多种垂向轮轨关系的对比及改进的车-线-桥系统迭代模型的建立
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摘要
对比分析非线性赫兹接触、线性赫兹接触、刚性接触这3种轮轨接触模型对车-线-桥垂向耦合系统动力分析结果的影响,并建立改进的车-线-桥耦合系统迭代计算模型。车辆模型采用多体系统动力学建立,轨道-桥梁模型采用有限元方法建立,根据不同的轮轨接触模型,建立相应的轮轨力计算公式,并采用分离迭代法计算耦合系统振动响应。在数值算例中,以高速列车通过5跨简支梁桥为计算背景,对不同轮轨接触模型的仿真计算结果进行对比分析。针对传统车-线-桥耦合系统迭代计算模型计算效率低的问题,建立改进的迭代计算模型。研究结果表明:线性赫兹接触模型与非线性赫兹接触模型得到的车体加速度、轮轨力、钢轨和桥梁的位移和加速度均较吻合,但前者的计算效率较低;忽略轮对惯性力的刚性接触模型无法得到准确的钢轨和桥梁加速度;改进模型通过建立包含轮轨接触弹簧的车辆模型来提高车辆子系统的迭代稳定性,其计算效率比传统模型提高近7倍;为保证计算结果的准确性,车-线-桥耦合振动计算中应考虑时间步内的迭代计算。
The influence of three types of wheel, i.e. rail contact model-nonlinear Hertz contact, linear Hertz contact and rigid contact on the dynamical analysis result of train-track-bridge vertical coupled system were compared, and an improved iteration model for train-track-bridge coupled system was established. The vehicle model was established by multi-body system dynamics and the track-bridge model was established by finite element method. Depending on different wheel-rail contact models, the corresponding wheel-rail force calculation formulas were established, and the iterative method were used to calculate the coupled system vibration. In numerical case, taking a high-speed train traveling across a five-span simply supported beam bridge for case study, the calculation results of train-track-bridge coupled vibration withr different wheel-rail contact models were compared. Aiming at the problem of low efficiency of the iterative computation model for the traditional train-track-bridge coupled system, an improved iteration model was established. The results show that the vehicle body acceleration, wheel-rail force, displacement and acceleration of the rail and bridge of the linear Hertz contact model are in good agreement with those of the nonlinear Hertz contact model, but the computational efficiency is lower than that of the latter; rigid contact model which neglects the inertia force of the wheel is unable to obtain accurate rail and bridge acceleration. The improved model is to improve the iterative stability of the vehicle subsystem by establishing the vehicle model including the wheel-rail contact spring. The calculation efficiency of improved model is about 7 times greater than that of the conventional model. In order to ensure the accuracy of results, the iterative calculation in the time step should be taken into account in the calculation of train-track-bridge coupled vibration.
The influence of three types of wheel, i.e. rail contact model-nonlinear Hertz contact, linear Hertz contact and rigid contact on the dynamical analysis result of train-track-bridge vertical coupled system were compared, and an improved iteration model for train-track-bridge coupled system was established. The vehicle model was established by multi-body system dynamics and the track-bridge model was established by finite element method. Depending on different wheel-rail contact models, the corresponding wheel-rail force calculation formulas were established, and the iterative method were used to calculate the coupled system vibration. In numerical case, taking a high-speed train traveling across a five-span simply supported beam bridge for case study, the calculation results of train-track-bridge coupled vibration withr different wheel-rail contact models were compared. Aiming at the problem of low efficiency of the iterative computation model for the traditional train-track-bridge coupled system, an improved iteration model was established. The results show that the vehicle body acceleration, wheel-rail force, displacement and acceleration of the rail and bridge of the linear Hertz contact model are in good agreement with those of the nonlinear Hertz contact model, but the computational efficiency is lower than that of the latter; rigid contact model which neglects the inertia force of the wheel is unable to obtain accurate rail and bridge acceleration. The improved model is to improve the iterative stability of the vehicle subsystem by establishing the vehicle model including the wheel-rail contact spring. The calculation efficiency of improved model is about 7 times greater than that of the conventional model. In order to ensure the accuracy of results, the iterative calculation in the time step should be taken into account in the calculation of train-track-bridge coupled vibration.
