Research on Long-Wave Irregularity of Metro Rail and Wheel-Rail Short-Wave Roughness Spectra
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摘要:
为建立用于地铁振动噪声数值仿真预测的轮轨宽频激励模型，依托北京地铁线路实测轨道长波不平顺、钢轨表面粗糙度和青岛地铁实测车轮踏面不圆顺数据，开展地铁轨道长波不平顺选取与轮轨短波粗糙度谱研究. 首先，采用Welch法对实测轨道不平顺数据进行功率谱密度估计，并给出了钢轨短波不平顺功率谱和车轮不圆顺功率谱表达式及其拟合参数；长波方面，以速度等级对应的单项高低TQI值相近原则选取典型轨道谱；短波方面，以四分位数分别将钢轨表面短波不平顺功率谱和车轮不圆顺功率谱划分为五个等级，并考虑二者相干性提出轮轨粗糙度谱. 研究结果表明：依据单项高低TQI值相近原则，选取的美国六级谱与北京设计速度80 km/h的地铁线路轨道长波（1～42 m）不平顺功率谱吻合良好；钢轨表面短波不平顺功率谱和车轮不圆顺功率谱在同一短波波长下幅值分布均具有显著的偏态分布特征；短波0.01～1.00 m内的不同等级大小轮轨粗糙度谱主要受车轮不圆顺谱主导，严重时甚至超过了铁科院短波谱.
Abstract:To establish a wheel-rail broadband excitation model for numerical simulation and prediction of metro vibration noise, a study was conducted on the selection for long-wave irregularity of metro rail and wheel-rail short-wave roughness spectra based on measured data of long-wave irregularity of metro rail and rail surface roughness from Beijing metro lines, as well as wheel tread out-of-roundness (OOR) from Qingdao metro lines. Firstly, the Welch method was applied to the measured data of rail irregularity to estimate the power spectral density, and the expressions for the short-wave irregularity power spectrum of rail and the OOR power spectrum of wheel, as well as their fitting parameters were provided. In terms of long wavelength, typical rail spectra were selected according to the principle of similarity in individual high and low TQI values corresponding to speed classes. Regarding short wavelength, the short-wave irregularity power spectrum of the rail surface and the OOR power spectrum of the wheel were respectively divided into five grades based on quartiles, and a wheel-rail roughness spectrum was proposed by considering their coherence. The results show that the selected American sixth grade spectrum aligns well with the long-wave (1–42 m) irregularity power spectrum of metro lines with 80 km/h designed by Beijing, according to the principle of similarity in individual high and low TQI values. Both the short-wave irregularity power spectrum of the rail surface and the wheel OOR power spectrum exhibit a significantly skewed amplitude distribution under the same short wavelength. The wheel-rail roughness spectra of different levels in the short-wave range of 0.01–1 m are mainly dominated by the wheel OOR spectrum, and in severe cases, it even exceeds the short-wave spectrum recommended by the China Academy of Railway Sciences.
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图 3 长波不平顺功率谱与美国六级谱对比
Figure 3. Comparison of long-wave irregularity power spectrum with American sixth grade spectrum
图 4 钢轨表面短波不平顺功率谱密度幅值分布特征
Figure 4. Characteristic of amplitude value distribution of short-wave irregularity power spectral density of rail surface
图 5 钢轨表面短波不平顺功率谱分位谱
Figure 5. Quantile spectrum of short-wave irregularity power spectrum on rail surface
