Dynamic interaction between metro vehicle and steel spring floating slab track under emergency braking condition
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摘要: 为了优化坡道上钢弹簧浮置板轨道的设计, 在考虑轮轨纵向作用关系与钢弹簧浮置板轨道特点的基础上, 运用多体动力学理论和有限元法建立了紧急制动条件下地铁车辆与钢弹簧浮置板轨道动力相互作用模型, 利用多体动力学软件UM验证了模型的有效性, 分析了车辆与轨道的动力响应。研究结果表明: UM软件与本文模型计算得到的车体纵向加速度和轮轨纵向力平均相对误差分别为1.3%、2.8%;在紧急制动过程中, 车体始终处于向前点头和纵向振动的状态, 导致前轮增载, 后轮减载; 由于板与板之间不连续, 钢轨和浮置板之间会产生纵向相对错动, 须注意钢轨与浮置板之间不协调的纵向变形; 间隔2组扣件布置一对隔振器方案(方案1) 所得板端钢轨垂向位移比板中大0.2 mm, 间隔2组扣件布置一对隔振器, 再间隔3组扣件布置一对隔振器方案(方案2) 所得板端钢轨垂向位移比板中小0.5 mm; 2种布置方案下, 轨道纵向变形相差不超过5%, 扣件和钢弹簧受到的纵向作用力相差不超过15%;短波轨道不平顺显著加剧了钢轨和浮置板的垂向振动效应, 不平顺状态下钢轨最大垂向加速度可达15g左右; 钢弹簧浮置板轨道可以降低传递到基础底部的垂向振动, 加速度降幅约为0.2 m·s-2, 但会显著放大低频段钢轨、浮置板的垂向振动, 振动量增幅约为15 dB。Abstract: To optimize the design of steel spring floating slab track on the grade, based on the consideration of longitudinal wheel-rail relationship and structure characteristics of steel spring floating slab track, the dynamic interaction model of metro vehicle and steel spring floating slab track under the emergency braking condition was established through the multi-body dynamics theory and finite element method. The validity of the model was verified through the multi-body dynamics software UM. The dynamic responses of vehicle and track under the emergency braking condition were analyzed. Research result shows that the average relative errors of longitudinal acceleration of car body and longitudinal wheel-rail force calculated by the UM and the model in this paper are 1.3% and 2.8%, respectively. During the emergency braking process, the car body is always in the state of forward pitching and longitudinal vibration, resulting in the increased load in the front wheel and the decreased load in the rear wheel. Owing to the discontinuities between the slabs, a longitudinal relative dislocation occurs between the track and floating slab. The special attentions should be paid to the longitudinal uncoordinated deformation between the rail and floating slab. For the scheme of arranging a pair of isolators at the intervals of two sets of fasteners (scheme 1), the vertical displacement of rail at the end of slab is 0.2 mm larger than that at the middle of slab. For the scheme of arranging a pair of isolators at the intervals of two sets of fasteners, then arranging a pair of isolators at the intervals of three sets of fasteners (scheme 2), the vertical displacement of rail at the end of slab is 0.5 mm smaller than that at the middle of slab. Under the two layout schemes, the difference of longitudinal deformation of track is no more than 5%, and the difference of longitudinal force acting on fastener and steel spring is no more than 15%. The short wave track irregularity significantly increases the vertical vibrations of rail and floating slab, and the maximum vertical acceleration of rail can reach up to approximately 15g in the presence of track irregularity. Steel spring floating slab can reduce the vertical vibration transmitted to the bottom of the foundation, and the acceleration decreases by approximately 0.2 m·s-2. However, the low-frequency vertical vibrations of rail and floating slab amplify significantly, and the vibration increases by approximately 15 dB.
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图 8 紧急制动过程车辆响应时程
Figure 8. Time histories of vehicle responses during emergency braking
图 11 不同位置的钢轨与浮置板纵向位移差
Figure 11. Longitudinal displacement differences between rail and floating slab at different positions
图 12 不同布置方案下浮置板隔振效果
Figure 12. Vibration isolation results of floating slab under different layout schemes
图 13 轨道结构垂向振动分析结果
Figure 13. Analysis results of vertical vibration of track structure
图 14 轮载点钢轨纵向位移
Figure 14. Longitudinal displacements of rail at wheel-rail contact points
表 1 车辆与轨道参数
Table 1. Parameters of vehicle and track
参数名称 参数值 车体质量mc/kg 2.04×104 车体转动惯量Jc/ (kg·m2) 6.60×105 二系垂向刚度ksz/ (N·m-1) 4.50×106 二系垂向阻尼csz/ (N·s·m-1) 1.20×105 二系纵向刚度ksx/ (N·m-1) 2.00×105 二系纵向阻尼csx/ (N·s·m-1) 2.50×106 1/2车辆定距lc/m 6.30 转向架质量mt/kg 7.95×102 转向架转动惯量Jt/ (kg·m2) 3.38×102 1/2车辆轴距lt/m 1.10 一系垂向刚度kpz/ (N·m-1) 2.08×105 一系垂向阻尼cpz/ (N·s·m-1) 1.00×105 一系纵向刚度kpx/ (N·m-1) 1.00×107 一系纵向阻尼cpx/ (N·s·m-1) 1.00×105 轮对质量mw/kg 5.53×102 扣件垂向刚度kz1/ (N·m-1) 3.43×107 扣件垂向阻尼cz1/ (N·s·m-1) 3.00×104 扣件纵向刚度kx1/ (N·m-1) 7.50×107 扣件纵向阻尼cx1/ (N·s·m-1) 6.00×104 钢弹簧垂向刚度kz2/ (N·m-1) 6.30×106 钢弹簧垂向阻尼cz2/ (N·s·m-1) 8.00×103 钢弹簧纵向刚度kx2/ (N·m-1) 7.56×106 钢弹簧纵向阻尼cx2/ (N·s·m-1) 6.00×104 
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表 2 不同布置方案下轨道动力响应峰值
Table 2. Peak values of dynamic responses of track under different layout schemes
轨道动力响应指标 方案1 方案2 钢轨 板中垂向位移/mm 2.500 2.800 板端垂向位移/mm 2.700 2.300 板中纵向位移/mm 0.083 0.086 板端纵向位移/mm 0.079 0.080 浮置板 板中垂向位移/mm 2.200 2.500 板端垂向位移/mm 2.600 2.100 板中纵向位移/mm 0.064 0.066 板端纵向位移/mm 0.064 0.066 扣件 板中垂向力/kN 24.8 24.8 板端垂向力/kN 29.4 29.5 板中纵向力/N -456.0 -454.0 板端纵向力/N -688.0 -685.0 钢弹簧 板中垂向力/kN 24.7 30.0 板端垂向力/kN 27.6 25.4 板中纵向力/N -482.0 -549.0 板端纵向力/N -474.0 -544.0
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