Load identification and distribution characteristics of high-speed train bogie frame
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摘要: 以某型高速列车转向架构架为对象, 研究了高速列车转向架构架载荷识别与分布特性; 分析了基于动应力响应识别构架载荷的原理并基于截断奇异值法对构架载荷进行了反推识别, 采用核密度估计法对构架载荷极值分布特性进行了分析, 基于3σ准则获得了不同出现概率下的构架载荷极值区间, 利用雨流计数法编制了构架载荷的二维载荷谱并基于Goodman方程将二维载荷谱等效转换为一维载荷谱, 基于一维载荷谱分析了各载荷系载荷的累积频次分布规律。研究结果表明: 对于本文研究对象而言, 当截断数目为1时, 载荷识别结果的相对误差最小; 载荷极小值与载荷极大值的概率密度分布整体相对于坐标系的纵坐标轴对称, 涵盖载荷范围越大的载荷系, 其概率密度的极值越低; 齿轮箱载荷系极大值与极小值涵盖的载荷范围最大, 最大载荷达到25 kN, 制动载荷系、侧滚载荷系与横向载荷系次之, 最大载荷达到了15 kN, 浮沉载荷系的最大载荷约为5 kN, 扭转载荷系极值涵盖的范围最小, 最大极值约为3 kN; 随着出现概率的增大, 各载荷系极值区间也逐渐变大; 各载荷系的二维载荷谱均有明显的载荷频次极值, 各载荷系的载荷频次极值均出现在低幅值区域; 对于二维载荷谱等效后的一维载荷谱累积频次分布, 各载荷系总累积频次相当, 齿轮箱载荷系的最大载荷幅值明显大于其他载荷系, 其他载荷系的最大载荷幅值由大到小依次为侧滚载荷系、制动载荷系、浮沉载荷系、横向载荷系和扭转载荷系。Abstract: The bogie frame of a certain model high-speed train was taken as the research object, the load identification and distribution characteristics of high-speed train bogie frame was studied. The principle of identifying frame load based on the dynamic stress response was analyzed, and the frame load was back deduced and identified based on the truncated singular method. The extreme value distribution characteristics of frame load were analyzed by the kernel density estimation method, and the extreme value ranges of frame load under different occurrence probabilities were obtained based on the 3σ criterion. The two-dimensional load spectrum of frame load was compiled by the rain-flow counting method, and the two-dimensional load spectrum was equivalent to one-dimensional load spectrum based on the Goodman equation. Based on the one dimensional load spectrum, the cumulative frequency distribution rule of loads in each load system was analyzed. Analysis result shows that for the object studied in this paper, when the number of truncation is 1, the relative error of load identification result is the smallest. The probability density distributions of the minimum load and maximum load are symmetrical relative to the longitudinal axis of coordinate system. The larger the load range is, the lower the probability density is. The maximum and minimum load ranges of gearbox load system are the largest, the maximum load extremum is 25 kN. The braking load system, lateral rolling load system and transverse load system are the second, the maximum load is 15 kN. The maximum load of floating load system is about 5 kN. The extreme value of torsional load system is the smallest, and the maximum load is about 3 kN. With the increase of occurrence probability, the occurrence range of extreme value of each load system increases gradually. The two-dimensional load spectrums of all load systems have obvious load frequency extremums that appear in the low amplitude region. For the one-dimensional cumulative frequency distribution of load spectrum after the equivalence of two-dimensional load spectrum, the total cumulative frequency time of each load system is almost equivalent. The maximum load amplitude of gearbox load system is significantly greater than those of other load systems. From large to small, the maximum load amplitudes of other load systems are lateral rolling load system, braking load system, floating load system, transverse load system and torsional load system, respectively.
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图 5 载荷极值累积概率密度分布
Figure 5. Cumulative probability density distributions of extreme loads
图 6 转向架构架各载荷系二维载荷谱
Figure 6. Two-dimensional load spectrum of each load system of bogie frame
图 7 一维载荷谱累积频次分布
Figure 7. Cumulative frequency distributions of one dimensional load spectrums
表 1 载荷-应力传递矩阵
Table 1. Load-stress transfer matrices
测点 载荷类型 1 2 3 4 5 6 1 -0.92 0.29 -4.06 0.48 1.37 0.52 2 0.69 -0.23 -0.80 0.26 0.34 -0.26 3 0.23 0.00 7.38 1.04 -7.32 -1.80 4 0.76 -0.06 -2.23 -0.11 4.64 0.26 5 0.76 -0.29 -3.15 1.33 -2.69 -1.89 6 0.53 -0.23 0.06 -0.34 0.06 18.20 7 18.23 -19.68 -19.63 1.18 0.11 2.40 8 0.92 0.17 -2.92 -0.32 -1.43 -2.92 9 -4.73 2.52 -2.46 0.38 4.81 3.26 
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表 2 不同截断数目下的正则化载荷与相对误差
Table 2. Regularization loads and relative errors under different truncation numbers
变量 载荷类型 截断数目 k=1 k=2 k=3 k=4 k=5 正则化载荷 1 0.27 -0.04 -0.36 -0.39 -0.27 2 0.38 0.04 0.36 0.38 0.29 3 0.88 0.94 0.35 0.31 0.31 4 -0.55 -0.25 -0.05 -0.05 -0.02 5 0.73 0.76 0.13 0.18 -0.01 6 1.02 1.02 1.08 1.06 -0.05 相对误差/% 1.08 1.20 1.73 1.73 4.82
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表 3 不同出现概率对应的转向架构架载荷极值区间
Table 3. Extreme load ranges of bogie frame with different occurrence probabilities
KN 载荷极值类型 载荷系 不同出现概率(%)下的载荷极值区间 68.27 95.45 99.73 载荷极大值 浮沉 [2.83, 4.84] [1.82, 5.85] [0.82, 6.86] 侧滚 [5.07, 9.91] [2.65, 12.34] [0.23, 14.76] 扭转 [1.44, 2.21] [1.05, 2.60] [0.67, 2.98] 横向 [1.92, 4.78] [0.49, 6.20] [-0.93, 7.63] 齿轮箱 [13.30, 20.88] [9.51, 24.67] [5.72, 28.46] 制动 [1.66, 8.73] [-1.88, 12.27] [-5.41, 15.81] 载荷极小值 浮沉 [-3.10, -1.40] [-3.95, -0.55] [-4.80, 0.30] 侧滚 [-8.53, -5.06] [-10.27, -3.33] [-12.01, -1.59] 扭转 [-1.81, -1.24] [-2.10, -0.95] [-2.39, -0.67] 横向 [-5.70, -1.11] [-7.99, 1.19] [-10.29, 3.48] 齿轮箱 [-21.86, -13.36] [-26.12, -9.11] [-30.37, -4.85] 制动 [-9.36, -3.56] [-12.26, -0.66] [-15.16, 2.24]
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