Theoretical Research and Simulation of Train Derailment with Folding Catastrophe Theory
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摘要: 随着轨道交通的发展,列车成为出行货运的重要交通工具,所以找到有效的评价列车脱轨的方法成为研究重点。本文研究了直线道路上列车行驶过程的状态突变现象。将突变理论运用到列车脱轨研究分析中,基于初等突变理论里的折叠突变,考虑列车横向振动加速度以及重心偏转角对列车脱轨的影响,建立列车脱轨事故折叠突变模型。对直线上行驶的列车临近脱轨时受力分析,依据弹性势能不变值原理以及泰勒展开式,推导出列车脱轨事故的折叠突变势函数方程,通过分析突变模型的平衡曲线以及分叉集,给出了列车运行时脱轨的危险区。应用Simpack软件建立车辆轨道模型,施加不同类型的路面激励谱,将仿真结果与突变模型中的平衡曲线和分叉集进行分析对比,得到:当列车运行导致横向振动加速度由平衡曲线下半支跃升到上半支时,脱轨系数增大,列车脱轨风险增大。最终得到基于折叠突变理论的新的列车脱轨评价方法。Abstract: With the development of rail transit, trains have become an important means of transport for freight transportation, so finding an effective method to evaluate train derailment has become a research focus. We study the phenomenon of sudden state changes in trains on straight roads and apply the catastrophe theory to accident analysis of train derailment. Based on the folding catastrophe in the elementary catastrophe theory, considering the influence of the train's lateral vibration acceleration and the deflection angle of the center of gravity on the train derailment, the folding catastrophe model of the train derailment accident is established. When it is approaching derailment, according to the principle of invariable value of elastic potential energy and Taylor expansion, the folding catastrophe potential function equation of the train derailment accident is deduced. By analyzing the balance curve and bifurcation set of the catastrophe model, give out of the danger zone of derailment during train operation. The Simpack software was used to establish the vehicle track model, and different types of road excitation spectra were applied. The simulation results were analyzed and compared with the balance curve and bifurcation set in the catastrophe model. It was obtained that when the train was running, the lateral vibration acceleration jumped from the lower half of the balance curve. In the upper half of the branch, the derailment coefficient increases and the risk of train derailment increases. Finally, a new train derailment evaluation method based on folding catastrophe theory is obtained.
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表 1 C64k型敞车计算参数
参数 数值 参数名称 数值 自重/kg 22 500 空车重心高度/mm 1 400 载重/kg 61 000 重车重心高度/mm 1 800 空车车体质量/kg 14 000 轮对滚圆直径/mm 840 轮对滚圆间距/mm 1 500 曲线半径/mm 0 迎风面高度/mm 2 050 行驶速度/(km·h−1) 120 风力作用点距离
轨面的高度/mm2 107 横向风力/N 1 239 -
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