车辆/轨道耦合作用下高速列车车轮振动影响灵敏度分析

肖乾; 程玉琦; 罗佳文; 周生通; 周前哲; 曹涛影

doi:10.19818/j.cnki.1671-1637.2021.06.012

车辆/轨道耦合作用下高速列车车轮振动影响灵敏度分析

doi: 10.19818/j.cnki.1671-1637.2021.06.012

华东交通大学载运工具与装备教育部重点实验室，江西南昌 330013

基金项目:

国家自然科学基金项目 51975210

大功率交流传动电力机车系统集成国家重点实验室开放课题 13221430000480

详细信息

作者简介:
肖乾(1977-)，男，湖南常德人，华东交通大学教授，工学博士，从事车辆-轨道耦合动力学研究

通讯作者:
程玉琦(1995-)，女，江西上饶人，华东交通大学工学硕士研究生

中图分类号: U260.11
计量
- 文章访问数: 477
- HTML全文浏览量: 212
- PDF下载量: 67
- 被引次数: 0
出版历程
- 收稿日期: 2021-07-21
- 网络出版日期: 2022-02-11
- 刊出日期: 2021-12-01

Sensitivity analysis of high-speed train wheel vibration influenced by vehicle-track coupling

Key Laboratory of Conveyance and Equipment of Ministry of Education, East China Jiaotong University, Nanchang 330013, Jiangxi, China

Funds:

National Natural Science Foundation of China 51975210

Open Poject of State Key Laboratory of Heavy Duty AC Drive Electric Locomotives System Integration 13221430000480

More Information

Author Bio:
XIAO Qian(1977-), male, professor, PhD, jxraiph@foxmail.com

Corresponding author: CHENG Yu-qi(1995-), female, graduate student, 745357588@qq.com

摘要

摘要: 考虑车辆一系、二系悬挂参数和轨道参数的随机性，在多体动力学软件UM当中建立了CRH2动车组拖车的随机性仿真模型；采用最优拉丁超立方试验设计方法抽取车辆参数和轨道参数的随机样本，利用多目标优化软件iSight调用随机样本，联合UM完成了随机样本仿真分析；在有限试验设计样本和仿真数据的限制下，以最佳近似精度为目标，结合最小角回归、低阶交互截断和留一法交叉验证等实现了多项式混沌展开，构建多项式混沌展开代理模型；采用Sobol法进行全局灵敏度分析，研究了直线、曲线2种工况下车辆参数和轨道参数随机耦合作用对于车轮振动特性的影响，找出了主要影响因子，并考虑了多参数之间的交互效应。研究结果表明：多项式混沌展开法能够基于已有的样本比较好地拟合出代理模型，计算出Sobol灵敏度系数，平均误差低于3%，从而可以高效、定量地分析各参数耦合作用对车轮振动的影响；转臂节点横向刚度、一系弹簧垂向刚度、一系弹簧横向刚度和二系横向减振器阻尼是对车轮振动响应方差具有较大贡献的车辆参数，轨道横向、垂向刚度是对车轮振动响应方差具有较大贡献的轨道参数，各参数之间存在明显交互效应。
- 车轮振动 /
- 多项式混沌展开代理模型 /
- Sobol法 /
- 全局灵敏度分析 /
- 交互效应
Abstract: A random simulation model for one trailer of the CRH2 EMU was established based on the multi-body dynamics software UM under considering the randomness of the primary and secondary suspension parameters of the vehicle and track parameters. The optimal Latin hypercube experimental design method was used to extract the random samples of the parameters, the multi-objective optimization software iSight was used to select the random samples, and the UM was used to analyze the samples. Under the limitation of limited experimental design samples and simulation data, a polynomial chaos expansion surrogate model was built by combining the minimum angle regression, low-order interactive truncation and leave-one-out cross-validation to achieve the polynomial chaos expansion in order to reach the best approximate accuracy. The Sobol method was used to analyze the global sensitivity of polynomial chaos expansion surrogate model to study the influence of the random coupling action of vehicle and track parameters on the wheel vibration characteristics under the straight line and curve working conditions. The key factors were studied and the coupling action of multi-parameters was considered. The results show that the polynomial chaos expansion method can fit an accurate surrogate model based on the existing samples and calculate the Sobol sensitivity coefficient with an average error (less than 3%) so as to analyze the effect of the coupling of various parameterss on the wheel vibration efficiently and quantitatively. The vehicle parameters, such as the lateral stiffness of the boom node, the vertical stiffness of the primary spring, the lateral stiffness of the primary spring and the damping of the secondary transverse shock absorber, have an obvious contribution to the variance of the wheel vibration response. The track parameters, such as the lateral and vertical stiffnesses of the track, have a large contribution to the variance of the wheel vibration response. There are obvious interaction effects between the various parameters. 2 tabs, 16 figs, 31 refs.
- wheel vibration /
- polynomial chaos expansion surrogate model /
- Sobol method /
- global sensitivity analysis /
- interaction effect

