## 3 Reliability Sensitivity Analysis of Emergence Extension
### Reliability Analysis  
#### 3.1.1 Starting Reliability Analysis of Emergency Extension  
As illustrated in Table 1, the amplitudes and directions of all the forces acting on the NLG and the corresponding torque on shock absorber strut rotation axis vary during the process of emergency extension. Therefore, it is necessary to carry out force balance analysis and reliability analysis in the whole process of emergency extension. To ensure that the NLG can be lowered in an emergency, the relationship between active torques and passive torques is investigated. The above nine forces act on strut rotation axis in the form of torque. The total torque is expressed as  
\[M_{T}=\sum_{i=1}^{9}M_{i}=M_{1}+M_{2}+M_{3}+M_{4}+M_{5}+M_{6}+M_{7}+M_{8}+M_{9} \tag{7}\]  
Based on the starting reliability, the emergency extension is successful as \(M_{T}>0\), or the emergency extension fails. Obviously, the nine torques significantly influence the normal start-up of emergency extension. When \(M_{T}<0\), the emergency extension cannot be realized. It is necessary to further analyze the relationship between torque and strut angle. Regarding the flight speed 270 Kts, the changing trend of each torque and total torque with strut rotation angle during emergency extension are shown in Figure 3.  
As shown in Figure 3, (1) all the torques vary with the strut rotation angle during the emergency extension. Merely, the torque on strut rotation axis M\({}_{9}\) stops to act on the emergence extension system after about 2.66 degrees (\({}^{\circ}\)) of landing gear angle, because the point at 2.66\({}^{\circ}\) of landing gear angle indicates that the upper-lock is unlocked to finish its mission, and its unlocking force on the emergence extension system does not exist after 2.66\({}^{\circ}\) of landing gear angle; (2) the torques M\({}_{1}\) and M\({}_{9}\) are conductive to the emergence extension in the whole process, and the torque M\({}_{3}\) lowers the emergence extension system in [0-2.66\({}^{\circ}\)] and stop work after 2.66\({}^{\circ}\); (3) the torques M\({}_{5}\) and M\({}_{6}\) provide a resistance against emergence extension, in which M\({}_{5}\) is much larger than M\({}_{6}\), which is very small in the whole lowering process; (4) the torques M\({}_{2}\), M\({}_{4}\), M\({}_{7}\), and M\({}_{8}\) have both a positive and negative effect on emergence extension, in which M\({}_{2}\), M\({}_{7}\) and M\({}_{8}\) are firstly positive torques at 21.8\({}^{\circ}\), 69.2\({}^{\circ}\) and 35.1\({}^{\circ}\), respectively, and then negative while M\({}_{4}\) is firstly adverse and then beneficial for emergence extension; (5) the torque of M\({}_{T}\) reaches the minimum at 2.66\({}^{\circ}\) (unlocking completion stage) and 100.1\({}^{\circ}\) (ready locking stage), which indicate the two critical points inducing the failure of the emergence extension system.  
Figure 3: Change of NLG torques with strut rotation angle at 270 Kts.  
By importing the nine torques and variable coefficients \(C_{i}\) (\(i=1,2,\ldots,9\)) with strut rotation angle into Equation (3), the starting reliability index \(\beta\) can be computed by  
\[\beta=\frac{\sum\limits_{i=1}^{9}M_{i}}{\sqrt{\sum\limits_{i=1}^{9}C_{i}^{2}M_{ i}{}^{2}}} \tag{8}\]  
where \(i\) is the \(i\)th torque.  
With respect to Equation (8), the failure probability can be obtained by the standard normal distribution function. Regarding the relevant engineering tests and empirical data [30; 31; 32; 33], the variable coefficients of nine torques are listed in Table 3.