## 2 Reliability Modeling of NLG EmergencyExtension
### Fault Tree Analysis of Emergency Extension  
During the process of emergency extension, it must be ensured that the NLG always rotates around the strut rotation axis. The torques of all components are induced by external loads and impact on the emergency extension. These torques are listed in Table 1.  
Table 1 shows the analysis of the torque produced by the forces acting on the strut during emergency extension. The active torques produced by landing gear mass force play a leading role in the early stages of emergency extension. In the later period of emergency extension, the aerodynamic resistance torque of landing gear plays a leading role. Owing to the linkage design of the landing gear door and landing gear, the aerodynamic force of forward door and after door produces a torque during the whole process of emergency extension. The spring torque of the lock mechanism is inevitable. The spring force should ensure the safety of the lock mechanism. The retractable actuator cylinder is fixed on the airframe, because the piston rod of the retractable actuator cylinder is connected and moves with the shock absorber strut in the process of lowering and rotation. Meanwhile, the hydraulic oil rapidly flows in the actuator cylinder and return pipeline, to generate the damping torque of emergency extension, which is determined by piston speed, return pipeline length, and so on. From the above analysis, we can summarize the main reasons inducing the failure of emergency extension \(T\) as follows.  
1 Excessive resistance torque on strut rotation axis (denoted by \(X_{1}\)). The aerodynamic force of the landing gear door is too large for the driving mechanism to overcome the passive torque by the active torque of shock absorber strut, so that the landing gear cannot be lowered and locked.  
2 Imprecise extension of landing gear (denoted by \(X_{2}\)). The landing gear cannot be lowered to a predetermined position owing to the motion accuracy of the mechanism.  
3 Unlocked upper-lock. The upper-lock is unlocked (denoted by \(X_{3}\)).  
4 The lower-lock is not locked (denoted by \(X_{4}\)).  
5 Static strength failure of landing gear emergency extension (denoted by \(X_{5}\)).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning** \\ \hline M\({}_{1}\) & Torque on strut rotation axis produced by the gravity of NLG \\ M\({}_{2}\) & Torque on strut rotation axis produced by the gravity of door \\ M\({}_{3}\) & Torque on strut rotation axis produced by the aerodynamic force of strut and wheel \\ M\({}_{4}\) & Torque on strut rotation axis produced by the spring force of locking mechanism \\ M\({}_{5}\) & Torque on strut rotation axis produced by damping force \\ M\({}_{6}\) & Torque on strut rotation axis produced by friction \\ M\({}_{7}\) & Torque on strut rotation axis produced by after-door aerodynamic force \\ M\({}_{8}\) & Torque on strut rotation axis produced by forward-door aerodynamic force \\ M\({}_{9}\) & Torque on strut rotation axis produced by the unlocking force of upper-lock \\ M\({}_{\text{T}}\) & Total torque \\ \hline \hline \end{tabular}
\end{table}
Table 1: Explanations of torques.  
In respect of the five fault reasons, the fault tree of emergency extension is established as shownin Figure 2, in which the five bottom events indicate five failure reasons in the fault tree. Obviously, the failure of one bottom event will lead to the failure of emergency extension.