The pursuit of sustainable manufacturing has placed immense pressure on industries to reduce their environmental footprint. Within the broader manufacturing sector, foundry operations, particularly sand casting services, are significant energy consumers and contributors to greenhouse gas emissions. Traditional assessments often focus solely on total carbon emissions, which provides a limited view. A more scientific and effective approach is needed to evaluate the relationship between carbon emissions and production efficiency, enabling sand casting services to target meaningful energy conservation and emission reduction activities. This article, from the perspective of a service provider, delves into the modeling and evaluation of Carbon Emission Efficiency (CEE) specifically for sand casting processes.
The foundational step in any carbon efficiency analysis is the accurate quantification of emissions. For sand casting services, carbon emissions originate from a complex interplay of equipment operation, material consumption, and energy use throughout the production sequence. To systematically capture this, we propose a Process Carbon Source (PCS) model. Emissions are categorized into two primary types: Equipment Carbon Sources and Non-Equipment Carbon Sources.
Equipment Carbon Sources are further divided into idle/standby emissions and load emissions. Their calculation fundamentally depends on power ratings and operational time. The basic formulas are:
$$C_{PC} = P_o \times t \times E_e$$
$$C_{LC} = (P_o + \mu m_e P_w) \times t \times E_e$$
Here, \(C_{PC}\) represents idle/standby carbon, \(P_o\) is the idle/standby power, \(t\) is the operating time, and \(E_e\) is the carbon emission factor for electricity. \(C_{LC}\) is the load carbon, where \(\mu\) is the equipment power loss coefficient, \(m_e\) is the load mass, and \(P_w\) is the additional power per unit weight.
Non-Equipment Carbon Sources encompass emissions from material consumption, direct energy use (like natural gas), and waste treatment. Their calculation models are:
$$C_{MC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot U_i) \cdot E_e$$
$$C_{UC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot Q_i \cdot \phi_i) \cdot E_e$$
$$C_{EC} = \sum_{i=1}^{n} V_i \cdot E_i$$
In these equations, \(C_{MC}\) is material consumption carbon, \(U_i\) is the quantity of the i-th material consumed, and \(ES_k\) is the electricity consumed in the k-th processing stage. \(C_{UC}\) is unwanted output carbon (e.g., waste sand treatment), where \(Q_i\) is the quantity of the i-th waste and \(\phi_i\) is its treatment difficulty coefficient. \(C_{EC}\) is direct energy carbon, with \(V_i\) being the volume of the i-th energy source (like natural gas) and \(E_i\) its specific carbon factor.
The total carbon emission for a sand casting service process (\(C_{pro}\)) is the sum of all these sources:
$$C_{pro} = C_{eq} + C_{neq} = (C_{PC} + C_{LC}) + (C_{MC} + C_{EC} + C_{UC})$$
However, the total carbon figure is only half the story. True efficiency for sand casting services is defined as the capability to reduce process carbon emissions while enhancing productivity, considering factors like production capacity, equipment status, resource input, and environmental impact. Therefore, we model Sand Casting Carbon Efficiency (SCE) as a four-dimensional function:
$$SCE = \{ SCE_{cp}, SCE_{eq}, SCE_{e}, SCE_{t} \}$$
The Four-Dimensional Carbon Efficiency Model for Sand Casting Services
1. Production Capacity Carbon Efficiency (\(SCE_{cp}\))
This dimension evaluates how much carbon is emitted per unit of production output. It is the ratio of total process carbon emissions to the production capacity (\(CP\)). For high-volume, small-part sand casting services, capacity may be measured in molds per hour; for other services, it might be tons of castings per unit time.
$$SCE_{cp} = \frac{C_{eq} + C_{neq}}{CP} = \frac{(C_{PC} + C_{LC}) + (C_{MC} + C_{EC} + C_{UC})}{CP}$$
Calculating production capacity requires understanding the hierarchical organization (process, cell, department) of the sand casting service. Capacity can be aggregated by summing capacities of parallel resources or determined by the bottleneck in a series. The formulas for equipment and labor-driven process capacity are:
$$CP_{eq} = \sum_{i=1}^{n} \frac{T_{wi} \times \eta_{eqi}}{t_{ri}} \quad \text{and} \quad CP_{pr} = \sum_{j=1}^{m} \frac{T_{pwj} \times \eta_{prj}}{t_{rj}}$$
where \(T_w\) and \(T_{pw}\) are effective working times, \(\eta\) are efficiency factors, and \(t_r\) are standard times.
