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摘要: 为了对地铁车辆的运行性能实现更准确的评估和更有效的优化，借助有限元理论和子结构理论建立了车体和转向架构架等关键零部件的柔性动力学模型；基于天棚半主动控制算法和柔性多体动力学理论，建立了考虑半主动控制悬挂的地铁车辆刚柔耦合动力学模型；考虑轨道随机不平顺的影响，研究了半主动控制悬挂以及结构柔性对地铁车辆运行稳定性和乘坐舒适性的影响。研究结果表明：相对于传统的悬挂装置，天棚半主动控制极大降低了车辆的振动加速度，并使其变化趋势更加平缓，对车辆的低频振动有明显的抑制作用；采用本文的研究参数，天棚半主动控制在直线段可使车辆的垂向Sperling指标和垂向振动加速度均方根(RMS)分别降低26.8%和7.5%，使车体横向Sperling指标和横向振动加速度RMS分别降低8.8%和4.9%，而在曲线段，天棚半主动控制可使车辆垂向Sperling指标和垂向振动加速度RMS分别降低25.1%和5.7%，使横向Sperling指标和横向振动加速度RMS分别降低15.6%和8.3%，车辆的乘坐舒适性和运行稳定性大幅提升；考虑结构柔性时，车辆的垂向Sperling指标和垂向振动加速度RMS相比于未考虑结构柔性时分别增大了4.3%和6.8%，横向Sperling指标和横向振动加速度RMS分别增大了3.0%和3.4%。可见，车体和构架的结构柔性对车辆的动态特性有较大影响，在对车辆运行稳定性和乘坐舒适性进行计算和评估时不可忽略。Abstract: To realize more accurate evaluation and more effective optimization of the running performance of metro vehicles, based on the finite element theory and substructure theory, the flexible dynamics models of critical parts, such as car body and bogie frame, were established. Based on the algorithm of semi-active skyhook control and the theory of flexible multi-body dynamics, the rigid-flexible coupling dynamics model of a metro vehicle was established considering a semi-active control suspension.The effect of random track irregularity was considered, and the influences of semi-active control suspension and structural flexibility on the running stability and ride comfort of metro vehicles were investigated. Analysis results show that compared to the traditional suspension device, the semi-active skyhook control can significantly reduce the vibration acceleration of the vehicle and decrease its variation trend, suppressing the low-frequency vibration of the vehicle obviously. Based on the parameters adopted in this study, the semi-active skyhook control decreases the vertical Sperling index and root mean square (RMS) of vertical vibration acceleration on the straight segment by 26.8% and 7.5%, respectively, and 8.8% and 4.9% for lateral vibration acceleation, respectively. The semi-active skyhook control decreases the values of vertical vibration acceleration on the curve segment by 25.1% and 5.7%, respectively, and 15.6% and 8.3% for lateral vibration acceleration, respectively. Thus, the ride comfort and running stability of the vehicle improve significantly. Under considering the structural flexibility, the vertical Sperling index and RMS of vertical vibration acceleration of the vehicle increase by 4.3% and 6.8%, respectively, compared to those under no considering the structural flexibility, and 3.0% and 3.4% for lateral vibration acceleration, respectively. Thus, the structural flexibilities of the car body and frame significantly influence the dynamic characteristics of the vehicle and should be considered in calculating and evaluating the vehicle running stability and ride comfort. 5 tabs, 21 figs, 29 refs.
