# A Geometric Model for a Shield TBM Steering Simulator
## 6 Conclusions  
This study aims to develop the mathematical models for the shield TBM steering and apply the models into the TBM simulator. The concept of curved excavation and the TBM steering model were overviewed first. Next, the mathematical formulae, including the articulation jack operations and shield jack operations, were created for the simulation based on the steering mechanism. Then, curved excavations were simulated using a Python program based on different articulation systems and different planned routes to reflect the mathematical formulae. Moreover, simulations with different cases were tested to identify the effect of two articulation angles and two rotation angles on the horizontal tendency and vertical tendency. Finally, the proposed mathematical formulae were applied in the TBM simulator to simulate the articulation operations. Firstly, the reference points estimated from one cycle simulation used in the 'X-type' system and 'V-type' system were compared. Due to the difference in location of the articulation point, differences of reference point between both systems occur during the articulation work, and the final reference points obtained from 'X-type' and 'V-type' have some errors. Secondly, two simulations with different planned routes were executed without considering pitch and yaw. The estimated rear-middle reference points are almost equal to the tracking point of the route, if the pitch and yaw are not considered. In contrast, the deviations between the tracking point of the route and the rear-middle reference points occur if the pitch and yaw are considered. Even though the articulation angles are adjusted to be nearly identical to the direction angles of the planned route, there will be deviations during the curved excavation caused by pitch and yaw. Therefore, it is expected that the TBM operator attempts to control the shield jacks or articulation jacks to reduce deviations after or during the one cycle of curved excavation. Also, these deviations caused by pitch and yaw could differ depending on the magnitude and the direction of the articulation angle. Thirdly, simulations with different cases were tested to identify the impact of articulation angles in the horizontal direction and vertical direction and rotation angles (pitch and yaw) on the horizontal tendency and vertical tendency calculated from the deviations. It is confirmed that the yaw affects the horizontal tendency, while the pitch only affects the vertical tendency. As both rotation angles increase, higher tendencies are estimated as a result. Lastly, the articulation angles in both directions strongly influence the horizontal tendency and vertical tendency. As the articulation angles in the horizontal direction or vertical direction increase, the smaller the estimated magnitude of tendencies. Lastly, the proposed mathematical models were applied and tested in the TBM simulator as the final stage of the study. Generally, there are four groups for selecting shield jacks. The speed of each shield jack group can control the length of each shield jack group. The segment plane is always perpendicular to the rear shield axis during the curved excavation. Therefore, each shield jack group should be extended with different jack speeds depending on the curved direction. However, this study assumed that a group of shield jacks have the same extension speed. Therefore, it is difficult to consider the one-sided extension of the shield jack in parallel with articulation jack operations during the excavation. Future studies should focus on considering the jack speed of each shield jack group independently. In addition, this study only focused on a shield TBM steering simulator. Future research will be aimed at the development of a steering system for an open (gripper) TBM simulator. Conceptualization, B.P. and S.-H.C.; methodology, B.P. ; software, B.P. and C.L. ; validation, W.-Y.L., S.D. and T.-H.K. ; formal analysis, C.L., W.-Y.L. and T.-H.K. ; investigation, B.P., C.L. and S.-W.C.; resources, W.-Y.L. and S.D. ; data curation, W.-Y.L.