Similarity of Small-Scale Wheelset-Track Model for Investigation of Rail Corrugation
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摘要: 为了研究地铁小半径曲线线路的钢轨波磨现象，基于轮轨间饱和蠕滑力引起摩擦自激振动导致钢轨波磨的理论，对全尺寸和缩尺轮轨模型的相似性进行了研究. 分别建立1∶1和1∶5车辆-轨道系统的动力学模型，确定每个车辆模型在通过小半径曲线线路时前转向架导向轮对与轨道间的蠕滑力饱和情况；根据动力学仿真所得轮轨接触参数，建立轮对-轨道-轨枕有限元模型；采用复特征值分析研究各个轮轨系统的稳定性. 研究结果表明：全尺寸和缩尺车辆模型分别通过小半径曲线线路时，导向轮对内外车轮上的蠕滑力均接近饱和；轮对两端垂向悬挂力的偏差小于3%，轮轨接触角的偏差小于5%；相似不稳定振动模态对应的频率偏差均小于3%；缩尺轮轨模型在动力学表现及稳定性方面与全尺寸模型具有良好的相似性，故可用缩尺模型对钢轨波磨的形成机理进行理论与试验研究.Abstract: In order to study rail corrugation on sharp metro curved tracks, based on the theory that the friction-induced vibration causes rail corrugation, the similarity between a full-scale and a small-scale wheelset-track models was studied. Firstly, to determine if the wheel-rail creep force was saturated, 1∶1 and 1∶5 dynamics models of vehicle-track system were established, respectively. Curve negotiations of these two models were simulated. Secondly, two finite element models were established whose wheel-rail contact parameters were from the dynamic simulation. Finally, using the complex eigenvalue analysis studied the stability of each wheelset-track system.The results show that when 1∶1 and 1∶5 vehicle models negotiate the sharp curved line respectively, creep forces on the inner and outer wheels of leading wheelsets are approximately saturated. Deviations of the vertical suspension force on two axle-ends of the wheelset and the wheel-rail contact angle are less than 3% and 5%, respectively. Frequency deviations of all similar unstable vibration modes are lower than 3%. The small-scale wheelset-track model has good similarity with full-scale model in the dynamic performance and the stability; therefore, the small-scale model can be used to study the formation mechanism of rail corrugation, both theoretically and experimentally.
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Key words:
- rail corrugation /
- friction /
- small-scale wheelset-track model /
- similarity study /
- numerical simulation
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图 1 轮轨间蠕滑力饱和状态
Figure 1. Saturated conditions of the creep force between the wheel and the rail
图 3 导向轮对两端的垂向悬挂力
Figure 3. Vertical suspension force on two ends of the leading wheelset
图 4 轮轨间法向接触力及蠕滑力
Figure 4. Normal contact force and creep force between the wheel and the rail
图 6 小半径曲线轨道上等效阻尼比的分布
Figure 6. Distributions of effective damping ratios on a sharp curved track
图 7 小半径曲线轨道上轮轨系统的摩擦自激振动模态
Figure 7. Mode shapes of self-excited vibration of the wheelset-track system on a sharp curved track
表 1 车辆-轨道系统动力学模型的基本参数
Table 1. Basic parameters of dynamic model of the vehicle-track system
参数名称 原数值 缩尺系数 缩尺后数值 质量 m/kg m 53 m/125 转动惯量 I/（kg•m2） I 54 I/625 刚度 K1/（kN•m−1） K1 5 K1/5 阻尼 C1/（kN•m−1） C1 52 C1/25 杨氏模量 E/GPa 210 1 210 泊松比 V 0.3 1 0.3 摩擦系数 μ 0.45 1 0.45 运行速度 v/（km•h−1） 60 5 12 曲线区段超高 H/m 0.1 5 0.02 曲线区段半径 R/m 350 5 70 轨道总长度 L/m 700 5 140 
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表 2 轮对-钢轨系统的有限元模型参数
Table 2. Parameters of finite element models of the wheelset-track system
参数名称 1:1 1:5 左侧横向悬挂力/kN 0.233 0.046 左侧垂向悬挂力/kN 53.681 0.439 右侧横向悬挂力/kN 0.204 0.046 右侧垂向悬挂力 /kN 49.164 0.382 轨枕间距 LS/mm 625 125 摩擦系数 0.45 0.45 轮轨材料密度/(kg•m−3) 7800 7800 轮轨材料杨氏模量/GPa 210 210 轮轨材料泊松比 0.3 0.3 轨枕材料密度/(kg•m−3) 2500 2500 轨枕材料杨氏模量/GPa 35 35 轨枕材料泊松比 0.2 0.2
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