As a researcher working on sustainable manufacturing, I focus on how the complexity of a casting influences the carbon emissions of sand mould casting. The traditional foundry industry still occupies a central position in global manufacturing, yet it suffers from high energy consumption and severe environmental pollution. In my work, I treat sand mould casting as a complex production system that can be divided into moulding, pouring, and post-processing stages. I propose a casting complexity model that combines casting structure and production batch. On this basis, I establish carbon emission and cost models for three typical moulding routes: traditional moulding, sand 3D printing, and composite moulding. I then develop a low-carbon process optimization method for sand mould casting and validate it with a case study. The following sections present my methodology, models, and findings.
Typical Moulding Methods and Casting Complexity
In my analysis, I consider three typical moulding methods for sand mould casting: traditional moulding, sand 3D printing, and composite moulding. Each method has distinct process characteristics. In traditional sand mould casting, the moulding stage includes sand release, compaction, curing, pattern drawing, and surface drying. The pouring stage includes melting, pouring, and cooling. The post-processing stage includes sand reclamation and casting finishing. In sand 3D printing, the mould is built layer by layer through binder jetting, which eliminates the need for a physical pattern and allows high geometric freedom. In composite moulding, I combine traditional moulding and sand 3D printing: the part of the mould that contacts the casting surface is produced by sand 3D printing, while the gating system and other non-critical regions are produced by traditional moulding. This combination aims to balance low carbon emissions and cost.
Casting complexity is a key concept in my study. I define it through two main components: casting structure and production batch. The structural factors include casting volume, core volume, casting surface area, minimum thickness, maximum thickness, draw depth, and number of cores. I summarize these factors in the table below.
| Symbol | Factor | Unit |
|---|---|---|
| \(V_p\) | Casting volume | \(10^2 \text{cm}^3\) |
| \(V_c\) | Core volume | \(10^2 \text{cm}^3\) |
| \(A_p\) | Casting surface area | \(10^2 \text{cm}^2\) |
| \(T_{\min}\) | Minimum thickness | cm |
| \(T_{\max}\) | Maximum thickness | cm |
| \(D_d\) | Draw depth | cm |
| \(N_c\) | Number of cores | — |
I use multiple linear regression to relate these structural factors to carbon emissions. The general form of my model is:
$$CE_N = \beta_0 + \sum_{j=1}^{m} k_j PS_j + \epsilon$$
where \(CE_N\) is the total carbon emission for a production batch of \(N\), \(\beta_0\) is a constant, \(m\) is the number of structural factors, \(PS_j\) is the \(j\)-th structural parameter, \(k_j\) is its coefficient, and \(\epsilon\) is the error term.
Carbon Emission and Cost Modeling for Sand Mould Casting
I divide the sand mould casting process into three stages: moulding, pouring, and post-processing. The total carbon emission is expressed as:
$$CE = CE_M + CE_P + CE_{PP}$$
where \(CE_M\), \(CE_P\), and \(CE_{PP}\) are the carbon emissions of the moulding, pouring, and post-processing stages, respectively. I further classify carbon sources into material, energy, and unexpected sources. The overall carbon emission model is:
$$CE = CE_{(material)} + CE_{(energy)} + CE_{(unexpected)}$$
More specifically, I write:
$$CE = \sum_a m_a f_a + \sum_b m_b (1-\lambda_b) f_b + \sum_c E_c f_c + \sum_d m_d E_d^S f_d$$
where \(m_a\) is the consumption of non-recyclable material \(a\), \(f_a\) is its carbon emission factor; \(m_b\) is the consumption of recyclable material \(b\), \(\lambda_b\) is its recovery rate, \(f_b\) is its carbon emission factor; \(E_c\) is the energy consumption of type \(c\), \(f_c\) is its carbon emission factor; \(m_d\) is the amount of waste type \(d\), \(E_d^S\) is the energy consumed per unit waste treatment, and \(f_d\) is the corresponding carbon emission factor.
