轨道减振器超弹性本构模型参数优化Parameter Optimization of the Track Damper Superelastic Constitutive Model

DOI: 10.12677/OJTT.2021.101002, PDF, HTML, XML, 下载: 84  浏览: 146

Abstract: A simulated analysis has been carried out on the vertical stiffness of the track damper by 2 groups of the parameters of the Mooney-Rivlin superelastic constitutive model, which are corresponding to the rubber hardness of 70 and 75. The relative errors between the stiffness values of the simulated analysis and the stiffness value of the actual measurement are 9.46% and 14.43% respectively, which shows that the parameters of the constitutive model have a significant influence on the precision of the simulated analysis and the parameter optimization is necessary. By the functional relation established by the least square method between the parameters of the constitutive model and the rubber hardness, 4 levels of C10 and C01 are selected respectively in the hardness range from 70 to 75 to design a 4 levels and 2 factors orthogonal test. By means of the simulated analysis of the vertical stiffness based on the orthogonal test, the optimized parameters are obtained, namely C10 = 0.707, C01 = 0.165. The relative error between the stiffness value of the simulated analysis and the stiffness value of the actual measurement is as low as 1.01%, which means that the precision of the simulated analysis is improved effectively.

1. 引言

2. 轨道减振器结构及工作特性

Figure 1. Diagram of the track damper

3. 轨道减振器垂向静刚度测试

Figure 2. Test equipment of the track damper vertical stiffness

$K=\frac{{F}_{2}-{F}_{1}}{{D}_{2}-{D}_{1}}$ (1)

Table 1. Test results of the track damper vertical stiffness

4. 轨道减振器垂向静刚度仿真计算

4.1. 橡胶Mooney-Rivlin本构模型

$\left\{\begin{array}{l}{I}_{1}={\lambda }_{1}{}^{2}+{\lambda }_{2}{}^{2}+{\lambda }_{3}{}^{2}\hfill \\ {I}_{2}={\lambda }_{1}{}^{2}{\lambda }_{2}{}^{2}+{\lambda }_{2}{}^{2}{\lambda }_{3}{}^{2}+{\lambda }_{3}{}^{2}{\lambda }_{1}{}^{2}\hfill \\ {I}_{3}={\lambda }_{1}{}^{2}{\lambda }_{2}{}^{2}{\lambda }_{3}{}^{2}\hfill \end{array}$ (2)

$W=W\left({I}_{1},{I}_{2},{I}_{3}\right)$ (3)

$W={W}_{d}\left(\stackrel{¯}{{I}_{1}},\stackrel{¯}{{I}_{2}}\right)+{W}_{b}\left(J\right)$ (4)

$J={\lambda }_{1}{\lambda }_{2}{\lambda }_{3}$ (5)

$\left\{\begin{array}{c}\stackrel{¯}{{I}_{1}}={J}^{-2/3}{I}_{1}\\ \stackrel{¯}{{I}_{2}}={J}^{-2/3}{I}_{2}\end{array}$ (6)

$W=\underset{i+j=1}{\overset{N}{\sum }}{C}_{ij}{\left(\stackrel{¯}{{I}_{1}}-3\right)}^{i}{\left(\stackrel{¯}{{I}_{2}}-3\right)}^{j}+\underset{i=1}{\overset{N}{\sum }}\frac{1}{{D}_{i}}{\left(J-1\right)}^{2i}$ (7)

$N=1$，则只有线性部分的应变能被保留下来，即Mooney-Rivlin模型。

$W={C}_{10}\left(\stackrel{¯}{{I}_{1}}-3\right)+{C}_{01}\left(\stackrel{¯}{{I}_{2}}-3\right)+\frac{1}{{D}_{1}}\left(J-1\right)$ (8)

${\lambda }_{3}={\left({\lambda }_{1}{\lambda }_{2}\right)}^{-1}$ (9)

$W={C}_{10}\left(\stackrel{¯}{{I}_{1}}-3\right)+{C}_{01}\left(\stackrel{¯}{{I}_{2}}-3\right)$ (10)

4.2. 垂向静刚度仿真计算

Figure 3. Finite element analysis model

Table 2. Parameters of Mooney-Rivlin rubber constitutive model

Table 3. Simulation results of the track damper vertical stiffness

5. 轨道减振器垂向静刚度仿真计算

5.1. 确定正交试验的因子与水平

Figure 4. Curve of C10-rubber hardness

Figure 5. Curve of C01-rubber hardness

Table 4. Factors and levels of the orthogonal test

5.2. 正交试验

Table 5. Table of the vertical stiffness orthogonal test

6. 总结

1) 本文分别选取了橡胶邵氏硬度为70和75的Mooney-Rivlin橡胶超弹性本构模型参数来进行轨道减振器垂向静刚度有限元计算。但使用这2组本构模型参数所得的结果均与实测垂向静刚度之间存在较大误差，误差分别为9.46%和14.43%。表明Mooney-Rivlin橡胶本构模型参数的选取对于仿真结果的影响较大，需要对参数进行优化。

2) 利用最小二乘法对已有的Mooney-Rivlin橡胶本构模型的2个参数C10C01与橡胶硬度的关系进行了曲线拟合，由得到的函数关系式设计了2因子4水平的正交试验。通过对比16组试验的轨道减振器垂向静刚度仿真结果与实测结果之间的误差，得到了优化后橡胶本构模型参数为C10 = 0.707，C01 = 0.165，其垂向静刚度仿真结果与实测误差仅为1.01%，表明本文提出的方法有效地提高了轨道减振器橡胶元件的有限元仿真精度。

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