Dynamics modelling of positioning rubber joint of a bogie based on physical parameters
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摘要: 针对高速列车转向架悬挂系统中的弹性橡胶件, 开展了基于物理参数的橡胶件非线性动力学建模方法研究; 为准确模拟其非线性刚度与阻尼的硬度相关性、结构尺寸相关性、激励频率相关性和激励位移幅值相关性, 采用有限元软件ABAQUS中的Mooney-Rivlin橡胶本构模型表征橡胶件的刚度与其结构尺寸和胶料硬度之间的相关性, 采用包括分数导数阻尼力元、摩擦力元和弹簧力元的动力学模型表征橡胶件刚度和阻尼的频变、幅变特性, 采用最小二乘法实现基于台架试验的模型参数识别; 对橡胶垫和定位橡胶节点的非线性特性进行仿真和台架试验, 验证了动力学模型的有效性; 在SIMPACK软件中定义自编力元, 进行车辆动力学性能分析, 有限元模型为动力学模型提供了基础的模型参数。分析结果表明: 橡胶垫和定位橡胶节点的刚度与胶料邵氏硬度基本呈正比关系, 硬度80 HA对应的刚度约为60 HA时的2倍; 载荷作用方向的胶料越少其对应方向的刚度越大; 橡胶垫的轴向和径向刚度解耦, 分别受高度和内外径尺寸影响, 橡胶垫轴向刚度随高度的下降率为0.2~0.6 MN·m-1·mm-1; 定位橡胶节点的芯轴尺寸改变引起其轴向和径向刚度同时变化, 定位橡胶节点径向刚度随内径的增长率为3.1~5.2 MN·m-1·mm-1; 采用非线性橡胶件动力学模型的车辆动力学仿真结果与传统等效力元模型结果差异为20%, 说明橡胶垫和定位橡胶节点动态参数的非线性对车辆动力学性能有显著影响。Abstract: Aiming at the elastic rubber components in the suspension system of a high-speed train bogie, the nonlinear dynamics modelling method for the rubber component was studied based on the physical parameters. In order to accurately simulate the correlations between the nonlinear stiffness and the damping hardness, structural dimensions, excitation frequency and excitation displacement amplitude, the Mooney-Rivlin rubber constitutive model in the software ABAQUS was used to characterize the correlation between the rubber component's stiffness and the structural dimensions and rubber hardness. A dynamics model, including a fractional derivative damping force element, a friction force element, and a spring force element, was used to characterize the frequency-dependency and amplitude-dependency of stiffness and damping of a rubber component. The least squares method was used to identify the model parameters based on the lab tests. The nonlinear characteristics of rubber bearing and positioning rubber joint were numerically simulated and tested in the lab to validate the proposed model. The vehicle dynamics performance analysis was performed by using an user-coded force element defined in the software SIMPACK, and the finite element model was used to provide the basic model parameters for the dynamics model. Analysis result shows that the stiffnesses of rubber bearing and positioning rubber joint are basically proportional to the Shore hardness of rubber material, and the stiffness corresponding to the hardness of 80 HA is about twice that at 60 HA. The less the rubber material in the direction of load action, the greater the stiffness in the corresponding direction. The axial and radial stiffnesses of rubber bearing are decoupled, which is affected by the height and the size of inner and outer diameters, respectively, and the decrease rate of the axial stiffness of rubber bearing with the increase of height is 0.2-0.6 MN·m-1·mm-1. Both the axial and radial stiffness of positioning rubber joint varies with the change of mandrel size, and the increase rate of radial stiffness with the increase of inner diameter is 3.1-5.2 MN·m-1·mm-1. The vehicle dynamics simulation results by using the nonlinear rubber component dynamics model are 20% different from the results by using a conventional equivalent force element model, which means the nonlinearities of dynamics parameters of the rubber bearing and positioning rubber joint have severe influence on the vehicle dynamics.
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Key words:
- vehicle engineering /
- vehicle dynamics /
- bogie /
- rubber component /
- dynamic characteristic /
- nonlinear /
- dynamics simulation
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图 2 基于物理参数的橡胶件动力学建模方法
Figure 2. Modelling method of rubber component's dynamics based on physical parameters
图 3 橡胶垫和定位橡胶节点的有限元模型
Figure 3. Finite element models of rubber bearing and positioning rubber joint
图 4 橡胶垫轴向刚度与胶料硬度的相关性
Figure 4. Correlation between axial stiffness of rubber bearing and rubber material hardness
图 5 橡胶垫轴向刚度与结构高度的相关性
Figure 5. Correlation between axial stiffness of rubber bearing and structural height
图 6 定位橡胶节点径向刚度与胶料硬度的相关性
Figure 6. Correlation between radial stiffness of positioning rubber joint and rubber material hardness
图 7 定位橡胶节点径向刚度与内径的相关性
Figure 7. Correlation between radial stiffness of positioning rubber joint and inner diameter
图 8 橡胶件动力学模型输出力组成
Figure 8. Output force components of rubber component's dynamics model
图 10 正弦信号sin(2πt)及其不同阶数的分数导数
Figure 10. Sinewave sin(2πt) and its different orders' fractional derivative
图 13 定位橡胶节点动态参数的仿真与试验结果对比(频率6 Hz)
Figure 13. Comparison of dynamic parameters of positioning rubber joint between simulation and experimental results (at frequency 6 Hz)
图 14 定位橡胶节点动态参数的仿真与试验结果对比(频率12 Hz)
Figure 14. Comparison of dynamic parameters of positioning rubber joint between simulation and experimental results (at frequency 12 Hz)
表 1 橡胶件非线性力元的输入参数
Table 1. Input parameters for nonlinear force element of rubber component
参数 单位 构架上的力元标记点 转臂上的力元标记点 初始载荷(纵向、横向和垂向) N 线性弹簧刚度(纵向、横向和垂向) N·m-1 分数导数阶数(纵向、横向和垂向) 迭代步数 等效阻尼系数(纵向、横向和垂向) N·s·m-1 最大摩擦力(纵向、横向和垂向) N 最大摩擦力之半位移(纵向、横向和垂向) mm 
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表 2 橡胶件非线性力元的输出参数
Table 2. Output parameters for nonlinear force element of rubber component
参数 单位 标记点相对位移(纵向、横向和垂向) m 标记点相对速度(纵向、横向和垂向) m·s-1 弹簧力(纵向、横向和垂向) N 阻尼力(纵向、横向和垂向) N 摩擦力(纵向、横向和垂向) N 总输出力(纵向、横向和垂向) N
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