Multi-objective optimization for dynamics parameters of high-speed trains under side wind
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摘要: 为改善高速列车横风下运行的动力学性能, 提高运行平稳性和安全性, 以轮轴横向力和轮重减载率为优化目标, 对高速列车动力学模型的悬挂参数进行多目标优化设计; 建立高速列车多体动力学参数化模型, 依照大风限速标准, 加载列车在横风下以不同速度运行的气动力数据, 选取了止挡间隙、一系悬挂纵向和垂向刚度、二系悬挂纵向和垂向刚度、一系垂向减振器刚度、二系横向和垂向减振器刚度、抗蛇形减振器刚度及阻尼11个变量; 搭建高速列车动力学模型优化平台, 对高速列车多体动力学参数化模型的设计参数与轮轴横向力和轮重减载率的相关性进行分析, 得到列车各悬挂参数对轮轴横向力和轮重减载率的影响趋势; 基于相关性结果, 采用NCGA、AMGA和NSGA-Ⅱ遗传算法对高速列车的动力学参数进行优化设计。分析结果表明: 采用NSGA-Ⅱ算法的优化结果最为理想; 与轮轴横向力和轮重减载率相关性最大的参数为抗蛇形减振器刚度, 为反效应; 优化后列车的动力学性能得到明显的改善, 轮重减载率从原始的0.78整体优化到0.63以下, 且最小可以优化到0.49, 最高可降低37.2%;轮轴横向力从原始的16.8 kN整体优化到9.6 kN以下, 且最小可以优化到5.79 kN, 最高可降低65.5%;得到了优化目标的Pareto前沿最优解, 确定了列车各动力学参数设计变量的最优解集, 并对最优解集在其他列车速度和风速组合下的运行工况进行验证, 适用性较好。Abstract: To improve the dynamics property and the running stability and safety of high-speed train under side wind, the wheel shaft lateral force and the wheel load reduction rate were taken as the optimization goals, the multi-objective optimization design for the suspension parameters of high-speed train dynamics model was carried out, and the multi-body dynamics parameterized model of high-speed train was modeled. According to the wind speed limit standard, the aerodynamic data of high-speed train under side wind at different speeds were loaded. Total 11 variables were extracted such as the stop clearance, the first suspension longitudinal and vertical stiffnesses, the second suspension longitudinal and vertical stiffnesses, the first vertical shock absorber stiffness, the second lateral and vertical shock absorber stiffnesses, snake-resistant shock absorber stiffness and damping. The high-speed train dynamics model optimization platform was built. The correlation between the design parameters of multi-body dynamics parameterized model of high-speed train with the wheel shaft lateral force and the wheel load reduction rate was carried out, and the influence trend of suspension parameters on the wheel shaft lateral force and the wheel load reduction rate was obtained. Based on the correlation results, the optimization design for the high-speed train dynamics parameters was proceeded by using the NCGA, AMGA, and NSGA-Ⅱ genetic algorithm. Analysis result shows that the optimization result of NSGA-Ⅱalgorithm is ideal. The factor that has the biggest correlation with the wheel shaft lateral force and the wheel load reduction rate is the snake-resistant shock absorber stiffness, and with an adverse effect. After the optimization, the dynamics property of high-speed train has a marked improvement. The wheel load reduction rate decreases from the origin value 0.78 to 0.63 wholly, and the minimum value can be 0.49, reducing by up to 37.2%. The wheel shaft lateral force decreases from the origin value 16.8 kN to 9.6 kN wholly, and the minimum value can be 5.79 kN, reducing by up to 65.5%. The Pareto frontier optimal solution is got, the optimal solution set of each dynamics parameter design variable is determined, and the optimal solution sets with high applicability are verified at other wind speed and train speed states.
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图 3 设计变量对轮重减载率的相关性
Figure 3. Correlation between design variables and rate of wheel load reduction
图 4 设计变量对轮轴横向力的相关性
Figure 4. Correlation between design variables and wheel shaft lateral force
表 1 参与优化的动力学参数
Table 1. Dynamics parameters for optimization
变量名称 止挡间隙/mm 一系悬挂纵向刚度/(kN·m-1) 一系悬挂垂向刚度/(kN·m-1) 二系悬挂纵向刚度/(kN·m-1) 二系悬挂垂向刚度/(kN·m-1) 二系垂向减振器阻尼/(kN·s·m-1) 二系横向减振器阻尼/(kN·s·m-1) 一系垂向减振器刚度/(kN·m-1) 二系横向减振器刚度/(kN·m-1) 二系垂向减振器刚度/(kN·m-1) 抗蛇形减振器刚度/(kN·m-1) 变量简写 B P1 P2 S1 S2 D1 D2 T1 T2 T3 T4 
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表 2 优化前后的动力学参数变量和目标值
Table 2. Dynamics parameters variables and target values before and after optimization
解集 B/mm P1/(kN·m-1) P2/(kN·m-1) T1/(kN·m-1) D2/(kN·s·m-1) T2/(kN·m-1) S1/(kN·m-1) S2/(kN·m-1) D1/(kN·s·m-1) T3/(kN·m-1) T4/(kN·m-1) 轮轴横向力/kN 轮重减载率 0 45 54 100 1 923 133 95 919 4 518 4 087 71 5 609 9 784 16.8 0.78 1 42 55 101 1 920 133 76 600 4 309 4 736 68 5 605 9 893 5.8 0.55 2 42 53 101 1 922 130 99 857 4 377 4 109 80 5 609 9 788 5.7 0.56 3 41 54 121 1 455 116 97 003 4 518 4 194 74 5 605 9 784 5.9 0.55 4 43 54 121 1 468 116 97 003 4 521 4 206 74 5 605 9 889 5.9 0.55 5 42 54 120 1 468 136 99 691 4 610 4 194 74 5 605 9 875 5.9 0.56 6 43 51 121 1 914 133 99 902 4 446 4 670 74 5 605 9 874 6.4 0.54 7 42 121 120 1 914 130 95 561 4 374 4 672 64 5 605 9 303 6.6 0.51 8 42 124 120 1 914 135 95 561 4 442 4 694 74 5 605 9 876 6.6 0.53 9 42 124 120 1 914 135 96 342 4 442 4 615 74 5 605 9 876 6.7 0.49
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表 3 不同车速-风速组合下的目标值
Table 3. Target values at different train speed and wind speed
工况 轮轴横向力 轮重减载率 优化前/kN 优化后/kN 减小率/% 优化前 优化后 减小率/% 1 12.40 10.40 16.1 0.75 0.63 16.1 2 12.80 8.50 33.6 0.74 0.61 17.5 3 16.80 5.79 65.5 0.78 0.49 37.2 4 12.60 11.80 6.3 0.73 0.64 12.3
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