﻿ 浮筏隔振系统拓扑优化减重研究
 舰船科学技术  2019, Vol. 41 Issue (4): 66-70 PDF

1. 中国舰船研究院，北京 100192;
2. 渤海造船厂集团有限公司，辽宁 葫芦岛 125005;
3. 大连理工大学船舶工程学院，辽宁 大连 116024

Topology optimization weight loss research of the floating raft isolation system
WANG Feng1, SHAO Hai-zheng2, CUI Hong-yu3
1. China Ship Research and Development Academy, Beijing 100192, China;
2. Bohai Shipyard Group CO., Ltd., Huludao 125005, China;
3. School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian 116024, China
Abstract: With the development of the vibration isolation technology, a growing number of actual ships adopt the floating raft isolation system, and obtain a good effect on vibration isolation. The difference of raft body’s structure and mass has a great effect on the performance of vibration isolation, so this paper uses the topology optimization method to optimize the floating raft isolation system and design a new raft structure, at the same time, uses power flow analysis method to study the vibration energy transfer characteristics in the floating raft isolation system. The numerical simulation result can show that the optimization raft structure under the condition of losing weight still has a good performance of vibration isolation.
Key words: floating raft     topology optimization     power flow     vibration isolation     weight loss
0 引　言

1 筏体结构拓扑优化设计

 $\left\{ \begin{array}{l} {\rm{Find}}\;\;\;\;x = {({x_1},{x_2}\text{，} \cdots ,{x_n})^{\rm T}}\text{，}\\ {\rm Min}\;\;\;\;C\left( x \right) = {F^{\rm T}}U\text{，}\\ {\rm s.t.}\;\left\{ \begin{array}{l} V \leqslant f{V_0}\text{，}\\ F = KU\text{，}\\ 0 < {x_{\min }} \leqslant {x_i}\leqslant 1\text{，}(i = 1,2, \cdots ,n)\text{。} \end{array} \right. \end{array} \right.$ (1)

 ${E_i} = x_i^p{E_0}\text{，}\;\;\;\;\;\left( {i = 1,2, \cdots ,n} \right)\text{。}$ (2)

 $\left\{ \begin{array}{l} F{\rm{ind}}\;\;\;\;x = {({x_1},{x_2}, \cdots ,{x_n})^{\rm T}}\text{，}\\ Min\;\;\;\;C\left( x \right) = {F^T}U = {U^{\rm T}}KU =\\ \begin{array}{*{20}{c}} {}&{} \end{array}\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{} \end{array}\displaystyle\sum\limits_{i = 1}^n {x_i^p{u_i}^T{k_0}{u_i}} \text{，}\\ {\rm{s.t.}}\;\left\{ \begin{array}{l} V = \displaystyle\sum\limits_{i = 1}^n {{x_i}{v_i}} \leqslant f{V_0}\text{，}\\ F = KU\text{，}\\ 0 < {x_{\min }} \leqslant {x_i} \leqslant 1\text{，}({{i}} = 1,2, \cdots ,{{n}})\text{。} \end{array} \right. \end{array} \right.$ (3)

${k_i} = x_i^p{k_0},V = \displaystyle\sum\limits_{i = 1}^n {{x_i}{v_i}}$ 代入上式，可得：

 $\frac{{p{{\left( {{x_i}} \right)}^{\left( {p - 1} \right)}}u_i^{\rm T}{k_0}{u_i}}}{{{\lambda _1}{v_i}}} = 1\text{，}$ (4)

$C_i^k = \dfrac{{p{{\left( {{x_i}} \right)}^{\left( {p - 1} \right)}}u_i^{\rm T}{k_0}{u_i}}}{{{\lambda _1}{v_i}}}$ ，将其作为SIMP模型优化设计准则法的变量迭代因子。

 $x_i^{k + 1} = \left\{ \begin{array}{l} {\left( {C_i^k} \right)^\xi }x_i^k\;\;if \text{，}\;\;\;{x_{\min }} < {\left( {C_i^k} \right)^\xi }x_i^k < 1\text{，}\\ {x_{\min }}\text{，}\;\;\;\;\;\;\;\;\;{\rm if}\;\;\;{\left( {C_i^k} \right)^\xi }x_i^k < {x_{\min }}\text{，}\\ 1\text{，}\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm if}\;\;\;\;{\left( {C_i^k} \right)^\xi }x_i^k \geqslant 1\text{。} \end{array} \right.$ (5)

 图 1 Optistruct中的有限元模型 Fig. 1 The raft’s finite element model by Optistruct

1）优化变量：离散结构的优化空间之后，每个离散单元的材料相对密度（其值在0～1之间）。

2）优化响应：上层隔振器与筏体连接点处的静力位移（共12个）；下层隔振器与筏体连接点处的静力位移（共6个）；筏体的质量。

3）优化约束：筏体上部承载有较大重量的机械设备，除了需要考虑整个浮筏隔振系统的隔振性能，还需要保证筏体结构上的响应较小，即具有一定程度的强度，以此来保证整个系统的承载。因此，优化模型中以下端隔振器与筏体连接的6个节点的位移以及上端隔振器与筏体连接的12个节点的位移为约束条件。

