基于Newmark-β预测校正积分法的高速车辆垂向—纵向耦合振动研究
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摘要
为有效评估轮对动平衡对车辆垂向和纵向振动系统的影响,以CRH_2型动车组为研究对象,建立具有13个自由度的车辆垂向—纵向耦合振动数学模型,基于Newmark-β预测校正积分法,应用Matlab软件求解系统的振动响应,计算结果与传统多体动力学软件UM的相一致,验证了数学模型和求解算法的准确可靠。在此基础上,分析轮对动平衡对车辆垂向和纵向振动响应的影响,提出优化措施。结果表明:速度为60和300km·h~(-1)时轮对动平衡引起的激扰力频率与车辆自振频率接近,对应的振动频率为6和31 Hz,车辆运行平稳性降低;采用非线性纵向刚度牵引拉杆,可以有效降低由轮对动平衡引起的6和31 Hz左右的车辆振动,提高乘坐舒适性。
Taking the CRH_2 EMU as the research object,a mathematical model with 13 degrees of freedom for the longitudinal-vertical coupling vibration of vehicle was established to effectively evaluate the influence of wheelset dynamic balance on the vertical and longitudinal vibration system of vehicle.Based on Newmark-βforecast-correction integral method,the vibration response of the system was solved by Matlab software.The calculation results agreed well with those obtained by traditional multi-body dynamic software UM.The accuracy and reliability of the mathematical model and the algorithm were verified.On this basis,the effects of wheelset dynamic balance on the vertical and longitudinal vibration responses of vehicle were analyzed,and the optimization measures were proposed.Results show that,when the speed is 60 and 300 km·h~(-1),the frequency of excitation force caused by the dynamic balance of wheelset is close to the natural frequency of vehicle.The corresponding vibration frequency is 6 and 31 Hz,and the vehicle running stability decreases.The use of nonlinear longitudinal stiffness traction rod can effectively reduce vehicle vibration around 6 and 31 Hz caused by the dynamic balance of wheelset,and improve ride comfort.
Taking the CRH_2 EMU as the research object,a mathematical model with 13 degrees of freedom for the longitudinal-vertical coupling vibration of vehicle was established to effectively evaluate the influence of wheelset dynamic balance on the vertical and longitudinal vibration system of vehicle.Based on Newmark-βforecast-correction integral method,the vibration response of the system was solved by Matlab software.The calculation results agreed well with those obtained by traditional multi-body dynamic software UM.The accuracy and reliability of the mathematical model and the algorithm were verified.On this basis,the effects of wheelset dynamic balance on the vertical and longitudinal vibration responses of vehicle were analyzed,and the optimization measures were proposed.Results show that,when the speed is 60 and 300 km·h~(-1),the frequency of excitation force caused by the dynamic balance of wheelset is close to the natural frequency of vehicle.The corresponding vibration frequency is 6 and 31 Hz,and the vehicle running stability decreases.The use of nonlinear longitudinal stiffness traction rod can effectively reduce vehicle vibration around 6 and 31 Hz caused by the dynamic balance of wheelset,and improve ride comfort.
引文
[1]康熊,侯茂锐,常崇义,等.动车组晃车相关轮轨关系问题研究[R].北京:中国铁道科学研究院,2014.
[2]SUZUKI Y,CHONAN S.Theoretical Analysis for Flexural Vibration Damping Method of Rolling Stock Carbody[J].Transactions of the Japan Society of Mechanical Engineers:Series C,1996,62(598):2132-2139.
[3]TAKIGAMI T,TOMIOKA T.Investigation to Suppress Bending Vibration of Railway Vehicle Carbodies Using Piezoelectric Elements[J].Quarterly Report of RTRI,2005,46(4):225-230.
[4]曾京,邬平波,郝建华.铁道客车系统的垂向减振分析[J].中国铁道科学,2006,27(3):62-67.(ZENG Jing,WU Pingbo,HAO Jianhua.Analysis of Vertical Vibration Reduction for Railway Vehicle Systems[J].China Railway Science,2006,27(3):62-67.in Chinese)
[5]朱浩,刘少军,黄中华,等.铁道车辆垂向主动悬挂的预见控制[J].中国铁道科学,2005,26(2):90-95.(ZHU Hao,LIU Shaojun,HUANG Zhonghua,et al.Preview Control of the Vertical Active Suspension of Railway Vehicle[J].China Railway Science,2005,26(2):90-95.in Chinese)
[6]佐佐木军章.改善高速列车的横向乘坐舒适度——半主动悬挂减振装置的应用[J].铁道学报,2004,26(1):105-115.(SASAKI Kimiaki.Improving Lateral Ride Comfort of High-Speed Trains Applying Semi-Active Suspension System to High-Speed Trains[J].Journal of the China Railway Society,2004,26(1):105-115.in Chinese)
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[9]胡晓依,侯茂锐.转向架耦合振动数值分析及性能评估方法研究[R].北京:中国铁道科学研究院,2012.
