﻿ 基于遗传算法改进的DDAM风机隔振装置抗冲击仿真实验
 舰船科学技术  2020, Vol. 42 Issue (1): 146-150 PDF

Simulation experiment of anti - impact of vibration isolation device of DDAM fan based on genetic algorithm
ZHOU Ma-jun, XUE bin, XUE Cheng, WU Jun-jie, XIA Zhao-wang
School of Energy and Power, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: The dynamic design analysis method (DDAM) of the anti-impact performance of ship equipment in GJB-1060.1-91 can evaluate the anti-impact performance of the equipment from stress, but in many cases, the equipment acceleration response needs to evaluate the anti-impact performance of the equipment. In this paper, the impact spectrum of the two-layer vibration isolation device of ship fan is designed based on DDAM method. Results show that the synthesis of time-domain signal conversion after the impact of the general and the impact of the DDAM method design spectrum has a good consistency, and the time domain to encourage maximum stress under the shock signal and spectrum error of 9%. The stress and acceleration shock response of the double-deck vibration isolation device are calculated based on the time domain signal of the impact spectrum, which is helpful for the analysis method of the impact resistance performance of ship equipment in GJB-1060.1-91 to be widely used in engineering.
Key words: DDAM     shock response spectrum     genetic algorithm     time domain synthesis     the time domain analysis
0 引　言

1 动力学设计分析方法

1.1 舰船设备抗冲击性能动力学设计分析方法 1.1.1 无阻尼系统的运动微分方程
 $\left[ {{m}} \right]\left\{ {\ddot x} \right\}{\rm{ + }}\left[ k \right]\left\{ x \right\}{\rm{ = }}0\text{，}$ (1)

1.1.2 模态因子Pa和有效模态质量Mna
 ${{{P}}_a}{\rm{ = }}\frac{{{{\left\{ {{{\bar x}_i}} \right\}}^{\rm{T}}}\left[ m \right]}}{{{{\left\{ {{{\bar x}_i}} \right\}}^{\rm{T}}}\left[ m \right]\left\{ {{{\bar x}_i}} \right\}}}\text{，}$ (2)
 ${M_{na}} = {P_a}\sum\limits_i {{m_i}{{\bar x}_i} = \frac{{{{\sum\limits_i {\left[ {{m_i}{{\bar x}_i}} \right]} }^2}}}{{\sum\limits_i {{m_i}{{\bar x}_i}^2} }}}\text{。}$ (3)
1.1.3 基础激励的响应

 $\left[ {{m}} \right]\left\{ {\ddot x} \right\}{\rm{ + }}\left[ k \right]\left\{ x \right\}{\rm{ = - }}\left[ {{m}} \right]\left\{ 1 \right\}\ddot z\left( t \right)\text{。}$ (4)

 ${\ddot q_i} + {\omega _i}^2{q_i} = - \frac{{{{\left\{ {{{\bar x}_i}} \right\}}^{\rm T}}\left[ m \right]\left\{ 1 \right\}}}{{{{\left\{ {{{\bar x}_i}} \right\}}^{\rm T}}\left[ m \right]\left\{ {{{\bar x}_i}} \right\}}}\ddot z\left( t \right)\text{，}$ (5)

 ${\ddot q_i} + {\omega _i}^2{q_i}{\rm{ = }} - {p_a}\ddot z\left( t \right)\text{，}$ (6)

 ${q_i} = - \frac{{{p_i}}}{{{\omega _i}^2}}\int_0^t {z\left( \tau \right)} \sin {\omega _i}\left( {t - \tau } \right){\rm d}\tau \text{。}$ (7)

 ${q_{im}} = - \frac{{{p_i}{v_i}}}{{{\omega _i}}}\text{，}$ (8)

i阶模态中最大的位移为：

 $\left\{ {{x_i}} \right\} = \left\{ {{{\bar x}_i}} \right\}{q_{im}}\text{，}$ (9)

i阶模态中的动态力为：

 $\left\{ {{F_i}} \right\} = \left[ k \right]\left\{ {{{\bar x}_i}} \right\}{q_{im}}\text{，}$ (10)

 ${F_{ia}} = {m_i}{\bar x_{ia}}{P_a}{A_i}\text{。}$ (11)
1.2 舰船设备抗冲击性能动力学设计模态合成方法

 ${x_i} = {x_{ib}} + \sqrt {\sum\limits_a {{x_{ia}}^2 - x_{ib}^2} }\text{。}$ (12)

