The imperative for sustainable manufacturing has placed significant pressure on energy-intensive industries to reduce their environmental footprint. As a foundational manufacturing process, sand casting is a major consumer of energy and a notable source of greenhouse gas emissions, particularly within the broader mechanical manufacturing sector. While technological advancements and the adoption of modern production lines are common strategies for improvement, the scientific evaluation of the effectiveness of these technical renovation schemes in terms of carbon reduction remains a critical challenge. A systematic methodology is needed to assess whether proposed upgrades genuinely enhance carbon efficiency—the relationship between productive output and carbon emissions—rather than merely shifting environmental burdens. This article, drawing from my research, proposes a comprehensive framework for evaluating the carbon efficiency validity of technical improvement plans in sand casting production, with a focus on the process characteristics inherent to manufacturing sand casting parts.
The core of the methodology lies in a two-tiered modeling approach: first, quantifying the carbon emissions from the process itself, and second, defining metrics for carbon efficiency. The evaluation model then integrates these elements with a novel weighting scheme that considers the intrinsic advantages of each proposed technical solution.
1. Process Carbon Source Modeling for Sand Casting
To accurately quantify emissions, the sand casting process is decomposed into its fundamental carbon-generating activities, termed “Process Carbon Sources.” Based on an analysis of the material, energy, and pollution flows during the production of sand casting parts, five distinct categories of carbon sources are defined:
1. Idle (Standby) Carbon Source (PC): Represents emissions from equipment in a basic running or standby state.
$$ C_{PC} = P_o \cdot t_{PC} \cdot E_e $$
where $P_o$ is the idle/standby power, $t_{PC}$ is the idle time, and $E_e$ is the carbon emission factor for electricity.
2. Load Carbon Source (LC): Represents emissions from equipment under operational load.
$$ C_{LC} = (P_o + \mu \cdot W_e \cdot P_w) \cdot t_{LC} \cdot E_e $$
where $P_w$ is the additional power per unit load weight, $t_{LC}$ is the load operation time, $\mu$ is the equipment power loss coefficient, and $W_e$ is the load weight.
3. Material Consumption Carbon Source (MC): Embodies emissions from the production stages of consumed materials (e.g., sand, binders, metals).
$$ C_{MC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (E_{S_k} \cdot U_i) \cdot E_e $$
where $U_i$ is the mass of the $i$-th material, and $E_{S_k}$ is the electricity consumed per unit mass of the $i$-th material at its $k$-th processing stage.
4. Energy Consumption Carbon Source (EC): Accounts for direct emissions from the combustion of non-electric energy sources like natural gas or coke.
$$ C_{EC} = \sum_{i=1}^{n} V_i \cdot E_i $$
where $V_i$ is the consumption volume of the $i$-th energy source, and $E_i$ is its carbon emission factor.
5. Undesirable Output Carbon Source (UC): Captures the indirect emissions from treating waste and pollutants generated during the process (e.g., waste sand, fumes, defective castings).
$$ C_{UC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (E_{U_k} \cdot Q_i \cdot \phi_i) \cdot E_e $$
where $Q_i$ is the mass of the $i$-th undesirable output, $E_{U_k}$ is the electricity consumed per unit mass for its $k$-th treatment stage, and $\phi_i$ is a treatment difficulty coefficient.
2. Carbon Efficiency Calculation Model for Sand Casting
Carbon efficiency measures the ability to reduce emissions while maintaining or increasing productivity. For the multi-faceted process of creating sand casting parts, a four-dimensional carbon efficiency model is constructed, as summarized in the table below.
