Analysis method on time-history characteristics of rail supporting force for mixed passenger and freight railway with ballastless track
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摘要: 采用Tekscan压力测量系统现场测试了遂宁—重庆客货共线无砟轨道钢轨支点压力, 提出了高斯函数型钢轨支点压力时程表达式, 并通过现场实测数据对其进行验证; 根据钢轨支点压力时程表达式, 采用时序式加载法对轨道结构模型施加荷载, 并将其动力响应结果分别与车辆-轨道-路基垂向耦合振动模型的计算结果和现场实测结果进行对比。研究结果表明: 现场实测客货车对钢轨支点的最大压力分别为29.91和82.49 kN, 与中国铁道科学研究院测试结果的相对误差小于20%, 故Tekscan压力测量系统可精确测试钢轨支点压力; 高斯函数拟合所得客货车对钢轨支点压力的时程曲线与实测曲线的相关系数分别为0.962 7和0.966 7, 最大压力与现场实测值的相对差异分别为5.15%和0.46%, 最小压力与现场实测值的相对差异分别为7.23%和24.11%, 故采用高斯函数能较好地模拟客货车对钢轨支点压力的时程曲线, 且货车作用下钢轨支点压力时程的模拟精度略高于客车; 基于时序式加载法的荷载激励-轨道-路基模型计算结果与车辆-轨道-路基垂向耦合振动模型计算结果和现场测试结果相比, 轨道板最大位移相对差异分别为5.41%和2.70%, 底座板最大位移相对差异分别为2.86%和5.71%, 轨道板最大加速度相对差异分别为14.00%和23.20%, 底座板最大加速度相对差异分别为13.61%和8.73%。可见, 基于时序式加载法和高斯函数型钢轨支点压力时程表达式的荷载激励-轨道-路基模型可靠, 该方法无需建立车体模型, 既能保证计算效率, 又具有很高的精度。Abstract: The rail supporting force for mixed passenger and freight railway with ballastless track in the Suining to Chongqing Railway was tested on site by the Tekscan pressure measurement system. A Gaussian function type time-history expression of rail supporting force was proposed and verified by the field test data. According to the time-history expression of rail supporting force, the loads were applied to the track structure model through the sequential loading method, and the dynamic response results were compared with those obtained from the vehicle-track-subgrade vertical coupling vibration model and the field test. Research result shows that the maximum field measured rail supporting forces of passenger and freight train are 29.91 and 82.49 kN, respectively. The relative differences are less than 20% in comparison with the test result obtained by the China Academy of Railway Sciences. Therefore, the Tekscan pressure measurement system can accurately measure the rail supporting force. For the passenger and freight train, the correlation coefficients of rail supporting force time-history curves fitted by the Gaussian function and the field measured curves are 0.962 7 and 0.966 7, respectively. The relative differences between the fitted maximum rail supporting forces and the field measured values are 5.15% and 0.46%, respectively, and the relative differences between the fitted minimum rail supporting forces and the field measured values are 7.23% and 24.11%, respectively. Therefore, the Gaussian function can well simulate the time-history curves of rail supporting force under the actions of passenger and freight trains, and the simulation accuracy to freight train is slightly higher than to passenger train. Compared with the results of vehicle-track-subgrade vertical coupling vibration model and field test, the relative differences of the maximum displacements of track slab obtained from the load excitation-track-subgrade model based on the sequential loading method are 5.41% and 2.70%, respectively, the relative differences of the maximum displacements of base plate are 2.86% and 5.71%, respectively, the relative differences of the maximum acceleration of track slab are 14.00% and 23.20%, respectively, and the relative differences of the maximum accelerations of base plate are 13.61% and 8.73%, respectively. Therefore, the load excitation-track-subgrade model based on the sequential loading method and the Gaussian function type time-history expression of rail supporting force is reliable. This method does not need to establish the car body model, and not only ensure the calculation efficiency, but also have a very high accuracy.
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图 7 现场实测客车对钢轨的支点压力
Figure 7. Field measured rail supporting force imposed by passenger train
图 8 现场实测货车对钢轨的支点压力
Figure 8. Field measured rail supporting force imposed by freight train
图 12 钢轨支点压力的高斯函数拟合曲线与现场实测曲线对比
Figure 12. Comparison of rail supporting force curves between Gaussian function fitting and field test
图 13 钢轨支点压力时程表达式示意
Figure 13. Schematic of time-history expression of rail supporting force
图 14 车辆-轨道-路基垂向耦合振动模型
Figure 14. Vehicle-track-subgrade vertical coupling vibration model
表 1 CRH2动车组计算参数
Table 1. Calculation parameters of CRH2 MU
参数 CRH2型车 车体质量/kg 39 600 转向架质量/kg 3 500 轮对质量/kg 2 000 车体点头惯量/ (kg·m2) 1.94×106 转向架点头惯量/ (kg·m2) 1.75×103 一系悬挂刚度/ (N·m-1) 1.18×106 一系悬挂阻尼/ (N·s·m-1) 1.89×106 二系悬挂刚度/ (N·m-1) 1.96×104 二系悬挂阻尼/ (N·s·m-1) 4.00×104 
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表 2 CRTS Ⅰ型板式无砟轨道结构计算参数
Table 2. Calculation parameters of CRTS Ⅰ ballastless slab track structure
部件 参数 取值 部件 参数 取值 钢轨 每延米质量/kg 60 路基 面刚度/ (MPa·m-1) 76 扣件 阻尼/ (kN·s·m-1) 20 CA砂浆 阻尼/ (kN·s·m-1) 270 动刚度/ (kN·mm-1) 50 弹性模量/MPa 300 间距/m 0.629 厚度/m 0.05 轨道板 弹性模量/MPa 3.65×104 底座板 弹性模量/MPa 3.25×104 长度/m 4.96 宽度/m 3.0 宽度/m 2.40 厚度/m 0.3 厚度/m 0.19 泊松比 0.2
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