## 考虑弯折波的舰载机拦阻过程仿真分析1)

*南京航空航天大学航空学院,南京 210016

## SIMULATION ANALYSIS OF ARRESTING PROCESS FOR CARRIER AIRCRAFT CONSIDERING KINK-WAVE1)

GAO Lele*, LIU Rongmei,*,2), YAO Niankui, CHEN Jianping*

*College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Shenyang Aircraft Design and Research Institute, Shenyang 110035, China

 基金资助: 1)江苏高校优势学科建设工程资助项目(PAPD)

Abstract

Based on nonlinear Euler-Bernoulli beam theory, a discretized model of the arresting cable considering the kink-wave is developed to study the phenomenon of the kink-wave and analyze the influence of the kink-wave during the arresting process of carrier aircraft. The numerical simulation result of the arresting process shows that the kink-wave exists in the whole arresting process. The hook load fluctuates due to the kink-wave. This fluctuation is most intense at the initial period of the arresting process. Then the fluctuation gradually attenuates. The existence of the kink-wave significantly shortens the stopping time and stopping displacement, and also makes the maximum value of the arresting cable tension larger. In addition, there are obvious differences in propagation direction, angle of cable tension and average velocity of the kink-wave between the odd and even numbered kink-waves.

Keywords： kink-wave; carrier aircraft; arresting cable; discretized model

GAO Lele, LIU Rongmei, YAO Niankui, CHEN Jianping. SIMULATION ANALYSIS OF ARRESTING PROCESS FOR CARRIER AIRCRAFT CONSIDERING KINK-WAVE1). Mechanics in Engineering, 2022, 44(2): 285-292 DOI:10.6052/1000-0879-21-408

## 1 舰载机拦阻系统简化

### 图1

Fig.1   Arresting system of carrier aircraft

$\ddot{{z}}=2n\ddot{{x}}$

### 图2

Fig.2   Simplified model of arresting system

$m\ddot{{y}}=F_{\rm T} -H-F_{{\rm f}} -F_{{\rm d}}$

$M\ddot{{x}}=4nT-F$

$\overline{{M}}\ddot{{z}}=2T-\overline{{F}}$

$\left. {\begin{array}{ccc} \overline{{M}}&=&\dfrac{M}{4n^{2}} \\ \overline{{F}}&=&\dfrac{F}{2n} \\ \end{array}} \right\}$

$T=\frac{Eq}{D}\varDelta$

## 2 拦阻索建模

### 图3

Fig.3   Discretized model of arresting cable

$q_{i} =(r_{i}^{\rm T}, \theta_{i}^{\rm T})^{\rm T}=(r_{ix},r_{iy},r_{iz},\theta_{ix},\theta_{iy},\theta_{iz} )^{\rm T}$

$\left. {\begin{array}{l} m_{i} =\rho qL_{0} \\ J_{ix} =\dfrac{1}{2}m_{i} r^{2} \\ J_{iy} =J_{iz} =\dfrac{1}{4}m_{i} \left( {r^{2}+\dfrac{L_{0}^{2}}{3}} \right) \\ \end{array}} \right\}$

$B_{i+1}$对$B_{i}$的柔性力$F_{i}$如图4所示,$B_{i}$对$B_{i+1}$的柔性力$F_{i}^{\prime }=-F_{i}$,$F_{i}$和$F_{i}^{\prime}$均是基于$O_{i} x_{i} y_{i} z_{i}$下的表达。

### 图4

Fig.4   Flexible force of $B_{i+1}$ to $B_{i}$

$F_{i} =F_{i}^{0} -F_{ix}^{0} BQ_{i}$
$\boldsymbol{B}=\left[\begin{array}{cccccc}0 & 0 & 0 & 0 & 0 & 0 \\0 & \frac{6}{5 L_{0}} & 0 & 0 & 0 & -\frac{1}{10} \\0 & 0 & \frac{6}{5 L_{0}} & 0 & -\frac{1}{10} & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & -\frac{1}{10} & 0 & \frac{2 L_{0}}{15} & 0 \\0 & -\frac{1}{10} & 0 & 0 & 0 & \frac{2 L_{0}}{15}\end{array}\right]$
$Q_{i}=\left[\begin{array}{cc}A_{i}^{-1} & 0 \\0 & A_{i}^{-1}\end{array}\right]\left(\boldsymbol{q}_{i}-\boldsymbol{q}_{i+1}\right)-\left[\begin{array}{c}L_{0} \\0 \\0 \\0 \\0 \\0\end{array}\right]$

$F_{i}^{0} =(F_{ix}^{0},F_{iy}^{0},F_{iz}^{0},T_{ix}^{0},T_{iy}^{0},T_{iz}^{0} )^{\rm T}$,具体表示为

$\boldsymbol{F}_{i}^{0}=-\boldsymbol{K} \boldsymbol{Q}_{i}-\boldsymbol{C} \boldsymbol{V}_{i}$
$\boldsymbol{V}_{i}=\left[\begin{array}{cc}\boldsymbol{A}_{i}^{-1} & \mathbf{0} \\\mathbf{0} & \boldsymbol{A}_{i}^{-1}\end{array}\right]\left[\dot{\boldsymbol{q}}_{i}-\dot{\boldsymbol{q}}_{i+1}\right]$

