城轨列车实际运行工况是变速载的，传统的定常转速齿轮研究不能满足动态特性分析的需要。为此，提出一种新的时变速载齿轮系统动态特性研究方法。综合考虑时变啮合刚度、时变外部激励、静态传递误差、随机位移激励以及非线性侧隙的影响，建立城轨列车时变速载齿轮系统扭振模型。通过分析直齿轮啮合过程，修正齿轮啮合频率计算公式。基于微元法思想，计算城轨列车惰行工况、牵引工况和制动工况的速度、转速以及转角，得到时变啮合刚度的变化规律。研究结果揭示牵引工况的齿轮扭振运动在这三种运行工况中的扭振功率密度最低。在惰行工况下，齿轮系统低速运行呈现分频的现象，高速运行有陷入混沌运动的趋势；在牵引工况下，齿轮系统随转速的提高稳定性有所下降；在制动工况下，齿轮系统的扭振不显示含啮合频率的影响。
Urban rail vehicle works under the conditions of the variable speed, and the traditional method of gear system under constant speed condition cannot meet the needs of the dynamic characteristics analysis. Therefore, a new method of gear system under the time-varying load and speed condition is proposed to investigate the dynamic characteristics. Considering the influences of the time-varying mesh stiffness, time-varying external excitation, the static transmission error, random displacement excitation and nonlinear backlash, the torsional vibration model of the gear system is established. The calculation formula of gear meshing frequency is corrected by analyzing the meshing process of spur gears. Based on the cumulative integral method, the velocity, the rotational speed and the angle of the shaft are calculated for the conditions of the coasting, traction and braking, respectively. The results reveal that the power density of the gear torsional vibration in the traction condition is the lowest among the three working conditions. Under the coasting condition, the gear system presents fractional frequency phenomenon at low speed, and it has a trend of turning into chaos at high speed; under the traction condition, the stability of the gear system is decreased with the rotational speed; under the braking condition, the torsional vibration of the gear system does not show the influence of the meshing frequency.
[1] 李润芳,王建军. 齿轮系统动力学[M]. 北京:科学出版社,1997. LI Runfang,WANG Jianjun. Dynamics of gear system[M]. Beijing:Science Press,1997.
[2] 申永军,杨绍普. 齿轮系统的非线性动力学与故障诊断[M]. 北京:科学出版社,2014. SHEN Yongjun,YANG Shaopu. Nonlinear dynamics and fault diagnosis of gear system[M]. Beijing:Science Press,2014.
[3] MA Hui,ZENG Jin,FENG Ranjiao,et al. Review on dynamics of cracked gear systems[J]. Engineering Failure Analysis,2015(55):224-245.
[4] 魏莎,韩勤锴,褚福磊. 考虑不确定性因素的齿轮系统动力学研究综述[J]. 机械工程学报,2016,52(1):1-19. WEI Sha,HAN Qinkai,CHU Fulei. Review on research of uncertain dynamics for gear system[J]. Journal of Mechanical Engineering,2016,52(1):1-19.
[5] LIU Changzhao,QIN Datong,LIM T C,et al. Dynamic characteristics of the herringbone planetary gear set during the variable speed process[J]. Journal of Sound & Vibration,2014,333(24):6498-6515.
[6] FARSHIDIANFAR A,SAGHAFI A. Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J]. Nonlinear Dynamics,2014,75(4):783-806.
[7] WEN Yubing,YANG Jianming,WANG Shiyu. Random dynamics of a nonlinear spur gear pair in probabilistic domain[J]. Journal of Sound & Vibration,2014,333(20):5030-5041.
[8] ZHOU Shihua,SONG Guiqiu,SUN Mengnan,et al. Nonlinear dynamic response analysis on gear-rotor-bearing transmission system[J]. Journal of Vibration & Control,DOI:10.1177/1077546316667178,2016.
[9] ZHOU Shihua,SONG Guiqiu,REN Zhaohui,et al. Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations[J]. Chinese Journal of Mechanical Engineering,2016,29(2):281-292.
[10] 黄冠华,王兴宇,梅桂明,等. 内外激励下高速列车齿轮箱箱体动态响应分析[J]. 机械工程学报,2015,51(12):95-100. HUANG Guanhua,WANG Xingyu,MEI Guiming,et al. Dynamic response analysis of gearbox housing system subjected to internal and external excitation in high-speed train[J]. Journal of Mechanical Engineering,2015,51(12):95-100.
[11] 黄冠华,周宁,张卫华,等. 动态激励下高速列车齿轮传动系统振动特性分析[J]. 铁道学报,2014,36(12):20-26. HUANG Guanhua,ZHOU Ning,ZHANG Weihua,et al. Vibration characteristics of gear transmission system of high-speed train under dynamic excitation[J]. Journal of the China Railway Society,2014,36(12):20-26.
[12] HUANG Guanhua,XU Sisi,ZHANG Weihua,et al. Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train[J]. Journal of Central South University,2017(24):726-735.
[13] HUANG Guanhua,ZHOU Ning,ZHANG Weihua. Effect of internal dynamic excitation of the traction system on the dynamic behavior of a high-speed train[J]. Proceedings of the Institution of Mechanical Engineers Part F Journal of Rail & Rapid Transit,2016,230(8):1899-1907.
[14] 张丽,任尊松,孙守光,等. 考虑齿轮传动影响的高速动车组电动机吊架载荷及动应力研究[J]. 机械工程学报,2016,52(4):133-140. ZHANG Li,REN Zunsong,SUN Shouguang,et al. Research on dynamic load and stress of high-speed emu motor hanger considering influence of gear transmission system[J]. Journal of Mechanical Engineering,2016,52(4):133-140.
[15] 李广全,刘志明,王文静,等. 高速动车组齿轮箱疲劳裂纹机理分析研究[J]. 机械工程学报,2017,53(2):99-105. LI Guangquan,LIU Zhiming,WANG Wenjing,et al. Fatigue crack mechanism study on high-speed emu gearbox[J]. Journal of Mechanical Engineering,2017,53(2):99-105.
[16] TIAN Xinhao. Dynamic simulation for system response of gearbox including localized gear faults[D]. Alberta:University of Alberta,2004.
