As a foundational process in manufacturing, sand casting plays a critical role in producing various industrial components, especially sand casting parts. However, the industry faces significant challenges due to high energy consumption and substantial carbon emissions. To address this, I propose a methodology for constructing process carbon sources based on event procedure nodes, enabling systematic calculation and analysis of carbon emissions in sand casting production. This approach transforms traditional process descriptions into a standardized form of process carbon sources, facilitating low-carbon optimization. In this article, I will detail the models, methods, and applications, with a focus on enhancing the environmental performance of sand casting parts manufacturing.
The concept of process carbon sources stems from definitions by the Intergovernmental Panel on Climate Change (IPCC) and the British Standards Institute (BSI), which describe carbon sources as fluxes, processes, systems, or mechanisms that release carbon into the environment. In sand casting, I categorize process carbon sources into five types based on their roles in production activities: Material Consumption Carbon Source (MC), Non-Expectation Carbon Source (UC), No-Load (Standby) Carbon Source (PC), Load Carbon Source (LC), and Energy Consumption Carbon Source (EC). Each type corresponds to specific emission generation mechanisms during process execution. The calculation models for these carbon sources are summarized in Table 1.
| Serial Number | Process Carbon Source Type | Symbol | Meaning of Process Carbon Source | Calculation Model for Process Carbon Source |
|---|---|---|---|---|
| 1 | Material Consumption Carbon Source | MC | Carbon emissions generated from consuming various materials during process execution. | $$C_{MC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot U_i) \cdot E_e$$ |
| 2 | Non-Expectation Carbon Source | UC | Carbon emissions generated from treating pollutants during process execution. | $$C_{UC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot Q_i \cdot \phi_i) \cdot E_e$$ |
| 3 | No-Load (Standby) Carbon Source | PC | Carbon emissions generated while equipment maintains a running state waiting to enter a working state. | $$C_{PC} = P_o \cdot t \cdot E_e$$ |
| 4 | Load Carbon Source | LC | Carbon emissions generated during equipment operation under load conditions. | $$C_{LC} = (P_o + \mu \cdot W_e \cdot P_w) \cdot t \cdot E_e$$ |
| 5 | Energy Consumption Carbon Source | EC | Carbon emissions generated from energy consumption other than electricity during process execution. | $$C_{EC} = \sum_{i=1}^{n} V_i \cdot E_i$$ |
In these formulas, $P_o$ represents the no-load or standby power of casting equipment, $t$ is the operating time, $E_e$ is the carbon emission coefficient for electricity, $P_w$ is the additional power per unit weight of equipment, $\mu$ is the power loss coefficient, $W_e$ is the load weight, $U_i$ is the quantity of the $i$-th material consumed, $ES_k$ is the electricity consumption at the $k$-th processing stage of materials, $V_i$ is the amount of the $i$-th energy type consumed, $E_i$ is the carbon emission coefficient for the $i$-th energy, $Q_i$ is the quantity of the $i$-th non-expectation substance produced, and $\phi_i$ is the treatment difficulty coefficient for the $i$-th non-expectation substance.
To further characterize these carbon sources, I define eight feature elements that describe the attributes of sand casting processes, as shown in Table 2. These elements include Time Element (TCE), Load Element (WCE), Load Power Element (LCE), No-Load Power Element (PCE), Standby Element (SCE), Non-Expectation Element (UCE), Material Element (MCE), and Energy Element (ECE). They capture key parameters such as duration, power characteristics, and resource consumption, which are essential for carbon emission calculations. For instance, in producing sand casting parts, the time and load elements directly influence the energy use during molding and pouring stages.