$\boldsymbol{K}=\left[\begin{array}{cccccc}K_{11} & 0 & 0 & 0 & 0 & 0 \\0 & K_{22} & 0 & 0 & 0 & K_{26} \\0 & 0 & K_{33} & 0 & K_{35} & 0 \\0 & 0 & 0 & K_{44} & 0 & 0 \\0 & 0 & K_{53} & 0 & K_{55} & 0 \\0 & K_{62} & 0 & 0 & 0 & K_{66}\end{array}\right]$
$C=CK$

$\left.\begin{array}{l}K_{11}=E q / L_{0} \\K_{22}=\left\{12 E I_{z z} /\left[L_{0}^{3}\left(1+P_{y}\right)\right]\right\} R_{k b} \\K_{33}=\left\{12 E I_{y y} /\left[L_{0}^{3}\left(1+P_{z}\right)\right]\right\} R_{k b} \\K_{44}=\left[G I_{x x} / L_{0}\right] R_{k t} \\K_{55}=\left\{\left(4+P_{z}\right) E I_{y y} /\left[L_{0}\left(1+P_{z}\right)\right]\right\} R_{k b} \\K_{66}=\left\{\left(4+P_{y}\right) E I_{z z} /\left[L_{0}\left(1+P_{y}\right)\right]\right\} R_{k b} \\K_{26}=K_{62}=\left\{-6 E I_{z z} /\left[L_{0}^{2}\left(1+P_{y}\right)\right]\right\} R_{k b} \\K_{35}=K_{53}=\left\{6 E I_{y y} /\left[L_{0}^{2}\left(1+P_{z}\right)\right]\right\} R_{k b}\end{array}\right\}$
$\left.\begin{array}{l}I_{x x}=\frac{\pi}{2} r^{4} \\I_{y y}=I_{z z}=\frac{\pi}{4} r^{4} \\P_{y}=12 E I_{z z} A S Y /\left(G q L_{0}^{2}\right) \\P_{z}=12 E I_{y y} A S Z /\left(G q L_{0}^{2}\right)\end{array}\right\}$

### 2.2 理想弯折波分析

$c=\sqrt {\left( {1+\dfrac{\sigma_{0} }{E}} \right)\frac{E}{\rho }}$

$\overline{{c}}=\sqrt {\dfrac{1}{\rho_{1} }\dfrac{T_{1} }{1+\varepsilon_{1} }}$

$1+\varepsilon_{1} =\frac{1+{\sigma }/{E}}{1+{\sigma_{0} }/{E}}$

$\overline{{c}}=\sqrt {\frac{\sigma \left( {1+{\sigma_{0} }/{E}} \right)}{\rho \left( 1+{\sigma }/{E} \right)}}$

$u=\dfrac{\dfrac{\sigma -\sigma_{0} }{E}}{1+{\sigma_{0}}/{E}}c$

$w=\overline{{c}}-u\left( {1-\frac{\overline{{c}}}{c}} \right)$

$w=c\left[\left(\frac{1}{2}\right)^{\frac{1}{3}}\left(\frac{v_{0}}{c}\right)^{\frac{2}{3}}-\left(\frac{1}{2}\right)^{\frac{2}{3}}\left(\frac{v_{0}}{c}\right)^{\frac{4}{3}}\right]$

### 2.3 离散模型的验证

Table 1  Comparison between theoretical value and simulation value of kink-wave velocity

## 3 舰载机拦阻过程仿真分析

### 图5

Fig.5   Hydraulic damping force

### 图6

Fig.6   Shape of arresting cable

### 图7

Fig.7   Displacement of carrier aircraft

### 图8

Fig.8   Velocity of carrier aircraft

### 图9

Fig.9   Acceleration of carrier aircraft

### 图10

Fig.10   Tension at the junction of arresting hook and arresting cable

### 图11

Fig.11   Angle of cable tension

### 图12

Fig.12   Average velocity of kink-wave in each ranking

### 图13

Fig.13   Nondimensional load vs nondimensional displacement

### 图14

Fig.14   Nondimensional load vs nondimensional displacement in MIL-STD-2066

## 4 结论

(1) 弯折波在整个拦阻过程均存在,在甲板滑轮与钩索结合点之间来回传递。

(2) 弯折波的存在,使得拦阻索拉力角产生规律性变化,还使得钩索结合点处拦阻索拉力出现波动,从而使拦阻钩载荷和舰载机加速度出现波动,且这种波动在拦阻初期最为剧烈,之后逐渐减弱。弯折波的存在明显缩短了拦停时间和拦停位移,还使得拦阻索拉力最大值更大,从而使得拦阻过程对拦阻索强度要求更高。

(3) 奇数重弯折波与偶数重弯折波传播方向相反,偶数重弯折波平均波速大于奇数重弯折波平均波速。奇数重弯折波结束前后,拦阻索拉力角平稳变化。偶数重弯折波结束前后,拦阻索拉力角突然减小,且在拦阻初期,这种突减现象极为明显。

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