# Dynamic Simulation of Underground Cable Laying for Digital Three-Dimensional Transmission Lines
## 4 Engineering Examples and Analysis of Results
### Cable Laying System Reliability Verification  
In the cable laying digital model [21], the segmented calculation is carried out according to the cable laying path, and the total traction force is equal to the sum of the traction force of each segment. According to the simplified schematic diagram of the cable laying path in Figure 6, the traction force required for cable laying is calculated [22]. (1) The cable is led from the cable tray. According to the basic principle of the traction force calculation, the friction force of the cable tray hole and the shaft can be converted into the gravity calculation of about 15 m length of the laid cable:  
\[F_{\text{Cable real}}=15\times 9.8W \tag{3}\]  
(2) Traction of the cable from A \(\rightarrow\) B:  
\[F_{1}=9.8W\Big{\{}h_{1}-R_{1}\Big{[}1-\text{sin}\Big{(}\frac{\pi}{2}-\theta_{ 1}\Big{)}\Big{]}\Big{\}}\times\csc\theta_{1}(\mu\cos\theta_{1}-\sin\theta_{1}) \tag{4}\]  
(3) Traction of the cable from B \(\rightarrow\) C:  
\[F_{2}=9.8\mu WR_{1}\cos\Big{(}\frac{\pi}{2}-\theta_{1}\Big{)}-9.8 WR_{1}+9.8W \sqrt{R_{1}^{2}-\Big{[}R_{1}\cos\Big{(}\frac{\pi}{2}-\theta_{1}\Big{)}\Big{]} ^{2}} \tag{5}\]  
(4) Traction of the cable from C \(\rightarrow\) D:  
\[F_{3}=9.8 WL_{CD}(\mu\cos\theta_{2}+\sin\theta_{2}) \tag{6}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Modulus of** & **Shear** & **Caliber** & **Cross-** \\  & **Elasticity** & **Modulus** & **d/mm** & **Sectional Area** \\  & **E/GPa** & **G/GPa** & **A/mm\({}^{2}\)** & **A/mm\({}^{2}\)** \\ \hline electric cable & 115.0 & 41.5 & 87.3 & 5982.7 \\ tow rope & 181.4 & 69.8 & 14 & 86.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of cable and traction rope. Figure 5: Cable laying system model. Figure 6: Simplified diagram of cable laying path. (5) Traction of the cable from D \(\rightarrow\) E:  
\[F_{4}=9.8\mu WL_{DE} \tag{7}\]  
(6) Traction of the cable from E \(\rightarrow\) F:  
\[F_{5}=9.8 WL_{EF}(\mu\cos\theta_{3}-\sin\theta_{3}) \tag{8}\]  
(7) When calculating the traction force required for cable laying, it is also necessary to take into account the traction rope, which is usually converted into 5 m of cable self-weight:  
\[F_{6}=5\times 9.8W \tag{9}\]  
(8) The traction force required for cable laying is the sum of the above-segmented forces:  
\[F_{\text{total}}=F_{\text{Cable real}}+F_{1}+F_{2}+F_{3}+F_{4}+F_{5}+F_{6} \tag{10}\]  
After the end of the construction simulation, in the virtual prototype, ADAMS post-processes the random extraction of the cable and traction rope micro-segment axial velocity to verify that its axial motion speed meets the engineering requirements. Figure 7 shows the axial velocity of a micro-segment of the cable and hauling rope. The cable and hauling rope extract in the stationary state under the action of the traction force to produce acceleration; then, axial velocity suddenly increases, gradually stabilizes at 6 m/min after 13 s, and the traction speed of the traction machine is consistent with the actual requirements of the project. It is necessary to verify not only the axial velocity of the cable but also to check whether the axial force of the cable in the cable laying system meets the engineering requirements. After the end of the cable laying simulation, the axial sleeve force of the cable and traction rope micro-segments are randomly extracted in the virtual prototype ADAMS post-processing and compared with the theoretical axial sleeve force in the numerical model to verify the reliability of the cable laying system. Figure 8 shows the dynamic axial tensile force diagram of the cable and traction rope in the cable laying simulation. Figure 7: Dynamic speed change of cable laying. (**a**) Tow rope axial velocity. (**b**) Axial velocity of cable micro-segments. The axial tension at each position of the cable and traction rope in the cable laying system is compared with its numerical model, and the error coefficients at each position of the cable and traction rope in the cable laying system are calculated.