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图 5 直线段垂向振动加速度功率谱
Figure 5. Power spectra of vertical vibration accelerations on straight segment
图 6 直线段横向振动加速度功率谱
Figure 6. Power spectra of lateral vibration accelerations on straight segment
图 7 直线段垂向Sperling指标和RMS曲线
Figure 7. Curves of vertical Sperling indexes and RMSs on straight segment
图 8 直线段横向Sperling指标和RMS曲线
Figure 8. Curves of lateral Sperling indexes and RMSs on straight segment
图 10 曲线段车体垂向振动加速度功率谱
Figure 10. Power spectra of vertical vibration accelerations on curve segment
图 11 曲线段车体横向振动加速度功率谱
Figure 11. Power spectra of lateral vibration acceleration on curve segment
图 12 曲线段垂向Sperling指标和RMS曲线
Figure 12. Curves of vertical Sperling indexes and RMSs on curve segment
图 13 曲线段横向Sperling指标和RMS曲线
Figure 13. Curves of lateral Sperling indexes and RMSs on curve segment
图 14 悬挂对直线段振动加速度的影响
Figure 14. Influences of suspension on vibration accelerations on straight segment
图 15 不同悬挂下直线段垂向振动加速度功率谱
Figure 15. Power spectra of vertical vibration accelerations on straight segment with different suspensions
图 16 不同悬挂下直线段横向振动加速度功率谱
Figure 16. Power spectra of lateral vibration accelerations on straight segment with different suspensions
图 17 不同悬挂下直线段Sperling指标和RMS曲线
Figure 17. Curves of Sperling indexes and RMSs on straight segment with different suspensions
图 18 悬挂对曲线段振动加速度的影响
Figure 18. Influences of suspensions on vibration accelerations on straight segment
图 19 不同悬挂下曲线段垂向振动加速度功率谱
Figure 19. Power spectra of vertical vibration accelerations on curve segment with different suspensions
图 20 不同悬挂下曲线段横向振动加速度功率谱
Figure 20. Power spectra of lateral vibration accelerations on curve segment with different suspensions
图 21 不同悬挂下曲线段Sperling指标和RMS曲线
Figure 21. Curves of Sperling indexes and RMSs on curve segment with different suspensions
表 1 车体振型与频率
Table 1. Vibration modes and frequencies of car body
阶数 频率/Hz 描述 1 4.96 侧墙一阶弯曲 2 6.19 车顶一阶弯曲 3 7.37 菱形变形 4 8.69 一阶垂向弯曲 5 13.27 侧墙二阶弯曲 6 14.16 车顶二阶弯曲 7 14.34 车体一阶扭转 8 17.06 端墙内凹 
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表 2 计算工况
Table 2. Calculation conditions
工况 线路 模型 悬挂 直线 曲线 刚体 刚柔耦合 被动 半主动 1 √ √ √ 2 √ √ √ 3 √ √ √ 4 √ √ √ 5 √ √ √ 6 √ √ √
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表 3 轨道参数
Table 3. Parameters of track
参数 数值 钢轨横截面积/m2 7.745×10-3 钢轨弹性模量/MPa 2.1×10-5 钢轨惯性力矩/m4 3.214×10-5 扣件间距/m 0.6 扣件刚度/(MN·m-1) 30 扣件阻尼/(kN·s·m-1) 10 轨道类型 整体道床轨道 曲线半径/m 800 曲线段长度/m 100 过渡曲线长度/m 50 超高/m 0.095
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表 4 地铁车辆动力学参数
Table 4. Dynamics parameters of metro vehicle
参数 数值 轮对质量/t 1.878 构架质量/t 4.007 车体质量/t 35.443 轮对绕x、y、z轴的惯量/(t·m2) 1.055、0.139、1.055 构架绕x、y、z轴的惯量/(t·m2) 1.194、0.876、2.099 车体绕x、y、z轴的惯量/(t·m2) 50.929、1 410.960、1 401.490 一系纵、横、垂向刚度/(MN·m-1) 7.0、4.0、0.9 一系纵、横、垂向阻尼/(kN·s·m-1) 10、10、10 二系纵、横、垂向刚度/(kN·m-1) 220.1、220.1、341.9 二系纵、横、垂向阻尼/(kN·s·m-1) 60、60、80 车轮名义滚动圆半径/m 0.42 车轮踏面型式 LM踏面
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表 5 天棚控制参数
Table 5. Parameters of skyhook control
kN·s·m-1 参数 横向 垂向 Cmin 20.58 28.00 Cmax 102.90 140.00 Cs 58.80 80.00
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