﻿ 舰载机拦阻着舰起落架动态响应分析
 舰船科学技术  2022, Vol. 44 Issue (16): 45-49    DOI: 10.3404/j.issn.1672-7649.2022.16.009 PDF

Dynamic response analysis on landing gear of carrier-based aircraft arresting
ZHANG Jiang-hua, CHEN Jian-ping, LIU Xiao-fei, TONG Ming-bo
College of Aeronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract: During the process of arresting landing, it is necessary to determine the true dynamic response of landing gear, because the landing distance of carrier-based aircraft is short and the load is large. Aiming at the complexity of arresting landing, the dynamics model of a carrier aircraft arresting landing was established by LMS.virtual.Lab Motion. Under the condition of free flight, the aircraft landed with different horizontal ground speeds and different sinking speeds. Through the simulation analysis, the larger the sinking speed or the smaller the horizontal ground speed, the larger the main landing gear load, nose landing gear presents the opposite situation. The analysis results can provide a reference for the research on the arresting landing process and the design of landing gear structure of the carrier-based aircraft.
Key words: carrier-based aircraft     landing gear     load     arresting landing
0 引　言

1 自由飞行钩住及说明 1.1 自由飞行钩住

 图 1 自由飞行钩住 Fig. 1 Free flight engagement
1.2 舰载机几何参数

 图 2 舰载机示意图 Fig. 2 Carrier-based aircraft diagram

2 舰载机拦阻着舰多体动力学模型 2.1 基本假设

1）机体做刚性处理，即不考虑机体旋转部件及弹性变形的影响。

2）不考虑大气湍流、甲板运动对机体扰动的影响。

3）对于着舰过程中燃油消耗所引起舰载机质量以及质心位置的变化，则不予以考虑。

4）着舰过程中，仅考虑舰载机纵向平面内的运动。

2.2 坐标系定义

1）大地坐标系（ ${O_d}{x_d}{y_d}{z_d}$

2）机体坐标系（ ${O_b}{x_b}{y_b}{z_b}$

3）气流坐标系（ ${O_a}{x_a}{y_a}{z_a}$

4）减震支柱坐标系（ ${O_c}{x_c}{y_c}{z_c}$

2.3 相关力计算模型 2.3.1 气动载荷模型

 $\left\{ {\begin{array}{*{20}{c}} {L = \dfrac{1}{2}\rho {V^2}{S_A}{C_L}}，\\ {D = \dfrac{1}{2}\rho {V^2}{S_A}{C_D}}，\\ {{M_z} = \dfrac{1}{2}\rho {V^2}{S_A}l{m_z}} 。\end{array}} \right.$ (1)

2.3.2 缓冲器力模型

 ${F_c} = {F_a} + {F_{oil}} + {F_f} + {F_s}。$ (2)

 ${F_a} = \left\{ \begin{array}{*{20}{l}} {{F_{a1}} = {A_{a1}}{P_{01}}{{\left( {\dfrac{{{V_{01}}}}{{{V_{01}} - {A_{a1}}S}}} \right)}^{{n_1}}}} ，\\ {F_{a2}} = {A_{a1}}\left[ {{P_{01}}{{\left( {\dfrac{{{V_{01}}}}{{{V_{01}} - {A_{a1}}S}}} \right)}^{{n_1}}} - {P_a}} \right] + \\ {A_{a2}}\left[ {{P_{02}}{{\left( {\dfrac{{{V_{02}}}}{{{V_{02}} - {A_{a2}}(S - {S_0})}}} \right)}^{{n_2}}} - {P_a}} \right]，\end{array} \right.$ (3)
 ${F_{oil}} = \frac{{\rho {A_h}^3\dot S}}{{2{{({C_d}{A_{01}})}^2}}}\left| {\dot S} \right| 。$ (4)

 ${F_f} = \frac{{\dot S}}{{\left| {\dot S} \right|}}{\mu _{km}}{F_a} ，$ (5)
 ${F_s} = \left\{ {\begin{array}{*{20}{c}} {{k_{\lim it}}S}，\\ 0，\\ {{k_{\lim it}}(S - {S_{\max }})} ，\end{array}\begin{array}{*{20}{c}} {S < 0}，\\ {0 \leqslant S \leqslant {S_{\max }}} ，\\ {S > {S_{\max }}} 。\end{array}} \right.$ (6)

2.3.3 轮胎力模型

 ${{\boldsymbol{F}}_t} = {k_t}\varepsilon + {c_t}\dot \varepsilon 。$ (7)

 ${k_t} = \frac{{6{W_{\max }}}}{{{D_{mdis}}^2}} - \frac{{2{F_{\max }}}}{{{D_{mdis}}}}，$ (8)
 ${c_t} = \frac{{6{W_{\max }}}}{{{D_{mdis}}^3}} - \frac{{3{F_{\max }}}}{{{D_{mdis}}^2}}。$ (9)