HTML全文

图 1 车辆/轨道耦合动力学模型

Figure 1. Vehicle-track coupling dynamics model

下载: 全尺寸图片幻灯片

图 2 整车模型

Figure 2. Vehicle model

下载: 全尺寸图片幻灯片

图 3 轨道谱

Figure 3. Orbital spectrums

下载: 全尺寸图片幻灯片

图 4 UM-iSight联合仿真流程

Figure 4. UM-iSight joint simulation process

下载: 全尺寸图片幻灯片

图 5 直线工况下设计参数对车轮垂向加速度的灵敏度

Figure 5. Sensitivities of design parameters to wheel vertical acceleration under straight line condition

下载: 全尺寸图片幻灯片

图 6 直线工况下计参数对车轮垂向加速度的二阶交互效应

Figure 6. Second-order interaction effects of design parameters to wheel vertical acceleration under straight line condition

下载: 全尺寸图片幻灯片

图 7 直线工况下设计参数对车轮垂向位移的灵敏度

Figure 7. Sensitivities of design parameters to wheel vertical displacement under straight line condition

下载: 全尺寸图片幻灯片

图 8 直线工况下设计参数对车轮横向加速度的灵敏度

Figure 8. Sensitivities of design parameters to wheel lateral acceleration under straight line condition

下载: 全尺寸图片幻灯片

图 9 直线工况下设计参数对车轮横向位移的灵敏度

Figure 9. Sensitivities of design parameters to wheel lateral displacement under straight line condition

下载: 全尺寸图片幻灯片

图 10 曲线工况下设计参数对车轮垂向加速度的灵敏度

Figure 10. Sensitivities of design parameters to wheel vertical acceleration under curved condition

下载: 全尺寸图片幻灯片

图 11 曲线工况下设计参数对车轮垂向加速度的二阶交互效应

Figure 11. Second-order interaction effects of design parameters on wheel vertical acceleration under curved condition

下载: 全尺寸图片幻灯片

图 12 曲线工况下设计参数对车轮垂向位移的灵敏度

Figure 12. Sensitivities of design parameters to wheel vertical displacement under curved condition

下载: 全尺寸图片幻灯片

图 13 曲线工况下设计参数对车轮横向加速度的灵敏度

Figure 13. Sensitivities of design parameters to wheel lateral acceleration under curved condition

下载: 全尺寸图片幻灯片

图 14 曲线工况下设计参数对车轮横向加速度的二阶交互效应

Figure 14. Second-order interaction effects of design parameters on wheel lateral acceleration under curved condition

下载: 全尺寸图片幻灯片

图 15 曲线工况下设计参数对车轮横向位移的灵敏度

Figure 15. Sensitivities of design parameters to wheel lateral displacement under curved condition

下载: 全尺寸图片幻灯片

图 16 曲线工况下设计参数对车轮横向位移的二阶交互效应

Figure 16. Second-order interaction effect of design parameters on wheel lateral displacement under curved condition

下载: 全尺寸图片幻灯片

表 1 参数

Table 1. Parameters

参数代号	参数含义	参数初始值	变化范围/%
T1	轨道侧滚刚度/(N·m^-1)	1.37×10⁷	±20
T2	转臂节点横向刚度/(N·m^-1)	1.00×10⁵
T3	轨道横向刚度/(N·m^-1)	1.47×10⁷
T4	一系弹簧横向刚度/(N·m^-1)	9.80×10⁵
T5	空气弹簧横向刚度/(N·m^-1)	1.59×10⁵
T6	转臂节点垂向刚度/(N·m^-1)	6.60×10⁵
T7	轨道垂向刚度/(N·m^-1)	4.40×10⁷
T8	一系弹簧垂向刚度/(N·m^-1)	1.76×10⁶
T9	轨道横向阻尼/[(N·s)·m^-1]	6.50×10⁶
T10	轨道垂向阻尼/[(N·s)·m^-1]	4.00×10⁴
T11	二系横向减振器阻尼/[(N·s)·m^-1]	5.88×10⁴
T12	一系垂向减振器阻尼/[(N·s)·m^-1]	1.96×10⁴
T13	二系垂向减振器阻尼/[(N·s)·m^-1]	4.00×10⁴

