# Parametric Analysis on Landing Gear Strut Friction of Light Aircraft for Touchdown Performance
## 3 Analysis of Strut Friction Effect on Touchdown Performance Using RSM
### Sensitivity Analysis  
In this subsection, a global sensitivity analysis based on the [PERSON]'s method is executed to obtain the influence of the design variables on the four landing response functions in the design space. According to the theory of [PERSON]'s method [25], the first-order indices represent the sensitivity of the single variable, and the total-effect indices denote all order sensitivity of a variable, including the interaction effects with other variables. The sensitivity analysis results of each design variable under the four RS functions of landing response are shown in Figure 10. It can be seen that the sensitivity indices distribution of design variables on max friction load and max overloading are approximately the same. The friction force has a considerable proportion of the shock-strut total force, which directly reflects the max overloading, and the larger the friction force is, the larger the overloading is. Therefore, the friction force can be considered as the design object for improving the touchdown performance by revising the variables in the design space. Moreover, the lower bearing width (\(d_{B}\)) is the most influential variable for the max friction load, the max overloading, and the shock absorber stroke. It indicates that the lower bearing should be widened to reduce the normal reaction force induced by the additional bending moments.  
Figure 11 illustrates the top two noticeable variables affecting the four landing responses while the coded values of other variables are set to be zero. The top two sensitive variables for the max friction load and the max overloading are the distance between the lower bearing and wheel axis (\(L_{d}\)), and the lower bearing width (\(d_{B}\)). The similarity of variation trend in Figure 11a,c also demonstrates the correlation between these two landing responses. In Figure 11a,c, when the value of the lower bearing width (\(d_{B}\)) at a low level, the response value increases rapidly as the lower bearing width (\(d_{B}\)) decreases and the distance between the lower bearing and wheel axis (\(L_{d}\)) increases, proceeding toward an unfavorable level. Moreover, when the value of the lower bearing width (\(d_{B}\)) at a high level, the values of these two landing responses are at a stable and favorable level.  
Figure 11b shows that the shock-strut efficiency is at a stable and beneficial level when the distance between the lower bearing and wheel axis (\(L_{d}\)) is at a high level and the wheel moment of inertia (\(I_{w}\)) is at a low level. The wheel moment of inertia affects the acting duration of ground longitudinal force. The longer the acting duration, the higher the energy absorption efficiency of the strut friction load, which is reflected in the shock-strut efficiency as shown in Figure 11b.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Response** & **RS Function** \\ \hline \multirow{4}{*}{Max load of strut friction} & \(F_{\text{max}}=1.128+0.107f_{2}+0.124d_{-}-0.09d_{A}-0.179d_{B}+0.035L_{b}-0. 048I_{I}+0.048I_{2}-0.055L_{w}\) \\  & \(-0.005t_{A}d_{B}-0.035t_{B}-0.018L_{d}d_{A}-0  
Figure 11: The top two sensitive variables influence on the four landing responses: (**a**) Max load of strut friction; (**b**) Shock-strut efficiency; (**c**) Max overloading of the sprung mass; (**d**) Shock absorber stroke.  
Figure 10: The sensitivity indices for the four landing responses: (**a**) Max load of strut friction; (**b**) Shock-strut efficiency; (**c**) Max overloading of the sprung mass; (**d**) Shock absorber stroke.  
Figure 11d denotes the effect of the top two noticeable parameters on shock absorber stroke, namely, the half-axle distance (\(r_{k}\)) and the lower bearing width (\(d_{B}\)). The half-axle distance (\(r_{k}\)) affects the shock strut bending moments induced by the ground vertical force. As the strut friction is mainly generated by the ground vertical force, the larger value of the half-axle distance (\(r_{k}\)) leads to the smaller shock absorber stroke.