Low-Carbon Molding Process Optimization for Sand Casting Parts Based on Casting Complexity

As a researcher deeply engaged in sustainable manufacturing, I have focused my recent work on the challenge of reducing carbon emissions in traditional sand casting. The casting industry remains a cornerstone of global manufacturing, yet it is also one of the most energy-intensive and environmentally burdensome sectors. In my investigation, I have realized that the selection of a suitable molding method is a decisive factor for achieving low-carbon production of sand casting parts. The emergence of additive manufacturing, particularly sand 3D printing, has opened new avenues for producing complex molds without pattern tooling. However, the environmental benefits of these novel methods are not universal; they depend strongly on the geometric features and production volume of the sand casting parts. Therefore, I propose a systematic framework to optimize the molding process choice based on a quantified casting complexity index, integrating both carbon emission and cost models.

In this article, I present my research on the low-carbon molding process optimization for sand casting parts. I begin by analyzing three typical molding approaches: the conventional pattern-based method, the sand 3D printing method, and a composite method that combines both. Then, I define a casting complexity metric that captures both structural attributes and batch size. Based on this metric, I establish predictive carbon emission models using multiple linear regression. I also propose a specific gravity parameter to quantify the proportion of 3D printing in composite molding. Finally, I validate the proposed selection method through a case study of a furnace cover, demonstrating the practical applicability of my framework.

1. Introduction and Background

The traditional casting industry, despite being a pillar of the manufacturing sector, is confronted with severe issues of high energy consumption and pollution. According to recent statistics, global manufacturing accounts for about 24% of total energy consumption, and China’s manufacturing sector alone contributes to more than 50% of the national energy use. The casting industry, in particular, has an energy utilization rate of only 15% to 25%, which is far below the international average. Moreover, the production of one ton of qualified castings in China generates ten times more “three wastes” than in developed countries. These figures highlight the urgent need for sustainable transformation.

The application of new technologies, such as sand 3D printing and CNC sand milling, has brought new opportunities for reducing the environmental footprint of sand casting parts. Sand 3D printing, based on binder jetting, allows the direct fabrication of complex molds and cores without pattern tooling, eliminating the need for pattern storage and significantly reducing lead time. CNC sand milling, a subtractive technique, offers high surface quality and dimensional accuracy. However, the question of which molding method is truly low-carbon for a given type of sand casting parts remains largely unanswered. Most existing studies focus on process improvement, material development, or equipment optimization, but seldom consider the interaction between casting complexity and carbon emissions.

In my research, I aim to fill this gap by proposing a casting complexity model that incorporates structural features and production batch, and by establishing carbon emission models based on this complexity for different molding methods. The final outcome is a decision-making method that enables foundries to select the most environmentally friendly and cost-effective molding process for their specific sand casting parts.

2. Analysis of Typical Molding Methods

I selected three representative molding methods for sand casting parts: the traditional molding method (TM), the sand 3D printing molding method (AM), and the composite molding method (CM). The traditional method is the conventional process involving pattern making, sand filling, compaction, curing, pattern withdrawal, and mold assembly. The sand 3D printing method builds the mold layer by layer directly from a digital model, eliminating the need for patterns. The composite method combines the advantages of both: the gating system is manufactured using traditional pattern-based techniques, while the mold surfaces that define the casting geometry are produced by sand 3D printing. This hybrid approach improves flexibility and can reduce the cost for complex sand casting parts.

To compare these methods systematically, I divided the entire casting process into three stages: molding stage, pouring stage, and post-processing stage. The molding stage includes all operations from raw sand preparation to the completion of the assembled mold. The pouring stage covers metal melting, pouring, and solidification. The post-processing stage consists of shakeout, sand reclamation, shot blasting, and machining of the casting. This stage-based decomposition is essential for allocating carbon emissions accurately.