| No. | Carbon Efficiency Type | Calculation Model | Description |
|---|---|---|---|
| 1 | Production Capacity Carbon Efficiency ($SCE_{cp}$) | $$ SCE_{cp} = \frac{(C_{PC}+C_{LC}) + (C_{MC}+C_{EC}+C_{UC})}{C_P} $$ | Total emissions per unit of production output per hour. A lower value indicates higher efficiency. |
| 2 | Equipment Utilization Carbon Efficiency ($SCE_{eq}$) | $$ SCE_{eq} = \frac{\sum_{i=1}^{n}(C_{iPC} + C_{iLC})}{EP_{eq}} $$ | Equipment-related emissions per unit of overall equipment effectiveness (OEE). A lower value is better. |
| 3 | Energy Consumption Carbon Efficiency ($SCE_{e}$) | $$ SCE_{e} = \frac{\sum_{i=1}^{n}(C_{iLC} + C_{iPC} + C_{iEC})}{C_{process}} $$ | Ratio of equipment and direct energy emissions to total process emissions. A lower, dimensionless value is better. |
| 4 | Production Cycle Carbon Efficiency ($SCE_{t}$) | $$ SCE_{t} = \frac{\sum_{i=1}^{n}(C_{iLC}+C_{iPC}+C_{iMC}+C_{iEC}+C_{iUC})}{\sum_{j=1}^{m} \Delta_j (t_2 – t_1)} $$ | Total emissions per hour of the production cycle. A lower value indicates higher efficiency. |
Where $C_P$ is the production capacity (e.g., molds/hour or tons/hour), $EP_{eq}$ is the Overall Equipment Effectiveness, $C_{process}$ is the total carbon emissions of the process stage, and $\Delta_j (t_2 – t_1)$ is the duration of the $j$-th production cycle.
For a simplified yet comprehensive metric, an Integrated Carbon Efficiency ($ICE$) index is proposed, combining production capacity and equipment utilization aspects:
$$ ICE = \frac{ \frac{C_{PC} + C_{LC}}{EP_{eq}} + (C_{MC} + C_{EC} + C_{UC}) }{C_P} $$
This index serves as a key performance indicator for evaluating the carbon efficiency of systems producing sand casting parts.
3. Validity Evaluation Model Based on Self-Advantage Degree
The “carbon efficiency validity” of a technical renovation plan is defined as a set of characteristics measuring its effectiveness in lowering emissions and improving productivity. The feature set $PUE_{CE}$ is:
$$ PUE_{CE} = \{ PU_{CC}, PU_{CCE}, PU_{CPCS}, PU_{CKPMA}, PU_{COT} \} $$
These represent features related to total carbon impact ($PU_{CC}$), carbon efficiency impact ($PU_{CCE}$, e.g., $ICE$), process carbon source impact ($PU_{CPCS}$), key process module area impact ($PU_{CKPMA}$), and other influences ($PU_{COT}$). Through expert assessment (e.g., Fuzzy Delphi method), a final set of key validity evaluation indicators $I_{PLA} = \{I_{PLA_1}, I_{PLA_2}, …, I_{PLA_p}\}$ is determined.
The crux of the evaluation is to determine objective weights for these indicators. Traditional methods often ignore the intrinsic strengths of the proposed plans themselves. This methodology introduces the concept of “Self-Advantage Degree” ($sd$), which quantifies how close a plan’s performance is to the ideal positive solution across all indicators, based on a weighting that maximizes its own perceived advantage.
Given $n$ alternative plans $PLA = \{pla_1, pla_2, …, pla_n\}$ and $m$ evaluation indicators $I_{PLA}$, a standardized decision matrix $SM_{PLA}$ is constructed from the plans’ performance data. For each plan $pla_i$, its self-advantage degree model seeks the weight vector $w_i = (w_{i1}, w_{i2}, …, w_{im})^T$ that maximizes its relative closeness to the positive ideal solution ($u_o$, best values) versus the negative ideal solution ($u_w$, worst values):
$$
\begin{aligned}
\text{Maximize } & sd_i = \frac{ed_{w_i}}{ed_{o_i} + ed_{w_i}} = \frac{\sum_{j=1}^{m} (u^*_{ij} – u_{w_j})^2 w_{ij}^2}{\sum_{j=1}^{m} (u^*_{ij} – u_{o_j})^2 w_{ij}^2 + \sum_{j=1}^{m} (u^*_{ij} – u_{w_j})^2 w_{ij}^2} \\
\text{Subject to } & \sum_{j=1}^{m} w_{ij} = 1, \quad 0 \leq w_{ij} \leq \kappa
\end{aligned}
$$
where $ed_{o_i}$ and $ed_{w_i}$ are the weighted Euclidean distances to the positive and negative ideal points, respectively, and $\kappa$ is a weight restriction coefficient (typically 0.5). Solving this for all $n$ plans yields a self-advantage weight matrix $M_{ADV}$. The final comprehensive weight vector $w_E$ is derived as the normalized principal eigenvector of the matrix $M_{ADV}M_{ADV}^T$, which integrates the perspective of all plans:
$$ \lambda_{max} = \max \sum_{i=1}^{n} [w_i^{*T}w_i^*]^2, \quad \text{s.t.} \quad \|w\|_2 = 1 $$
$$ w_E = \lambda^*_{max} = \{w^*_1, w^*_2, …, w^*_m\} $$
The final validity evaluation score $Y$ for each plan is then calculated by:
$$ Y = (y_1, y_2, …, y_n)^T = SM_{PLA} \cdot w_E $$
The plan with the most favorable score is deemed to have the highest carbon efficiency validity.