[10]李鸿晶,王通,廖旭.关于Newmark-β法机理的一种解释[J].地震工程与工程振动,2011,31(2):55-62.(LI Hongjing,WANG Tong,LIAO Xu.An Interpretation on Newmark-βMethods in Mechanism of Numerical Analysis[J].Earthquake Engineering and Engineering Vibration,2011,31(2):55-62.in Chinese)
[11]赵琪,尹韶平,王中,等.基于Newmark-β法的鱼雷推进轴系动力响应分析[J].航海工程,2015,44(1):117-121.(ZHAO Qi,YIN Shaoping,WANG Zhong,et al.Analysis of Dynamic Response for the Torpedo Propulsion-Shaft System Based on Newmark-βMethod[J].Ship&Ocean Engineering,2015,44(1):117-121.in Chinese)
[12]侯茂锐,常崇义,胡晓依,等.高速列车横向稳定性仿真分析[J].中国铁道科学,2012,33(增):25-32.(HOU Maorui,CHANG Chongyi,HU Xiaoyi,et al.Simulation Analysis on the Lateral Stability of High-Speed Train[J].China Railway Science,2012.33(Supplement):25-32.in Chinese)
[13]British Standards Institution.BS-EN 13260—2009 Railway Applications-Wheelsets and Bogies-Wheelsets-Product Requirements[S].London:the Standards Policy and Strategy Committee,2009.
[2]SUZUKI Y,CHONAN S.Theoretical Analysis for Flexural Vibration Damping Method of Rolling Stock Carbody[J].Transactions of the Japan Society of Mechanical Engineers:Series C,1996,62(598):2132-2139.
[3]TAKIGAMI T,TOMIOKA T.Investigation to Suppress Bending Vibration of Railway Vehicle Carbodies Using Piezoelectric Elements[J].Quarterly Report of RTRI,2005,46(4):225-230.
[4]曾京,邬平波,郝建华.铁道客车系统的垂向减振分析[J].中国铁道科学,2006,27(3):62-67.(ZENG Jing,WU Pingbo,HAO Jianhua.Analysis of Vertical Vibration Reduction for Railway Vehicle Systems[J].China Railway Science,2006,27(3):62-67.in Chinese)
[5]朱浩,刘少军,黄中华,等.铁道车辆垂向主动悬挂的预见控制[J].中国铁道科学,2005,26(2):90-95.(ZHU Hao,LIU Shaojun,HUANG Zhonghua,et al.Preview Control of the Vertical Active Suspension of Railway Vehicle[J].China Railway Science,2005,26(2):90-95.in Chinese)
[6]佐佐木军章.改善高速列车的横向乘坐舒适度——半主动悬挂减振装置的应用[J].铁道学报,2004,26(1):105-115.(SASAKI Kimiaki.Improving Lateral Ride Comfort of High-Speed Trains Applying Semi-Active Suspension System to High-Speed Trains[J].Journal of the China Railway Society,2004,26(1):105-115.in Chinese)
[7]TOMIOKA T,TAKIGAMI T,FUKUYAMA A,et al.Prevention of Carbody Vibration of Railway Vehicles Imbalanced Wheelsets with Displacement-Dependent Rubber Bush[J].Journal of Mechanical Systems for Transportation and Logistics,2010,3(1):131-142.
[8]黄彩虹,曾京,罗仁,等.牵引拉杆纵向刚度对高速客车车体弹性振动的影响[J].交通运输工程学报,2010,10(3):46-51.(HUANG Caihong,ZENG Jing,LUO Ren,et al.Effect of Longitudinal Stiffness of Traction Rod on Car Body Elastic Vibration for High-Speed Passenger Car[J].Journal of Traffic and Transportation Engineering,2010,10(3):46-51.in Chinese)
[9]胡晓依,侯茂锐.转向架耦合振动数值分析及性能评估方法研究[R].北京:中国铁道科学研究院,2012.
[10]李鸿晶,王通,廖旭.关于Newmark-β法机理的一种解释[J].地震工程与工程振动,2011,31(2):55-62.(LI Hongjing,WANG Tong,LIAO Xu.An Interpretation on Newmark-βMethods in Mechanism of Numerical Analysis[J].Earthquake Engineering and Engineering Vibration,2011,31(2):55-62.in Chinese)
[11]赵琪,尹韶平,王中,等.基于Newmark-β法的鱼雷推进轴系动力响应分析[J].航海工程,2015,44(1):117-121.(ZHAO Qi,YIN Shaoping,WANG Zhong,et al.Analysis of Dynamic Response for the Torpedo Propulsion-Shaft System Based on Newmark-βMethod[J].Ship&Ocean Engineering,2015,44(1):117-121.in Chinese)
[12]侯茂锐,常崇义,胡晓依,等.高速列车横向稳定性仿真分析[J].中国铁道科学,2012,33(增):25-32.(HOU Maorui,CHANG Chongyi,HU Xiaoyi,et al.Simulation Analysis on the Lateral Stability of High-Speed Train[J].China Railway Science,2012.33(Supplement):25-32.in Chinese)
[13]British Standards Institution.BS-EN 13260—2009 Railway Applications-Wheelsets and Bogies-Wheelsets-Product Requirements[S].London:the Standards Policy and Strategy Committee,2009.