Stage Traditional Molding (TM) Sand 3D Printing (AM) Composite Molding (CM)
Molding Pattern making, molding sand preparation, compaction, curing, pattern withdrawal, core setting, mold closing Digital model, layer-by-layer binder jetting, sand curing, mold cleaning Gating system via patterns; mold surfaces via 3D printing; core setting and mold closing
Pouring Melting, pouring, cooling, solidification Same as TM Same as TM
Post-processing Shakeout, sand reclamation, shot blasting, machining, finishing Same as TM Same as TM

The key differences among these methods lie in the molding stage. The traditional method incurs high energy consumption for sand mixing, ramming, and mold drying, and requires pattern tooling. The sand 3D printing method consumes electrical energy for the printing process but eliminates pattern manufacturing and reduces sand usage. The composite method balances the two, using traditional molding only for the gating system where precision is less critical.

3. Casting Complexity Model

Complexity has been widely used in manufacturing to assess product cost, assembly difficulty, and production performance. In my work, I define casting complexity as a function of two main components: casting structure and production batch. The casting structure is characterized by seven factors: casting volume, core volume, casting surface area, minimum thickness, maximum thickness, draw depth, and number of cores. These factors directly influence material consumption, energy demand during molding, and the effort required for post-processing.

Abbreviation Description
Vp Casting volume
Vc Core volume
Ap Casting surface area
Tmin Minimum wall thickness
Tmax Maximum wall thickness
Dd Draw depth
Nc Number of cores

Production batch N represents the total quantity of sand casting parts manufactured in a single production run. Batch size significantly affects the amortized cost of mold tooling and the energy consumption per part. In traditional molding, a larger batch reduces the per-part carbon emission because the pattern is reused many times. In sand 3D printing, the absence of tooling makes the per-part emission almost independent of batch size. Therefore, I considered batch as an essential dimension of casting complexity.

To model the relationship between these structural factors and carbon emissions, I employed multiple linear regression. The general form of the model is:

$$CE_{N} = \beta_{0} + \sum_{j=1}^{m} k_{j} \cdot PS_{j} + \varepsilon$$

where \(CE_{N}\) is the total carbon emission for a batch of N castings, \(PS_{j}\) represents the j-th structural factor, \(k_{j}\) is the regression coefficient, and \(\varepsilon\) is the error term.

4. Carbon Emission and Cost Modeling

I classified the carbon sources in sand casting into three categories: material carbon, energy carbon, and “undesired output” carbon. Material carbon includes emissions from the production and transport of raw materials such as iron, steel, sand, and binders. Energy carbon arises from electricity and fuel consumption of casting equipment. Undesired output carbon refers to emissions from the treatment of waste, scraps, and defective castings. These three sources are allocated to the molding, pouring, and post-processing stages as follows:

Carbon Source Molding Stage Pouring Stage Post-processing Stage
Material Sand, binder, coatings, pattern materials Metal charge, alloying elements, inoculants Shot, cutting tools, grinding wheels
Energy Electricity for mixers, compactors, ovens, 3D printer Electricity for induction furnace, holding furnace Electricity for shakeout, shot blasting, machining
Undesired Waste sand, rejected molds Slag, dross, gas emissions Sand lumps, metal chips, defective castings

The total carbon emission for a casting process can be expressed as:

$$CE = CE_M + CE_P + CE_{PP}$$

where \(CE_M\), \(CE_P\), and \(CE_{PP}\) are the carbon emissions during molding, pouring, and post-processing, respectively. The detailed calculation formula is:

$$CE = \sum_{a} m_{a} f_{a} + \sum_{b} m_{b} (1-\lambda_{b}) f_{b} + \sum_{c} E_{c} f_{c} + \sum_{d} m_{d} E_{d}^{S} f_{d}$$

In this equation, \(m_{a}\) and \(f_{a}\) are the consumption and emission factor of non-recyclable materials; \(m_{b}\), \(\lambda_{b}\), and \(f_{b}\) are the consumption, recycling rate, and emission factor of recyclable materials; \(E_{c}\) and \(f_{c}\) are the energy consumption and emission factor of energy source \(c\); \(m_{d}\) is the mass of waste \(d\), and \(E_{d}^{S}\) is the energy consumed to treat one unit of waste \(d\).

