In the context of increasing global attention to resource consumption and environmental pollution, manufacturing industries are being urged to improve resource efficiency and reduce environmental impacts. Sand casting, as a fundamental manufacturing process, is characterized by high energy consumption and significant pollutant emissions. Therefore, quantitative analysis and optimization of energy consumption and emissions in sand casting are essential for achieving sustainable manufacturing. In this paper, I propose a systematic method for calculating and optimizing carbon emissions of sand casting parts based on process parameters. The process parameters are classified into independent, coupling, and inherent property parameters. Carbon sources are classified into material, energy, and undesired sources. Models for each source are established and integrated with the process parameters. A low-carbon optimization model is developed and solved using a genetic algorithm. A case study of a motor housing demonstrates that the optimized process parameters reduce total carbon emissions by 2.71% while maintaining casting quality. The proposed method enables designers to estimate carbon emissions during the process design phase and supports low-carbon process design for sand casting parts.
1. Introduction
The global climate change crisis has prompted governments and industries to re-evaluate manufacturing practices. Manufacturing is responsible for nearly one-third of global energy consumption and 36% of carbon dioxide emissions. Among various manufacturing technologies, sand casting is one of the most energy-intensive and polluting processes. In China, the casting industry consumes 25% to 30% of the total energy used in mechanical industry, with an energy utilization rate of only 17%. Since more than 60% of castings worldwide are produced by sand casting, the environmental impact of this process cannot be ignored.
Researchers have studied carbon emissions in casting processes from various perspectives, including life cycle assessment, energy efficiency improvement, and waste heat recovery. However, most existing methods focus on calculating emissions after the process is defined, or on improving equipment efficiency. There is a lack of methods that allow designers to estimate and reduce carbon emissions during the process design phase, when the key process parameters are still being selected. This paper addresses this gap by proposing a parameter-based carbon emission calculation and optimization method that can be applied at the design stage of sand casting parts.
The objectives of this work are threefold. First, I analyze the characteristics of sand casting process parameters and classify them appropriately. Second, I establish carbon emission models for different carbon sources based on these parameters. Third, I develop an optimization approach using a genetic algorithm to minimize carbon emissions while ensuring casting quality. A case study is presented to validate the method.
2. Analysis of Sand Casting Process Parameters
Sand casting process design includes various activities, such as determining the parting surface, core design, gating system, and process parameters. The process parameters directly affect the material, energy, and waste flows of the process. To establish a quantitative relationship between parameters and emissions, I classify the parameters into three categories based on their characteristics and design dependencies:
| Type | Definition | Examples |
|---|---|---|
| Independent process parameters (IP) | Parameters determined directly from product drawings and manufacturing capabilities | Machining allowance, draft angle, wall thickness |
| Coupling process parameters (CP) | Parameters that are designed based on other parameters or process conditions | Pouring temperature, cooling time, pouring time |
| Inherent property parameters (IAP) | Parameters defining the intrinsic properties of materials used | Metal grade, sand type, binder type |
Let PDP denote the set of sand casting process parameters. The three subsets satisfy the relation:
$$ PDP = IP \cup CP \cup IAP $$
This classification enables us to map each process parameter to the specific carbon sources it influences. For example, IP affects the amount of metal poured and the amount of sand used, while CP directly impacts melting energy and auxiliary material consumption. IAP determines emission factors and chemical reaction outputs.
3. Carbon Emission Modeling of Sand Casting Process
According to the characteristics of the sand casting process, the total carbon emissions are divided into three categories: material carbon emissions, energy carbon emissions, and undesired carbon emissions. The corresponding carbon sources are shown below.
3.1 Material Carbon Source Model
Material carbon emissions include both direct emissions from chemical reactions and indirect emissions from material production and transportation. According to the recycling characteristics of materials, the material carbon source is divided into three types: one-time materials, recyclable materials, and shared materials.
3.1.1 One-time material carbon emissions
One-time materials are consumed directly in the process and cannot be recovered. They include pig iron, alcohol, coatings, etc. The carbon emission is calculated as:
$$ CM^{ot} = \sum_{i=1}^{n} m_i \cdot f_i $$
where \(m_i\) is the consumption of the \(i\)-th one-time material, and \(f_i\) is its carbon emission coefficient.
