## 5 Comparison of Theoretical and Simulation Results  
Figure 7 shows a comparison between the cylinder strokes obtained from the simulation and theoretical results. It can be seen that the mean displacement of cylinders in each group were linearly related to the advancing distance of the shield machine. In the set motion mode, the shield machine moved forward and deflected toward the \(Y\)-axis and \(Z\)-axis, which explains the phenomenon where the mean displacements of cylinders in Group A and B were smaller than that in Group C and D. Figure 8 shows the displacement distribution of the thrust cylinders at the end of the simulation. The final strokes of cylinders in Group A and Group B (top and left groups) were smaller than the reference value (the driving distance of shield machine), and cylinder strokes in Group C and Group D were larger than the reference. This is consistent with the movement characteristics of the shield machine deflecting upward (\(Y\) direction) and left (\(Z\) direction).  
Figure 9 shows the attitude angles variation with the difference of mean cylinder strokes between groups. As can be seen from Figure 9, the pitch angle of the shield machine is in direct ratio to the difference of mean cylinder strokes between Group A and C, and the yaw angle is in direct ratio to that between Group B and D. The slope of the curve was related to the structural parameters.  
Figure 8: Displacement distribution of thrust cylinders at 50 s (unit: mm).  
Figure 7: Mean Displacements of thrust cylinders in different groups.  
The cylinder of No.4 (top-left), No.11 (down-left), No.18 (down-right) and No.25 (up-right) were picked out, and their velocity variations with time are plotted in Figure 10. It can be seen that velocities presented a decreasing trend with time and decreased faster and faster. The velocity of cylinder No.4 was maximal, and the velocity of cylinder No.18 was minimal. The velocities of cylinder No.11 and No.25 were basically equal. This is because the shield machine deflected in the direction of top-left.  
Figure 11 shows the velocities distribution of thrust cylinders at 10 s and 30 s. It was found that the velocities of cylinders in Group A and Group B (top and left groups) were smaller than those in Group C and Group D. It indicated that the velocity of the thrust cylinder in the deflection direction of the shield machine was the smallest, and that in the opposite direction, it was the largest.  
Figure 10: Velocity–time diagram of different cylinders.  
Figure 9: The attitude angles variation with the difference of mean cylinder strokes.  
Figure 12 shows the accelerations of cylinders with time. It can be seen that acceleration increased with time in the negative direction, but more and more slowly. The acceleration of cylinder No.4 was minimal, and the velocity of cylinder No.18 is maximal. The velocities of cylinder No.11 and No.25 were basically equal. As can be seen from Figure 13, the acceleration distribution of cylinders was different from the velocities. The acceleration of the thrust cylinder in the deflection direction of the shield machine was the smallest. Both the difference in velocity and acceleration among cylinders confirmed the movement characteristics of shield machine.  
Figure 11: Velocity distribution of thrust cylinders (unit: mm/s). (**a**) t = 10 s. (**b**) t = 30 s.  
Figure 12: Acceleration–time diagram of different cylinders.