2. Equipment Utilization Carbon Efficiency (\(SCE_{eq}\))
This metric focuses on the efficiency of the equipment itself. It is the ratio of equipment-related carbon emissions to the Overall Equipment Effectiveness (OEE), which considers availability, performance rate, and quality rate.
$$SCE_{eq} = \frac{\sum_{i=1}^{n} (C^i_{PC} + C^i_{LC})}{EP_{eq}}$$
where \(EP_{eq} = \sum \eta_{eq} \cdot TR_i \cdot DR_i \cdot PR_i = \sum \eta_{eq} \cdot \frac{N_{qi}}{t_{ai} t_{opi} C_{dri}}\). A lower \(SCE_{eq}\) indicates that equipment is producing usable output with relatively lower carbon emissions from its operation, a key goal for lean sand casting services.
3. Energy Consumption Carbon Efficiency (\(SCE_{e}\))
This dimension highlights the proportion of total carbon that comes directly from energy use (both electrical and direct fuels). It helps sand casting services identify how much of their carbon footprint is tied to energy versus materials.
$$SCE_{e} = \frac{\sum_{i=1}^{n} (C^i_{LC} + C^i_{PC} + C^i_{EC})}{C_{pro}}$$
A high \(SCE_{e}\) suggests energy consumption is the dominant source of emissions, pointing towards initiatives like equipment upgrades or heat recovery as priority areas for improvement.
4. Production Cycle Carbon Efficiency (\(SCE_{t}\))
This is a time-based efficiency measure, representing the average carbon emission intensity per unit of production cycle time. It encourages sand casting services to reduce both emissions and cycle times.
$$SCE_{t} = \frac{\sum_{i=1}^{n} (C^i_{LC} + C^i_{PC} + C^i_{MC} + C^i_{EC} + C^i_{UC})}{\sum_{j=1}^{m} \Delta_j}$$
where \(\Delta_j\) is the duration of the j-th production cycle. Optimizing for a lower \(SCE_{t}\) drives simultaneous improvements in environmental and operational performance.
Evaluating Carbon Efficiency Using Grey Relational Analysis
With multiple sand casting service lines or process routes, a comprehensive evaluation method is needed to rank them based on the four SCE dimensions. Grey Relational Analysis (GRA) is ideal for this multi-criteria, “poor-information” decision-making. The steps are as follows:
Step 1: Construct the Decision and Ideal Matrices. For \(m\) alternative process routes and the four SCE indicators, create the decision matrix \(CM\). Then, form the ideal matrix \(PCM\) by appending a row containing the optimal value for each indicator (e.g., the minimum value for all SCE metrics, as lower is better).
Step 2: Normalize the Data. To make different indicators comparable, normalize each value. Since lower SCE is better, we use the following normalization for cost-type indicators:
$$v_j(k) = \frac{\min_j cm_j(k)}{cm_j(k)}$$
where \(v_j(k)\) is the normalized value for alternative \(j\) on indicator \(k\), and \(cm_j(k)\) is the original value. This yields the normalized matrix \(V\).
Step 3: Calculate Grey Relational Coefficients. The coefficient \(\psi_j(k)\) measures the relationship between alternative \(j\)’s indicator \(k\) and the ideal value \(v(k)\).
$$\psi_j(k) = \frac{\min_j \min_k |v(k) – v_j(k)| + \xi \max_j \max_k |v(k) – v_j(k)|}{|v(k) – v_j(k)| + \xi \max_j \max_k |v(k) – v_j(k)|}$$
where \(\xi\) is the distinguishing coefficient, typically set to 0.5.
Step 4: Compute the Weighted Grey Relational Grade. Assign weights \(w_k\) to each of the four SCE dimensions (e.g., using entropy or AHP methods). The overall score for each sand casting service line is:
$$\gamma_j = \sum_{k=1}^{4} \psi_j(k) \cdot w_k$$
Step 5: Rank the Alternatives. The sand casting service line with the highest \(\gamma_j\) is the most carbon-efficient according to the multi-dimensional model.