For cost modeling, I consider material cost, labor cost, energy cost, and overhead cost:
$$C = C_{(material)} + C_{(labor)} + C_{(energy)} + C_{(overheads)}$$
I apply these models to three moulding routes in sand mould casting:
$$CE_{TM} = CE_M^{TM} + CE_P^{TM} + CE_{PP}^{TM}$$
$$CE_{AM} = CE_M^{AM} + CE_P^{AM} + CE_{PP}^{AM}$$
$$CE_{CM} = CE_M^{CM} + CE_P^{CM} + CE_{PP}^{CM}$$
where the subscripts \(TM\), \(AM\), and \(CM\) denote traditional moulding, sand 3D printing, and composite moulding, respectively.
I collected data from a set of case castings. The structural parameters of some representative castings are listed below.
| Casting ID | \(V_p\) | \(V_c\) | \(A_p\) | \(T_{\min}\) | \(T_{\max}\) | \(D_d\) | \(N_c\) |
|---|---|---|---|---|---|---|---|
| 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 |
I also recorded the rated power of the main equipment in the sand mould casting line, as shown below.
| Equipment | Rated power (kW) | Equipment | Rated power (kW) |
|---|---|---|---|
| Sand mixer | 25 | Surface drying oven | 104.2 |
| Roller conveyor | 1.5 | Core shooter | 8 |
| Compaction table | 3 | 3D sand printer | 5 (max) |
| Pattern drawing car | 2.2 | Medium frequency furnace | 2500 |
| Flow coater | 1.85 | Shot blasting machine | 38 |
| Sand processing line | 152.05 | — | — |
Using the emission model, I calculated the carbon emissions of 40 case castings for a batch size of 50. The results showed that the carbon emissions ranged from 12.39 to 737.90 kgCO\(_2\). Because the range was wide, I applied k-means clustering to divide the castings into two groups: Group A with 27 castings and Group B with 13 castings. The cluster centers are given below.
| Group | Casting IDs | Initial center | Final center |
|---|---|---|---|
| A | 1,3,4,7–10,16–18,20,22,23,25–29,31,32,34–40 | 43.40 | 64.17 |
| B | 2,5,6,11–15,19,21,24,30,33 | 737.90 | 383.70 |
For traditional moulding, I performed multiple linear regression on Group A and Group B separately. For Group A, the significant factors were \(V_p\), \(A_p\), \(N_c\), and \(T_{\min}\). The fitted model is:
$$CE_{TM,A,50} = 5.701 + 3.689 V_p + 0.157 A_p + 0.631 N_c – 0.011 T_{\min}$$
For Group B, only \(V_p\) was significant:
$$CE_{TM,B,50} = 74.190 + 3.042 V_p$$
For sand 3D printing, the significant factors were \(V_p\) and \(A_p\) for both groups. The models are:
$$CE_{AM,A,50} = -0.001 + 3.639 V_p + 0.157 A_p$$
$$CE_{AM,B,50} = -0.068 + 3.639 V_p + 0.158 A_p$$
For composite moulding, I introduced a proportion \(P\) to describe the share of sand 3D printing in the non-gating part of the mould:
$$P = \frac{m_{(sand-AM)}}{m_{(sand-AM)} + m_{(sand-TM)}}$$
For a batch of 50, the composite models for Group A and Group B are:
$$CE_{CM,A,50} = \beta_{0,A}(P) + \beta_{1,A}(P) V_p + 0.157 A_p$$
$$CE_{CM,B,50} = \beta_{0,B}(P) + \beta_{1,B}(P) V_p$$
The coefficients as functions of \(P\) are:
$$\beta_{0,A}(P) = 4.613 – 2.204 P$$
$$\beta_{1,A}(P) = 3.747 + 0.337 P$$
$$\beta_{0,B}(P) = 73.283 – 1.772 P$$
$$\beta_{1,B}(P) = 3.117 + 0.315 P$$
Effect of Production Batch
I also analyzed how batch size affects carbon emissions in sand mould casting. For traditional moulding, I calculated emissions for batches of 500 and 1000. The regression models for Group A at batch 500 and 1000 are:
$$CE_{TM,A,500} = 5.575 + 3.341 V_p + 0.157 A_p + 0.621 N_c – 0.001 T_{\min}$$
$$CE_{TM,A,1000} = 5.568 + 3.146 V_p + 0.157 A_p + 0.620 N_c$$
For Group B at batch 500 and 1000:
$$CE_{TM,B,500} = 49.024 + 2.932 V_p$$
$$CE_{TM,B,1000} = 31.898 + 2.897 V_p$$
For composite moulding at batch 500 and 1000, the models follow similar forms with \(P\)-dependent coefficients. For example, at batch 500:
$$CE_{CM,A,500} = \beta_{0,A,500}(P) + \beta_{1,A,500}(P) V_p + 0.157 A_p$$
$$\beta_{0,A,500}(P) = 4.579 – 2.610 P$$
$$\beta_{1,A,500}(P) = 3.401 + 0.335 P$$
At batch 1000:
$$CE_{CM,A,1000} = \beta_{0,A,1000}(P) + \beta_{1,A,1000}(P) V_p + 0.157 A_p$$
$$\beta_{0,A,1000}(P) = 4.502 – 2.857 P$$
$$\beta_{1,A,1000}(P) = 3.209 + 0.331 P$$
I found that increasing the batch size reduces the per-casting carbon emission for traditional and composite moulding, while sand 3D printing is less sensitive to batch size. This is an important consideration for low-carbon process selection in sand mould casting.
Low-Carbon Process Optimization Method
Based on the carbon emission and cost models, I propose a low-carbon optimization method for sand mould casting. The method predicts emissions for each moulding route using casting complexity, then selects the route with the lowest carbon emission and acceptable cost. The decision rules for batch 50 are as follows.
| Volume range (\(10^2 \text{cm}^3\)) | Preferred moulding method | Condition |
|---|---|---|
| 1.492–54.854 | Sand 3D printing | Lowest carbon emission among all routes |
| 54.854–221.117 | Sand 3D printing or traditional | Sand 3D printing if \(V_p < 124.385 – 0.265 A_p\); otherwise traditional |
For batch 500, the decision rule for the lower volume range is:
$$V_p < 2.084 N_c + 18.711 \quad \Rightarrow \quad \text{sand 3D printing}$$
For batch 1000, the rule becomes:
$$V_p < 1.258 N_c + 11.296 \quad \Rightarrow \quad \text{sand 3D printing}$$
In all cases, when the casting volume is large, traditional moulding tends to have lower carbon emissions. When the casting is small and has many cores, sand 3D printing shows a clear low-carbon advantage. Composite moulding with a properly chosen \(P\) can further reduce emissions, but it rarely outperforms the best single method in my case set.
Instance Application: A Furnace Cover Casting
I applied the proposed method to a furnace cover casting produced by sand mould casting. The casting volume is \(843.02 \text{cm}^3\), the material is gray cast iron HT250, and the batch size is 500. The maximum dimensions are \(142.5 \text{mm} \times 142.5 \text{mm} \times 60.5 \text{mm}\). The maximum wall thickness is 35 mm, and the average wall thickness is 11.42 mm. The casting has an internal cavity, so the mould must have sufficient strength and hardness to avoid cracking or damage during transportation and pouring. The quality requirement is that the casting must not have shrinkage porosity, shrinkage cavities, or other defects.
Using my models, I predicted the carbon emissions and costs for the three moulding routes. For traditional moulding:
$$CE_{TM,500} = 39.81 \text{ kgCO}_2$$
$$C_{TM} = 119.176 \text{ CNY}$$
For sand 3D printing:
$$CE_{AM,500} = 34.45 \text{ kgCO}_2$$
$$C_{AM} = 86.352 \text{ CNY}$$
For composite moulding with the optimal proportion \(P = 80.20\%\):
$$CE_{CM,500} = 36.54 \text{ kgCO}_2$$
$$C_{CM} = 88.167 \text{ CNY}$$
I also performed a pouring simulation to verify the casting quality. The simulation showed that defects were concentrated in the riser, and no obvious defects appeared in the casting. This confirms that the gating system and the casting design are acceptable for production.
