Study on mechanical behavior of unsupported sections of ballast track based on wheel-rail dynamics model
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摘要: 为研究有砟线路轨枕暗坑空吊病害激励下的轮轨力学行为和钢轨挠曲变形特征，以中国典型有砟线路结构和服役车辆悬挂系统参数构建轮轨动力学仿真模型，细化空吊区轨枕与道砟接触状态，数值模拟了车辆以200 km·h-1的运行速度通过1~3根轨枕在对称空吊和非对称空吊工况下的轮轨相互作用行为，分析了空吊区域轮轨垂向力及钢轨挠曲位移最大值、轨道动态不平顺和轮重变化率等参数与空吊轨枕数量、深度之间的映射关系。研究结果表明：轨枕空吊改变了左右股钢轨轨下基础支承刚度，进而引起左右侧钢轨挠曲位移、轮轨垂向力的差异较大，形成动态高低、三角坑、水平等轨道动态不平顺和较大轮重变化率，参数最大值与空吊区轨枕个数、空吊深度、轨枕和道砟接触状态有关，受轨道自身刚度的影响，在空吊量大于1.6 mm时上述参数不再随空吊深度发生变化；非对称轨枕空吊工况下，左右侧轨枕空吊差异主要形成动态水平不平顺，其幅值与减载侧轮重变化率呈现负相关，在相同空吊量下时两者随空吊轨枕根数的增加而增大，在3根轨枕单侧空吊最大轮重变化率约为-0.28；对称空吊工况下，左右侧轨道动态高低不平顺的幅值相当，动态水平不平顺幅值较小，3根轨枕对称空吊时最大轮重变化率约为0.03。本文研究成果可为轨枕空吊区轮轨相互作用、动静态轨道不平顺差异分析、初期空吊病害特征辨识和预警技术提供科学参考。Abstract: To study the wheel-rail mechanical behavior and rail deflection deformation characteristics under the excitation of unsupported sleepers of ballast tracks, the wheel-rail dynamics simulation model was constructed based on the typical Chinese ballast track structure and the suspension system parameters of in-service vehicles. The contact state between the sleepers and the ballast in the unsupported area was refined. The wheel-rail interaction behaviors of the vehicle passing through 1-3 sleepers at a running speed of 200 km·h-1 under symmetrical and asymmetrical sleepers were numerically simulated. The mapping relationships of the wheel-rail vertical force, the maximum rail deflection displacement, track dynamic irregularities, the change rate of the wheel load, and other parameters in the unsupported area with the number and depth of unsupported sleepers were demonstrated. Research results show that the unsupported sleepers change the supporting stiffness of the foundation under the left and right rails, thereby causing significant differences in the deflection displacements of the left and right rails and the vertical forces of the wheel-rail and resulting in dynamic irregularities of the track such as dynamic height, triangular pits, and horizontal irregularities, as well as a large rate of change in wheel load. The maximums of the above parameters are related to the depth and the number of unsupported sleepers and the contact state between the unsupported sleepers and ballast. Due to the stiffness of the track itself, the above parameters no longer change when the number of unsupported sleepers is greater than 1.6 mm. Under the cases of asymmetrical unsupported sleepers, the difference in the unsupported sleepers of the left and right rails mainly forms dynamic horizontal irregularities, and its amplitude is negatively correlated with the rate of change of the wheel load on the unloaded side. At the same number of unsupported sleepers, they both increase with the number of the unsupported sleepers, and the maximum change rate of wheel load is about -0.28 under the case of one-side three unsupported sleepers. Under the cases of symmetrical unsupported sleepers, the amplitudes of the dynamic height irregularities of the left and right tracks are comparable, while the amplitudes of the dynamic horizontal irregularities are relatively small. When there are symmetrical unsupported sleepers, the maximum change rate of wheel load is approximately 0.03. The research results of this paper can provide scientific references for the wheel-rail interaction in the unsupported sleeper area, the analysis of the differences in the dynamic and static track irregularities, the identification of the characteristics of initial unsupported sleepers, and early warning technologies.
