论文速递 | 考虑车轮椭圆度随机性下基于直接概率积分法的列车振动特性概率分析框架

文摘 2024-07-31 19:00 德国

A DPIM-based probability analysis framework to obtain railway vehicle vibration characteristics considering the randomness of OOR wheel

考虑车轮椭圆度随机性下基于直接概率积分法的列车振动特性概率分析框架

引用格式 | Cited by

Wang TF, Zhou JS, Sun WJ, Gong D, Zhou K, Zhang ZF, Liu ZX, Li GS, 2024. A DPIM-based probability analysis framework to obtain railway vehicle vibration characteristics considering the randomness of OOR wheel. Probabilistic Engineering Mechanics, 75: 103587.

DOI: 10.1016/j.probengmech.2024.103587

摘要 | Abstract

车轮椭圆度 (out-of-roundness, OOR) 是导致车辆振动的主要激励源之一。然而，车轮椭圆度具有随机性，这意味着使用确定性方法无法全面评估车辆的振动行为。因此，本文提出了一种概率分析框架，在考虑车轮椭圆度随机性的情形下获得车辆振动特性。通过将高维变量简化为半径、幅值和相位几个独立变量，推导出随机车轮椭圆度的概率模型。然后，对带有椭圆度车轮的垂直车轨耦合系统进行建模。进一步采用直接概率积分法 (direct probability integral method, DPIM) 来分析从激励到响应概率的演变。最后，计算了车辆随机振动的统计量。通过数值算例验证了所提框架。结果表明，由车轮 Gauss 分布椭圆度引起的车辆随机振动概率密度函数 (probability density function, PDF) 形状由于轮轨接触力的非线性偏离了 Gauss 分布，而表现出右偏形状，显著影响了动力性能。随着车轮椭圆度幅值均值或变异系数线性增加，车辆 Sperling 指数可靠性呈现出二次或双斜率下降。因此，基于可靠性考虑，提出了车轮椭圆度幅值的维护阈值。与蒙特卡罗模拟相比，所提框架在计算效率上至少提高了一个数量级。

关键词: 列车, 车轮椭圆度, 随机动力学, 概率分析, 维护策略

The OOR (out-of-roundness) wheel is one of the main excitation sources causing vehicle vibration. However, the OOR wheel occurs randomly, indicating that the vibration behavior of a vehicle cannot be comprehensively evaluated using a deterministic approach. Thus, a probability analysis framework is proposed to obtain vehicle vibration characteristics while considering the randomness of the OOR wheel. The probability model of the random OOR wheel is derived by reducing the high-dimensional variables into a few independent variables of the radius, amplitude, and phase. Then, the vertical vehicle-track coupled system with OOR wheels is modelled. A DPIM (direct probability integral method) is further developed to analyze the evolution of excitation to response probabilities. Finally, the statistics of the random vibration of the vehicle are calculated. The proposed framework is verified using a numerical case. Results show that the PDF (probability density function) shape of the vehicle random vibration, induced by the Gaussian-distributed OOR wheel, deviates from the Gaussian distribution due to the nonlinear wheel/rail contact force. Instead, it exhibits a right-skewed shape, significantly impacting the dynamic performance. As the mean or coefficient of variation of the OOR wheel amplitude increases linearly, the reliability of the vehicle Sperling index experiences a quadratic or double-sloping decrease. Consequently, a maintenance threshold for OOR wheel amplitudes is given based on reliability considerations. Compared to Monte Carlo simulation, the proposed framework offers a computational efficiency improvement of at least one order of magnitude.

Keywords: Railway vehicle; OOR wheels; Random dynamics; Probability analysis; Maintenance strategy

图 1: 车轮椭圆度: (a) 角坐标; (b) 空间坐标

Fig. 1. OOR wheel in (a) the angle coordinate and (b) the spatial coordinate

图 2: 车轨垂向耦合动力学模型

Fig. 2. Vertical vehicle-track coupled dynamic model

图 3: 概率分析框架流程图

Fig. 3. Flowchart of the probability analysis framework

图 4: 车轮随机椭圆度测量

Fig. 4. Measurement for the random OOR wheel

图 5: 粗糙度水平的概率密度函数: (a) 1-3 阶谐波; (b) 4-6 阶谐波; (c) 7-10 阶谐波

Fig. 5. PDF of the roughness level for the (a) 1st - 3rd harmonic orders; (b) 4th - 6th harmonic orders; (c) 7th - 10th harmonic orders

图 6: 轴箱垂直振动数值模型与观测对比: (a) 时域; (b) 频域

Fig. 6. Vertical vibration of the axle box from the numerical model and the measurement are compared in (a) the time domain and (b) the frequency domain

图 7: 8 Hz 振福的概率密度函数对比

Fig. 7. Comparison of PDFs of the amplitude at 8 Hz

图 8: 车辆随机振动的概率分析: (a) 由所提框架和不同样本蒙特卡罗模拟获得的 1 阶谐波生成的 8 Hz 振幅概率密度函数对比; (b) 2-10 阶谐波生成的振幅概率密度函数

Fig. 8. Probability analysis of vehicle random vibration: (a) A comparison of PDFs of the amplitude at 8 Hz generated with the 1st harmonic order, which are obtained from the proposed framework and MCSs for different samplings; (b) PDFs of the amplitude generated with the 2nd - 10th harmonic orders

图 9: 车体随机振动变化范围

Fig. 9. Variation range of car body random vibration

图 10: Sperling 指数统计分析: (a) 概率密度函数; (b) 可靠度

Fig. 10. Statistical analysis for the Sperling index: (a) PDF; (b) Reliability

图 11: 粗糙度水平与 Sperling 指数之间的相关性

Fig. 11. Correlation between roughness level and Sperling index

图 12: 1 阶粗糙度水平均值对 Sperling 指数的影响: (a) Sperling 指数的概率密度函数; (b) Sperling 指数 2.5 的可靠度变化规律

Fig. 12. Influence of the mean of the 1st order roughness level on the Sperling index: (a) PDF of the Sperling index; (b) Change rule of reliability of the Sperling index (=2.5)

图 13: 1 阶粗糙度水平变异系数对 Sperling 指数的影响: (a) Sperling 指数的概率密度函数; (b) Sperling 指数 2.5 的可靠度变化规律

Fig. 13. Influence of the coefficient of variation of the 1st order roughness level on the Sperling index: (a) PDF of the Sperling index; (b) Change rule of the reliability of the Sperling index (=2.5)

作者信息 | Authors

王腾飞 Teng-Fei Wang