非线性轮对陀螺系统的稳定性及分叉研究
Stability and Bifurcation of Nonlinear Gyroscopic Wheelset System

针对轮对陀螺效应，运用能量法分析了轮对蛇形运动机理，建立了蛇形运动能量流；基于打靶法分析了非线性轮对陀螺系统的Hopf分叉，并对比分析了陀螺系统和非陀螺系统的分叉解；最后，引入稳定性系数和陀螺力贡献率，定量分析了陀螺力对蛇形运动稳定性的影响。研究结果表明，在轮对陀螺系统中，陀螺力不做功，但具有增稳功能。陀螺力对系统稳定性的影响随速度的增大显著变大，当轮对高速运行时，陀螺力影响较为显著。因此，在高速列车稳定性分析中应将陀螺力作为一个重点分析对象。
Aiming at the gyroscopic effect of the wheelset, the hunting motion mechanism is researched with the energy integration method, and the energy flow of the wheelset hunting motion is obtained. The Hopf bifurcation is analyzed using the shooting method, and a comparison between the gyroscopic system and the non-gyroscopic system is presented, along with the effect of the wheel spin phenomenon on critical speed. Moreover, the definition of the stability coefficient and gyroscopic forces contribution rate are proposed, and the impact of gyroscopic forces on stability is quantitatively analyzed. The results show that the gyroscopic force does not work in the wheelset system, but the system becomes more stable. The gyroscopic contributory ratio for stabilization significantly increases with increasing velocity when the operation speed is high enough. Thus, the effect of gyroscopic forces cannot be ignored and should be a key factor in the actual analysis.