## 2 Hoisting Model
### Modelling Process  
According to the relevant parameters of the large cage hoisting system above, the global dynamic simulation model of the actual hoisting system was established using multi-body dynamics simulation software \"Adams\". The characteristics of the model state that the dynamics of the wire rope on the lifting side and the lowering side, as well as the coupling effect of the rope with the friction pulley and the guide pulley, are unified as a whole. The mine system is a multi-rope friction hoisting system of the shaft tower. The global simulation model is then simplified as follows:  
The pulleys are simplified as uniform materials, and the groove shape is ideal and regular;  
The weight of the tail rope is simplified as a time-varying force corresponding to the lifting height, which is applied to both the cage and the balance hammer;  
The actual lifting system is supported by six steel ropes. In the model, only a single steel rope is established, and the load is calculated according to 1/6 of the original load;  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Item** & **Unit** & **Friction Pulley** & **Guide Pulley** \\ \hline \multirow{6}{*}{Hoist} & Type & & JKM-5 \(\times\) 6 \\  & Lifting height & m & 425 \\  & Pulleys Spacing & m & Vertical:13/horizontal:3.35 \\  & Diameter & m & 5 & 5 \\  & Number & & 6 & 6 \\  & Friction coefficient & & 0.25 & 0.25 \\  & wrap angle & \(\circ\) & 187.42 \\ \hline \hline \multicolumn{2}{c}{**Item**} & **Unit** & **Hoisting rope** & **Tail rope** \\ \hline \multirow{6}{*}{Rope} & Type & & \(54\times 36\)WS + FC & \(216\times 34\times 4\times 19\) + FC \\  & Diameter/Width \(\times\) Thickness & mm & 54 & \(216\times 34\) \\  & Number & & 6 & 3 \\  & Density & kg/mm\({}^{3}\) & \(4.72\times 10^{-6}\) & 23 \\  & Total length & m & 523.08 & 481.5 \\ \hline \multicolumn{2}{c}{**Item**} & **Unit** & \\ \hline \multirow{6}{*}{Load} & Cage mass & & \(0.65\times 10^{5}\) \\  & Balance hammer mass & & \(0.95\times 10^{5}\) \\  & MAX & kg & \(1.2\times 10^{5}\) \\  & Test load(total) & MID & & \(0.95\times 10^{5}\) (mainly discussed) \\  & MIN & & \(0.7\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of large cage hoisting system.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Stage** & \multicolumn{2}{c}{**Acceleration (m/s\({}^{2}\))**} & **Speed (m/s)** & **Time (s)** \\ \hline \multirow{4}{*}{Main acceleration} & Varying & 0–0.6 & 0.51 & 1.71 \\  & Constant & 0.6 & 9.43 & 14.87 \\  & Varying & 0.6–0 & 9.95 & 1.71 \\ \cline{1-1} \cline{2-5}  & \multicolumn{2}{c}{Total} & & 18.29 \\ \hline Constant speed & Constant & 0 & 9.95 & 24.45 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operating parameters (Acceleration and Constant Speed stage).  
On the basis of the above simplification, the friction pulley, guide pulley, wire rope, cage and balance hammer are established. The model is shown in Figure 2. The parameters of the model are consistent with those of the hoist equipment mentioned above. According to the relevant provisions of the China coal industry standard MT 234-1991 \"3T Tramcar, Multi-rope tank cage for vertical shaft\" and MT 235-2011 \"Vertical multi-rope cage balance hammer\", the 3D models of the cage and balance hammer are established.