重载铁路轨道不平顺谱的分析和表征

Analysis and Expression of Track Irregularity Spectrum of Heavy-haul Railway

轨道不平顺的数学表达对线路状态评估和轮轨动力学分析具有重要意义。计算和分析大秦和朔黄重载铁路2~70 m波长范围内的轨道不平顺谱特征,提出重载铁路轨道不平顺的数学描述,可用于轨道不平顺序列模拟和线路状态评估。数据来源为这两条铁路的高低、轨向、水平和轨距轨道不平顺实测数据。使用小波分析和Welch修正周期图法计算轨道不平顺谱,并与国内外标准轨道谱进行对比;使用多项式拟合算法拟合轨道不平顺谱包络,并使用国内外标准谱拟合公式进行拟合实验对比。最后,给出了发生在钢轨焊缝位置的周期不平顺表达式,并结合轨道拟合谱的逆傅里叶变换方法,对轨道不平顺空间序列进行数值模拟。研究表明:大秦和朔黄轨道不平顺谱的频率和幅度特征基本一致,因此可以使用统一的拟合公式进行拟合;提出的8阶多项式拟合公式能精确地拟合轨道不平顺谱的形状;随机不平顺和周期不平顺的共同表达使轨道不平顺拟合谱的形状和轨道不平顺的数值模拟更为合理和准确。

The mathematical expression of track irregularities is of great significance to the evaluation of track status and the analysis of wheel-rail dynamics.In this paper,the power spectral density(PSD)of track irregularity in the 2~70 m wavelength range for Datong—Qinhuangdao and Shuozhou—Huanghua heavy-haul railways was calculated and analyzed,and the mathematical description of track irregularity of the heavy haul railway was proposed for the simulation of track irregularity sequence and the evaluation of the line status.The data source is the measured data of the vertical profile,alignment,cross-level,guage and track irregularity of the two railways.The PSD of track irregularity was calculated by wavelet analysis and Welch modified periodogram method and was compared with the PSD standards at home and abroad.A polynomial fitting method was used to match the PSD envelopes,and the fitting results of the proposed 8-order polynomial formula were compared with those of the standard spectral fitting formulas at home and abroad.Finally,the periodic irregularity expression at the position of the rail weld was given,and was combined with the PSD inversion method to simulate the track irregularity sequences.The results show that the PSD curves of the two railways exhibit similar features in wavelength and amplitude,and thus can be statistically averaged and fitted in uniform formula.The proposed 8-order polynomial formula achieves the best matching performance.The combinations of the mathematical descriptions help the PSD curves and numerical simulations more reasonable and precise.