# Parametric Analysis on Landing Gear Strut Friction of Light Aircraft for Touchdown Performance
## 2 Landing Gear Modeling and Validating
### Bearing Normal Force Analysis  
The effects of ground forces on the absorber strut contain the normal force on the bearing area between the outer cylinder and the piston rod, and the strut elastic deformation. Additional bending moments will be generated at the bearing area to ensure that the deformation of the outer cylinder and the piston rod remains consistent within the supporting area. It is embodied by the reaction force on the upper and lower surfaces of the bearing, which increases the total normal force on the bearing area. Figure 3 is a schematic diagram of the internal force analysis for the half-axle main landing gear in the _xoz_ plane and the _yoz_ plane under the ground vertical force and longitudinal force. Figure 2: Representation of Stribeck curves: (**a**) The classic Stribeck curve; (**b**) Stribeck curve without discontinuity. \(N\) and \(M\) in Figure 3 denote the normal forces and additional bending moments, the subscripts \"A\" and \"B\" mean the acting points point A and point B, the superscripts \"\(x\)\" and \"\(y\)\" indicate the _xoz_ plane and the _yoz_ plane, respectively. \(F_{T}\) is the internal force acting on the intersection point of the upper and lower torque link. To simplify the calculation process, the following assumptions are made for the landing gear strut in this work. The outer cylinder is simplified to a cantilever beam model, and the piston rod is simplified to an overhanging beam model. The flexible deformation of the outer cylinder and the piston rod is considered under the small deformation assumption, which uses the equivalent area moment of inertia of the simplified uniform beam for calculation, as shown in Figure 4.  
\(I_{1}\) and \(I_{2}\) in Figure 4 represent the equivalent area moment of inertia of the outer cylinder and the piston rod, respectively. In the _xoz_ plane and the _yoz_ plane, the outer cylinder and the piston rod are subjected to the external forces and the internal forces at the bearing area. The deformation and rotation angle of the outer cylinder and the piston rod at the upper and lower bearing area can be calculated using the external force and the contact internal force. The deformation and rotation angle on the piston rod are recorded as \(w_{A}\), \(w_{B}\), \(\theta_{A}\), and \(\theta_{B}\). The deformation and rotation angle on the piston rod are written as \(w_{A}\), \(w_{B}\)', \(\theta_{A}\)', and \(\theta_{B}\)', respectively. According to the coordinated relationship of deformation, it is concluded that  
\[w_{A}=w_{A}\text{'},\ w_{B}=w_{B}\text{'},\ \theta_{A}=\theta_{A}\text{'}, \theta_{B}=\theta_{B}\text{'}. \tag{10}\]  
Figure 4: Schematic of uniform beam with equivalent area moment of inertia. Figure 3: Schematic of main landing gear (MLG) load analysis. The calculation results of four equations for normal forces and bending moments on point A and point B in the \(xoz\) plane and \(yoz\) plane can be described as  
\[\left\{ \begin{array}{l}N_{A}^{x}=-\frac{F_{D}b_{2}}{I_{1}+I_{2}},\ M_{A}^{x}= \frac{I_{d}F_{D}I_{2}+L_{B}F_{D}I_{2}}{I_{1}+I_{2}},\\ N_{B}^{x}=\frac{F_{D}I_{1}}{I_{1}+I_{2}},\ M_{B}^{x}=\frac{I_{d}F_{D}I_{1}}{I_{1 }+I_{2}},\\ N_{A}^{y}=\frac{F_{D}I_{2}}{I_{1}+I_{2}},\ M_{A}^{y}=-\frac{I_{d}F_{D}I_{2}-F_{ v}I_{2}+F_{t}L_{D}I_{2}}{I_{1}+I_{2}},\\ N_{B}^{y}=\frac{F_{D}I_{2}}{I_{1}+I_{2}},\ M_{B}^{y}=\frac{F_{D}I_{1}+F_{D}I_{2 }}{I_{1}+I_{2}}.\end{array} \right. \tag{11}\]  
The normal forces and bending moments are resulting from the reaction forces on the upper and lower surfaces of bearings, as shown in Figure 5.  
The reaction force on the upper and lower surfaces of bearings can be calculated by the equations  
\[\left\{ \begin{array}{l}N_{A}^{1x,1y}-N_{A}^{2x,2y}=N_{A}^{x,y},\\ \left(N_{A}^{1x,1y}+N_{A}^{2x,2y}\right)\cdot\frac{d_{A}}{2}=M_{A}^{x,y},\\ N_{B}^{1x,1y}-N_{B}^{2x,2y}=N_{B}^{x,y},\\ \left(N_{B}^{1x,1y}+N_{B}^{2x,2y}\right)\cdot\frac{d_{B}}{2}=M_{B}^{x,y},\end{array} \right.