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
Qinghua GuanXing DuZefeng WenShulin Liangand Maoru Chi