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图 1 轮轨动力学模型与空吊轨枕示意
Figure 1. Wheel-rail dynamics model and schematic of unsupported sleeper
图 4 道砟与轨枕中部支承状态演化过程
Figure 4. Evolution process of support state between ballast and middle of sleeper
图 5 道砟与轨枕间支承作用的力学特性
Figure 5. Mechanical characteristics of support between ballast and sleeper
图 7 钢轨挠曲位移仿真计算结果与解析解对比曲线
Figure 7. Comparisons curves between simulation calculation results and analytical solutions of rail deflection displacement
图 8 轮轨垂向力及钢轨最大挠曲位移波形
Figure 8. Waveforms of wheel-rail vertical force and maximum rail deflection displacement
图 9 200 km·h-1时不同空吊状态下轮轨垂向力及最大挠曲位移曲线
Figure 9. Wheel-rail vertical forces and maximum deflection displacements under unsupported sleeper cases at 200 km·h-1
图 10 200 km·h-1时不同空吊工况下轮重变化率及动态高低不平顺曲线
Figure 10. Change rates of wheel load and dynamical height irregularity under unsupported sleeper cases at 200 km·h-1
图 11 单侧空吊时轮轨垂向力和钢轨挠曲位移波形(d1=1.0 mm)
Figure 11. Waveforms of wheel-rail vertical forces and rail deflection displacements under one-sided unsupported sleeper cases (d1=1.0 mm)
图 12 单侧空吊时轨道动态不平顺及轮重变化率波形(d1=1.0 mm)
Figure 12. Waveforms of track dynamic irregularity and change rate of wheel load under one-sided unsupported sleeper cases (d1=1.0 mm)
图 13 单侧空吊时各参数随空吊量变化曲线
Figure 13. Curves of variation of parameters with depth of unsupported sleepers under one-sided unsupported sleeper cases
图 14 不同空吊量下道砟等效支承弹簧应力波形
Figure 14. Spring stress waveforms of equivalent support of ballast under different depth of unsupported sleepers
图 15 非对称空吊下钢轨挠曲位移及轮轨垂向力(d2=1.0 mm)
Figure 15. Rail deflection displacement and wheel-rail vertical force under asymmetrical unsupported sleeper cases (d2=1.0 mm)
图 16 非对称空吊时各参数随空吊量变化曲线
Figure 16. Variation curves of parameters with depth of unsupported sleepers under asymmetrical unsupported sleeper cases
图 17 轨枕对称空吊时各参数随空吊量变化曲线
Figure 17. Variation curves of parameters with depth of unsupported sleepers under symmetrical unsupported sleeper cases
图 18 某有砟线路轨枕空吊区轮轨垂向力及轮重变化率
Figure 18. Wheel-rail vertical forces and change rates of wheel load in unsupported sleeper area on a ballast track
表 1 轮轨动力学模型主要参数
Table 1. Parameters of wheel-rail dynamics model
参数名称 量值 轮轨材料 泊松比 0.3 密度/(mg·mm-3) 7.8 弹性模量/GPa 210 切线模量/GPa 21 屈服强度/MPa 542 混凝土轨枕 泊松比 0.22 密度/(mg·mm-3) 2.6 弹性模量/GPa 35 静载荷/kN 70.3 轮轨间摩擦因数 0.3 车轮滚动圆半径/mm 430 轨枕间距/mm 650 一系悬挂弹簧(垂向) 刚度/(kN·mm-1) 1.03 阻尼/(N·s·mm-1) 20 一系横向悬挂 刚度/(kN·mm-1) 5.5 车体和构架等效的质点块质量/t 23.2 扣件支承弹簧 刚度/(kN·mm-1) 22 阻尼/(N·s·mm-1) 40 道砟等效弹簧 刚度/(kN·mm-1) 75 阻尼/(N·s·mm-1) 80 每米钢轨质量/kg 60.43 轮对空心轴半径/mm 30 同一转向架轴距/m 2.5 
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表 2 单侧空吊时各物理参数最值(d2=0)
