## 3 Design and Calculation Results of Vertical Shaft Multi-Rope Friction
### Dynamic Analysis and Calculation of the Hoisting System
#### 3.4.2 Dynamic Tension and Dynamic Anti-Slip Safety Coefficient of Hoisting Rope  
The dynamic tension of the hoisting rope at different stages in different rope selection schemes is shown in Figures 10-12. The dynamic anti-slip safety coefficients of the hoisting rope at different stages in different rope selection schemes is shown in Figures 13-15. In Figure 10, 1 represents the stage of heavy load accelerating upward, 2 represents the stage of heavy load moving upward at a constant speed, 3 represents the stage of heavy load decelerating upward, 4 represents the stage of crawling, 5 represents the stage of parking, 6 represents the stage of heavy load accelerating downward, 7 represents the stage of heavy load moving downward at a constant speed, 8 represents the stage of heavy load decelerating downward, 9 represents the stage of crawling, 10 represents the stage of parking. As can be seen from Figures 10-12, the changing trends of the dynamic tension exerted on the hoisting wire rope at the heavy-load end in different stages for different rope selection schemes are basically consistent with the changing trend of the acceleration control curve, both exhibiting a five-stage variation. This indicates that the dynamic tension on the hoisting wire rope at the heavy-load end is positively correlated with the acceleration. The greater the acceleration, the greater the dynamic tension it undergoes. The dynamic tension of the hoisting wire rope at the light-load end has an opposite changing trend to the acceleration control curve. This is because the movement direction of the light-load end is opposite to that of the heavy-load end, resulting in an opposite changing trend of the dynamic tension. Further observations reveal that the differences in dynamic tension on both sides of pulley for three rope selection schemes are the greatest in the heavy-load accelerated hoisting stage and the heavy-load decelerated lowering stage, which are \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Position of the Heavy-Load End**} & \multirow{2}{*}{**Calculation Parameter**} & \multicolumn{4}{c}{**Hoisting Rope**} \\ \cline{3-6}  & & & **Round** & **Triangular** & **Compacted** \\  & & & **Strand** & **Strand** & **Strand** \\ \hline \multirow{6}{*}{Displacement mass of hoisting system} & \multirow{2}{*}{Left cage} & Maximum displacement mass at heavy-load end, \(m_{1}\)/(t) & \multirow{2}{*}{332} & \multirow{2}{*}{312} & \multirow{2}{*}{335} \\ \cline{3-6}  & & Minimum displacement mass at light-load end, \(m_{2}\)/(t) & \multirow{2}{*}{229} & \multirow{2}{*}{210} & \multirow{2}{*}{234} \\ \cline{3-6}  & & Maximum displacement mass at heavy-load end, \(m_{3}\)/(t) & \multirow{2}{*}{329} & \multirow{2}{*}{310} & \multirow{2}{*}{334} \\ \cline{3-6}  & & Minimum displacement mass at light-load end, \(m_{4}\)/(t) & \multirow{2}{*}{232} & \multirow{2}{*}{212} & \multirow{2}{*}{235} \\ \cline{3-6}  & & Total displacement mass of hoisting system, \(\sum M\)/(t) & \multirow{2}{*}{736} & \multirow{2}{*}{696} & \multirow{2}{*}{744} \\ \cline{3-6}  & & Left cage & & 0.94 & 0.78 & 0.95 \\ \cline{2-6}  & & Right cage & \(a_{max}\)/(m/s\({}^{2}\)) & \multirow{2}{*}{0.93} & \multirow{2}{*}{0.76} & \multirow{2}{*}{0.94} \\ \cline{3-6}  & & Actual acceleration/deceleration value = 0.8\(\cdot\)Min & \multirow{2}{*}{0.74} & \multirow{2}{*}{0.61} & \multirow{2}{*}{0.75} \\ \cline{3-6}  & & [Left, Right \(a_{max}\)] & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dynamic calculations of hoisting system with different rope selection schemes (displacement mass and limiting acceleration/deceleration calculation). 1556.3 kN, 1448.9 kN, and 1576 kN respectively. Among them, the second scheme that adopts the fiber core wire rope has the smallest tension difference. This is attributed to the relatively light unit weight of the fiber core wire rope, which has a relatively small influence on the tension difference.