| Serial Number | Process Carbon Source Feature Element | Symbol | Meaning |
|---|---|---|---|
| 1 | Time Element | TCE | Represents the duration that a process activity maintains the same state, including no-load working time ($t_p$), load working time ($t_l$), and standby time ($t_s$). |
| 2 | Load Element | WCE | The magnitude of load during process execution. |
| 3 | Load Power Element | LCE | Power characteristics under load state during process execution. |
| 4 | No-Load Power Element | PCE | Power characteristics under no-load state during process execution. |
| 5 | Standby Element | SCE | Power characteristics under standby state during process execution. |
| 6 | Non-Expectation Element | UCE | Non-expectation features of pollutant objects produced during process execution, including waste gas, slag, waste sand, wastewater, etc. |
| 7 | Material Element | MCE | Various material resource objects consumed during process execution, including materials, water, gas, oil, etc. |
| 8 | Energy Element | ECE | Energy objects consumed other than electricity during process activities. |
Building on these foundations, I develop an event procedure node model to formalize the sand casting process. A sand casting process event procedure node (EPP) is defined as a set of processes that reflect the information states of participating objects under the action of operation or execution events. The $i$-th event procedure node is expressed as:
$$EPP_i = \{ EP_i, P_i, WU_i, EO_i \}$$
Here, $EP_i = (ep_1, ep_2, \ldots, ep_l)$ represents the set of events contained in the node, $P_i = (p_{i1}, p_{i2}, \ldots, p_{io})$ is the set of processes, $WU_i = (wu_{i1}, wu_{i2}, \ldots, wu_{iu})$ denotes the set of work units required, and $EO_i = (eo_{i1}, eo_{i2}, \ldots, eo_{iv})$ is the set of resource objects involved or produced, such as materials, energy, and emissions. This model serves as a functional collection that describes relationships among events, processes, time, and resources, enabling state tracking during production, which is crucial for optimizing the manufacturing of sand casting parts.
Each process in sand casting involves a series of operation activities, which I describe as procedure events. A single procedure event $ep$ is defined as:
$$ep = ep(eid, ea, esc, tm, es)$$
where $eid$ is the event identifier, $ea$ is the attribute set of participating objects, $esc$ is the event type set, $tm$ is the timestamp at the observation point, and $es$ is the state set at time $tm$. For a process $p_i$ composed of event set $EP$, it can be described as:
$$p_i = (pid, EP, pat, T)$$
with $pid$ as the process identifier, $pat$ as the attribute set, and $T$ as the duration set for events. To handle relationships among events, I define operation symbols based on complex event processing principles, as listed in Table 3. These symbols formalize the execution logic in sand casting processes, such as sequencing and conditional activation, which affect carbon emission patterns during the production of sand casting parts.
| Name, Symbol Representation | Expression | Meaning of Procedure Event Execution |
|---|---|---|
| AND “$\wedge$” | $ep_a \wedge ep_b$ | If event $ep_a$ is activated and event $ep_b$ is activated, then event $ep(ep_a \wedge ep_b)$ is activated, regardless of activation order. |
| OR “$\vee$” | $ep_c \vee ep_d$ | If either event $ep_c$ or event $ep_d$ is activated, then event $ep(ep_c \vee ep_d)$ is activated, regardless of activation order. |
| NOT “$\neg$” | $\neg ep_e$ | If event $ep_e$ is not activated, then event $ep(\neg ep_e)$ is activated. |
| SEQUENCE “;” | $ep_f; ep_g$ | If event $ep_f$ is activated before event $ep_g$, then event $ep(ep_f; ep_g)$ is activated. |
| CONDITION CONSTRAINT “WITHIN” | $WITHIN(ep_i, WTI)$ | If event $ep_i$ is under condition $WTI$, then event $ep_{WITHIN(ep_i, WTI)}$ is activated, with $WTI \neq \emptyset$. |
To capture state transitions during process execution, I construct a procedure event state matrix. Assuming a process $p$ has $n$ states, such as start, run, pause, interrupt, and stop, denoted as $S(p) = [s(p)_1, s(p)_2, \ldots, s(p)_n]$, the state vector for event $ep_i$ is:
$$esm(ep_i) = [t(ep_i)_1, t(ep_i)_2, \ldots, t(ep_i)_j, \ldots, t(ep_i)_n]$$
where $t(ep_i)_j$ is the duration of the $j$-th state during event $ep_i$. For a process with $m$ events, the state matrix $ESM(p)$ is an $m \times n$ matrix:
$$ESM(p) =
\begin{bmatrix}
esm(ep_1) \\
esm(ep_2) \\
\vdots \\
esm(ep_i) \\
\vdots \\
esm(ep_m)
\end{bmatrix}
\times
\begin{bmatrix}
s(p)_1 \\
s(p)_2 \\
\vdots \\
s(p)_j \\
\vdots \\
s(p)_n
\end{bmatrix}^T
=
\begin{bmatrix}
t(ep_1)_1 & t(ep_1)_2 & \ldots & t(ep_1)_j & \ldots & t(ep_1)_n \\
t(ep_2)_1 & t(ep_2)_2 & \ldots & t(ep_2)_j & \ldots & t(ep_2)_n \\
\vdots & \vdots & & \vdots & & \vdots \\
t(ep_i)_1 & t(ep_i)_2 & \ldots & t(ep_i)_j & \ldots & t(ep_i)_n \\
\vdots & \vdots & & \vdots & & \vdots \\
t(ep_m)_1 & t(ep_m)_2 & \ldots & t(ep_m)_j & \ldots & t(ep_m)_n
\end{bmatrix}$$
This matrix describes the state durations for all events in a process, allowing calculation of total event running time: $t_{ep_i} = \sum_{j=1}^{n} t(ep)_{ij}$. For sand casting parts production, this helps quantify energy consumption periods, such as in molding or cooling stages.
