# Selection Methodology of an Electric Actuator for
## 3 Analysis
### Air Spring Force  
In the oleo-pneumatic shock absorber, air is mainly used to store part of the absorbed impact energy [24]. The air spring force is influenced by a lot of factors, refer Equation (17), whereas hydraulic force during compression is given by Equation (18). \[F_{a}=A_{p}[P_{o}(\frac{V_{o}}{V_{o}-A_{p}S})^{\gamma}-P_{atm}] \tag{17}\]  
\[F_{H}=\rho(\frac{A_{p}^{3}}{2(\alpha_{D}A_{orifice})}+\frac{n.A_{piston-at- rebound}^{3}}{2(\alpha_{Dr}A_{Rebound-orifice})})S|S| \tag{18}\]  
Details of variables used for the calculation of these forces are provided in the nomenclature section. The pressure in the upper chamber of oleo-pneumatic only depends on the air volume and, hence, on the position of the piston. As the strut compresses, pressure increases, while volume decreases. Accordingly, if the initial pressure and volume is known for the strut, then the pressure and volume can be calculated through out the compression stroke by using the Equations (19) and (20). Where \(\gamma\) is a polytropic constant and defines the iso-thermal or ploytropic behaviour of gas in the equations. Iso-thermal compression is observed while taxiing, because, during taxi, the compression is slow and there is much time for heat exchange, while ploytropic compression is observed during impact, because, at that time, strut undergoes very fast compression. \[V=V_{o}-(\pi\times(P_{dia}/2)^{2}\times S) \tag{19}\]  
\[P=P_{o}\times(V_{o}/V)^{\gamma} \tag{20}\]  
To find out the impact loads on landing gear, a drop test was conducted while using the MSC ADAMS(r). For modeling the behavior of oleo-pneumatic, a nonlinear spring was modeled in the MSC  
Figure 9: Forces acting on nose landing gear strut. Impact force (\(F_{I}\)), Braking force (\(F_{B}\)), Axial force (\(F_{L}\)) acted on actuator at touchdown. ADAMS(r), which reflected the properties nonlinear pressure in the system as shown in Figure 10, whereas, for the purpose of damping characteristics, a nonlinear curve for the damping constant was defined. ADAMS formulate a Lagrange equation of motion that leads to the second order differential equation. These differential equations are called kinetic differential equations, and it regards the external forces and their influence according to the time variation [25]. An equivalent drop height was also calculated in order to accurately simulate the drop test of landing gear by using law of conservation of energy, which leads to Equation (21). \[H=\frac{W_{L}V^{2}}{W_{g}2g} \tag{21}\]  
where \(W_{L}\) is weight of aircraft at landing and \(W_{g}\) weight of landing gear. As per aircraft specifications, approximately 15% of the total weight of an aircraft acts on the nose wheel [26]. For the purpose of a drop test, landing gear was fixed in the test rig and a dummy weight equal to 15% (240 kg) of aircraft total weight at time of landing was therefore applied. The drop height was calculated to be 0.32 m for the aircraft vertical landing speed of 2.5 m/s. After calculating the equivalent drop height, spring characteristics, and damping constant, the landing gear was tested in MSC ADAMS(r) software, Figure 11 shows the assembly setup for drop test. Figure 11: Drop test setup design, modelling, & simulation. Figure 10: Iso-thermal and Polytropic behavior of Oleo Pneumatic Strut. Time-dependent nose landing gear shock absorber responses are shown in the form of the reaction forces being generated in vertical direction for normal 15% weight on the nose landing gear at different landing weights of aircraft Figure 12. The aircraft under study is a light weight long endurance aircraft with fuel capacity of 380 kg. Accordingly, the first case was studied at a maximum takeoff weight of aircraft, while the second case was studied for the landing after consuming half of the aircraft fuel and third case was studied for the landing after consuming all of the aircraft fuel.