# Research on High-Speed Vibration and Structure Optimization of Multiwire Sawing Machine
## 3 Results
### Structural Optimization and Dynamics Verification
#### 3.4.2 Sensitivity Screening  
By performing the correlation analysis of the parameters of this machine tool model, 131-dimensional variables were finally determined to be optimized, and five optimization targets were identified: the maximum deformation of the main frame (MD-Z), subframe (MD-F), electric control cabinet (MD-K), base bracket (MD-T), and first-order inherent frequency (M1) of the whole frame.  
Due to there being numerous size variables, sensitivity screening was performed to obtain the sizes that have a greater impact on the optimization target. The range of test points was set according to the size variable interval, and the Spearman method was used for sensitivity analysis; the closer the correlation value in the results was to one, the greater the influence it had on the optimization target. The dimensions with a correlation greater than 0.5 were screened out, and finally, 15 parameters with the greatest influence on each optimization target were obtained, as shown in Table 2 below. The positions of variables in the multi-wire saw machine are illustrated in Figure 13.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size Code** & **Correlation** &
\begin{tabular}{c} **Maximum** \\ **Related Object** \\ \end{tabular} & **Interval Value** & **Instruction** \\ \hline det D & 0.56 & M1 & 0–20 mm & Shaft diameter variation \\ det H & 1.00 & M1 & 0–200 mm & Decreased center of gravity \\ XS1 & 0.98 & MD-T & 0.6–1.0 & Rib thickness factor of \\  & & & & main frame \\ K1 & 0.86 & MD-T & 30–50 mm & Host frame bezel width \\  & & & & Thickness of top plate of \\ CT & 0.77 & MD-T & 30–50 mm & main frame \\  & & & & Thickness of front base plate of \\  & & & & main frame \\ XS4 & 0.57 & M1 & 0.6–1.0 & Subframe rib thickness factor \\ K2 & 0.64 & MD-F & 30–50 mm & Sub-rack bezel thickness \\ K3 & 0.68 & MD-F & 30–50 mm & Sub-frame right frame thickness \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main parameters of sensitivity screening results.  
Figure 12: Flow chart of the structure optimization scheme.  
The remaining model dimensions are set as additional variables according to the relationship between the parameters so that they follow the changes in the 15 main parameters derived from sensitivity screening for the subsequent structural optimization of the whole multi-wire sawing machine.  
The design criteria for rib panels as important structures for reducing structural weight and enhancing auxiliary support are as follows:  
\[\eta=\frac{h}{XT}\leq 5 \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size Code** & **Correlation** & \begin{tabular}{c} **Maximum** \\ **Related Object** \\ \end{tabular} & **Interval Value** & **Instruction** \\ \hline FAT & 0.79 & MD-F & 15–40 mm & \begin{tabular}{c} Subframe rear base \\ plate thickness \\ \end{tabular} \\ FDT & 0.64 & MD-F & 20–40 mm & Thickness of subframe top plate \\ FCT & 0.63 & MD-F & 20–50 mm & Thickness of right bottom plate \\  & & & & of subframe \\ K7 & 0.73 & MD-K & 30–50 mm & \begin{tabular}{c} Electric control cabinet \\ bezel thickness \\ \end{tabular} \\ CCT & 0.77 & MD-T & 20–50 mm & \
\begin{tabular}{c} Electric control cabinet base \\ plate thickness \\ \end{tabular} \\ K5 & 0.53 & MD-T & 20–50 mm &
\begin{tabular}{c} Thickness of the bottom \\ bracket bezel \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 13: Position of the main parameters in the frame.  
where \(\eta\) denotes the relative height of the rib panels; \(h\) denotes the height of the rib panels, and \(XT\) denotes the thickness of the base plate.  
The thickness of rib panels depends on the thickness of the base plate and the rib thickness coefficient, and their relationship is as follows:  
\[t=XT\times XS \tag{3}\]  
where \(t\) denotes the thickness of rib panels, and \(XS\) denotes the rib thickness factor.