Next, I integrate this with a weighted directed graph model to form a comprehensive sand casting process model based on event procedures. The model is defined as:
$$GPM = (EPP, \{R, RPP, REP\}, \{PF, EP\}, \{IFP, WP_p, WE_p\})$$
Here, $\{R, RPP, REP\}$ are directed edge sets, where $RPP$ links feature elements to nodes, and $REP$ links event elements to nodes. $\{PF, EP\}$ are element object sets, with $PF = \{TCE, WCE, LCE, PCE, SCE, UCE, MCE, ECE\}$ being the eight feature elements. $\{IFP, WP_p, WE_p\}$ are weight sets, where $WP_p$ reflects attribute values of feature elements, and $WE_p$ reflects attribute values of event sets, specifically the state matrix $ESM(p)$. The relationship between $m$ procedure events and the eight feature elements is represented by a matrix $CPCSM$:
$$CPCSM =
\begin{bmatrix}
TCE_1 & WCE_1 & LCE_1 & PCE_1 & SCE_1 & UCE_1 & MCE_1 & ECE_1 \\
TCE_2 & WCE_2 & LCE_2 & PCE_2 & SCE_2 & UCE_2 & MCE_2 & ECE_2 \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
TCE_i & WCE_i & LCE_i & PCE_i & SCE_i & UCE_i & MCE_i & ECE_i \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
TCE_m & WCE_m & LCE_m & PCE_m & SCE_m & UCE_m & MCE_m & ECE_m
\end{bmatrix}$$
The construction steps for $GPM$ involve building a base weighted directed graph model, adding feature element nodes $PF$ and procedure event sets $EP$, and integrating them with weights. This model facilitates carbon emission analysis by mapping process states to carbon source parameters, which is vital for assessing the environmental impact of sand casting parts.
Based on the event procedure node model, I propose a method to construct process carbon sources for sand casting. The steps are as follows:
Step 1: Establish the event set for the production process event procedure node. For node $EPP$, let the event set be $EP = (ep_1, ep_2, \ldots, ep_m)$ with $m$ events.
Step 2: Build the state matrix $ESM$ for the event procedure node using Equation (5).
Step 3: Based on the event set $EP$ and state matrix $ESM$, construct the process carbon source composition matrix $PCSM$ for each event. This matrix describes the relationship between procedure events and process carbon sources:
$$PCSM =
\begin{bmatrix}
r_{pcs11} & r_{pcs12} & r_{pcs13} & r_{pcs14} & r_{pcs15} \\
r_{pcs21} & r_{pcs22} & r_{pcs23} & r_{pcs24} & r_{pcs25} \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
r_{pcsi1} & r_{pcsi2} & r_{pcsi3} & r_{pcsi4} & r_{pcs15} \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
r_{pcsm1} & r_{pcsm2} & r_{pcsm3} & r_{pcsm4} & r_{pcsm5}
\end{bmatrix}$$
where $r_{pcsij}$ is a relationship function: $r_{pcsij} = 1$ if the $i$-th event involves the $j$-th process carbon source, and $0$ otherwise. The five carbon source types are ordered as $PC, LC, MC, EC, UC$. The transformation is expressed as:
$$[EP][ESM] \rightarrow PCSM$$
Step 4: Convert to obtain the process carbon sources for the event procedure node. Let $PCS = \{PC, LC, MC, EC, UC\}$ with matrix $[PCS] = [PC, LC, MC, EC, UC]^T$. Then, the process carbon source composition set $EP_{pcs}$ is:
$$EP_{pcs} = PCSM \cdot [PCS] =
\begin{bmatrix}
r_{pcs11} \cdot PC & r_{pcs12} \cdot LC & r_{pcs13} \cdot MC & r_{pcs14} \cdot EC & r_{pcs15} \cdot UC \\
r_{pcs21} \cdot PC & r_{pcs22} \cdot LC & r_{pcs23} \cdot MC & r_{pcs24} \cdot EC & r_{pcs25} \cdot UC \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
r_{pcsn1} \cdot PC & r_{pcsn2} \cdot LC & r_{pcsn3} \cdot MC & r_{pcsn4} \cdot EC & r_{pcsn5} \cdot UC
\end{bmatrix}$$
