﻿ 一种用于动力传动系统的橡胶隔振器优化设计研究
 舰船科学技术  2017, Vol. 39 Issue (8): 91-95 PDF

Research on optimization design of rubber isolator for the use of propulsion system
LIU Wen-xi, ZHOU Qi-dou
Department of Naval Achitecture Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Design a kind of rubber isolator to reduce the force which is from the power transmission system acting on the ship. Analyze the system working principle, and build the dynamics analysis model to obtain the initial parameters of the power transmission system. The characteristics of the neoprene are described by the Mooney-Rivlin model, and the coefficients C01 and C10 of the model are obtained by fitting the experimetal data of stress and strain. On the basis of practical working status of the power transmission system, the fundmental configuration and sizes are decided firstly, and then design the optimum arithmetic, in which the variables includes the bolt preload , the sizes of the rubber elememt, the space from the frontal plate to the back plate and the maximum VON MISES stress for rubber and metal, and the stiffness of the isolator is treated as target value, and the nonlinear finite element method is used for numerical simulation. As a result, the isolator is made, and it has the optimum configuration and is fit for the demand of use and reducing vibration.
Key words: rubber isolator     optimum arithmetic     Mooney-Rivlin model     nonlinear     finite element method
0 引　言

1）通常橡胶金属减振器要求橡胶和金属粘接在一起，橡胶件与金属件除破坏外不会脱开。而文中设计的隔振器橡胶元件结构形式统一，构型简单，与其他构件，如连接金属板、弹性防松圈及其他橡胶元件等没有粘连在一起，因此，拆卸方便、适应性强。

2）安装时，通过螺栓调节施加到隔振系统的预紧力，就可以保证在工作时隔振系统各个组件之间不脱开、不分离。

3）材料和结构的复杂性决定了只能通过实验确定大多数隔振器的性能[48]，而文中设计的隔振器是由橡胶件和金属件构成，因此，能够采用数值计算的方式确定其性能，效率高，成本低。

1 隔振系统简化模型及减振理论

 图 1 船用旋转设备工作过程示意图 Fig. 1 Schematic diagram of rotating equipment working process

 图 2 脉动力f的传递路径 Fig. 2 Transmission path of fluctuating force f

 图 3 整体隔振效果图 Fig. 3 Overall effect of isolating system figure

 图 4 脉动力f的传递路径 Fig. 4 Transmission path of fluctuating force f

 图 5 两自由度集中质量隔振系统模型 Fig. 5 Model of two freedom lumped mass isolating vibration system

 $\left\{ {\begin{array}{*{20}{l}}\!\!\! {{m_1}{{\ddot y}_1} + {c_1}{{\dot y}_1} - {c_1}{{\dot y}_2} + {k_1}{y_1} - {k_1}{y_2} = {f_0}\sin (\omega t)}\text{，}\\\!\!\! {{m_2}{{\ddot y}_2} - {c_1}{{\dot y}_1} + ({c_1} + {c_2}){{\dot y}_2} - {k_1}{y_1} + ({k_1} + {k_2}){y_2} = 0}\text{。}\end{array}} \right.$ (1)

$\omega _1^2 = \displaystyle\frac{{{k_1}}}{{{m_1}}},\omega _2^2 = \frac{{{k_2}}}{{{m_2}}}$ ${\omega _{{n}}}$ 为系统固有频率，当粘性阻尼c1c2等于0时，解方程（1），则 ${\omega _{{n}}}$ 等于

 $\omega _n^2 \!=\! \frac{{\omega _1^2}}{2}\left[ {(1 \!+\! \frac{{{m_1}}}{{{m_2}}} \!+\! \frac{{\omega _2^2}}{{\omega _1^2}}) \! \pm \! \sqrt {{{(1 \!+\! \frac{{{m_1}}}{{{m_2}}}\! +\! \frac{{\omega _2^2}}{{\omega _1^2}})}^2} \!-\! 4\frac{{\omega _2^2}}{{\omega _1^2}}} } \right]\text{。}$ (2)

${f_{{\rm{T}}0}}\sin (\omega t)$ 表示从传力结构到壳体的传递力， ${f_{{{T}}0}}$ 为幅值，为计算方便，用复数表示式（1）中的变量，如方程（3）所示。