2.3.4 拦阻力模型

 图 3 拦阻力力学模型 Fig. 3 Arresting force model

 图 4 拦阻载荷-行程曲线 Fig. 4 Arresting force-displacement curve

${\theta _p}$ =7°， ${V_v}$ =2.4 m/s的条件下，对舰上结合速度51.5 m/s、56.8 m/s和62.1 m/s进行仿真分析。

 ${L_C} = \frac{{{L_0}}}{{\cos \beta }} = \frac{{{L_0}\sqrt {{h^2} + {s^2}} }}{s} 。$ (10)
2.4 拦阻着舰动力学方程

 图 5 舰载机着舰过程受力示意图 Fig. 5 Force diagram of Carrier aircraft airframe load landing process landing process

 $\begin{split} & {m_b}\left( {\left[ {\begin{array}{*{20}{c}} {\dfrac{{{\text{d}}u}}{{{\text{d}}t}}} \\ {\dfrac{{{\text{d}}v}}{{{\text{d}}t}}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&{ - r} \\ r&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} u \\ v \end{array}} \right]} \right) = \left[ {\begin{array}{*{20}{c}} {P - {L_C}\cos \beta } \\ {{L_C}\sin \beta } \end{array}} \right] + \\ & {{\boldsymbol{T}}_{ba}}\left[ {\begin{array}{*{20}{c}} { - D} \\ L \end{array}} \right] + {{\boldsymbol{T}}_{bd}}\left[ {\begin{array}{*{20}{c}} 0 \\ { - {m_b}g} \end{array}} \right] + \sum\limits_{i = N,ML,MR} {{{\boldsymbol{T}}_{bc}}\left[ {\begin{array}{*{20}{c}} {{F_{ixc}}} \\ {{F_{iyc}}} \end{array}} \right]，}\end{split}$ (11)

 $\begin{split} & {I_z}\dot r = {L_C}{\left[ {\begin{array}{*{20}{c}} {\sin \beta } \\ { - \cos \beta } \end{array}} \right]^{\text{T}}}\left[ {\begin{array}{*{20}{c}} {{d_x}} \\ {{d_y}} \end{array}} \right] + \sum\limits_{i = N,ML,MR} {{{\left[ {\begin{array}{*{20}{c}} {{F_{{\text{iyc}}}}} \\ {{F_{ixc}}} \end{array}} \right]}^{\text{T}}}} \left[ {\begin{array}{*{20}{c}} {{R_{xi}}} \\ {{R_{yi}}} \end{array}} \right] +\\ & \sum\limits_{i = N,ML,MR} {\left( {{f_{xi}}{\Delta _{yi}}} \right)} + {M_z}，\end{split}$ (12)

 $\begin{split} & {m_q}_i\left( {\left[ {\begin{array}{*{20}{c}} {\dfrac{{{\text{d}}{u_i}}}{{{\text{d}}t}}} \\ {\dfrac{{{\text{d}}{v_i}}}{{{\text{d}}t}}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&{ - r} \\ r&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{u_i}} \\ {{v_i}} \end{array}} \right]} \right) = \\ & {{\mathbf{T}}_{bd}}\left[ {\begin{array}{*{20}{c}} { - {f_{txi}}} \\ {{F_{tyi}} - {m_q}_ig} \end{array}} \right] - {{\mathbf{T}}_{bc}}\left[ {\begin{array}{*{20}{c}} {{F_{ixc}}} \\ {{F_{iyc}}} \end{array}} \right]，\end{split}$ (13)
 ${I_{\omega i}}\frac{{{\text{d}}{\omega _{\omega i}}}}{{{\text{d}}t}} = {f_{txi}}\left( {{R_{0i}} - {\varepsilon _i}} \right)。$ (14)

3 仿真分析

 图 6 前起落架轴向载荷-时间曲线 Fig. 6 Axis load-time curves of nose landing gear

 图 7 主起落架轴向载荷-时间曲线 Fig. 7 Axis load-time curves of main landing gear

 图 8 俯仰角变化规律 Fig. 8 Pitching angle
3.1 舰上结合速度对起落架轴向载荷的影响

3.2 下沉速度对起落架轴向载荷的影响

${\theta _p}$ =7°， ${V_E}$ =51.5 m/s条件下，对初始下沉速度1.2 m/s，2.4 m/s，3.2 m/s，3.8 m/s，4.3 m/s进行仿真。

 图 9 重心处下沉速度下前、主起落架触舰时刻的下沉速度 Fig. 9 Sink speed of nose and main gear at landing time during different sinking speed

 图 10 前起落架轴向载荷-时间曲线 Fig. 10 Axis load-time curves of nose landing gear

 图 11 主起落架轴向载荷-时间曲线 Fig. 11 Axis load-time curves of main landing gear
4 结　语

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