﻿ 一种基于刚度准则的橡胶减振器设计方法
 舰船科学技术  2018, Vol. 40 Issue (4): 53-57 PDF

1. 海军工程大学 振动与噪声研究所，湖北 武汉 430033;
2. 船舶振动噪声重点实验室，湖北 武汉 430033

A method to study the compact design of rubber absorber based on static stiffness
XIAO Quan-shan1,2, ZHAO Ying-long1,2, JIN Zhu1,2
1. Institute of Noise and Vibration, Naval University of Engineering, Wuhan 430033, China;
2. National Key Laboratory on Ship Vibration and Noise, Wuhan 430033, China
Abstract: Static stiffness as one of key parameter to evaluate the bearing capacity of rubber absorber, is the principal evaluating index while design and produce. In order to analyze the whole static stiffness of rubber absorber, firstly, static stiffness model was calculated based on the stiffness theory of rubber. Then, software of finite element analysis of Abaqus is used to calculate the static stiffness model. The calculate results shows that the difference between theoretical calculation result and finite analysis result is not great, which indicate that the static stiffness model is reasonable. Finally, constraint condition under cabin environment is established, compact design of rubber absorber which based on the static stiffness model and constraint condition has been finished.
Key words: rubber absorber     static stiffness     finite element analysis     compact design
0 引　言

1 静刚度模型

 图 1 橡胶减振器结构示意图 Fig. 1 The structure of rubber absorber

 $K = \frac{A}{H}{m_z}E\text{。}$

 ${K_T} = \frac{S}{L}{m_x}G\text{。}$

 ${K_\alpha } = \frac{{{A_L}{m_z}}}{H}E\text{，}$

 ${K_\beta } = \frac{{{A_L}{m_x}}}{H}G\text{，}$

 ${K_z} = 2{K_\alpha }\left( {\cos {\phi ^2} + \frac{1}{k}\sin {\phi ^2}} \right)\text{，}$

2 静刚度仿真 2.1 材料本构模型及参数

 $W\left( {{I_1},{I_2}} \right) = \sum\limits_{i,j = 0}^n {{C_{ij}}} {\left( {{I_1} - 3} \right)^i}{\left( {{I_2} - 3} \right)^j} + \sum\limits_{i = 1}^n {\frac{1}{{{D_i}}}{{\left( {J - 1} \right)}^{2i}}} \text{。}\!\!\!$

 $W = {C_{10}}\left( {{I_1} - 3} \right) + {C_{01}}\left( {{I_2} - 3} \right) + \frac{1}{{{D_1}}}{\left( {J - 1} \right)^2}\text{，}$

 \begin{aligned}& G = 2({C_{01}} + {C_{10}}),\;K = \frac{2}{{{D_1}}}\text{，}\\& E = \frac{{9KG}}{{3K + G}},\;\nu = \frac{{3K - 2G}}{{6K + 2G}}\text{。}\end{aligned}

2.2 不同载荷下位移仿真计算

 图 2 橡胶减振器有限元模型 Fig. 2 The finite elements model of rubber absorber

 图 3 变载下橡胶减振器垂向位移 Fig. 3 The vertical displacement under variable load

 图 4 11 kN下橡胶元件平均应力云图 Fig. 4 The von Mises of rubber under 11 kN

2.3 静刚度仿真计算

 图 5 2 kN下橡胶减振器的垂向位移 Fig. 5 The vertical displacement under 2 kN

 图 6 10 kN下橡胶减振器的垂向位移 Fig. 6 The vertical displacement under 10 kN
3 结构尺寸设计

 图 7 静刚度随橡胶元件角度Φ变化 Fig. 7 The value of static stiffness with variable Φ

 图 8 刚度随橡胶块厚度H变化 Fig. 8 The value of static stiffness with variable H

 图 9 橡胶减振器垂向轮廓图 Fig. 9 The vertical sketch of rubber absorber

 \begin{aligned}& {\frac{s}{{4H}} \leqslant \cos \phi \leqslant \frac{s}{{2H}}}\text{，}\end{aligned}
 \begin{aligned}{K_z} = 2{K_\alpha }\left( {\cos {\phi ^2} + \frac{1}{k}\sin {\phi ^2}} \right) = 4000\text{。}\end{aligned}

 图 10 约束条件下H与Φ关系 Fig. 10 The relation curve of H and Φ under constraint condition

 $H = - 32.7\phi + 45.6\;\text{，}\;{\text{其中}}\phi \in \left( {\frac{\pi }{5},\frac{{2\pi }}{7}} \right)\text{。}$

4 结　语

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