Vibration Fatigue Fracture Mechanism of e-Type Clip Under Rail Corrugation Excitation
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摘要:
为研究地铁小半径曲线轨道上e型弹条异常断裂的原因，通过长期跟踪和测量成都地铁X号线钢轨波磨的发展情况，并基于摩擦自激振动理论，建立轮对−轨道−扣件系统的全实体单元有限元模型；采用隐式动态分析方法和谐响应分析方法，研究短波长波磨、长波长波磨对e型弹条振动疲劳寿命的影响. 研究表明，这2种类型的钢轨波磨都会导致地铁e型弹条振动疲劳寿命减小；波磨幅值越大，导致弹条的振动疲劳寿命越小；钢轨波磨不仅能够引起e型弹条产生与钢轨波磨“同频”的受迫振动，还容易激发弹条产生该频率的倍频振动；对于短波长波磨而言，由于2倍频的存在，在相同波深幅值的短波长波磨影响下，25 mm 和40 mm波长的钢轨波磨最容易导致e型弹条产生振动疲劳断裂；波长为120 mm的长波长波磨的波深幅值较大时，激发出的6倍频振动导致弹条的振动疲劳寿命急剧减小；由于振动强度的减弱，波长为240 mm的长波长波磨对弹条振动疲劳寿命的影响有限.
Abstract:To study the reason for the abnormal fracture of e-type clips on small-radius curved subway tracks, the development of rail corrugation on Line X of the Chengdu Metro over an extended period was monitored and measured. Based on the theory of friction-induced self-excited vibration, a comprehensive solid finite element model of the wheelset−rail−fastening system was established. The effects of short-pitch rail corrugation and long-pitch rail corrugation on the vibration fatigue life of e-type clips were studied by means of implicit dynamic analysis and harmonic response analysis. The study reveals that both types of rail corrugation result in a decrease in the vibration fatigue life of the e-type clips. Greater amplitude of rail corrugation indicates shorter vibration fatigue life of the clips. Rail corrugation can not only induce the e-type clip to generate forced vibrations at the frequency matching that of the rail corrugation but also easily trigger vibrations at multiples of this frequency in the e-type clips. For short-pitch rail corrugation, due to the existence of a frequency twice that of the rail corrugation, the rail corrugation with wavelengths of 25 mm and 40 mm is most likely to lead to vibration fatigue failure of the e-type clips under the influence of short-pitch and long-pitch rail corrugation with the same wave depth amplitude. When the wave depth amplitude of long-pitch rail corrugation with a wavelength of 120 mm is large, the vibration fatigue life of the clips decreases sharply due to the excited 6-fold vibration. However, the long-pitch rail corrugation with a wavelength of 240 mm has only a limited impact on the vibration fatigue life of the clips due to the attenuation of vibration intensity.
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图 1 小半径曲线轨道的低轨上产生的短波长波磨和长波长波磨
Figure 1. Short-pitch and long-pitch rail corrugation arising on low rail of small-radius curved tracks
图 2 发生在钢轨波磨区域的e型弹条断裂
Figure 2. e-type clip fracture occurring in rail corrugation area
图 4 地铁e型弹条振动加速度的PSD分析结果
Figure 4. PSD analysis results of vibration acceleration of e-type clip
图 9 e型弹条振动加速度的谐响应分析结果
Figure 9. Harmonic response analyis results of vibration acceleration of e-type clip
图 10 轮对-轨道-扣件系统有限元模型
Figure 10. Finite element model of wheelset‒rail‒fastening system
图 11 预测得到的轮轨系统不稳定振动的频率
Figure 11. Predicted unstable vibration frequencies in wheelset‒rail system
图 12 添加了周期性不平顺的有限元模型（振幅放大8倍）
Figure 12. Finite element model with periodic irregularity （vibration amplitude is enlarged by 8x）
图 13 不同轨道上的弹条振动加速度
Figure 13. Vibration acceleration of e-type clip on different tracks
图 14 e型弹条振动加速的PSD分析结果
Figure 14. PSD analysis resukts of vibration acceleration of e-type clip
图 15 钢轨波磨影响下的e型弹条振动疲劳寿命云图
Figure 15. Cloud map of vibration fatigue life of e-type clip under influence of rail corrugation
图 16 短波长波磨的幅值、波长变化对弹条振动疲劳寿命的影响
Figure 16. Effect of amplitude and wavelength variation in short-pitch rail corrugation on vibration fatigue life of clip
图 18 不同“低通信号”下的e型弹条振动疲劳寿命
Figure 18. Vibration fatigue life of e-type clips under influence of different “low-pass signals”
图 19 长波长波磨的幅值变化对弹条振动疲劳寿命的影响
Figure 19. Effect of amplitude variation in long-pitch rail corrugation on vibration fatigue life of clip
图 20 长波长波磨引起的弹条振动加速度PSD分析结果
Figure 20. PSD analysis results of vibration acceleration of clip caused by long-pitch rail corrugation
表 1 两处曲线轨道的线路参数
Table 1. Line parameters of two curved tracks
位置 缓和曲线
长度/m超高/
mm曲线
半径/m曲线
长度/m第1处
曲线轨70 85 500.00 199.280 第2处
曲线轨60 115 350.00 651.031 
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表 2 发生在弯轨上的钢轨波磨的位置信息及类型
Table 2. Types and location information of rail corrugation at curved tracks
区段 第1次观测
（开通前）第2次观测
（空载试运营）第3次观测
（开通后两个月）第4次观测
（开通后一年）R = 350 m的曲线轨道低轨 无波磨 短波：
22～25 mm短波：
22～30 mm短波，22～30 mm、40～50 mm
长波，120～250 mmR = 350 m的曲线轨道高轨 无波磨 无波磨 无波磨 无波磨 R = 500 m的曲线轨道高轨和低轨 无波磨 无波磨 无波磨 无波磨 直线轨道 无波磨 无波磨 无波磨 无波磨
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表 3 扣件系统的材料参数
Table 3. Material parameters of fastening system
部件 密度/
（g·cm−3）弹性模量/
MPa泊松比 轨距挡块 1.57 8500 0.4 弹条 7.8 2.06 × 105 0.3 铁垫板 7.8 1.73 × 105 0.26
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