## 3 Analysis and Results
### Effects of Structural Parameters on Slip Anchoring Performance
#### 3.2.2 The Effect Law Analysis of Slip Tooth Inclination Angle on Anchoring Performance  
The inclination angle of slip teeth was found to exert significant influence on the contact pressure distribution between slips and casing wall. It was observed that, when the inclination angle of slip teeth was excessively large, the slips demonstrated reduced capability to effectively penetrate the casing wall. Conversely, an insufficient inclination angle was shown to compromise the slip teeth's unidirectional load-bearing capacity.  
A finite element model of the slip was constructed for slip tooth inclination angles of 60\({}^{\circ}\), 65\({}^{\circ}\), 70\({}^{\circ}\), 75\({}^{\circ}\), and 80\({}^{\circ}\). Numerical simulations were performed to systematically investigate the effect of slip tooth inclination angle on cavity seating contact characteristics. The analysis was conducted to establish the correlation between different slip tooth inclination angles and the corresponding contact pressure distribution patterns at the slip-casing interface.  
The contact pressure between the casing and the slip at varying slip tooth inclination angles is presented in Figure 12a, while the corresponding contact pressure indicators are tabulated in Table 3. As the inclination angle of the slip teeth was increased, a slight upward trend in the contact pressure between the slip and the casing was observed; however, this change was minimal. The standard deviation of the contact pressure reached its peak  
\begin{table}
\begin{tabular}{c c c c} \hline
**Slip Tooth Apex Angle \(\alpha\) (\({}^{\circ}\))** & **Peak Contact Pressure (MPa)** & **Average Contact Pressure (MPa)** & **Standard Deviation of Contact Pressure** \\ \hline
60 & 921 & 655.6 & 101.28 \\
65 & 956 & 669.51 & 101.63 \\
70 & 1018 & 705.33 & 146.22 \\
75 & 1062 & 752.71 & 126.19 \\
80 & 1121 & 775.19 & 125.77 \\
90 & 1031 & 656.28 & 112.93 \\ \hline \end{tabular}
\end{table}
Table 2: Contact pressure indicators between casing and slip teeth at varying tooth apex angles.  
when the inclination angle was 70\({}^{\circ}\), which depicts the stress distribution across different inclination angles.  
Figure 12: Stress curves of slips and casing under varying slip tooth inclination angles. (**a**) Contact pressure between slips and casing. (**b**) Equivalent stress of slips. (**c**) Equivalent stress of casing.  
The equivalent stress of the slip first decreased and then increased with increasing inclination angle, reaching a minimum value at 75\({}^{\circ}\). This indicated that the slip structure exhibited optimal stability at inclination angles of 70\({}^{\circ}\) and 75\({}^{\circ}\); Figure 12b,c. show the equivalent stress distribution in the casing under different slip tooth inclination angles. Negligible variation was detected across all tested angles, ensuring that the casing remained structurally intact during the setting and sealing processes.  
Based on the analysis of stress distribution across varying inclination angles, 70\({}^{\circ}\) and 75\({}^{\circ}\) were identified as the preferred slip tooth inclination angles for reliable anchoring performance. Additionally, it was observed that the fifth slip tooth exhibited higher contact pressure with the casing compared to other teeth, indicating uneven stress distribution. Further investigation is required to explore the multi-factor influences on the mechanical behavior of slip structures.