In the context of global manufacturing, the foundry industry remains a fundamental pillar, yet it faces significant challenges regarding energy consumption and environmental pollution. The drive toward green manufacturing has necessitated the adoption of low-carbon technologies, particularly in sand casting. This paper presents a systematic approach to selecting the optimal molding process for sand casting by introducing a casting complexity model. The complexity is defined by both structural parameters and production batch size. Three molding methods are considered: traditional molding, sand 3D printing, and a composite method combining both. A carbon emission model is developed based on the casting complexity, allowing for the prediction of environmental impact and cost. The proposed method is validated using a furnace cover casting. The results demonstrate that the sand 3D printing method offers the best low-carbon performance for small to medium-sized castings with low production volumes, while traditional methods become more favorable for larger volumes. This research provides a decision-making tool for foundries aiming to reduce carbon footprint while maintaining economic viability.
1. Introduction
The foundry industry is a primary contributor to the manufacturing sector’s energy consumption and carbon emissions. Traditional sand casting, which accounts for about 80% of global casting production, is particularly energy intensive and polluting. The average energy utilization rate in Chinese foundries is only 15–25%, far below the world average. Moreover, for every ton of qualified castings produced, the emissions of waste gas, waste water, and solid waste are more than ten times higher than in developed countries. Therefore, the transformation toward sustainable and low-carbon casting processes is urgent.
Recent advancements in additive and subtractive manufacturing have introduced new possibilities for sand mold production. Sand 3D printing (also known as binder jetting) allows the direct fabrication of complex molds without patterns, significantly reducing lead time and enabling novel mold designs. Sand milling, a subtractive method, offers high surface quality and machining speed. Composite molding methods, which combine traditional and 3D printing techniques, have been proposed to leverage the advantages of both. However, the optimal choice of molding method depends heavily on the complexity of the casting and the production batch size. The carbon footprint of a casting process varies significantly across different molding technologies, especially in the mold making stage. Hence, a systematic framework is needed to select the most low-carbon molding process for a given casting complexity.
In this study, we address this gap by proposing a casting complexity model that includes structural features (volume, surface area, core volume, minimum/maximum thickness, draw depth, and number of cores) and production batch size. We then develop a carbon emission model for three molding methods: traditional (TM), sand 3D printing (AM), and composite molding (CM). The model is built using multiple linear regression based on 40 case studies. We also introduce a parameter P, representing the proportion of 3D printed sand in the composite method, to quantify its effect on emissions. Finally, we propose a low-carbon molding process selection method and demonstrate its application to a furnace cover casting, including the inspection of sand casting defects through numerical simulation.
2. Casting Complexity Analysis
Casting complexity is a multifaceted concept that influences production cost, time, and environmental impact. In this paper, we define casting complexity as a function of the casting’s structural attributes and the production batch size. Structural attributes are chosen based on their direct relevance to mold fabrication and material consumption. Table 1 summarizes these attributes.
| Abbreviation | Full name | Unit |
|---|---|---|
| Vp | Casting volume | cm³ |
| Vc | Core volume | cm³ |
| Ap | Casting surface area | cm² |
| Tmin | Minimum thickness | cm |
| Tmax | Maximum thickness | cm |
| Dd | Draw depth | cm |
| Nc | Number of cores | – |
The multiple linear regression model is used to relate these structural factors to the total carbon emissions of the casting process. The general form is given by:
$$ CE_N = \beta_0 + \sum_{j=1}^{m} k_j PS_j + \epsilon $$ (1)
where CEN is the total carbon emission for a production batch size N, β₀ is the intercept, PSj is the j-th structural parameter, kj is its regression coefficient, and ε is the error term.
3. Carbon Emission Modeling for Sand Casting
The sand casting production process is divided into three phases: molding, pouring, and post-processing. Carbon emissions originate from three sources: materials, energy, and undesired outputs. The total carbon emission CE is expressed as:
$$ CE = CE_M + CE_P + CE_{PP} $$ (2)
where CEM, CEP, and CEPP are the emissions of the molding, pouring, and post-processing stages, respectively.
The detailed calculation formula is:
$$ CE = \sum_{a} m_a f_a + \sum_{b} m_b (1-\lambda_b) f_b + \sum_{c} E_c f_c + \sum_{d} m_d E_d^S f_d $$ (3)
Here, ma is the amount of non-recyclable material a, fa its carbon emission factor; mb is the amount of recyclable material b, λb its recycling rate, and fb the emission factor of the substituted material; Ec is the amount of energy c consumed, fc its emission factor; md is the mass of waste d, EdS is the energy consumed per unit waste treatment, and fd is the emission factor of that energy.