下载: 导出CSV

表 2 PCE模型拟合精度检验

Table 2. Fitting accuracy test of PCE model

检验序号	车轮垂向加速度/%	车轮垂向位移/%	车轮横向加速度/%	车轮横向位移/%
1	0.00	0.03	0.93	4.71
2	0.00	0.08	0.83	2.32
3	0.00	0.21	2.50	3.74
4	0.00	0.15	0.13	0.40
5	0.00	0.03	0.60	3.24
6	0.00	0.16	2.19	3.88
7	0.00	0.14	1.21	3.11
8	0.00	0.43	3.32	2.72
9	0.00	0.12	0.18	4.71
10	0.00	0.15	2.19	0.82
11	0.00	0.03	0.57	4.30
12	0.00	0.19	1.01	3.44
13	0.00	0.07	2.52	0.98
14	0.00	0.40	3.75	1.26
15	0.00	0.18	0.42	6.97
16	0.00	0.60	2.00	1.05
17	0.00	0.24	0.94	2.87
18	0.00	0.48	0.74	1.55
19	0.01	0.31	0.07	4.87
20	0.00	0.51	4.38	1.59

下载: 导出CSV

参考文献(31)

[1]	杨光, 任尊松, 孙守光. 考虑弹性的高速旋转轮对振动特性研究[J]. 振动工程学报, 2016, 29(4): 714-719. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201604019.htm YANG Guang, REN Zun-song, SUN Shou-guang. Research on the vibration characteristics of high-speed rotation elastic wheelset[J]. Journal of Vibration Engineering, 2016, 29(4): 714-719. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201604019.htm
[2]	李哲, 高军伟, 张柏娜. 基于RFID的列车轮对识别与振动监控系统设计[J]. 仪表技术与传感器, 2020(11): 64-67, 73. doi: 10.3969/j.issn.1002-1841.2020.11.014 LI Zhe, GAO Jun-wei, ZHANG Bai-na. Design of train wheelset identification and vibration monitoring system based on RFID[J]. Instrument Technique and Sensor, 2020(11): 64-67, 73. (in Chinese) doi: 10.3969/j.issn.1002-1841.2020.11.014
[3]	庞学苗, 李建伟, 邢宗义, 等. 基于频率切片小波变换的轨道列车轮对振动信号分析[J]. 铁道机车车辆, 2015, 35(增刊1): 26-31. https://www.cnki.com.cn/Article/CJFDTOTAL-TDJC2015S1008.htm PANG Xue-miao, LI Jian-wei, XING Zong-yi, et al. Analysis of wheel-rail vibration signal based on frequency sliced wavelet transform[J]. Railway Locomotive and Car, 2015, 35(Sup1): 26-31. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDJC2015S1008.htm
[4]	马卫华, 许自强, 罗世辉, 等. 轮轴弯曲刚度对轮轨垂向动态载荷影响分析[J]. 机械工程学报, 2012, 48(6): 96-101. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201206016.htm MA Wei-hua, XU Zi-qiang, LUO Shi-hui, et al. Influence of the wheel axle bending stiffness on the wheel/rail vertical dynamical load[J]. Chinese Journal of Mechanical Engineering, 2012, 48(6): 96-101. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201206016.htm
[5]	张宝安. 柔性轮对结构振动对车辆动力学性能的影响[J]. 计算机辅助工程, 2013, 22(3): 19-23, 28. doi: 10.3969/j.issn.1006-0871.2013.03.004 ZHANG Bao-an. Effect of structure vibration of flexible wheelset on vehicle dynamics performance[J]. Computer Aided Engineering, 2013, 22(3): 19-23, 28. (in Chinese) doi: 10.3969/j.issn.1006-0871.2013.03.004
[6]	HAUG E J, WEHAGE R A, MANI N K. Design sensitivity analysis of large-scale constrained dynamic mechanical systems[J]. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 1984, 106(2): 156-162. doi: 10.1115/1.3258573
[7]	余衍然, 李成, 姚林泉, 等. 基于傅里叶幅值检验扩展法的轨道车辆垂向模型全局灵敏度分析[J]. 振动与冲击, 2014, 33(6): 77-81. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201406014.htm YU Yan-ran, LI Cheng, YAO Lin-quan, et al. Global sensitivity analysis on vertical model of railway vehicle based on extended Fourier amplitude sensitivity test[J]. Journal of Vibration and Shock, 2014, 33(6): 77-81. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201406014.htm
[8]	张旭明, 王德信. 结构灵敏度分析的解析方法[J]. 河海大学学报, 1998, 26(5): 47-52. https://www.cnki.com.cn/Article/CJFDTOTAL-HHDX805.008.htm ZHANG Xu-ming, WANG De-xin. Analytical method of structural sensitivity analysis[J]. Journal of Hohai University, 1998, 28(5): 47-52. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HHDX805.008.htm