3.1.2 Recyclable material carbon emissions
Recyclable materials, such as molding sand and return scrap, are recovered and reused. The net emission depends on the recycling rate. The calculation is:
$$ CM^{r} = \sum_{j=1}^{m} m_j (1 – \lambda_j) f_j $$
where \(\lambda_j\) is the recycling rate of the \(j\)-th recyclable material.
3.1.3 Shared material carbon emissions
Shared materials are consumed slowly over a long period, such as steel shot and furnace lining. The emission is allocated to each casting based on the ratio of the casting weight to the total weight processed during the consumption period:
$$ m_k = M_k \cdot \frac{M_{ca}}{M_{aca}} $$
$$ CM^{s} = \sum_{k=1}^{h} M_k \cdot \frac{M_{ca}}{M_{aca}} \cdot f_k $$
3.2 Energy Carbon Source Model
Energy consumption includes electricity and fuels such as natural gas and coal. Electricity only has indirect emissions from power generation, while fuels also have direct emissions from combustion. The energy carbon emission is:
$$ CE = E_e \cdot f_E + \sum_{l=1}^{n} \left( E_l \cdot f_l + E_l \cdot f_f \right) $$
where \(E_e\) is the electricity consumption, \(f_E\) is the carbon coefficient of electricity, \(E_l\) is the consumption of the \(l\)-th fuel, \(f_l\) is the carbon coefficient of its production, and \(f_f\) is the carbon coefficient of its combustion.
3.3 Undesired Carbon Source Model
Undesired emissions are generated from waste treatment and chemical decomposition of binders. The carbon emission from waste treatment is:
$$ CU = \sum_{h=1}^{s} M_h \cdot E_h^S \cdot f_E $$
where \(M_h\) is the amount of the \(h\)-th waste, and \(E_h^S\) is the electricity consumption per unit waste treatment.
4. Carbon Emission Calculation Based on Process Parameters
Based on the classification of process parameters, the total carbon emission of sand casting parts is expressed as:
$$ C = \sum_{i=1}^{n} C_i^{IP} + \sum_{j=1}^{n} C_j^{CP} + \sum_{k=1}^{n} C_k^{IAP} $$
4.1 Emissions Based on Independent Parameters
Independent parameters mainly affect the mass of metal, amount of sand, and other primary materials. The material carbon emission based on IP is:
$$ CM^{IP} = \sum_a F_a^{ot}(x^{IP}) \cdot f_a + \sum_b F_b^{r}(x^{IP}) \cdot (1-\lambda_b) f_b + \sum_c F_c^{s}(x^{IP}) \cdot f_c $$
The energy carbon emission based on IP includes equipment electricity and recycling energy:
$$ CE^{IP} = \sum_d f_d^E(x^{IP}) \cdot f_E + \sum_e F_e^{r}(x^{IP}) \cdot E_e^r \cdot f_E $$
Undesired carbon emissions based on IP are calculated from the waste generated by material consumption:
$$ CU^{IP} = \sum_g \lambda_g^{ot}(x^{IP}) \cdot E_g \cdot f_E + \sum_o \lambda_o^{r}(x^{IP}) \cdot E_o \cdot f_E + \sum_f \lambda_f^{s}(x^{IP}) \cdot E_f \cdot f_E $$
4.2 Emissions Based on Coupling Parameters
Coupling parameters such as pouring temperature determine the melting energy and auxiliary material consumption. The material emission is:
$$ CM^{CP} = \sum_q F_q^{ot}(x^{CP}) \cdot f_q $$
The energy emission from melting is:
$$ CE^{CP} = E_{se}(x^{CP}) \cdot F_{se}^r(x^{IP}) \cdot f_E $$
The undesired emission from chemical reactions during melting is:
$$ CU^{CP} = \sum_s F_s(x^{CP}) \cdot a_s \cdot F_{se}^r(x^{IP}) $$
4.3 Emissions Based on Inherent Property Parameters