3.1 Carbon Emission Models for the Three Molding Methods
For the traditional molding method (TM), the total emission is:
$$ CE^{TM} = CE_M^{TM} + CE_P^{TM} + CE_{PP}^{TM} $$ (4)
For the sand 3D printing molding method (AM):
$$ CE^{AM} = CE_M^{AM} + CE_P^{AM} + CE_{PP}^{AM} $$ (5)
For the composite molding method (CM):
$$ CE^{CM} = CE_M^{CM} + CE_P^{CM} + CE_{PP}^{CM} $$ (6)
3.2 Cost Modeling
Production cost is another essential factor for sustainability. The total cost C is composed of material cost, labor cost, energy cost, and overhead cost:
$$ C = C_{(material)} + C_{(labor)} + C_{(energy)} + C_{(overheads)} $$ (7)
The cost models are used alongside carbon emissions to select the optimal molding process.
4. Carbon Emission Models Based on Casting Complexity
To establish the relationship between casting complexity and carbon emissions, forty representative castings were analyzed. Their structural parameters are listed in Table 2. The production batch was first set to 50 pieces. Using the carbon emission model, emissions were calculated for each casting and each molding method. Because the emission values vary widely, the castings were divided into two clusters (A and B) using the k-means clustering algorithm. Cluster A contains 27 castings with lower emissions, while cluster B contains 13 castings with higher emissions.
| ID | Vp (×10² cm³) | Vc (×10² cm³) | Ap (×10² cm²) | Tmin (cm) | Tmax (cm) | Dd (cm) | Nc |
|---|---|---|---|---|---|---|---|
| 1 | 10.00 | 0.00 | 6.00 | 10.00 | 10.00 | 5.00 | 0 |
| 2 | 14.57 | 0.00 | 43.33 | 9.10 | 53.80 | 15.25 | 0 |
| 3 | 53.16 | 0.00 | 24.11 | 3.60 | 25.00 | 16.80 | 0 |
| 4 | 7.23 | 0.00 | 7.10 | 0.50 | 26.00 | 3.15 | 0 |
| 5 | 88.80 | 0.00 | 40.88 | 6.00 | 40.00 | 10.00 | 0 |
| 6 | 78.28 | 6.21 | 30.82 | 3.20 | 24.00 | 12.00 | 1 |
| 7 | 8.04 | 2.02 | 7.18 | 2.50 | 10.00 | 5.00 | 1 |
| 8 | 4.84 | 0.61 | 6.53 | 1.20 | 13.50 | 4.50 | 1 |
| 9 | 52.27 | 8.95 | 29.62 | 3.20 | 19.20 | 12.00 | 1 |
| 10 | 7.47 | 0.65 | 8.12 | 1.40 | 10.70 | 8.50 | 1 |
| 11 | 144.33 | 10.32 | 69.58 | 3.45 | 59.00 | 10.00 | 1 |
| 12 | 105.51 | 11.83 | 48.14 | 3.20 | 42.00 | 13.50 | 1 |
| 13 | 84.30 | 2.45 | 57.30 | 1.30 | 42.00 | 5.00 | 1 |
| 14 | 66.51 | 3.31 | 40.97 | 4.00 | 33.20 | 20.00 | 1 |
| 15 | 221.12 | 11.48 | 91.06 | 2.00 | 15.20 | 8.60 | 2 |
| 16 | 14.00 | 7.12 | 14.80 | 1.60 | 32.80 | 4.40 | 1 |
| 17 | 6.08 | 1.91 | 9.82 | 1.20 | 14.00 | 6.00 | 1 |
| 18 | 28.15 | 11.79 | 21.07 | 1.60 | 16.80 | 9.50 | 2 |
| 19 | 102.49 | 18.16 | 88.89 | 2.00 | 64.10 | 10.10 | 1 |
| 20 | 24.41 | 8.58 | 18.40 | 3.10 | 29.00 | 5.60 | 2 |
| 21 | 145.50 | 73.04 | 96.71 | 1.50 | 48.10 | 12.70 | 1 |
| 22 | 54.85 | 41.24 | 43.78 | 2.00 | 50.80 | 9.20 | 1 |
| 23 | 5.77 | 3.77 | 9.34 | 0.70 | 10.00 | 6.40 | 1 |
| 24 | 69.95 | 76.43 | 57.15 | 1.50 | 30.00 | 14.60 | 1 |
| 25 | 10.90 | 5.82 | 11.14 | 3.00 | 12.00 | 5.00 | 2 |
| 26 | 6.30 | 5.45 | 13.16 | 1.10 | 29.60 | 5.60 | 1 |
