## 5 A Case Study
### Analysis of Structure Layer of Product  
The \(Ft\) was decomposed into two parts, i.e., \(Ft_{1}\), and \(Ft_{3}\). It could be obtained based on the component modules of cutting machine that the \(Ft_{3}\) was mainly independently controlled by the moving component of cutting head, which was not influenced after the working mode was changed, but there was hidden danger of transmission chain fracture in the delivery system due to the working mode of \"cut material running through window\". Therefore, the \(Ft_{1}\) was extracted as the core function item in initial decomposition. The multi-layer FBS decomposition of the delivery system is shown in Figure 7. The following parts of the delivery system of cutting machine could be obtained from the structure layer: 01-Bristle brick support plate, 02-Upper slide rail, 03-Lower slide rail, 04-Main beam, 05-Brick, 06-Motor, 07-Driving shaft, 08-Flange bearing, 09-Driven shaft, 10-Sprocket, 11-Chain.  
The above parts were partially reduced to obtain the assembling parts of the product function body, namely, 01-Bristle brick support plate, 02-Upper slide rail, 03-Lower slide rail, 04-Main beam, 07-Driving shaft, 09-Driven shaft, 10-Sprocket, 11-Chain. The corresponding matter-element models are, respectively: \(M_{1},M_{2},M_{3},M_{4},M_{7},M_{9},M_{10},M_{11}\).  
The feature matter-element package units of all parts were constructed as follows:  
\(M_{1}\) = {\(M_{1-1}\)(Bristle brick mounting hole), \(M_{1-2}\)(Plate body mounting hole), \(M_{1-3}\)(Plate body)};  
\(M_{2}\) = {\(M_{2.1}\)(Square through hole), \(M_{2.2}\)(Rail body), \(M_{2.3}\)(Mounting hole)};  
\(M_{3}\) = {\(M_{3.1}\)(Square through hole), \(M_{3.2}\)(Rail body), \(M_{3.3}\)(Mounting hole)};  
\(M_{4}\) = {\(M_{4.1}\)(Beam body)};  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Functional** & \begin{tabular}{c} **Ideal** \\ **Domain \(X_{0}\)** \\ **(m/min)** \\ \end{tabular} & \begin{tabular}{c} **Extended** \\ **Domain \(X\)** \\ **(m/min)** \\ \end{tabular} & \begin{tabular}{c} **Optimal** \\ **Point \(x_{0}\)** \\ **(m/min)** \\ \end{tabular} & \
\begin{tabular}{c} **Actual Value** \\ **Function** \\ **(m/min)** \\ \end{tabular} &
\begin{tabular}{c} **Dependent** \\ **Function** \\ **Value k(x)** \\ \end{tabular} \\ \hline \(FP\) & (40,50) & (30,50) & 50 & 35 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dependent function value calculation.  
\(M_{7}\) = {\(M_{7}\)-1(Power transmission sprocket section), \(M_{7}\)-2(Bearing section), \(M_{7}\)-3(Sprocket section), \(M_{7,4}\)(Intermediate section), \(M_{7,5}\)(Sprocket section), \(M_{7,6}\)(Bearing section)];  
\(M_{9}\) = {\(M_{9-1}\)(Bearing section), \(M_{9,2}\)(Sprocket section), \(M_{9,3}\)(Intermediate section), \(M_{9,4}\)(Sprocket section), \(M_{9,5}\)(Bearing section)];  
\(M_{10}\) = {\(M_{10-1}\)(Mounting hole), \(M_{10,2}\)(Sprocket body)];  
\(M_{11}\) = {\(M_{11-1}\)(Chain body)}.  
A correlation network (Figure 8) was constructed with the feature matter-element packages of the above parts as nodes. A feature matter-element relationship set was constructed by extracting all feature matter-element nodes in Figure 8:  
\(R\) = {\(r_{1}\)-Dimension relationship; \(r_{2}\)-Fit relationship; \(r_{3}\)-Position relationship; \(r_{4}\)-Transmission relationship; \(r_{5}\)-Boolean relationship; \(r_{6}\)-Connection relationship].  
The values of 6 types of correlation relationships between all feature matter-element nodes were recorded in a matter-element correlation matrix of delivery system of cutting machine, as shown in Table 4, which clearly described the dimension relationship, fit relationship, position relationship, transmission relationship, Boolean relationship, and connection relationship between feature matter-element nodes.