Vibration characteristics of bogie hunting motion based on root loci curves

基于蛇行运动根轨迹的转向架振动特性研究

Vibration behaviors of bogie hunting motion contain key information that dominates the dynamic performance of rail vehicles,in which the eigenvalue of each mode reflects the damping ratio and the natural frequency.This paper focuses on the root loci curves of bogie hunting motion,starting from a rigid bogie,then to a bogie with flexible primary suspension.With regard to the rigid bogie,analytical formulas for the eigenvalues,the critical speed as well as the corresponding hunting frequency are derived and verified.While for the flexible bogie,the root loci curves are calculated numerically.The study shows that both free rigid bogie and free wheelset are dynamically unstable at any speed.The critical speed increases with diminished wheel-rail conicity,track gauge,and wheelset and bogie inertia,and with increased wheelbase and wheel radius.The dominating factors such as the stiffness of the primary suspension and the wheel-rail conicity should be optimized for a practical design.The influences of the damping coefficients and the variations of creep coefficients are negligible.The motor suspension affects the root loci curves and the critical speed significantly.Both inappropriate motor suspension design and rigidly suspended motor reduce the critical speed.The increase of critical speed by a motor suspension can only be achieved when the lower natural frequency of the motor-bogie frame-wheelsets system coincides with or is close to the hunting frequency.Special care should be taken for the design of motor suspension,the first is to avoid the decreased damping ratio in a certain speed range below the critical speed and the second is that the variations of parameters should not induce the rapid reduction of the critical speed.The main feature of the present study is that the root loci curves,which are derived as analytical formulas or calculated numerically,are used to study the vibrational behaviors of bogie hunting motion.Both the influencing laws of the dominating parameters and the principles regarding the motor suspension are significant for the stability design of modem railway vehicles which may use innovative structures/materials as well as modem control and monitoring technologies.

转向架蛇行运动的振动性态蕴含着主导铁道车辆动力学行为的关键信息,其中各个模态的特征值反映了其振动阻尼比和固有频率.本文着眼于转向架蛇行运动的根轨迹,从刚性转向架开始,扩展到具有一系悬挂的柔性转向架.对于刚性转向架,推导并验证了蛇行运动特征值、临界速度及对应蛇行频率的解析公式.对于柔性转向架,通过数值方法求解根轨迹.研究表明,在任何速度下,自由状态的刚性转向架和自由轮对均是动力学不稳定的;转向架临界速度随等效锥度、轨距、轮对和构架惯性参数的下降以及轴距和轮径的增大而提高;一系悬挂刚度和等效锥度是影响临界速度的关键参数,在车辆系统设计中应进行综合优化;阻尼系数及蠕滑系数变化对临界速度的影响可忽略.电机悬挂对转向架根轨迹和临界速度影响显著,不当的电机悬挂设计以及电机刚性架悬均会降低转向架临界速度;通过电机悬挂来提高临界速度只有在满足电机-构架-轮对系统的低阶固有频率与蛇行频率相等或接近时才能实现.对于电机悬挂设计而言,需要特别注意,一是要避开临界速度以下的低阻尼比区,二是系统参数的变化不应导致临界速度的急剧下降.本文旨在通过解析的或经过数值计算的根轨迹来表征转向架蛇行运动的振动性态,所总结的转向架蛇行运动关键参数影响规律和电机悬挂设计原则,可为采用新结构、新材料以及先进控制和监控系统的现代轨道车辆稳定性设计提供参考.