## 4 Virtual Prototype Modeling and Simulation
### Modeling Process and Model Assumptions  
The prototype model was built up in ADAMS 2017, as shown in Figure 5. The detailed modeling process was as follows:  
1. Firstly, every part of the shield machine was established in Solid Works software, and then assembled into an assembly model based on the relative position relationships between parts. According to the assembly of the three-dimensional specific model, it was saved in the format of _parasolid_ (\"_x_t_) and imported into Adams.
2. Assigned attributes to parts of shield machine. Established the constraints, joints between parts, boundary conditions, motions, and measurements in Adams.
3. A fixed pair was set between the segment and the ground. One sliding pair and two spherical pairs were used on each cylinder branch chain according to the motion of the cylinders.
4. The \"general point motion\" was used to plan the trajectory of the shield machine. The \"general point motion\" was added at Marker B (the distributing center of front hinges of cylinders) and the trajectory parameter equation of the marking point was set as: \[\begin{array}{l}x=1500\,\mathrm{mm}\times\sin(\frac{\pi t}{100})\\ y=z=25\,\mathrm{mm}\times\sin(\frac{\pi t}{100})\end{array}\] (37)
5. Establish the corresponding measurements to observe the following variables: \(\phi\), \(\theta\), \(\psi\), \(\omega_{x}\), \(\omega_{y}\), \(\omega_{z}\), \(\alpha_{x}\), \(\alpha_{y}\), \(\alpha_{z}\) of Marker B with regarding to Marker A (the distributing center of the gripper shoes of cylinders), and \(l\), \(\overset{\bullet}{l}\), \(\overset{\bullet}{l}\) of all thrust cylinders.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Model Parameters** & **Value** \\ \hline
1 & Outer diameter of shield (\(D\)) & 6560 mm \\
2 & Thickness of shield shell (\(\delta\)) & 60 mm \\
3 & Radius of the distribution of the cylinders (\(R_{0}\)) & 2990 mm \\
4 & Length of shield body (\(L_{total}\)) & 8000 mm \\
5 & Length of the front shield (\(L_{BC}\)) & 1800 mm \\
6 & Thrust cylinder specification & \(\Phi\)220/180 \(\times\) 2150 mm \\
7 & Number of thrust cylinders (\(n\)) & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The structure and dimension information of the model.  
Figure 4: Distribution of thrust cylinders in each group.  
Set the duration for simulation as 50 s, so that the driving distance of the shield machine was exactly 1500 mm. Set the simulation step size as 1 s, that is, the numerical model will be calculated 50 times in total.  
The position and attitude should keep changing continuously and smoothly when the shield machine is advancing, and satisfy the coordination of position and attitude with consideration of the coupling. Moreover, the target pose point on the desired trajectory should be within the workspace of the shield thrust mechanism. The parametric equations of driving function for target pose were solved based on Equation (37) and further plotted, as shown in Figure 6.  
Due to the complexity of the shield thrust system, it is impossible to establish a completely accurate model. In order to obtain the approximate model grasping the main characteristics, the following assumptions were made in the numerical model:  
1. All parts of the shield machine were rigid bodies;
2. The clearance and damping of shield thrust system were ignored;
3. The end face of the segment connected with cylinder shoes was regarded as a smooth plane.  
Figure 5: The virtual prototype model of shield machine.  
Figure 6: Target shield pose parameters variation with time.