## 3 Results  
### Geometric Analysis of the Tail Brush Compression and the Resulting Pressure  
As shown in Figures 3 and 4, the difference between the initial height of the shield tail brush and the shield tail clearance results in a 90 mm initial compression deformation of the tail brush at the initial installation, which would exert a non-negligible pressure on the segment. In addition, when the position of the shield shell is shifted, the compression deformation of the tail brush around the segment and the corresponding pressure upon the segment will change to be uneven accordingly. To calculate the distribution of this pressure, it is first necessary to calculate the compression deformation distribution of the tail brush around the segment. We established a coordinate system with the shield shell center as the origin when it was at the design position, and assumed that the center of the shield shell was shifted in the  
Figure 8: Pressure-compression curve and the fitting functions for the wire brush. direction of the angle \(\beta\) with the horizontal direction under arbitrary posture adjustment; thus, the diagram representing the relative positions of the shield shell, the tail brush, and the segment is illustrated in Figure 9.  
As shown in Figure 8, \(\Delta d_{0}\) denotes the initial compression deformation of the tail brush, \(\Delta d_{1}\) denotes the maximum compression deformation of the tail brush along the circumference at a given state of the shield posture adjustment, while \(\Delta d_{2}\) denotes the minimum compression deformation; \(r_{1}\) is the outer diameter of the segment, \(r_{2}\) is the outer diameter of the shield shell, \(\delta_{0}\) denotes the initial shield tail clearance and \(\beta\) is the angle between the shift direction of the shield shell circle center and the horizontal direction due to posture adjustment. Under any posture adjustment, there always exists a maximum value and a minimum value for the compression deformation of the tail brush around the segment, both of which vary with the offset of the shield center (Figure 10), and half of the difference between these two values is equal to the offset of the shield center. In other words, the offset of the shield shell center under any posture adjustment is:  
\[\Delta d_{p}=\frac{\Delta d_{1}-\Delta d_{2}}{2} \tag{3}\]  
Figure 10: Relationship between the maximum and minimum compression deformation of the tail brush and the shield offset. Figure 9: The relative positions of the shield shell, tail brush, and the segment under arbitrary posture adjustment. The coordinates of the center are:  
\[\left(\Delta d_{p}cos\beta,\Delta d_{p}sin\beta\right) \tag{4}\]  
The circle equation for the initial state of the shield shell is:  
\[{x_{2}}^{2}+{y_{2}}^{2}={r_{2}}^{2} \tag{5}\]  
The circle equation for the shield shell under any posture adjustment is:  
\[\left(x_{2}-\Delta d_{p}cos\beta\right)^{2}+\left(y_{2}-\Delta d_{p}sin\beta \right)^{2}={r_{2}}^{2} \tag{6}\]  
The circle equation of the outer surface of the segment is:  
\[{x_{1}}^{2}+{y_{1}}^{2}={r_{1}}^{2} \tag{7}\]  
The clearance between any position on the circumference of the shield shell and the segment is:  
\[\delta=r_{2}-\sqrt{\left(x_{1}-\Delta d_{p}cos\beta\right)^{2}+\left(y_{1}- \Delta d_{p}sin\beta\right)^{2}} \tag{8}\]  
Consequently, the increment of the tail brush compression deformation at any position on the outer surface of the segment can be described thus:  
Figure 9.0  
Combining the tail brush compression deformation (Equation (8)) with the pressure-compression relationship (Equation (2)), the tail brush pressure upon the segment at any position on the segment periphery can be calculated using the following equation:  
\[p=\left\{ \begin{array}{cc}0.4289d&0\;\mathrm{mm}<d<78\;\mathrm{mm}\\ 8e^{-5}d^{4}-0.0332d^{3}+5.0804d^{2}-344.02d+8714.7&d>78\;\mathrm{mm}\\ d=\Delta d+\Delta d_{0}&\end{array} \right.