# Research on Process Quality Prediction and Control of Spindle Housings in Flexible Production Lines
## 2 Flexible Production Line for Spindle Housing
### Spindle Housing Critical Process Machining Features Model  
The machining process of spindle housing mainly includes milling, drilling, tapping, and boring. Consider the machining process of the spindle housing as an example for establishing the complex network model. To visualize and express the correlations among the machining features of the spindle housing process, the machining features and their correlations are abstractly represented as a binary graph G = (V, E) to determine the machining features and the number of machining features, according to Table 1.  
The machining features of the spindle housing are abstracted as points, and the correlation relationships among the machining features are outlined as edges. If the edge in the network model is expressed as vi\(\rightarrow\)vj, it means that vj is processed with vi as the benchmark or that vj is evolved from vi; if there is no connection between the nodes, it means that there is no correlation between the machining features. As shown in Figure 3.  
A complex network graph of machining features visualizes the relationships among individual machining features but cannot accurately determine the criticality of the nodes in the model. To further analyze the identification, the structural relationship of the complex network is abstractly represented as an adjacency matrix A, where aij\(\in\){0, 1}, (i,j = 1,2,..., n), indicates whether there is an association relationship between node i and node j. If the value of a is 0, it suggests an association relationship between network node i and node j, and if the value is 1, then there is no association relationship. \[A= \begin{bmatrix}a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nm}\end{bmatrix} \] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Code** & **Code Meaning** & **Number of Features** \\ \hline XCMZ & The left side of the box & 1 \\ XCMY & The right side of the box & 1 \\ DWCMZ & The left side of the left rail & 1 \\ DWCMY & Right rail outer side & 1 \\ DWCMY\_Q & The Notch on the outside of the right rail & 3 \\ XCMZ\_K & Bottom hole on the left side of the box & 8 \\ XCMY\_K & Bottom hole of the right side of the box & 10 \\ DWCMZ\_K & Bottom hole of the outer side of the left rail & 4 \\ DWCMY\_QK & Bottom hole of the outer side of the right rail & 4 \\ DWCMY\_QK & Bottom hole of the outer rail outer side notch & 6 \\ XCMY\_GK & The right side of the box processes positioning holes & 2 \\ XCMZ\_GK & Process positioning holes on the left side of the box & 3 \\ DM & Box top surface & 1 \\ ZZM & Spindle mounting surface & 1 \\ DGM & Guide rail mounting end face & 2 \\ DGM\_L & Guide rail mounting elevation & 4 \\ DJDM & Motor base bottom surface & 1 \\ PHM & Balancing cylinder mounting end face & 1 \\ PHM\_K & Balancing cylinder mounting end face bottom hole & 6 \\ DJM & The motor mount end face & 1 \\ DM\_K & Bottom hole of the top surface of the box & 28 \\ ZZM\_K & Bottom hole of the spindle mounting end & 8 \\ DGM\_K & Bottom hole of mounting end of the guide rail & 7 \\ PHM\_K & Bottom hole of the balancing cylinder mounting end & 6 \\ DJM\_K & Bottom hole of the motor mounting end & 5 \\ ZZK & Spindle hole & 1 \\ LMZK & Motor mount hole & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spindle box machining feature code table. Figure 3: Complex network model of spindle box machining features: (**a**) Complex network model; (**b**) complex network exclusion force model. Following the characterization principle of the adjacency matrix A, which is resolved into matrices with values of 0 or 1, the importance and criticality of the machining features in the nodes of the complex network model are identified by further analyzing and calculating the values of the feature topology parameters of the adjacency matrix. In the established complex network-based spindle case machining feature model, the extracted nodes and the adjacency matrix are obtained according to the correlations among the machining features.