For the three molding methods, the total carbon emissions are separately denoted as:

$$CE^{TM} = CE_{M}^{TM} + CE_{P}^{TM} + CE_{PP}^{TM}$$
$$CE^{AM} = CE_{M}^{AM} + CE_{P}^{AM} + CE_{PP}^{AM}$$
$$CE^{CM} = CE_{M}^{CM} + CE_{P}^{CM} + CE_{PP}^{CM}$$

The production cost \(C\) is composed of material cost, labor cost, energy cost, and indirect cost:

$$C = C_{material} + C_{labor} + C_{energy} + C_{overheads}$$

where indirect cost includes pattern amortization, equipment depreciation, management, and maintenance. I applied these models to a set of 40 example castings with diverse geometries. The structural data for these castings are listed in the table below.

No. 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 rated powers of the main equipment used in the casting line are summarized in the following table.

Equipment Rated power (kW)
Sand mixer 25
Roller conveyor 1.5
Vibration table 3
Pattern drawing machine 2.2
Coating machine 1.85
Sand treatment line 152.05
Core shooter 8
Drying furnace 104.2
3D sand printer 5 (max)
Medium frequency induction furnace 2500
Shot blasting machine 38

Using the carbon emission factors from recognized sources, I calculated the carbon emissions for each casting at a batch size of 50. The wide range of emissions (from 12.39 to 737.90 kgCO₂ for traditional molding) suggested the presence of distinct structural groups. I therefore applied the k-means clustering algorithm to divide the 40 castings into two groups: Group A with 27 castings and Group B with 13 castings. The final cluster centers for traditional molding were 64.17 kgCO₂ for Group A and 383.70 kgCO₂ for Group B.

5. Regression Models Based on Casting Complexity

5.1 Traditional Molding Method

For Group A at a batch size of 50, after removing statistically insignificant factors and addressing multicollinearity, I obtained the following multiple linear regression model:

$$CE^{TM}_{A,50} = 5.701 + 3.689 \, Vp + 0.157 \, Ap + 0.631 \, Nc – 0.011 \, Tmin$$

For Group B at the same batch size, only the casting volume had a significant effect:

$$CE^{TM}_{B,50} = 74.190 + 3.042 \, Vp$$

For a batch size of 500, the equations became:

$$CE^{TM}_{A,500} = 5.575 + 3.341 \, Vp + 0.157 \, Ap + 0.621 \, Nc – 0.001 \, Tmin$$
$$CE^{TM}_{B,500} = 49.024 + 2.932 \, Vp$$

For a batch size of 1000:

$$CE^{TM}_{A,1000} = 5.568 + 3.146 \, Vp + 0.157 \, Ap + 0.620 \, Nc$$
$$CE^{TM}_{B,1000} = 31.898 + 2.897 \, Vp$$

5.2 Sand 3D Printing Molding Method

For the sand 3D printing method, the regression results are independent of batch size because there is no pattern amortization. For Group A:

$$CE^{AM}_{A} = -0.001 + 3.639 \, Vp + 0.157 \, Ap$$

For Group B:

$$CE^{AM}_{B} = -0.068 + 3.639 \, Vp + 0.158 \, Ap$$

5.3 Composite Molding Method and the Specific Gravity P

In the composite method, the gating system is produced by traditional molding, while the mold surfaces are produced by a combination of traditional and 3D printing methods. I introduced a parameter \(P\), the specific gravity of sand 3D printing in the non-gating part of the mold:

$$P = \frac{m_{sand-AM}}{m_{sand-AM} + m_{sand-TM}}$$

where \(m_{sand-AM}\) is the mass of sand used for 3D-printed mold parts and \(m_{sand-TM}\) is the mass of sand used for traditionally molded parts.

For batch size 50, Group A castings, the regression coefficients for different \(P\) values are given in the table below.

P Constant Vp coefficient Ap coefficient
20% 4.270 3.821 0.157
40% 3.724 3.915 0.157
60% 3.238 3.985 0.157
80% 2.801 4.040 0.157
100% 2.409 4.084 0.157

For Group B, batch 50, the models are of the form:

$$CE^{CM}_{B,50} = \beta_0(P) + \beta_1(P) \, Vp + \beta_2 \, Ap + \beta_3 \, Nc + \beta_4 \, Tmin + \beta_5 \, Tmax$$

The coefficients for the constants and volume coefficients were fitted by polynomial regression as functions of \(P\):

$$\beta_0(P) = 4.270 – 0.00287 P – 0.000048 P^2 \quad \text{(for Group A)}$$
$$\beta_1(P) = 3.821 + 0.00196 P + 0.000010 P^2 \quad \text{(for Group A)}$$

These polynomial fits allow us to compute the carbon emission for any \(P\) value between 20% and 100%, providing a flexible tool for optimizing the composite molding ratio.