4）优化目标：筏体在满足一定隔振特性和刚度的前提条件下，质量最小。

2 筏体结构拓扑优化结果分析

 图 2 优化后密度分布云图 Fig. 2 The density nephogram of optimized raft

 图 3 优化筏体结构图 Fig. 3 Optimized raft’s structure drawing
3 优化筏体结构的有限元分析

1）优化筏体的模态和振型

 图 4 优化筏体前四阶固有振型 Fig. 4 The previous four natural modes of optimized raft

2）初始筏体和优化筏体的应力分布

 图 5 优化前后筏体结构应力对比图 Fig. 5 The stress diagram of before and after optimization raft

4 浮筏隔振系统功率流有限元分析

 $F\left( t \right) = \operatorname{Re} \left\{ {\tilde F \cdot {e^{i\omega t}}} \right\}\text{，}$ (6)
 $X\left( t \right) = \operatorname{Re} \left\{ {\tilde X \cdot {e^{i\omega t}}} \right\}\text{，}$ (7)
 $\begin{array}{l} P = \dfrac{1}{T}\displaystyle\int_0^T {F\left( t \right)} \cdot V\left( t \right) \cdot {\rm d}t= \\ \ \ \ \mathop {}\limits^{} \dfrac{1}{T}\displaystyle\int_0^T {{\mathop{\rm Re}\nolimits} \left\{ {\tilde F \cdot {e^{i\omega t}}} \right\}} \cdot {\mathop{\rm Re}\nolimits} \left\{ {i\omega \tilde X \cdot {e^{i\omega t}}} \right\} \cdot {\rm d}t\text{。} \end{array}$ (8)

$\tilde F = F' + iF''$ $\tilde X = X' + iX''$ $F'$ $F''$ $X'$ $X''$ 均为实数。

 $\begin{split} P =& \dfrac{1}{T}\displaystyle\int_0^T {\left[ {F'\cos \omega t - F''\sin \omega t} \right]}\times \\ &\left( { - \omega } \right)\left[ {X'\sin \omega t + X''\cos \omega t} \right] \cdot {\rm d}t= \\ &\left( { - \omega } \right) \times \left( {\dfrac{1}{2}F'X'' - \dfrac{1}{2}X'F''} \right) ={\text{π}}f\left( {X'F'' - F'X''} \right)\text{。}\!\!\!\! \end{split}$ (9)

 图 6 优化前后浮筏隔振系统有限元模型 Fig. 6 The finite element model of before and after optimization floating raft

 图 7 优化前后浮筏隔振系统功率流传递曲线 Fig. 7 The powerflow's transfer curve of before and after optimization floating raft

5 结　语

 [1] 马永涛, 周炎. 舰船浮筏隔振技术综述[J]. 舰船科学技术, 2008, 30(4): 22-26. DOI:10.3404/j.issn.1672-7649.2008.04.002 [2] 张乐. 浮筏系统隔振优化设计[J]. 中国水运, 2014, 14(2): 150-151. [3] 杨德庆, 郭凤骏. 振级落差约束下齿轮箱基座拓扑构型设计[J]. 振动与冲击, 2008, 27(6): 173-177. DOI:10.3969/j.issn.1000-3835.2008.06.040 [4] 汪玉, 陈国钧, 华宏星, 等. 船舶动力装置双层隔振系统的优化设计[J]. 中国造船, 2001, 42(1): 45-49. DOI:10.3969/j.issn.1000-4882.2001.01.008 [5] 刘克龙, 姚卫星, 穆雪峰. 基于Kriging代理模型的结构形状优化方法研究[J]. 计算力学学报, 2006, 23(3): 344-347. DOI:10.3969/j.issn.1007-4708.2006.03.017 [6] 赵晓明, 黄浩. 基于ANSYS的舰艇浮筏隔振系统特性[J]. 机电设备, 2017, 34(3): 1-4. [7] 严济宽, 沈密群, 尚国清. 浮筏结构动力参数的选定[J]. 噪声与振动控制, 1995(1): 2-9. [8] 华宏星, 林莉. 浮筏系统频率响应灵敏度分析[J]. 中国造船, 1999(3): 92-97. [9] 张华良, 傅志方. 浮筏隔振系统各主要参数对系统隔振性能的影响[J]. 振动与冲击, 2000, 19(2): 5-8. DOI:10.3969/j.issn.1000-3835.2000.02.002 [10] 郑学贵. 舰船浮筏减振特性研究[J]. 舰船科学技术, 2018(2): 7-9. [11] SCIULLIA, D. D. J. Inmanb. Isolation design for a flexible system[J]. Journal of Sound and Vibration, 1998, 246(N0. 2): 251-267. [12] LI, W. L., M. DANIELSW. ZHOU. Vibrational power transmission from a machine to its supporting cylindrical shell[J]. Journal of Sound and Vibration, 2002, 257(2): 283-299. DOI:10.1006/jsvi.2001.3835 [13] XIONG, Y P, J T XINGW G. Price. Power flow analysis of complex coupled systems by progressive approaches[J]. Journal Of Sound And Vibration, 2001, 239(2): 275-295. DOI:10.1006/jsvi.2000.3159 [14] 伍先俊, 朱石坚. 基于有限元分析的功率流计算技术及隔振系统优化设计[J]. 船舶力学, 2005, 9(4): 138-145. DOI:10.3969/j.issn.1007-7294.2005.04.019