﻿ 舰载雷达TR组件冲击计算方法分析
 舰船科学技术  2021, Vol. 43 Issue (12): 155-160    DOI: 10.3404/j.issn.1672-7649.2021.12.028 PDF

Analysis of shock computation method for TR module in shipborne radar
ZHU Zeng-hui, MENG Qing-qin
The 724 Research Institute of CSSC, Nanjing 211153, China
Abstract: In order to meet the anti-shock and lightweight design requirements of TR module in shipborne radar, DDAM and time domain simulation method were used to compute and analyze the shock response of TR module. It can be seen from the computation results that stress distribution area and danger area obtained by two shock computation methods were the same. The maximum stress in three directions was located on the guide pin, the stress was less than the yield strength of the corresponding material, and the vertical shock stress was the largest. The stress computed by time domain simulation method was less than that of DDAM, but the computation time was obviously higher than that of DDAM. Furthermore, the structural optimization improvement suggestions were put forward by analyzing the shock stress distribution of TR module. It is suggested that time domain simulation method with high computation accuracy and reasonable computation results should be used instead of DDAM for shock analysis of TR module, which is shipborne equipment with strict weight control located in the ship mast area. The research results can provide theoretical support for the anti-shock and lightweight design of shipborne equipment.
Key words: TR module     DDAM     time domain simulation method     Shock spectrum
0 引　言

TR组件是舰载雷达的关键部件，具有放大发射和接收信号、改变信号幅值相位等功能。雷达天线面阵由多个TR组件组成，TR组件研制过程中除满足低噪声、高效率和大功率等基本要求外，应考虑小型化和轻量化设计。

1 分析模型描述

 图 1 TR组件结构几何模型 Fig. 1 Geometric model of TR module structure

 图 2 TR组件有限元模型 Fig. 2 Finite element model of TR module
2 TR组件DDAM冲击计算分析

DDAM（Dynamic Design Analysis Method）计算方法由美国海军实验室提出，美国海军结合大量实船水下非接触爆炸试验采集的设备冲击响应数据，归纳得到舰载设备冲击设计谱。DDAM基于模态叠加法，将分析模型从单个多自由度系统转化成多个单自由度系统，依据对TR组件分析模型模态计算得到的各阶模态频率、模态质量和模态参与因子，推导出相应的冲击输入响应谱，合成每一阶的模态应力和位移以计算组件的冲击最大响应量[4-5]。对TR组件DDAM计算方法进行理论分析。

TR组件冲击作用下运动微分方程为[6-7]

 ${\boldsymbol{M}}\ddot x + {\boldsymbol{K}}x = - {\boldsymbol{M}}n\ddot y(t)。$ (1)

 ${P_k} = \frac{{{\alpha _k}^{\rm{T}}Mn}}{{{\alpha _k}^{\rm{T}}M{\alpha _k}}}，$ (2)

k阶模态质量mk的表达式为：

 ${m_k} = \sum\limits_n {\left( {{m_n}{\phi _{kn}}{P_k}} \right)}。$ (3)

TR组件总质量为各阶模态质量之和，第k阶模态质量即冲击作用下第k阶模态被激励的质量。

TR组件DDAM设计冲击谱与其模态质量有关，由于冲击响应量受到雷达天线阵面和固定基础处相互作用影响，设计冲击谱数值与舰船种类、分析对象安装区域等因素有关，雷达天线阵面安装在舰船甲板部位，TR组件采用弹性设计，表1为GJB 1060.1-91规定的DDAM设计冲击谱。

 ${A_s} = 98.1 \times \frac{{19.05 + {{m}}{}_k}}{{2.72 + {{m}}{}_k}} ，$ (4)
 ${V_s} = 1.52 \times \frac{{5.44 + {{m}}{}_k}}{{2.72 + {{m}}{}_k}} 。$ (5)

DDAM计算方法规定每个方向参与分析的模态质量之和与总质量的比例大于80%，并提取模态质量占比大于1%的模态参与计算，以提高TR组件冲击求解精度和可靠性。设计冲击加速度取Ak两者的较小值, ωk为第k阶模态质量mk的圆频率[9]

 图 3 TR组件前6阶模态振型 Fig. 3 The first six-orders mode shapes of TR module

 图 4 DDAM计算应力云图 Fig. 4 Stress nephogram computed by DDAM
3 TR组件时域模拟法冲击计算分析

DDAM基于模态计算，通过对各阶模态冲击响应进行NRL合成得到总的冲击响应，NRL合成法中最大应力值为绝对值，未考虑设备非线性结构特性、阻尼效应和各阶模态响应相位差对计算结果的影响。因此，DDAM计算量小，对计算机硬件要求较低，且计算结果具有可靠性，但计算应力值偏保守，不利于TR组件等舰载设备的轻量化抗冲击设计。早期受到计算机硬件的限制，具有线性或者弱非线性的舰载设备适合采用DDAM进行冲击计算。近些年来，计算机硬件性能有了明显的提升，有限元软件冲击算法趋于成熟完善，研究人员逐渐采用求解精度更高但计算量大的时域模拟法代替DDAM对舰载设备进行瞬态动力学计算，时域模拟法可对线性或者非线性的复杂模型进行求解，冲击输入载荷为实测冲击时域曲线或者标准冲击时域曲线，实测冲击时域曲线更为真实，但其冲击波形复杂，每次试验舰载设备处采集的冲击谱都不一致，具有随机性。标准冲击时域曲线参考德国军标BV0430-85规定的冲击谱，将冲击试验数据归纳得到的三折线冲击频域响应谱转化成等效的标准冲击时域曲线，标准时域曲线参数较为简单，且接近实测冲击谱，适合作为时域模拟法的输入载荷。

 ${\boldsymbol{M}}\mathop z\limits^{..} (t + \Delta t) + {\boldsymbol{C}}\mathop z\limits^. (t + \Delta t) + {\boldsymbol{K}}(t)z(t) = R(t + \Delta t) - F(t)。$ (6)

 图 5 组合半正弦波时历曲线 Fig. 5 Two-time history of half-sine wave

TR组件时域模拟法计算中的分析模型前处理和边界约束条件和DDAM相同，在有限元软件中输入组合半正弦波时间历程曲线载荷后对其进行瞬态动力学计算。

 图 6 不同冲击方向上最大应力时历曲线 Fig. 6 Time history of maximum stress in different shock directions

 图 7 时域模拟法计算瞬时应力云图 Fig. 7 Stress nephogram computed by time domain simulation method

4 冲击计算方法比较

5 结　语

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