钢轨模态阶数对高速铁路轮轨高频动力响应的影响研究
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摘要
为了能更准确计算高速铁路轮轨高频动力响应,本文针对考虑扣件胶垫幅频变动力特性的车辆-轨道垂向耦合动力学模型,研究了钢轨模态阶数对轮轨系统高频动力响应结果的影响。研究结果表明:(1)当扣件胶垫采用幅频变模型时,传统钢轨模态阶数(0. 5倍扣件总数)会导致轮轨力、轮对加速度和钢轨加速度时域结果的最大值偏大;(2)钢轨模态阶数的取值对轮轨系统在低频范围的动力仿真结果影响不大;而在中高频段的主频段范围,轮轨系统的动力响应幅值随着钢轨模态阶数的增大而逐渐降低;(3)根据轮轨系统时频域计算结果可知,当扣件胶垫采用幅频变模型时,为准确计算高速铁路轮轨高频动力响应,本文建议将钢轨模态阶数至少应等于轨道结构中的扣件总数。
In order to calculate the high-frequency dynamic response of high-speed railway wheel-rail system more accurately,the effect of rail modal order on the high frequency dynamic response of wheel-rail system is studied based on the vehicle-track vertical coupled dynamic model considering the amplitude-frequency variation dynamic properties of fastening pad in this paper. The results show:( 1) When the amplitude-frequency variation model is used for the fastening pad,the modal mode of the traditional rail( 0. 5 times the number of fasteners) would cause the maximum value of the wheel-rail force,the wheelset acceleration and the rail acceleration time domain results to be large;( 2) The value of the modal order of the rail had little effect on the dynamic simulation results of the wheel-rail system in the lowfrequency range; In the main frequency range of the middle and high frequency bands,the dynamic response amplitude of the wheel-rail system gradually decreased as the modal order of the rail increased;( 3) According to the calculation results of wheel-rail system in time-frequency domain,it was suggested that the rail modal order should be at least equal to the total number of fasteners in the track structure in order to accurately calculatethe high-frequency dynamic response of high-speed railway wheels and rails when the amplitude-frequency variation model is used for the fastening pads.
In order to calculate the high-frequency dynamic response of high-speed railway wheel-rail system more accurately,the effect of rail modal order on the high frequency dynamic response of wheel-rail system is studied based on the vehicle-track vertical coupled dynamic model considering the amplitude-frequency variation dynamic properties of fastening pad in this paper. The results show:( 1) When the amplitude-frequency variation model is used for the fastening pad,the modal mode of the traditional rail( 0. 5 times the number of fasteners) would cause the maximum value of the wheel-rail force,the wheelset acceleration and the rail acceleration time domain results to be large;( 2) The value of the modal order of the rail had little effect on the dynamic simulation results of the wheel-rail system in the lowfrequency range; In the main frequency range of the middle and high frequency bands,the dynamic response amplitude of the wheel-rail system gradually decreased as the modal order of the rail increased;( 3) According to the calculation results of wheel-rail system in time-frequency domain,it was suggested that the rail modal order should be at least equal to the total number of fasteners in the track structure in order to accurately calculatethe high-frequency dynamic response of high-speed railway wheels and rails when the amplitude-frequency variation model is used for the fastening pads.
引文
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[12]翟婉明.车辆-轨道耦合动力学(第四版)[M].北京:科学出版社,2015.ZHAI Wanming. Vehicle-track Coupling Dynamics(Fourth Edition)[M]. Beijing:Science Press,2015.
[2]李成辉.高低不平顺不利波长及其与车速关系[J].西南交通大学学报,1997,32(6):633-636.LI Chenghui. Relationship between Irregular Wave Length andVehicle Speed[J]. Journal of Southwest Jiaotong University,1997,32(6):633-636.
[3]徐志胜,翟婉明,王开云,等.车辆-轨道系统振动响应分析—Timoshenko梁与Euler梁轨道模型的比较[J].地震工程与工程振动,2003,23(6):74-79.XU Zhisheng,ZHAI Wanming,WANG Kaiyun,et al. VibrationResponse Analysis of Vehicle-track System-comparison of TrackModels between Timoshenko Beam and Euler Beam[J]. EarthquakeEngineering and Engineering Vibration,2003,23(6):74-79.
[4]高建敏,翟婉明,王开云.高速行车条件下轨道几何不平顺敏感波长研究[J].铁道学报,2012,34(7):83-88.GAO Jianmin,ZHAI Wanming,WANG Kaiyun. Study on SensitiveWavelength of Geometry Irregularity of Track under Condition ofHigh-speed Operation[J]. Journal of Railway,2012,34(7):83-88.
[5]刘子煊.扣件胶垫动态幅频变特性对高速轮轨动力响应的影响研究[D].成都:西南交通大学,2017.LIU Zixuan. Study on Influence of Dynamic Amplitude-frequencyVariation Characteristics of Fastener Gasket on Dynamic Response ofHigh-speed Wheeltrack[D]. Chengdu:Southwest Jiaotong University,2017.
[6]唐振寰.橡胶隔振器动力学建模及动态特性研究[D].南京:南京航空航天大学,2013.TANG Zhenhuan. Study on Dynamic Modeling and DynamicCharacteristics of Rubber Vibration Isolator[D]. Nanjing:NanjingUniversity of Aeronautics and Astronautics,2013.
[7]韦凯,王丰,牛澎波,等.钢轨扣件弹性垫板的动态黏弹塑性力学实验及理论表征研究[J].铁道学报,2018,40(12):115-122.WEI Kai,WANG Feng,NIU Pengbo,et al. Research on DynamicViscoplastic and Elastoplastic Mechanics Experiment and TheoreticalCharacterization of Elastic Pad for Rail Fasteners[J]. Journal ofRailway,2018,40(12):115-122.
[8]陈文,孙洪广,李西成,等.力学与工程问题的分数阶导数建模[M].北京:科学出版社,2010.CHEN Wen, SUN Hongguang, LI Xicheng, et al. FractionalDerivative Modeling of Mechanical and Engineering Problems[M].Beijing:Science Press,2010.
[9]张攀.高铁无砟轨道扣件系统弹性垫板温/频变动力特征及其影响研究[D].成都:西南交通大学,2016.ZHANG Pan. Research on Temperature/Frequency Variable DynamicCharacteristics of Elastic Cushion Plate in Ballastless Track FastenerSystem of High-speed Railway and Its Influence[D]. Chengdu:Southwest Jiaotong University,2016.
[10] Berg M. A Non Linear Rubber Spring Model for Rail VehicleDynamics Analysis[J]. Vehicle Syst. Dyn. 1998,30(Issue 3-4):97–212.
[11] Kai Wei,Feng Wang,Ping Wang,et al. Effect of Temperature-andFrequency-dependent Dynamic Properties of Rail Pads on High-speedVehicle-track Coupled Vibrations[J]. Vehicle System Dynamics,2017,55(3):351-370.
[12]翟婉明.车辆-轨道耦合动力学(第四版)[M].北京:科学出版社,2015.ZHAI Wanming. Vehicle-track Coupling Dynamics(Fourth Edition)[M]. Beijing:Science Press,2015.