The inherent property parameters include material grade and sand type. The material emission based on IAP is:
$$ CM^{IAP} = \sum_t F_t^{ot}(x^{IAP}) \cdot f_t $$
Energy emission based on IAP for fuel usage is:
$$ CE^{IAP} = \sum_l F_l^{El}(x^{IAP}) \cdot (f_l + f_f) $$
Undesired emission from gas evolution of sand binders is:
$$ CU^{IAP} = F(x^{IAP}) \cdot V_s \cdot f_g $$
4.4 Total Carbon Emission Model
Combining equations (7)–(16), the total carbon emission model based on process parameters is:
$$
\begin{aligned}
C =& \sum_a F_a^{ot}(x^{IP}) \cdot f_a + \sum_b F_b^{r}(x^{IP}) \cdot (1-\lambda_b) f_b + \sum_c F_c^{s}(x^{IP}) \cdot f_c \\
&+ \sum_d f_d^E(x^{IP}) \cdot f_E + \sum_e F_e^{r}(x^{IP}) \cdot E_e^r \cdot f_E \\
&+ \sum_g \lambda_g^{ot}(x^{IP}) \cdot E_g \cdot f_E + \sum_o \lambda_o^{r}(x^{IP}) \cdot E_o \cdot f_E + \sum_f \lambda_f^{s}(x^{IP}) \cdot E_f \cdot f_E \\
&+ \sum_q F_q^{ot}(x^{CP}) \cdot f_q + E_{se}(x^{CP}) \cdot F_{se}^r(x^{IP}) \cdot f_E + \sum_s F_s(x^{CP}) \cdot a_s \cdot F_{se}^r(x^{IP}) \\
&+ \sum_t F_t^{ot}(x^{IAP}) \cdot f_t + \sum_l F_l^{El}(x^{IAP}) \cdot (f_l + f_f) + F(x^{IAP}) \cdot V_s \cdot f_g
\end{aligned}
$$
5. Low-Carbon Optimization Model
5.1 Optimization Variables
Based on the sensitivity analysis of process parameters, four variables are selected as optimization variables: machining allowance \(e\), draft angle \(\alpha\), fillet radius \(r\), and pouring temperature \(T\). These variables significantly affect material consumption and melting energy.
5.2 Objective Function
The objective is to minimize the total carbon emission \(C\) while satisfying casting quality constraints:
$$ \min F[e, \alpha, r, T] = C(e, \alpha, r, T) $$
where the carbon emission \(C\) is calculated using the model described in equation (17).
5.3 Constraints
The feasible ranges for the four variables are determined by casting standards and practical experience.
| Parameter | Constraint |
|---|---|
| Machining allowance \(e\) | \(e_{min} \le e \le e_{max}\) |
| Draft angle \(\alpha\) | \(0 \le \alpha \le \alpha_{max}\) |
| Fillet radius \(r\) | \(r_{min} \le r \le r_{max}\) |
| Pouring temperature \(T\) | \(T_l + \Delta T_{min} \le T \le T_l + \Delta T_{max}\) |
For the case study, the constraints are:
$$ 3.5 \le e \le 9 \ \text{mm}, \quad 0.42 \le \alpha \le 3^\circ, \quad 4 \le r \le 10 \ \text{mm}, \quad 1440 \le T \le 1450 \ ^\circ\text{C} $$
6. Genetic Algorithm for Optimization
The optimization problem is solved using a genetic algorithm (GA) implemented in MATLAB. The GA parameters are set as follows:
| Parameter | Value |
|---|---|
| Population size | 100 |
| Maximum generations | 150 |
| Elite probability | 0.05 |
| Crossover probability | 0.8 |
| Mutation probability | 0.01 |
The fitness function is derived from the objective function. For minimization problems, the fitness is defined as:
$$ Fitness(x) = \begin{cases} C_{max} – C(x) & \text{if } C(x) < C_{max} \\ 0 & \text{otherwise} \end{cases} $$
The genetic algorithm iteratively performs selection, crossover, and mutation to find the optimal set of process parameters. The convergence of the fitness function and the optimal individual are recorded during the optimization run.