The $i$-th event is represented in process carbon source form as:
$$ep_{pcs}^i \rightarrow \{ r_{pcs11} \cdot PC, r_{pcs12} \cdot LC, r_{pcs13} \cdot MC, r_{pcs14} \cdot EC, r_{pcs15} \cdot UC \}$$
For the entire node, the expression is:
$$EP_{pcs} \rightarrow \left\{ \left[ \sum_{i=1}^{m} r_{pcs11} \right] \cdot PC, \left[ \sum_{i=1}^{m} r_{pcs12} \right] \cdot LC, \left[ \sum_{i=1}^{m} r_{pcs13} \right] \cdot MC, \left[ \sum_{i=1}^{m} r_{pcs14} \right] \cdot EC, \left[ \sum_{i=1}^{m} r_{pcs15} \right] \cdot UC \right\}$$
where $\sum_{i=1}^{m} r_{pcsij}$ indicates the quantity of each carbon source type. The carbon emission calculation for the $j$-th event procedure node with $m$ events is:
$$C_{EPP_j} = [C_{ep1}, C_{ep2}, \ldots, C_{epi}, \ldots, C_{epm}]^T = CPCSM \gamma EP_{pcs} = CPCSM \gamma (PCSM \cdot [PCS])$$
Here, $\gamma$ denotes mapping and summation of matrices. For the $i$-th event in the node:
$$C_{epi} = CPCSM_i \gamma EP_{pcs}^i = CPCSM_i \gamma (PCSM_i \cdot [PCS])$$
The parameters for the eight feature elements are derived from work unit sets $WU$, resource object sets $EO$, and feature element definitions. This method systematically translates sand casting processes into carbon source expressions, enabling precise emission calculations for sand casting parts.
To validate the methodology, I apply it to a sand molding production line in a foundry enterprise. This line produces vehicle housing parts, which are typical sand casting parts made from HT250 material with a theoretical weight of 0.36 tons including the gating system. The process steps include sand mixing, transportation, molding, closing, cleaning, and curing. For this example, I focus on the sand mixing event procedure node $EPP_1$, which comprises four events: feeding ($ep_1$), mixing ($ep_2$), pause ($ep_3$), and sand discharge ($ep_4$). The event set is $EP = (ep_1, ep_2, ep_3, ep_4)$, with state durations as shown in Table 4.
| Procedure State | Average Execution Time (hours) for $ep_1$ | Average Execution Time (hours) for $ep_2$ | Average Execution Time (hours) for $ep_3$ | Average Execution Time (hours) for $ep_4$ |
|---|---|---|---|---|
| Start | 0.01 | 0.08 | 0 | 0 |
| Run | 0.14 | 0.50 | 0.07 | 0.05 |
| Pause | 0.08 | 0.07 | 0 | 0 |
| Interrupt | 0 | 0 | 0 | 0 |
| Stop | 0.01 | 0.01 | 0 | 0.01 |
Using Equation (5), the state matrix $ESM(EP)$ is constructed:
$$ESM(EP) =
\begin{bmatrix}
0.01 & 0.14 & 0.08 & 0 & 0.01 \\
0.08 & 0.50 & 0.07 & 0 & 0.01 \\
0 & 0.07 & 0 & 0 & 0 \\
0 & 0.05 & 0 & 0 & 0.01
\end{bmatrix}$$
Following Step 3, the $PCSM$ matrix is derived:
$$PCSM =
\begin{bmatrix}
1 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 1
\end{bmatrix}$$
Thus, the process carbon source representation for $EPP_1$ is:
$$EP_{pcs1} = PCSM_1 \cdot [PCS] =
\begin{bmatrix}
PC & LC & MC & 0 & UC \\
PC & LC & 0 & 0 & UC \\
PC & 0 & 0 & 0 & 0 \\
PC & LC & 0 & 0 & UC
\end{bmatrix}$$
This translates to: $EP_{pcs1} \rightarrow \{ [4] \cdot PC, [3] \cdot LC, [1] \cdot MC, [0] \cdot EC, [3] \cdot UC \}$. For carbon emission calculation, I use enterprise data: the sand mixer has average standby power of 0.4 kW, no-load power of 3 kW, and load power of 0.6 kW/ton; the feeding equipment has standby power of 0.1 kW, no-load power of 1 kW, and load power of 0.1 kW/ton. Event durations are: $t_{p1} = 0.01$ h (no-load), $t_{l1} = 0.14$ h (load), $t_{s1} = 0.09$ h (standby) for $ep_1$; similar values for other events. Loads are $ep_1 = 2$ t, $ep_2 = 2$ t, $ep_3 = 0$ t, $ep_4 = 2$ t. Non-expectation emissions (dust) are $ep_1 = 0.0001$ t, $ep_2 = 0.0001$ t, $ep_4 = 0.0001$ t. Material consumption (resin sand) is 2 tons for $ep_1$. Other energy consumption is negligible. The feature element relationship matrix $CPCSM$ is:
