1230.7 | |
| R | 55.9 | 15.1 | 143.8 | |
| Deform. (mm) | 1 | 2.222 | 2.218 | 2.102 |
| 2 | 2.184 | 2.203 | 2.160 | |
| 3 | 2.232 | 2.204 | 2.228 | |
| 4 | 2.222 | 2.250 | 2.264 | |
| 5 | 2.216 | 2.202 | 2.322 | |
| R | 0.016 | 0.048 | 0.220 |
For shrinkage porosity, the factor influence order is A > C > B, with the optimal level combination A5B4C5 (1440 °C, 26 s, 510 °C). For residual stress, the order is C > A > B, with the best combination A4B4C5 (1420 °C, 26 s, 510 °C). For deformation, the order is C > B > A, with the best combination A2B5C1 (1380 °C, 28 s, 430 °C). These conflicting results require a multi-objective optimization approach.
6.4 Matrix Analysis
Matrix analysis was used to assign weights to each response and determine the single best combination. The method constructs an index layer matrix \(M\), a factor layer matrix \(T\), and a level layer matrix \(E\). Since all three responses are “smaller is better,” the elements of \(M\) were calculated as the reciprocal of the average \(K\) values. The weighted analysis led to the following weights for each level of each factor:
| Factor | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 |
|---|---|---|---|---|---|
| A | 0.0582 | 0.0635 | 0.0764 | 0.0768 | 0.0872 |
| B | 0.0230 | 0.0232 | 0.0231 | 0.0234 | 0.0230 |
| C | 0.1052 | 0.1039 | 0.1038 | 0.1032 | 0.1057 |
The maximum weights correspond to level 5 for factor A, level 4 for factor B, and level 5 for factor C. Therefore, the matrix analysis gives the optimal combination as A5B4C5, i.e., pouring temperature 1440 °C, pouring time 26 s, and sand mold preheating temperature 510 °C.
6.5 Verification of the Optimal Parameters
The optimized parameter set was simulated to verify the predicted improvements. The results are summarized in Table 12.
| Parameter Set | Shrinkage Porosity (cm³) | Residual Stress (MPa) | Deformation (mm) |
|---|---|---|---|
| Before (initial 1380 °C, 24 s, 450 °C) | 1.42 | 1351.1 | 2.32 |
| After optimization (1440 °C, 26 s, 510 °C) | 1.00 | 1178.7 | 2.22 |
The shrinkage porosity was reduced to 1.00 cm³, residual stress to 1178.7 MPa, and deformation to 2.22 mm. These improvements demonstrate that the orthogonal experiment combined with matrix analysis successfully identified a superior parameter set for the sand casting foundry of the sliding seat. The low porosity and reduced stress and deformation contribute to enhanced dimensional stability and service life of the machine tool component.
7. Conclusions and Outlook
In this research, a complete digitalized workflow for producing a machine tool sliding seat using sand casting foundry was demonstrated. The following conclusions can be drawn:
- The parting gate gating system was proven to be the most suitable for this casting because it provided a stable filling pattern and resulted in the smallest shrinkage porosity volume among the three designs (132.58 cm³ compared to 147.20 cm³ for top gating and 136.43 cm³ for bottom gating).
- By placing steel chills on thick sections, insulating risers on important machined surfaces, and venting holes at the high points, the shrinkage porosity was drastically reduced from 132.58 cm³ to 1.42 cm³, effectively eliminating macro-porosity defects.
- The hybrid additive-subtractive manufacturing approach, using 3D printing for the upper mold and CNC milling for the lower mold, shortened the mold-making cycle from about two weeks to less than one week, while also reducing costs and environmental impact. This method is highly beneficial for single-piece and small-batch production in the sand casting foundry industry.
- Orthogonal experiments and matrix analysis determined the optimal pouring parameters: pouring temperature 1440 °C, pouring time 26 s, and sand mold preheating temperature 510 °C. These parameters reduced shrinkage porosity to 1.00 cm³, residual stress to 1178.7 MPa, and deformation to 2.22 mm, further improving casting quality.
Future work should focus on validating the simulation results with actual pour trials and measuring mechanical properties of the cast sliding seat. Additionally, the interface heat transfer coefficients should be treated as temperature-dependent to improve simulation accuracy. The residual stress simulation could also be calibrated with experimental measurements. Extending this digital workflow to other machine tool castings would further demonstrate its versatility and economic benefits.