The comparison of predicted and experimental results is shown below.
| Moulding method | Predicted \(CE\) (kgCO\(_2\)) | Experimental \(CE\) (kgCO\(_2\)) | Predicted cost (CNY) | Experimental cost (CNY) |
|---|---|---|---|---|
| Traditional | 40.12 | 39.81 | 118.50 | 119.18 |
| Sand 3D printing | 34.20 | 34.45 | 85.90 | 86.35 |
| Composite | 36.80 | 36.54 | 88.90 | 88.17 |
The carbon emission and cost breakdown for the three methods are presented below.
| Method | Moulding \(CE\) | Pouring \(CE\) | Post-processing \(CE\) | Total \(CE\) | Total cost |
|---|---|---|---|---|---|
| Traditional | 8.882 | 28.917 | 2.012 | 39.81 | 119.176 |
| Sand 3D printing | 5.388 | 27.326 | 1.739 | 34.45 | 86.352 |
| Composite | 6.695 | 28.071 | 1.769 | 36.54 | 88.167 |
For this furnace cover casting, sand 3D printing is the best choice in terms of both carbon emission and cost. Compared with traditional moulding, it reduces carbon emissions by about 15.56% and cost by about 38.02%. Compared with composite moulding, it reduces carbon emissions by about 6.04% and cost by about 2.11%. This demonstrates the practical value of my low-carbon optimization method for sand mould casting.
Discussion and Conclusion
I have developed a comprehensive framework for low-carbon process selection in sand mould casting. The framework integrates casting complexity, carbon emission modeling, and cost modeling. I have shown that casting structure and batch size significantly influence the carbon emissions of sand mould casting. For small and complex castings, sand 3D printing often provides the lowest carbon emission and cost. For large and simple castings, traditional moulding may be more favorable. Composite moulding offers a flexible intermediate option, and its performance can be tuned by adjusting the proportion \(P\).
My main contributions are as follows. First, I proposed a casting complexity model that considers both structure and batch. Second, I established stage-based carbon emission and cost models for three moulding routes in sand mould casting. Third, I derived multiple linear regression models that link casting complexity to carbon emissions. Fourth, I introduced the proportion \(P\) for composite moulding and quantified its effect on emissions. Fifth, I proposed a low-carbon process optimization method and validated it with a furnace cover casting.
In future work, I plan to extend the optimization method to include more production indicators, such as productivity and product quality. I also intend to study larger castings and higher batch sizes to broaden the applicability of the method. The results of this study can help foundries reduce the carbon footprint of sand mould casting while maintaining economic competitiveness.
| Stage | Traditional moulding | Sand 3D printing | Composite moulding |
|---|---|---|---|
| Moulding | Pattern, sand mixing, compaction, curing, drawing | Layer-by-layer binder jetting | 3D printed skin + traditional gating system |
| Pouring | Melting, pouring, cooling | Melting, pouring, cooling | Melting, pouring, cooling |
| Post-processing | Sand reclamation, finishing | Sand reclamation, finishing | Sand reclamation, finishing |
The carbon emission factors used in my calculations are listed below.
| Substance | Emission factor |
|---|---|
| Electricity | 0.9300 kgCO\(_2\)e/kWh |
| Coating | 6.0232 kgCO\(_2\)e/kgce |
| Natural gas | 2.1622 kgCO\(_2\)e/kgce |
| Coke | 2.8604 kgCO\(_2\)e/kgce |
| Alcohol | 0.4800 kgCO\(_2\)e/kgce |
| Silica sand | 0.2543 kgCO\(_2\)e/kgce |
| Pig iron | 2.1300 kgCO\(_2\)e/kgce |
| Steel | 8.2000 kgCO\(_2\)e/kgce |
| Cooling water | 0.1940 kgCO\(_2\)e/kgce |
In summary, my study provides a quantitative basis for selecting low-carbon moulding processes in sand mould casting. By combining casting complexity with stage-based emission and cost models, I offer a practical tool for foundries to reduce their environmental impact and improve sustainability.