考虑齿轮副动态激扰的机车动力学分析
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摘要
齿轮传动系统作为铁路机车驱动系统中的核心和关键部件之一,用来传递和增大牵引电机输出扭矩,具有传递效率高、传动平稳、结构紧凑等优点,其设计及动力学研究是机车转向架设计和机车动力学研究的重要组成部分。齿轮系统振动的不断加剧,对驱动装置的动态响应以及机车的动力学性能势必造成影响。为了保障列车运行时的可靠性和安全性,提高驱动系统的运行性能,需要我们对齿轮副动态激扰本身以及其对机车动力学性能、驱动装置动态响应的影响进行全面分析和研究。
本文介绍了机车齿轮副动态激励中刚度激励和误差激励的产生原因、影响因素及计算方法。应用MATLAB软件编制程序,采用石川法仿真模拟了齿轮副轮齿啮合刚度,采用误差等效法模拟了齿轮误差激励,基于齿轮副非线性动力学方程计算模拟了某型C0-Co式重载机车驱动装置的齿轮副动态激励。应用计算多体动力学软件SIMPACK建立该型机车的动力学模型,对该机车直线运行、曲线通过动力学性能进行仿真计算。结果表明：机车各项动力学评价指标均符合TB/T2360-93《铁道机车动力学性能试验鉴定方法及评定标准》。同时对比分析了有无齿轮副动态激扰影响两种情况下,机车动力学性能以及构架、驱动装置动态响应的变化。结果表明：直线运行中,齿轮副动态激扰对驱动电机的动态响应影响最大,对构架的动态响应影响次之,对机车的动力学性能影响最小；且齿轮副动态激励对驱动电机的垂向加速度影响最大,对驱动电机的横向加速度影响次之,对驱动电机的纵向加速度影响最小；齿轮副动态激扰对机车运动稳定性和曲线通过性能影响不明显。为了改善齿轮副动态激扰影响下驱动装置的振动状况,对牵引电机吊挂刚度以及驱动装置质量等结构参数进行分析研究,从而得到更加适合该机车的参数。
Gear transmission system as a core and key part of locomotive is used to transmit the output torque of traction motor and drive the wheelsets, it has high transmission efficiency, stable transmission, compact structure and so on. It's structural design and dynamics have become an important part of the bogie design and locomotive dynamics. However, the negative impact on dynamic performance of the driving system and locomotive is increasingly obvious with rising vibration of the gear system. In order to ensure the reliability and safety of the locomotive and improve the performance of the driving system, it is necessary and important to make an intensive study on the dynamics of locomotive and driving system under the influence of dynamic excitation of gear-pair.
In this paper, the cause, influencing factors and numerical simulation methods of internal dynamic excitation of locomotive gear-pair were introduced. Based on the application of MATLAB software programming, Ishikawa method was used to simulate the variation of gear meshing stiffness in the meshing process. Error equivalent method was adopted to simulate the gear error excitation. Nonlinear dynamic equation of a gear-pair was applied to obtain the dynamic excitation of gear-pair conforming to the locomotive dynamic model parameters. A heavy-haul locomotive dynamic model was established with tools of multi-body dynamics software SIMPACK, and dynamic index of locomotive was calculated in the curved and straight track conditions. Simulation results showed that all the locomotive dynamic performance conformed to the TB/T2360-93《Railway locomotive—Specification for evaluation the dynamic performance and accreditation test》.At the same time, the change of the locomotive dynamic performance was analyzed with or without the dynamic excitation of gear-pair. Simulation results showed that among influence of the dynamic excitation of gear-pair to dynamic performance, the motor was the most, the bogie was less, and the carbody was the least. And among the influence on dynamic performance of the motor, vertical dynamic performance was the most, lateral dynamic performance was the less, and longitudinal dynamic performance was the least. The dynamic excitation of gear-pair had no effect on locomotive curving performance. In order to improve the vibration of axis-mounted motor under the influence of the dynamic excitation of gear-pair, the structural parameters of locomotive driving system was analyzed, and the optimal value was obtained.
本文介绍了机车齿轮副动态激励中刚度激励和误差激励的产生原因、影响因素及计算方法。应用MATLAB软件编制程序,采用石川法仿真模拟了齿轮副轮齿啮合刚度,采用误差等效法模拟了齿轮误差激励,基于齿轮副非线性动力学方程计算模拟了某型C0-Co式重载机车驱动装置的齿轮副动态激励。应用计算多体动力学软件SIMPACK建立该型机车的动力学模型,对该机车直线运行、曲线通过动力学性能进行仿真计算。结果表明：机车各项动力学评价指标均符合TB/T2360-93《铁道机车动力学性能试验鉴定方法及评定标准》。同时对比分析了有无齿轮副动态激扰影响两种情况下,机车动力学性能以及构架、驱动装置动态响应的变化。结果表明：直线运行中,齿轮副动态激扰对驱动电机的动态响应影响最大,对构架的动态响应影响次之,对机车的动力学性能影响最小；且齿轮副动态激励对驱动电机的垂向加速度影响最大,对驱动电机的横向加速度影响次之,对驱动电机的纵向加速度影响最小；齿轮副动态激扰对机车运动稳定性和曲线通过性能影响不明显。为了改善齿轮副动态激扰影响下驱动装置的振动状况,对牵引电机吊挂刚度以及驱动装置质量等结构参数进行分析研究,从而得到更加适合该机车的参数。
Gear transmission system as a core and key part of locomotive is used to transmit the output torque of traction motor and drive the wheelsets, it has high transmission efficiency, stable transmission, compact structure and so on. It's structural design and dynamics have become an important part of the bogie design and locomotive dynamics. However, the negative impact on dynamic performance of the driving system and locomotive is increasingly obvious with rising vibration of the gear system. In order to ensure the reliability and safety of the locomotive and improve the performance of the driving system, it is necessary and important to make an intensive study on the dynamics of locomotive and driving system under the influence of dynamic excitation of gear-pair.