$$CPCSM =
\begin{bmatrix}
t_{p1}=0.01 & t_{l1}=0.14 & t_{s1}=0.09 & 2 & 0.1 & 1 & 0.1 & 0.0001 & 2 & 0 \\
t_{p2}=0.08 & t_{l2}=0.50 & t_{s2}=0.08 & 2 & 0.6 & 3 & 0.4 & 0.0001 & 0 & 0 \\
t_{p3}=0 & t_{l3}=0 & t_{s3}=0.07 & 0 & 0.6 & 3 & 0.4 & 0 & 0 & 0 \\
t_{p4}=0 & t_{l4}=0.05 & t_{s4}=0.01 & 2 & 0.6 & 3 & 0.04 & 0.0001 & 0 & 0
\end{bmatrix}$$
Applying Equation (18) with carbon emission coefficients (e.g., $E_e = 4.035$ kg CO2/kWh for electricity, and material emission factors), the carbon emissions for $EPP_1$ are computed. For instance, $C_{ep1} = 31.68105$ kg CO2, primarily due to material consumption. The breakdown by carbon source type is: $C_{PC} = 1.90856$ kg CO2, $C_{LC} = 2.59718$ kg CO2, $C_{MC} = 31.4358$ kg CO2, $C_{EC} = 0$ kg CO2, and $C_{UC} = 0.1668$ kg CO2. This analysis highlights that material consumption is the largest contributor, emphasizing the need for optimizing sand usage in sand casting parts production.
The event procedure node model also supports aggregation of multiple events, which is useful for complex processes. Consider two processes $p_a$ and $p_b$ within a node, with event state matrices $ESM_a$ and $ESM_b$. To form a combined state matrix $ESM_{EPP}$, I first extend each matrix with attributes: $ESM^* = ESM \times [esc, tm, te_p]^T$, where $esc$ is event type, $tm$ is activation time, and $te_p$ is running time. Then, aggregation is performed by concatenation: $ESM_{EPP} = [ESM^*_a; ESM^*_b]$. For events of the same type, similarity-based aggregation can simplify the matrix. If $k$ events have similar states, they are merged using:
$$ep = ep_l + ep_{l+1} = [t(ep)_{l1} + t(ep)_{(l+1)1}, \ldots, t(ep)_{lj} + t(ep)_{(l+1)j}, \ldots, t(ep)_{ln} + t(ep)_{(l+1)n}, esc_i, (tm_l, tm_{l+1}), te_{p_l} + te_{p_{l+1}}]$$
For two processes with $u$ and $v$ events in type $i$, if all events are similar ($k = u = v$), the aggregated matrix is $EPM^{i}_{p_a+p_b} = EPM^{i}_{p_a} + EPM^{i}_{p_b}$. If only $k < \min(u,v)$ events are similar, the matrix becomes $EPM^{i}_{p_a+p_b} = [EPM^{i}_{p_a}(k) + EPM^{i}_{p_b}(k)] \oplus [EPM^{i}_{p_a}(u-k) \oplus EPM^{i}_{p_b}(v-k)]$, where $\oplus$ denotes matrix concatenation. This aggregation capability enhances scalability for large-scale production of sand casting parts, allowing efficient carbon emission modeling across multiple processes.
In conclusion, I have developed a methodology for constructing process carbon sources in sand casting based on event procedure nodes. This approach formalizes sand casting processes through event-driven models, enabling systematic transformation into carbon source expressions for emission calculation. The integration of feature elements and state matrices provides a robust framework for analyzing and optimizing carbon footprints, particularly in the manufacturing of sand casting parts. The application to a sand molding line demonstrates practical utility, revealing key emission hotspots such as material consumption. Future work could focus on dynamic carbon efficiency optimization and real-time monitoring systems. By advancing these methods, the sand casting industry can move toward greener production, contributing to sustainable manufacturing goals while maintaining the quality and efficiency of sand casting parts.