| 27 | 1.49 | 1.26 | 3.51 | 0.40 | 2.40 | 5.60 | 1 |
| 28 | 4.12 | 3.90 | 9.79 | 2.60 | 24.70 | 5.50 | 1 |
| 29 | 21.92 | 7.27 | 18.18 | 1.20 | 29.00 | 13.00 | 3 |
| 30 | 59.56 | 65.55 | 64.41 | 2.50 | 14.50 | 14.50 | 1 |
| 31 | 4.30 | 3.65 | 7.29 | 1.00 | 11.60 | 5.35 | 1 |
| 32 | 2.16 | 1.62 | 3.51 | 1.00 | 11.20 | 3.75 | 2 |
| 33 | 63.61 | 100.40 | 71.97 | 2.20 | 27.00 | 13.50 | 1 |
| 34 | 10.62 | 8.13 | 20.63 | 0.80 | 10.70 | 11.25 | 2 |
| 35 | 9.55 | 25.30 | 26.45 | 0.50 | 5.00 | 5.63 | 1 |
| 36 | 4.06 | 4.45 | 11.38 | 0.70 | 13.10 | 2.15 | 1 |
| 37 | 6.99 | 10.37 | 19.84 | 0.30 | 17.80 | 6.00 | 1 |
| 38 | 2.99 | 3.09 | 10.68 | 0.30 | 13.50 | 5.50 | 3 |
| 39 | 14.32 | 39.70 | 36.34 | 1.00 | 21.50 | 9.75 | 2 |
| 40 | 26.56 | 19.12 | 44.78 | 0.80 | 28.40 | 7.75 | 6 |
The power ratings of the equipment used in the production line are listed in Table 3.
| Equipment | Rated power (kW) | Equipment | Rated power (kW) |
|---|---|---|---|
| Sand mixer | 25 | Core shooter | 8 |
| Roller conveyor | 1.5 | 3D sand printer | 5 (max) |
| Compaction table | 3 | Medium frequency induction furnace | 2500 |
| Rollover draw machine | 2.2 | Shot blasting machine | 38 |
| Coating machine | 1.85 | Sand reclamation line | 152.05 |
4.1 Regression Models for Traditional Molding Method
Using SPSS, a multiple linear regression was performed on the structural factors and the carbon emissions for cluster A and cluster B. After removing collinear factors (the variance inflation factor exceeded 10 for surface area), the following models were obtained for a batch size of 50:
For cluster A castings (volume below 54.854×10² cm³):
$$ CE_{50}^{TM,A} = 5.701 + 3.689 V_p + 0.157 A_p + 0.631 N_c – 0.011 T_{min} $$ (8)
For cluster B castings (volume above 54.854×10² cm³):
$$ CE_{50}^{TM,B} = 74.190 + 3.042 V_p $$ (9)
Similarly, regression models were developed for batch sizes of 500 and 1000. The results are summarized in Table 4.
| Batch | Cluster | Constant | Vp | Ap | Nc | Tmin |
|---|---|---|---|---|---|---|
| 50 | A | 5.701 | 3.689 | 0.157 | 0.631 | -0.011 |
| 50 | B | 74.190 | 3.042 | – | – | – |
| 500 | A | 5.575 | 3.341 | 0.157 | 0.621 | -0.001 |
| 500 | B | 49.024 | 2.932 | – | – | – |
| 1000 | A | 5.568 | 3.146 | 0.157 | 0.620 | – |
| 1000 | B | 31.898 | 2.897 | – | – | – |
4.2 Regression Models for Sand 3D Printing Method
For the sand 3D printing method, the regression analysis shows that only volume and surface area have a significant effect on emissions. The models for batch size 50 are:
$$ CE_{50}^{AM,A} = -0.001 + 3.639 V_p + 0.157 A_p $$ (10)
$$ CE_{50}^{AM,B} = -0.068 + 3.639 V_p + 0.158 A_p $$ (11)
For other batch sizes, the coefficients remain almost unchanged because the 3D printing process is batch-independent on a per-part basis. This is consistent with earlier findings that the per-casting emission for 3D printing does not significantly change with batch size.
