Lateral Bifurcation Behavior of a Four-Axle Railway Passenger Car

We investigate the kinematics and dynamics of a high-speed four-axle railway passenger car, which has 17 degrees of freedom, considering the lateral motion, roll and yaw angles of the car body and the bogie frame, and the lateral motion and yaw angle of the four wheelsets. The creep forces and the flange forces between the oscillating wheels and the rails are main nonlinearities and can be estimated by the Vermeulen–Johnson creep force laws and a piecewise linear function, respectively. The dynamical equations for the motion of the vehicle running with constant speed along an ideal, rigid, straight, and perfect track are formulated, and the lateral bifurcation behavior of the vehicle system is investigated numerically. The results indicate that both stable and unstable orbits are obtained, and the linear and nonlinear critical speeds are determined as well. Several kinds of dynamical behaviors, such as stationary equilibrium point, symmetric or asymmetric periodic oscillations, and symmetric or asymmetric chaotic motions, are found and described in great detail within the investigated speed range.