# A Geometric Model for a Shield TBM Steering Simulator
## 4 Example of Curved Excavation Simulation
### Effect of Articulation Angles and Rotation Angles on Tendencies  
To determine the effect of both factors on horizontal and vertical tendency, simulations were undertaken for only ten cycles (Table 6). The maximum pitch for the test condition was \(<\)3.0\({}^{\circ}\), based on the TBM data recorded in a specific TBM tunneling site. The maximum yaw for the test was determined to be same as maximum pitch. The maximum articulation angles in the horizontal and vertical directions were determined to be 2.5\({}^{\circ}\) and 0.5\({}^{\circ}\), respectively, as averages of specifications for different machine manuals produced by different TBM manufacturers.  
The average horizontal and vertical tendencies for cases 0-5 (Table 6) depend on yaw angle (Figure 15). As yaw increases from 0.0\({}^{\circ}\) to 2.5\({}^{\circ}\), the magnitude of average horizontal tendency also increases from 0.00% to 4.34%, while vertical tendency is constant at 0.00%.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Simulation Conditions**} \\ \cline{2-6}
**Case Number** & \multicolumn{2}{c}{**Type of Rotation Angle**} & \multicolumn{2}{c}{**Type of Articulation Angle**} \\ \cline{2-6}  & **Pitch (\#)** & **Yaw (\#)** & **Horizontal Direction (\(\alpha\))** & **Vertical Direction (\(\beta\))** \\ \hline
0 & & & 0 & & \\
1 & & 0.5 & & & \\
2 & & 1.0 & & & \\
3 & 0 & 1.5 & & 0.5 & 0.5 \\
4 & & 2.0 & & & \\
5 & & 2.5 & & & \\ \hline
6 & 0.5 & & & & \\
7 & 1.0 &  
The average horizontal and vertical tendencies for cases 6-10 (Table 6) are shown in Figure 16 depending on pitch angle, with Case 0. As pitch increases from 0.0\({}^{\circ}\) to 2.5\({}^{\circ}\), the average vertical tendency increases from 0.00% to 4.35%, while horizontal tendency is constant at 0.00%.  
Overall, yaw only affects the horizontal tendency, while pitch only affects the vertical tendency.  
The average horizontal and vertical tendencies for cases 11-16 (Table 6) vary with articulation angle in the horizontal direction (Figure 17). With an articulation of 0.00\({}^{\circ}\), both tendencies are constant to -1.745. As the horizontal articulation angle increases, the average horizontal tendency decreases from 1.745 to 1.742, 1.734, 1.720, 1.701, to 1.678, as the vertical tendency decreases from 1.745 to 1.741, 1.732, 1.718, 1.698, to 1.674.  
Figure 16: Variation of horizontal and vertical tendency with pitch angle.  
Figure 15: Variation in horizontal and vertical tendency with yaw angle.  
The average horizontal and vertical tendencies obtained for cases 17-21 (Table 6) vary with articulation angle in the horizontal direction (Figure 18). The average horizontal tendency decreases from 1.745 to 1.743, while the average vertical tendency decreases from 1.745 to 1.743, depending on the vertical articulation angle.  
The average horizontal and vertical tendencies for cases 22-26 (Table 6) vary with articulation angle in the horizontal and vertical direction (Figure 19). The average horizontal tendency decreases from 1.745 to 1.741, 1.732, 1.717, 1.697, to 1.673, while vertical tendency decreases from 1.745 to 1.742, 1.733, 1.719, to 1.676 as the articulation angles in both directions increase.  
Figure 17: Variation of horizontal and vertical tendency with horizontal articulation angle.  
Figure 18: Variation in horizontal and vertical tendency with vertical articulation angle.  
The articulation angles in both directions have a strong influence on the horizontal and vertical tendencies, with both decreasing with increasing articulation angle. If the articulations in both directions change together, both tendencies decrease more (note the difference between Figures 17 and 19). It seems that the articulation angles in either direction can impact both tendencies independently.