Calculation method of wheel-rail interaction forces for subway integrated ballast bed during station entry and exit focusing on frequency range of interest in environmental vibration
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摘要:
为准确预测和控制地铁进出站过程引发的环境振动问题，发展了一套适用于地铁进出站加减速过程的高效轮轨相互作用力计算方法。基于移动时域格林函数法，构建了地铁列车匀速运行工况下的轮轨相互作用力计算模型，并将计算结果与频域轮轨力计算法的结果进行了对比验证；进一步考虑轨道参数激励的影响，构建了参数激励的等效粗糙度样本，通过移动粗糙度和格林函数的求解方法，得到了变速运行条件下的轮轨力时程，并对其频谱特性进行分析。研究结果表明：在3~600 Hz，2种方法所得轮轨力频谱基本吻合，动态轮轨力波动范围约为50~90 kN，与轴荷载相比波动幅度达20 kN；参数激励在过枕频率(27.8、55.6 Hz等)处产生显著峰值，等效粗糙度曲线呈跨中余弦分布；所提出的方法能够快速、高效地求解环境振动主要关注频段内地铁进出站全过程的非稳态轮轨中高频相互作用力；在计算性能上，有效规避了构建过长轨道模型以及求解大规模自由度矩阵轮轨力的传统难题；在模型精度方面，考虑了轨道引入的参数激励特性以及轮轨非线性接触，使模型更贴合实际工程情况。本方法为准确预测地铁进出站引起的环境振动提供了可靠的输入，对合建类项目的减振设计与环境评估提供了参考。
Abstract:To accurately predict and control environmental vibrations induced by the subway during station entry and exit, in this paper, an efficient method suitable for the acceleration and deceleration processes of subway station entry and exit for calculating wheel-rail interaction forces throughout the entire process was developed. Based on the moving time-domain Green's function method, a calculation model for wheel-rail interaction forces under the working condition of subway running at a constant speed was established. The calculation results were compared and verified with those from the frequency-domain wheel-rail force calculation method. By considering the influence of track parameter excitation, equivalent roughness samples of parameter excitation were established. Through the solution methods of moving roughness and Green's function, the time history of wheel-rail forces under variable speed operation conditions was obtained, and the spectral characteristics were analyzed. Research results show that within the frequency range of 3 - 600 Hz, the wheel-rail force spectra obtained by the two methods are basically consistent; the fluctuation range of dynamic wheel-rail forces is approximately 50 - 90 kN; the fluctuation amplitude reaches 20 kN compared with the axle load. Parameter excitation generates significant peaks at sleeper-passing frequencies (27.8, 55.6 Hz, etc.), and the equivalent roughness curve exhibits a mid-span cosine distribution. The proposed method can quickly and efficiently solve the non-stationary medium-high frequency wheel-rail interaction forces throughout the entire process of subway station entry and exit within the frequency range of primary interest for environmental vibration. In terms of computational performance, the traditional challenges of constructing excessively long track models and solving wheel-rail forces with large-scale degree-of-freedom matrices are efficiently avoided. Regarding model accuracy, the method incorporates the parameter excitation characteristics induced by the track and the nonlinear wheel-rail contact, making the model more aligned with actual engineering conditions. This approach provides reliable input for accurately predicting the environmental vibrations caused by subways entering and exiting the stations, offering references for vibration reduction design and environmental assessment in integrated construction projects.
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图 1 粗糙度幅值-波长谱(波数间隔为0.1 rad·m-1)
Figure 1. Roughness amplitude-wavelength spectrum (wavenumber interval of 0.1 rad·m-1)
图 4 计算得到的轮轨力时程曲线
Figure 4. Time history curves of wheel-rail forces obtained through calculation
图 5 频域法及移动时域格林函数法的轮轨力幅值曲线
Figure 5. Wheel-rail force amplitude curves of frequency-domain method and moving time-domain Green's function method
图 6 跨中及扣件上方位置的钢轨原点速度导纳幅值
Figure 6. Rail origin velocity admittance amplitude at mid-span and above fastener locations
图 7 光滑粗糙度激励下的动态轮轨力时程曲线
Figure 7. Time-history curves of dynamic wheel-rail force under smooth roughness excitation
图 8 光滑粗糙度激励下的动态轮轨力频谱
Figure 8. Frequency spectrum of dynamic wheel-rail force under smooth roughness excitation
图 10 参数激励等效得到的波数域粗糙度幅值谱
Figure 10. Wavenumber domain roughness amplitude spectrum obtained through parameter excitation equivalence
图 12 地铁车辆出站过程中移动距离
Figure 12. Distance-time curve of a subway vehicle during station exit process
图 14 参数激励等效粗糙度-时间曲线
Figure 14. Equivalent roughness-time curve of parameter excitation
图 15 粗糙度激励的轮轨力-时间曲线
Figure 15. Wheel-rail force-time curve induced by roughness excitation
图 16 参数激励的轮轨力-时间曲线
Figure 16. Wheel-rail force-time curve induced by parameter excitation
图 17 粗糙度激励轮轨力的时间-频率映像
Figure 17. Time-frequency map of wheel-rail force induced by roughness excitation
图 18 参数激励轮轨力的时间-频率映像
Figure 18. Time-frequency map of wheel-rail force induced by parameter excitation
表 1 轨道计算参数
Table 1. Track calculation parameters
变量 数值 钢轨密度/(kg·m-3) 7 850 钢轨弹性模量/(N·m-2) 2.1×1011 钢轨剪切模量/(N·m-2) 8.1×1010 钢轨横截面面积/m2 7.69×10-3 钢轨二次惯性矩/m4 3.055×10-5 钢轨截面剪切系数 0.4 钢轨扣件的垂向刚度/(N·m-1) 4.0×107 钢轨扣件的损失因子 0.25 扣件间距/m 0.6 扣件在纵向上的支撑宽度/m 0.25 轨道板长宽高/m 5.90×2.50×0.25 板下连续支撑刚度/(N·m-2) 6.67×109 轴荷载/t 15 一半轮对的质量/kg 890 
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