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摘要: 以心轨顶宽20、35、50 mm处的辙叉区钢轨关键截面作为研究对象，基于NURBS曲线理论建立辙叉区钢轨廓形重构方法；以关键截面钢轨廓形上若干型值点为设计变量，以打磨材料去除量的减少和脱轨系数的降低为目标，以钢轨廓形几何特征和降低钢轨滚动接触疲劳为约束条件，设计出18号道岔辙叉区钢轨经济性打磨廓形；建立了轮轨接触有限元模型和车辆-轨道耦合动力学模型，进行了轮轨接触应力与动力学指标计算。分析结果表明：优化的打磨廓形接触点分布均匀，具有良好的轮轨接触几何特性；钢轨打磨材料去除量在2号截面处降低了17.2%；各截面Mises应力分别降低了8.7%、8.3%和11.5%，轮轨接触应力降幅分别为12.9%、15.8%和18.0%；列车逆侧向过岔时，轮轨横向力与车体横向振动加速度分别降低了10.3%和15.6%，脱轨系数与轮重减载率分别降低了8.1%和10.6%，疲劳因子降低了12.2%。可见，优化廓形在保证列车运行安全性的同时，提升了列车运行的平稳性以及辙叉区钢轨的使用寿命。Abstract: For the critical section of a rail in the frog area with top widths of 20, 35 and 50 mm of the core rail as the research object, the rail profile reconstruction method was developed to analyze the frog area based on the NURBS curve theory. Several types of data points on the rail profile of the key section were set as design variables, and the reduction of the removal amount of grinding material and derailment coefficient were taken as the objective, and the geometric characteristics of the rail profile and the rolling contact fatigue reduction of the rail were used as constraints, the economic grinding profile of the rail in the frog area of No.18 turnout was designed. The wheel-rail contact finite element model and vehicle-track coupling dynamic model were established, and the wheel-rail contact stresses and dynamics indexes were calculated. Analysis results show that the optimized grinding profile contact points are evenly distributed and have good wheel-rail contact geometric characteristics. The removal amount of the rail grinding material decreases by 17.2 % in section 2. The Mises stresses of each section decrease by 8.7%, 8.3%, and 11.5%, respectively, and the wheel-rail contact stresses decrease by 12.9%, 15.8%, and 18.0%, respectively. When the train reversely passing turnout branch, wheel-rail lateral force and lateral vibration acceleration of the car body decrease by 10.3% and 15.6%, respectively, the derailment coefficient and the wheel-load reduction rate decrease by 8.1% and 10.6%, respectively, and the fatigue index decreases by 12.2%. Therefore the optimized profile not only ensures train operation safety, but also improves train operation stability and the service life of the rail in frog areas. 5 tabs, 14 figs, 26 refs.
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图 2 拟合廓形与标准廓形曲线对比
Figure 2. Comparison between fitting profile and standard profile curves
图 12 优化前后轮轨接触应力对比
Figure 12. Comparison of wheel-rail contact stresses between optimized and standard profiles
图 13 列车侧逆向过岔动力学响应
Figure 13. Vehicle dynamics responses when train reversely passing turnout branch
图 14 优化前后的滚动接触疲劳因子
Figure 14. Rolling contact fatigue indices of optimized and standard profiles
表 1 拟合廓形与标准廓形的相关系数
Table 1. Correlation coefficients between fitting profile and standard profile
情况 型值点个数 rswt 时间/h 1 13 0.89 10 2 16 0.94 23 3 19 0.97 51 
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表 2 NURBS拟合廓形关键参数
Table 2. Key parameters of NURBS fitting profile
型值点 型值点坐标 权因子权重 控制点坐标 横坐标 纵坐标 横坐标 纵坐标 1 -54.22 -16.79 0.6 -54.43 -16.09 2 -50.88 -6.31 1.0 -51.01 -8.31 3 -39.72 -1.57 1.0 -46.47 -3.07 4 -25.27 -0.53 1.0 -33.27 -0.83 5 0.00 0.00 0.9 -1.00 0.20 6 27.81 -1.45 0.8 26.81 -1.25 7 36.04 -2.77 0.9 35.04 -2.57 8 41.39 -6.54 1.0 41.59 -6.34 9 44.27 -11.48 1.0 44.57 -11.28 10 45.10 -16.06 0.7 45.40 -15.86 11 48.42 -12.88 0.9 49.42 -12.68 12 54.25 -10.24 0.9 55.25 -10.04 13 59.59 -9.07 1.0 60.09 -8.87 14 64.99 -10.24 1.0 65.49 -10.04 15 70.24 -13.06 0.9 70.74 -12.86 16 73.82 -17.44 0.7 74.32 -17.24
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表 3 车辆系统基本动力学参数
Table 3. Basic dynamics parameters of vehicle system
参数 取值 参数 取值 车体质量/kg 4.24×104 一系悬挂横向刚度之半/(kN·m-1) 4 000 车体摇头惯量/(kg·m2) 2.08×106 一系悬挂纵向刚度之半/(kN·m-1) 2.8×104 车体侧滚惯量/(kg·m2) 2.27×106 一系悬挂垂向阻尼之半/(kN·s·m-1) 17.7 车体点头惯量/(kg·m2) 7.06×105 一系悬挂横向阻尼之半/(kN·s·m-1) 0 构架质量/kg 3 100 一系悬挂纵向阻尼之半/(kN·s·m-1) 0 构架摇头惯量/(kg·m2) 2 250 二系悬挂横向刚度之半/(kN·m-1) 148 构架侧滚惯量/(kg·m2) 2 810 二系悬挂纵向刚度之半/(kN·m-1) 205 构架点头惯量/(kg·m2) 5 050 二系悬挂纵向刚度之半/(kN·m-1) 145 车轮质量/kg 1 850 二系悬挂垂向阻尼之半/(kN·s·m-1) 31.6 车轮摇头惯量/(kg·m2) 717 二系悬挂横向阻尼之半/(kN·s·m-1) 24.5 车轮侧滚惯量/(kg·m2) 717 二系悬挂纵向阻尼之半/(kN·s·m-1) 343 一系悬挂垂向刚度之半/(kN·m-1) 1 216 车轮名义滚动圆半径/m 0.43
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表 4 18号高速道岔辙叉区钢轨各关键截面参数
Table 4. Key section parameters of rail in frog area of No.18 high-speed turnout
mm 长心轨 距离尖端长度 0 599 895 1 518 4 000 顶宽 20 40 50 71 71 顶高 -5.0 -1.6 0 0 0
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表 5 辙叉区轨道系统动力学参数
Table 5. Dynamics parameters of track system in frog area
参数 取值 参数 取值 钢轨单位质量/(kg·m-1) 60.64 岔枕单位质量/(kg·m-1) 154 钢轨侧滚惯性矩/m4 0.33×10-4 岔枕侧滚惯性矩/m4 2.49×10-4 钢轨摇头惯性矩/m4 0.52×10-5 道床单位质量/(kg·m-1) 69.94 道床侧滚惯性矩/m4 0.5×10-4 道床摇头惯性矩/m4 0.08×10-4 钢轨横向刚度/(N·m-1) 5.0×107 岔枕横向刚度/(N·m-1) 5.0×107 钢轨垂向刚度/(N·m-1) 2.5×107 岔枕垂向刚度/(N·m-1) 1.0×108 钢轨横向阻尼/(kN·s·m-1) 1.2×104 岔枕横向阻尼/(kN·s·m-1) 4.9×104 钢轨垂向阻尼/(kN·s·m-1) 2.7×104 岔枕垂向阻尼/(kN·s·m-1) 9.4×104
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