A minimal order model to investigate the hunting stability of a bogie with mechanically connected wheelsets

In this paper, the hunting stability of a two-axle bogie is studied with a simplified mathematical model. First, a four degree of freedom model of the bogie where the wheelsets are elastically connected, is developed, and the governing equations are obtained. In the model, contact forces at rail/wheel interfaces are calculated with Kalker's linear theory, and the nonlinear equations of motion are solved numerically. Second, the nonlinear governing equations are simplified with the use of a linear contact force model. Hence, time domain responses are obtained analytically. Numerical and analytical predictions show a good match, and it is concluded that the simpler contact model can represent the dynamics of the system successfully, especially in the stable state of the bogie. Third, the corresponding eigenvalue problem is formulated from the linear equations, and complex eigenvalues are calculated over the operational speed range of the bogie. It is observed that the natural frequencies of the system are speed dependent, and either one or both of the wheelsets may become unstable at certain parameter sets. Finally, stability maps are generated for several parameters, and a better understanding about the effects of system parameters on the stability of two-axle bogie is obtained.