Simulation of nonlinear characteristics of vertical vibration of railway freight wagon varying with train speed

Traditional vertical vibration models of rail vehicle usually have high degrees of freedom, which affects the efficiency of numerical simulation. Regardless of the coupling effect between the vehicle and rail, a six degree of freedom (6DOF) quarter model with vertical displacement and rotation angle is selected as the dynamic model. This accomplished by comparing the simulation results of half model and quarter model of the railway freight wagon, and the vertical vibration characteristics of the railway freight wagon when the wagon speed is changed. To further illustrate the nonlinear vibration characteristics and evolution laws of the car body and bogie frame of the freight wagon, the bifurcation diagrams, maximum Lyapunov exponent curves, axis trajectory curves, phase plane plots, Poincaré sections, and amplitude spectras are drawn and adopted to research the dynamic responses. The simulations reveal the complex vibration behavior such as periodic, quasi-periodic, multi-periodic, and chaotic motion. Some research results can help the industry to better design the speed limits of such railway freight wagons, and deeply understand or utilize the vertical vibration law of railway freight wagon in future research.