Influence of frequency-dependent characteristics of double-layer nonlinear fastener system on wheel-rail dynamics characteristics
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摘要: 为研究双层非线性扣件系统频变特性对轮轨动力特性的影响，基于锤击法测得了该扣件系统在100~1 000 Hz内的动刚度；建立了轨道结构有限元模型和轮轨瞬态滚动接触有限元模型，在模型中考虑扣件系统的频变特性，基于轨道结构模型分析了扣件系统频变特性对钢轨振动特性的影响，利用轮轨瞬态滚动接触模型分析其对轮轨动力特性的影响。研究结果表明：扣件系统在垂向、横向和纵向的动刚度随频率增大，总体呈现出增大的趋势；扣件系统频变特性导致340 Hz以上钢轨振动更加显著，同时钢轨振动峰值所对应的频率向更高频段移动，340~700 Hz频段钢轨振动响应的变化是频变刚度和频变阻尼共同作用的结果，800~900 Hz频段的变化主要受扣件系统频变刚度的影响；钢轨振动响应的这种变化对小半径曲线段通过频率在340 Hz以上的短波长波磨有较大影响，因此，考虑扣件系统频变特性有益于提高该频段短波长波磨的预测精度；扣件系统频变刚度对轴箱振动加速度和轮轨力的影响较小，其最大值降低了约2%；扣件系统频变阻尼对这两者的影响较大，频变阻尼使轴箱振动加速度和轮轨力在100~470 Hz频段增大，在470~1 000 Hz频段减小；扣件系统频变特性对最大轮轨接触应力影响较小，考虑频变刚度时对应的轮轨接触应力略大，考虑频变阻尼时对应的轮轨接触应力略小。Abstract: To study the influence of frequency-dependent characteristics of double-layer nonlinear fastener system on wheel-rail dynamics characteristics, the dynamic stiffness of the fastener system within the frequency range of 100-1 000 Hz was obtained by hammering method. The finite element models of track structure and wheel-rail transient rolling contact were established. The frequency-dependent characteristics of the fastener system were considered in the models. Based on the track structure model, the influence of the frequency-dependent characteristics of the fastener system on the rail vibration characteristics was analyzed. The influence of the fastener system on the wheel-rail dynamics characteristics was analyzed by using the transient rolling contact model. Research results show that the dynamic stiffnesses of the fastener system in the vertical, lateral, and longitudinal directions generally increase with frequency. The frequency-dependent characteristics of the fastener system lead to more significant rail vibration at the frequency of above 340 Hz, and the frequency range corresponding to the peak rail vibration shifts towards higher frequencies. The changes in rail vibration response within the frequency range of 340-700 Hz are caused by the combined effects of frequency-dependent stiffness and damping, while the changes within the frequency range of 800-900 Hz are primarily influenced by the frequency-dependent stiffness of the fastener system. These changes in rail vibration response have a significant impact on the passing frequency of short-wavelength rail corrugation at above 340 Hz in small-radius curve sections. Therefore, considering the frequency-dependent characteristics of the fastener system is beneficial for improving the prediction accuracy of short-wavelength rail corrugation in this frequency range. The frequency-dependent stiffness of the fastener system has a relatively small impact on axle box vibration acceleration and wheel-rail forces, and the maximum value reduces by about 2%. However, the frequency-dependent damping of the fastener system has a significant impact on both. The frequency-dependent damping increases axle box vibration acceleration and wheel-rail forces within the frequency range of 100-470 Hz and reduces them within the frequency range of 470-1 000 Hz. The frequency-dependent characteristics of the fastener system have little effect on the maximum wheel-rail contact stress. When frequency-dependent stiffness is considered, the corresponding wheel-rail contact stress is slightly higher, and when frequency-dependent damping is considered, the corresponding wheel-rail contact stress is slightly lower.
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图 5 双层非线性扣件轨道结构有限元模型(单位：mm)
Figure 5. Finite element model of track structure with double-layer nonlinear fastener (unit: mm)
图 6 轮轨瞬态滚动接触有限元模型
Figure 6. Finite element model of wheel-rail transient rolling contact
图 9 扣件系统频变特性对钢轨振动特性的影响
Figure 9. Influences of frequency-dependent characteristic of fastener system on rail vibration characteristic
图 10 扣件系统频变刚度对轴箱振动加速度的影响
Figure 10. Influence of frequency-dependent stiffness of fastener system on axle box vibration acceleration
图 11 扣件系统频变阻尼对轴箱振动加速度的影响
Figure 11. Influence of frequency-dependent damping of fastener system on axle box vibration acceleration
图 12 扣件系统频变刚度对垂向轮轨力的影响
Figure 12. Influence of frequency-dependent stiffness of fastener system on vertical wheel-rail force
图 13 扣件系统频变阻尼对垂向轮轨力的影响
Figure 13. Influence of frequency-dependent damping of fastener system on vertical wheel-rail force
表 1 轨道结构模型参数
Table 1. Parameters of track structure model
参数 数值 钢轨弹性模量/Pa 2.059×1011 钢轨泊松比 0.3 钢轨密度/(kg·m-3) 7 790 道床板弹性模量/Pa 3.25×1010 道床板泊松比 0.2 道床板密度/(kg·m-3) 2 500 轮对弹性模量/Pa 2.1×1011 轮对泊松比 0.3 轮对密度/(kg·m-3) 7 800 地基支撑刚度/(N·m-1) 1.70×108 地基支撑阻尼/(N·s·m-1) 31 000 
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表 2 轮轨瞬态滚动接触模型参数
Table 2. Parameters of wheel-rail transient rolling contact model
参数 数值 簧上质量/t 14 一系悬挂垂向刚度/(N·m-1) 0.98×106 一系悬挂垂向阻尼/(N·s·m-1) 8 200 车轮前进速度/(km·h-1) 60 车轮角速度/(rad·s-1) 39.682 5
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表 3 模型计算工况
Table 3. Model calculation conditions
工况 考虑扣件系统频变刚度 考虑扣件系统频变阻尼 1 否 否 2 是 否 3 否 是 4 是 是
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表 4 各工况下最大轮轨接触应力
Table 4. Maximum wheel-rail contact stresses under each condition
工况 1 2 3 4 接触斑 
最大接触应力/MPa 1 988 1 997 1 952 1 970 与工况1差异百分比/% 0.45 -1.81 -0.91
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