 $\left\{ \begin{array}{l}\!\!\!\! {f_0}\sin (\omega t) = {\mathop{\rm Re}\nolimits} (f(\omega ).{e^{{\rm{j}}\omega t}})\text{，} \\\!\!\!\! {y_1}(t) = {\mathop{\rm Re}\nolimits} ({Y_1}(\omega ).{e^{{\rm{j}}\omega t}}) = {\mathop{\rm Re}\nolimits} ({H_1}(\omega ) \cdot f(\omega ).{e^{{\rm{j}}\omega t}})\text{，}\\\!\!\!\! {y_2}(t) = {\mathop{\rm Re}\nolimits} ({Y_2}(\omega ).{e^{{\rm{j}}\omega t}}) = {\mathop{\rm Re}\nolimits} ({H_2}(\omega ) \cdot f(\omega ).{e^{{\rm{j}}\omega t}})\text{，}\\\!\!\!\! {f_{{{T}}0}}\sin (\omega t) \!=\! {\mathop{\rm Re}\nolimits} ({f_T}(\omega ).{e^{{\rm{j}}\omega t}}) \!=\! {\mathop{\rm Re}\nolimits} ({H_3}(\omega ) \cdot f(\omega ).{e^{{\rm{j}}\omega t}})\text{。}\!\!\!\!\!\!\!\!\!\!\!\end{array} \right.$ (3)

 ${Y_2} = {f_0} \cdot \left| {{H_2}(\omega )} \right|\text{，}$ (4)
 ${T_A} = 20\log (\frac{{{f_{T0}}}}{{{f_0}}}) = 20\log (\left| {{H_3}(\omega )} \right|)\text{。}$ (5)
2 橡胶材料模型常数的试验确定

 $W\left( {{I_1},{I_2}} \right) = {C_{10}}\left( {{I_1} - 3} \right) + {C_{01}}\left( {{I_2} - 3} \right)\text{，}$ (6)

 $\sigma = - pI + 2\left( {\frac{{\partial W}}{{\partial {I_1}}} + {I_1}\frac{{\partial W}}{{\partial {I_2}}}} \right)B - 2\frac{{\partial W}}{{\partial {I_2}}}{B^2}\text{，}$ (7)

 ${I_1} = tr\left( B \right),{I_2} = \left[ {{I_1}^2 - tr\left( {{B^2}} \right)} \right]/2,{I_3} = \det \left( B \right)\text{。}$ (8)

3 隔振器优化设计 3.1 初始参数和基本构型

 图 6 隔振器的初始结构形式 Fig. 6 Isolator initial configuration

 ${k_1} \leqslant 3.32 \times {10^8}\;{\rm{N/m}}{\text{。}}$

 ${k_2} \leqslant 1.81 \times {10^6}\;{\rm{N/m,}}$

 ${k_s} = {k_2}/1.5 = 1.20 \times {10^6}\;{\rm{N/m}}\text{。}$
3.2 基于非线性有限元法隔振器构型优化

1）分3个阶段：第1阶段是螺栓预紧力由0逐步增大到最大的系统变形计算过程；第2阶段在螺栓预紧力最大的状态下，将静载荷由0逐步增大到最大，施加到传力结构上；第3阶段计算隔振器水平方向静刚度；

2）在螺栓预紧状态下，计算隔振系统在水平方向的一阶振动固有频率；

3）根据一阶振动固有频率，计算隔振器水平方向动刚度值。

 图 7 橡胶减振元件外形 Fig. 7 Configuration of the rubber elememt

 图 8 隔振器的整体装配图 Fig. 8 Assembling drawing of the isolator

 图 9 隔振器的基本尺寸 Fig. 9 Detail sizes of the isolator

 ${k_s} = 2\;210.0/1.92 = 1.151 \times {10^6}\;{\rm{N/m}}{\text{。}}$
 图 10 传力结构在水平方向的相对位移 Fig. 10 Comparative displacement of the transmitting force structure in the horizontal direction

 图 11 隔振器水平方向一阶振型 Fig. 11 First horizontal vibration model

 ${k_2} = ({m_1} + {m_2}){(2\pi {f_n})^2}\text{。}$ (9)

 图 12 隔振器的压缩变形 Fig. 12 Horizontal compression deformation of rubber isolator

 图 13 隔振器的应力云图 Fig. 13 MISES stress of rubber isolator

 图 14 橡胶减振元件的应力云图 Fig. 14 MISES stress of rubber elemrnts
4 结　语

1）对于类似上述结构形式的橡胶隔振器，文中的设计方法可行，即先采用线性系统设计系统初始参数，然后用非线性数值计算方法对橡胶隔振器进行优化设计，确定最终参数；

2）本文设计的橡胶隔振器满足实际的使用要求，能够正常工作。

3）设计橡胶金属隔振器时，在隔振器的材料和结构不是非常复杂的情况下，采用本文所述的数值仿真的优化设计方法既实用又高效。

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