[9]	聂祚兴, 于德介, 李蓉, 等. 基于Sobol'法的车身噪声传递函数全局灵敏度分析[J]. 中国机械工程, 2012, 23(14): 1753-1757. doi: 10.3969/j.issn.1004-132X.2012.14.027 NIE Zuo-xing, YU De-jie, LI Rong, et al. Global sensitivity analysis of autobodies' noise transfer functions based on Sobol' method[J]. China Mechanical Engineering, 2012, 23(14): 1753-1757. (in Chinese) doi: 10.3969/j.issn.1004-132X.2012.14.027
[10]	SOBOL I M, LEVITAN Y L. On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index[J]. Computer Physics Communications, 1999, 117(1/2): 52-61.
[11]	SOBOL I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and Computers in Simulation, 2001, 55(1/2/3): 271-280.
[12]	SOBOL I M. Theorems and examples on high dimensional model representation[J]. Reliability Engineering and System Safety, 2003, 79(2): 187-193. doi: 10.1016/S0951-8320(02)00229-6
[13]	BIGONI D, TRUE H, ENGSIG-KARUP A P. Sensitivity analysis of the critical speed in railway vehicle dynamics[J]. Vehicle System Dynamics, 2014, 52(Sup1): 272-286. doi: 10.1080/00423114.2014.898776
[14]	邵永生, 李成, 成明. 基于Sobol'法的轨道车辆平稳性的全局灵敏度分析[J]. 铁道科学与工程学报, 2018, 15(3): 748-754. doi: 10.3969/j.issn.1672-7029.2018.03.027 SHAO Yong-sheng, LI Cheng, CHENG Ming. Sensitivity analysis of rail vehicle front end energy absorption structure based on Sobol' method[J]. Journal of Railway Science and Engineering, 2018, 15(3): 748-754. (in Chinese) doi: 10.3969/j.issn.1672-7029.2018.03.027
[15]	陈秉智, 汪驹畅. 基于Sobol'法的轨道车辆前端吸能结构灵敏度分析[J]. 铁道学报, 2020, 42(3): 63-68. doi: 10.3969/j.issn.1001-8360.2020.03.008 CHEN Bing-zhi, WANG Ju-chang. Global sensitivity analysis of energy-absorbing structure for rail vehicle based on Sobol' method[J]. Journal of the China Railway Society, 2020, 42(3): 63-68. (in Chinese) doi: 10.3969/j.issn.1001-8360.2020.03.008
[16]	张慧云. 基于径向基函数网络的高速列车参数设计与优化[D]. 成都: 西南交通大学, 2015. ZHANG Hui-yun. The high-speed train parameter design and optimazation based on radial basis function[D]. Chengdu: Southwest Jiaotong University, 2015. (in Chinese)
[17]	周生通, 祁强, 周新建, 等. 轴弯曲与不平衡柔性转子共振稳态响应随机分析[J]. 计算力学学报, 2020, 37(1): 20-27. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202001004.htm ZHOU Sheng-tong, QI Qiang, ZHOU Xin-jian, et al. Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults[J]. Chinese Journal of Computational Mechanics, 2020, 37(1): 20-27. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG202001004.htm
[18]	周生通, 张沛, 肖乾, 等. 单盘悬臂转子启动过程峰值响应全局灵敏度分析[J]. 振动与冲击, 2021, 40(11): 17-25. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202111004.htm ZHOU Sheng-tong, ZHANG Pei, XIAO Qian, et al. Global sensitivity analysis for peak response of a cantilevered rotor with single disc during start-up[J]. Journal of Vibration and Shock, 2021, 40(11): 17-25. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202111004.htm
[19]	周生通, 王迪, 肖乾, 等. 基于广义多项式混沌的跨座式单轨车辆随机平稳性分析[J]. 振动与冲击, 2021, 40(6): 190-200. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202106026.htm ZHOU Sheng-tong, WANG Di, XIAO Qian, et al. Stochastic stationarity analysis of a straddle monorail vehicle using the generalized polynomial chaos method[J]. Journal of Vibration and Shock, 2021, 40(6): 190-200. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202106026.htm
[20]	FORMAGGIA L, GUADAGNINI A, IMPERIALI I, et al. Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model[J]. Computational Geosciences, 2013, 17(1): 25-42. doi: 10.1007/s10596-012-9311-5
