Track–Bridge Longitudinal Dynamic Interaction during High-Speed Train Braking Process
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摘要:
为研究高速列车制动动态过程对简支梁桥墩墩顶纵向力的影响规律，首先，采用多体系统动力学仿真方法计算获得高速列车轨面制动力时程曲线，对WJ-8型小阻力扣件进行纵向阻力试验，揭示加载频率和竖向荷载对扣件纵向阻力特性的影响规律；然后，将车轮竖向力和纵向力作为移动集中荷载作用于钢轨上，考虑不同扣件所分担的不同程度动态竖向力及对应的随竖向力而变化的扣件纵向阻力，建立了高速铁路多跨简支梁梁轨纵向相互作用有限元模型；最后，采用动力时程方法分析了不同制动停车位置和不同跨数对梁轨动力响应的影响，并与静力计算结果进行比较. 结果表明：扣件纵向阻力受加载频率影响不大但对其承受的竖向力敏感；制动停车位在最后一跨桥台位置时，钢轨纵向力及墩台顶纵向力达到最大；随着跨数增加，钢轨纵向力及墩台顶纵向力均增加，但在8跨之后几乎不再变化；静力分析和动力分析所得钢轨纵向应力和位移最大量值存在差异，对应的动力放大系数约为1.05；受列车纵向制动力最大的桥墩的动力放大系数约为1.07，而受力较小桥墩的动力放大系数达到了1.93.
Abstract:To investigate the influence of the dynamic braking process of high-speed trains on the longitudinal force at the pier tops of simply supported beam bridges, the rail-level braking force time-history curve was first calculated and obtained via multibody system dynamics simulation. Longitudinal resistance tests were then conducted on WJ-8 type low-resistance fasteners to reveal the law governing the influence of loading frequency and vertical load on the longitudinal resistance properties of the fasteners. Finally, a finite element model for longitudinal track–bridge interaction in multi-span simply-supported girder bridges was established. In this model, the wheel’s vertical and longitudinal forces were applied as moving concentrated loads on the rail, taking into account the uneven distribution of dynamic vertical force among the fasteners and their corresponding vertical-load-dependent longitudinal resistances. The influence of braking stop position and number of spans on the dynamic response of the track–bridge system was analyzed using the dynamic time-history method, and the results were compared with those from static analysis. The findings indicate that the longitudinal resistance of the fasteners is not significantly influenced by the loading frequency but is sensitive to the vertical load they carry. The longitudinal forces in the rail and at the pier tops are maximized when the train stops braking at the abutment of the final span. While these forces increase with the number of spans, they stabilize beyond eight spans. A discrepancy is observed between the dynamic and static analysis results for the maximum rail stress and displacement, yielding a dynamic amplification factor of approximately 1.05. Furthermore, the dynamic amplification factor is about 1.07 for the pier experiencing the greatest braking force, but can reach up to 1.93 for piers subjected to smaller forces.
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图 1 紧急制动工况下列车制动力时程曲线
Figure 1. Time-history curve of train braking force under emergency braking condition
图 2 扣件纵向阻力试验装置
1.竖向千斤顶；2.纵向作动器；3.分配横梁；4.力传感器；5.位移传感器；6.钢轨及扣件.
Figure 2. Testing apparatus for longitudinal resistance of fasteners
图 4 不同纵向加载频率下WJ-8型扣件纵向阻力（竖向无载）
Figure 4. Longitudinal resistance of WJ-8 fastener under different longitudinal loading frequencies （with no vertical load）
图 5 WJ-8型扣件动刚度随纵向加载频率的变化（竖向有载）
Figure 5. Dynamic stiffness of WJ-8 fasteners as a function of longitudinal loading frequency （with vertical load）
图 6 扣件纵向阻力特性随竖向荷载的变化
Figure 6. Longitudinal resistance properties of fasteners as a function of vertical load
图 7 考虑列车行驶过程中扣件实际阻力变化的线桥相互作用模型
1. 钢轨；2. 桥梁；3. 模拟竖向无载时扣件纵向阻力的杆单元；4. 模拟竖向有载时扣件纵向阻力的杆单元；5. 桥梁中性轴；A. 路基.
Figure 7. Track–bridge interaction model incorporating variation of actual fastener resistance during train movement
图 8 制动停车位置对最大钢轨纵向应力的影响
Figure 8. Influence of braking stop position on maximum longitudinal rail stress
图 9 不同制动停车位置工况下钢轨纵向应力极值分布
Figure 9. Distribution of extreme values of rail’s longitudinal stress under different braking stop position scenarios
图 10 不同制动停车位置工况下各墩台顶纵向力最大值
Figure 10. Maximum longitudinal forces at top of each pier under different braking stop position scenarios
图 11 制动停车位置对部分桥墩顶部纵向力最大值的影响
Figure 11. Influence of braking stop position on maximum longitudinal force at top of a subset of piers
图 12 桥梁跨数对钢轨最大纵向应力的影响
Figure 12. Influence of bridge span number on maximum longitudinal stress of rail
图 13 不同位置处钢轨纵向应力极值分布
Figure 13. Distribution of extreme values of rail’s longitudinal stress at different locations
图 14 桥梁跨数对部分墩台顶部纵向力最大值的影响
Figure 14. Influence of bridge span number on maximum longitudinal force at top of a subset of piers
图 15 部分桥墩顶部纵向力静、动力时程曲线
Figure 15. Time-history curves of longitudinal static and dynamic force at top of a subset of piers
表 1 制动停车位置工况表
Table 1. Braking stop position scenarios
工况
名称制动停车位置 #1_R 列车车头到达第 1 跨简支梁右端时完成制动停车 #3_R 列车车头到达第 3 跨简支梁右端时完成制动停车 #5_R 列车车头到达第 5 跨简支梁右端时完成制动停车 #8_R 列车车头到达第 8 跨简支梁右端时完成制动停车 #10_R 列车车头到达第 10 跨简支梁右端时完成制动停车 
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表 2 加载侧线路钢轨静、动力计算结果比较
Table 2. Comparison of static and dynamic force calculation results for rail on loading-side track
截面
位置钢轨纵向位移/mm 钢轨纵向应力/MPa 静力 动力 放大系数 静力 动力 放大系数 0 号台 0.35 0.35 1.024 5.99 6.09 1.017 1 号墩 0.65 0.67 1.031 7.60 7.80 1.025 5 号墩 1.11 1.15 1.036 3.95 4.11 1.042 6 号墩 1.09 1.14 1.048 2.96 3.04 1.026 9 号墩 0.68 0.70 1.029 −3.62 −3.67 1.014 10 号台 0.26 0.27 1.016 −5.24 −5.28 1.009
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表 3 桥梁各墩台顶纵向力静、动力计算结果比较
Table 3. Comparison of calculation results of longitudinal static and dynamic force at top of each pier
kN 截面位置 桥梁各墩台顶纵向力 放大系数 静力 动力 0 号台 163.69 169.64 1.036 1 号墩 44.39 46.69 1.052 2 号墩 54.53 56.83 1.042 3 号墩 61.85 65.55 1.060 4 号墩 66.36 69.99 1.055 5 号墩 67.55 72.26 1.070 6 号墩 65.64 70.32 1.071 7 号墩 57.88 61.18 1.057 8 号墩 37.20 56.66 1.523 9 号墩 24.12 46.63 1.933
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