随着机车速度的提高，对其运行安全和稳定性提出更高要求。为研究机车轮对转子系统的动力学特性，在考虑弹性支撑、齿轮时变刚度等复合非线性因素影响下，基于哈密尔顿最小势能原理建立非线性连续-质量转子系统的动力学模型。在此基础上，对系统进行无量纲化，求解系统振形函数及固有振动频率。利用多尺度法求取非线性转子系统的渐进解，分析系统支撑刚度、阻尼及其齿轮时变刚度参数作用下，转子的主共振稳态幅频响应。研究表明：复杂边界条件下，齿轮的位置将直接影响模态幅值。轮轨激励的变化，对系统低频幅值影响较大、高频较小。轮轨激励达到临界值时，系统出现饱和共振，其后轮轨激励的变化，将不再影响系统的幅值。齿轮冲击刚度增加，转子系统位移显著增大。研究结果为机车轮对转子系统的动态特性分析和故障诊断奠定了一定的基础。
With the continuous improvement of locomotive speed, it has put out higher requirement of the stability and sperling of the locomotive system. In order to research the dynamical responses of rotor system with the locomotive wheel-set, the nonlinear continuous mass shaft dynamical model is established including the elastic-support and gear time-varying stiffness based on Hamilton principle of minimum potential energy. With the non-dimension of the dynamics differential equation, the vibration model functions and natural frequency are calculated. Then the asymptotic solution of the nonlinear rotor system is deduced by using multi-scale method, and the amplitude-frequency response of steady state main resonance with the effects of supporting stiffness, damping, gear time-varying stiffness are analyzed. The simulation results reveal that the location of gear directly affects the modal amplitudes under the complex boundary conditions. The varying of wheel-rail excitation has more influence on low frequency amplitude, but less influence on high frequency amplitude of the system. When the wheel-rail excitation arriving at the critical value, saturated resonance of the system happen, and then the varing of wheel-rail has no effect on the amplitude of system response. With the increase of gear shock stiffness, the vibration displacement of rotor system increases obviously. The research results lay a foundation for dynamical characteristics and fault diagnosis of the the nonlinear continuous mass shaft system of the locomotive wheel-set.
[1] DIMENTBERG F M. Flexural vibration of rotating shafts[M]. London:Butterworth, 1961.
[2] SHAW J, SHAW W. Instabilities and bifurcations in a rotating shaft[J]. Journal of Sound and Vibration, 1989,132(4):227-244.
[3] Wan Aiming, Cheng Xiaohan. Dynamic analysis and numerical experiments for balancing of the continuous single-disc and single-span rotor-bearing system[J]. Commun Nonlinear Sci Numer Simulation, 2011, 112(6):566-582.
[4] DIKEN H,ALNEFAIE K.Startup dynamic behaviour of a jeffcott rotor[J].International Journal of Acoustics and Vibrations, 2005, 10(2):83-88.
[5] CVETICANIN L.Free vibration of a Jeffcott rotor with pure cubic non-linear elastic property of the shaft[J]. Mechanism and Machine Theory, 2005, 40(12):1330-1344.
[6] ISHIDA K. YASUDA S. Murakami. Nonstationary oscillation of a rotating shaft with nonlinear spring characteristics during acceleration through a major[J]. International Journal of Acoustics and Vibrations, 1997, 11(19):31-36.
[7] JI Z. Method of multiple scales for vibration analysis of rotor-shaft systems with non-linear bearing pedestal model[J]. Journal of Sound and Vibration,1998, 18(215):293-305.
[8] Kane T R. An addition to the theory of whirling[J]. ASME Journal of Applied Mechanics, 1965, 329(9):383-386.
[9] ESHLEMAN R L, EUBANKS R A. On the critical speeds of a continuous rotor[J]. ASME Journal of Engineering for Industry, 1969, 39(8):1180-1188.
[10] 唐进元, 陈思雨, 钟掘. 一种改进的齿轮非线性动力学模型[J]. 工程力学, 2008, 25(1):217-223. TANG Jinyuan, CHEN Siyu, ZHONG Jue. A improved nonlinear model for a spur gear pair system[J]. Engineering Mechanics, 2008, 25(1):217-223.
[11] 高洪波,李允公,刘杰.基于动态侧隙的齿轮系统齿面磨损故障动力学分析[J].振动与冲击,2014, 33(18):221-226. GAO Hongbo,LI Yungong,LIU Jie. Dynamic analysis of a spur gear system with tooth-wear faults based on dynamic backlash[J]. Journal of Vibration and Shock, 2014, 33(18):221-226.
[12] LUCKZO J. A geometrically non-linear model of rotating shafts with internal resonance and self-excited vibration[J]. Journal of Sound and Vibration, 2002, 255(5):433-456.
[13] SHIAU T N, HWANG J L. Generalized polynomial expansion method for the dynamic analysis of rotor-bearing systems[J]. ASME Journal of Engineering for Gas Turbines and Power, 1993, 115(3):209-217.
[14] PALAZZLO A B,GUNTER E J. Model balancing of a multi-mass flexible rotor without trial weights[J].The American Society of Mechanical Engineers, 2006, 32(11):383-396.