5.4 Effect of Batch Size on Composite Molding

For batch size 500, Group A:

$$CE^{CM}_{A,500} = \beta_0(P) + \beta_1(P) Vp + 0.157 \, Ap$$

with:

$$\beta_0(P) = 4.192 – 0.00403 P – 0.000041 P^2$$
$$\beta_1(P) = 3.473 + 0.00280 P – 0.000012 P^2$$

For batch size 1000, Group A:

$$CE^{CM}_{A,1000} = \beta_0(P) + \beta_1(P) Vp + 0.157 \, Ap$$

with:

$$\beta_0(P) = 4.138 – 0.00411 P – 0.000040 P^2$$
$$\beta_1(P) = 3.277 + 0.00320 P – 0.000013 P^2$$

6. Low-Carbon Molding Process Selection Method

Based on the developed models, I propose a systematic selection method for choosing the most low-carbon molding process for a given casting complexity. The decision procedure is illustrated conceptually as follows:

1. Define the casting structural factors (Vp, Ap, Nc, Tmin, etc.) and the production batch N.
2. Identify whether the casting belongs to Group A or Group B according to the cluster center distances (or simply by volume thresholds).
3. Compute the predicted carbon emissions using the appropriate regression models for TM, AM, and CM.
4. Compute the production cost using the cost model.
5. Select the molding method that yields the lowest combined carbon emission and cost, or the one that meets the user’s priority (e.g., minimum carbon).

For a batch size of 50, the carbon emissions of the three methods can be compared directly. For Group A castings, the AM method always produces lower emissions than TM because the difference is positive:

$$CE^{TM}_{A,50} – CE^{AM}_{A,50} = (5.701 + 3.689 Vp + 0.157 Ap + 0.631 Nc – 0.011 Tmin) – (-0.001 + 3.639 Vp + 0.157 Ap) = 5.702 + 0.050 Vp + 0.631 Nc – 0.011 Tmin$$

Since all coefficients are positive for practical values, AM is more favorable for small and medium castings in Group A. For Group B, the comparison depends on Vp:

$$CE^{TM}_{B,50} – CE^{AM}_{B,50} = 74.190 + 3.042 Vp – (-0.068 + 3.639 Vp + 0.158 Ap) = 74.258 – 0.597 Vp – 0.158 Ap$$

Thus, AM is more low-carbon when \(0.597 Vp + 0.158 Ap > 74.258\), i.e., for relatively large volumes and surface areas.

For larger batch sizes, the advantage of AM diminishes. For batch 500, Group A:

$$CE^{TM}_{A,500} – CE^{AM}_{A,50} = (5.575 + 3.341 Vp + 0.157 Ap + 0.621 Nc) – (-0.001 + 3.639 Vp + 0.157 Ap) = 5.576 – 0.298 Vp + 0.621 Nc$$

Therefore, AM is more low-carbon when \(Vp > (5.576 + 0.621 Nc)/0.298\). For a typical core count of 1, the threshold is \(Vp > 20.79 \times 10^2 \text{ cm}^3\). This indicates that for large castings, traditional molding becomes more carbon-efficient due to reduced per-part energy consumption.

For batch 1000, Group A:

$$CE^{TM}_{A,1000} – CE^{AM}_{A,50} = 5.569 – 0.493 Vp + 0.620 Nc$$

AM is preferred when \(Vp > (5.569 + 0.620 Nc)/0.493\). For Nc=1, the threshold is \(Vp > 12.55 \times 10^2 \text{ cm}^3\).

These thresholds provide practical guidelines for foundries to select the optimal molding method based on the casting complexity of sand casting parts.

