Frequency domain calibration and establishment method for load spectrum of bogie frame
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摘要: 分析了时域内准静态载荷-应力传递关系, 以载荷间互谱密度的参数作为载荷耦合作用的表征量, 基于多轴频域疲劳基本理论推导了频域内等效应力的表达式; 得到了与多轴加载等效的分立载荷系的表达式; 为保证载荷谱计算损伤可以覆盖线路实测损伤, 以应力信号自功率谱密度的0阶谱矩作为表征损伤的参量, 约束载荷对测点损伤的贡献占比, 根据损伤一致性原则, 采用NSGA-Ⅱ多目标优化算法进行载荷校准; 对国内某型地铁转向架构架进行线路测试, 获得了载荷和应力数据, 并进行了数据分析。研究结果表明: 载荷系中构架横向载荷的线路实测方差最大, 为5.08, 电机横向载荷方差最小, 为0.02;频域内考虑载荷耦合效应的损伤校准精度为1.08×10-5, 而采用时域分立谱的损伤校准精度为2.91×10-3, 频域法比时域法的校准精度提高了99.63%;频域内考虑耦合作用的载荷校准系数的综合调整倍数为31.81, 相比时域内采用分立谱校准系数的调整倍数下降了41.71%, 频域法的系数调整最大倍数为6.99, 时域法为15.68, 前者比后者降低了55.42%。可见: 频域内考虑载荷耦合作用的校准方法在误差精度上要优于时域内采用分立谱的校准方法; 频域法的系数调整比例的分散度低于时域法, 校准载荷更接近实测载荷, 校准结果可信度高; 由于校准过程中考虑了载荷间的关联性, 研究得到的载荷系可同时应用于试验台多轴加载以及仿真独立加载, 实现了2种加载方式的统一, 为构架载荷谱的建立方式提出了新思路。Abstract: The quasi-static load-stress transfer relationship in time-domain was analyzed. The parameters of cross-spectral density between loads were taken as the characterization of load coupling effect. Based on the basic theory of multi-axis frequency-domain fatigue, the expression of equivalent stress in frequency-domain was derived. The expressions of discrete load system equivalent to the multi-axis load were obtained. In order to ensure that the damage calculated by load spectrum can cover the measured damage of test line, the 0-order spectral moment of the self-power spectral density of stress signal was taken as the parameter to characterize the damage, and the contribution ratio of load to the damage at the measured point was restrained. According to the principle of damage consistency, load calibration was carried out by using the NSGA-Ⅱ multi-objective optimization algorithm. The line test on a domestic metro bogie frame was carried out, the load and stress data were obtained, and the data processing and analysis were carried out. Analysis result shows that in the load system, the measured variance of the transverse load of frame is the largest, which is 5.08, and the variance of the transverse load of motor is the smallest, which is 0.02. The damage calibration accuracy considering load coupling effect in frequency domain is 1.08×10-5, while the damage calibration accuracy using the time-domain discrete spectrum is 2.91×10-3. The calibration accuracy of frequency-domain method is 99.63% higher than that of time-domain method. The comprehensive adjustment multiple of load calibration coefficient considering the coupling effect in frequency domain is 31.81, which is 41.71% lower than that using the discrete spectrum in time domain. The maximum coefficient adjustment multiple of frequency-domain method is 6.99, and the multiple of time-domain method is 15.68, the former is 55.42% lower than the latter. So the calibration method considering the load coupling effect in frequency domain is superior to the calibration method using the discrete spectrum in time domain in terms of error accuracy. The dispersion of coefficient adjustment ratio of frequency-domain method is lower than that of time-domain method. The calibration load is closer to the measured load, and the reliability of calibration results is high. Because the correlation between loads is taken into account in the calibration process, the load system can be applied to multi-axis loading of test bed and independent loading of simulation. The unification of the two loading modes is realized, which provides a new idea for the establishment of frame load spectrum.
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表 1 载荷系相关系数
Table 1. Correlation coefficients among load systems
载荷 1 2 3 4 5 6 7 8 9 10 11 1 1.00 0.15 -0.19 -0.16 0.06 0.04 -0.20 -0.12 -0.04 -0.03 -0.03 2 1.00 0.06 0.55 -0.03 0.14 -0.69 -0.04 0.10 0.05 0.60 3 1.00 0.60 0.05 -0.15 0.72 0.10 -0.15 -0.06 -0.53 4 1.00 -0.11 -0.17 0.86 0.03 0.14 -0.07 -0.63 5 1.00 -0.35 0.12 -0.05 -0.06 -0.37 -0.07 6 1.00 -0.18 -0.03 0.08 0.39 0.09 7 1.00 -0.06 0.09 -0.09 -0.61 8 1.00 0.38 -0.02 -0.02 9 1.00 -0.04 0.11 10 1.00 0.08 11 1.00 
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表 2 优化后的准静态载荷校准系数解集
Table 2. Optimized solution sets of calibration coefficients for quasi-static loads
解集 浮沉 侧滚 扭转 构架横向 构架纵向 制动 菱形 电机垂向 电机横向 齿轮箱垂向 横向减振器 1 4.10 3.05 0.50 1.77 4.31 9.94 1.64 2.02 1.59 0.58 5.10 2 4.10 5.56 0.50 1.51 3.90 6.99 1.95 1.56 2.48 0.67 5.10 3 9.52 8.08 0.35 4.47 4.42 11.58 2.44 0.85 2.41 0.88 9.52 4 9.29 8.23 0.49 4.53 4.20 11.58 2.76 0.77 2.29 0.88 9.29 5 9.48 8.08 0.48 4.33 4.01 11.35 2.55 0.88 2.67 0.71 9.48
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表 3 载荷系方差
Table 3. Variances of load system
载荷编号 分立载荷校准方差 分立载荷等效方差 1 0.61 0.82 2 3.57 1.83 3 2.52 3.98 4 0.92 -9.82 5 0.06 0.16 6 0.11 0.06 7 10.48 6.76 8 0.44 0.56 9 0.01 0.01 10 0.12 0.05 11 0.18 0.04
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