Application in Sand Casting Services
Consider a foundry offering sand casting services for a batch of small gearbox housings. They have four different molding line configurations (L1 to L4) with varying levels of automation, from manual-heavy (L1) to fully integrated automated lines (L4). Using the PCS model, the carbon emissions for each line were calculated over a standard batch of 20 molds, as shown in the table below.
| Line ID | Process Description | \(C_{PC}\) (kgCO₂e) | \(C_{LC}\) (kgCO₂e) | \(C_{MC}\) (kgCO₂e) | \(C_{EC}\) (kgCO₂e) | \(C_{UC}\) (kgCO₂e) | Total \(C_{pro}\) (kgCO₂e) |
|---|---|---|---|---|---|---|---|
| L1 | Manual sand handling, mechanical molding | 7.2 | 10.5 | 95.0 | 3.1 | 4.8 | 120.6 |
| L2 | Semi-automated, hot-box process | 6.1 | 12.0 | 85.0 | 2.1 | 2.7 | 107.9 |
| L3 | Automated continuous line | 5.7 | 11.0 | 89.0 | 1.7 | 2.4 | 109.8 |
| L4 | High-pressure automated line | 7.0 | 15.0 | 93.0 | 2.9 | 3.6 | 121.5 |
The production parameters for each line were also recorded:
| Line ID | Molding Rate (molds/hr) | Equipment Efficiency (OEE) | Cycle Time (hrs/batch) |
|---|---|---|---|
| L1 | 30 | 0.60 | 0.667 |
| L2 | 42 | 0.87 | 0.476 |
| L3 | 40 | 0.83 | 0.500 |
| L4 | 40 | 0.79 | 0.500 |
Applying the four-dimensional SCE model, we calculate the carbon efficiency metrics for each sand casting service line:
| Carbon Efficiency | L1 | L2 | L3 | L4 |
|---|---|---|---|---|
| \(SCE_{cp}\) (kgCO₂e/mold) | 2.010 | 1.285 | 1.373 | 1.519 |
| \(SCE_{eq}\) (kgCO₂e/OEE point) | 29.50 | 20.84 | 20.12 | 27.85 |
| \(SCE_{e}\) (ratio) | 0.172 | 0.187 | 0.168 | 0.205 |
| \(SCE_{t}\) (kgCO₂e/hr) | 180.9 | 226.6 | 219.6 | 243.0 |
Using GRA with equal weights for simplicity, the normalized matrix \(V\) and the calculated Grey Relational Grades \(\gamma_j\) are:
$$V =
\begin{bmatrix}
1.000 & 1.000 & 0.842 & 0.744\\
0.639 & 0.705 & 0.914 & 0.933\\
0.683 & 0.682 & 0.818 & 0.904\\
0.756 & 0.944 & 1.000 & 1.000\\
0.639 & 0.682 & 0.818 & 1.000
\end{bmatrix}, \quad \gamma_1=0.453, \quad \gamma_2=0.759, \quad \gamma_3=0.845, \quad \gamma_4=0.576$$
The ranking is \(\gamma_3 > \gamma_2 > \gamma_4 > \gamma_1\). This result is critical for the sand casting service provider. While Line L4 had the highest absolute carbon emissions (121.5 kg), it is not the worst performer in terms of integrated carbon efficiency. Line L1, despite lower total emissions than L4, ranks last due to its very poor production capacity and equipment utilization efficiency. Line L3, the automated continuous line, is identified as the most carbon-efficient process route. It balances good production rate, high equipment utilization, and relatively low energy-based emissions, even though its total carbon is slightly higher than Line L2’s.
Conclusion and Implications for Sand Casting Services
The proposed modeling and evaluation framework provides sand casting services with a powerful tool to move beyond simple carbon accounting. By decomposing carbon efficiency into four distinct dimensions—production capacity, equipment utilization, energy consumption share, and production cycle intensity—the model offers a nuanced view of environmental performance. The integration of Grey Relational Analysis allows for a holistic comparison of different production lines or process technologies.
For managers and engineers in sand casting services, this approach enables targeted decision-making. A line with a high \(SCE_{eq}\) score needs focus on improving OEE through preventive maintenance or process stabilization. A line with a high \(SCE_{e}\) suggests investing in energy-efficient equipment or alternative fuels. The ultimate goal is to drive down all four SCE metrics simultaneously, leading to genuinely sustainable and competitive sand casting services.
Future work could integrate real-time data from IoT-enabled foundry equipment to create dynamic carbon efficiency dashboards. Furthermore, expanding the model to include the full lifecycle of the casting, from raw material extraction to end-of-life recycling, would provide an even more comprehensive sustainability assessment for advanced sand casting services. The path to low-carbon manufacturing is complex, but with precise models and evaluations, sand casting services can effectively navigate it, reducing their environmental impact while enhancing productivity and profitability.