图 6 车轮不圆顺功率谱密度幅值分布特征
Figure 6. Characteristic of amplitude value distribution of wheel OOR power spectral density
图 9 轮轨粗糙度谱与典型轨道谱的对比
Figure 9. Comparison of wheel-rail roughness spectrum with typical rail spectrum
表 1 （TG/GW102—2019）中规定的质量指数管理值
Table 1. Quality index management value specified in TG/GW102–2019
速度等级 左高低 右高低 左轨向 右轨向 轨距 水平 三角坑 TQI值 v≤80 km/h 2.2～2.5 2.2～2.5 1.8～2.2 1.8～2.2 1.4～1.6 1.7～1.9 1.9～2.1 13.0～15.0 80＜v≤120 km/h 1.8～2.2 1.8～2.2 1.4～1.9 1.4～1.9 1.3～1.4 1.6～1.7 1.7～1.9 11.0～13.0 120＜v≤ 160 km/h 1.5～1.8 1.5～1.8 1.1～1.4 1.1～1.4 1.1～1.3 1.3～1.6 1.4～1.7 9.0～11.0 v＞160 km/h 1.1～1.5 1.1～1.5 0.9～1.1 0.9～1.1 0.9～1.1 1.1～1.3 1～1.4 7.0～9.0 
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表 2 常见典型轨道谱时域样本TQI值
Table 2. TQI values of time domain samples of common typical rail spectra
轨道不平顺 左高低 右高低 左轨向 右轨向 轨距 水平 三角坑 TQI值 美国五级谱 3.2～4.7 3.1～4.7 2.8～5.0 2.6～5.0 1.7～2.9 1.7～2.8 1.9～2.1 13.0～15.0 美国六级谱 2.1～3.6 2.3～3.6 2.0～3.4 2.2～3.5 1.3～2.3 1.6～2.0 1.7～1.9 11.0～13.0 德国高干扰谱 2.6～4.8 2.6～4.4 2.0～3.0 2.0～3.0 0.4～0.7 1.8～3.0 1.4～1.7 9.0～11.0 德国低干扰谱 1.8～2.4 1.8～2.4 1.3～2.0 1.3～2.0 0.4～0.5 1.2～1.7 1～1.4 7.0～9.0 中国高速谱 0.5～0.6 0.5～0.7 0.5～0.6 0.4～0.7 0.3～0.5 0.4～0.6 1～1.4 7.0～9.0
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表 3 钢轨表面短波不平顺功率谱分级系数
Table 3. Classification coefficient of short-wave irregularity power spectrum on rail surface
等级 $ {A}_{1} $ $ {K}_{1} $ $ {A}_{2} $ $ {K}_{\text{2}} $ $ b $ R1 0.0098 4.31 0.0026 3.10 − 0.9559 R2 − 0.2423 R3 0 R4 0.2582 R5 2.1930
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表 4 车轮不圆顺功率谱分级系数
Table 4. Classification coefficient of wheel OOR power spectrum
等级 A k W1 1.37 × 10−5 2.80 W2 1.9 × 10−4 2.8 W3 7 × 10−4 2.9 W4 2 × 10−3 2.9 W5 1.5 × 10−2 2.5
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表 5 原始谱与轮轨粗糙度谱的关系
Table 5. Relationship between original spectrum and wheel-rail roughness spectrum
功率谱 W1 W2 W3 W4 W5 钢轨R2 L1 L2 L3 L4 L5 钢轨R3 L6 L7 L8 L9 L10 钢轨R4 L11 L12 L13 L14 L15
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表 6 轮轨粗糙度谱公式参数取值
Table 6. Parameter value of wheel-rail roughness spectrum formula
等级 $ {A}_{1} $ $ {K}_{1} $ $ {A}_{2} $ $ {K}_{2} $ L1 6.2 × 10−3 4.2238 1.6 × 10−3 3.0005 L2 7.8 × 10−3 4.0307 2.2 × 10−3 2.8566 L3 1.02 × 10−2 3.8848 3.3 × 10−3 2.8430 L4 2.05 × 10−2 3.8082 7.0 × 10−3 2.8225 L5 4.85 × 10−2 3.1758 2.17 × 10−2 2.4426 L6 1.05 × 10−2 4.2440 2.7 × 10−3 3.0211 L7 7.6 × 10−3 4.0264 2.1 × 10−3 2.8544 L8 9.9 × 10−3 3.8785 3.2 × 10−3 2.8426 L9 1.39 × 10−2 3.7058 5.2 × 10−3 2.8089 L10 3.8 × 10−2 3.0519 1.95 × 10−2 2.4435 L11 6.0 × 10−3 4.2223 1.6 × 10−3 2.9991 L12 7.6 × 10−3 4.0257 2.1 × 10−3 2.8557 L13 9.9 × 10−3 3.8781 3.2 × 10−3 2.8435 L14 1.39 × 10−2 3.7057 5.2 × 10−3 2.8092 L15 3.80 × 10−2 3.0527 1.94 × 10−2 2.4421
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