7. Case Study: Motor Housing
7.1 Process Conditions
The proposed method is applied to the production of a motor housing for a central air-conditioning compressor. The casting material is HT250 gray cast iron, with a finished weight of 579.69 kg. The sand molding system uses resin-bonded sand with a recycling rate of 96.25%. The process flow and equipment power ratings are summarized below.
| Process step | Equipment power (kW) |
|---|---|
| Sand mixing | 11.5 |
| Roller conveyor | 2.2 |
| Drying oven | 104.2 |
| Vibrating table | 3 |
| Flow coating machine | 1.85 |
| Bridge stripping machine | 6.6 |
| Hardener proportioning | 1.5 |
| Sand reclamation line | 178.5 |
The carbon emission coefficients of relevant materials and energy are listed in the following table.
| Category | Item | Carbon coefficient |
|---|---|---|
| Energy | Electricity | 0.93 kgCO₂e/kWh |
| Energy | Natural gas | 2.1622 kgCO₂e/kgce |
| Energy | Alcohol | 0.48 kgCO₂e/kgce |
| Material | Silica sand | 0.02543 kgCO₂e/kgce |
| Material | Pig iron | 2.13 kgCO₂e/kgce |
| Material | Steel scrap | 8.2 kgCO₂e/kgce |
| Material | Coating | 6.0232 kgCO₂e/kgce |
| Material | Tap water | 0.194 kgCO₂e/kgce |
7.2 Original Process Parameter Scheme (Scheme 1)
The original design parameters are:
| Parameter | Value |
|---|---|
| Draft angle | 2° |
| Machining allowance | 9 mm |
| Fillet radius | 8 mm |
| Pouring temperature | 1446 °C |
| Sand gas evolution | 15.5 ml/g |
| Cooling time | 24 h |
The casting was simulated using ProCAST to verify its quality. The simulation showed complete solidification with only minor shrinkage in the gating system and the base, which are acceptable. The weight of a single casting is calculated from the part weight plus the changed material due to the process parameters:
$$ M_C = M_P + (V_e + V_\alpha – V_r) \cdot \rho_{HT250} $$
For scheme 1:
$$ V_e = 1907008.80 \ \text{mm}^3, \quad V_\alpha = 1342319.15 \ \text{mm}^3, \quad V_r = 240266.82 \ \text{mm}^3 $$
$$ M_C = 579.69 + (1907008.80 + 1342319.15 – 240266.82) \times 7.2 \times 10^{-6} = 601.36 \ \text{kg} $$
Using the carbon emission models, the emissions are calculated and summarized below.
| Category | IP | CP | IAP | Total |
|---|---|---|---|---|
| Material carbon | 1748.83 | 52.27 | 35.10 | 1836.20 |
| Energy carbon | 142.10 | 422.53 | 14.68 | 579.31 |
| Undesired carbon | 0.04 | 2.72 | 3.60 | 6.36 |
| Total | 1890.97 | 477.52 | 53.38 | 2421.86 |
The total carbon emission for scheme 1 is 2421.86 kgCO₂e. The largest contributor is the material carbon source (75.82%), followed by energy (23.92%) and undesired emissions (0.26%).
7.3 Optimized Process Parameter Scheme (Scheme 2)
The genetic algorithm is applied to minimize the carbon emission. The optimal individual obtained is:
$$ e = 3.5 \ \text{mm}, \quad \alpha = 0.42^\circ, \quad r = 10 \ \text{mm}, \quad T = 1440 \ ^\circ\text{C} $$
The optimized process parameters (scheme 2) are listed below.