4. Case Study: Technical Renovation of a Molding Line
The methodology was applied to evaluate four proposed technical renovation plans for a manual molding line in a foundry enterprise. The original process for producing sand casting parts involved significant manual operations like hand ramming, manual pattern drawing, and core setting, leading to high emissions and low efficiency.
Key Process Module Areas ($PMA$) were identified: $PMA_1$: Sand Mixing & Testing; $PMA_2$: Sand Filling, Compaction & Drawing; $PMA_3$: Coating; $PMA_4$: Core Setting, Closing, Transfer & Weighting; $PMA_5$: Material & Mold Transportation. The baseline carbon emissions and efficiency were calculated.
Four distinct renovation plans (A, B, C, D) were proposed, each with different technological focuses (e.g., upgrading specific PMAs, optimizing logistics). Their projected performance data for key validity indicators were collected. For this evaluation, the selected indicators $I_{PLA}$ were: Integrated Carbon Efficiency ($ICE$), Total Process Emissions ($C_{process}$), Material Carbon Source ($C_{MC}$), Undesirable Output Carbon Source ($C_{UC}$), and carbon emissions from three key PMAs: Transportation ($C_{KPMA_1}$), Compaction ($C_{KPMA_2}$), and Sand Mixing ($C_{KPMA_3}$).
The evaluation data matrix was constructed and standardized. The positive and negative ideal points were determined as the best and worst values among the four plans for each indicator. The self-advantage degree model was solved for each plan, yielding the self-advantage weight matrix $M_{ADV}$. The final integrated weight vector $w_E$ was calculated as:
$$ w_E = [0.084, 0.094, 0.192, 0.140, 0.220, 0.110, 0.160] $$
This indicates, for instance, that emissions from the Transportation PMA received the highest weight (0.220) in the final evaluation under this methodology.
The final validity scores were computed:
| Plan | Validity Score ($y_i$) | Rank |
|---|---|---|
| Plan B | 0.458824 | 1 |
| Plan D | 0.496873 | 2 |
| Plan C | 0.499386 | 3 |
| Plan A | 0.534308 | 4 |
Plan B was identified as the most valid solution. Analysis revealed that Plan B’s strength lay in its balanced and significant reduction across multiple carbon source categories and key process modules, particularly in non-transport areas, which aligned well with the comprehensively derived weights. This result provided a scientifically-grounded recommendation for the foundry’s investment decision, moving beyond simple cost or single-metric analysis.
5. Conclusion
This article presents a robust, multi-layered methodology for constructing and applying a carbon efficiency validity model tailored for the sand casting industry. By first establishing granular process carbon source models and multi-dimensional carbon efficiency metrics, the framework enables precise quantification of the environmental performance of operations dedicated to sand casting parts. The innovative self-advantage degree weighting mechanism introduces a fair and objective way to integrate the inherent strengths of different technical renovation proposals into the evaluation, leading to a more holistic and strategic assessment. The case study demonstrates the practical viability of the method, showing how it can guide foundries toward selecting renovation plans that truly and effectively balance productivity enhancement with meaningful carbon emission reductions. Future work will focus on extending the application of this validity evaluation model to a wider range of manufacturing processes and incorporating dynamic, real-time data for continuous improvement.