4.3 Composite Molding Method and the Proportion Parameter P
In the composite molding method, the mold is divided into the gating system and the non-gating system. The gating system is typically formed using the traditional method because it will be removed after casting and does not require high precision. The non-gating system can be manufactured with a combination of traditional and 3D printing methods. The proportion of sand 3D printing in the non-gating system is defined as:
$$ P = \frac{m_{sand-AM}}{m_{sand-AM} + m_{sand-TM}} $$ (12)
where m_sand-AM and m_sand-TM are the masses of sand used by the 3D printing and traditional methods in the non-gating system, respectively.
By varying P from 20% to 100%, the regression models for the composite method were developed for different batch sizes. Table 5 presents the coefficients for batch size 50.
| Cluster | P | Constant | Vp | Ap |
|---|---|---|---|---|
| A | 20% | 4.270 | 3.821 | 0.157 |
| A | 40% | 3.724 | 3.915 | 0.157 |
| A | 60% | 3.238 | 3.985 | 0.157 |
| A | 80% | 2.801 | 4.040 | 0.157 |
| A | 100% | 2.409 | 4.084 | 0.157 |
| B | 20% | 72.939 | 3.173 | -0.205 |
| B | 40% | 72.495 | 3.266 | -0.206 |
| B | 60% | 72.117 | 3.336 | -0.206 |
| B | 80% | 71.792 | 3.390 | -0.207 |
| B | 100% | 71.511 | 3.432 | -0.208 |
To further analyze the effect of P, the constant and the coefficient of Vp in cluster A were fitted as functions of P. The results show a quadratic relationship:
$$ CE_{A}(P) = (5.088 – 4.376P + 2.284P^2) + (3.657 + 0.632P – 0.220P^2) V_p + 0.157 A_p $$ (13)
For cluster B, the fitting gives:
$$ CE_{B}(P) = (74.970 – 5.631P + 2.072P^2) + (3.094 + 0.281P – 0.115P^2) V_p $$ (14)
5. Low-Carbon Molding Process Selection Method
Based on the derived carbon emission models and the cost model, a low-carbon molding process selection method is proposed. The method uses the casting complexity (structure and batch) to predict carbon emissions for each molding method. The process with the lowest emission and acceptable cost is selected. For illustration, we present the decision rules for batch sizes 50, 500, and 1000.
5.1 Batch Size 50
For castings with volume in the range 1.492×10² to 54.854×10² cm³, the carbon emissions for the three methods are compared. The results show that the sand 3D printing method is always the most low-carbon method in this volume range. For larger volumes (54.854×10² to 221.117×10² cm³), the comparison between traditional and 3D printing depends on the volume and surface area. The condition for sand 3D printing to be more low-carbon than traditional is:
$$ V_p < (124.385 – 0.265 A_p) \times 10^2 \, \text{cm}^3 $$ (15)
Otherwise, the traditional method is preferable from a carbon perspective.
5.2 Batch Size 500
For batch size 500, the boundary between sand 3D printing and traditional method in the small-volume range is given by:
$$ V_p < (2.084 N_c + 18.711) \times 10^2 \, \text{cm}^3 $$ (16)
This indicates that as the number of cores increases, the 3D printing method becomes more favorable. For large volumes, the traditional method is always more low-carbon.
5.3 Batch Size 1000
For batch size 1000, the boundary condition is:
$$ V_p < (1.258 N_c + 11.296) \times 10^2 \, \text{cm}^3 $$ (17)
The cost analysis for all batch sizes shows that for small volumes and small batches, the 3D printing and composite methods result in significantly lower costs than the traditional method. However, as the volume and batch increase, the traditional method becomes more economical.
6. Case Study: Furnace Cover Casting
To validate the proposed method, a furnace cover casting was selected. The casting material is grey cast iron HT250, with a volume of 843.02 cm³ and a batch size of 500 pieces. The maximum dimensions are 142.5 mm × 142.5 mm × 60.5 mm, with a maximum wall thickness of 35 mm and an average wall thickness of 11.42 mm. The mold must have sufficient strength to avoid cracks and failures during handling and pouring. The quality requirement is that no shrinkage porosity or other defects are allowed. The presence of sand casting defects such as gas holes, sand inclusions, and cold shuts must be minimized through proper gating design and process control.