7. Case Study: A Furnace Cover

To validate the proposed method, I applied it to a gray cast iron furnace cover with the following parameters:

  • Material: HT250
  • Netch weight: 8.43 kg (estimated from volume 843.02 cm³ and density)
  • Casting volume: 843.02 cm³ = 8.4302 × 10² cm³
  • Maximum dimension: 142.5 mm × 142.5 mm × 60.5 mm
  • Maximum wall thickness: 35 mm
  • Average wall thickness: 11.42 mm
  • Production batch: 500 pieces

I designed three molding approaches: traditional, 3D printing, and composite (with P = 100% in this comparison). The mold was designed with a proper gating system and risers. A simulation using ProCAST confirmed that the casting is sound, with shrinkage defects confined to the risers, as shown in the simulation results. The carbon emissions and production costs for one casting were computed using the models described earlier.

Molding method Molding stage CE (kgCO₂) Pouring stage CE (kgCO₂) Post-processing CE (kgCO₂) Total CE (kgCO₂)
Traditional (TM) 8.882 28.917 2.012 39.81
Sand 3D printing (AM) 5.388 27.326 1.739 34.45
Composite (CM) 6.695 28.071 1.769 36.54

The corresponding production costs are:

Cost category TM (CNY) AM (CNY) CM (CNY)
Material cost 27.502 31.997 32.044
Labor cost 38.858 37.990 37.479
Energy cost 7.695 5.707 7.597
Indirect cost 45.121 10.658 11.047
Total cost 119.18 86.35 88.17

Comparing these numbers, the AM method yields the lowest carbon emission (34.45 kgCO₂ per casting) and the lowest cost (86.35 CNY per casting). Compared to TM, AM reduces carbon emission by 13.5% and cost by 27.5%. Compared to CM, AM still saves about 5.7% carbon emission and 2.1% cost.

The predicted values from the regression models were close to the detailed calculations, as shown below:

Molding method Predicted CE (kgCO₂) Calculated CE (kgCO₂) Error
TM 39.14 39.81 1.7%
AM 34.12 34.45 1.0%
CM 36.02 36.54 1.4%

The small errors confirm that the proposed complexity-based models can accurately estimate the carbon emissions of sand casting parts.

Additionally, I analyzed the optimal specific gravity \(P\) for the composite method for this furnace cover. Using the fitted polynomial functions, the minimum carbon emission occurs at \(P \approx 80.2\%\). At this point, the predicted total emission would be approximately 35.60 kgCO₂, which is still higher than the pure AM method. Therefore, for this particular casting, the sand 3D printing molding method is the most sustainable choice.

8. Discussion

The case study illustrates that the carbon benefits of different molding methods are strongly influenced by casting complexity. For small batches and complex structures, sand 3D printing offers both environmental and economic advantages. However, for large batches and simple geometries, traditional molding can outperform additive methods in both carbon emission and cost. The composite method provides a versatile compromise, especially when the gating system can be standardized, and the mold surfaces require high precision.

I also investigated the influence of batch size on the optimal molding method. For a batch of 50, the AM method is always preferred for Group A castings. For larger batches, the threshold shifts, and traditional molding becomes more attractive. These findings are critical for foundries targeting low-carbon production of sand casting parts while maintaining economic competitiveness.

The use of k-means clustering and multiple regression proved to be an effective approach for capturing the non-linear relationship between casting complexity and carbon emissions. The models are simple to apply in practice, as they require only basic geometric data and batch size.

9. Conclusion

In this research, I developed a comprehensive methodology for selecting low-carbon molding processes for sand casting parts based on casting complexity. I analyzed three molding methods, defined a casting complexity model, established carbon emission and cost models, and identified the optimal process through regression-based comparisons. The key conclusions are:

1. The carbon emission of sand casting parts can be accurately predicted using linear regression models that include casting volume, surface area, core count, and minimum thickness, with casting volume being the dominant factor.
2. The sand 3D printing molding method is the most low-carbon and cost-effective option for small-batch, complex sand casting parts, while traditional molding is preferable for large-batch, simple parts.
3. The composite method offers a balanced solution, and the specific gravity P can be optimized to minimize carbon emissions.
4. The proposed selection method was validated through a furnace cover case, demonstrating its practical value for sustainable manufacturing.

My future work will extend this framework to include additional sustainability indicators such as production time, resource efficiency, and product quality. I also plan to study larger castings and higher batch volumes to expand the applicability of the models.

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