In this paper, the cause, influencing factors and numerical simulation methods of internal dynamic excitation of locomotive gear-pair were introduced. Based on the application of MATLAB software programming, Ishikawa method was used to simulate the variation of gear meshing stiffness in the meshing process. Error equivalent method was adopted to simulate the gear error excitation. Nonlinear dynamic equation of a gear-pair was applied to obtain the dynamic excitation of gear-pair conforming to the locomotive dynamic model parameters. A heavy-haul locomotive dynamic model was established with tools of multi-body dynamics software SIMPACK, and dynamic index of locomotive was calculated in the curved and straight track conditions. Simulation results showed that all the locomotive dynamic performance conformed to the TB/T2360-93《Railway locomotive—Specification for evaluation the dynamic performance and accreditation test》.At the same time, the change of the locomotive dynamic performance was analyzed with or without the dynamic excitation of gear-pair. Simulation results showed that among influence of the dynamic excitation of gear-pair to dynamic performance, the motor was the most, the bogie was less, and the carbody was the least. And among the influence on dynamic performance of the motor, vertical dynamic performance was the most, lateral dynamic performance was the less, and longitudinal dynamic performance was the least. The dynamic excitation of gear-pair had no effect on locomotive curving performance. In order to improve the vibration of axis-mounted motor under the influence of the dynamic excitation of gear-pair, the structural parameters of locomotive driving system was analyzed, and the optimal value was obtained.
引文
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[2]王开云,刘建新,翟婉明,蔡成标.铁路行车安全性与舒适性研究.交通运输工程学报.2006,6(3)： 9-12
[3]赵怀耘.轮对空心轴架悬机车驱动系统动力学研究.成都：西南交通大学博士论文,2009.
[4]李润方,王建军.,齿轮系统动力学.北京：科学出版社,1997.
[5]郑光泽.齿轮传动系统动态性能优化分析研究.重庆大学硕士学位论文,2004.
[6]李润方,陶泽光,林腾,唐倩.齿轮啮合内部动态激励数值模拟.机械传动,2001.25(2)：1-3.
[7]宋少芳.齿轮副非线性动力学模型的建立与分析.吉林大学硕士学位论文,2005.
[8]林绍中.计算机辅助齿形误差分析.漳州职业技术学院学报.2005,7：61-65.
[9]薛磊江,刘同义.有关齿轮误差测量几个问题的探讨.计量与测技术.19993：8.
[10]连级三.电传动机车概论.成都：西南交通大学出版社,2001.
[11]鲍维千.内燃机车总体及走形部.北京：中国铁道出版社,2007.
[12]K.Umezawa. Vibration of Power Transmission Helical Gear with Narrow Face-width. ASME Paper.1984,84(159):150-159.
[13]T.Iwatsubo.Couppled Lateral-Torsional Vibration of Rotor System Trained by Gears. ASME Paper.1984,27:271-277.
[14]H.Vinayak, R.Singh. Dynamic Analysis of Flexible Gears for High Power Density Transmissions. Proc. Inter Gearing'94.1994:105-110.
[15]H.Houjon, K.Umezawa, S.Matsumura. Vibration Analysis of a Pair of Helical Gears Mounted on Elastic Shafts. ASME Power Transmission and Gearing Conference,1996,88:501-508.
[16]K. J.Huang, T.S.Liu. Dynamic Analysis of a Spur Gear by the Dynamic Stiffness Method. Journal of Sound and Vibration,2000,234(2),311-329.
[17]A.Andersson, L.Vedmar. A Dynamic Model to Determine Vibrations in Involute Helical Gears. Journal of Sound and Vibration,2003,260,195-212.
[18]G.W.Blankenship, A.Kahaman. Steady State Forced Response of a Mechanical Oscillator with Combined Parametric Excitation and Clearance Type Non-linearity. Journal of Sound and Vibration.1995,185(5):742-765.
[19]L.Vedmar, A.Andersson. A Method to Determin Dynamic Loads on Spur Gear Teeth and on Bearing. Journal of Sound and Vibration.2003,267:1065-1084.
[20]W.D.Mark,1982,The transfer function method for gear system dynamic applied to conventional and minimum excitation gearing designs,NASA Contractor Report 3626.
[21]H.Kohler and R.Regan,1985,The derivation of gear transmission error from pitch error records,Proc.Inst.
[22]S.V.Neriya,R.B.Bhat, T.S.Sanker. On the Dynamic Response of a Helical Geared System Subjected to a Static Translation error in the Form of Deterministic and Filterd White Noise Inputs. Journal of Vibration,1988,110:501-506.
[23]A.Kahraman,R.Singh. Nonlinear Dynamic of a Spur Gear Pair. Journal of Sound and Vibration,1990,103(2):447-459
[24]J.P.Raclot, P.Velex. Simulation of the Dynamic Behaviour of Single and Multi-Stage Geared Systems with Shape Deviations and Mounting Errors by Using a Spectral Method. Journal of Sound and Vibration,1999,220(5),861-903.
[25]H.N.Ozguven. Dynamic Analysis of High Speed Gear by Using Loaded Static Transmission Error. Journal of Sound and Vibration.1988,125(1):71-83.
[26]J.S.Chen, F.L.Litvin, A.A.Shabana. Computerized Simulation of Meshing and Contact of Loaded Gear Drives. Proc. Inter Gearing'94,1994:161-166.
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