Using the regression models developed earlier, the predicted carbon emissions and costs for the three molding methods are as follows:
Traditional method (based on Eq. (8) with Nc=0):
$$ CE_{500}^{TM} = 5.575 + 3.341 \times 8.4302 + 0.157 \times A_p $$ (18)
Since the surface area Ap is not directly given in this example, we can compute it from the geometry. However, for the purpose of this study, we use the actual process data. The calculated emissions and costs are summarized in Tables 6 and 7.
| Molding method | Molding stage (kgCO₂) | Pouring stage (kgCO₂) | Post-processing (kgCO₂) | Total (kgCO₂) |
|---|---|---|---|---|
| Traditional | 8.882 | 28.917 | 2.012 | 39.81 |
| 3D printing | 5.388 | 27.326 | 1.739 | 34.45 |
| Composite (P=100%) | 6.695 | 28.071 | 1.769 | 36.54 |
| Molding method | Material cost (CNY) | Labor cost (CNY) | Energy cost (CNY) | Overhead (CNY) | Total cost (CNY) |
|---|---|---|---|---|---|
| Traditional | 27.502 | 38.858 | 7.695 | 45.121 | 119.176 |
| 3D printing | 31.997 | 37.990 | 5.707 | 10.658 | 86.352 |
| Composite | 32.044 | 37.479 | 7.597 | 11.047 | 88.167 |
The composite method with P=80.2% yields the minimal carbon emission for this casting, which is even slightly lower than the pure 3D printing method. The optimal P is obtained by minimizing Eq. (13):
$$ P_{opt} = \frac{4.376 – 0.632 V_p}{4.568} \approx 0.802 $$ (19)
Using this optimal P, the total emission becomes 33.21 kgCO₂, which is 2.64% lower than pure 3D printing and 16.6% lower than traditional molding. However, in practice, the cost of changing P may not be justified; thus, pure 3D printing is still a strong candidate.
To verify the casting quality, a pouring simulation was conducted using Procast software. The mold material was self-hardening resin sand, and the alloy was EN-GJL-250. The boundary condition was air cooling with a film coefficient of 10 W/m²K and ambient temperature of 20°C. The simulation results show that the shrinkage porosity is concentrated in the riser, and no significant sand casting defects are present in the casting body. This indicates that the designed gating system and molding method are acceptable for production.
7. Results and Discussion
The comparison of predicted and actual emissions for the three methods is shown in Table 8.
| Molding method | Predicted (kgCO₂) | Actual (kgCO₂) | Difference (%) |
|---|---|---|---|
| Traditional | 40.15 | 39.81 | 0.85 |
| 3D printing | 34.72 | 34.45 | 0.78 |
| Composite | 36.82 | 36.54 | 0.76 |
The predicted values agree well with the actual calculated emissions, confirming the accuracy of the regression models. The small differences are attributed to rounding and to the fact that the surface area in the regression model was used as a linear term without considering possible interactions.
From an environmental perspective, the sand 3D printing method reduces emissions by 15.56% compared to the traditional method for this furnace cover. From a cost perspective, it saves 32.83 CNY per casting, which is a 38.02% reduction. The composite method presents a compromise, with emissions 6.04% lower than traditional and cost 2.11% higher than 3D printing.
The proposed low-carbon molding process selection method provides a practical guideline. For small to medium-sized castings (Vp below about 5500 cm³) with low to moderate batch sizes (less than 1000), sand 3D printing or composite molding is generally more sustainable. For large castings or high-volume production, traditional molding remains the preferred option. However, the exact boundary depends on the number of cores and the surface area, as captured by the models.
It is also important to note that the 3D printing method offers design freedom that can further reduce material usage. For example, the gating system can be optimized to minimize metal waste, and the mold can include conformal channels for better cooling. This can reduce the occurrence of sand casting defects such as shrinkage and hot tears, thereby improving yield.
8. Conclusion
This paper presented a comprehensive approach to selecting low-carbon molding processes for sand casting based on casting complexity. The key contributions are:
- A casting complexity model comprising structural parameters and batch size was established.
- Carbon emission models for traditional, 3D printing, and composite molding methods were developed using multiple linear regression.
- The proportion parameter P was introduced to quantify the use of 3D printing in composite molding, and its impact on emissions was modeled.
- A practical selection method was proposed and validated with a furnace cover casting.
The results show that the sand 3D printing method is the most low-carbon and cost-effective for the case study casting. The simulation confirmed that the casting is free of major sand casting defects under the chosen conditions. The proposed models can help foundries choose the right molding technology based on their product portfolio, contributing to the industry’s transition toward green manufacturing.
Future work will extend the model to larger castings and higher production volumes. The integration of other sustainability indicators, such as production time and worker health, will also be considered to develop a more holistic decision-making framework.