引文
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[2]王宁波,任伟新,肖祥.列车-桥梁耦合振动研究综述[J].力学进展,2012,42(5):634-643.WANG Ningbo,REN Weixin,XIAO Xiang.The state of art of study on vehicle-bridge coupling vibration[J].Advances in Mechanics,2012,42(5):634-643.
[3]郑国琛,祁皑,颜学渊.考虑车轨垂向耦合福州地铁振源加速度研究[J].振动、测试与诊断,2015,35(2):328-401.ZHENG Guochen,QI Ai,YAN Xueyuan.Research on acceleration of vibration source from Fuzhou metro considering vehicle-track vertical coupled model of vibration[J].Journal of Vibration,Measurement&Diagnosis,2015,35(2):328-401.
[4]周毅.CRTSⅢ型板式轨道减振特性研究[D].成都:西南交通大学土木工程学院,2011:14-16.ZHOU Yi.Research on vibration-reduction performance of CRTSⅢslab ballastless track[D].Chengdu:Southwest Jiaotong University.School of Civil Engineering,2011:14-16.
[5]LU Feng,LIN Jiahao,KENNEDY D,et al.An algorithm to study non-stationary random vibrations of vehicle–bridge systems[J].Computers and Structures,2009,87(3):177-185.
[6]全顺喜.高速道岔几何不平顺动力分析及其控制方法研究[D].成都:西南交通大学土木工程学院,2012:49-50.QUAN Shunxi.Study on dynamic analysis and coutrol methods of the geometric irregularity in high-speed turnout[D].Chengdu:Southwest Jiaotong University.School of Civil Engineering,2012:49-50.
[7]WANG Tonlo,CHU Kuanghan.Railway bridge/vehicle interaction studies with new vehicle model[J].Journal of Structural Engineering,1991,117(7):2099-2116.
[8]葛玉梅,袁向荣.机车-桁架桥梁耦合振动研究[J].西南交通大学学报,1998,33(2):138-142.GE Yumei,YUAN Xiangrong.Study on dynamic interacttion between a moving locomotive and a steel-truss bridge[J].Journal of Southwest Jiaotong University,1998,33(2):138-142.
[9]林玉森,李小珍,强士中.车桥耦合振动中2种轮轨接触模型的比较分析[J].中国铁道科学,2007,28(6):70-74.LIN Yusen,LI Xiaozhen,QIANG Shizhong.Contrast analysis of two wheel-rail contact models in the coupling vibration of vehicle-bridge system[J].China Railway Science,2007,28(6):70-74.
[10]PABLO A,ZHANG Nan,GOICOLEA JOSE M,et al.Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways[J].Journal of Sound and Vibration,2013,332(5):1231-1251.
[11]余志武,毛建锋,谈遂,等.车桥竖向随机振动的概率密度演化分析[J].中南大学学报(自然科学版),2015,46(4):1420-1426.YU Zhiwu,MAO Jianfeng,TAN Sui,et al.Probability density evolution analysis of track-bridge vertical coupled vibration with irregularity random excitation[J].Journal of Central South University(Science and Technology),2015,46(4):1420-1426.
[12]翟婉明,夏禾.列车-轨道-桥梁动力相互作用理论与工程应用[M].北京:科学出版社,2011:212-213.ZHAI Wanming,XIA He.Train-track-bridge dynamic interaction:theory and engineering application[M].Beijing:Science Press,2011:212-213.
[13]夏禾,张楠,郭薇薇,等.车桥耦合振动工程[M].北京:科学出版社,2014:120-126.XIA He,ZHANG Nan,GUO Weiwei,et al.Coupling vibration of train-bridge system[M].Beijing:Science Press,2014:120-126.
[14]朱志辉,余志武,朱玉龙,等.车-桥振动诱发周围环境及建筑物振动分析[J].铁道学报,2013,35(4):102-109.ZHU Zhihui,YU Zhiwu,ZHU Yulong,et al.Analysis on environment and building vibration induced by passing trains on bridge structures[J].Journal of the China Railway Society,2013,35(4):102-109.
[15]范俊杰.现代铁路轨道[M].2版.北京:中国铁道出版社,2004:6-7.FAN Junjie.Modern railway track[M].2nd ed.Beijing:China Railway Publishing Press,2004:6-7.