[21]	SUDRET B. Global sensitivity analysis using polynomial chaos expansions[J]. Reliability Engineering and System Safety, 2008, 93(7): 964-979. doi: 10.1016/j.ress.2007.04.002
[22]	GARCIA-CABREJO O, VALOCCHI A. Global sensitivity analysis for multivariate output using polynomial chaos expansion[J]. Reliability Engineering and System Safety, 2014, 126: 25-36. doi: 10.1016/j.ress.2014.01.005
[23]	黄悦琛, 宋长青, 郭荣化. 基于广义多项式混沌展开的无人机飞行性能不确定性分析[J]. 飞行力学, 2021, 39(4): 25-32, 51. https://www.cnki.com.cn/Article/CJFDTOTAL-FHLX202104005.htm HUANG Yue-chen, SONG Chang-qing, GUO Rong-hua. Uncertainty analysis of unmanned aerial vehicle flight performance using general polynomial chaos expansion[J]. Flight Dynamics, 2021, 39(4): 25-32, 51. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FHLX202104005.htm
[24]	王晗, 严正, 徐潇源, 等. 基于稀疏多项式混沌展开的孤岛微电网全局灵敏度分析[J]. 电力系统自动化, 2019, 43(10): 44-52. doi: 10.7500/AEPS20180625006 WANG Han, YAN Zheng, XU Xiao-yuan, et al. Global sensitivity analysisfor islanded microgrid based on sparse polynomial chaos expansion[J]. Automation of Electric Power Systems, 2019, 43(10): 44-52. (in Chinese) doi: 10.7500/AEPS20180625006
[25]	刘安民, 高峰, 张青斌, 等. 基于多项式混沌展开方法的翼伞飞行不确定性[J]. 兵工学报, 2021, 42(7): 1392-1399. doi: 10.3969/j.issn.1000-1093.2021.07.006 LIU An-min, GAO Feng, ZHANG Qing-bin, et al. Application of PCE method in parafoil-flight uncertainty analysis[J]. Acta Armamentarii, 2021, 42(7): 1392-1399. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.07.006
[26]	WIENER N, The homogeneous chaos[J]. American Journal of Mathematics, 1938, 60(4): 897. doi: 10.2307/2371268
[27]	GHANEM R, GHOSH D. Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition[J]. International Journal For Numerical Methods in Engineering. 2007, 72(4): 486-504. doi: 10.1002/nme.2025
[28]	胡军, 张树道. 基于多项式混沌的全局敏感度分析[J]. 计算物理, 2016, 33(1): 1-14. doi: 10.3969/j.issn.1001-246X.2016.01.001 HU Jun, ZHANG Shu-dao. Global sensitivity analysis based on polynomial chaos[J]. Chinese Journal of Computational Physics, 2016, 33(1): 1-14. (in Chinese) doi: 10.3969/j.issn.1001-246X.2016.01.001
[29]	赵威, 卜令泽, 王伟. 稀疏偏最小二乘回归-多项式混沌展开代理模型方法[J]. 工程力学, 2018, 35(9): 44-53. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201809007.htm ZHAO Wei, BU Ling-ze, WANG Wei. Sparse partial least squares regression-polynomial chaos expansion metamodeling method[J]. Engineering Mechanics, 2018, 35(9): 44-53. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201809007.htm
[30]	周如意, 丰文浩, 邓宗全, 等. 轮地力学模型参数灵敏度分析与主参数估计[J]. 航空学报, 2021, 42(1): 524076. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202101020.htm ZHOU Ru-yi, FENG Wen-hao, DENG Zong-quan, et al. Sensitivity analysis and dominant parameter estimation of wheel-terrain interaction model[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(3): 524076. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202101020.htm
[31]	付娜, 李成辉, 赵振航, 等. 车辆-轨道耦合作用下桥上减振双块式无砟轨道减振性能研究[J]. 铁道科学与工程学报, 2018, 15(5): 1095-1102. doi: 10.3969/j.issn.1672-7029.2018.05.001 FU Na, LI Cheng-hui, ZHAO Zhen-hang, et al. Study on the vibration reduction performance of double-block ballastless damping track on bridge under vehicle-track coupling effect[J]. Journal of Railway Science and Engineering, 2018, 15(5): 1095-1102. (in Chinese) doi: 10.3969/j.issn.1672-7029.2018.05.001