Smoothing Methods of Wheel Out-of-Roundness Signals and Their Effects on Polygonal Wear Prediction
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摘要:
车轮踏面通常存在麻坑等缺陷，实测车轮非圆化信号往往包含高频噪声干扰，有时也会因为客观因素致使信号首尾端点不闭合. 车轮非圆化是车辆-轨道耦合动力学模型中重要的轮轨界面激扰，对轮轨动力相互作用仿真和车轮非圆化磨耗预测具有重要影响，选取合适的平滑方法是保证仿真结果准确性的关键. 本文对基于EN 15610标准、傅里叶级数、移动平均和形态学滤波等4种常用方法在实测车轮非圆化信号处理中的平滑效果展开研究，并讨论4种方法在车轮多边形磨耗预测中的适用性. 结果表明：在处理实测非圆化信号时，傅里叶级数和移动平均2种方法能够在保留原始信号的波形特征下达到良好的平滑去噪效果并保证车轮不圆数据首尾闭合；此外，2种方法也适合在多边形磨耗预测中使用，使用时建议傅里叶级数的阶数取值大于60，移动平均的平滑窗口长度取17 mm左右.
Abstract:As defects such as pitting usually occur on the wheel tread, the measured wheel out-of-roundness (OOR) signals often contain high-frequency noise interference, and sometimes the signals are discontinuous at the start and end points due to objective factors. Wheel OOR is an important wheel-rail interface excitation in the vehicle-track coupled dynamics model, exerting significant effects on the simulation of dynamic wheel-rail interaction and wheel OOR wear prediction. Selecting the suitable smoothing method is key to ensuring the accuracy of the simulation results. The smoothing effects of four commonly adopted methods based on the EN 15610 standard, Fourier series, moving average, and morphological filtering on processing wheel OOR signals were investigated, and the applicability of the four methods in predicting polygonal wear was discussed. The results indicate that the two methods of Fourier series and moving average can achieve sound smoothing and de-noising effect, preserve the waveform characteristics of original signals, and ensure continuity and differentiability at the start and end points of wheel OOR data when processing measured wheel OOR signals. Additionally, the two methods are also suitable for application in polygonal wear prediction. When the two methods are employed, the order of the Fourier series should be greater than 60 and the smoothing window length of moving average should be about 17 mm.
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Key words:
- wheel /
- out-of-roundness /
- data smoothing /
- Fourier series /
- moving average /
- morphological filtering /
- polygonal wear prediction
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图 4 不同方法平滑后的三分之一倍频程波长
Figure 4. One-third octave wavelength after smoothing with different methods
图 8 不平滑磨耗下的车轮多边形预测结果
Figure 8. Wheel polygon prediction results in unsmoothed wear conditions
图 9 傅里叶级数平滑方法中采用不同k值的最终车轮多边形粗糙度水平
Figure 9. Final wheel polygonal roughness levels using different k values in Fourier series smoothing method
图 10 移动平均平滑方法中采用不同窗口长度N的最终车轮多边形磨耗预测结果
Figure 10. Final wheel polygonal wear prediction results using different window lengths N in moving average smoothing method
图 11 移动平均和傅里叶级数2种平滑方法的最终车轮多边形磨耗预测结果对比
Figure 11. Comparison of final wheel polygonal wear prediction results using moving average and Fourier series methods
图 12 4种平滑方法的最终车轮多边形磨耗预测结果对比
Figure 12. Comparison of final wheel polygonal wear prediction results of four smoothing methods
图 13 2种平滑更新策略对多边形磨耗预测的影响
Figure 13. Effects of two smoothing update strategies on polygonal wear prediction
表 1 4种平滑方法处理结果的评价指标
Table 1. Evaluation indexes of processing results of four smoothing methods
方法 均方根误差 信噪比 平滑度 互相关系数 标准EN 15610 2.25 21.09 0.20 0.99 傅里叶级数 2.42 20.48 0.03 0.99 移动平均 2.48 20.25 0.03 0.99 形态学滤波 2.47 20.29 0.03 0.99 
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表 2 车辆−轨道耦合动力学模型主要参数
Table 2. Main parameters of vehicle-track coupled dynamics model
数值 参数 39.106 车体质量/t 2.495 构架质量/t 1.560 轮对质量/t 13.700 转臂节点纵向刚度/（MN•m−1） 1.182 一系钢簧垂向刚度/（MN•m−1） 0.240 二系悬挂垂向刚度/（MN•m−1） 0.46 车轮半径/m 8.9 车辆定距/m 2.5 轴距/m 40 扣件垂向刚度/MN•m−1 0.63 轨枕间距/m
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