## 5 Experimental Verification of the Methodology
The method of grinding cold rolling rolls during the rotation of the grinding wheels, compared with the grinding method with the rearrangement of the rolls from machine to machine, provides greater accuracy of the roll, since the installation bases do not change during the processing of the roll. The conducted research on the grinding of rolls has shown that, with an increase in the number of finishing operations, the machine processing time of the roll decreases. The labor intensity of the roll processing is the lowest for rolls of size \(d\times l=500\times 740\) mm, \(d\times l=500\times 1200\) mm, and \(d\times l=480\times 1680\) mm with one finishing operation, and for rolls of sizes \(d\times l=690\times 1680\) mm and \(d\times l=900\times 2800\) mm, with two finishing operations. Based on the above, it can be concluded that the complexity of processing rolls and the optimal number of finishing grinding operations largely depends on the size of the roll. Figure 11 shows the data for calculating the optimal number of operations when grinding rolls to obtain a surface roughness of \(Ra_{0}=0.50\) um; \(Ra_{1}=0.025\) um, depending on the diameter and length of the roll barrel. With an increase in the allowance for processing, the surface roughness after pregrin \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Machine Grinding Time of the Roll**} & \multicolumn{3}{c}{**Machine Grinding Time of the Roll**} \\
**Rolls Size** & \multicolumn{3}{c}{\(T_{M}\), Min during \(n\) Finishing**} & \multicolumn{3}{c}{\(T_{K}\), Min} \\ \(d\times l\) & \multicolumn{3}{c}{**Operations**} & \multicolumn{3}{c}{**during \(n\) Finishing Operations**} \\ \cline{2-9}  & \(n=1\) & \(n=2\) & \(n=3\) & \(n=4\) & \(n=1\) & \(n=2\) & \(n=3\) & \(n=4\) \\ \hline \(500\times 740\) & 18.6 & 7.6 & 5.8 & 5.1 & 73.2 & 87.5 & 111.9 & 137.6 \\ \hline \(500\times 1200\) & 30.2 & 12.3 & 9.4 & 8.2 & 86.0 & 97.7 & 115.9 & 141 \\ \hline \(480\times 1680\) & 40.2 & 16.4 & 12.5 & 11.0 & 97.0 & 97.2 & 119.3 & 144 \\ \hline \(690\times 1680\) & 55 & 22.1 & 16.8 & 14.8 & 113 & 108.3 & 124.0 & 148.2 \\ \hline \(900\times 2800\) & 113 & 45 & 34.5 & 30.5 & 177 & 129 & 143 & 165 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated data on the machine time and labor intensity of finishing grinding of rolls. Figure 11: Dependence of the optimal number of finishing operations of grinding rolls to obtain a surface roughness of \(Ra=0.04\)–\(0.02\) μm. It is advisable to process all rolls whose dimensions correspond to points lying below line 1 in one operation, and rolls whose dimensions correspond to points lying above line 1 in two operations. The points \(A,B,C,D\), and \(E\) are marked by the standard sizes of the rolls, according to which the calculations were summarized. Most of the rolls obtaining a surface roughness of \(Ra_{0}=0.04\)-\(0.02\,\upmu\)m can be processed with a single finishing operation. However, rolls of sizes \(d\times l=690\times 1680\) mm and \(d\times l=90\times 2800\) mm should be processed with two finishing operations. Figure 12 shows the dependence of the optimal values of the surface roughness after pre-grinding on the processing allowance when grinding cold rolling rolls \(d\times l=500\times 1200\) mm to obtain a surface roughness of \(Ra=0.02-0.01\)\(\upmu\)m when conducting the process in one, two, and three operations.