2 基于DDAM的风机双层隔振装置仿真实验 2.1 有限元建模

 图 1 风机双层隔振装置有限元模型 Fig. 1 Finite element model of the double-layer vibration isolation device of the fan
2.2 设计冲击谱

2.3 筏体的应力合成

 图 2 垂向冲击时筏体的应力云图 Fig. 2 Stress cloud diagram of raft during vertical impact
3 冲击谱基于遗传算法的时域信号合成

3.1 冲击谱的时域信号形式

 $x = \sum\limits_{i = 1}^n {{A_i}} {e^{ - \xi {\omega _i}t}}\sin \left( {{\omega _i}t + {\varphi _i}} \right)\text{。}$ (13)

3.2 改进的递归数字滤波法的冲击谱计算

 ${y_i} = {b_0}{x_i} + {b_1}{x_{i - 1}} + {b_2}{x_{i - 2}} + {q_1}{y_{i - 1}} + {q_2}{y_{i - 2}}\text{。}$ (14)

 $\left\{ \begin{gathered} {b_0} = 1 - \exp \left( { - D} \right){{\sin \left( E \right)} / E}\text{，} \\ {b_1} = 2\exp \left( { - D} \right)\left[ {{{\sin \left( E \right)} / E} - \cos \left( E \right)} \right] \text{，} \\ {b_2} = 2\exp \left( { - D} \right)\left[ {{{\left[ {\exp ( - D)} \right]} / E} - {{\sin E} / E}} \right] \text{，} \\ {q_1} = 2\exp ( - D)\cos (E) \text{，} \\ {q_2} = - \exp ( - 2D)\text{，} \\ D = \xi {\omega _n}\vartriangle t \text{，} \\ {\omega _n} = 2\pi {f_n}\text{，} \\ {\omega _0} = {\omega _n}\sqrt {1 - {\xi ^2}} \text{，} \\ E = {\omega _0}\vartriangle t \text{，} \\ {y_1} = 0 \text{，} \\ {y_2} = 0 \text{。} \\ \end{gathered} \right.$
3.3 冲击谱的时域信号合成

 $F = \sum\limits_{i = 1}^n {\frac{{{{\left( {y({f_i}) - {y_0}({f_i})} \right)}^2}}}{n}}\text{。}$ (15)

 图 3 适应度值变化图 Fig. 3 Variation of fitness values

 图 4 最佳个体幅值和相位 Fig. 4 Optimal individual amplitude and phase

 图 5 冲击信号时间历程 Fig. 5 Time history of impact signal

 图 6 冲击谱曲线 Fig. 6 Shock spectrum curve
4 风机双层隔振装置时域冲击仿真实验

 图 7 上层隔振器下端的加速度响应 Fig. 7 Acceleration response at lower end of upper vibration isolator

 图 9 筏体垂向冲击的应力云图 Fig. 9 Stress cloud diagram of vertical impact of raft

 图 8 上层隔振器上端的加速度响应 Fig. 8 Acceleration response at upper end of upper vibration isolator
5 结　语

1）本文基于GJB-1060.1-91中的动力学设计分析方法设计了风机双层隔振装置的冲击谱，并对风机双层隔振装置进行抗冲击计算，得到的筏体的应力云图表明，应力主要集中在隔振器安装的部位，且最大应力远远小于材料的许用值，可以保证筏体在冲击环境中的安全性。

2）利用衰减正弦基波的组合形式表示待合成的冲击时域信号，通过遗传算法和改进的递归数字滤波法获得冲击谱的时域信号。冲击谱时域信号转换后的频域信号与DDAM设计的冲击谱具有很好的一致性。通过遗传算法对冲击信号时域合成，可以解决GJB-1060.1-91中DDAM方法只能在频域上计算的缺点，而且相比较于德国军标BV043-85中通过经验公式设计的三角波或半正弦波，更符合爆炸冲击时域信号的特点，有助于拓展GJB-1060.1-91中舰船设备抗冲击性能分析方法的工程应用范围。

3）对风机双层隔振装置进行抗冲击计算，上层隔振器上端的冲击加速度响应峰值为14g，与输入冲击加速度峰值212g相比降低了198g，表明风机双层隔振装置的隔冲效果明显。

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