本文选取具有滞后非线性悬挂的高速转向架为目标，建立其数学模型和运动微分方程。应用统计线性化方法将其非线性方程线性化，用常微分方程稳定性理论对转向架蛇行运动进行理论分析，得到防止转向架蛇行运动的充分条件，并研究了转向架设计参数对临界速度的影响，为转向架的设计和参数选取提供依据。 In this paper, aiming at high-speed bogie with hysteresis nonlinear suspension, the mathematical model and differential equations of motion are established. The statistical linearization method is used to linearize the nonlinear equations. The theoretical analysis of the bifurcation behavior of the bogie based on the theory of the stability of ordinary differential equations shows that the bifurcation of the bogie can be prevented. The bifurcation of bogie design parameters to the critical speed Influence, provide the basis for the bogie design and parameter selection.