Table 2. Maximum values of physical parameters under one-sided unsupported sleeper cases (d2=0)
d1/mm 钢轨挠曲位移最大值/mm 轮轨垂向力最值/kN 轨道动态不平顺幅值/mm 轮重变化率 左股 右股 左侧 右侧 左高低 右高低 水平 三角坑 左侧 右侧 1根轨枕 0.1 0.71 0.71 69.05 71.84 0.01 0.01 0.00 0.01 -0.02 0.02 0.6 0.78 0.76 64.92 76.71 0.08 0.06 0.02 0.08 -0.08 0.09 1.0 0.81 0.78 62.76 79.87 0.11 0.08 0.03 0.12 -0.11 0.12 2.0 0.82 0.78 62.44 80.07 0.12 0.08 0.04 0.12 -0.13 0.14 2根轨枕 0.1 0.72 0.72 68.30 72.45 0.02 0.02 0.01 0.02 -0.03 0.03 0.6 0.83 0.80 60.45 80.46 0.13 0.10 0.04 0.14 -0.14 0.14 1.0 0.89 0.83 56.18 84.41 0.19 0.13 0.06 0.19 -0.20 0.20 2.0 0.90 0.84 55.81 85.51 0.20 0.14 0.06 0.21 -0.21 0.22 3根轨枕 0.1 0.73 0.72 67.73 73.04 0.03 0.02 0.01 0.03 -0.04 0.04 0.6 0.87 0.82 57.52 83.63 0.17 0.12 0.05 0.17 -0.18 0.19 1.0 0.93 0.86 52.09 88.29 0.23 0.16 0.07 0.24 -0.26 0.26 2.0 0.96 0.88 50.54 89.53 0.26 0.18 0.08 0.26 -0.28 0.27
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表 3 非对称空吊工况下各参数最值(d2=1.0 mm)
Table 3. Maximum values of parameters under asymmetrical unsupported sleeper cases (d2=1.0 mm)
d1/mm 钢轨位移/mm 轮轨垂向力/kN 轨道动态不平顺/mm 轮重变化率 左股 右股 左侧 右侧 左高低 右高低 水平 三角坑 左侧 右侧 1根轨枕 0.1 0.80 0.83 78.67 63.72 0.10 0.13 -0.03 0.13 0.12 -0.09 0.6 0.87 0.88 74.31 68.04 0.17 0.18 -0.01 0.18 0.06 -0.03 1.2 0.92 0.92 68.77 73.43 0.22 0.22 0.00 0.23 -0.02 0.04 2.0 0.92 0.91 68.63 73.54 0.22 0.22 0.01 0.23 -0.02 0.05 2根轨枕 0.1 0.86 0.91 83.00 57.84 0.16 0.21 -0.05 0.21 0.18 -0.18 0.6 0.98 1.00 75.79 65.90 0.28 0.30 -0.02 0.31 0.08 -0.06 1.2 1.07 1.07 68.76 73.29 0.37 0.37 0.01 0.38 -0.02 0.04 2.0 1.09 1.08 67.84 74.48 0.39 0.38 0.01 0.40 -0.03 0.06 3根轨枕 0.1 0.89 0.96 86.34 54.11 0.19 0.26 -0.06 0.26 0.23 -0.23 0.6 1.05 1.07 76.99 63.97 0.34 0.37 -0.02 0.38 0.10 -0.09 1.2 1.16 1.15 67.72 73.78 0.46 0.45 0.01 0.48 -0.04 0.05 2.0 1.21 1.19 65.87 75.52 0.51 0.49 0.02 0.52 -0.06 0.07
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表 4 对称空吊工况下各参数最值(d1=d2)
Table 4. Maximum values of parameters under symmetrical unsupported sleeper cases (d1=d2)
d1/mm 钢轨位移/mm 轮轨垂向力/kN 轨道动态不平顺/mm 轮重变化率 左股 右股 最小值 最大值 左高低 右高低 水平 三角坑 减载 增载 1根轨枕 0.1 0.72 0.72 69.69 70.69 0.02 0.02 0.00 0.03 -0.01 0.01 1.0 0.91 0.91 69.20 72.38 0.21 0.21 0.00 0.22 -0.02 0.03 2.0 0.93 0.93 67.57 72.77 0.23 0.23 0.00 0.24 -0.04 0.04 2根轨枕 0.1 0.74 0.74 69.68 70.67 0.04 0.04 0.00 0.04 -0.01 0.01 1.0 1.05 1.05 68.66 71.56 0.35 0.35 0.00 0.36 -0.02 0.02 2.0 1.14 1.14 68.26 72.16 0.44 0.44 0.00 0.45 -0.03 0.03 3根轨枕 0.1 0.75 0.75 69.68 70.66 0.05 0.05 0.00 0.05 -0.01 0.01 1.0 1.13 1.13 68.91 71.44 0.43 0.43 0.00 0.45 -0.02 0.02 2.0 1.29 1.29 67.73 71.56 0.59 0.59 0.00 0.61 -0.03 0.02
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