| Parameter | Scheme 1 | Scheme 2 |
|---|---|---|
| Draft angle | 2° | 0.42° |
| Machining allowance | 9 mm | 3.5 mm |
| Fillet radius | 8 mm | 10 mm |
| Pouring temperature | 1446 °C | 1440 °C |
The casting quality of scheme 2 was again verified using ProCAST. The simulation showed acceptable quality with minor shrinkage in permitted areas. The casting weight for scheme 2 is calculated as:
$$ V_e = 741614.53 \ \text{mm}^3, \quad V_\alpha = 281777.57 \ \text{mm}^3, \quad V_r = 375416.91 \ \text{mm}^3 $$
$$ M_C = 579.69 + (741614.53 + 281777.57 – 375416.91) \times 7.2 \times 10^{-6} = 584.36 \ \text{kg} $$
Using the same emission models, the carbon emissions for scheme 2 are calculated:
| Category | IP | CP | IAP | Total |
|---|---|---|---|---|
| Material carbon | 1709.03 | 51.06 | 34.70 | 1794.79 |
| Energy carbon | 142.10 | 398.74 | 14.32 | 555.16 |
| Undesired carbon | 0.04 | 2.65 | 3.60 | 6.29 |
| Total | 1851.17 | 452.46 | 52.61 | 2356.24 |
7.4 Comparison and Discussion
The total carbon emission of sand casting parts is reduced by 65.62 kgCO₂e, which corresponds to a 2.71% reduction. The reduction in energy carbon is the largest in absolute terms: 24.15 kgCO₂e (4.17%). This is mainly because the pouring temperature was lowered from 1446 °C to 1440 °C, which reduced the electricity consumption during melting. The material carbon emission also decreased by 41.40 kgCO₂e (2.25%) due to the reduction in machining allowance and draft angle, which directly reduces the amount of metal poured. The undesired carbon emission decreased slightly by 0.06 kgCO₂e (1.00%).
| Carbon source | Scheme 1 (kgCO₂e) | Scheme 2 (kgCO₂e) | Change (kgCO₂e) | Change (%) |
|---|---|---|---|---|
| Material carbon | 1836.20 | 1794.79 | -41.41 | -2.25% |
| Energy carbon | 579.31 | 555.16 | -24.15 | -4.17% |
| Undesired carbon | 6.36 | 6.29 | -0.07 | -1.10% |
| Total | 2421.86 | 2356.24 | -65.62 | -2.71% |
From the perspective of parameter types, the carbon emissions under CP (coupling parameters) decreased by 25.06 kgCO₂e (5.25%), which is the largest percentage reduction. The emissions under IP decreased by 39.80 kgCO₂e (2.10%) because of reduced material consumption. The emissions under IAP decreased by only 0.76 kgCO₂e (1.43%).
| Parameter type | Scheme 1 | Scheme 2 | Change | Change (%) |
|---|---|---|---|---|
| IP | 1890.97 | 1851.17 | -39.80 | -2.10% |
| CP | 477.52 | 452.46 | -25.06 | -5.25% |
| IAP | 53.38 | 52.61 | -0.77 | -1.43% |
The results confirm that the melting process is the dominant energy consumer in sand casting. In scheme 2, the melting energy accounts for 71.82% of the total energy carbon, which is slightly lower than the 72.94% in scheme 1. This indicates that controlling the pouring temperature is an effective measure for reducing the carbon footprint of sand casting parts. Furthermore, optimizing the independent process parameters such as machining allowance and draft angle can significantly reduce material-related carbon emissions without compromising casting quality.
8. Conclusions
This paper presents a method for calculating and optimizing carbon emissions of sand casting parts based on process parameters. The main contributions are summarized as follows:
- The sand casting process parameters are classified into independent, coupling, and inherent property parameters. This classification enables a systematic mapping between process design decisions and carbon emissions.
- Carbon emission models for material, energy, and undesired sources are established. The material carbon source model distinguishes one-time, recyclable, and shared materials, which reflects the unique characteristics of sand casting.
- A low-carbon optimization model is formulated with four key process parameters as variables. The model is solved using a genetic algorithm to find the optimal parameter combination that minimizes total carbon emissions.
- A case study of a motor housing demonstrates that the optimized scheme reduces total carbon emissions by 2.71%, with a 5.25% reduction in emissions related to coupling parameters. The casting quality remains acceptable as verified by simulation.
The proposed method supports designers in creating low-carbon process plans for sand casting parts during the design phase. It can be easily integrated into existing CAD/CAM systems and helps foundry enterprises achieve sustainability targets. Future work will extend the method to optimize the gating system design and consider casting defect prediction in the carbon emission model.